Synthesis and Design of Demethaniser Flowsheets
for Low Temperature Separation Processes
A thesis submitted to The University of Manchester for the degree of
Doctor of Philosophy
in the Faculty of Engineering and Physical Sciences
2011
Muneeb Nawaz
Under the supervision of
Dr. Megan Jobson
Prof. Robin Smith
Centre for Process Integration
School of Chemical Engineering and Analytical Science
2
TABLE OF CONTENTS
List of Figures ..........................................................................................................7
List of Tables ..........................................................................................................10
Abstract ...................................................................................................................12
Declaration .............................................................................................................13
Copyright Statement ...............................................................................................13
Dedication...............................................................................................................14
Acknowledgements .................................................................................................15
Nomenclature .........................................................................................................16
Publications and presentations ..............................................................................21
Chapter 1 Introduction ....................................................................................22
1.1 Background......................................................................................................22
1.2 Motivation and objective of the work............................................................27
1.3 Thesis outline ...................................................................................................28
1.4 Contributions of this work..............................................................................29
Chapter 2 Literature Review ...........................................................................31
2.1 Introduction .....................................................................................................31
2.2 Process synthesis..............................................................................................31
2.3 Separation process synthesis ..........................................................................35
2.3.1 Knowledge-based methods............................................................................................. 36
2.3.2 Optimisation based methods .......................................................................................... 38
2.4 Synthesis of low-temperature separation processes .....................................40
2.5 Commercial applications of demethaniser flowsheets..................................42
2.5.1 Demethaniser flowsheet design and optimisation .......................................................... 47
2.6 Design and simulation methods for distillation columns .............................49
2.6.1 Shortcut design methods ................................................................................................ 50
2.6.2 Rigorous simulation methods ......................................................................................... 51
2.6.3 Minimum reflux calculation........................................................................................... 54
3
2.6.4 Distillation column design by boundary value approach................................................ 58
2.7 Conclusions ......................................................................................................63
Chapter 3 Demethaniser Column Design Method .........................................65
3.1 Introduction .....................................................................................................65
3.2 Model implementation ....................................................................................66
3.3 Product Composition Specification................................................................67
3.4 Boundary value method for multicomponent feed mixtures.......................69
3.5 Boundary value method with energy balance...............................................71
3.5.1 Calculation of rectifying section composition profile .................................................... 74
3.5.2 Calculation of stripping section composition profile...................................................... 75
3.6 Extended boundary value method for two phase feed .................................77
3.7 Double feed Column Design by Boundary Value Method...........................80
3.7.1 Composition profiles ...................................................................................................... 82
3.8 Extended boundary value method for column with side reboilers .............85
3.8.1 Composition Profiles for a column with side reboilers .................................................. 85
3.8.2 Illustrative example ........................................................................................................ 88
3.9 Extended boundary value design method for a reboiled absorption column
...........................................................................................................................91
3.9.1 Calculation of composition profiles ............................................................................... 92
3.10 Case studies ......................................................................................................94
3.10.1 Case study 1: HYSYS sample case (Turbo-expander plant) ........................................ 94
3.10.2 Case study 2: Multiple reflux stream hydrocarbon recovery process......................... 100
3.11 Conclusions ....................................................................................................105
Chapter 4 Demethaniser Flowsheet DESIGN AND Simulation Methodology.
.......................................................................................................107
4.1 Introduction ...................................................................................................107
4.2 Heat integration in demethaniser flowsheet................................................108
4.2.1 Heat recovery in multistream heat exchanger .............................................................. 110
4.2.2 Illustrative example ...................................................................................................... 111
4.3 Modelling of flowsheet units .........................................................................113
4.3.1 Demethaniser column model........................................................................................ 113
4.3.2 Flash unit model ........................................................................................................... 114
4
4.3.3 Turbo-expander Model................................................................................................. 115
4.3.4 Refrigeration cycle model ............................................................................................ 117
4.4 Flowsheet simulation and evaluation...........................................................125
4.4.1 Recycle loop convergence............................................................................................ 127
4.5 Case Study......................................................................................................129
4.5.1 Problem inputs.............................................................................................................. 130
4.5.2 Results .......................................................................................................................... 131
4.6 Conclusions ....................................................................................................134
Chapter 5 Fixed Structure Flowsheet Optimisation Using Nonlinear
Programming .......................................................................................................136
5.1 Degrees of freedom of demethaniser system - Optimisation variables .....136
5.1.1 Demethaniser operating pressure ................................................................................. 140
5.1.2 Flash temperature ......................................................................................................... 142
5.1.3 Split ratio of vapour from flash column ....................................................................... 144
5.1.4 Effect of side reboiler duty........................................................................................... 146
5.1.5 Summary of decision variables .................................................................................... 147
5.2 Process optimisation......................................................................................147
5.2.1 Objective function ........................................................................................................ 148
5.2.2 Process constraints ....................................................................................................... 150
5.2.3 Optimisation algorithm................................................................................................. 151
5.2.4 Fixed structure optimisation approach ......................................................................... 153
5.3 Case study ......................................................................................................154
5.3.1 Process constraints ....................................................................................................... 156
5.3.2 Optimisation variables.................................................................................................. 157
5.3.3 Results .......................................................................................................................... 158
5.3.4 Effect of feed and product price changes on optimisation............................................ 160
5.4 Conclusions ....................................................................................................163
Chapter 6 Demethaniser Flowsheet Synthesis by Stochastic Optimisation 164
6.1 Superstructure representation for demethaniser flowsheet ......................164
A. Use of a second flash unit ................................................................................................. 166
B. Side reboilers..................................................................................................................... 166
C. Internal reflux stream ....................................................................................................... 166
D. Use of external refrigeration cycle................................................................................... 166
6.1.1 Summary ...................................................................................................................... 166
6.2 Choice of optimisation method.....................................................................167
5
6.3 Simulated annealing ......................................................................................170
6.4 Annealing schedule parameters ...................................................................173
6.4.1 Initial annealing temperature........................................................................................ 173
6.4.2 Acceptance criterion..................................................................................................... 173
6.4.3 Markov chain length..................................................................................................... 174
6.4.4 Cooling schedule .......................................................................................................... 174
6.4.5 Termination criterion.................................................................................................... 175
6.5 Simulated annealing moves ..........................................................................176
6.5.1 Flash unit move ............................................................................................................ 176
6.5.2 Side reboiler move ....................................................................................................... 177
6.5.3 Internal reflux stream move.......................................................................................... 177
6.5.4 Operating conditions move .......................................................................................... 177
6.6 Move probabilities .........................................................................................177
6.7 Stochastic optimisation framework .............................................................178
6.8 Case Study......................................................................................................180
6.8.1 Background .................................................................................................................. 180
6.8.2 Problem inputs.............................................................................................................. 181
6.8.3 Results .......................................................................................................................... 184
6.9 Conclusions ....................................................................................................188
Chapter 7 Conclusions and Future Work.....................................................190
7.1 Conclusions ....................................................................................................191
7.1.1 Discussion .................................................................................................................... 192
7.1.2 Limitations ................................................................................................................... 193
7.2 Future work ...................................................................................................195
References.............................................................................................................197
Appendix A: MATLAB-HYSYS Interface for physical properties and Vapour-
liquid equilibrium data.........................................................................................209
Appendix B: Cost Estimation...............................................................................213
B.1 Capital cost estimation..................................................................................213
B.1.1 Annualised capital cost ................................................................................................ 216
B.1.2 Capital cost estimation for distillation columns........................................................... 217
B.1.3 Capital cost estimation for heat exchangers................................................................. 218
B.2 Operating cost estimation .............................................................................218
6
B.2.1 Steam cost.................................................................................................................... 219
B.2.2 Electricity Cost ............................................................................................................ 220
B.2.3 Cooling water cost ....................................................................................................... 220
Final word count 46788
7
List of Figures
Figure 1.1 World marketed energy use by fuel type (EIA 2011)..............................22
Figure 1.2 World natural gas consumption 2007-2035 (trillion cubic feet),.............23
Figure 1.3 UK gas production and demand to 2020 .................................................24
Figure 1.4 Total Ethane extraction from US gas processing (Fasullo, 2008) ...........26
Figure 2.1 Representation of onion model (Smith and Linnhoff, 1988)...................33
Figure 2.2 Case-based reasoning cyclic process (Farkas et al., 2003) ......................34
Figure 2.3 The interaction between process, HEN and refrigeration system (Wang, 2004)............................................................................................40
Figure 2.4 Gas subcooled process (Campbell and Wilkinson, 1981) .......................43
Figure 2.5 Cold residual reflux process (Pitman et al., 1998)...................................44
Figure 2.6 Recycle Split-Vapour process (Pitman et al., 1998) ................................45
Figure 2.7 Recycle Split-Vapour with Enrichment process (Campbell et al., 1999).........................................................................................................45
Figure 2.8 Enhanced NGL recovery process (Nasir et al., 2003) .............................46
Figure 2.9 Technip Cryomax Multiple Reflux Process (Barthe and Gahier, 2009).........................................................................................................47
Figure 2.10 A typical demethaniser column .............................................................50
Figure 2.11 Schematic diagram of an equilibrium stage (Seader and Henley, 1998).........................................................................................................53
Figure 2.12 Composition profiles in a ternary diagram (Doherty and Malone, 2001).........................................................................................................56
Figure 2.13 Schematic of the rectifying section of a distillation column .................59
Figure 3.1 Interlinking MATLAB with HYSYS ......................................................66
Figure 3.2 Schematic of the rectifying section..........................................................73
Figure 3.5 Feed mixing for feed injection between two stages.................................79
Figure 3.8 Schematic of the stripping section with lower feed.................................84
Figure 3.9 Schematic of column stripping section with side heaters ........................86
Figure 3.10 Molar flow profiles: new model (BVM) vs. HYSYS............................90
Figure 3.11 Composition profiles for key components: new model (BVM) vs. HYSYS ...............................................................................................90
Figure 3.13 HYSYS process simulation diagram of a typical expander plant..........95
Figure 3.14 Molar flow profiles: boundary value method (BVM) vs. HYSYS simulation results......................................................................................99
Figure 3.15 Liquid composition profiles: BVM vs. HYSYS simulation results........................................................................................................99
8
Figure 3.16 Process flowsheet diagram of multiple reflux stream hydrocarbon recovery process (Patel and Foglietta, 2010) ....................101
Figure 3.17 Molar flow profiles: Boundary value method vs. HYSYS..................104
Figure 3.18 Liquid composition profiles (key components): Boundary value method vs. HYSYS ................................................................................104
Figure 4.1 Generalized gas processing scheme for ethane recovery (Yan et al., 2008).................................................................................................108
Figure 4.2 Composite curves for multistream exchanger (Hewitt and Pugh, 2007).......................................................................................................112
Figure 4.3 T-H curve for an isenthalpic expansion................................................115
Figure 4.4 Pressure-Temperature-Enthalpy Diagram (Wang, 2004) .....................116
Figure 4.5 A Simple vapour-compression refrigeration cycle: a)Flow diagram, b) Temperature-enthalpy diagram (Smith, 2005)....................118
Figure 4.6 Recommended operating temperature range of some refrigerants (Smith, 2005)..........................................................................................120
Figure 4.7 A cascade refrigeration cycle.................................................................122
Figure 4.8 The effect of partition temperature on the total shaftwork (Lee 2001).......................................................................................................123
Figure 4.9 Methods for recycle convergence a) Successive substitution method, b) Wegstein method (Smith, 2005). .........................................128
Figure 4.10 Molar flow profiles: Boundary value method vs. HYSYS..................133
Figure 4.11 Liquid composition profiles: Boundary value method vs. HYSYS...................................................................................................133
Figure 5.1 HYSYS process flowsheet diagram of a typical GSP demethaniser process for NGL recovery ......................................................................138
Figure 5.2 Effect of demethaniser operating pressure on power consumption.......141
Figure 5.3 Effect of demethaniser operating pressure on ethane recovery .............141
Figure 5.4 Effect of flash temperature on total power consumption.......................143
Figure 5.5 Effect of flash temperature on ethane recovery in NGL........................143
Figure 5.6 Effect of vapour split ratio on power requirement.................................145
Figure 5.7 Effect of vapour split ratio on ethane recovery......................................145
Figure 5.8 Effect of side reboiler duty on refrigeration power requirement ...........146
Figure 5.9 Price comparison of natural gas, crude oil , ethane and NGL (EIA 2011).......................................................................................................150
Figure 5.10 Optimisation framework for a fixed structure flowsheet.....................153
Figure 5.11 Process flowsheet diagram of multiple reflux stream hydrocarbon recovery process (Ohara et al., 2008)................................155
Figure 6.1 Superstructure for demethaniser flowsheet synthesis ............................165
9
Figure 6.2 Flowchart for simulated annealing algorithm (Choong and Smith, 2004).......................................................................................................172
Figure 6.3 Flow of information in optimisation framework ...................................179
Figure 6.4 Process flowsheet diagram of a typical GSP demethaniser process (Chebbi et al., 2008) ...............................................................................182
Figure 6.5 Case study – Optimised flowsheet.........................................................187
10
List of Tables
Table 1.1 Typical composition of natural gas (Mokhatab et al., 2006) ....................24
Table 1.2 UK NTS gas specifications (Jackson et al., 2006) ....................................25
Table 2.1 Hierarchy of decisions in design (Douglas, 1985) ....................................32
Table 3.1 Molar Feed Compositions .........................................................................88
Table 3.2 Validation results: Boundary value design results vs. HYSYS simulation results......................................................................................89
Table 3.3 Feed gas composition – from HYSYS source and simplified for this case study...........................................................................................96
Table 3.4 Column feed streams – flow rates and conditions ....................................96
Table 3.5 Molar compositions of demethaniser feed streams...................................97
Table 3.6 Column details from HYSYS....................................................................97
Table 3.7 Comparison of simulation results from HYSYS and the boundary value design method .................................................................................98
Table 3.8 Column inputs: Material streams (Patel and Foglietta, 2010).................101
Table 3.9 Column inputs: Material streams (Patel and Foglietta, 2010).................102
Table 3.10 Column inputs: Energy streams (from HYSYS simulation).................102
Table 3.11 Molar composition of column input streams ........................................102
Table 3.12 Comparison of simulation results: Boundary value design method vs. HYSYS. ............................................................................................103
Table 4.1 Stream data for multistream exchanger...................................................111
Table 4.2 Cascade refrigeration cycle vs. simple refrigeration cycle .....................125
Table 4.3 Feed gas composition - from Chebbi et al. (2008)* and simplified for this case study ...................................................................................130
Table 4.4 Specified temperature and pressure of feed and products (Chebbi et al., 2008).................................................................................................130
Table 4.5 Comparison of column simulation results: Boundary value design method vs. HYSYS. ...............................................................................132
Table 4.6 Simulation results: Shortcut model vs HYSYS ......................................134
Table 5.1 Feed gas composition - from Chebbi et al. (2008)..................................137
Table 5.2 Effect of demethaniser operating pressure on flowsheet performance............................................................................................140
Table 5.3 Effect of flash feed temperature on flowsheet performance ...................142
Table 5.4 Effect of vapour split ratio on flowsheet performance............................144
Table 5.5 Effect of side reboiler duty on flowsheet performance ...........................146
Table 5.6 Specified temperature and pressure of feed and products (Ohara et al., 2008).................................................................................................154
11
Table 5.7 Feed gas composition from patent (Ohara et al., 2008) and simplified for this case study..................................................................154
Table 5.8 Values and bounds of optimisation variables.........................................157
Table 5.9 Simulation results of shortcut model and HYSYS..................................158
Table 5.10 Comparison of optimisation results with base case ..............................159
Table 5.11 Optimisation variables – Base case vs. optimised case.........................159
Table 5.12 Prices of feed and products ...................................................................161
Table 5.13 Comparison of optimisation results with base case ..............................162
Table 5.14 Optimisation variables – Base case vs. optimised case.........................162
Table 6.1 Design constants employed for case study..............................................180
Table 6.2 Simulated annealing parameters ............................................................181
Table 6.3 Feed gas composition - from Chebbi et al. (2008)* and simplified for this case study ...................................................................................181
Table 6.4 Specified temperature and pressure of feed and products (Chebbi et al., 2008).................................................................................................182
Table 6.5 Move probabilities and limits of optimisation variables.........................183
Table 6.6 Simulation results: Shortcut model vs HYSYS ......................................184
Table 6.7 Optimisation results of three solutions from a family of solutions .........185
Table 6.8 Decision variables for base case and best three cases.............................186
12
Abstract
A demethaniser process is characterised by interactions between the complex distillation column and other flowsheet units, including the turbo-expander, flash units, multistream exchangers and refrigeration system. When a design problem dealing with demethaniser flowsheets is approached in a systematic way, the number of alternatives to be studied is generally very large. The assessment of all possible flowsheets with numerous options is a time consuming task with many simulations required to select the most economic option. This research presents a systematic approach for demethaniser flowsheet synthesis to generate cost-effective designs with minimal time and effort.
A demethaniser column has many degrees of freedom, including the operating pressure, multiple feeds, the number and duty of side reboilers and the flow rate of the external reflux stream. The additional feed and side reboiler streams enhance the efficiency of the process, but complicate process modelling. The number of design variables is also augmented by additional degrees of freedom such as the location and the order of feeds, the number of stages and the reflux ratio in the column. The complexity of the demethaniser column precludes the use of the Fenske–Underwood–Gilliland shortcut design method. A semi-rigorous boundary value method is proposed for the design of complex demethaniser columns for application within an optimisation framework for process synthesis and evaluation. The results of the proposed design methodology are shown to be in good agreement with those of rigorous simulation.
A simplified flowsheet simulation model based on a sequential modular approach is developed that is able to account for various configurations and inter-connections in the demethaniser process. Improved shortcut models for flash units, the turbo-expander, compressor and refrigeration cycle have been proposed for exploitation in a synthesis framework. A methodology accounting for heat integration in multistream exchangers is proposed. The simplified simulation model is applied for the optimisation of a flowsheet of fixed configuration. The nonlinear programming technique of sequential quadratic programming (SQP) is used as the optimisation method. A case study is presented to illustrate the application of the optimisation approach for maximising the annual profit. A generalised superstructure has been proposed for demethaniser flowsheet synthesis that includes various structural combinations in addition to the operational parameters. The various options included in the superstructure and their effects on flowsheet performance are discussed. A stochastic optimisation technique, simulated annealing, is applied to optimise the superstructure and generate energy-efficient and cost-effective flowsheets. The application of the developed synthesis methodology is illustrated by a case study of relevance to natural gas processing. The results allow insights to be obtained into the important trade-offs and interactions and indicate that the synthesis methodology can be employed as a tool for quantitative evaluation of preliminary designs as well as to facilitate evaluation, selection and optimisation of licensed demethaniser flowsheets.
13
Declaration
No portion of the work referred to in this thesis has been submitted in support of an
application for another degree or qualification of this or any other university or
other institution of learning.
Muneeb Nawaz
Copyright Statement
I. The author of this thesis (including any appendices and/or schedules to this
thesis) owns any copyright in it (the “Copyright”) and he has given The
University of Manchester the right to use such Copyright for any
administrative, promotional, educational and/or teaching purposes.
II. Copies of this thesis, either in full or in extracts, may be made only in
accordance with the regulations of the John Rylands University Library of
Manchester. Details of these regulations may be obtained from the
Librarian. This page must form part of any such copies made.
III. The ownership of any patents, designs, trade marks and any and all other
intellectual property rights except for the Copyright (the “Intellectual
Property Rights”) and any reproductions of copyright works, for example
graphs and tables (“Reproductions”), which may be described in this thesis,
may not be owned by the author and may be owned by third parties. Such
Intellectual Property Rights and Reproductions cannot and must not be
made available for use without the prior written permission of the owner(s)
of the relevant Intellectual Property Rights and/or Reproductions.
IV. Further information on the conditions under which disclosure, publication
and exploitation of this thesis, the Copyright and any Intellectual Property
Rights and/or Reproductions described in it may take place is available
from the Head of School of Chemical Engineering and Analytical Science.
14
Dedication
To
My mother for her love and prayers
15
Acknowledgements
I am in many ways indebted to my supervisor Dr. Megan Jobson for her guidance
and direction without which this project could not have been realized. She has
guided and supported me with her perfect mixture of competence, enthusiasm and
patience. Also, I would like to thank my co-supervisor, Prof. Robin Smith, for his
support and advice when most needed.
Special thanks to Paritta Prayoonyong for helping me during the early stages of
this research. I am grateful to all the students at process integration for providing a
stimulating and friendly environment. I want to thank Yanis, Bostjan, Ankur,
Imran, Anestis, Lu, Yongwen, Elias, Sonia and Michael for transforming the office
into a fun place to work in.
I would also like to thank to Salman, Atif, Babur and Bilal. Without their
friendship and company, my life in Manchester would not have been that
interesting and enjoyable.
I am grateful for the financial support provided by University of Engineering and
Technology, Lahore, Pakistan.
Last, but not the least, I want to express my gratitude to my brother Zuhaib and
sister Saba for all their love and support during all these years.
16
Nomenclature
AC annualised capital cost of the equipment
B molar flow rate of bottom product
pC
Heat capacity,
c number of components
D Molar flow rate of the distillate in eq. 2.3
F molar flow rate of feed
E equality constraint functions
G flow rate capacity of utility in Eq. 5.8
h molar enthalpy flow rate
i component i
I inequality constraint functions
( )xH Hessian matrix of the Lagrange function in Eq. 5.11
( )xJ the Jacobian matrix of the constraint functions in Eq. 5.12
L molar flow rate of liquid
m coefficients fitted to the light key component recovery Eq. 3.1
n coefficients fitted to the heavy key component recovery Eq. 3.1
N number of stages
OC cost associated with the use of utility in Eq. 5.8
P pressure
P profit
q liquid fraction of feed stream
Q heating or cooling duty
Q& heat transferred in a zone in Eq. 4.1
r fractional recovery key component in Eq.3.2
17
R reflux ratio (molar)
Rmin minimum reflux ratio
s reboil ratio (molar)
T Temperature,
U Overall heat transfer coefficient between a process unit and the
surroundings,
minV minimum vapour flow in the top section of column
W Power
x vector of liquid mole fraction
y vector of vapour mole fractions
Greek letters
α relative volatility
iβ local volumetric heat transfer coefficient in Eq.4.1
ε pressure ratio, Pout/Pin in Eq. 4.11
θ root of the Underwood equation (2.1)
lmT∆
log mean temperature difference
η efficiency
µ vector of Lagrange multipliers for inequality constraint functions
in Eq. 5.10
ω random number
ρ density
σ standard deviation of the values of the objective function in Eq.
6.6 γ ratio of heat capacities CP/CV of refrigerant in Eq. 4.11
λ vector of Lagrange multipliers for equality constraint functions in
Eq. 5.10
18
Subscripts and Superscripts
0, 1, 2 stage number
1,2 side-reboiler number
a annealing
act actual
B bottom product
cond condenser
D distillate
e, E error, defined in eq. (3.13)
evap evaporator
F feed
HK heavy key
id ideal
in inlet
is isentropic
L, l liquid phase
L lower feed
LK light key
m, n stage number
M middle section
out outlet
op operating cost
prod product
R, rec rectifying section
reb reboiler
RM raw material
S, strip stripping section
sat saturated
U upper feed
19
ut utility
V, v vapour phase
Z error, defined in eq. (3.17) and
(3.33)
Acronyms
BVM boundary value method
CRR cold residue reflux
FUG Fenske-Underwood-Gilliland
GA genetic algorithm
GSP gas subcooled process
HEN heat exchanger network
HK heavy key
HHK heavier than heavy key
LK light key
LLK lighter that light key
LMTD log mean temperature difference
LP linear programming
LPG liquefied petroleum gas
MILP mixed integer linear programming
MINLP mixed integer nonlinear programming
MM million
20
NAG numerical algorithm group
NLP nonlinear programming
NGL natural gas liquids
OHR over head recycle process
OECD organisation for economic co-operation and development
RSV recycle split-vapour
RSVE recycle split-vapour with enrichment
SA simulated annealing
SQP successive quadratic programming
VLE vapour-liquid equilibrium
21
Publications and presentations
• Nawaz, M. and Jobson, M., ‘A new simplified method for design of complex
demethaniser columns’ Chemical Engineering Research and Design. 89
(2011) 1333-1347
• Nawaz, M., Jobson, M., and Smith R., ‘Process design and optimization of
complex demethanizer flowsheets’ AIChE 2010 Annual Meeting, Salt Lake
City USA
• Nawaz, M. and Jobson, M., ‘Synthesis and optimization of demethaniser
flowsheets for low temperature separation processes’ Distillation and
Absorption, Netherlands, (2010).
• Nawaz, M. and Jobson, M., ‘Boundary value design method for complex
distillation columns’ Distillation and Absorption, Netherlands, (2010).
• Nawaz, M. and Jobson “Modelling and optimization of demethaniser
flowsheets for sub-ambient separation systems”. Fluid Separation Subject
Group Event, IChemE. BP Sunbury, London (2010).
• Nawaz, M., Jobson, M., and Smith R., ‘Synthesis and optimization of low
temperature separation processes’. Process Integration Research Consortium
Annual Meeting Manchester, U.K, 2009.
• Nawaz, M., and Jobson M., ‘Design of sub-ambient complex distillation
columns’. 118th International Summer Course. BASF Aktiengesellschaft,
Ludwigshafen, Germany (2008).
Chapter 1 Introduction
22
CHAPTER 1 INTRODUCTION
1.1 Background
About one fifth of the world's primary energy demand is met by natural gas (EIA
2011). US Energy Information Administration (EIA) expects this share to rise over
the next twenty years. Figure 1.2 presents the energy consumption of various fuels
projected over the 2007-2035 period. Measured per energy unit, combustion of
natural gas is cleaner than other fossil fuels both concerning global emissions and
local pollutants (Balat, 2009). Therefore, it could be used to bridge the gap and
reduce emissions from coal before enough energy from renewable sources
becomes available (Mokhatab et al., 2006).
Figure 1.1 World marketed energy use by fuel type (EIA 2011)
Chapter 1 Introduction
23
According to EIA International energy outlook report 2010, natural gas
consumption will increase by 44 percent from 108 trillion cubic feet in 2007 to 156
trillion cubic feet in 2035 as shown in Figure 1.2. The natural gas demand is
expected to increase as the world economy rebounds from the recent economic
downturn. The largest projected increase in natural gas production is for the non-
OECD (Organisation for Economic Co-operation and Development) region, with
the major increments coming from the Middle East, Africa and Russia.
Figure 1.2 World natural gas consumption 2007-2035 (trillion cubic feet),
The UK relies on natural gas to provide energy for heating and electricity more
than any other primary energy source. 39% of the UK’s primary energy comes
from gas, compared with 35% from oil, 15% from coal, 9% from nuclear and 2%
from other sources (UK Parliament, 2003). Figure 1.3 presents the production and
demand of natural gas in UK. The supply gap is shown to increase by 100 bcm
(billion cubic meter) by 2020.
Chapter 1 Introduction
24
Figure 1.3 UK gas production and demand to 2020
The main constituent of natural gas is methane. The other constituents are
paraffinic hydrocarbons such as ethane, propane, and the butanes and impurities
such as nitrogen, carbon dioxide and hydrogen sulphide. Trace quantities of argon,
hydrogen, and helium may also be present. The composition of natural gas varies
depending on the field or reservoir from which it is extracted (Mokhatab et al.,
2006). Table 1.1 outlines the typical composition of raw natural gas before it is
refined.
Table 1.1 Typical composition of natural gas (Mokhatab et al., 2006)
Name Formula Volume (%) Methane CH4 > 85
Ethane C2H6 3-8
Propane C3H8 1-2
Butane C4H10 < 1
Pentane C5H12 < 1
Carbon dioxide CO2 1-2
Hydrogen sulphide H2S <1
Nitrogen N2 1-5
Helium He <0.5
Chapter 1 Introduction
25
After the separation of the impurities (H2S, N2), natural gas liquids (NGL) recovery
is the next step. NGL recovery refers to the process of extracting ethane, propane,
butane and other heavier hydrocarbon products from natural gas. These
hydrocarbons have a greater value as pure components than as a part of the sales
gas. Methane is mainly utilised as a residential and industrial fuel, ethane and
propane for petrochemical synthesis and C2+ components are used in auto fuels
(Fissore and Sokeipirim, 2011).
Worldwide, the gas processing industry meets a wide variety of economic and
recovery objectives, which range from meeting a specification for gas
transportation, to achieving high ethane recovery for providing feed to an ethylene
production plant (Mcmahon, 2004). In UK, the various issues regarding natural gas
include the gas quality from imports, depletion of existing offshore UK gas fields
and a drop in the number of new UK gas field developments (Jackson et al., 2006).
These issues have led to evaluation of more marginal (lower quality) gas fields that
would need special treatment and processing facilities to meet certain
specifications. In UK the natural gas is transported through the national
transmission system (NTS), by the National Grid. The required specifications for
the UK NTS are given in Table 1.2.
Table 1.2 UK NTS gas specifications (Jackson et al., 2006)
Specification Unit Limit
Wobbe Index MJ/sm3 47.2 – 51.41
Nitrogen mol % 5 (max)
carbon dioxide mol % 2 (max)
Oxygen ppmv 10 (max)
Hydrogen sulphide mg/sm3 5 (max)
Total sulphur ppmv 50 (max)
The Wobbe index is used as standard for calculating the heating value of the gas.
gravityspecificGas
HHVIndexWobbe =
where HHV is the higher heating value of the gas (MJ/m3)
Chapter 1 Introduction
26
The extent to which NGL are to be recovered is a balance between capital,
operating cost and the benefits of producing a range of products. It is important to
consider all the implications before any process is selected. The calorific value of
ethane is approximately 1.8 times that of methane (Poling et al., 2001). According
to Farry (1998), a typical natural gas stream with around 5% ethane content, will
have a 4% higher calorific value than a stream consisting of methane only. As a
result, the presence of ethane does not affect the properties of natural gas at low to
medium concentrations. Therefore, the decision to recover ethane from natural gas
is mainly governed by ethane market economics.
The main use of ethane is in ethylene production where it competing with other
NGL and petroleum feedstocks. On average, ethane constitutes 45% of the US
ethylene feedstock mix and it provides the highest ethylene yield of all the
feedstocks (Fasullo, 2008). A study was performed by Envantage Inc. (Fasullo,
2008) to access the outlook of US ethane production. The extraction of ethane from
the natural gas was shown to be dependent on the ratio of price of gas to crude oil.
When this ratio is higher the extraction of ethane is decreased as naphtha from
crude is used as the petrochemical feedstocks.
Figure 1.4 Total Ethane extraction from US gas processing (Fasullo, 2008)
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Chapter 1 Introduction
27
1.2 Motivation and objective of the work
Ever since the discovery and recognition of natural gas as a desirable fuel, the need
for its transportation to markets has led to the development of treatment and
processing technologies. In order to be competitive in the global market, the
natural gas industry is trying to increase profits, reduce environmental impacts,
being safer and developing a commitment to sustainability in order to be
competitive. Such opportunities include energy savings, cost reductions, increasing
quality standards and eliminating bottlenecks (Sharratt et al., 2008).
Despite recent success of membrane separation and pressure swing adsorption in
natural gas industry, low-temperature processing remains the most important route
for the separation and purification of natural gas components, especially when high
recoveries are required (Mak, 2009, Bullin and Hall, 2000). These systems are
highly interactive and interlinked to each other. Due to the complex interactions
between the separation system and the refrigeration system, synthesis and
optimisation of low-temperature gas separation processes remains a major
challenge to process engineers (Tahouni et al., 2010) . The interactions between the
separation and refrigeration systems need to be considered at the early stages of the
design which affects the process heat integration decisions leading to energy
savings in the overall process (Yiqing et al., 2009).
The recovery of heavier components from natural gas, employing a demethaniser
flowsheet is an example of low temperature gas separation process. The
demethanisation process is characterised by interactions between the complex
distillation column and other flowsheet components, including turbo expander,
flash units, multistream exchangers and external refrigeration system (Mehrpooya
et al., 2006).
The demethaniser is a low-temperature distillation column that makes a separation
between methane and heavier hydrocarbons, to provide pipeline quality methane
and recover natural gas liquids. The demethaniser has many degrees of freedom,
including the operating pressure, the location and the order of feeds, the number
Chapter 1 Introduction
28
and duty of side reboilers and the flow rate of the external reflux stream (Khoury,
2005). The complexity of the demethaniser column does not allow the use of the
Fenske–Underwood–Gilliland shortcut design method. Therefore, there is a need to
develop an appropriate design model for the demethaniser column which is
suitable for application within an optimisation framework for process synthesis and
evaluation.
The current approach for the design of the NGL recovery processes employing
expander based demethaniser column flowsheets is based on previous experience,
design heuristics and process simulation (Jibril et al., 2005). Despite the industrial
importance of the demethaniser process in natural gas separation processes, no
systematic method is available for the design of demethaniser processes (Chebbi et
al., 2010, Mehrpooya et al., 2009, Sharratt et al., 2008). Therefore, a
comprehensive approach for synthesis is required to generate effective and
economic design without excess requirements of engineering time and effort. In
this work, the objective is to develop a synthesis framework for demethaniser
flowsheets. This framework can systematically perform a screening and scoping of
integrated demethaniser flowsheets. In the framework, various possible options
available in these flowsheets are considered.
1.3 Thesis outline
Chapter 2 presents a critical review of relevant publications concerning various
aspects of this work. The challenges faced by design engineers for separation
process synthesis in general and specifically low-temperature separation processes
are highlighted. Various commercial applications and flowsheet options for the
demethaniser processes are also reviewed. Finally, a range of design methods for
distillation columns are discussed, along with their suitability for the design of
demethaniser column.
Chapter 3 presents a new simplified method for the design of demethaniser
columns based on the boundary value method. The design method accommodates
the use of complex column features such as multiple feeds, side heaters, external
Chapter 1 Introduction
29
reflux, etc. The validation of the proposed methodology against the rigorous stage
by stage calculation in a commercial simulation software is also presented.
Chapter 4 discusses a flowsheet design methodology based on a sequential
modular simulation approach. In this chapter, shortcut design models for various
units of the demethaniser flowsheet are developed. The validation of the new
integrated process model is performed by rigorous simulation of a typical
demethaniser process using the Aspen Tech simulation package HYSYS®.
Chapter 5 is dedicated to the optimisation of a flowsheet of fixed structure
flowsheet by employing a nonlinear technique, sequential quadratic programming,
where the design variables to be optimised are chosen following a sensitivity
analysis. Simultaneous optimisation of these variables is carried out to create cost-
effective design solutions while maintaining the performance specifications of the
process, as illustrated by a case study.
A systematic approach for the synthesis of demethaniser flowsheets based on
stochastic optimisation is proposed in Chapter 6. The structural options
incorporated in the superstructure are discussed. The use of simulated annealing, a
stochastic optimisation technique, to optimise the superstructure is proposed. A
case study is presented to demonstrate the applicability of the approach.
A summary of the research and conclusions are provided in Chapter 7.
Suggestions to extend the research are also discussed.
1.4 Contributions of this work
This thesis presents a novel optimisation-based synthesis of system consisting of
demethaniser flowsheets, i.e. to generate a few promising flowsheet configurations
with appropriate operating conditions. The main contributions of this work are
highlighted below:
Chapter 1 Introduction
30
� A novel extension of the established boundary value design method is
proposed in Chapter 3 for modelling demethaniser columns incorporating
o Multi-component feed mixtures
o Two-phase feed
o Columns with side reboilers
o Columns with an external reflux stream
� An novel integrated model for the demethaniser flowsheets is developed in
Chapter 4.
� A nonlinear constrained optimisation problem is formulated in Chapter 5
for fixed structure demethaniser flowsheets.
� In Chapter 6 a demethaniser flowsheet synthesis methodology is proposed
based on stochastic optimisation.
Chapter 2 Literature review
31
CHAPTER 2 LITERATURE REVIEW
2.1 Introduction
This chapter reviews relevant publications concerning different aspects of this
work. Process synthesis, including separation system synthesis, occupies a central
place in process engineering literature. Process synthesis plays a key role in the
identification of the best flowsheet structure to carry out a specific task, such as
conversion of raw material into a product, or separation of a multi-component
mixture.
This first section introduces the area of process synthesis along with the various
challenges faced by design engineers for process synthesis. The discussion is then
elaborated for separation processes and literature on separation process synthesis is
reviewed. Low-temperature separations are discussed in the next section. The
discussion of low-temperature synthesis is further extended for demethaniser
processes for NGL recovery. Various commercial demethaniser processes are also
reviewed.
Finally, shortcut and rigorous methods for the design of distillation columns are
reviewed. The suitability for these design methods for the demethaniser column
design is also discussed.
2.2 Process synthesis
Process synthesis is concerned with the activities in which the various process
elements are combined and the flowsheet of the process is generated so as to meet
Chapter 2 Literature review
32
design objectives. Hence, in process synthesis usually we know process inputs and
outputs but are either required to revamp the flowsheet or create a new flowsheet
(Barnicki and Siirola, 2004).
Traditionally, process synthesis methods can be classified into two groups:
heuristic methods and optimisation based methods. The heuristic methods are
based on the long-term experience of engineers and researchers. The main idea of
the optimisation-based approach is to formulate the synthesis of a flowsheet in the
form of an optimisation problem. It requires an explicit or implicit representation
of a superstructure of process flowsheets from among which the optimal solution is
selected (Westerberg, 2004).
Douglas (1985) has proposed a hierarchical heuristic procedure for chemical
process design where heuristic rules are applied at different design levels to
generate the alternatives. Shortcut calculations, based on economic criteria, are
carried out at every stage of process design. The hierarchy is shown in Table 2.1.
Table 2.1 Hierarchy of decisions in design (Douglas, 1985)
The hierarchical heuristic method of Douglas (1985) emphasizes the strategy of
decomposition and screening. However, the major limitation of this method, with
its sequential nature, is the difficulty to take into account the interactions between
different design levels. The inability to capture interactions also causes problems in
the systematic handling of multi-objective issues within hierarchical design. As a
result, the hierarchical heuristic method offers no guarantee of finding the best
possible design (Li and Kraslawski, 2004).
Level 1. Batch versus continuous
Level 2. Input-output structure of the flowsheet
Level 3. Recycle structure of the flowsheet
Level 4. General structure of the separation system
Level 5. Energy integration
Chapter 2 Literature review
33
Smith and Linnhoff (1988) proposed an ‘onion model’ for decomposing the
chemical process design into several layers (Figure 2.2). In the onion model, the
synthesis process begins at the centre of the onion with the synthesis of the
reaction system, and then proceeds outward. The reactor design affects the
separation and the recycle structures, which are designed next. The reactor, the
separator and the recycle system then dictate the heat recovery requirements.
Finally, the process utility system is designed to satisfy the heating and cooling
requirements of the process. The onion model is an example of sequential and
hierarchical nature of process flowsheet synthesis. Synthesis decisions are made at
each layer of the onion that ensures a feasible product flowsheet.
Figure 2.1 Representation of onion model (Smith and Linnhoff, 1988)
Another heuristic based approach involves the design of the process according to
the phenomena involved in the process. According to this method, reasoning for
design should be started at the level of phenomena occurring in the building
blocks. Gavrila and Iedema (1996) developed a design methodology based on
phenomena-driven process design. The methodology employs kinetic and
thermodynamic knowledge to propose structural and operational design
alternatives. Although the phenomena-based concept of Gavrila and Iedema (1996)
can be used to model conventional units, however, the methodology does not
support the modelling of complex and innovative designs.
Chapter 2 Literature review
34
More recently, a new approach has been developed for process synthesis which is
based on the case-based reasoning. This approach tries to solve new synthesis
problems by reusing solutions that were applied to similar problems in the past.
Farkas et al. (2003) described the main phases of the case-based reasoning
activities as a cyclic process (see Figure 2.2). During the first step, ‘Retrieval’, a
new problem is matched against problems of previous cases by calculating the
value of similarity functions, in order to find the most similar problem and its
solution. If the proposed solution does not meet the necessary requirements of the
new problem, case-based reasoning proceeds onto the next step, ‘Adaptation’, and
creates a new solution. The returned solution and new problem together form a
new case that is incorporated in the case base during the ‘Learning’ stage.
However, case-based reasoning has the disadvantage that the old design cases
strongly influence the approach and there are no methods available for adaptation
to support innovative design (Li and Kraslawski, 2004).
Figure 2.2 Case-based reasoning cyclic process (Farkas et al., 2003)
Grossmann and Daichendt (1996) discussed the major challenges in process
synthesis. They discussed that it is difficult to combine the heuristic search,
optimisation and targeting approaches in such a way that, on the one hand, the
integration is conceptually consistent and rigorous, and on the other it exploits the
Chapter 2 Literature review
35
strengths of each approach. A second issue raised by Grossmann and Daichendt
(1996) is that in most cases, mixed integer non-linear programming (MINLP) or
non-linear programming (NLP) models for process synthesis involve non-
convexities which may give rise to several local optimal solutions. The values of
the objective function differ largely between these solutions because of the large
number of structural alternatives in these process synthesis problems. As a result,
the optimisation algorithm can be trapped in local optima. Because of these
reasons, Grossmann and Daichendt (1996) suggested that there is a strong need for
developing global optimisation methods that are relevant to process synthesis.
In process synthesis, the separation system synthesis remains a very challenging
task (Koolen, 2001, Montolio-Rodriguez and Linke, 2011). Separation process
synthesis addresses a wide range of separation problems such as the selection and
identification of separation technologies, the sequencing of separation tasks and
the determination of appropriate conditions for unit operations (Seuranen et al.,
2005). The next section gives an overview of various approaches to separation
process synthesis.
2.3 Separation process synthesis
When a synthesis problem dealing with multicomponent mixtures and a variety of
separation technologies is approached in a systematic way, the number of
separation alternatives to be studied is generally very large. A screening tool can
reduce the number of design options in the early phases of design before a more
detailed study is undertaken. The tool can also provide a quick estimate of
alternatives without detailed simulation-based analysis, and can be used in the
conceptual process design phase (Caballero and Grossmann, 2004). Most of the
developed separation synthesis methods can be categorized into knowledge-based
and optimisation methods.
Chapter 2 Literature review
36
2.3.1 Knowledge-based methods
Sargent et al., (2004) noted that the current approaches for separation process
synthesis are not able to describe reliably every physical phenomenon and
engineering practice. They suggested that it is not possible to make all the rigorous
time consuming calculations at the early stages of synthesis for all process
alternatives. In practice, engineers rely on their experience and knowledge to select
the alternatives for further study. Thereafter, they usually proceed with more
advanced methods, for instance rigorous simulations.
Various heuristic rules have been proposed by different researchers, such as
heuristic functions (Lu and Motard, 1985) and vapour loads (Malone et al., 1985).
Siirola (1996) discussed that knowledge based generation methods involve a set of
unit operations, using process and thermodynamics constraints. These are used for
flowsheet synthesis by progressively transforming a given feed stream into
products.
Barnicki and Fair (1990), (1992) created a comprehensive rule-based system for
reducing the number of process alternatives in a separation process synthesis. Their
work contains a comprehensive set of heuristics for application to separations of
liquids and gas/vapour mixtures and offers an advice on separation technology
selection and sequencing. A range of separation technologies including
condensation, cryogenic distillation, physical and chemical absorption, membrane
separation were considered. They employed quantitative indicators to rank the feed
components in a list according to the physicochemical property exploited by the
separation technology. The relative position of key components in the ranked list
indicates whether a separation technology is suitable for a feed mixture. However,
the rule based system proposed by Barnicki and Fair (1990), (1992) is more
suitable for initial feasibility screening as compared to process design, as a design
methodology is required for the relevant separation unit.
Jaksland and Gani (1996) also presented an approach for the design and synthesis
of separation processes which employs physicochemical properties and their
Chapter 2 Literature review
37
relationships to separation techniques. For a specified multicomponent separation
problem, subsets of feasible separation techniques are first identified for a binary
mixture and user-specified separation tasks. The number of alternatives for each
separation task is then reduced by systematically analysing the relationships
between properties, separation technique and conditions of operation. After the
final step, an estimate of the final process flowsheet is produced with a list of
possible alternatives for the separation tasks.
Another knowledge based technique known as the attainable region (AR) was
developed by Glasser et al. (1987) for process synthesis. The initial work focused
on reaction systems and was based on the idea of Horn (1961). Horn defined the
AR as the set of all possible outcomes, for the system under consideration, that can
be achieved using the fundamental processes operating within the system, and that
satisfies all constraints placed on the system. Glasser et al. (1987) approached the
idea of the AR from a geometric perspective by considering a reactor as a system
comprising the only reaction and mixing processes.
Recently (Metzger et al., 2009) used attainable region analysis to optimise particle
breakage in a ball mill. The discussed that after the AR is known, a path between
the feed point and a point in the AR can be found. This path can be a combination
of reaction, mixing and other fundamental processes, which could in turn be
interpreted as a process layout with specified operating conditions. Hence by
finding the AR, the optimum process specifications to achieve points in the AR can
also be found.
As knowledge based methods are based on heuristics, they can ignore the potential
of alternative novel process configurations and operating strategies.
Chapter 2 Literature review
38
2.3.2 Optimisation based methods
The optimisation-based methods formulate the synthesis problem for a flowsheet
in the form of an optimisation problem and mostly involve mathematical
programming. These methods consist of an objective function and equality and
inequality constraints. In the separation process synthesis problem, both
continuous and discrete variables exist, which complicates the optimisation
procedure. Continuous variables are to represent states (temperature, pressure, etc.)
and flow rates. Discrete variables describe the topology of a process network or
represent the existence or non-existence of unit operations (Biegler et al., 1997).
Optimisation based process synthesis approach which involves systematic
generation of alternatives approach is highly combinatorial. Grossmann and
Biegler (2004) discussed that the main problem in using the approach of systematic
generation of alternatives is the inability of the algorithm to select wisely among
the alternatives at decision points. This shortcoming of pure systematic generation
algorithms can be solved by using superstructure optimisation (Caballero and
Grossmann, 2006) .
Superstructure optimisation is a process synthesis approach in which the structure
of a process and the operating parameters can be determined simultaneously.
Theoretically, the superstructure initially includes many redundant paths and
alternative units for achieving the design objectives. Then optimisation is
performed to remove the superfluous paths and equipment alternatives to find the
best solution (Grossmann and Biegler, 2004).
Andrecovich and Westerberg (1985) and Shah and Kokossis (2002) adopted
superstructure approaches while addressing the separation synthesis problem using
sequence of simple columns (a single feed and two product column). In their work,
a superstructure is first constructed, within which all possible sequences of simple
distillation columns are embedded. The synthesis problem is formulated as a mixed
integer linear programme (MILP) or a mixed integer non-linear programme
Chapter 2 Literature review
39
(MINLP) and an optimisation algorithm is implemented to obtain the solution. The
combinatorial characteristic of MINLP results in a large number of possible
combinations even for a modest number of binary variables (Floudas and
Gounaris, 2009).
The problem of global optimality in MINLPs have been solved by a number of
techniques: the Outer Approximation algorithm and its variants (Duran and
Grossmann, 1986, Caballero et al., 2005) handle MINLPs such that the binary
variables participate linearly and the continuous variables participate in a convex
manner; the Generalized Outer Approximation algorithm, (Fletcher and Leyffer,
1994), applies to problems with convex functions in the continuous and not
necessarily separable binary variables; the Generalized Benders Decomposition
algorithm, GBD (Floudas et al., 1989) is designed for problems with a convex
continuous part and binary variables in linear or mixed bilinear terms. A detailed
description of these methods is given by Biegler and Grossmann (2004).
Although modern tools such as the General Algebraic Modelling System (GAMS)
facilitate the implementation of different equation systems and provide solvers, the
correct implementation of the system of equations remains still a difficult task due
to the mere size and complexity of the problem (Henrich et al., 2008).
Stochastic optimisation methods are a potential alternative to conventional
methods for solving MINLP problems. These methods appear to overcome most of
the drawbacks suffered by their conventional counterparts. The stochastic methods
make random moves based on an algorithm to explore the solution space. The
search for the optimum is based on the values of the objective function at different
points of the search space. Consequently, discontinuous or non-differentiable
problems can also be optimised. In addition, most stochastic algorithms can avoid
becoming trapped at local optima, making these methods suitable for optimising
non-convex problems (Wang and Li, 2010).
Chapter 2 Literature review
40
2.4 Synthesis of low-temperature separation processes
A separation is considered low-temperature if it requires utility at sub-ambient
temperatures. Examples of processes involving low-temperature separation are
ethylene plants, natural gas liquids (NGL) recovery plants and air separation
plants.
A sub-ambient process usually comprises three major parts, namely: the separation
process, the heat exchanger network and the refrigeration system (Wang and
Smith, 2005), as shown in Figure 2.3. In a typical sub-ambient process, the feed
gas mixture, after compression, is cooled in a network of heat exchangers to the
desired pressure and temperature required for the separation. A sequence of
separation units is used to separate the feed mixture into the required products. The
separation process rejects heat at low-temperatures. This heat is removed by a
refrigeration system.
Figure 2.3 The interaction between process, HEN and refrigeration system
(Wang, 2004)
Refrigeration systems are typically more expensive than other utilities in terms of
energy per unit, because of the high operating cost and capital intensive
compressors associated with them. The operating costs for the refrigeration
systems are often dominated by the cost of shaft work to drive the compressors. In
ProductsFeed HE Network
Separation system
Refrigeration system
Compressor system
Chapter 2 Literature review
41
sub-ambient processes, the design of the refrigeration system dictates the energy
consumption and capital investment of the whole process (Mehrpooya et al., 2009).
Due to the complex interactions between the separation system and the
refrigeration system, synthesis and optimisation of low-temperature gas separation
processes remains a major challenge to process engineers. These systems are
highly interactive and interlinked to each other (Tahouni et al., 2010). Any
modifications in the separation process or in the heat exchanger network will have
a downstream impact on the shaft work requirement of the refrigeration system.
The different design considerations incur trade-offs between energy savings and
extra capital investment.
Wang and Smith (2005) presented a synthesis framework for screening low-
temperature heat-integrated separation systems based on separation task
representation. A separation task is defined as a sharp separation between two
adjacent (in volatility order) components. Their methodology is based on a
sequence superstructure where each separation task was further developed with
several device representations. Wang and Smith (2005) applied a stochastic
optimisation framework using genetic algorithm and further fine-tuned the results
using successive quadratic programming. They found that employing a hybrid
optimisation method results in a robust methodology for the optimisation of
complex low-temperature processes. However, a high computational time was
reported as a disadvantage in the research of Wang (2004). Moreover, the feed to
the distillation column is limited to the saturation conditions, thus not allowing a
two-phase feed.
Recently, Markowski et al. (2007) developed a new approach for energy
optimisation of a sequence of heat-integrated distillation columns for low
temperature processes. The adopted a sequential approach for the design of the
separation system, the refrigeration system and the heat exchanger network. Pinch
analysis was applied for heat integration within the separation sequence. However,
the refrigeration system is not heat integrated with the separation sequence.
Chapter 2 Literature review
42
In summary, the above discussion shows that there are still gaps in literature in the
area of low-temperature separation processes such as: accounting for various
interactions and structural options in the overall flowsheet, simultaneous
optimisation of key design variables in the separation and refrigeration system and
solving a nonlinear problem for flowsheet synthesis to generate practical designs
for commercial applications.
2.5 Commercial applications of demethaniser flowsheets
Among low-temperature separations, one of the important processes is the
recovery of natural gas liquids. Increase in the price of energy sources and global
economic problems have required cryogenic natural gas liquid recovery plants to
become more complex and efficient (Bullin and Hall, 2000, Chebbi et al., 2010).
NGL recovery plants commonly uses cryogenic or absorption processes. There is a
degree of overlap between the cryogenic process using a demethaniser, and the
enhanced absorption processes incorporating refrigeration for improved recovery.
Mehra and Gaskin (1999) compared the cryogenic and absorption processes for
ethane recovery from natural gas. According to them selection of the adequate
technology is dictated by a balance between various factors such as feed
compositions, feed pressure and recovery specifications of products.
In the case of cryogenic turbo-expander processes, a significant portion of the
refrigeration can be obtained via expansion of the feed stream. These processes
readily achieve very low-temperatures (down to around –100°C) and therefore
provide high recovery of the heavy hydrocarbons, with proprietary processes able
to achieve >90% ethane recovery and essentially complete recovery of propane
and heavier hydrocarbons (Mokhatab et al., 2006).
In the 1970’s Ortloff Engineers Inc. developed and patented various processes for
NGL recovery. Based on these patents, there are around 235 expander based NGL
recovery plants in the world (Ortloff, 2011). Pitman et al. (1998) described the
main features of these processes and compared them to the new generation
Chapter 2 Literature review
43
processes proposed by Ortloff Engineers Inc. in the 1980’s and later. Various
process schemes were compared by Pitman et al. (1998) in terms of recovery and
the relative compression power. They discussed that the main characteristic for
most of these processes is to split the vapour from the flash column and employ a
part of it to generate the reflux for the demethaniser tower. For the ethane
recovery, the most widely employed split-vapour-process is the gas subcooled
process (GSP) (Campbell and Wilkinson, 1981) shown in Fig. 2.4.
In a simplified version of the gas subcooled process, the high-pressure feed gas is
cooled, flashed and separated in a high pressure separator into vapour and liquid
streams. The vapour stream is expanded in a turbo-expander which drops the
pressure and partially liquefies it. The turbo-expander simultaneously produces
cooling/condensing of the gas and useful work which may be used to recompress
the sales gas. The liquid from the flash drum is throttled through a valve to about
the same pressure as the expander discharge and fed to an intermediate tray as
lower feed. The vapour from the expander is fed to the top of the demethaniser
column as top feed, and the valve outlet stream is fed to an intermediate tray as the
lower feed (Jibril et al., 2005).
Figure 2.4 Gas subcooled process (Campbell and Wilkinson, 1981)
Chapter 2 Literature review
44
The ethane recovery level in the GSP process is limited by the composition of the
stream acting as an external reflux for the column. In order to overcome this
restriction in recovery, new processes were developed by Ortloff Engineers Inc.
These include the cold residue reflux (CRR), the recycle split vapour (RSV), the
recycle split vapour with enrichment (RVSE) processes (Pitman et al., 1998).
The cold residue recycle (CRR) process is a modification of the gas subcooled
process to achieve higher ethane recovery levels (Figure 2.5). The process
flowsheet is similar to that of the GSP, except that a compressor and a condenser
have been added to the overhead system to take a portion of the residue gas and
provide additional reflux for the demethaniser. This process is attractive for high
ethane recovery (Wilkinson et al., 2002).
Figure 2.5 Cold residual reflux process (Pitman et al., 1998)
Figure 2.6 illustrates the Recycle Split-Vapour (RSV) (Pitman et al., 1998) process
which employs the split vapour feed as the external reflux stream for the
demethaniser. The external reflux stream is produced by withdrawing a small
portion of the residue gas, condensing and sub cooling and flashing it down to the
demethaniser pressure. The additional cost of adding a compressor in the CRR
process is avoided. Although there is a slight decrease in the ethane recovery as
compared to that of CRR process, the lower capital cost and process simplicity
justifies the slight loss of ethane recovery (Campbell et al., 1996).
Chapter 2 Literature review
45
Figure 2.6 Recycle Split-Vapour process (Pitman et al., 1998)
The Recycle Split-Vapour with Enrichment (RSVE) (Campbell et al., 1999)
process shown in Figure 2.6 is a variation of the RSV process, where the recycle
stream withdrawn from the residue gas is mixed with the split-vapour feed before
being cooled in an exchanger. The mixing, thus avoids the need of a separate
exchanger. The advantage of RSVE process is the result of lower capital
investment than RSV process. However, the ethane recovery in this process is
slightly lower than in the RSV process due to mixing the recycle stream with the
split-vapour feed.
Figure 2.7 Recycle Split-Vapour with Enrichment process (Campbell et al.,
1999)
Chapter 2 Literature review
46
Some other companies have developed competitive designs in order to improve
NGL recovery. (Nasir et al., 2003) explored the processes for NGL recovery
developed by Ortloff and compared them with that designed by International
Process Services (IPSI) Inc. (see Figure 2.8). The scheme proposed by IPSI uses a
side-draw taken from the bottom of the column which is used to cool the inlet gas.
The IPSI stripping gas process generates internal refrigeration by expanding a
liquid stream from the demethaniser. This arrangement eliminates the need of
external refrigeration. The flashed vapour is then compressed and returned to the
demethaniser as stripping gas while the flashed liquid combines with the
demethaniser bottom product.
Figure 2.8 Enhanced NGL recovery process (Nasir et al., 2003)
Barthe and Gahier (2009) discussed the CRYOMAX process from Technip France.
The process is known as multiple reflux ethane recovery. A high recovery of
ethane upto 95% can be achieved through this process by employing the multiple
reflux associated with a turbo-expander. The use of multistream exchangers also
enhances the energy efficiency of the process thorough heat integration the heat
integration. The process involves two vapour-liquid separators at different
pressures.
Chapter 2 Literature review
47
Figure 2.9 Technip Cryomax Multiple Reflux Process (Barthe and Gahier,
2009)
To summarize, processes for NGL recovery include a range of potential options.
The selection of an appropriate demethaniser flowsheet for the NGL recovery is
thus a difficult task. The choice of flowsheet structure and operating conditions
affect the recovery level. A systematic methodology for demethaniser flowsheet
synthesis for NGL recovery is thus required. Some of the previous work in the area
of design and optimisation of NGL recovery processes is discussed in the next
section.
2.5.1 Demethaniser flowsheet design and optimisation
There is a lack of academic research in the area of demethaniser process synthesis
and optimisation. One of the earliest studies for optimisation of demethaniser
process was performed by Bandoni et al. (1989), in which they divided the
demethaniser flowsheets into two sections; the compression and above-ambient
heat exchange section and the separation, expansion and below-ambient heat
exchange section. Cold tank temperature and demethaniser operating pressure were
studied as optimisation variables. Energy balance was also performed over the
second section which provided guidelines for the process selection.
Chapter 2 Literature review
48
Diaz et al., (1996) integrated a process simulator and a MINLP algorithm to
optimise the revamp design of an ethane recovery process. A range of natural gas
mixtures with 6–25% of heavy components is studied in order to determine the
optimal plant topology and operating parameters under different process conditions
However, their work was limited to a few configurations and the use of MINLP
algorithm does not guarantee a global optimum.
Mehrpooya et al. (2006) simulated an existing NGL recovery unit using HYSYS.
Two modifications were considered suitable for optimisation: turbo-expander and
turbo-expander exchanger configurations to find the best revamping alternative. A
genetic algorithm was used for optimisation to calculate the maximum profit. This
study however, is not useful in the conceptual design for process synthesis.
Two turbo-expander ethane recovery processes were analysed by Chebbi et al.
(2008): the conventional turbo-expander process (without external reflux) and the
gas subcooled process (GSP). They considered four different gas feeds with
varying proportions of ethane and heavier components. They noted the effect of
demethaniser operating pressure on ethane recovery for the two processes. The
GSP was shown to yield higher ethane recovery for a lean feed and at lower
demethaniser operating pressure compared to the conventional turbo-expander
process. The work by Chebbi et al. (2008) does not account for the complex
interactions between other flowsheet units and is restricted to only one
optimisation variable (column operating pressure).
In a more recent study by Chebbi et al. (2010), simulation of ethane recovery
employing a conventional turboexpander process was performed using Aspen
HYSYS. The use of external refrigeration was also studied in addition to the
column operating pressure. Both the capital and operating cost were calculated in
detail to compare a range of feeds with varying ethane composition. The study,
however, is focused only on comparing the use of refrigeration against the heat
recovery from top product for different operating pressures.
Chapter 2 Literature review
49
To summarize, market competition requires a constant development and
improvement in processing technologies. This is the case for demethaniser
processes; the complex nature of these flowsheets makes their design and
optimisation challenging. No systematic procedure has been described in the
literature to identify the appropriate process technology and operating conditions to
achieve an optimal design for particular product specifications. Therefore, a
flowsheet synthesis and design methodology for demethaniser flowsheets is
required which can be employed as a tool for quantitative evaluation of
preliminary designs as well as to facilitate evaluation, selection and optimisation of
licensed demethaniser flowsheets.
2.6 Design and simulation methods for distillation columns
In order to develop a systematic method for the synthesis and optimisation of
demethaniser flowsheets, a simplified design model for the complex demethaniser
column design is required. As this design model is to be integrated in an
optimisation framework for flowsheet synthesis, it is essential that it allows rapid
execution while offering a sufficiently accurate representation of the process. The
column design model should be able to predict realistically the separation
performance and the column energy requirements.
Demethaniser columns have complex features; including multiple feeds to the
column, side reboilers for heat recovery and an external reflux stream. A typical
demethaniser column is represented in Figure 2.10.
Chapter 2 Literature review
50
External reflux
Multip le feeds
Side reboilers
Figure 2.10 A typical demethaniser column
This section provides a description of some of the existing models for the design
and simulation of distillation columns. These models can be classified into shortcut
and rigorous models.
2.6.1 Shortcut design methods
Shortcut methods for distillation design rely on simplifying assumptions to solve
the column design equations. Analysing a distillation problem on the basis of these
methods is useful for preliminary estimations and for determining the column
operating limits. Shortcut methods are usually capable of calculating the required
number of stages for a given separation problem, whereas rigorous methods
usually assume a fixed number of stages and are more appropriate for simulation
of a column rather than the column design (Khoury, 2005).
The most common shortcut method for the design of distillation columns is the
Fenske-Underwood-Gilliland (FUG) method, as given by Seader and Henley,
(1998). The FUG method has two basic assumptions: constant molar flow within
each section of the column, and constant relative volatility throughout the column.
For a simple distillation column with one feed, one top product and one bottom
Chapter 2 Literature review
51
product, the method requires the specification of the feed conditions and
composition and the recoveries of light and heavy key components. The FUG
method gives reliable results for separation of relatively ideal mixtures and simple
columns. The FUG method, however, cannot be applied for the design of a
demethaniser column, as both the assumptions of constant molar overflow and
constant relative volatility are not applicable in this case.
Suphanit (1999) improved the standard FUG method, taking into account its
limiting assumptions, i.e., constant molar overflow within each column section and
constant relative volatilities throughout the column. At minimum reflux, there are
usually two pinches in a multicomponent distillation column. Constant vapour
flow can only be assumed in the section between the two pinches. Suphanit (1999)
applied the Underwood equations only in the pinch zones, rather than assuming
constant molar flow in the whole column, and applied an enthalpy balance around
the top section of the column to estimate the condenser duty and vapour flow rate
at the top of the column. The reboiler duty was calculated through an overall
enthalpy balance.
Although the method by Suphanit (1999) gives better results for the minimum
reflux compared to those from Underwood equations, the complex features of the
demethaniser column, including multiple feeds, side reboilers and an external
reflux stream, cannot be addressed by using the FUG with enthalpy balance.
Therefore there is a need to develop a new shortcut design method for the
demethaniser column.
2.6.2 Rigorous simulation methods
Rigorous simulation methods for distillation column design involve the
formulation and solution of a large number of linear and nonlinear equations that
represent material and energy balances and phase equilibrium relations (Khoury,
2005). The main assumptions in the rigorous method are that phase equilibrium is
achieved on each stage and that the entrainment of liquid drops in the vapour phase
Chapter 2 Literature review
52
and vapour bubbles in the liquid phase is negligible. Although rigorous solution
methods require fewer assumptions than shortcut methods, they require numerical
solution algorithms (Seader and Henley, 1998). In comparison, the short cut
models can be solved by employing simple calculations without the need of
complex numerical iterative methods.
Rigorous methods have been developed for a fixed configuration column. Thus,
parameters such as the number of trays, feed tray location, and location of side
heaters and coolers are all fixed. Therefore, the column is completely specified by
defining a number of additional performance specifications equal to the number of
degrees of freedom of the column. The model is then solved to determine all the
other unknown variables.
Rigorous methods need good initialisation in order to converge. Moreover, more
computation time is required, compared with shortcut models.. For a sample
equilibrium stage, as shown in Figure 2.9 the mass balance equations, enthalpy
balance equations and equilibrium equations (known as MESH equations together
with summation equation) for the ith
component on stage j can be written as
(Seader and Henley, 1998):
Mass balance equation for each component i
( ) ( ) 0yVWxULzFxVxLM j,ijjj,ijjj,ij1j,i1j1j,i1jj,i =+−+−++= ++−− ( 2.1)
Energy balance equation for stage j
( ) ( ) 0QhVWhULhFhVhLH ivjjLjjFjV1jL1jjjjj1j1j
=−+−+−++=+− +− ( 2.2)
Phase equilibrium for each component i
0xKyE j,ij,ij,ij,i =−= ( 2.3)
Mole fraction summation for stage j
∑ =−= 01j,ij,y yS (Vapour mole fraction) ( 2.4)
∑ =−= 01j,ij,y xS (Liquid mole fraction) ( 2.5)
Chapter 2 Literature review
53
Figure 2.11 Schematic diagram of an equilibrium stage (Seader and Henley, 1998)
Equations 2.1 to 2.5 making up the generalized column model include nonlinear
equations. Their number increases with the number of components present in the
system. The analytical solution of these equations is not possible; numerical
iterative techniques are required. Many algorithms have been proposed for solving
the equations, a good description of which is presented by Seader and Henley
(1998). Due to the complexity of the equations, most solution algorithms are prone
to convergence difficulties in complex column situations. Contributing to these
difficulties is the large variation in the relative magnitudes of the variables round-
off errors. These equations also result in sparse matrices. Sparse matrices are
widely used in scientific computation, especially in large-scale optimization,
computational fluid dynamics and the numerical solution of partial differential
equations (Shah and Gilbert, 2004). The structure of sparse matrices can be
exploited in numerical techniques, however they require special algorithms for
solutions (Saad, 2003), which may not be necessarily available in commercial
simulation software packages.
1jV +
Vapour from
stage below
Liquid from
stage above
1jL −
Heat transfer
jQ Feed
jU
Vapour side
stream
jW
1
1
1
1
+
+
+
+
j
j
V
j,i
P
T
h
y
j
1j
1j
L
1j,i
P
T
h
x
1j
−
−
−
−
j
j
L
j,i
P
T
h
x
j
1j
1j
L
1j,i
P
T
h
x
1j
−
−
−
−
Stage j
Temperature Tj
Pressure Pj
j,F
j,F
F
j,i
P
T
h
z
F
j
j
jV
jL
Liquid side
stream
Chapter 2 Literature review
54
2.6.3 Minimum reflux calculation
One of the most decisive variables in the design of distillation column is the
minimum reflux ratio, which directly affects the reboiler and condenser duties, the
energy costs of which dominate the process economics in low-temperature
separation systems. For single columns, it is well known that minimum energy
requirements generally correspond to minimum reflux and/or boil-up ratios and an
infinite number of equilibrium stages, so that the column just performs the desired
separation and exhibits one or more pinch points. Most methods for determining
minimum energy requirements are based on either directly finding pinch points or
rigorous column simulations.
The best known method for the calculation of minimum reflux is the Underwood
method, as already explained in Section 2.6.1, which involves the calculation of
minimum vapour flow rate. The Underwood equation describes the minimum
reflux condition, i.e. the minimum allowable reflux for a specified separation
(King, 1980) and is used to find all the roots between the relative volatilities of
light and heavy key components:
qx
i
Fi i −=−
∑ 1θα
α
( 2.6)
Where: αi is the relative volatility of component i.
xF,i is the mole fraction of the component i in the feed stream.
q is the liquid fraction of feed stream.
θ is the root of the Underwood equation given by HKLK αθα <<
Chapter 2 Literature review
55
The minimum vapour flow in the top section and is determined by the following
equation:
min
i
DiV
xi =
−∑
θα
α
( 2.7)
Where xDi is the mole fraction of component i in the top product.
Vmin is the minimum vapour flow in the top section.
The minimum reflux ratio (Rmin) is calculated as:
1minmin −=
D
VR
( 2.8)
where D is the molar flow rate of the top product. The minimum vapour flow in
the bottom section ( '
minV ) is calculated using the following equation:
( )FqVV −−= 1min
'
min ( 2.9)
where F is the molar flow rate of the feed,
q is the quality of feed
However, as discussed in Section 2.6.1, the Underwood method fails to provide
accurate results when applied for the calculation of minimum reflux in the case of
demethaniser column.
For the calculation of the minimum reflux, Levy et al. (1985) presented the
boundary value method (BVM), based on finite difference approximations of
column composition profiles in the form of ordinary difference equations under the
assumption of constant molar overflow. In this method, the liquid composition
profiles of a ternary mixture can be plotted on a triangular diagram. Composition
profiles are calculated starting from the fully specified product compositions. The
specified product compositions are identified as feasible if the two composition
Chapter 2 Literature review
56
profiles intersect each other. For higher reflux ratios, the number of theoretical
stages can be counted from the composition profiles and the feed location is
indicated from the intersection between the two composition profiles (Figure 2.12).
A set of the product specifications is infeasible if the two compositions profiles do
not intersect for any reflux ratio.
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
Feed
Bottom
Distillate
Nonane Pentane
Hexane
Strippingprofile
Rectifyingprofile
product
Figure 2.12 Composition profiles in a ternary diagram (Doherty and Malone,
2001)
A similar method derived from the boundary value method called the ‘zero
volume’ method is presented by Julka and Doherty (1990). This method involves
the determination of the minimum reflux ratio by finding the pinch points without
calculating the liquid composition profiles. At minimum reflux, for direct splits,
the stripping node, the rectifying node, and the feed composition are aligned (Julka
and Doherty, 1990). Hence, the minimum reflux ratio can be determined by
varying the reflux ratio iteratively until any three of these points, i.e. the feed
composition, the saddle pinch point and stable node pinch are collinear.
Chapter 2 Literature review
57
Koehler et al. (1995) developed a method for the calculation of minimum reflux
ratio based on a reversible distillation model. This reversible distillation model
assumes that heat can be transferred to and from a column at zero temperature
difference and that no contact of non-equilibrium liquid and vapour streams is
allowed. The column material and equilibrium relations are used to derive the path
equations for reversible distillation. The solution of this reduced set of equations
requires the flow rates of the most and least volatile components to be specified at
the feed plate. According to Koehler et al. (1995), the concentration reached in a
reversible distillation column section for any given amount of energy is exactly the
same as the stationary concentration that is obtained in an adiabatic constant molar
overflow section, provided the same amount of energy is introduced only at the
ends of the column – this is the minimum energy requirement for the section.
Bausa et al. (1998) developed the rectification body method (RBM) for the
determination of minimum energy demands for multicomponent distillation. The
approach is based on geometrical analysis of plate-to-plate composition profiles.
After fixing all product compositions, the amount of the trace components is set to
a non-zero value, since all feed components have to appear in both products in a
finite column. The BVM requires checking all profiles for intersection. Rather than
calculating the manifold of plate-to-plate profiles, RBM approximates the manifold
using all available information. In this method, the accuracy of the minimum reflux
calculations is limited to the case where the composition profiles are not highly
curved, as the method is based on the linear approximation of the curved
concentration profiles.
In summary, most of the methods for calculating minimum reflux ratio have been
used for both ideal and non-ideal mixtures for simple distillation columns. At
present, there is no method for determining the minimum ratio for a complex
column such as a demethaniser. Rigorous simulation methods can be applied to
simulate the column at the expense of computational time. Furthermore, these
methods are mainly used for the simulation of the column of a fixed column
Chapter 2 Literature review
58
design. However, in this work, the distillation column model is to be used for
conceptual design and synthesis of demethaniser flowsheets.
The boundary value method proposed by Levy et al. (1985) is chosen for the
design of a demethaniser column because of its well established theoretical
background and its ability to generate the column design, given the feed and the
product recovery specifications, as do other shortcut distillation design methods.
However, the method needs to be modified and developed further to include the
various modelling and design issues associated with a demethaniser. A detailed
introduction to the original boundary value method for distillation column design
is provided in the next section.
2.6.4 Distillation column design by boundary value approach
The number of theoretical stages in the boundary value method can be counted
from the composition profiles and the feed location is indicated from the
intersection between the two composition profiles (Figure 2.12). A proposed
separation (i.e. a set of the product specifications) is infeasible if the two
composition profiles do not intersect for any reflux ratio.
The original boundary value method is based on the following key assumptions:
� Vapour-liquid equilibrium is achieved on each plate
� The molar flow rates are constant in each section of the column
� The feed enters the column as a saturated liquid
These assumptions simplify the model. The constant molar overflow assumption
allows the material and energy balances to be decoupled, thereby permitting the
composition profiles for the distillation column to be calculated using the material
balance and equilibrium equations (Levy et al., 1985). The assumption of a
saturated liquid feed calculates the reboil ratio from the given reflux ratio.
However, this assumption also limits the applicability of the method, as the method
cannot take into account two-phase or vapour feed conditions.
Chapter 2 Literature review
59
The boundary value method decomposes a single feed column into two sections,
i.e., rectifying section and stripping section. The composition profiles, which
represent the liquid mole fraction on each stage ( i,nx ) can be generated from both
the top and bottom product compositions. The composition profile for the
rectifying section is calculated by performing a mass balance around the rectifying
section. The calculation for the number of stages is started from the top of the
column. If a total condenser is used, the condenser is not counted as an equilibrium
stage, while in the case of a partial condenser, the vapour and liquid leaving the
condenser are in equilibrium, so it is counted as a stage.
Figure 2.13 Schematic of the rectifying section of a distillation column
Stage 1
yn+1,i
Vn+1
xn-1,i
Ln-1
xn,i
Ln
11 V,y i,
Stage n
D,x i,D ,
1V
y i,n
Condenser
Lo
Chapter 2 Literature review
60
Levy and Doherty (1986) calculated the overall and component mass balances
around the rectifying section (see Fig 2.13)
DLV n1n +=+ ( 2.10)
Dx Lx Vy iD,ni,ni1,ni,1n +=++ 11 −=∀ c,.....i ( 2.11)
The constant molar overflow assumption gives:
0-1nn L L L == ( 2.12)
Rearranging equations 2.10 to 2.12 we get:
i,Di,ni,n xR
xR
Ry
1
1
11
++
+=+ 11 −=∀ c,.....i
( 2.13)
where: xn,i is the mole fraction of component i in liquid phase leaving stage n.
yn+1,i is the mole fraction of component i in vapour phase entering stage n.
D
LR o= is the reflux ratio
The calculation of the rectifying composition profile starts from the given top
product specification. The reflux entering the top stage of column has the same
composition as the distillate in the case of a total condenser. In the case of a partial
condenser it can be calculated from the equilibrium calculations of the vapour
product leaving the partial condenser. The composition of the vapour (y1,i) leaving
the top stage is calculated from the mass balance (Eq. 2.13). The composition of
the liquid (x1,i) leaving that stage is calculated using the vapour-liquid equilibrium
calculation. This procedure of calculating (yn+1,i) from the mass balance and (xn,i)
from equilibrium relations continues and the liquid composition data points form
the rectifying composition profile.
Chapter 2 Literature review
61
.
The mass balance around the stripping section (Fig 2.14) gives
BVL m1m +=+ ( 2.14)
The component balance gives
iB,im,mi1,m1m BxyVxL +=++ 11 −=∀ c,.....i ( 2.15)
The constant molar overflow assumption gives:
11-mm VV V ==
( 2.16)
and m1m L L =+ ( 2.17)
B
Vs =
xm+1,i
Lm+1
ym-1,i
Vm-1
ym,i
Vm
xm+1,i
Lm+1
Reboiler B, xB,i
Stage m
x2,i, L2
Figure 2.14 Schematic of stripping section of a distillation column
Chapter 2 Literature review
62
Rearranging equations (2.14) to (2.16), we get,
i,Bi,mi,m xs
ys
sx
1
1
11
++
+=+ 11 −=∀ c,.....i
( 2.18)
where: x i1,m+ is the mole fraction of component i in liquid phase leaving stage m.
y im, is the mole fraction of component i in vapour phase leaving stage m.
B
Vs 1= is the boil-up ratio
In the column, the boil-up ratio is not an independent variable. The boil-up ratio
and reflux ratio are connected via the overall mass and energy balance equations
(Julka and Doherty, 1990).
( ) 1qxx
xxqRs
iD,iF,
iF,iB, −+
−
−+=
( 2.19)
where q is the feed condition and is defined by Eq. 2.20 (Doherty and Malone,
2001):
−
−=
sat,lF
sat,vF
Fsat,v
F
hh
hhq
( 2.20)
where: Fh is molar enthalpy of the feed calculated from the specified feed
composition and condition.
sat,v
Fh is the saturated vapour molar enthalpy of the feed
sat,l
Fh is the saturated liquid molar enthalpy of the feed
Chapter 2 Literature review
63
The feed quality thus indicates the liquid fraction of the feed: negative values of q
indicate a superheated vapour feed, a value of q = 0 indicates a saturated vapour
feed, a value of q = 1 a saturated liquid feed and values of q greater than unity
relates to a subcooled liquid feed.
The calculation of the stripping composition profile starts from the bottom product
specification. The vapour phase leaving the reboiler is assumed to be in
equilibrium with the liquid phase, therefore, the reboiler is counted to be an
equilibrium stage. Composition of the vapour leaving the reboiler is calculated
from the vapour liquid equilibrium calculation. Next, the liquid composition on the
bottom stage can be calculated through Eq. 2.18 while the vapour phase
composition (ym,i) is again calculated using bubble point calculation for given
liquid phase composition (xm,i.). This calculation yields the liquid composition data
points which then form the stripping composition profile.
The boundary value method requires the two composition profiles to intersect each
other to provide the column design details. The number of theoretical stages can be
counted from the composition profiles; the feed location is indicated from the
intersection point between the two composition profiles. This method has been
modified and extended in Ch. 3 to accommodate different design and modelling
issues associated with the demethaniser column.
2.7 Conclusions
This chapter introduces some challenges for separation process synthesis that have
been addressed in the literature. Generally, complete separation synthesis strategies
either do not exist; or the available quantitative approaches are restricted to one or
two separation technologies with connectivity constraints imposed between
different separations (Biegler et al., 1997).
Chapter 2 Literature review
64
Low-temperature separation processes are characterized by complex interactions
between the separation, heat recovery and refrigeration sections. These interactions
are prominent in the demethaniser flowsheets, where any change in one of the sub-
processes affects the others. For the synthesis of a demethaniser flowsheet,
flowsheet configurations and the associated operating conditions need to be
selected to achieve a good performance especially with respect to operating cost
and product value. There is a need for a systematic way to find the appropriate
separation technique and operating conditions for such processes to achieve an
optimal design for a particular feed and product specifications. This work presents
an approach to optimise and screen the various design options for their viability for
the process synthesis of demethaniser flowsheets.
Chapter 3 Demethaniser column design method
65
CHAPTER 3 DEMETHANISER COLUMN DESIGN
METHOD
3.1 Introduction
There is a need to develop a column design procedure that not only provides
reliable process screening, but also simultaneously generates good initialization for
simulation purposes. Given a separation task, before detailed sizing and device
selection, applying a shortcut model can help to make quick decisions about
equipment feasibility, approximate size and cost estimates (Barnicki and Siirola,
2004).
It was discussed in Chapter 2 that none of the existing short-cut design methods
could be applied for the design of a demethaniser column. This chapter presents a
new simplified design method for complex demethaniser columns. The new
method is an extension of the boundary value method which has been applied
previously to asses the feasibility of and to design azeotropic distillation columns
(Levy et al., 1985). As already explained in Section 2.6.4, the boundary value
method (BVM) utilizes composition profiles to design a column and calculate its
energy requirements.
The BVM method is extended to be applied to a multicomponent mixture. Energy
balance is included in the composition profiles calculation. The method is also
modified to include the other important characteristics of the demethaniser column
such as two feed streams, the side reboilers and an external reflux stream. Finally a
new model is developed where the demethaniser is modelled as a reboiled absorber
column. Case studies are presented to show the application of the new design
Chapter 3 Demethaniser column design method
66
method; developed model results are validated by comparing against rigorous
simulation results in a commercial simulation package.
3.2 Model implementation
The links between various process simulation and physical property estimation
softwares in the wide area of computer aided process engineering led to the
development of CAPE-OPEN (Barrett & Yang, 2005). It is a standard developed
by the CAPE-OPEN Laboratories Network (CO-Lan) consortium (CAPE-OPEN,
2011) to create an effective integration of different modelling approaches. The
CAPE-OPEN standard divides the interchanging programmes into two software
components. The first is a process modelling environment (PME) represented by a
simulation engine, external software and external simulator (Jaworski and
Zakrzewska, 2011). The second group is called process modelling components
(PMC), which are normally databases for use within a PME. The PMC packages
can be used for computing thermo-physical properties and simulation of a
particular unit operation (Fermeglia and Pricl, 2009).
The boundary value method calculation procedure involving the mass and energy
balance equations has been written in MATLAB (version 7.5) which is a numerical
computing environment and programming language. In this work, MATLAB is
selected as the programming language as it provides a complete environment for
programming and interactive data analysis (The Mathworks, 2010).
Figure 3.1 Interlinking MATLAB with HYSYS
M A T L AB H Y S Y S
V L E an d E n th a lp y
M a ss a nd E n erg y
B a la n c e
Chapter 3 Demethaniser column design method
67
This has been interfaced with AspenTech HYSYS 2006.5® for vapour-liquid
equilibrium and enthalpy calculations. HYSYS can be accessed from external
software, using a method called automation. By writing a code in the external
software, information of a stream or unit operation can be sent to and received
from HYSYS. This methodology is employed in this work for the calculation of
the physical properties, thus avoiding the complexity associated with the coding of
equations of state in MATLAB. This interface also exploits the robustness of
HYSYS physical properties databases and algorithms. The details of the interface
are provided in Appendix A.
3.3 Product Composition Specification
Usually, a separation problem involving a new design requires some design
specifications. These include the feed composition and condition, and the
separation objective in terms of the product recovery and/or purity. In the case of a
demethaniser, normally the product specifications are given in terms of methane
recovery in the top product and ethane in the bottom product. The feed mixture to
be separated the light key (LK) and heavy key (HK) components, and the non-key
components.
There is rarely any information on the product distributions in the first place
because at the conceptual design stage, the product distribution is typically not
available until a rigorous simulation is carried out. It is difficult to arbitrarily
specify the product distribution because it cannot be guaranteed that such product
compositions will be feasible. This is particularly true in multi-component
separations involving more than three components, as there is a considerable
uncertainty in product distribution. The estimation of non-key components in the
products is important as the product specification acts as the initial point for the
composition profiles to be generated (Castillo et al., 1998).
In this work the Hensgtebeck-Geddes correlation (See (King, 1980) references
within) is used to calculate the distribution of the non-key components in the
distillate and bottom product, given the relative volatility of the components and
Chapter 3 Demethaniser column design method
68
the product specifications in terms of key components. Once the distribution of the
two products is specified, the composition of the overhead and bottom products
can be calculated. This satisfies one of the basic requirements of the boundary
value method which is to know the composition of all the components in the
products.
The Hensgtebeck-Geddes correlation assumes that there is an orderly pattern for
the distribution of the components into the overhead and bottom product with
respect to the relative volatility. In order to account for product distribution of the
non-key components at a finite reflux ratio, the product distribution is first
estimated at total reflux ratio (King, 1980). This is based on the assumption that
the non key components distribute according to following equation (Sinnott,
2003):
nln α mb
dln i
i
i +=
( 3.1)
where
id – distillate flowrate for component i
ib – bottom flowrate for component i
iα – relative volatility of component i relative to the heavy component
m and n - coefficients fitted to the light and heavy key component recoveries
Equation ( 3.1) reveals that a plot of
i
i
b
dln vs. ilnα yields a straight line.
According to Yaws et al. (1981), the Hensgtebeck-Geddes equation for the light
and heavy key component can be can be formulated in terms of fractional recovery
as following:
nlnα mr1
rln LK
LK
LK +=
−
( 3.2)
nlnα mr1
rln HK
HK
HK +=
−
(3.3)
Chapter 3 Demethaniser column design method
69
where
LKr – Fractional recovery of light key component in top product
LKα – Relative volatility for light key component relative to heavy key component
The two unknown variables, (m and n), will be determined by solving two linear
Eq. 3.2 and 3.3. The two equations correspond to the recoveries and the relative
volatilities of the LK and the HK components in the column respectively. Once m
and n values are established, then the above equations can be applied to estimate
the non-key recovery at a given relative volatility for each of the non-key
components.
3.4 Boundary value method for multicomponent feed mixtures
The boundary value design method was originally developed for ternary mixtures.
For ternary mixtures, intersection of the composition profiles can be visualised
easily on the two-dimensional triangular diagrams. In the case of demethaniser
flowsheets, the feed is seldom a ternary mixture, typically containing more than
five components. Therefore the boundary value method needs to be modified to be
applicable for multicomponent feed mixtures.
Previous work on multicomponent mixtures has addressed issues such as graphical
representation and profile intersection. Thong and Jobson (2001) used manifolds
(the sets of all possible composition profiles) to establish the intersection of
composition profiles in the case of multicomponent systems. This method requires
the specification of the mole fraction of key components, rather than full
specification of product compositions. The distribution of trace components is
allowed to vary. The set of all compositions satisfying this partially specified
product with a specific purity is called the product region. For a given product
region, composition manifolds can be generated for given values of the reflux ratio
and stage number.
The composition manifold is similar to a point on a composition profile.
Composition profiles are, however, calculated for a fully specified product
composition, whereas the composition manifolds are generated for a product
Chapter 3 Demethaniser column design method
70
region. Composition manifolds have the advantage that they can be used in
multicomponent mixtures. Intersection is achieved when either the rectifying
composition manifold and the stripping stage composition line intersect, or the end
point of the stripping stage composition line lies inside the volume formed by the
rectifying composition manifold and the top product mole fraction (Thong and
Jobson, 2001). Every intersection of a rectifying composition manifold and a
stripping stage composition line will indicate potentially feasible operating
parameters.
In another method to approximate the intersection between the stripping and
rectifying profiles, Amminudin et al. (2001) used a ‘minimum distance’ criterion.
In this method, the rectifying and striping profiles are constructed in the usual way,
starting from the product compositions for the given reflux and reboil ratios. The
intersection of profiles is assessed by calculating the shortest distance in mole
fraction space between the two profiles. If any two points on a pair of profiles are
within this specified minimum distance, the lines are considered to ‘intersect’.
The composition manifold and minimum distance techniques are used to identify
the intersection numerically, rather than graphically. The ‘composition manifold’
method results in multiple solutions for a range of different product compositions
and reflux and boil up ratios. Thus the method can lead to different column
designs. The column design is optimised in the overall flowsheet optimisation. So
at this stage in the development of a design model the minimum distance method
(Amminudin et al., 2001) is used to approximate the profile intersection. This
method is also easier to formulate within the overall synthesis framework.
The intersection between the rectifying and the stripping section according to the
‘minimum distance’ criterion is calculated by the following equation.
Distance = ( )2
∑ −stripn,irecn,i xx
c,...,i 1=∀
( 3.3)
where:
=recn,ix Mole fraction of component i in the rectifying composition profile
stripn,ix = Mole fraction of component i in the stripping composition profile
Chapter 3 Demethaniser column design method
71
The distance between the liquid composition profiles is calculated for every pair
of stages, one from the rectifying and other from the stripping section. The
difference can be interpreted as the geometrical distance in mole fraction space
between one point on the rectifying profile and another point on the stripping
profile in the composition space. Therefore, the pair of stages that gives the
smallest value of the sum of difference is selected as the candidate for the profile
intersection. If the least sum of difference is the same or smaller than some
'minimum distance', it is approximated that the profiles intersect. In practice, a
value of 0.1 for the 'minimum distance' is found suitable for mixtures containing 6
to 10 components (Amminudin et al., 2001). The feed stage location will be the
stage on the stripping section that corresponds to this minimum difference. At this
minimum difference, the non-integer number of stages is rounded up to obtain an
integer number of stages.
3.5 Boundary value method with energy balance
The original boundary value method introduced by Levy et al. (1985) is limited by
the assumption of constant molar overflow which means that the vapour and liquid
flows are constant from plate to plate in each section of the column. The key
underlying assumption for this condition is that the molar heats of vaporisation of
all components are equal and do not depend on temperature (Doherty and Malone,
2001). In the case of a demethaniser these assumptions are not applicable: due to
the large difference in the size of the methane and ethane molecules, there is a
significant difference between their latent heats of vaporisation.
Knight and Doherty (1986) incorporated the heat effects in the calculation of the
composition profiles, avoiding the constant molar overflow assumption. In this
work, their approach is further explored to include the heat balance in the boundary
value method. The heat balance equations are integrated with the original set of
mass balance Equations (2.11 and 2.15) and then solved simultaneously.
Chapter 3 Demethaniser column design method
72
Equation ( 3.4) gives the overall energy balance for an adiabatic simple column
condBDrebF QBhDhQFh ++=+ ( 3.4)
where: F is the feed flowrate
rebQ is the duty of reboiler
D is the distillate flowrate
fh is the specific molar enthalpy of the feed
Dh is the molar enthalpy of top product
Bh is the molar enthalpy of reflux stream
condQ is the duty of condenser
Throughout this work, the pressure is assumed to be constant along the column as
well as other unit operations in the overall flowsheet. Although, in reality, a
pressure profile is developed along the column as a result of liquid loading in the
stages and the pressure drop due to friction. The pressure profile in a column may
affect the separation efficiency and the reboiler and condenser duties due to the
dependence of the relative volatilities and the enthalpy of vaporisation on the
pressure.
However, as the design methodology proposed in this work is aimed at conceptual
design and process synthesis, pressure drop in the column can be neglected. This
argument is also supported by the uniformity of column pressure profiles across
the different flowsheets, which is linked to a minimal propagation of the pressure
factor to the comparison of alternative demethaniser flowsheets. The effect of
pressure drop in the demethaniser column design calculations is also shown to be
negligible as illustrated by an example in Section 3.8.2.
Chapter 3 Demethaniser column design method
73
Figure 3.2 Schematic of the rectifying section
The individual heat loads can be evaluated by performing energy balances across
the appropriate units. The energy across the condenser (Fig 3.2) is given by
( )( )DhRhhRQ DL,rV,r
cond −−+= 121 ( 3.5)
where: R is the reflux ratio
V,rh2 is the molar enthalpy of vapour stream entering the condenser
Dh is the molar enthalpy of top product
L,rh1 is the molar enthalpy of reflux stream
Similarly, the reboiler duty ( rebQ ) is determined from the energy balance over the
column:
condFBDreb QFhBhDhQ +−+= ( 3.6)
DD h,x,D
Qcond
rV,rr y,h,V 222
r1
Lr,1
r1 x,h,L
r
nV 1+
V,rnh 1+ r
ny 1+
rnL
L,r
nh r
nx
Stage n
Stage 1
Chapter 3 Demethaniser column design method
74
3.5.1 Calculation of rectifying section composition profile
The rectifying section composition profile is calculated by solving material and
energy balances simultaneously along with vapour-liquid equilibrium. Equations
( 3.7) and ( 3.8) are the material and energy balances for the rectifying section
respectively (Figure 3.2).
( ) 01 =−−+ + i,Dr
i,nrn
ri,n
rn DxxLyDL c,.....i 1=∀ ( 3.7)
( ) 01 =+−−+ + condD
L,r
n
r
n
V,r
n
r
n QDhhLhDL ( 3.8)
where condQ is determined from Eq. 3.5.
The calculation starts with the given top product specification (xD,i). The vapour-
liquid equilibrium and the enthalpy data for different streams are calculated using
HYSYS as explained in Section 3.2. For a given reflux ratio, the rectifying liquid
composition profile is calculated starting from the reflux composition ( r
i,nx ) using
the set of Equations ( 3.7) and ( 3.8) and vapour-liquid equilibrium. For the
calculation of liquid flow in the rectifying section Ln, the error in the energy
balance (E) is calculated, starting from the top of the column and proceeding down
stage by stage.
( ) condD
r
n
r
n
V,r
nn QDhhLhDLE +−−+= +1 ( 3.9)
This error is minimized by using Broyden's method with the value of nL being
updated every iteration. Broyden's method is a Quasi-Newton method for the
numerical solution of nonlinear equations in more than one variable (Eyert, 1996).
For solving an equation, Newton's method uses the Jacobian matrix and its
determinant, at every iteration. However, this computation is a difficult and
expensive operation. The Broyden's method computes the Jacobian only at the first
iteration, and to do a rank-one update at the other iterations (Sorensen and Asterby,
2009).
Chapter 3 Demethaniser column design method
75
The final value of rnL is computed and the energy balance is then applied over the
whole rectifying section in the same manner. The calculation is continued to the
next stage down the column by solving material and energy balances (Equations
( 3.7) and ( 3.8)), for r
i,ny 1+ and r
nL , simultaneously with vapour-liquid equilibrium
for r
inx , . The calculation is stopped when the composition profile reaches its pinch
point where there is no change in composition from one stage to the next. These
data points, calculated from the above calculation are then connected to plot the
rectifying section composition profile.
3.5.2 Calculation of stripping section composition profile
The stripping section composition profile is calculated by performing material,
energy and equilibrium calculations across the stripping section (Figure 3.3) in a
similar manner to the rectifying section.
Stage 2
Stage m
Bi,B h,x,B
V,ssi,
sh,y,V 111
Stage 1
s
mL 1+
si,mx 1+
V,smh 1+
s
mV
si,my
V,smh
L,ssi,
sh,x,L 222
Figure 3.3 Schematic of the stripping section
Chapter 3 Demethaniser column design method
76
The material and energy balances are:
( ) 01 =−−+ + i,Bi,m
s
m
s
i,m
s
m BxyVxBV c,.....i 1=∀ ( 3.10)
( ) 01 =+−−+ + rebBV,s
ms
mL,s
ms
m QBhhVhBV ( 3.11)
where rebQ is calculated from rearranging Equation ( 3.11).
( )( )BhhsshQ BL,sV,s
reb ++−= 21 1 ( 3.12)
when BVs s
1= , is specified; otherwise, if the feed condition is specified, rebQ is
calculated from Eq. ( 3.6).
For a given bottom product composition ( i,Bx ) and reboil ratio (s), the liquid
composition profile of the stripping section is calculated starting from the bottom
product composition. The vapour composition from the reboiler ( sy1 ) in
equilibrium with the bottom product is determined from the bubble point
calculation. The liquid composition entering the reboiler ( si,x2 ) is then calculated
from the set of equations ( 3.10) and ( 3.11).
The calculation is continued to the next stage up the column by solving the
material and energy balances (equations ( 3.10) and ( 3.11)), for si,mx 1+ and s
mV ,
together with vapour-liquid equilibrium for si,my . For the calculation of vapour flow
in the stripping section s
mV , the error in the energy balance between the two stages
in the stripping section ( Z ) is calculated and minimized by applying the Broyden’s
method as before.
( ) rebBV,s
ms
mV,s
ms
m QBhhVhBVZ +−−+= ( 3.13)
The stripping section composition profile is plotted by calculating the liquid
composition ( mi,sx ) at each of the stripping stage. The calculation is continued until
the composition profile either reaches its pinch point or intersects the rectifying
profile.
Chapter 3 Demethaniser column design method
77
3.6 Extended boundary value method for two phase feed
The original boundary value model (Levy et al., 1985) makes two assumptions
regarding the feed; firstly, the feed is fed onto one stage, i.e. both liquid and vapour
fraction are fed to the same stage, and, secondly, the feed tray behaves as an
equilibrium stage, i.e. both mixing and equilibrium mass transfer occur on the
same tray. Under these assumptions the liquid composition of the last stage of the
stripping section profile has to be exactly the same as the liquid composition
calculated from the last stage of the rectifying section. For a feasible column
design, not only do the overall balances have to be satisfied, but also the section
profiles have to form a continuous profile between the bottom and the top product
(Julka and Doherty, 1990). The intersection of either the liquid or the vapour
composition profiles indicates a feasible design, irrespective of the feed quality and
the number of components.
The assumption that the feed is introduced to only one equilibrium tray can
practically be achieved if the feed is not in the two-phase region, i.e. if it is either a
saturated or subcooled liquid, a saturated or superheated vapour. In the case of a
demethaniser column, the feeds to the column are usually two-phase feeds. For the
case of two-phase feeds, the most practical solution is to inject the feed between
two stages (Kister, 1992), i.e. the liquid fraction of the feed is added to the stage
below and the vapour fraction to the stage above the injection point. Groemping et
al. (2004) developed a feasibility criterion for two-phase feeds, based on the
assumption that the feed stream mixes with the streams passing between the two
column sections. This approach is employed in this work for the design of columns
with two-phase feeds.
According to Julka and Doherty (1990), as described before, the profile is
continuous if the feed is introduced to one plate (Figure 3.4 ) and if the profiles of
stripping and rectifying section intersect. This reasoning is based on the equality of
the vapour stream leaving the feed stage, ( smV ) and the vapour entering the stage
above the feed, ( rnV 1+ ).
Chapter 3 Demethaniser column design method
78
However, if a two-phase feed is introduced between the last stripping stage, and
the last rectifying stage, we have to take into account the mixing of the vapour
phase of the feed, vF with the vapour flow leaving the feed stage, smV and that of
the liquid phase of the feed, LF with the liquid entering from the feed stage r
nL as
shown in Figure 3.5. The material balance on the feed stage is performed by
assuming that the feed is entered above stage m , i.e. the liquid fraction of the feed
is introduced to the last stripping stage m and the vapour fraction to the last
rectifying stage n. Because the liquid and vapour streams do not exchange mass
between the stages (liquid is flowing through the down comer and the vapour
through the active column diameter), the balances over the two phases are
independent of each other (Groemping et al., 2004).
Fx,q,F
1-n stage
Rectifying
n stage
Rectifying
1-m stage
Stripping
m stage
Stripping
si,m
sm y,V 11 −−
ri,n
rn y,V 11 ++ r
i,nrn x,L
si,m
sm x,L
Figure 3.4 Feed mixing for feed injection completely onto feed stage (as in
(Julka and Doherty (1990))
Chapter 3 Demethaniser column design method
79
Figure 3.5 Feed mixing for feed injection between two stages
The overall and component balances for the vapour phase are:
V
m
s
r
n FVV +=+1 ( 3.14)
i,FV
r
i,n
m
s
r
i,n
r
n vyFyVyV += +++ 111 11 −=∀ c,...,i ( 3.15)
The overall and component balances for the liquid phase balance are:
( 3.16)
i,FL
r
i,n
r
n
s
i,m
s
m LxFxLyL +=++ 11 11 −=∀ c,...,i ( 3.17)
It should be stressed that the feed stream mixing method employed in this work is
based on the assumption that the feed stream mixes with the streams passing
between the two column sections. If there is no mixing point, then the feasibility
test does not apply and the feasibility criterion by Julka and Doherty (1990) has to
i,Fx,q,F
ri,n
rn x,L
ri,n
rn x,L 11 −−
ri,n
rn y,V
si,m
sm x,L
1-n Stage
n Stage
1-m Stage
m Stage
s
i,m
s
m x,L 11 ++
vF
ri,n
rn y,V 11 ++
LF si,m
sm y,V
si,m
sm y,V 11 −−
L
r
n
s
m FLL +=+1
Chapter 3 Demethaniser column design method
80
be used instead, which uses the assumption that the complete feed stream is fed to
a single stage. For a liquid feed added between two stages, the equations derived
by Julka and Doherty (1990) apply, i.e. the liquid and vapour composition profiles
intersect:
r
i,n
s
i,m xx 1+= ( 3.18)
and r
i,n
s
i,m yy 1+= ( 3.19)
Where a vapour feed is introduced between two stages, the stage index where the
liquid profiles intersect is one stage further up the column.
ri,n
si,m xx 11 ++ = ( 3.20)
ri,n
si,m yy 1+= ( 3.21)
For example, if for a saturated liquid feed, the liquid composition lines for n = 15
rectifying stages and 20=m stripping stages intersect, then there will be a feasible
design featuring 14115 =−=n rectifying stages and 20=m stripping stages.
Whereas, if the feed is a saturated vapour and the same stage composition lines
intersect, the feasible design will feature 15=n rectifying stages and
19120 =−=m stripping stages.
3.7 Double feed Column Design by Boundary Value Method
This section provides a detailed discussion of the boundary value method for
double-feed columns for multicomponent mixtures. Normally, in the case of
demethaniser columns, the upper feed is the turboexpander outlet while the lower
feed is the liquid product from a separator (flash unit) after being expanded in a
Joule- Thomson valve (Fig. 3.6). The boundary value method needs to be modified
for a double feed column design.
Chapter 3 Demethaniser column design method
81
Levy and Doherty (1986) extended the boundary value design method to double-
feed columns. The divided the column into three sections, namely the rectifying
section, middle section, and stripping section (Figure 3.7). The specifications for
the double-feed column design by the boundary value method are: column
pressure, which is assumed constant throughout the column; upper and lower feed
compositions and flowrates; top and bottom product compositions and flowrates;
lower feed condition; reflux ratio; either reboil ratio or upper feed condition. The
product specifications are chosen to satisfy the product purity requirements and
material balance over the column.
In this work the method by Levy and Doherty (1986) is applied to introduce a
second feed in the column. The method starts with the column specifications. The
composition profiles of all column sections are then generated according to the
column specifications using material and energy balances along with phase
equilibrium calculations. The intersection of composition profiles identifies the
separation feasibility and is used to obtain the column design parameters, such as
the number of theoretical stages, feed stages, and feed condition.
Figure 3.6 A basic demethaniser flowsheet with external reflux
External reflux
stream Reflux heat exchanger
Chapter 3 Demethaniser column design method
82
The overall mass balance gives:
BDFF LU +=+ ( 3.22)
and from the component balance
( )
i,Bi,D
i,BLUFLFU
xx
xFFxFxFD
i,Li,U
−
+−+=
( 3.23)
3.7.1 Composition profiles
Once all specifications of the double-feed column are given, the rectifying,
stripping and middle section profiles of the column are calculated using material
and energy balances and phase equilibrium of the mixture. The rectifying and
stripping composition profiles for a double-feed column are generated in the same
way as for a single-feed column as explained in Section 3.5. However, the
rebQ
LL F,F,L hxF
UU F,F,U hxF
i,Dx,D
Rectifying section
BB h,x,B
Middle section
Stripping section
Figure 3.7 Schematic of the two-feed section
condQ
Chapter 3 Demethaniser column design method
83
composition profile of the middle section can be calculated by performing a mass
balance around the middle section. Prayoonyong (2009) showed that the
calculation of the middle section profile can be done in two ways. In the first
method, which is the top-down approach the number of stages in the middle
section is calculated in the downward direction. The composition profile is
calculated starting from the upper feed stage specification and terminates where the
profile intersects the stripping section composition profile, which indicates the
lower feed stage. The second method, the bottom-up approach, calculates the
number of stages starting from the specified lower feed stage and terminates at the
upper feed stage where the middle section composition profile intersects the
rectifying section composition profile (Prayoonyong, 2009)
In this work, the bottom-up approach is applied. The procedure for the middle
profile calculation according to the bottom-up approach can be summarized as:
� A stage in the stripping profile is arbitrarily chosen as the lower feed
location e.g. stage m in Fig 3.8. The location of the stage is an additional
degree of freedom.
� The vapour composition of stage m is determined by a bubble point
calculation for the liquid composition of stage m (xm,i). The value of xm,i is
already known from the stripping composition profile.
� The liquid composition of the next stage m+1 is calculated from the
material and energy balances (the set of Eq. ( 3.24) and ( 3.25)).
The calculation is continued by solving the material, energy and vapour-liquid
equilibrium calculations until the intersection between the middle and rectifying
section composition profiles occurs at the upper feed point.
( ) 01 =−−−−+ + i,FLi,BM
i,mM
mM
i,mLM
m LxFBxyVxFBV ( 3.24)
( ) 01 =++−−−+ + rebFLBV,M
mM
mL,M
mLM
m QhFBhhVhFBVL
( 3.25)
where ( )( )BhhsshQ BL,sV,S
reb ++−= 21 1 ( 3.26)
when B
Vs 1= is specified, otherwise, when the upper feed condition is specified:
condFLFUBDreb QhFhFBhDhQLU
+−−+= ( 3.27)
Chapter 3 Demethaniser column design method
84
Figure 3.8 Schematic of the stripping section with lower feed
For given feed qualities and the reflux ratio, all stripping stages can be selected as
potential lower feed stages. The number of stages for the middle section is counted
as the number of stages from one stage above the lower feed stage to the stage
where the middle section composition profile intersects the rectifying section
composition profile. The number of stages for the rectifying section is counted
from the top of the column to the stage at the intersection between the middle and
the rectifying section composition profiles. At the intersection, the fractional
number of stages is calculated and rounded up to obtain an integer number of
stages.
The design variables of a double-feed column include the thermal conditions of
upper and lower feeds, reflux ratio, reboil ratio, and the ratio of upper-to-lower
feed rate. To apply the column design procedure, the lower feed condition must be
specified; otherwise, the middle section profile cannot be calculated continuing
Stage 2
Stage m
Bi,B h,x,B
V,ssi,
sh,y,V 111
Reboiler (stage 1)
L,ss
i,
sh,x,L 222
s
s
m
i,my
,V
1
1
−
−
vs
mh,
1−
s
im
s
m
x
L
,
,
Ls
mh,
LL FFL h,x,F
M
Mm
i,my
,V
V,Mmh
Mi,m
Mm
x
,L
1
1
+
+
L,Mmh 1+
Chapter 3 Demethaniser column design method
85
from the stripping section of the column. The design procedure also requires the
ratio of upper-to lower feed rate to be specified. As a result, there are three
variables remaining, i.e. reflux ratio, reboil ratio and upper feed condition, of
which two degrees of freedom are chosen and the other variable is calculated from
the overall energy balance of the column.
Many feasible designs may be found, as several middle section profiles are
obtained, corresponding to various lower feed locations. Searching for feasible
designs using trial and error is tedious and time consuming. In this work, finding
feasible designs is performed systematically where the feed stage location is
optimised locally to minimise the number of stages, whereas the other design
variables are optimised globally, i.e. through flowsheet optimisation. Local
optimisation of the lower feed stage location is sufficient, i.e. by minimising
number of stages, as the number of stages is independent of reboiler and condenser
duties.
3.8 Extended boundary value method for column with side
reboilers
Side reboilers in low-temperature distillation columns are particularly important
because they enable heat recovery at temperatures lower than the temperature of
the column reboiler. The use of a side reboiler in the demethaniser provides greater
energy efficiency and reduces the duty of the main reboiler. The main benefit is
that the side reboiler provides a below-ambient heat sink, so reduces the
requirement for external refrigeration to pre-cool the feed to the desired
temperature in the cold separator as shown in Fig. 3.6 This heat recovery is likely
to be cost effective, as the cost of refrigeration increases as the temperature is
decreased (Elliot et al., 1996).
3.8.1 Composition Profiles for a column with side reboilers
Side reboilers are normally placed in between a lower feed and the main reboiler
(Foglietta and Patel, 2007). In addition to the specifications required for the
double-feed column design by the boundary value method as explained in Section
3.7.1, the duty and location of the side reboilers must also be specified.
Chapter 3 Demethaniser column design method
86
Similar to the double feed column design, the column is divided into the rectifying,
middle and stripping sections. The calculation of the rectifying section is
performed as explained in Section 3.5. The calculation of the stripping section
composition profile needs some modifications to account for the side reboilers. In
order to avoid complexity in the model, the side reboilers are modelled as side
heaters, where heat is input to the specified stages in the column as shown in
Figure 3.9. The flow rate, condition, composition and stream temperatures of the
side reboiler draw and return are thus not explicitly modelled.
Figure 3.9 Schematic of column stripping section with side heaters
The stripping section composition profile in this case is calculated by performing
material, energy and equilibrium calculations across the stripping section (Figure
3.9. In order to explain the procedure, two side heaters having a duty of (Q1) and
(Q2) are entered at specified stages (m/) and (m//) respectively. The stage (m)
represents the lower feed location. The first step is to calculate the reboiler duty
Side Reboiler 2
Duty Q2
Side Reboiler 1
Duty Q1
L,sss h,x,L 222
Stage 2
Stage m
Bi,B h,x,B
v,sss h,y,V 111
Qreb
,x,F
LFL FLh
Stripping Section 1
Stripping Section 2
Stripping Section 3
Stage m//
Stage m/
Chapter 3 Demethaniser column design method
87
(Qreb) from an overall balance of the column. This is obtained by introducing the
side heaters duties into Eq. 3.6 which yields
( ) 21 QQQFhBhDhQ condFBDreb −−+−+= ( 3.28)
The stripping section is further divided into three sections. The first section from
the bottom starts from the bottom product and finishes at /m stage. The
composition profiles in this section are calculated by a similar procedure as
explained in Section 3.5.2 by equations ( 3.10) and ( 3.11).
For a given bottom product composition, i,Bx and a reboil ratio s, the liquid
composition profile of the first stripping section is calculated starting from the
bottom product composition. The vapour composition from the reboiler ( si,y1 ) in
equilibrium with the bottom product is determined from the bubble point
calculation. The liquid composition entering the reboiler ( si,x2 ) is then calculated
from the set of equations ( 3.10) and ( 3.11). The calculation is continued to the next
stage up the column to the first side heater location (stage m/). For the calculation
of vapour flow in the first stripping section ( s
mV ), the error in the energy balance
between the two stages (Z) is calculated and minimized by applying Broyden’s
method
( ) rebB
v,s
m
s
m
v,s
m
s
m QBhhVhBVZ +−−+= ( 3.29)
For the second section, between the two side heaters, the equations for the energy
balance and the error in the energy balance (equations ( 3.10) and ( 3.11)) are
modified to include the duty of first side heater Q1:
( ) 011 =++−−+ + QQBhhVhBV rebB
v,s
m
s
m
L,s
m
s
m ( 3.30)
( ) 11 QQBhhVhBVZ rebB
v,s
m
s
m
v,s
m
s
m ++−−+= ( 3.31)
Similarly for the third section between the second heater location m// and the lower
feed location, the two equations are updated accordingly.
Chapter 3 Demethaniser column design method
88
( ) 0211 =+++−−+ + QQQBhhVhBV rebBv,s
ms
mL,s
ms
m ( 3.32)
( ) 212 QQQBhhVhBVZ rebB
v,s
m
s
m
v,s
m
s
m +++−−+= ( 3.33)
The stripping section composition profile is plotted by calculating the liquid
composition xs on each stripping stage in all three sections. The intersection of the
profiles is then identified by the minimum distance criterion as explained in
Section 3.4.
3.8.2 Illustrative example
The design procedure of a double-feed column with side reboilers is demonstrated
by example: a five-component mixture of methane, ethane, propane, i-butane and
n-butane is to be separated in a demethaniser column. The upper feed flow rate is
2200 kmol/h while the lower feed flow rate is 800 kmol/h. Both the feed are
saturated liquids. The feed compositions are given in Table 3.1.
Table 3.1 Molar Feed Compositions
Component Upper Feed Lower Feed
Methane 0.865 0.65
Ethane 0.06 0.16
Propane 0.04 0.09
i-Butane 0.02 0.06
n-Butane 0.015 0.04
Total (kmol/h) 2200 800
The separation is carried out at a uniform pressure of 30 bar in the column. The
recovery of ethane in the bottom product is specified as 98%, while the mole
fraction of methane in the top product is specified as 99.5%. Side heater 1 with a
duty of 900 kW is introduced at eight stage above the reboiler of the column while
side heater 2 with duty of 600 kW is introduced at fourth stage above the reboiler.
A column with a partial condenser is employed in HYSYS for validation of the
boundary value model, results of which are presented below. The calculations were
Chapter 3 Demethaniser column design method
89
performed on an Intel® Core 2 Duo CPU 2.93 GHz processor with 4 GB RAM.
The shortcut model takes 1.12 seconds to solve while the HYSYS simulation for
column model takes around 2 seconds to converge. However, the time required to
setup a column simulation in HYSYS in this case is not accounted, which can vary
from 3 to 5 minutes depending on the column features.
Table 3.2 Validation results: Boundary value design results vs. HYSYS
simulation results
Results Boundary Value Method
HYSYS HYSYS with pressure drop
Number of stages 24 24* 24*
Upper feed location (from top)
6 6* 6*
Lower feed location (from top)
12 12* 12*
Reboiler duty (kW) 3580 3654 3646
Condenser duty (kW) 646 662 668
CPU time (sec) 1.12 2.0 2.0
*indicates specified values
The column flow and composition profiles for the key components are also
compared with the composition profiles obtained from HYSYS. The two profiles
are shown in Fig. 3.10 and Fig. 3.11, which demonstrate that the new model can
represent a complex demethaniser column with sufficient accuracy for the purpose
of conceptual design. It is evident from Fig. 3.11, that molar flows are not constant
in each column section, supporting the use of energy balances in calculating the
composition profiles. The third column in Table 3.2 presents the column
simulation results from HYSYS considering a pressure drop of 30 kPa over the
column. The condenser and reboiler duties are shown to vary by less than 1% in
the two cases, which shows that the assumption of neglecting the pressure drop
does not affect the design results significantly.
Chapter 3 Demethaniser column design method
90
0
500
1000
1500
2000
2500
3000
3500
0 5 10 15 20 25 30
Stage number (from top to bottom)
Mo
lar
flo
wra
te (
km
ol/
h)
Vapour (BVM)
Liquid (BVM)
Vapour (HYSYS)
Liquid (HYSYS)
Rectifying
section
First
stripping
section
Second
stripping
section
Third
stripping
section
Middle
section
Figure 3.10 Molar flow profiles: new model (BVM) vs. HYSYS
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 5 10 15 20 25 30
Stage number (from top to bottom)
Mo
le f
ract
ion
Methane (BVM)
Ethane (BVM)
Methane (HYSYS)
Ethane (HYSYS)
Rectifying
section
First
stripping
section
Middle
section
Third
stripping
section
Second
stripping
section
Figure 3.11 Composition profiles for key components: new model (BVM) vs.
HYSYS
Chapter 3 Demethaniser column design method
91
3.9 Extended boundary value design method for a reboiled
absorption column
As mentioned in Section 2.6, the top product from the demethaniser, methane, is
withdrawn as a vapour product and most commercial flowsheets do not have a
conventional condenser. The need for liquid in the upper section of the column is
fulfilled by introducing an external reflux stream to the top tray of the column.
This external reflux stream originates from the vapour stream of the flash column.
Before entering the column it is typically condensed in a reflux heat exchanger
which exchanges heat with the demethaniser top product as shown in Fig 3.6.
For the purpose of design using the boundary value method, the demethaniser is
treated as a reboiled absorber, with the external reflux stream analogous to the
solvent stream in an absorber. On the top tray, components that are volatile at the
tray temperature will exit the column with the overhead product. The rectifying
section uses a mass separating agent (external reflux) to remove heavy components
from the overhead, while the stripping section uses an energy separating agent (the
reboiler) to remove light components from the bottom product. The external reflux
rate affects the recovery of the heavy key component in the bottoms and the purity
of the light key component in the overhead, while the reboiler duty affects the
recovery of the light key in the overhead and the purity of the heavy key in the
bottoms.
In addition to the usual specifications for the reboiled absorber column design by
the boundary value method (i.e. column pressure, upper and lower feed
compositions and flowrates, top and bottom product compositions and flowrates,
lower feed condition, reboil ratio or upper feed condition), the flowrate and the
composition of the external reflux stream must also be specified.
Chapter 3 Demethaniser column design method
92
3.9.1 Calculation of composition profiles
The composition profiles for the different sections in a reboiled absorption column
are calculated based on the mass and energy balances along with the vapour-liquid
equilibrium. The column is divided into three sections as discussed in Section 3.7.
The stripping and middle section calculations are performed in a similar manner as
for the double-feed distillation column. The absorption section calculation in this
case differs from rectifying section calculations.
An external reflux stream with a flow Lo, composition xo,i and enthalpy Lh0 enters
at the top of the column stage as shown in Figure 3.12. The composition profile for
the absorption section is started from the distillate composition that leaves the top
of the column.
The overall balance on the top stage is
The overall material balance on the top stage is given by:
DLVLo +=+ 12 ( 3.34)
1+nV
i,ny 1+ vnh 1+
Stage 1
nV
i,ny ,
Vnh
Stage n
V2i2,2 h,y,V
VDiD, h,y,D L
oL
i,oo h,x,L
L
,i
h
x
L
1
1
1
Ln
i,n
n
h
x
L
1
1
1
−
−
−
Ln
i,n
n
h
x
L
Figure 3.12 Schematic of the top stage with external reflux stream
Chapter 3 Demethaniser column design method
93
while the component balance gives
i,DLi,i,
Li,oo DyxLyVxL +=+ 1122 11 −=∀ c,...,i ( 3.35)
Rearranging Eq. 3.35
( ) ( ) 01122 =+−+ i,DLi,
Li,ooi, DyxLxLyV 11 −=∀ c,...,i ( 3.36)
The energy balance on the top stage gives:
( ) ( ) 01122 =+−+ VD
LLoo
VDhhLhLhV ( 3.37)
Vapour-liquid equilibrium compositions and enthalpy are calculated using HYSYS
as explained in Section 3.2. The top stage calculations start from the external reflux
and the top product composition. Equilibrium is assumed to be achieved in the top
stage and the composition of the liquid leaving the stage is calculated assuming
vapour-liquid equilibrium. There are two remaining unknowns V2 and y2 which are
calculated by solving equations (3.36) and (3.37) simultaneously.
Similarly for the section from stage 1 to stage n, the balance equations can be
written as
( ) ( ) 011 =+−+++ i,Di,nnL
i,oonn DyxLxLyV ( 3.38)
( ) ( ) 011 =+−+
++VD
Lnn
Loo
Vn DhhLhLhV
n ( 3.39)
For the calculation of vapour flow in the absorption section, Vn+1, the error in the
energy balance e between the two stages in the absorption section is calculated as
follows:
( ) ( )D
L
nnLo
v
n DhhLhLhVeon
+−+=++ 11 ( 3.40)
This error is minimised using Broyden's method where the value of Vn+1 is updated
at every iteration. The final value of 1+nV is computed and the energy balance is
then applied over the whole rectifying section in the same manner.
Chapter 3 Demethaniser column design method
94
The calculation continues to the next stages down the column by solving material
and energy balances, Equation (3.38), (3.39) and (3.40), for i,ny 1+ and 1+nV ,
simultaneously with vapour-liquid equilibrium, for i,nx . The calculation stops
when the composition profile reaches its pinch point, where there is no change in
composition from one stage to the next. The liquid compositions obtained
comprise the absorption section composition profile. Having calculated the
composition profiles for the absorption, middle and the stripping section (including
side heaters), the profiles intersection is identified by the minimum distance
method.
3.10 Case studies
Two case studies are presented to illustrate application of the new column design
method presented in this work to different column configurations.
3.10.1 Case study 1: HYSYS sample case (Turbo-expander plant)
The first process is a typical turbo-expander flowsheet model, presented in the
library of sample cases in HYSYS (version 2006.5), “G-3: Turbo-expander plant”.
Figure 3.13 presents the HYSYS process flow diagram. The demethaniser column
is represented by T-100. The feed gas (1) passes through a series of coolers, shown
as a sub-flowsheet (FLOW-1), where it is cooled to the required temperature of
stream 13. The duties for these coolers are supplied by side reboilers (represented
as energy streams) of the demethaniser. Streams 80, 81 and 82 represent the duties
of the main reboiler and two side reboilers, respectively.
Stream 13 is fed to a flash separator (V-100), where it is separated into equilibrium
liquid and vapour fractions. The liquid fraction (16) feeds the demethaniser, while
the vapour passes through an expander (E-100) that generates power to drive the
compressor (K-100). The expander outlet stream (17) is then sent to a second flash
separator (V-101), the liquid product of which (18) feeds the top of the
Chapter 3 Demethaniser column design method
95
demethaniser as the external reflux, while the vapour bypasses the demethaniser
and is mixed with the demethaniser top product to form the final sales gas.
3.10.1.1 Problem inputs
The feed condition, and other options related to the thermodynamics (Peng-
Robinson equation of state, enthalpy-calculation options, etc.) are the same as used
in the original sample file. The process feed gas (1) is at a temperature of 37.8°C
and a pressure of 58.6 bar, with a molar flow rate of 4981 kmol/h. In this work,
components heavier than hexane as well as nitrogen and carbon dioxide, are
artificially eliminated from the feed in order to reduce the complexities that arise in
the presence of trace components in the calculations for establishing intersection of
profiles. This limitation of the design method is discussed further in Chapter 7. The
simplified composition of the feed for Case Study 1 and the original composition
from HYSYS are presented in Table 3.3.
Figure 3.13 HYSYS process simulation diagram of a typical expander plant
Chapter 3 Demethaniser column design method
96
Table 3.3 Feed gas composition – from HYSYS source and simplified for this
case study
Component HYSYS feed composition Simplified feed composition
Nitrogen 0.0055 0.00
Carbon dioxide 0.0091 0.00
Methane 0.8457 0.8605
Ethane 0.0820 0.0834
Propane 0.0340 0.0346
isobutane 0.0058 0.0059
n-Butane 0.0086 0.0088
isopentane 0.0028 0.0028
n-Pentane 0.0021 0.0021
n-hexane 0.0018 0.0018
n-Heptane 0.0012 0.0000
n-Octane 0.0005 0.0000
n-Nonane 0.0004 0.0000
n-Decane 0.0005 0.0000
Total Flow (kmol/h) 4981 4981
The demethaniser column in this example is a reboiled absorption column with
stream 18 providing reflux at the top of the column, while stream 16 is the only
other feed to the column. Table 3.4 and Table 3.5 present data for the demethaniser
feed streams.
Table 3.4 Column feed streams – flow rates and conditions
Stream Flow rate (kmol/h) Temperature (oC) Vapour fraction
Feed (16) 1187 -80.7 0.41
Reflux (18) 438 -92.8 0.0
Chapter 3 Demethaniser column design method
97
Table 3.5 Molar compositions of demethaniser feed streams
Component Feed (16) External reflux (18)
Methane 0.6414 0.58438
Ethane 0.1707 0.29594
Propane 0.1068 0.09607
i-Butane 0.0211 0.00953
n-Butane 0.0326 0.01085
i-Pentane 0.0113 0.00182
n-Pentane 0.0086 0.00105
n-hexane 0.0075 0.00036
Total Flow (kmol/h) 1190 441
Table 3.6 presents the column details obtained from the simulated flowsheet and is
used as specification to the BVM. Although there is a pressure drop in the HYSYS
simulation of the column, the pressure is assumed constant (19 bar) in the
boundary value design method. The feed flow rates and compositions, as well as
the side reboiler specifications (duty and locations) are used as inputs to the BVM.
The top and bottom product compositions are also needed for the BVM to calculate
the composition profiles. In this case study, the product composition specifications
are derived from the HYSYS simulation results.
Table 3.6 Column details from HYSYS
Molar ratio of methane to ethane in bottom product 0.02
Feed flow rate (kmol/h) 1189
Reflux flow rate (kmol/h) 440.7
Side heater 1 (stream 81) 698.2 kW
Side heater 2 (stream 82) 698.2 kW
3.10.1.2 Results and discussion
Table 3.7 presents the results of the boundary value design method and the
HYSYS simulation. It may be seen that the results are very similar with respect to
Chapter 3 Demethaniser column design method
98
overall flows, duties and internal flows and compositions. Some discrepancies in
the molar flow profiles and composition profiles may be attributed to the
assumption made in the boundary value design method of constant pressure in the
column. The simulation of the column is also performed with the actual feed
composition in HYSYS. The third column in Table 3.7 presents the results with the
actual feed composition. The reboiler duty without the feed simplification is shown
to be around 1% lower in this case compared to the results using the simplified
feed.
Table 3.7 Comparison of simulation results from HYSYS and the boundary
value design method
Results Shortcut design
method
HYSYS
(Simplified feed)
HYSYS
(Actual feed)
Number of Stages 12 12* 12*
Feed Location (from top of
column)
3 3* 3*
Distillate flow rate (kmol/h) 1043.7 1044.0 1031
Bottoms flow rate (kmol/h) 585.3 587.0 600
Reboiler Duty (kW) 965.2 938.1 922
CPU time 1.35 1.9 1.9
*indicates specified values
Chapter 3 Demethaniser column design method
99
0
200
400
600
800
1000
1200
0 2 4 6 8 10 12 14
Stage number (from top to bottom)
Mola
r fl
ow
(k
gm
ol/h
)
Vapour (HYSYS)
Liquid (HYSYS)
Vapour (BVM)
Liquid (BVM)
Rectifying
section
First strippping
section
Second strippping
section
Third strippping
section
Figure 3.14 Molar flow profiles: boundary value method (BVM) vs. HYSYS
simulation results
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0 2 4 6 8 10 12 14
Stage number (from top to bottom)
Mole
fra
ctio
n
Methane (HYSYS)
Ethane (HYSYS)
Propane (HYSYS)
Methane (BVM)
Ethane (BVM)
Propane (BVM)
Rectifying
section
First strippping
section
Second strippping
section
Third strippping
section
Figure 3.15 Liquid composition profiles: BVM vs. HYSYS simulation results
Chapter 3 Demethaniser column design method
100
It may be concluded that the boundary value design method provides results that
are sufficiently accurate to provide column design parameters for initialising
rigorous simulations. Nevertheless, complete agreement with simulation
approaches using different inputs and specifications is not expected. It is known
that the composition profiles are sensitive to trace components in the products and
to the approximation introduced by the tolerance used in the minimum distance
criterion applied for the estimation of profile intersection for multicomponent
mixtures. To improve agreement between HYSYS simulation results and those of
the design method, input variables, such as the specified product compositions,
column pressure and feed condition, may be manually adjusted by the user.
3.10.2 Case study 2: Multiple reflux stream hydrocarbon recovery process
This case study is based on the US patent no 7818979, “Multiple reflux stream
hydrocarbon recovery process”, assigned to ABB Lummus Global Inc. (Patel and
Foglietta, 2010). Figure 3.16 illustrates the process.
The ABB Lummus process differs from the turbo-expander process described in
Case Study 1 in that two multistream exchangers are employed to pre-cool the
feed. The first uses the demethaniser top product as the cooling medium, while the
second uses the side reboilers for cooling the feed gas. The demethaniser involved
in this process has three feed streams in addition to the reflux stream entering the
top of the column.
3.10.2.1 Problem inputs
The process feed gas is at a temperature of 32°C and a pressure of 55 bar. This
work neglects the presence of nitrogen and carbon dioxide in the feed, as in first
case study. The feed composition data from the patent application and simplified
for this case study are presented in Table 3.8.
Chapter 3 Demethaniser column design method
101
Figure 3.16 Process flowsheet diagram of multiple reflux stream hydrocarbon
recovery process (Patel and Foglietta, 2010)
Table 3.8 Column inputs: Material streams (Patel and Foglietta, 2010)
Component HYSYS feed
composition
Simplified feed
composition
Nitrogen 0.00186 0.00
Carbon dioxide 0.00381 0.00
Methane 0.8567 0.86160
Ethane 0.0756 0.07603
Propane 0.0332 0.03339
isobutane 0.0048 0.00483
n-Butane 0.00984 0.00990
isopentane 0.00274 0.00276
n-Pentane 0.00294 0.00296
n-hexane (used for C6 +) 0.00849 0.00854
Total Flow (kmol/h) 43856 43856
Chapter 3 Demethaniser column design method
102
The required data for the boundary value design of the demethaniser are given in
Table 3.9 and 3.10. The compositions of the external reflux and the three feed
streams to the column are presented in Table 3.11. The patent application provides
details of the material streams fed to the column, but the feed and side reboiler
locations are not specified explicitly. Therefore, a simulation of the process was
performed in HYSYS to provide reasonable values of unknown design data.
Table 3.9 Column inputs: Material streams (Patel and Foglietta, 2010)
Stream Flow rate
(kmol/h)
Temperature
(oC)
Vapour fraction
Reflux 4245 -90.12 0.00
Top feed 19520 -87.7 0.3
Middle feed 19520 -62.6 0.94
Lower feed 4812 -46.4 0.26
Table 3.10 Column inputs: Energy streams (from HYSYS simulation)
Table 3.11 Molar composition of column input streams
Component Reflux Top feed Middle feed Lower feed
Methane 0.975 0.909 0.909 0.470
Ethane 0.024 0.065 0.065 0.163
Propane 0.001 0.019 0.019 0.149
i-Butane 0.000 0.002 0.002 0.030
n-Butane 0.000 0.003 0.003 0.068
i-Pentane 0.000 0.000 0.000 0.022
n-Pentane 0.000 0.000 0.000 0.024
n-hexane 0.000 0.000 0.000 0.075
Stream Duty (kW)
Side reboiler at 18h stage 4894
Side reboiler at 21st stage 4027
Side reboiler at 24th stage 3452
Chapter 3 Demethaniser column design method
103
3.10.2.2 Results and discussion
The complex column is divided into sections based on the locations of feeds and
side reboilers. The results from the boundary value design method, including the
location of feed stages in the column, compositions and temperatures along the
column, can be used as initial guesses to help the HYSYS algorithm converge to
the required specification.
Table 3.12 compares the boundary value design results and simulation results from
HYSYS. It may be seen that there is excellent agreement between the product flow
rates and reboiler heat duty predicted by the two approaches. Figures 3.17 and 3.18
compare the molar flow profiles and composition profiles in the column obtained
from the two simulation models. The validation of the boundary value simulation
results, with reference to HYSYS simulation results, is thus demonstrated; it may
be concluded that the model captures the process behaviour satisfactorily and is
therefore useful for application in demethaniser flowsheet synthesis framework.
Table 3.12 Comparison of simulation results: Boundary value design method
vs. HYSYS.
Results Boundary value
design method
HYSYS
Number of Stages 28 28*
Top feed 5 5*
Middle feed 11 11*
Lower feed 16* 16*
Ethane recovery in bottoms (%) 89.2* 89.4
Methane recovery in top product (%) 99.85* 99.85
Distillate flow rate (kmol/h) 42323 42316
Bottoms flow rate (kmol/h) 5778 5785
Reboiler Duty (kW) 1193 1151
CPU time 1.26 2.0
*indicates specified values
Chapter 3 Demethaniser column design method
104
Figure 3.17 Molar flow profiles: Boundary value method vs. HYSYS
Figure 3.18 Liquid composition profiles (key components): Boundary value
method vs. HYSYS
Chapter 3 Demethaniser column design method
105
3.11 Conclusions
In this work, a new simplified method for the initial design of complex
demethaniser column is presented. The method is an extension and modification of
the boundary value method that requires the feed and product compositions,
column pressure and reflux/reboil ratio to be specified as design parameters. The
proposed column design method allows rigorous simulation of the demethaniser
column to be carried out without trial and error.
Energy balance is included in the calculation of the composition profiles to
overcome the constant molar overflow assumption in the original method. The
method also takes into account two-phase feeds by introducing the feed between
two stages and considering mixing at the feed stage. A minimum distance criterion
is used to identify the near-intersection of composition profiles in order to apply
the design method to multicomponent feed mixtures.
In the case of double-feed columns, the model decomposes the column into three
sections, namely the rectifying, the middle and the stripping sections. For each
section, the composition profile is calculated in the same manner as for a single-
feed column. The rectifying and stripping section composition profiles are
calculated starting from top and bottom product composition, respectively. Using
the bottom-up approach, the middle section composition profile is calculated from
a specified lower feed stage. The intersection between the rectifying and the
middle section liquid composition profiles is used for the column design.
The model also accommodates intermediate heating using side reboilers. In this
case the duty and location of the reboilers need to be specified. The column energy
balance is extended to include the duties of the side reboilers. Finally the boundary
value method is modified to be applied to a reboiled absorber. The composition
profile in the rectifying section in this case is modified to account for the use of an
external reflux stream, as is common practice.
Chapter 3 Demethaniser column design method
106
Two case studies are presented to illustrate the application of the design method to
a range of column configurations. The column design parameters obtained from
the boundary value method are used for initializing the rigorous simulation ion
HYSYS. HYSYS simulation results are shown to be in good agreement with those
of the proposed model. The extended boundary value method can be used for
assessing the feasibility of a proposed specification and generating designs for
finding the number of stages, feed stage locations and reboiler duty.
The design method developed in this work is useful for flowsheet design and
optimisation. The combination of this column design model and other models of
demethaniser flowsheet units will be employed in a synthesis framework. This will
also help in developing a systematic design method which will provide a powerful
tool for process design, selection and optimisation of demethaniser flowsheets.
Chapter 4 Demethaniser flowsheet design and simulation methodology
107
CHAPTER 4 DEMETHANISER FLOWSHEET
DESIGN AND SIMULATION
METHODOLOGY
4.1 Introduction
Numerous expansion processes are commonly used for NGL recovery in the gas
processing industry, particularly in the recovery of ethane from natural gas. Some
of these processes were discussed in Section 2.5 in detail. Mostly in the case of the
expander processes, the feed gas is cooled to a relatively low temperature to
achieve partial condensation, typically by heat exchange with the demethaniser
overhead vapour, side reboilers, and/or external propane refrigeration (Mokhatab et
al., 2006). In some process variations, a part of the demethaniser overhead product
is used to subcool a portion of vapour from flash unit to produce a low temperature
reflux, while a portion of the expander discharge is heated by the feed gas to form
a temperature-controlled column feed (Chebbi et al., 2010).
The cryogenic processes produce a liquid hydrocarbon stream through chilling the
feed gas. Low temperatures are needed when higher recoveries are required. The
low temperatures can be obtained through either mechanical refrigeration or via
turbo-expander processes. The use of turbo-expanders, combined with the
advantages of the plate fin multistream heat exchangers, also help to increase the
performance of these processes. Compression costs constitutes around 25 to 40%
of operating costs (Bai et al., 2006). Figure 4.1 shows the essential components of
a turbo-expander plant with a demethaniser column.
Chapter 4 Demethaniser flowsheet design and simulation methodology
108
Figure 4.1 Generalized gas processing scheme for ethane recovery (Yan et al.,
2008)
In this chapter a flowsheet design and simulation model is developed in which the
individual sub-systems of the demethanisation process, namely the separation,
refrigeration and heat recovery systems, are modelled in order to capture the
overall picture and achieve optimal design of demethaniser flowsheets. The
developed model will be employed in a synthesis framework so that promising
design options are easily identified at an early stage and a wide range of major
design options are considered.
4.2 Heat integration in demethaniser flowsheet
The methodology for the systematic design and evaluation of demethaniser
flowsheets is not complete without considering opportunities for heat integration
between the heat sources and sinks of the process. By allowing individual hot
process streams to exchange heat with cold process streams, the operating costs
can be reduced. Thus, any systematic design approach must contemplate heat
integration opportunities. In the present methodology, heat integration is
Power recovery
Chapter 4 Demethaniser flowsheet design and simulation methodology
109
considered at the very early stages to address demethaniser flowsheet synthesis
problem.
The heat integration methodology developed in this work considers the heat
recovery opportunities between the streams of the process and the background
process. In the present work, a refrigeration system may be present as a
background process. The heat recovery in the demethanisation process is carried
out in a multistream heat exchanger by setting recovery targets quantified using
pinch analysis.
The pinch analysis is widely used in the design and optimisation of heat exchanger
networks (HENs). Pinch analysis is a systematic methodology based on
thermodynamic principles to achieve utility savings by better process heat
integration and maximising heat recovery (Linnhoff and Boland, 1982). Three
important rules should be considered in the pinch design method. They are that
heat transfer should be avoided across the pinch, external heating should be
avoided below the pinch, and external cooling should be avoided above the pinch.
These requirements should be met in the process in order to reduce the external
utility loads.
Since the pinch analysis was introduced for the initial design of HENs by Linnhoff
and Boland (1982), it has been further developed significantly. Most of the
previous work focused on networks that consist of two-stream heat exchangers,
mostly shell and tube heat exchangers. However, multistream heat exchangers can
provide many advantages over conventional two-stream heat exchangers. A
multistream plate-fin heat exchanger is able to incorporate many streams and it is
characterized by compactness, flexibility and efficiency (Wang and Sunden, 2001).
Chapter 4 Demethaniser flowsheet design and simulation methodology
110
4.2.1 Heat recovery in multistream heat exchanger
In this work, pinch analysis is applied to determine the maximum amount of heat
recovered in the multistream exchanger, where the heat source is the warm feed
gas and the heat sink consists of side reboiler and the column top product. A quick
method for heat recovery in exchangers based on pinch analysis, as discussed by
Hewitt and Pugh (2007) is adopted in this work. This method will be employed in
the demethaniser flowsheet simulation model.
The methodology starts by performing the energy balance for the process as if all
of the exchanger heat transfer sides were independent. The stream data is used to
construct the composite curves and determine enthalpy intervals. The composite
curves represent the heat balance of an entire process. They are composed of a hot
and a cold composite curve. The hot composite curve represents the total heat that
must be removed from all hot streams that take part in the process; and the cold
composite curve, represents the total amount of heat that must be added to all cold
streams present in the process (Smith, 2005). When both curves are superimposed,
the overlap between them indicates the amount of heat that can be recovered within
the process, whereas the overshoot on both ends indicates the amount of external
heating and cooling required for the process to be in thermal balance.
The method assumes constant physical properties, which results in the composite
curves formed by straight lines where each change in slope is related to the entry
and exit of a stream. If a vertical line is drawn whenever a change in slope occurs,
the whole heat recovery process is sectioned into enthalpy intervals and is
characterized by a temperature field (inlet and outlet temperatures), a heat load and
a stream population.
The heating and cooling loads in the multistream exchanger should be balanced by
separately summing the duties on each side of the exchanger. The residual duty is
then reduced to zero by refrigeration or a heat source. The method is illustrated in
the following example.
Chapter 4 Demethaniser flowsheet design and simulation methodology
111
4.2.2 Illustrative example
Stream data are taken from Hewitt and Pugh (2007). There are six hydrocarbon gas
streams (three hot and three cold). The stream source and target temperatures along
with heat capacity are given in Table 4.1.
Table 4.1 Stream data for multistream exchanger
Stream Number pCM& (kW/K) Inlet Temperature
(K)
Outlet Temperature
(K)
Hot H1 10 300 150
Hot H2 5 250 100
Hot H3 8 200 150
Cold C1 15 90 130
Cold C2 5 120 210
Cold C3 20 170 250
The stream data are represented in terms of hot and cold composite curves using
the pinch analysis method. The resulting curves are shown in Figure 4.2. The pinch
temperature is 6 K. The composite curve is divided into zones corresponding to
linear sections of the hot and cold composite curves. Each of these zones
represents the actual heat transfer zones in the multistream exchanger and is
considered on its own.
Chapter 4 Demethaniser flowsheet design and simulation methodology
112
Figure 4.2 Composite curves for multistream exchanger (Hewitt and Pugh,
2007)
A mean volumetric coefficient for a zone containing n streams can be estimated
from the expression
∑=
=n
i i
i
z
z Q
B
Q
1 β
&&
( 4.1)
Where zQ& is the total heat transferred in zone z, (kW)
Bz the mean volumetric coefficient for the zone, (m3K-1)
iQ& the heat lost or gained by the ith stream in the zone, (kW) and
iβ the local volumetric heat transfer coefficient for the ith stream (kW/m3K) , and
is given in Engineering Sciences Data Unit - Selection and costing of heat
exchangers manual (ESDU 1997). In this example a typical value of 80 (kW/m3K)
is chosen.
Chapter 4 Demethaniser flowsheet design and simulation methodology
113
The log mean temperature difference (LMTD) is then calculated for each zone
(Tlm,z). The LMTD for a pure counter-flow exchangers with single phase streams of
constant specific heat capacity for a zone is given by:
( ) ( )( )
in,cout,h
out,cin,h
in,cout,hout,cin,hlm
TT
TTln
TTTTT
−
−
−−−=∆
( 4.2)
The multi stream exchanger is assumed to operate close to counter-current flow,
and Tlm,z can be calculated from Eq. 4.2, using the appropriate end temperatures of
the zone. The heat exchanger volume corresponding to the zone can then be
calculated using
z
z,m
z
z
TQ
Vβ
∆
&
=
( 4.3)
In this work, however the area of the exchanger is used for the calculation of the
cost of the heat exchanger as explained in Appendix B.
4.3 Modelling of flowsheet units
The mathematical models of the different units of the flowsheet are developed in
MATLAB. The physical properties are estimated by linking MATLAB with
HYSYS as explained in Section 3.2 and Appendix A. The models are developed so
that the output stream data including pressure, temperature, enthalpy, etc. can be
calculated for given input stream data and equipment operating parameters. The
shortcut models of the different units are explained below.
4.3.1 Demethaniser column model
The complex distillation column is simulated using a modified boundary value
method as explained in detail in Chapter 3. The method is employed for generating
the column design, verifying the separation performance and calculating energy
requirements.
Chapter 4 Demethaniser flowsheet design and simulation methodology
114
4.3.2 Flash unit model
The flash unit model is used to estimate flowrate and composition of the vapour
and liquid fractions of a mixture of known composition for a given temperature
and pressure. In this work, an isothermal flash model is applied where the flash
temperature and pressure are known. The basic assumptions for the model are:
1. Equilibrium is achieved between the liquid and vapour leaving the column
2. There is no entrainment of liquid in the vapour
3. There is no carry over of vapour in the liquid.
The component material balance can be represented by the following equations
(Seader and Henley, 1998):
iii LxVyFz += ( 4.4)
where F is the molar flow rate of the feed, V and L are the molar flow rates of the
vapour and liquid from the flash unit respectively, zi, yi, and xi represent the mole
fraction of component i in the feed, vapour and liquid stream of the flash unit
respectively.
The vapour-liquid equilibrium relationship for each component is defined by
ii xKy = ( 4.5)
Where Ki represents the vaporisation equilibrium ratio of component i and is
calculated using HYSYS as discussed before. The composition of the vapour and
liquid streams of the flash unit are estimated using the following equations (Seader
and Henley, 1998):
i
i
i
KF
V
F
V
zy
11
−+
=
( 4.6)
( ) 11 +−
=
F
VK
zx
i
i
i
( 4.7)
Chapter 4 Demethaniser flowsheet design and simulation methodology
115
where V/F is the fraction of the feed vaporised. The vapour fraction of the feed is
calculated by an iterative search using the following function:
( )( )
( )∑ =
+−
−=
N
ii
ii
KF
V
KzFVf 0
11
1/
( 4.8)
where N is the number of components in the mixture. A detailed account of flash
calculations can be found elsewhere (e.g. Walas, (1985); Seader and Henley,
(1998).
4.3.3 Turbo-expander Model
The use of a turbo-expander in the demethanisation processes is a widespread
industrial practice, where the work generated by the turbo-expander is used to
drive the compressors required for the final sales gas. Figure 4.3 indicates the
temperature and enthalpy relationship for a general expansion process. The line ab
shows the expansion of a saturated liquid fluid from pressure P1 to P2. The
temperature drop resulting from the stream pressure drop is employed to cool
down the feed gas and produce refrigeration.
Figure 4.3 T-H curve for an isenthalpic expansion
Chapter 4 Demethaniser flowsheet design and simulation methodology
116
The power produced can be represented using the enthalpy-entropy graphs. Figure
4.4 shows an enthalpy-entropy graph for propylene in which the proplylene is
expanded from a pressure of 862 kPa to 138 kPa. Various efficiency curves are
plotted on the graph indicating the output enthalpy which then determines the
power produced by the expander.
Figure 4.4 Pressure-Temperature-Enthalpy Diagram (Wang, 2004)
The isentropic efficiency is given by:
id
actis
W
W=η
( 4.9)
and the work generated by the expander is
( )outinisoutinactual HHHHW −=−= η ( 4.10)
Eq. 4.10 is employed in this work to calculate the power produced by the turbo-
expander with 80 % isη . The temperature of the discharge stream from expander is
given by Smith (2005):
Entropy, kJ/(kg.K)
En
tha
lpy
, k
J/k
g
Chapter 4 Demethaniser flowsheet design and simulation methodology
117
( ) n
n
inout TT1−
= ε ( 4.11)
The model thus requires the input conditions of the feed and the desired outlet
pressure to calculate the power produced by the expander.
4.3.4 Refrigeration cycle model
In the demethaniser processes, although most of the cooling of the feed gas is done
by internal heat recovery, any additional cooling requirement has to be fulfilled by
the use of external refrigeration cycles. Refrigeration cycles are highly energy
intensive; shaft power usually overwhelms capital investment and dominates the
final total cost of the cycle (Mehrpooya et al., 2009). Power consumption in the
refrigeration system is mainly based on the shaft power of the compressor. The
shaft power of a centrifugal compressor can be calculated with a simplified
formula derived from energy balance as explained by Smith (2005).
−
−=
−1
11
γ
γ
ηγ
γ
evap
cond
P
inevap
P
PFPW
( 4.12)
where W power required for compression (W)
Pevap, Pcond inlet and outlet pressures for the compressor (N⋅m –2)
Fin inlet volumetric flowrate (m3⋅s –1)
γ ratio of heat capacities CP/CV of refrigerant
ηis isentropic efficiency
ηP polytropic efficiency
Compression refrigeration cycles are the most common choices to provide the
required cooling. Figure 4.5(a) illustrates a typical simple compression
refrigeration cycle. Cooling required in the processes is provided through
evaporation of liquid refrigerant in an evaporator. Saturated refrigerant vapour
enters a compressor which increases the pressure of the refrigerant from the
evaporating pressure to the condensing pressure. Superheated vapour at high
Chapter 4 Demethaniser flowsheet design and simulation methodology
118
pressure is condensed to saturated liquid and heat is rejected to external heat sinks
in a condenser. Liquid refrigerant at Point 1 enters the expansion valve, in which
the pressure of the refrigerant is reduced from the condensing pressure to the
evaporating pressure (neglecting the pressure drops in piping and heat exchangers).
Through expansion, liquid refrigerant is partially vaporised. The liquid passes
through the evaporator and absorbs heat from the process to provide refrigeration.
Figure 4.5(b) illustrates the cycle on a temperature-enthalpy program.
Figure 4.5 A Simple vapour-compression refrigeration cycle: a)Flow
diagram, b) Temperature-enthalpy diagram (Smith, 2005)
Smith (2005) discussed that simple refrigeration cycles can be used to provide
cooling at as low as -40°C, while for temperatures lower than -40°C and in
situations when there is more than one heat source or heat sink available, complex
refrigeration configurations of multiple levels or cascade arrangements should be
considered. This is consistent with the fact that shaft power requirements increase
with a larger temperature difference between evaporation and condensation in a
refrigeration cycle. This relationship becomes clear from inspection of the equation
that allows estimating the ideal power requirement of a refrigeration cycle
(Haselden, 1971):
1 4
2 3
Condenser
Compressor
Expansion valve
T
H
4
2 Evaporation 3
1
Condensation
Evaporator
Chapter 4 Demethaniser flowsheet design and simulation methodology
119
−=
evap
evapcondevap
T
TT
η
QW
( 4.13)
Where
Qevap is the heat absorbed by the refrigerant from the heat source at
temperature Tevap,
Tcond is the temperature at which the refrigerant condenses, and
η is the mechanical efficiency of the compressor
The efficiency factor η is a function of refrigeration temperature. Typically a value
η can be set at 0.6 (ETSU 1992). In this work Eq. 4.13 is applied to calculate the
power requirement of a refrigeration cycle.
4.3.4.1 Selection of refrigerant
The refrigerant can be a pure component or a mixture of different components. A
pure refrigerant provides cooling at constant temperature when evaporating, while
mixed refrigerants provide cooling at a changing temperature even when
evaporating at constant pressure. In the present study, only pure refrigerant cycles
are considered, to avoid the complexity associated with the simulation and
optimisation of cycles with mixed refrigerants.
There are many factors affecting the choice of refrigerant for a compression
refrigeration cycle. Smith (2005) discusses the key points in the selection of the
refrigerants. These issues relate to the environmental impact, safety, corrosiveness,
economic analysis, and the physical properties affecting the operating parameters
of the refrigerants. In this section, the effects of freezing and normal boiling point,
latent heat, temperature-entropy curves of refrigerants are discussed and
suggestions for the operating temperature ranges of various refrigerants are
provided.
First of all, the freezing temperature of a refrigerant should be well below the
required cooling temperature to avoid the possibility of solid formation in the
Chapter 4 Demethaniser flowsheet design and simulation methodology
120
refrigeration system. Secondly, the refrigeration process is normally required to be
operated above atmospheric pressure to avoid air ingression. This means that the
selected refrigerant should have a normal boiling temperature below the required
evaporating temperature. In addition to these two conditions the latent heat of the
refrigerant at evaporating conditions should be considered. It is desirable to have a
refrigerant with a high latent heat when evaporating. The higher latent heat leads to
a lower refrigerant flowrate in the cycle. This helps to reduce the power
requirement of the compressor (Smith, 2005).
IncreasingPowerRequirement
Nitrogen
Methane
Ethylene
Ethane
Propane
Propylene
i-Butane
n-Butane
Ammonia
Chlorine
80 100100 120 140 160 180 200 220 240 260 280200 32030060
77 118
112 178
169 264
185 286
231
225
261
273
240
239
Temperature (K)
Figure 4.6 Recommended operating temperature range of some refrigerants
(Smith, 2005)
Figure 4.6 presents operating ranges of a number of refrigerants. Typically
evaporating pressure of refrigerant is set at a value just above the atmospheric
pressure. This prevents air ingression into the refrigeration system. The latent heat
is reduced if the refrigerant operating temperature is far above that of the normal
boiling point, thus affecting the economics of the process. The upper boundary of
the operating temperature range is set at a temperature corresponding with a heat of
vaporization of 50% of that of atmospheric pressure. The lower boundary of
operating temperature range is set at refrigerant normal boiling point of
Chapter 4 Demethaniser flowsheet design and simulation methodology
121
atmospheric pressure. More details discussion of selecting refrigerant for
compression refrigeration is given in Smith (2005).
Another factor to be considered in the choice of refrigerant relates to shape of the
two phase region on a temperature-entropy (T-S) diagram, as shown in Figure 4.8.
The steepness of the right-hand slope of the T-S curve affects the degree of
superheat of refrigerant after compression (Smith, 2005). The steeper the slope, the
less superheated the vapour after compressor. The less superheating results in the
increase of the coefficient of performance, as it decreases the average heat
rejection temperature. Thus the amount of cooling required for condensing the
refrigerant decreases.
Figure 4.8 Selection of refrigerant –Effect of two-phase curve shape
4.3.4.2 Choice of simple and cascade cycles
The decision whether to use simple or cascade cycles is based on the temperature
difference between evaporation and condensation. If the temperature difference is
relatively small, a refrigerant that is suitable for the simple cycle evaporation
temperature is selected. On the other hand, if the temperature difference between
evaporation and condensation exceeds the recommended temperature range of each
of the available refrigerants, a cascade cycle is selected.
A cascade refrigeration cycle is represented in Figure 4.7, the lower cycle extracts
heat at temperature T1,evap and lifts it to the upper cycle condenser temperature
T
S
T
S
Chapter 4 Demethaniser flowsheet design and simulation methodology
122
T2,cond. The condenser of the lower cycle and the evaporator of the upper cycle are
combined into a single heat exchanger.
Figure 4.7 A cascade refrigeration cycle
Lee (2001) noted that the choice of the partition temperature is dependent on the
nature of refrigerants used and refrigeration duties of the upper and lower cycles.
For example in a propylene-ethylene cascade refrigeration system for ethylene
recovery plants, usually the total refrigeration duty of the propylene cycle is much
larger than that of the ethylene cycle.
Lee (2001) represented the problem of finding the optimal partition temperature by
a plot of shaftwork vs. partition temperature for the upper cycle and lower cycle.
As seen in Figure 4.6, the shaft work consumption of both the upper cycle and the
lower cycle depend on the partition temperature. A lower partition temperature
would reduce the shaft work of the lower cycle but increase that of the upper cycle.
The overall shaft work consumption curve is a convex function for which an
optimal partition temperature can be identified. In this work the approach
presented by Lee (2001) is employed for the selection of optimal partition
temperature.
Partition
Temperature
T2,cond
W2
W1 Lower cycle
Upper cycle
T1,evap,
T2,evap
T1,cond
Chapter 4 Demethaniser flowsheet design and simulation methodology
123
Figure 4.8 The effect of partition temperature on the total shaftwork (Lee
2001)
The refrigeration system design approach adopted in this work is limited to simple
and cascaded refrigeration cycles. In practical design, it is frequent to encounter
single refrigerant multistage cycles featuring multiple evaporating stages and a
single condensing stage. According to Wang and Smith (2005) the difference
between the shaft power demand of simple cycles and the corresponding
multistage cycles is small; therefore, this work only incorporates the simple and
cascade refrigeration cycles.
In summary, in this study the decision making for refrigeration system selection
and calculation of power requirements is based on the temperature of the
evaporator. If Tevap> -36 oC a simple refrigeration cycle is employed with power
calculation by Eq. 4.14 with η = 0.6. If, however, Tevap< -36 oC, a cascade
refrigeration cycle is employed, where the optimal partition temperature is
estimated as discussed to calculate the power requirement of the cascade cycle.
In this work, propane is selected as the refrigerant for the simple cycle while i-
butane and ethane are chosen for the cascade refrigeration cycle. This choice of
refrigerant is based on two reasons, first is the availability of these refrigerants
within the process and second is the lower power consumption for the given range
Chapter 4 Demethaniser flowsheet design and simulation methodology
124
of evaporation temperature as shown in Figure 4.6. However, the automatic
selection of refrigerant is not included within the synthesis framework and is
suggested as a future work in Chapter 7.
4.3.4.3 Illustrative example: Cascade cycle vs. Simple cycle
An example is shown to demonstrate the advantages of using a cascade cycle
instead of a simple cycle in the case of large temperature difference between the
heat sink and heat source. In this example, 4000 kW cooling is required at a
temperature of -65°C.
As the cooling temperature of -65°C is below the normal boiling point of
propylene, a simple cycle of propylene is incapable of providing the required
cooling above the atmospheric pressure. From Figure 4.6, other refrigerants such
as ethane or ethylene can be employed. Ethane is chosen in this case as it has a
normal boiling temperature of 88.73°C and requires less shaft power that ethylene.
The configuration of the cascade is illustrated in Figure 4.7. Ethane is the
refrigerant in the lower cycle and propylene is used in the upper cycle. Aspen
HYSYS is applied for simulation of the cycles with physical properties calculated
by choosing Peng-Robinson as the fluid package. The heat sink is assumed to be
available at 0 oC, to compare against a simple cycle, as explained later. In
simulation, the partition temperature between the two cycles is set at -45 oC which
is near the normal boiling point of propylene. The total shaft power requirement in
this case is 3300 kW.
On the other hand, if the temperature of the available heat sink is assumed to be
reduced to the operating range of ethane, at 0 °C, and the cooling temperature and
duty are kept the same, then a simple refrigeration cycle using ethane is possible
for the modified temperature range. The comparison is made by simulating a
simple ethane cycle at the new condensing temperature in HYSYS. The results are
listed in Table 4.2. The total shaft power requirement in the single ethane cycle is
4321 kW which is about 130% of that in the cascade cycle. It demonstrates that
when there is a big temperature difference between refrigerant condensing and
evaporating, using simple cycle can be of very low efficiency.
Chapter 4 Demethaniser flowsheet design and simulation methodology
125
Table 4.2 Cascade refrigeration cycle vs. simple refrigeration cycle
4.4 Flowsheet simulation and evaluation
The flowsheet synthesis requires simulation of the process at given conditions
(optimisation variables) selected by the optimisation procedure. The two main
methods used for the flowsheet simulation are the sequential modular method and
the equation-oriented method. The sequential modular method performs the
calculations one block at a time in sequence, where a block typically represents a
unit operation. Process computations follow the material flow through the process,
which makes it easier to debug convergence failures (Biegler et al., 1997). The
known input streams and the known design parameters are generally required by
the block calculations to calculate the output streams. Recycle streams in this
approach are handled using tearing technique.
The main advantage of sequential modular approach relates to its robustness,
which ensures rigorous convergence, even in presence of extremely complex
modules that are treated in an autonomous way (Biegler et al., 1997). The
mathematical models of different modules can be developed and coded separately
Cascade Cycle
Ethane/propylene
Simple Cycle
Ethane
Cooling duty (kW) 4000 4000
Upper cycle -45
Evaporating Lower cycle -70
-70
Upper cycle 0
Temperature (°C)
Condensing Lower cycle -42
0
Upper cycle 7300 Condensing duty (kW)
Lower cycle 5558
8321
Upper cycle 1742 Shaft power consumption (kW)
Lower cycle 1558
4321
Total Shaft power consumption (kW) 3300 4321
Chapter 4 Demethaniser flowsheet design and simulation methodology
126
with different solution algorithms. Due to the structured information flow in the
sequential-modular approach, the error checking is fairly easy and generally allows
for easy debugging in the case of program failure (Chen and Stadtherr, 1985).
The main problems affecting the efficiency of the sequential-modular approach,
includes the handling of design specifications and the presence of multiple nested
iteration loops (Bimakr et al., 2008). The handling of design specifications by the
introduction of additional iteration loops is an inefficient way to handle simple
equations. The second problem with the sequential modular approach is that it
requires iterative handling of the recycle streams and may require a large number
of iterations to converge (Turton et al., 2008).
The equation-oriented approach or simultaneous approach assembles the equations
from all the modules into one large set of equations, which are then solved
simultaneously using an appropriate method (Biegler et al., 1997). In the equation-
oriented approach, each equipment module contributes to the governing equations
to be solved. Tearing of streams is not necessary in the equation-oriented approach
since all the governing equations are solved simultaneously (Kisala et al., 1987).
The simultaneous method is computationally efficient as all equations are solved
simultaneously; there is no need for nested iteration loops, as in the case of the
sequential approach. The design specifications are easy to handle in this case as
they are represented by simple equations within the large system. The
simultaneous approach also offers a great potential for process optimisation as the
simultaneous equations can be used as constraints in a generalized nonlinear
programming problem (Ishii and Otto, 2011).
For large flowsheets the number of equations will be quite high which may cause
problems in convergence of the flowsheet models (Bimakr et al., 2008). Most of
the equations formed are nonlinear and require good initial guesses to obtain a
converged solution. However, it is difficult to provide a good initial guess for large
and complex nonlinear systems. (Grossmann and Daichendt, 1996).
In this work the sequential modular approach is selected for flowsheet simulation
because of the advantages mentioned before. The flowsheet simulation begins by
specifying conditions of the flash unit. The cooling duty required to meet these
Chapter 4 Demethaniser flowsheet design and simulation methodology
127
operating conditions is evaluated based on the overall energy balance over the
whole flowsheet. If the feed cooling provided by ‘cold recovery’ from the top
product and the side reboiler is insufficient to achieve the flash temperature at the
selected pressure, external refrigeration is required; the refrigeration cycle
simulated with the short-cut model as explained in Section 4.4. The turbo-
expander, the compressor and the demethaniser are then simulated.
During the simulation of the flowsheet, the subroutines representing different units
are called sequentially, with the output of one unit serving as the input of the next.
The computation proceeds unit by unit from the feed to the product streams. The
recycle loops are torn at suitable points and estimated values are assigned to these
streams. Recycle loops are sequentially solved until the updated values of the tear
streams match the computed stream information. The recycle streams involved in
the flowsheet need to be solved iteratively in the sequential modular approach.
Some of the methods for the convergence of recycle loop are discussed in the next
section.
4.4.1 Recycle loop convergence
After various flowsheet subsystems have been modelled and partitioned, the next
step is to tear the recycle streams. This involves assigning values to the unknown
variables; then an iterative procedure is used, incorporating a suitable convergence
enhancement method to reduce the difference between the previous and currently
calculated values of the torn variables within a pre-assigned tolerance. Smith
(2005) notes that it is usual to specify a scaled error in the form:
Tolerancex
x)x(GTolerance ≤
−≤−
( 4.14)
where x is the initial estimate of the variable
G(x) is the resulting calculated value of the variable
Chapter 4 Demethaniser flowsheet design and simulation methodology
128
It is unlikely that the estimated values for the recycle stream will be within
tolerance for the initial estimate. If the convergence criteria are not met then the
convergence block needs to update the value of the recycle stream. The simplest
approach to this is a direct substitution or a repeated substitution (Smith, 2005). In
this approach, the sequence is calculated from an initial estimate, while the
calculated value then becomes the value for the next iteration. This substitution is
repeated until all convergence criteria are met.
G(x) = x
FlowsheetResponse
G(x)
xInitial Guess
G(x) = x
G(x)
xInitialGuess
Solution byLinearInterpolation
(a) (b)
Figure 4.9 Methods for recycle convergence a) Successive substitution
method, b) Wegstein method (Smith, 2005).
Figure 4.9 (a) shows a schematic representation of the successive substitution
strategy. The problem with this approach is that convergence requires many
iterations and some problems might fail to converge to the required tolerance
(Smith 2005).
Wegstein's method can be employed to accelerate convergence when the method
of successive substitution requires a large number of iterations. Figure 4.9(b)
illustrates the Wegstein method. At each iteration, the previous two iterates of G(x)
and x are extrapolated linearly to obtain the next value of x as the point of
intersection with the 450 line. Two direct substitution iterations are linearized. A
straight line equation can be written for the two iterations as:
Chapter 4 Demethaniser flowsheet design and simulation methodology
129
bax)x(G += ( 4.15)
Where a = slope of the line = 1
1
−
−
−
−
kk
kk
xx
)x(G)x(G
)(,)( 1−kk xGxG = calculated values of variables for iterations k and k-1
1, −kk xx = estimated values of variables for iterations k and k-1
Eq. (4.17) can be used for the calculation of the next estimate for recycle based on
the calculated value (G(xk)) and the previous value (xk).
[ ]kkkk x)x(G)q(xx −−+=+ 11 ( 4.16)
If q = 0 in Eq. (4.17), the method becomes direct substitution. If q < 0 acceleration
of the solution occurs. Bounds are normally set for the value of q to prevent
unstable behaviour (Smith, 2005).
In this work, the Wegstein method for the convergence of recycle streams is
employed as it requires fewer iterations for our system of demethaniser flowsheet.
4.5 Case Study
In this section the simulation model proposed in this chapter is applied to an
industrial demethanisation process. The case study has been adapted from Chebbi
et al. (2008). The main aim of this study is to validate the developed simulation
model to recover at least 98% of the methane to the top product and recover a
minimum of 70% of the ethane to the NGL product. The lean methane-rich sales
gas is used as fuel whereas the natural gas liquid (NGL) product serves as feed for
petrochemicals production.
Chapter 4 Demethaniser flowsheet design and simulation methodology
130
4.5.1 Problem inputs
In this work, components heavier than butane, as well as nitrogen, are artificially
eliminated from the plant feed (Chebbi et al., 2008) in order to reduce the
complexities that arise by the presence of trace components in the calculation for
establishing intersection of profiles for column design. The simplified composition
of the feed and the original composition from Chebbi et al. (2008) are presented in
Table 4.3.
Table 4.3 Feed gas composition - from Chebbi et al. (2008)* and simplified for
this case study
Component Actual feed* composition mole fraction
Simplified feed composition mol fraction
Nitrogen 0.01 0.000
Methane 0.76 0.784
Ethane 0.13 0.134
Propane 0.054 0.056
isobutane 0.026 0.027
isopentane 0.01 0.000
n-hexane 0.01 0.000
Total Flow (kmol/h) 4980 4980
The Peng-Robinson property prediction method, using the default parameters of
Aspen HYSYS 2006.5 is applied throughout. This equation of state is selected on
the basis of low to moderate pressure gas processing (Carlson, 1996). Table 4.4
provides the specified feed and product conditions.
Table 4.4 Specified temperature and pressure of feed and products (Chebbi et al., 2008)
Products Feed gas
Sales gas NGL
Temperature 37 oC 40 25
Pressure 60 bar 60 30
Chapter 4 Demethaniser flowsheet design and simulation methodology
131
The gas subcooled process (GSP) as given in Chebbi et al. (2008) is a typical
turboexpander based demethaniser process (Fig. 4.10). The feed gas is initially pre-
cooled by a side reboiler before entering a heat exchanger where it is cooled by the
top product from the demethaniser. The cold feed leaving the exchanger is further
cooled down by a chiller using an external refrigeration cycle. The exit stream is
fed to a flash unit, the liquid from which is sent to the demethaniser as the lower
feed, while the vapour is split into equal proportions. One portion is expanded and
sent as the upper feed to the demethaniser while the second portion is sent to the
top of demethaniser as an external reflux stream after being cooled by a heat
exchanger.
Figure 4.10 Process flowsheet diagram of a typical GSP demethaniser process
(Chebbi et al., 2008)
4.5.2 Results
The simulation of the process begins with the flash unit temperature, for which the
temperature and pressure are initially given (base case values). The cooling duty
required to meet the temperature is evaluated based on the overall energy balance
over the whole flowsheet.
Chapter 4 Demethaniser flowsheet design and simulation methodology
132
The complex distillation column is simulated using the modified boundary value
method explained in Chapter 3. In this case study, a two-feed column with one side
reboiler is used. The pressure in the column is assumed constant at 30 bar.
The process is simulated in Aspen HYSYS with the available data from Chebbi et
al. (2008). The data required for simulation of the demethaniser column is not
explicitly specified in the paper. The results from boundary value method are used
to initiate the column simulation in HYSYS. The column design results are
presented in Table 4.5. Figures 4.11 and 4.12 compare the molar flow profiles and
composition profiles in the column obtained from the BVM and rigorous HYSYS
simulation.
Table 4.5 Comparison of column simulation results: Boundary value design
method vs. HYSYS.
Results Units Boundary Value Model
HYSYS
Number of Stages - 28 28*
Top feed - 12 12*
Lower feed - 22 22*
Side reboiler duty (4th from bottom) kW 1500* 1500*
Distillate flow rate (kmol/h) kmol/h 4043 4044
Bottoms flow rate kmol/h 937 936
Reboiler temperature oC 30.5 30
Reboiler duty kW 1828 1845
CPU time sec 0.84 1.0
*indicates specified values
Chapter 4 Demethaniser flowsheet design and simulation methodology
133
0
1000
2000
3000
4000
5000
0 5 10 15 20 25 30
Number of stages (top to bottom)
Mola
r fl
ow
(k
mol/h
)
Vapour (HYSYS)
Liquid (HYSYS)
Vapour (BVM)
Liquid (BVM)
Rectifying
sectionMiddle
section
First
stripping
section
Second
stripping
Section
Figure 4.10 Molar flow profiles: Boundary value method vs. HYSYS
0.000
0.100
0.200
0.300
0.400
0.500
0.600
0.700
0 5 10 15 20 25 30
Number of stages (top to bottom)
Mo
le f
ract
ion
Methane(HYSYS)
Ethane (HYSYS)
Propane (HYSYS)
Methane(BVM)
Ethane (BVM)
Propane (BVM)
Rectifying
section
Middle
section
Second
stripping
section
First
stripping
section
Figure 4.11 Liquid composition profiles: Boundary value method vs. HYSYS
Chapter 4 Demethaniser flowsheet design and simulation methodology
134
The flowsheet simulation model predicts the recoveries of methane and ethane as
well as total power consumption. The simulation of the process in HYSYS
provides a rigorous basis for model validation. The simulation results for the
developed flowsheet model are in good agreement with those of the HYSYS, as
shown in Table 4.6. This indicates that the model accurately represents the overall
demethaniser process. The computation time for the simulation is 12.4 seconds on
an Intel® Core 2 Duo CPU 2.93 GHz processor with 4 GB RAM). The simulation
time for HYSYS is also presented in Table 4.6, where the time for setting up the
flowsheet unit models is not considered (usually setting up time is around 20-30
minutes depending on flowsheet complexity).
Table 4.6 Simulation results: Shortcut model vs HYSYS
* indicates specified values
4.6 Conclusions
In this chapter, a demethaniser flowsheet simulation approach is presented which
will be employed in a systematic framework for design and optimisation of
demethaniser flowsheets. Shortcut design models for different units of a complex
demethaniser flowsheet are developed. An integrated process simulation model is
presented which considers the demethaniser column and the heat recovery system
utilising multistream exchanger. The integrated process model is able to account
for interactions between the different unit operations in the process flowsheet.
Results Units Shortcut model HYSYS
Ethane recovery in NGL % 76.43* 76.43
Methane recovery in sales gas % 99.54* 99.54
Residue compressor power kW 2055 2042
Refrigeration power kW 2980 2950
Total power consumption kW 5035 4992
CPU time sec 12.4 20
Chapter 4 Demethaniser flowsheet design and simulation methodology
135
These interactions can be exploited for improving the performance of the overall
demethaniser system.
An industrially important process is simulated using the simplified models and
validated against rigorous simulation in HYSYS. The results show that the
developed model of the flowsheet is sufficiently accurate and is suitable for
applying in an optimisation framework for demethaniser flowsheet synthesis.
Chapter 5 Fixed structure flowsheet optimisation using nonlinear programming
136
CHAPTER 5 FIXED STRUCTURE FLOWSHEET
OPTIMISATION USING NONLINEAR
PROGRAMMING
Demethaniser flowsheets are normally proprietary designs. However, the majority
of these designs are based on similar flowsheet configurations with different
operating conditions. So this chapter discusses an approach for optimising a
demethaniser flowsheet with a fixed structure with the aim to optimise the
performance by appropriate choice of the operating conditions. A nonlinear
programming (NLP) technique is used for optimisation.
5.1 Degrees of freedom of demethaniser system - Optimisation
variables
The potential of a design variable to affect the performance of the process can be
identified using sensitivity analysis. The use of sensitivity analysis ascertains how
a given model output depends on the input parameters. The quantitative effects of
the design variable of interest on the key performance indicators can be identified.
If the value of the performance indicators varies significantly, it indicates that the
design variable of interest should be considered during optimisation.
In this work, sensitivity analysis is performed on the most commonly employed
demethaniser process for NGL recovery, the gas subcooled process (GSP). The
composition and condition of feed is obtained from Chebbi et al. (2008). The feed
gas is at 60 bar and 37 oC and its composition is given in Table 5.1. The sales gas
Chapter 5 Fixed structure flowsheet optimisation using nonlinear programming
137
is required at a pressure of 60 bar and a temperature of 40 oC, while the NGL
product is required at 25 bar.
Table 5.1 Feed gas composition - from Chebbi et al. (2008)
Component Feed composition
(Mole fraction)
Nitrogen 0.01
Methane 0.76
Ethane 0.13
Propane 0.054
isobutane 0.026
isopentane 0.01
n-hexane 0.01
Total Flow (kmol/h) 4980
AspenTech simulation package HYSYS® has been used in this work for
performing the sensitivity analysis. In order to achieve accurate results over the
range of temperature and pressure required in the process, an appropriate choice of
fluid package is critical (Elliot et al., 1996). Peng-Robinson is selected as the
equation of state for this process due to its accurate prediction of the process
components at the process conditions.
The flowsheet for the GSP process is shown in Figure 5.1. Dry feed gas flows
through a pre-cooler, where it is cooled to about –5 oC with the help of the
demethaniser top product. This pre-cooled feed then passes through the side
reboiler and the refrigeration cooler respectively. The side reboiler is used to
provide sub-ambient cooling through heat recovery from the column and reduce
the external refrigeration requirement. A simple refrigeration cycle using propane
as the refrigerant is also simulated in HYSYS to calculate the power requirements
in the compressor of the refrigeration cycle. The cooler lowers the temperature of
the feed to about -22 oC.
138
Chap
ter 5 F
ixed
structu
re flow
sheet o
ptim
isation u
sing n
onlin
ear pro
gram
min
g
Figure 5.1 HYSYS process flowsheet diagram of a typical GSP demethaniser process for NGL recovery
Chapter 5 Fixed structure flowsheet optimisation using nonlinear programming
139
The two phase stream produced as a result of cooling enters a vapour-liquid
separator where liquid and vapour are separated. The vapour product is split into
two streams (V1 and V2) in equal proportion, where stream V1 (acting as an
external reflux stream for the demethaniser) is then sent to the top of the
demethaniser after passing through a reflux cooler and a valve to reduce its
temperature and pressure to the desired conditions in the column. A reboiled
absorption column represents the demethaniser column with 30 stages including
the reboiler. The stream V2 is passed to an expander which reduces the pressure to
20 bar and enters the column as the top feed at the 12th stage. The power generated
by the expander is utilised in the compressor for sales gas.
The liquid from the vapour-liquid separator is sent directly to the column as the
lower feed on 23rd stage after passing through a throttle valve. Most of the heavier
components are recovered as NGL in the bottom product of demethaniser. The top
product, consisting mainly of methane, is used for cooling the reflux stream and
feed in the pre-cooler, and finally compressed to the required pipeline pressure of
60 bar in a recompressor.
The process flowsheet is reviewed to determine the available parameters, which
can be modified, i.e., to determine the number of degrees of freedom. Each of these
parameters is then taken one at a time, subjected to a case study (using the HYSYS
Databook tool) varying the selected parameter over a range which is usually
dependent on the process constraints. Once the effect of the parameter on the
performance indicators for the process has been noted, the parameter is reset to the
base case value. This process is then repeated for other decision variables.
The criteria that need to be met during the sensitivity analysis are listed below:
• Maximum methane to ethane ratio in the demethaniser bottom
product: 1.5% mol
• Minimum temperature approach in all heat exchangers: 2 °C
• 80% adiabatic efficiency for compressor and expander
Chapter 5 Fixed structure flowsheet optimisation using nonlinear programming
140
The decision variables selected in this work are the demethaniser column pressure,
temperature of the flash unit, split ratio of the vapour from the flash column and
the duty of the side reboiler. These variables are chosen on the basis of heuristics
and previous research (Diaz et al., 1996, Bandoni et al., 1989, Mehrpooya et al.,
2006).Various indicators can be used for evaluating the flowsheet performance. In
this work the ethane recovery and the total power requirements are the main
performance indicators. The effect of various process parameters on these
indicators is discussed in following sections.
5.1.1 Demethaniser operating pressure
The demethaniser operating pressure has a significant effect on the process
economics. Operating the column at higher pressures reduces the sales gas
compression power requirements. However, recovery of ethane is reduced at high
pressure as a result of a decrease in the relative volatility between the key
components. Therefore, an optimum value of the operating pressure needs to be
determined. In this work, the pressure is varied in the range 10 bar to 35 bar to
consider its effect on the flowsheet performance indicators.
Table 5.2 Effect of demethaniser operating pressure on flowsheet performance
Demethaniser operating pressure bar 10 15 20+ 25 30 35
Refrigeration power kW 941 941 941 941 941 941
Compressor power kW 6736 4964 3798 2944 2278 1737
Total power consumption kW 7677 5905 4739 3885 3219 2678
Overall ethane recovery % 86.6 84.3 81.1 77.5 73.3 68.8
Reboiler duty kW 411 980 1460 1882 2261 2610
+ indicates base case value
Figure 5.2 shows the effect of pressure on the total power consumption which is
the sum of compressor and refrigeration power requirements. By increasing the
column pressure from 10 to 35 bar, the total power is decreased significantly by
65%. This decrease is mainly due to the decrease in the power requirement in the
Chapter 5 Fixed structure flowsheet optimisation using nonlinear programming
141
sales gas compression. There is no change in the refrigeration power requirements
as evident from the results shown in Table 5.2.
Figure 5.2 Effect of demethaniser operating pressure on power consumption
Figure 5.3 illustrates that with the increase of column operating pressure from 10
to 35 bar, overall ethane recovery decreases from 86% to 68%, reflecting decrease
in the ease of separation, i.e. reduced relative volatility due to higher operating
pressure.
Figure 5.3 Effect of demethaniser operating pressure on ethane recovery
0
2000
4000
6000
8000
10000
0 5 10 15 20 25 30 35 40 Column operating pressure (bar)
To
tal
po
wer
co
nsu
mp
tio
n (
kW
)
50
60
70
80
90
0 5 10 15 20 25 30 35 40
Column operating pressure (bar)
Eth
an
e re
cov
ery
(%
)
Chapter 5 Fixed structure flowsheet optimisation using nonlinear programming
142
5.1.2 Flash temperature
The vapour to liquid ratio changes with the flash temperature. As a result, the
amount of lower feed entering the demethaniser is altered. A temperature range of
-35°C to -15°C is considered in this work, where results are shown in Table 5.3.
The upper limit of -15°C is chosen in order to meet the minimum approach
temperature criterion in the heat exchanger, a value of 2°C is applied in line with
the industrial practice (GPSA 2004). The lower limit of -35 °C follows the
selection of propane as refrigerant in the external refrigeration cycle (Smith, 2005).
Table 5.3 Effect of flash feed temperature on flowsheet performance
Flash feed temperature oC -35 -30 -25+ -20 -15
Refrigeration power kW 1765 1343 941 554 378
Compressor power kW 3871 3831 3798 3771 3749
Total power consumption kW 5636 5174 4739 4325 3927
Overall ethane recovery % 83.3 82.3 81.1 79.8 78.3
Reboiler duty kW 1928 1677 1460 1271 1109
+ indicates base case value
A decrease in the flash temperature mainly affects the power requirement of the
refrigeration cycle as the cooling load increases. The refrigeration power
consumption is shown to decrease by approximately 350% as the flash feed
temperature increases from -35 oC to -15 oC. There is also a slight decrease in the
power requirement of the recompressor with the decrease in the flash temperature
as shown in Table 5.3. The decrease of recompressor power is attributed to the fact
that the higher temperature results in more vapour being produced and hence, an
increase in the power produced in the turbo-expander. As the power produced by
the expander is used to drive the first compressor (Figure 5.1), so the net power
required by the recompressor to achieve the final specified pressure for sales gas is
decreased.
Chapter 5 Fixed structure flowsheet optimisation using nonlinear programming
143
Figure 5.4 Effect of flash temperature on total power consumption
Ethane recovery decreases by increasing the flash temperature from 83% to 78% as
shown in Figure 5.5. As the flash temperature is raised, less liquid is separated in
the vapour-liquid separator; hence the amount of lower feed is decreased. This has
an adverse effect on the ethane recovery.
Figure 5.5 Effect of flash temperature on ethane recovery in NGL
78
80
82
84
-40 -35 -30 -25 -20 -15 -10 Flash temperature (oC) o
Eth
an
e re
cov
ery
(%
)
0
2000
4000
6000
-40 -35 -30 -25 -20 -15 -10
Flash temperature (oC)
To
tal
po
wer
co
nsu
mp
tio
n (
kW
)
Chapter 5 Fixed structure flowsheet optimisation using nonlinear programming
144
5.1.3 Split ratio of vapour from flash column
The vapour from the flash column is divided into two streams as shown in Figure
5.1. The split ratio (external reflux to upper feed) is another important factor
affecting the flowsheet performance. In this work this ratio is increased from 0.2 to
0.7 as shown in Table 5.4.
Table 5.4 Effect of vapour split ratio on flowsheet performance
Flash vapour split ratio
(reflux/feed)
– 0.2 0.3 0.4 0.5+ 0.6 0.7
Refrigeration power kW 708 708 708 941 708 708
Compressor power kW 3517 3612 3699 3798 3862 3968
Total power kW 4225 4320 4407 4739 4570 4676
Overall ethane recovery % 50.3 60.8 71.0 81.1 88.6 92.1
Reboiler duty kW 1058 1154 1250 1460 1432 1716
Expander power generation kW 935 818 700 584 467 350
+ indicates base case value
The effect of the vapour split ratio on the flowsheet performance indicators is
shown in Figure 5.6 and 5.7. There is an increase in the total power consumption
which is mainly due to the increase in the compression power as the refrigeration
power stays constant (Table 5.4). A higher split ratio means less vapour (upper
feed) goes in the expander which leads to less power being generated in the
expander. As the power from expander is utilised in the compressor, hence the
power requirement of the recompressor is increased.
Chapter 5 Fixed structure flowsheet optimisation using nonlinear programming
145
Figure 5.6 Effect of vapour split ratio on power requirement
The ethane recovery is also shown to increase with the increase of the split ratio as
more reflux ensures a higher recovery in the bottom product. But this has a
penalty; a higher reboiler duty. The highest overall ethane recovery of 92% is
achieved at a vapour split ratio of 0.7, but at the cost of higher energy requirements
in both the column reboiler and the final compressor for the sales gas.
Figure 5.7 Effect of vapour split ratio on ethane recovery
0
20
40
60
80
100
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Split ratio
Eth
an
e re
cov
ery
(%
)
3000
3500
4000
4500
5000
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Split ratio
To
tal
po
wer
co
nsu
mp
tio
n (
kW
)
Chapter 5 Fixed structure flowsheet optimisation using nonlinear programming
146
5.1.4 Effect of side reboiler duty
The side reboiler in the demethaniser increases the overall energy efficiency by
reducing the main reboiler duty and pre-cooling the feed gas. The use of side
reboilers enables the heat recovery at temperatures lower than the temperature of
the column reboiler which consequently reduces the power required by the external
refrigeration system to pre-cool the feed to the desired temperature in the flash unit
(Figure 5.1).
For the sensitivity analysis, the side reboiler duty is increased from 0 to 2000 kW
and the effect of this increase on the performance indicators is shown in Table 5.5.
The refrigeration power is shown to decrease with the increase of side reboiler
duty (Figure 5.8). The compressor power and ethane recovery do not change with
the change in the duty of the side reboiler.
0
400
800
1200
1600
0 500 1000 1500 2000 2500
Side reboiler duty (kW)
Ref
rig
era
tio
n p
ow
er (
kW
)
Figure 5.8 Effect of side reboiler duty on refrigeration power requirement
Table 5.5 Effect of side reboiler duty on flowsheet performance
Side reboiler duty kW 0 500 1000+ 1500 2000
Refrigeration Power kW 1259 983 941 432 157
Compressor Power kW 3780 3780 3798 3780 3780
Total Power kW 5039 4763 4739 4212 3937
Overall ethane recovery % 80.3 80.3 81.1 80.2 80.2
Reboiler Duty kW 2342 1843 1343 845 347
+ indicates base case value
Chapter 5 Fixed structure flowsheet optimisation using nonlinear programming
147
5.1.5 Summary of decision variables
The key variables affecting the demethaniser process performance have been
identified by sensitivity analysis. The results show that there is a trade-off between
ethane recovery and the total compression power as an increase in one increases
the other when the selected parameters are varied. Therefore, an objective function
needs to be defined which can account for the trade-off between power consumed
and ethane recovery. The design variables are then varied to maximise the annual
profit or minimise the annualised cost.
Having identified the significance of each variable and its effect on the overall
processes performance, an appropriate optimisation technique can then be selected
to determine the optimal values of these variables to minimise or maximise the
objective function.
5.2 Process optimisation
The optimisation of a process involves the minimisation or maximisation of an
objective function by varying the process variables, subject to satisfying the
simulation model as well as some practical process-related linear and nonlinear
constraints. A suitable algorithm is also required to solve the optimisation problem.
Mathematically, the optimisation problem is represented as
( )z,ufMinz
( 5.1)
Subject to ( ) 0=z,uE ( 5.2)
( ) 0≤z,uI ( 5.3)
Where: ( )z,uf = nonlinear objective function
( )z,uE = equality constraints representing mass and energy balances, and
equilibrium expressions
( )z,uI = inequality constraints representing design specifications, operational and
safety restrictions and logical constraints
u = vector of dependent variables
z = vector of independent variables
Chapter 5 Fixed structure flowsheet optimisation using nonlinear programming
148
5.2.1 Objective function
Mathematically, finding an optimal solution requires the minimisation or
maximisation a specified objective function. In the process design stage, the
energy and cost investment are more easily quantified and may be of overriding
significance than other factors (i.e. safety, reliability, etc) because the economic
viability is crucial (Smith, 2005). The goal of the optimisation process in this work
is to maximise the profit from the process while respecting certain constraints,
which involve the maximisation of the product throughputs and/or minimisation of
operating costs.
The objective function for a fixed structure flowsheet optimisation is
Max ( )x,uP ( 5.4)
where
P = Annual profit
u = Optimisation variables
x = Process constraints
The annual profit is defined as:
ACCCPRP opRM −−−= ( 5.5)
where PR is the annual revenues from products, RMC is annual cost of the raw
materials, opC is the annual operating costs and AC is the annualised capital cost of
the equipments involved.
The product revenues PR is defined by
kodPr
k
kodPr FPPR ∑= ( 5.6)
where kodPrP is the sale price of component k in the product stream and k
odPrF is
the flow rate of component k in the product stream.
Chapter 5 Fixed structure flowsheet optimisation using nonlinear programming
149
The raw material cost is given by
kFeed
k
kFeedRM FPC ∑= ( 5.7)
where kFeedP refers to the material cost of component k in the feed stream and k
FeedF
is the flow rate of component k in the feed stream.
The operation costs (Cop) are defined as
∑=i
iutiop GOCC ( 5.8)
where, utiOC is the cost associated with the use of utility I and iG is the flow rate
capacity of utility i. The utilities include cooling water, electric power and LP
steam. The cost of these utilities cost is calculated in Appendix B. Annual
operating hours are 8600
Finally capital costs are defined as
∑=i
iACAC ( 5.9)
where ACi is the annualised capital cost for equipment i.
In this work, the capital cost of the equipments is calculated by the bare module
cost approach presented by Turton et al. (2008). A time period of 3 years and 5%
interest rate is assumed to estimate the annualised cost. The details of the method
to calculate the annualised capital cost is presented in Appendix B.
The volatility in the price of the natural gas and NGL over the last 5 years is a
significant issue facing the natural gas industry and energy companies. Price
volatility contributes to an uncertain climate for energy companies, consumers and
regulators. Figure 5.9 indicates the comparison of price movements of various
fuels over a three year period. The prices for natural gas and NGL are shown to
follow the same trend as that of crude oil. The ethane and NGL composite (C2+)
are higher than the raw natural gas from a wellhead.
Chapter 5 Fixed structure flowsheet optimisation using nonlinear programming
150
Figure 5.9 Price comparison of natural gas, crude oil , ethane and NGL (EIA
2011)
5.2.2 Process constraints
The various constraints applied in the optimisation of the demethaniser process are
listed and discussed below:
- Purity specification of sales gas
- Maximum methane mole fraction in demethaniser bottom product
- A lower bound on ethane recovery in the overall process
- Minimum approach temperature in heat exchangers
- Minimum amount of the external reflux stream
Each of these constraints has its own significance. The purity specification of sales
gas is important as it directly affects the heating value of the product gas, which is
normally specified by the customer. The methane specification in bottom product
is used by the boundary value method for column design. The lower bound on
ethane recovery is employed as it is usually specified externally. A minimum
approach temperature of ensures a finite heat exchanger area and avoids a
Chapter 5 Fixed structure flowsheet optimisation using nonlinear programming
151
temperature cross. Also, as the reflux to the column is provided by an external
stream from the flash column, another nonlinear constraint is imposed on the
minimum amount of the external reflux stream, as otherwise the top of the column
would dry up.
5.2.3 Optimisation algorithm
Successive quadratic programming (SQP) is selected as the optimisation algorithm
for a fixed structure demethanisation process. SQP is appropriate for solving
smooth nonlinear optimisation problems when the problem is not too large and
functions and gradients can be evaluated with sufficiently high precision (Hock
and Schittkowski, 1983).
For the SQP method, all the functions, including the objective function ( )xf and
constraints ( )xE , ( )xI must be continuously differentiable. The solution procedure
involves formulating and solving a quadratic sub-problem in each iteration. The
objective function and the constraints can be reformulated into one equation, which
is the Lagrange function, while the search direction is based on Newton's method.
The sub-problem is obtained by linearising the constraints and approximating the
Lagrangian function quadratically (Hock and Schittkowski, 1983).
Equations (5.1 to 5.3), representing the generic objective function and process
constraints, can be further rearranged into a Lagrange function (See Biegler 1997
references within):
( ) ( ) ( ) ( )( )2
2
1sxIxExf,,xL
TT −++= µλµλ ( 5.10)
Where:
µ,λ = vectors of Lagrange multipliers for equality and inequality constraint
functions respectively
Chapter 5 Fixed structure flowsheet optimisation using nonlinear programming
152
=s vector of constants included in the Lagrange function to avoid discontinuities
when the inequality constraint functions are modified into equality constraint
functions .
The quadratic function ( )pQ is given by:
( ) ( )λλλ xHgpQ minimiseTT
2
1−=
( 5.11)
subject to ( ) 0=λxJ ( 5.12)
Where:
g = the gradient vector of ( )xf at current value of x
( )xH = the positive definite approximation of the Hessian matrix of the Lagrange
function given by ( )
2
2
x
,,xL
∂
∂ µλ
( )xJ = the Jacobian matrix of the constraint functions evaluated at current value of
x , given by ( ) ( )
x
xIand
x
xE
∂
∂
∂
∂
This QP subproblem solution is used to form a search direction dk for a line search
procedure. In other words, the solution is used to form the next iterate
kkkk dxx α+=+1 ( 5.13)
where ix and id are the vectors of the iteration and kα is the step length parameter
The step length parameter αk is determined by an appropriate line search procedure
so that a sufficient decrease in a ‘merit’ function is obtained. The merit function is
formed from the objective function and a weighted sum of the constraint
infeasibility functions (Biegler et al., 1997). The initial iteration sets the step length
to a moderate value when the optimisation is closer to the optimum, however, the
step length can be reduced to converge the optimisation problem rapidly. The
optimisation problem can be terminated when the convergence criteria are satisfied
and the objective function has been maximised or minimised within the specified
tolerance.
Chapter 5 Fixed structure flowsheet optimisation using nonlinear programming
153
5.2.4 Fixed structure optimisation approach
The fixed structure optimisation of the flowsheet starts by defining a flowsheet
structure. The optimisation variables are then selected. The base case flowsheet is
simulated at initial conditions using the shortcut design models and sequential
modular approach as explained in Chapter 4. The size and cost of the flowsheet
equipments are calculated by functions developed in Matlab. The simulated
flowsheet is then evaluated in terms of the annual profit. For the SQP algorithm, an
optimisation function ‘‘fmincon’’ in Matlab is employed. The optimisation
framework is highlighted in Figure 5.10.
Figure 5.10 Optimisation framework for a fixed structure flowsheet
Objective function
Constraints
Variables
• Complex column model
• Heat recovery model in
multistream exchanger
• Refrigeration model
• Cost models
NLP optimiser
(SQP)
Flowsheet structure
Optimum flowsheet
Base case with
initial conditions
Chapter 5 Fixed structure flowsheet optimisation using nonlinear programming
154
5.3 Case study
A case study is presented to illustrate the design of an optimised NGL recovery
system by the application of the proposed optimisation framework. This case study
is based on the US patent ‘‘Process and apparatus for separation of hydrocarbons’’,
number 7357003 assigned to Toyo Engineering Corporation (Ohara et al., 2008).
Figure 5.11 illustrates the process.
In this work, the trace components nitrogen and carbon dioxide are artificially
eliminated from the feed in order to reduce the complexity introduced in the
calculation for composition profiles. The resulting simplified composition of the
feed and the original composition from the patent are presented in Table 5.7.
Table 5.6 Specified temperature and pressure of feed and products (Ohara et al., 2008)
Products
Feed gas Sales gas NGL
Temperature 17 oC 40 35
Pressure 62.4 bar 38 30
Table 5.7 Feed gas composition from patent (Ohara et al., 2008) and simplified for this case study
Component Original feed
composition
Simplified feed
composition
Nitrogen 0.010 0.00
Carbon dioxide 0.005 0.00
Methane 0.894 0.908
Ethane 0.049 0.049
Propane 0.022 0.023
isobutane 0.013 0.013
isopentane 0.006 0.0062
Total Flow (kmol/h) 13700 13700
155
Chap
ter 5 F
ixed
structu
re flow
sheet o
ptim
isation u
sing n
onlin
ear pro
gram
min
g
Figure 5.11 Process flowsheet diagram of multiple reflux stream hydrocarbon recovery process (Ohara et al., 2008)
113
Sales gas
Reboiler
NGL
C-102
SR1
SR2
112
111
110
109 108 106
105
104
107
103
E-103 R-101 C-100
B-100
V-101 V-100
E-101 R-100
Demethaniser
T-100 E-100
Feed gas
C-101
Chapter 5 Fixed structure flowsheet optimisation using nonlinear programming
156
The feed gas is cooled down to around -26 oC in the first multistream exchanger
(E-100) by heat exchange with the residue gas (120) and the lower side reboiler
(SR1) which is at a temperature of approximately -23 oC. The outlet stream (101)
is then further cooled down by using propane refrigerant (R-100) to -37 oC before
entering the second multistream exchanger (E-101). This exchanger utilizes the
second side reboiler (SR2) and the residue gas as the cold media.
The outlet stream from E101 (103) is a two-phase mixture which is separated into
the liquid fraction (104) and the vapour fraction (105) in a separator (V-100). The
liquid fraction is sent to the demethaniser as the lower feed. The vapour stream is
sent to an expander (B-100) where the pressure is decreased to 30 bar and useful
energy is generated. The outlet stream from the expander (106) is partially
liquefied and is separated into vapour and liquid streams in the second separator
(V-101). The liquid (107) is delivered to the column as the middle feed while the
vapour (108) is split into two parts: 60 % of stream 108 forms the top feed of
demethaniser while the rest is compressed to 62 bar. The compressed stream (111)
is then cooled and condensed in E103 by external refrigeration and demethaniser
top product respectively. The liquid stream exiting the exchanger (E-103) is then
depressurised to 30 bar and sent to the top of the demethaniser as a reflux stream
(112). The demethaniser recovers the ethane in the bottom product, while
separating the methane in the top product (113).
In the case study, the sale price of the products are obtained from US Energy
Information Administration (EIA 2011). The prices used are for November 2010
data. The sale gas, ethane and NGL (excluding ethane) prices are 4 $/GJ, 8 $/GJ
and 12 $/GJ respectively. The price of well head natural gas is 3.80 $/GJ (EIA
2011).
5.3.1 Process constraints
Various linear and nonlinear constraints are included in the formulation of the
optimisation problem. The nonlinear constraints are the specification of the
maximum allowed methane in the NGL product, the minimum ethane recovery in
Chapter 5 Fixed structure flowsheet optimisation using nonlinear programming
157
NGL and the limits of the optimisation variables, as shown in Table 5.8. The linear
constraints are the mass and energy balances of the process. The summation of
vapour split fractions to be equal to unity is also added as a linear constraint. These
constraints are:
• Ethane recovery in NGL %85≥
• Methane to ethane ratio in NGL 020.≤
• Minimum approach temperature in E-101, E102 and E-103 C.o51≤
• 1=+ ur xx
where xr is the fraction from the vapour splitter used as reflux and xu is the fraction
from splitter used as column feed.
5.3.2 Optimisation variables
The optimisation variables are selected on the basis of sensitivity analysis. The
objective function is the annual profit from the process as explained in Section
5.2.1. The decision variables which are manipulated for the optimisation of the
process are discussed in Table 5.8. The lower and upper bounds and the base case
values are also shown.
Table 5.8 Values and bounds of optimisation variables
Decision variable
Description Unit Lower bound
Upper bound
Base case
x1 Demethaniser operating pressure
bar 15 35 28
x2 First flash separator temperature
oC -40 -60 -40
x3 Split ratio (Reflux to upper feed)
0.2 0.8 0.5
x4 Side reboiler 1 duty kW 500 2000 1500
x5 Side reboiler 2 duty kW 1000 3000 1000
x6 Reflux compressor outlet pressure
bar 30 80 62
Chapter 5 Fixed structure flowsheet optimisation using nonlinear programming
158
5.3.3 Results
The process is simulated using the methodology presented in Chapter 4. The
conditions from the base case are used as the initial value for the simulation and
subsequent optimisation. The flowsheet simulation model calculates the recovery
of key components and total power requirements. The validation of the flowsheet
model is done by simulating the process in Aspen HYSYS. Table 5.9 compares the
simulation results from the shortcut model and HYSYS. The computation time for
the simulation using the simplified model developed in Chapter 4 is 22.4 seconds
on an Intel® Core 2 Duo CPU 2.93 GHz processor with 4 GB RAM). The
simulation time for HYSYS is also presented in Table 5.9, where the time for
setting up the flowsheet unit models is not considered.
Table 5.9 Simulation results of shortcut model and HYSYS
Results Unit Model HYSYS
Number of stages in column - 40 40*
Methane recovery in Sales Gas % 99.94* 99.95*
Ethane recovery in NGL product % 90.62 90.65
Reboiler duty kW 5740 5775
Reflux compressor power demand kW 2134 2155
Residue gas compressor power demand kW 1004 1028
Refrigeration system power demand kW 3585 3612
CPU time sec 22.4 30
* indicates specified values
The simulation model is then employed in the optimisation framework (Figure
5.9). The results of the optimisation are highlighted in Table 5.10. The overall
annual profit is shown to increase from 190 MM$ to 198 MM$. Thus the
optimised flowsheet shows an increase in annual profit of around 4%, compared to
the base case. The increase in profit is due to both the decrease in the total power
requirements of the flowsheet, and the increase in overall ethane recovery.
Chapter 5 Fixed structure flowsheet optimisation using nonlinear programming
159
Table 5.10 Comparison of optimisation results with base case
Total shaft power required deceased from 6.7 MW to 4.5 MW (33%). As utility
cost mainly comprises the electric power cost, this reduction in power
requirements has a pronounced effect on the overall objective function. Reboiler
duty is shown to decrease by 60%, owing to increased heat recovery by side
reboilers (Table 5.11). As the capital cost of the compressors and drivers are
directly dependent on the shaft power, so a decrease in power requirement gives a
lower capital cost. This eventually lowers the annualised capital cost as shown in
Table 5.10. The computation time for the optimisation using SQP is 24 minutes
and 38 seconds on an Intel® Core 2 Duo CPU 2.93 GHz processor with 4 GB
RAM).
Table 5.11 Optimisation variables – Base case vs. optimised case
Results Unit Base case Optimised case Residue compressor power kW 1004 1810
Reflux compressor power kW 2134 1080
Refrigeration power kW 3585 1590
Total shaft power requirement kW 6723 4480
Ethane recovery in NGL % 90.62 94.20
Reboiler duty kW 5740 2265
Annualised capital cost MM$ 13.94 12.42
Utility cost MM$ 11.38 6.62
Annual profit MM$ 190.4 198.24
Decision variable Unit Base case Optimised case
Demethaniser operating pressure bar 24 28
First flash separator temperature oC -40 -48
Split ratio (Reflux to upper feed) - 0.5 0.35
Side reboiler 1 duty kW 1500 2800
Side reboiler 2 duty kW 1000 2200
Reflux compressor outlet pressure bar 62 54
Chapter 5 Fixed structure flowsheet optimisation using nonlinear programming
160
Table 5.11 compares the values of optimisation variables for the base case and the
optimised case. The results indicate that operating the demethaniser at a lower
pressure enhances the separation efficiency and hence the recovery of ethane is
increased. However, this also results in a higher compression power in the sales
gas compressor. Another important optimisation variable is the outlet pressure of
the reflux compressor. Optimisation results in a lower outlet pressure of 54 bar,
which not only decreases the compression power requirements but also decreases
the external refrigeration requirement as the cooling duty is also decreased.
Table 5.11 also indicates a lower vapour split ratio in the optimum case compared
to the base case. This is contrary to the results obtained by the sensitivity analysis,
where both the ethane recovery and power requirements are shown to increase with
the increase of split ratio. However, in this case study an additional compressor and
refrigeration cooler is present compared to the gas subcooled process studied for
sensitivity analysis. The lower split ratio decreases the flowrate of reflux stream
entering the compressor and subsequent cooler, thus decreasing the overall power
requirements as shown in Table 5.10.
5.3.4 Effect of feed and product price changes on optimisation
As discussed in Section 5.2.1 the prices of feed gas and the NGL product is quite
volatile and varies generally with the price of crude oil. The calculation for the
price of electric power required for the plant is also based on natural gas fuel as
explained in detail in Appendix B. In order to study the effect of variation in prices
of raw materials, products and power, another range of data is selected based on
the historical prices as shown in Figure 5.9. The data for July 2008 is selected
which represents the values before the world’s economic recession. Table 5.12
indicates the prices.
Chapter 5 Fixed structure flowsheet optimisation using nonlinear programming
161
Table 5.12 Prices of feed and products
Component Price ($/GJ)
Feed gas 10
Sales gas 12
Ethane 18
NGL 22
The price of power is computed from Eq. B12 (Appendix B) and is $ 0.153 /KW.
The cooling water and steam cost are computed in the same manner for the new
price of natural gas. Table 5.13 presents the optimisation results for the new values
of the raw materials and products. The annualised profit in this case is shown to
increase from 394.22 MM$/yr to 410.62 MM$/yr. Thus the optimised flowsheet
shows an increase in annual profit of around 4.2 %, compared to the base case.
This percentage increase is similar to the first case with lower prices of both the
feed gas and NGL product.
The values of optimisation variables for the base case and the optimised case in
this scenario with different prices are presented in Table 5.14. The values are
similar to the previous case which shows that the price variations in the feed,
products and utilities do not affect the optimisation results significantly.
Chapter 5 Fixed structure flowsheet optimisation using nonlinear programming
162
Table 5.13 Comparison of optimisation results with base case
Table 5.14 Optimisation variables – Base case vs. optimised case
The case study successfully demonstrates that the developed optimisation
methodology for a fixed structure flowsheet is able to accommodate the complex
interactions among the various units and find the optimal values for the important
decision variables.
Results Unit Base case
Optimised case Residue compressor power kW 1004 1906
Reflux compressor power kW 2134 1034
Refrigeration power kW 3585 1320
Total shaft power requirement kW 6723 4260
Ethane recovery in NGL % 90.62 93.8
Reboiler duty kW 5740 2186
Annualised capital cost MM$/yr 13.94 12.20
Annual utility cost MM$/yr 13.42 7.18
Product revenues MM$/yr 1512.4 1520.82
Annual profit MM$/yr 394.22 410.62
Decision variable Unit Base case Optimised case
Demethaniser operating pressure bar 24 27.5
First flash separator temperature oC -40 -46
Split ratio (Reflux to upper feed) - 0.5 0.35
Side reboiler 1 duty kW 1500 2680
Side reboiler 2 duty kW 1000 2100
Reflux compressor outlet pressure bar 62 54
Chapter 5 Fixed structure flowsheet optimisation using nonlinear programming
163
5.4 Conclusions
In this chapter, an optimisation algorithm for demethaniser flowsheets of a fixed
structure is presented. Sensitivity analysis has been used to identify the potential of
a design variable for changing the objective function. From the sensitivity analysis
it can be seen that there are strong interactions between various decision variables
in the demethaniser flowsheet. Simultaneous optimisation of these variables is
needed to create cost-effective design solutions while maintaining the performance
specifications of the process.
The optimisation procedure uses a nonlinear programming technique, the
successive quadratic programming to maximise the annual profit of the process.
The results indicate that the proposed methodology offers an effective approach for
design and optimisation of demethaniser flowsheets with a defined structure. A
case study is presented that applies the developed optimisation approach to a
commercial process. The results indicate an increase of 4% in the annual profit.
The optimisation approach presented in this chapter, however, cannot take into
account the various structural options of the demethaniser flowsheet. Moreover,
NLP optimisation can get trapped in local optima and may not find the best
solution for the problem. So in order to avoid these conditions a stochastic
optimisation technique will be applied in Chapter 6 to accommodate the structural
options in the flowsheet and achieve a near global optimum solution.
Chapter 6 Demethaniser flowsheet synthesis by stochastic optimisation
164
CHAPTER 6 DEMETHANISER FLOWSHEET
SYNTHESIS BY STOCHASTIC
OPTIMISATION
The synthesis of process flowsheets involves the selection of the structure, which
for given reactants and product specifications, promises the best performance
typically in terms of highest profit or the lowest cost. In order to determine the
optimal structure of the flowsheet, a superstructure may be developed that shows a
wide range of the potential interconnections between flowsheet units. The optimal
configuration is then determined from many alternatives through structural and
parametric optimization of the superstructure.
6.1 Superstructure representation for demethaniser flowsheet
In this research work, a generalised superstructure is developed taking into account
the important features found in demethaniser flowsheets for NGL recovery. This
superstructure includes various process units, including one or more flash units
operating at various pressures, heat recovery from residual gas and side reboilers,
external refrigeration, and an internal reflux stream. The simultaneous optimisation
of these structural options along with operating conditions, such as column
pressure, flash temperature, etc., can lead to cost-effective and energy-efficient
flowsheets. Figure 6.1 shows a basic expansion-based demethaniser flowsheet
including a range of structural options indicated by dotted lines.
165
Chap
ter 6 D
emeth
aniser flo
wsh
eet synth
esis by sto
chastic o
ptim
isation
Figure 6.1 Superstructure for demethaniser flowsheet synthesis
D
C
B
A
Reflux exchanger
Flash unit (High pressure)
2nd Flash unit (Low pressure)
Internal reflux stream
NGL
Compressor
Sales gas
Demethaniser
Side reboilers
Splitter
Reboiler
Expander
Recompressor
Multistream exchanger
Feed gas
External refrigeration
Chapter 6 Demethaniser flowsheet synthesis by stochastic optimisation
166
The various structural options indicated in the demethaniser superstructure are
explained below.
A. Use of a second flash unit
The low pressure stream from the expander is normally sent to the demethaniser as
the top feed, but in some process variations, it can be sent to another flash unit
where it is separated into liquid and vapour fractions. The liquid is sent to the
column as a feed while the vapour is mixed with the stream coming from the first
flash unit and enters the top of the column as an external reflux stream.
B. Side reboilers
The use of a side reboiler in the demethaniser enhances the overall energy
efficiency by not only decreasing the main reboiler duty, but also reducing the
external refrigeration required to pre-cool the feed. In the superstructure, the dotted
lines in the multistream exchanger represent the presence of side reboilers in the
flowsheet.
C. Internal reflux stream
The liquid entering the top of the demethaniser is provided by an external reflux
stream obtained from a high pressure flash unit. In some cases, a portion of the top
product can also be used as an additional reflux stream as indicated in Figure 6.1.
D. Use of external refrigeration cycle
The use of an external refrigeration cycle for the cooling of the feed gas is also
embedded in the superstructure. The external refrigeration requirement depends on
the heat recovery within the process. The refrigeration system is designed
according to the shortcut method explained in Section 4.3.
6.1.1 Summary
The optimisation of demethaniser flowsheets is complicated by the interaction of
non-linear models for the different flowsheet units as discussed in Chapter 4. There
Chapter 6 Demethaniser flowsheet synthesis by stochastic optimisation
167
are both continuous decisions (operating variables), integer variables (number of
side reboilers) and binary integers (existence of units) in the flowsheet
superstructure. Demethaniser flowsheet synthesis problem can thus be formulated
as a mixed integer nonlinear programming (MINLP) problem. The MINLP
formulation accounts for both non-linear models and discrete variables describing
the process topology. MINLP problems are typically expressed as following
(Adjiman et al., 1998):
miny,x
( )y,xf ( 6.1)
Subject to
( ) 0=y,xh ( 6.2)
( ) 0≤y,xg ( 6.3)
where
- f(x, y) is a nonlinear objective function representing the performance criterion
- x is a vector of continuous variables representing flowrates, temperatures and
pressures of process streams and sizing of process units
- y is a vector of integer variables representing process alternatives
- ( )y,xh are the equality constraints representing mass and energy balances, and
equilibrium expressions
- g(x, y) are nonlinear constraints representing design specifications, operational
and safety restrictions and logical constraints
6.2 Choice of optimisation method
The solutions of integrated process synthesis problems needs to take into account
the limitations and applicability of optimisation technique. Generally, optimisation
tools start from an initial guess, search through the solution space, and converge to
an 'optimal' state. Deterministic methods in the form of MINLPs are most
frequently employed, where gradient information is used to evolve the search.
Chapter 6 Demethaniser flowsheet synthesis by stochastic optimisation
168
MINLP problems are considered to be one of the most difficult optimisation
problems, as discussed by Grossmann and Biegler (2004). The presence of non-
linear terms in the modelling equations for various units and the combinatorial
nature introduced by discrete variables results in a complex optimisation problem.
Bartfeld and Aguirre (2002) emphasized the importance of an efficient
initialization procedure to enhance the robustness of MINLP optimisation.
Conventional methods for solving MINLP problems involve the decomposition of
the problem into NLP and MILP sub-problems, which are then solved iteratively.
Among the conventional methods, the most commonly used are Branch and
Bound, Generalised Benders Decomposition and Outer Approximation methods. A
comprehensive review of these methods can be found in Grossmann and Daichendt
(1996), Biegler et al. (1997) and Grossmann and Biegler (2004).
The search algorithms used in the above methods for the NLP subproblems are
generally deterministic and need derivative calculations at each step. Grossmann
and Biegler (2004) noted that these search algorithm are likely to converge to a
local optimum instead of the global optimum. Moreover, NLP methods require a
good initial guess to ensure the convergence of the solution. These conventional
methods also require significant amount of computational time and memory; as for
every NLP subproblem solution, a linear approximation must be formulated and
solved as a MILP subproblem (Grossmann and Biegler, 2004). These shortcomings
of the traditional deterministic optimisation methods make them unsuitable for the
proposed synthesis framework. The use of gradient information limits the
application of these methods to problems with continuous and differentiable
functions.
An alternative for solving the problems associated with the conventional MINLP
methods is to use the stochastic optimisation methods, which were devised to
overcome non-convergence issues and reduce mathematical complexity (Hedar
and Fukushima, 2006). These methods do not require detailed problem formulation
or derivatives of the problem. The search for the optimum is based exclusively on
the values of the objective function at different points of the search space. Arora
(2004) showed that the stochastic optimisation techniques are effective in escaping
local optima by incorporating control mechanisms in the form of logical
Chapter 6 Demethaniser flowsheet synthesis by stochastic optimisation
169
conditions. They are also useful for finding globally optimal solutions for complex
non-linear and non-convex problems as compared to deterministic methods (Arora,
2004).
Stochastic methods perform a global search over all design options included in the
superstructure and the potential of the process with respect to a given objective
function is revealed. Paules and Floudas (1992) noted that although stochastic
optimisation will not converge on a local optimum, a solution within the global
solution space can be obtained that is close to the required ‘‘target’’ of the process.
If required, the resulting solution can be fine-tuned using gradient based
deterministic optimisation methods (Grossmann et al., 2000).
Commonly applied stochastic methods in process engineering problems include
Genetic Algorithms (GA) and Simulated Annealing (SA). GA methods use
techniques inspired by evolutionary biology such as inheritance, mutation,
selection, and crossover (Leboreiro and Acevedo, 2004). The search process of this
algorithm involves the selection of ‘individuals’ with highest ‘fitness’ generated by
a structured, yet random exchange of information (Mitchell, 2009). Various studies
have been reported in literature for the use of genetic algorithms for separation
system optimisation (Low and Sorensen, 2004, Boozarjomehry et al., 2009, Wang
and Smith, 2005). However, the drawback of GA is the large computational time
for estimating the required number of generations in order to obtain a solution to
within a certain level of accuracy (Wang et al., 2004).
Simulated Annealing (SA) is another stochastic optimisation algorithm, which has
been widely applied for process design due to its ease of implementation and its
robustness (e.g. Flouquet et al., 1994 ; Athier et al., 1997 ). However, simulated
annealing also requires a large computation time to search for solutions in the
vicinity of global optimum. Floquet et al. (1994) noted that SA will converge to a
globally optimal solution given an infinitely large number of iterations and a
temperature schedule that converges to zero sufficiently slowly.
The implementation of simulated annealing algorithm is relatively easier in a
systematic optimisation framework in comparison to other stochastic optimisation
methods (Zhong and Gang, 2009). SA offers flexibility with respect to the number
Chapter 6 Demethaniser flowsheet synthesis by stochastic optimisation
170
and type of optimisation variables, including continuous and discrete variables
(Vanlaarhoven and Aarts, 1987). In contrast to deterministic optimisation methods,
SA is less prone in converging to suboptimal solutions by not relying on local
gradient information. The robustness of SA makes it appropriate to account for
non-convex model equations. Therefore, in this work, stochastic optimisation is
carried out using simulated annealing. The simulated annealing algorithm is
described in detail in the next section.
6.3 Simulated annealing
The simulated annealing algorithms have been developed using an analogy to the
physical annealing of metals, where a metal in molten state at a very high
temperature is cooled down very slowly. In its molten state, metal atoms are
distributed randomly. When the system, i.e. the metal, is cooled, it reaches a state
of minimum energy. If the annealing process is carried out slowly such that at any
point in time the system is close to thermodynamic equilibrium, then the system
may reach a stable crystalline structure with minimum energy. However, if cooling
does not take place slowly enough or if the initial temperature is not high enough,
then the metal forms a glass-like metastable structure with higher energy than the
crystalline state. The analogy between the cooling process and the mathematical
optimisation become obvious when the undesirable metastable state and the
minimum energy crystalline structure are interpreted as a local and global
minimum, respectively (Kirkpatrick et al., 1983).
Metropolis et al. (1953) proposed an annealing algorithm to find the equilibrium
configuration of a group of atoms at a given temperature. In this algorithm, a
simulation is carried out at each step giving an atom a small random displacement
and computing the change in energy ( E∆ ). If the change in energy is negative,
then the displacement is accepted and used as starting point for the next step.
However, if the change in energy is positive, it is accepted with a probability given
by Eq.( 6.4):
Chapter 6 Demethaniser flowsheet synthesis by stochastic optimisation
171
=
aaTk
EexpP
∆
( 6.4)
Where Ta is the annealing temperature of the system.
ka is the Boltzman constant, 1.38 x 10-23 JK-1
Eq. 6.4 shows that with a decrease in temperature of the system, the probability of
accepting a positive change in energy also decreases. The system temperature
decreases according to the cooling schedule evaluating the new perturbations
during the cooling process. The algorithm terminates when the temperature of the
system reaches zero or the temperature of the solid state (Metropolis et al., 1953).
This work employs the simulated annealing algorithm of Kirkpatrick et al., (1983)
as given by Choong and Smith (2004), which is represented in Figure 6.2. The
simulated annealing process starts with an initial feasible solution at a reasonably
high value of the annealing temperature. The annealing temperature serves as a
control parameter for optimisation. The initial trial solution is modified by a
random change, known as a random move. The objective function of the new
solution is calculated and compared with that of the current trial solution. The
acceptance or rejection of the objective function depends on the magnitude of the
change and the current temperature in the cooling schedule. The modification
made to the current trial solution is then either accepted or rejected based on the
Metropolis acceptance criterion. This process of modification, simulation and
evaluation is repeated a number of times determined by the parameter known as
the Markov chain length, to obtain a set of sample solutions. Once several
candidate solutions have been obtained, the annealing temperature is reduced. This
cycle is continued until the termination criterion is satisfied.
Chapter 6 Demethaniser flowsheet synthesis by stochastic optimisation
172
Figure 6.2 Flowchart for simulated annealing algorithm (Choong and Smith,
2004)
Tem
per
atu
re l
oo
p
Mark
ov
loo
p
No
New Ta
Specify initial trial solution
Generate a new trial solution by making a random move
Evaluate objective function
Acceptance criterion met?
Final solution
Yes
Replace current state with modified state
Set initial annealing temperature
Termination criterion met?
Yes
No
Markov criterion met?
Apply cooling schedule
Yes
No
Chapter 6 Demethaniser flowsheet synthesis by stochastic optimisation
173
6.4 Annealing schedule parameters
The annealing schedule is described by the initial annealing temperature, the
cooling schedule, the acceptance criteria, the Markov chain length and the
termination criteria (Kirkpatrick et al., 1983). The selection of these parameters
affects the performance of simulated annealing. Guidelines for the selection of
annealing parameters selection are explained further below.
6.4.1 Initial annealing temperature
The initial annealing temperature depends on the nature of the problem and the
scale of objective function. Too high a temperature will unnecessarily increase the
algorithm convergence time. On the other hand, too low a temperature restricts the
number and magnitude of accepted uphill moves, thus limiting the ability of the
method to escape from local optima. Kirkpatrick et al. (1983) suggested that a
suitable initial temperature is one that results in an average acceptance probability
of about 0.8. Van Laarhoven and Aarts (1987) proposed an approach for selecting
initial annealing temperature.
o
ava
pln
fT
∆−=0
( 6.5)
Where avf∆ represent the average deterioration of the objective function for uphill
moves in a run where all the uphill moves are accepted, and po is the desired initial
acceptance probability.
6.4.2 Acceptance criterion
Any changes made by the simulated annealing algorithm to trial solutions are
accepted or rejected depending on the acceptance criterion chosen. An acceptance
criterion usually accepts a random move by the algorithm if it improves the
objective function. Many acceptance criteria are proposed in the literature
(Metropolis et al., 1953, Kirkpatrick et al., 1983, Hedar and Fukushima, 2006). In
this work, the original Metropolis acceptance criterion (Metropolis et al., 1953) has
been used, as this acceptance criterion has been observed to provide efficient
performance in simulated annealing algorithms (Zhong and Gang, 2009).
Chapter 6 Demethaniser flowsheet synthesis by stochastic optimisation
174
6.4.3 Markov chain length
The simulated annealing algorithm consists of two loops (Figure 6.2); the Markov
loop and the annealing temperature loop. The inner loop is the Markov loop while
the outer loop is formed by the annealing temperature. A sequence of moves
executed at each temperature corresponds to a Markov chain and the number of
these moves is known as the Markov chain length.
There is no systematic method to choose the length of the Markov chain. The
Markov chain length is dependent on the type and dimensionality of the problem
being solved (Marcoulaki and Kokossis, 1999). A balance between the quality of
the solution and computational time should be considered in selecting the value of
the Markov chain length. Too short a Markov chain length will lead to an
optimisation procedure converging to a local optimum; too long a Markov chain
length will increase the probability of finding the global optimum, however, at the
expense of an infinite computational time.
6.4.4 Cooling schedule
The reduction of the annealing temperature is controlled by the cooling schedule. It
is normal to let the temperature decrease until it reaches zero. However, this makes
the algorithm run for a lot longer, especially when a geometric cooling schedule is
being used (Van Laarhoven and Aarts 1987). In practice, it is not essential for the
annealing temperature to reach the temperature of the solid state as the chances of
accepting a worse move are almost the same as the temperature being equal to
zero.
The reduction of the annealing temperature must be slow enough to avoid being
trapped in a local optimum. However, too slow cooling will unnecessarily increase
the computational time. This work adopts the cooling schedule suggested by Van
Laarhoven et al. (1987), which is based on the statistical information gathered
during the previous Markov chain. According to Van Laarhoven et al. (1987),
Chapter 6 Demethaniser flowsheet synthesis by stochastic optimisation
175
annealing temperature at a given point on Markov chain, 1+k
aT is related to the value
of the previous iteration, kaT , by Equation ( 6.6):
( )1
1
3
11
−
+
++=
σ
θ k
ak
a
k
a
TlnTT
( 6.6)
Where:
θ is a parameter, indicative of the cooling rate, that is typically selected in the
range of 0 to 1.0; in this work the cooling parameter was set to 0.05.
σ represents the standard deviation of the values of the objective function
achieved at temperature .Tk
a A small value of σ results in a large annealing
temperature drop causing an early termination of the annealing process. The
following constraint is employed to overcome the above mentioned problem
(Vanlaarhoven and Aarts, 1987):
k
a
k
a
k
a T.TT 101 ≥≥ + ( 6.7)
The cooling schedule is applied at each temperature level until all the states in the
Markov chain have been evaluated. The number of moves at each temperature
level can be limited by imposing a condition to override the Markov chain length.
Marcoulaki and Kokossis (1999) proposed that a Markov process is finished when
the number of accepted configurations reaches half of the Markov chain length. In
this work, this criterion is chosen to determine the termination of a Markov
process.
6.4.5 Termination criterion
The decision to stop the search for the optimal solution in the simulated annealing
algorithm is made through the termination criterion being satisfied. Various criteria
are used to decide when to stop the search procedure. If any of these conditions is
met, the algorithm stops. These criteria are given below:
Chapter 6 Demethaniser flowsheet synthesis by stochastic optimisation
176
i. The annealing temperature reaches the lower boundary, Taf. (a value of 10-4 is
used in this work)
ii. No structure is accepted after a certain number of Markov loops. In this
work, this number is 10.
6.5 Simulated annealing moves
A move in simulated annealing refers to the process of generating a new candidate
solution from a current solution. The optimisation algorithm makes random moves
which depend on the nature of the optimisation problem and the variables
involved. Moves are provided to the current structure by changing the various
structural and operational parameters of the existing design. When a modification
is to be performed, a random number (ω) is generated. The random number, ω
takes a value between 0 and 1. The new value of a continuous variable is
calculated by the following expression (Knuth, 1981):
( )abax −+= ω ( 6.8)
where a and b are the lower and upper limits for the continuous variable x. The
new value of a discrete variable is calculated by:
( )[ ]1+−+= mnmy ω ( 6.9)
where m and n are the minimum and maximum allowable values for the discrete
variable y.
Randomly selected moves are performed to provide a new design for the
demethaniser flowsheet. Various simulated annealing moves employed in this
work are discussed below.
6.5.1 Flash unit move
The flash unit move controls the existence of a second flash unit in the process.
The existence of the second flash is a binary number, chosen randomly by
optimisation. The binary number 1 includes the additional flash on the process
Chapter 6 Demethaniser flowsheet synthesis by stochastic optimisation
177
stream from expander while 0 represents the non-existence of the second flash unit
(Fig 6.1).
6.5.2 Side reboiler move
The side reboiler move represents the addition or removal of a side reboiler to the
demethaniser column which affects the total heat recovery in the process. The use
of a side reboiler in the demethaniser provides greater energy efficiency and
reduction of the duty of the demethaniser bottom reboiler. The main benefit is the
reduction of the external refrigeration that is required to pre-cool the feed to the
desired temperature in the flash unit.
6.5.3 Internal reflux stream move
The reflux stream move indicates the presence of an additional reflux stream
obtained from the final sales gas (Figure 6.1).
6.5.4 Operating conditions move
The operating condition move changes the operating conditions related to
flowsheet such as demethaniser operating pressure, flash feed temperature, vapour
split ratio and side reboiler duty.
6.6 Move probabilities
During simulated annealing, the search is driven by random modifications. These
modifications are called perturbation moves, as they perturb the network from an
old state into a new state. All structural and operational parameters of the
superstructure can be changed across their associated range. The probability is
usually the same for each perturbation move, if unless additional information about
the process is available (Martin, 2009).
Chapter 6 Demethaniser flowsheet synthesis by stochastic optimisation
178
6.7 Stochastic optimisation framework
Figure 6.3 illustrates flow of information the stochastic optimisation framework.
The simulated annealing algorithm supplies the new trial solution as an input to the
simulation model of the process (developed in Chapter 4), and the simulation
model of the process returns the objective function (Eq. 5.4) for this trial solution.
The optimisation search changes the state of the superstructure and its effect on the
objective function.
During stochastic optimisation in the form of simulated annealing the discrete
options and continuous variables contained within the superstructure – i.e.
structural and operational parameters – are modified by the perturbation moves. A
perturbation move is performed on the initial structure, which is obtained from the
base case. This move is simulated and then either accepted or rejected based on the
acceptance criterion.
In cases, where the system performance is sensitive to a particular variable, a high
move probability can be allocated to this variable throughout the optimisation. As
these variables have a higher chance of being changed, less optimisation time is
spent on the variables having less significant effect on the objective function. Thus,
the optimisation framework can also accommodate heuristics in implementing the
optimisation.
A range of solutions are obtained for each SA run due to the annealing schedule
and the random nature of the search in simulated annealing. Therefore, multiple
runs of simulated annealing optimisation are implemented in this work. Once a run
is finished, its best solution becomes initial point to start the next run, with a
different random number seed. A total of three simulated annealing optimisation
runs is carried out to gain confidence in the optimised solution. The confidence in
the optimised solution is measured in terms of the standard deviation of final value
of objective function of optimisation runs.
Chapter 6 Demethaniser flowsheet synthesis by stochastic optimisation
179
Figure 6.3 Flow of information in optimisation framework
Input data
• Superstructure, initial structure
• Physical properties
Simulation of a specific structure
• Flowsheet simulation (Ch. 4)
• Objective function (Eq. 5.4)
Stochastic optimiser (Fig. 6.2)
• Simulated annealing
• Accept or reject SA moves
Simulated annealing moves
• Flowsheet structural changes
• Operational changes
Optimised flowsheet
• Flowsheet structure
• Operating parameters
• Objective function close to global optimum
Stochastic Optimisation
framework
Chapter 6 Demethaniser flowsheet synthesis by stochastic optimisation
180
6.8 Case Study
6.8.1 Background
A case study is presented in this section to illustrate the application and benefits of
the proposed synthesis methodology. The feed and products data is obtained from
Chebbi et al. (2008). The simulation of the process has been performed by the
developed model and validated against rigorous simulation data as discussed in
Chapter 4.
The main aim of this study is to apply the developed optimisation framework for
demethaniser flowsheet synthesis. The methodology aims to establish the optimal
configuration and operating conditions of the demethaniser flowsheet to recover at
least 98% of the methane to the top product and recover a minimum of 70% of the
ethane to the NGL product. The design constants employed in this case study are
given in Table 6.1.
Table 6.1 Design constants employed for case study
Annual operating hours 8600
Cost index factor CEPCI 560.4*
Column tray spacing 0.5 m
Column top and bottom spacing 10% of column height
Compressor/expander isentropic efficiency 0.8
* Dec. 2010 data (Marshall, 2011)
Table 6.3 presents the simulated annealing parameters employed in this work. As
discussed in Section 6.4, these parameters show the trade-off between the quality
of the final solution and the computational time required to reach the final solution.
For example, the algorithm may find a better solution in terms of the value of the
objective function by employing a longer Markov chain length at the expense of a
much longer time. Chen (2008) discussed that the performance of the final solution
increases only slightly after these parameters reach particular values, indicating
that the required computational time does not vary linearly with solution
Chapter 6 Demethaniser flowsheet synthesis by stochastic optimisation
181
performance. In this case study, these parameters are selected on the basis of
experience and trial and error.
Table 6.2 Simulated annealing parameters
Initial annealing temperature 41001 ×.
Final annealing temperature 41001 −×.
Cooling parameter 0.05
Markov chain length 20
Acceptance criteria Metropolis
6.8.2 Problem inputs
In this work, as in Chapter 4, components heavier than butane, as well as nitrogen,
are artificially eliminated in order to reduce the complexities that arise in the
presence of trace components in the calculations for establishing intersection of
profiles. The simplified composition of the feed and the original composition from
Chebbi et al. (2008) are presented in Table 6.3. The Peng-Robinson equation of
state, using the default parameters of Aspen HYSYS 2006.5 is applied in this case
study to estimate the physical properties and vapour liquid equilibrium. Table 6.3
provides the specified feed and product conditions.
Table 6.3 Feed gas composition - from Chebbi et al. (2008)* and simplified for
this case study
Component Actual feed*
composition mole fraction
Simplified feed
composition mol fraction
Nitrogen 0.01 0.000
Methane 0.76 0.784
Ethane 0.13 0.134
Propane 0.054 0.056
Isobutene 0.026 0.027
Isopentane 0.01 0.000
n-hexane 0.01 0.000
Total Flow (kmol/h) 4980 4980
Chapter 6 Demethaniser flowsheet synthesis by stochastic optimisation
182
Table 6.4 Specified temperature and pressure of feed and products (Chebbi et al., 2008)
Products
Feed gas Sales gas NGL
Temperature 37 oC 40 25
Pressure 60 bar 60 30
Figure 6.4 Process flowsheet diagram of a typical GSP demethaniser process
(Chebbi et al., 2008)
The gas subcooled process (GSP) as given in Chebbi et al. (2008) is a typical
turboexpander based demethaniser process (Fig. 6.4). The feed gas is initially pre-
cooled by a side reboiler before entering a heat exchanger where it is cooled by the
top product from the demethaniser. The cold feed leaving the exchanger is further
cooled down by a chiller using an external refrigeration cycle. The exit stream is
fed to a flash unit, the liquid from which is sent to the demethaniser as the lower
Chapter 6 Demethaniser flowsheet synthesis by stochastic optimisation
183
feed, while the vapour is split into equal proportions. One portion is expanded and
sent as the upper feed to the demethaniser while the second portion is sent to the
top of demethaniser as an external reflux stream after being cooled by a heat
exchanger.
Table 6.5 presents the optimisation boundaries imposed for each move. These
bounds take into consideration practical constraints. The limits on the split fraction
ensure that there is a minimum amount of liquid entering at the top of the column
as reflux. Some of the simulated annealing moves can also result in the failure of
the simulation model to converge. In this work, a constraint value is set to the
infeasible region in the case of simulation failure. This results in the rejection of
the move by optimisation.
Table 6.5 Move probabilities and limits of optimisation variables
Variable
Type
Move decision Lower
bound
Upper
bound
Move
probability
Demethaniser operating
pressure (bar)
15 35 0.15
Flash unit temperature (oC) -20 -60 0.15
Split ratio (reflux to upper
feed)
0.2 0.8 0.15
Continuous
variables
Side reboiler duty (kW) 0 2000 0.15
Flash unit move 0 1 0.15
Internal reflux move 0 1 0.1
Discrete
Variables
Number of side reboilers 1 3 0.15
Chapter 6 Demethaniser flowsheet synthesis by stochastic optimisation
184
6.8.3 Results
The simulation begins with the heat recovery in the multistream exchanger for a
given temperature of the flash unit feed stream. The side reboilers and external
refrigeration duties are evaluated based on the overall energy balance over the
whole flowsheet. The complex distillation column is simulated using the modified
boundary value method explained in Chapter 3. In this case study, a two-feed
column with a side reboiler is used. The other flowsheet units are simulated using
the shortcut design models as explained in Section 4.3 and employing the
sequential modular approach for flowsheet simulation. The validation of
simulation model is performed by simulating the flowsheet in Aspen HYSYS. The
validation and results are presented in detail in Section 4.5. Table 6.6 presents
some of the important results as obtained in Ch. 4.
Table 6.6 Simulation results: Shortcut model vs HYSYS
* indicates specified values
Table 6.7 presents a summary of the final three optimisation solutions from a
family of solutions for the demethaniser synthesis problem for annualised profit
optimisation. The product revenues along with the capital and utility contributions
to the cost of each solution are provided. It is evident from the results that the
operating costs generally dominate the total costs of the process as the reduction in
the operating costs is significant. The capital cost of the optimised solutions which
are increased due to the addition of an extra flash unit and a side heater in the
Results Units Shortcut model HYSYS
Ethane recovery in NGL % 76.43 76.43
Methane recovery in sales gas % 99.54* 99.54*
Residue compressor power kW 2055 2042
Refrigeration power kW 2980 2950
Reboiler temperature oC 30.3 30
Reboiler duty kW 1828 1845
Chapter 6 Demethaniser flowsheet synthesis by stochastic optimisation
185
optimised flowsheet configurations. The annual profit for the optimised flowsheet
is 139.8 MM$/yr compared to 129.6 MM$ in the base case. Thus the optimised
flowsheet shows over 8% increase in the annual profit compared to the base case.
Both structural and operational changes allow these savings to be achieved.
Table 6.7 Optimisation results of three solutions from a family of solutions
The best solution among a family of solutions is highlighted in Table 6.7. The
values of the optimisation variables of the final three solutions cases are presented
in Table 6.8. All the three solutions presented have the same structure, only the
operating conditions are different.
In the first solution, a lower pressure (25 bar vs 30 bar) in the demethaniser results
in higher power requirements (around 425 kW) in the recompressor. On the other
hand, the addition of a second side reboiler decreases the external refrigeration
power requirements by 1060 kW. So the total power requirements are shown to
Results Unit Base case First
solution
Second
solution
Third
solution
Ethane recovery in NGL % 76.43 82.22 82.14 81.8
Methane recovery in sales gas % 99.54 99.54 99.54 99.54
Residue compressor power kW 2055 2480 2560 2500
Refrigeration power kW 2980 1920 2035 2160
Total shaft power kW 5035 4400 4595 4680
Reboiler duty kW 1828 138 176 208
Annualised capital cost MM$/yr 6.0 6.2 6.25 6.29
Annual utility cost MM$/yr 8.53 5.25 5.52 5.64
Annual revenues MM$/yr 305.32 312.44 312.37 312.22
Annual profit MM$/yr 129.6 139.8 139.41 139.1
Chapter 6 Demethaniser flowsheet synthesis by stochastic optimisation
186
decrease by 13%. Moreover, the ethane recovery is enhanced by 5.8%, which
increases the revenue from product sales.
Table 6.8 Decision variables for base case and best three cases
Decision variables Units Base case
First solution
Second solution
Third solution
Demethaniser operating pressure bar 30 25 25.5 25.2
Flash unit temperature oC -35 -28 -30 -31
Split ratio (reflux to upper feed) - 0.5 0.65 0.65 0.60
First side reboiler duty kW 1500 1750 1700 1680
2nd side reboiler duty kW 0 1250 1250 1230
Number of flash units - 1 2 2 2
Internal reflux - 0 0 0 0
Number of side reboilers - 1 2 2 2
The optimised flowsheet for the first solution is shown in Figure 6.5. As seen from
the results listed in Table 6.5, in comparison with base case, the optimised
flowsheet has two flash units and two side reboilers. The addition of the second
flash unit is shown to increase the ethane recovery. The use of an additional side
reboiler reduces the external refrigeration requirement as evident from the lower
shaft work requirement for the refrigeration system (Table 6.7). The lower
refrigeration load also decreases the condenser load and hence less cooling water is
required. In addition to this, the main reboiler duty is also lowered. Therefore, the
overall operating cost is reduced.
The computation time for the design obtained using the proposed synthesis
approach for demethaniser process, using simulated annealing with three runs
optimisation is 94 minutes and 20 CPU seconds on an Intel® Core 2 Duo CPU
2.93 GHz processor with 4 GB RAM).
Figure 6.5 Case study – Optimised flowsheet
Chap
ter 6 D
emeth
aniser flo
wsh
eet synth
esis by sto
chastic o
ptim
isation
Chapter 6 Demethaniser flowsheet synthesis by stochastic optimisation
188
The developed synthesis methodology offers the user control over the optimisation
variables, the move probabilities in the case study can be adjusted to investigate
specific optimisation variables. External variables such as feed conditions and
composition, different product recoveries or change in price of power may also be
investigated by conducting parametric studies, which require successive
optimisation runs.
The profit calculation in the above case study is relatively simple, and the capital
and operating cost models employed in this work are not verified as accurate. The
flowsheet may need further analysis using more detailed cost models before being
accepted for investigation. The focus of this research is to develop a novel
synthesis approach aimed at conceptual design of demethaniser flowsheets.
Therefore, these issues are considered beyond the scope of this work.
6.9 Conclusions
In this chapter, a systematic methodology based on stochastic optimisation for the
synthesis and design of demethaniser flowsheets has been presented. A
superstructure is formulated for flowsheet optimisation which includes various
possible structural combinations. The superstructure-based approach allows one to
identify promising configurations systematically. Structural and operating issues
are addressed simultaneously to achieve the design specifications.
A stochastic optimisation algorithm, simulated annealing (SA), is employed in the
framework. Relevant parameters of the simulated annealing algorithm are
discussed; how these are chosen for demethaniser system design problem is
presented. The advantage of the simulated annealing optimisation algorithm is that
it does not need any derivative calculations, and it can accommodate the non-
linearity, non-differentiability and discontinuity of the problem formulation. The
SA algorithm can manage continuous and discrete variables simultaneously and
hence can optimise simultaneously both operating conditions and the structure of
the demethaniser system.
Chapter 6 Demethaniser flowsheet synthesis by stochastic optimisation
189
The developed optimisation approach is applied with the objective of maximising
profit of the process. The final optimised flowsheet shows considerable
improvement in annual profit, compared to the base case. The approach, however,
is generic; and is applicable to other objectives as well, e.g. minimising capital
investment, maximising throughput, etc. Although this new approach is developed
mainly for complex separations systems such as demethaniser flowsheets, the
approach can be applied more generally, with some modifications, to other heat-
integrated distillation systems such as ethylene production.
Chapter 7 Conclusions and future work
190
CHAPTER 7 CONCLUSIONS AND FUTURE WORK
Increasing energy costs and stricter gas purification specifications are creating a
challenge for the design and operation of gas treating processes with low operating
and capital costs. The recovery of natural gas liquids (NGL) is an important and
necessary part of the natural gas industry. Major challenges in NGL recovery
processes are, on one hand, the reduction of power consumption to reduce
greenhouse gas emissions and cost, and, on the other hand, maximising the
recovery of ethane and heavier components (Sharratt et al., 2008).
NGL recovery from natural gas offers an economic incentive due to the higher
value of the recovered components as feedstocks, over their fuel value as natural
gas components. The main market for ethane is ethylene production, where ethane
feeds are traditionally the most cost-effective due to the generation of fewer by-
products in comparison to naphtha feeds (Farry, 1998). The extent to which NGL
are to be recovered is a balance between capital, operating cost and the market for
range of products obtained used as feedstocks for other petrochemicals.
A large number of design alternatives are available for demethaniser processes
which must be evaluated when selecting an energy efficient process for a new gas
processing facility (Mehrpooya et al., 2006). Therefore, a comprehensive approach
for synthesis is required to generate effective and economic design without excess
requirements of engineering time and effort.
Chapter 7 Conclusions and future work
191
7.1 Conclusions
The new simplified models and optimisation-based approach presented in this
thesis are major contributions in the area of natural gas liquids recovery employing
demethaniser flowsheets. This work extends knowledge in this area by developing
a systematic procedure for grassroots design of demethaniser flowsheets. The new
short-cut model developed in this work for design of complex demethaniser
columns is a significant step forward in the modelling of these processes. The
optimisation-based approach presented in this thesis, which considers the
interactions between the demethaniser column and other flowsheet units same
time, overcomes a major limitation of the previous research work in this area, and
can achieve significantly better designs of demethaniser flowsheets compared to
designs achieved by previous approaches. The main contributions of this work are
highlighted below:
� A novel extension of the established boundary value design method is
proposed for modelling and designing demethaniser columns for
multicomponent mixtures. The proposed method represents the column
accurately, compared to alternative shortcut models, without compromising
the computation time excessively. The model accommodates complex
column features and can be used in the early stages of flowsheet design
with only basic information, such as feed properties and product
specifications. The model is validated against an equilibrium stage-by-stage
column model in AspenTech process simulation package HYSYS and is
shown to represent the process behaviour satisfactorily.
� A systematic representation of overall demethaniser flowsheet design and
simulation is developed. Opportunities for heat-integration and power
recovery are identified and exploited in the overall flowsheet to improve
the process economics.
� A nonlinear constrained optimisation problem is formulated for
optimisation of fixed structure demethaniser flowsheet. An industrial case
study is presented to illustrate the application of the fixed structure
Chapter 7 Conclusions and future work
192
optimisation approach, which can also be applied to compare various
licensed flowsheets for a specific objective function.
� A robust simulation and optimisation methodology based on superstructure
optimisation is proposed. The methodology applies a stochastic
optimisation technique to solve the superstructure to systematically
synthesize the flowsheet. The proposed approach is tested with an industrial
case study which gives a novel flowsheet design with an improvement in
annual profit of around 8%.
7.1.1 Discussion
Existing short-cut methods, for example based on the Fenske-Underwod-Gilliland
method, for modelling and design of distillation columns are not sufficiently
accurate to estimate the number of stages, reboiler duty and reboiler temperature of
a demethaniser column. A new design method for demethaniser columns is
developed, extending the established boundary value method (Levy and Doherty,
1986) for column design. The energy balance is included in the calculation of the
composition profiles to overcome the assumption of constant molar overflow in the
original boundary value method. The new design method takes into account two-
phase feeds by introducing the feed between two stages and considering mixing at
the feed stage. Multicomponent mixtures are represented without requiring
visualisation of the composition profiles, by the use of a minimum distance
criterion to indicate near-intersection of composition profiles. The model also
accommodates intermediate heating using side reboilers and the use of an external
reflux stream. Two case studies are presented to illustrate the application of the
design method to a range of column configurations.
A novel integrated process model for simulation of a demethaniser flowsheet is
presented; the model comprises shortcut design models for various units in the
demethaniser flowsheet. Heat recovery in a multistream exchanger is also
represented by the model. A typical process is simulated using the new process
model and validated against rigorous simulation results using HYSYS. The results
Chapter 7 Conclusions and future work
193
show that the shortcut model of the flowsheet is sufficiently accurate to be
employed in an optimisation framework for process synthesis.
The simplified simulation model takes into account interactions various flowsheet
units, as well as between process variables, and hence, can lead to energy-efficient
and cost-effective flowsheets. An approach is developed for process optimisation
of a flowsheet of fixed configuration. Important variables affecting the flowsheet
are extracted from a large number of process variables by sensitivity analysis. The
optimisation is carried out using a nonlinear programming technique, the
successive quadratic programming. A case study of industrial relevance is
presented to illustrate the application of the optimisation approach for maximising
the annual profit. A 4% increase in annual profit is obtained which indicates that
the proposed optimisation procedure for a fixed flowsheet structure offers an
effective way of design and optimisation of a demethanisation flowsheet of fixed
structure.
A superstructure is formulated for flowsheet synthesis to include various possible
structural combinations such as addition of a low pressure flash column, an
additional side reboiler and an internal reflux stream. The superstructure-based
approach allows one to identify promising configurations systematically.
Optimisation of structural and operating issues has been approached
simultaneously to achieve the design specifications and maximise the objective
function, in this case, annual profit. A stochastic optimisation methodology is used
to solve the superstructure to systematically synthesize the flowsheet. The
proposed approach is tested with a case study which gives a new flowsheet design
with around 8% improvement in annual profit, compared to the base case.
7.1.2 Limitations
The demethaniser design model used for the synthesis in this work is a simplified
model. The model is based on some assumptions that the vapour-liquid equilibrium
is achieved on every stage and the pressure drop over the column is zero. These
Chapter 7 Conclusions and future work
194
assumptions, however, have a minimal affect on the overall flowsheet design as the
optimisation framework is independent of the column model.
The application of boundary value approach to multicomponent systems is
accomplished by the 'minimum distance' criterion to approximate the intersection
of composition profiles. Complete agreement with simulation approaches using
different specifications will not be expected, given the sensitivity of the
composition profiles to trace components and the approximation introduced by the
minimum distance criterion applied in the boundary value method. To improve
agreement between HYSYS simulation results and those of the design method,
input variables, such as the specified product compositions, column pressure and
feed condition, may need to be manually adjusted.
The trace components present in the column feed are neglected and the feed is
simplified to overcome the complexity introduced by the presence of trace
components in the calculation of intersection of the composition profiles by
minimum distance approach. However, this assumption has a negligible affect on
the column design as discussed in Section 3.6.
Although the use of simulated annealing as the optimisation tool in this work
produces promising results, the long computational time required by its
implementation constitutes one of the weaknesses of this algorithm. As for any
other stochastic optimisation tool, the search for the solution space is random and
derivative free. This unique property is the primary merit of the strategy, but also
the cause for the long computational time. However, as the technology evolves
rapidly, the processing power of computers has increased exponentially in recent
years. Therefore it might not be a major issue of concern in the near future.
The superstructure optimisation approach can produce several near-optimal
designs with complex structures, some of which are likely to be impractical. In
order to improve the practical applicability of the framework, it is recommended to
Chapter 7 Conclusions and future work
195
include that sensitivity towards design variations should be considered, especially
in complex designs.
7.2 Future work
The side reboilers in the demethaniser column are modelled as side heaters in this
work where the duty and location of the heaters needs to be specified. This
approach simplifies the column design model by avoiding the mass and
equilibrium calculations that otherwise need to be performed. The boundary value
design model can be modified and updated further to overcome this limitation of
the model.
The superstructure presented in Chapter 6 can be extended to include more
demethaniser flowsheets options available in patents such as the addition of pre-
fractionator and inclusion of a stripping stream in the demethaniser stripping
section. Moreover, downstream columns for NGL fractionation like deethaniser,
depropaniser and debutaniser can also be included in the superstructure.
Heat integration in this work is performed by considering heat recovery in a
multistream exchanger. In some variations of demethaniser flowsheets, a network
of shell and tube heat exchangers are applied instead of a multistream exchanger
(Konukman and Akman, 2005). Heat integration with downstream NGL
fractionation columns can also be included in the overall synthesis framework. A
rigorous methodology for heat exchanger network design can be employed.
Another future research direction can involve the addition of the selection of
refrigerant for the external refrigeration cycle as an option in the synthesis
framework, where a database of different refrigerants can be developed. In addition
to the choice of refrigerant and the inclusion of complex refrigeration cycles in the
framework can also enhance its robustness.
Chapter 7 Conclusions and future work
196
The stochastic optimisation method offers higher chances to escape the local
optima of the objective function. This however, has the penalty of longer
computational time which can increases significantly with the complexity of the
problem. Therefore, it would be desired to speed up the optimisation process by
investigating hybrid processes (stochastic with deterministic) to achieve shorter
computational time. The use of hybrid optimisation can also help in fine tuning of
the results obtained from simulated annealing.
Finally, the capability of the proposed synthesis methodology to identify energy-
efficient and cost-effective configurations has been illustrated in Chapter 6. In
addition to economic efficiency (annual profit), some other industrially relevant
objectives for the demethaniser processes, such as system flexibility, controllability
and maintainability are also significant. It is challenging to accommodate these
factors in a systematic synthesis framework because of the lack of methods for
estimation these factors. Multi-objective optimisation is a challenging topic that
offers scope for future work.
197
References
(2003) Postnote, Available from
http://www.parliament.uk/documents/post/postpn230.pdf. Parliamentry
office of science and technology.
(ASME 2000) Section VIII, ASME Boiler and pressure vessel code. ASME, New
York.
(CAPE-OPEN, 2011) http://www.colan.org/index-1.html, Accessed July 11,
2011.
(EIA 2011) US Energy Information Administration,
http://tonto.eia.doe.gov/oog/info/twip/twip_propane.html, Accessed Feb.
2011.
(ESDU 1997) Engineering Sciences Data Unit, Selection and costing of heat
exchangers, Plate-fin type. London, UK., ESDUInternational plc, .
(ETSU 1992) Energy Technology Support Unit , Industrial refrigeration plant:
energy efficient operation and maintenance. Energy Efficiency Office,
Harwell.
(GPSA 2004) Gas Processors Suppliers Association, Engineering Data Book
Engineering Databook Volume 2, Section 16. Tulsa, Oklahama.
Adjiman, C. S., Schweiger, C. A. & Floudas, C. A. (1998) Mixed-integer nonlinear
optimization in process synthesis. Handbook of Combinatorial
Optimization, 1-76.
Amminudin, K. A., Smith, R., Thong, D. Y. C. & Towler, G. P. (2001) Design and
optimization of fully thermally coupled distillation columns: Part 1:
Preliminary design and optimization methodology. Chemical Engineering
Research and Design, 79, 701-715.
Andrecovich, M. J. & Westerberg, A. W. (1985) MILP Formulation for heat
integrated distillation sequence synthesis. AIChE Journal, 31, 1461-1474.
Arora, J. S. (2004) Introduction to Optimum Design. New York: McGraw-Hill.
Athier, G., Floquet, P., Pibouleau, L. & Domenech, S. (1997) Synthesis of Heat-
Exchanger Network by Simulated Annealing and NLP Procedures. AIChE
Journal, 43, 3007-3020.
198
Bai, L., Chen, R., Yao, J. & Elliot, D. (2006) Retrofit for NGL recovery
performance using a novel stripping gas refrigeration scheme. GPA Annual
Convention Proceedings.
Balat, M. (2009) Global trends on production and utilization of natural gas. Energy
Sources, Part B: Economics, Planning and Policy, 4, 333-346.
Bandoni, J. A., Eliceche, A. M., Mabe, G. D. B. & Brignole, E. A. (1989)
Synthesis and optimization of ethane recovery process. Computers &
Chemical Engineering, 13, 587-594.
Barnicki, S. D. & Fair, J. R. (1990) Separation system synthesis: a knowledge-
based approach. 1. Liquid mixture separations. Industrial & Engineering
Chemistry Research, 29, 421-432.
Barnicki, S. D. & Fair, J. R. (1992) Separation system synthesis: a knowledge-
based approach. 2. Gas/vapor mixtures. Industrial & Engineering
Chemistry Research, 31, 1679-1694.
Barnicki, S. D. & Siirola, J. J. (2004) Process synthesis prospective. Computers
and Chemical Engineering, 28, 441-446.
Barthe, L. & Gahier, V. (2009) Ethane recovery processes evolve to meet market
needs. 24th World gas conference. Argentina.
Barttfeld, M. & Aguirre, P. (2002) Optimal synthesis of multicomponent zeotropic
distillation processes. 1. Preprocessing phase and rigorous optimization for
a single unit. Industrial & Engineering Chemistry Research, 41, 5298-
5307.
Bausa, J., Watzdorf, R. v. & Marquardt, W. (1998) Shortcut methods for nonideal
multicomponent distillation: 1. Simple columns. AIChE Journal, 44, 2181-
2198.
Biegler, L. T. & Grossmann, I. E. (2004) Retrospective on optimization.
Computers & Chemical Engineering, 28, 1169-1192.
Biegler, L. T., Grossmann, I. E. & Westerberg, A. W. (1997) Systematic Methods
of Chemical Process Design, London, Prentice-Hall
Bimakr, F., Baniadam, M. & Fathikalajahi, J. (2008) Evaluation of performance of
an industrial gas sweetening plant by application of sequential modular and
simultaneous modular methods. Chemical and Biochemical Engineering
Quarterly, 22, 411-420.
Bullin, K. A. & Hall, K. R. (2000) Optimization of natural gas processing plants
including business aspects. GPA Annual Convention Proceedings.
199
Caballero, J. A. & Grossmann, I. E. (2004) Design of distillation sequences: From
conventional to fully thermally coupled distillation systems. Computers
and Chemical Engineering, 28, 2307-2329.
Caballero, J. A. & Grossmann, I. E. (2006) Structural considerations and modeling
in the synthesis of heat-integrated-thermally coupled distillation sequences.
Industrial and Engineering Chemistry Research, 45, 8454-8474.
Caballero, J. A., Miln, Y. D. & Grossmann, I. E. (2005) Rigorous Design of
Distillation Columns:Integration of Disjunctive Programming and Process
Simulators. Industrial & Engineering Chemistry Research, 44, 6760-6775.
Campbell, R. E. & Wilkinson, J. D. (1981) Hydrocarbon gas processing. U.S.
Patent 4,278,457, Ortloff Corporation.
Campbell, R. E., Wilkinson, J. D., Hudson, H. M. & Cueller, K. T. (1999)
Hydrocarbon gas processing, U.S. Patent 5881569. Elcor Corporation,
Texas.
Campbell, R. E., Wilkinson, J. D. & Husdson, H. M. (1996) Hydrocarbon gas
processing. U.S. Patent 5,568,737, ELCOR Corporation.
Carlson, E. C. (1996) Don't gamble with physical properties for simulations.
Chemical Engineering Progress, 92, 35-46.
Castillo, F. J. L., Thong, D. Y. C. & Towler, G. P. (1998) Homogeneous
azeotropic distillation. 1. Design procedure for single-feed columns at non-
total reflux. Industrial and Engineering Chemistry Research, 37, 987-997.
Chebbi, R., Al-Amoodi, N. S., Abdel Jabbar, N. M., Husseini, G. A. & Al
Mazroui, K. A. (2010) Optimum ethane recovery in conventional
turboexpander process. Chemical Engineering Research and Design, 88,
779-787.
Chebbi, R., Al Mazroui, K. A. & Abdel Jabbar, N. M. (2008) Study compares C2-
recovery for conventional turboexpander. Oil & Gas Journal, 106, 50-54.
Chen, H.-S. & Stadtherr, M. A. (1985) SIMULTANEOUS-MODULAR
APPROACH TO PROCESS FLOWSHEETING AND OPTIMIZATION.
PART I: THEORY AND IMPLEMENTATION. AIChE Journal, 31, 1843-
1856.
Chen, L. (2008) Heat-integrated crude oil distillation system design. . The
University of Manchester, UK.
Choong, K. L. & Smith, R. (2004) Optimization of batch cooling crystallization.
Chemical Engineering Science, 59, 313-327.
200
Diaz, S., Serrani, A., Bandoni, A. & Brignole, E. A. (1996) A study on the capital
and operating alternatives in an ethane extraction plant. Computers &
Chemical Engineering, 20, S1499-S1504.
Doherty, M. F. & Malone, M. F. (2001) Conceptual Design of Distillation Systems,
McGraw Hill.
Douglas, J. M. (1985) Hierarchical decision procedure for process synthesis.
AIChE Journal, 31, 353-362.
Duran, M. & Grossmann, I. (1986) An outer-approximation algorithm for a class
of mixed-integer nonlinear programs. Mathematical Programming, 36,
307-339.
Elliot, D. G., Chen, J. J., Brown, T. S., Sloan, E. D. & Kidnay, A. J. (1996) The
economic impact of fluid properties research on expander plants. Fluid
Phase Equilibria, 116, 27-38.
Eyert, V. (1996) A Comparative Study on Methods for Convergence Acceleration
of Iterative Vector Sequences. Journal of Computational Physics, 124, 271-
285.
Farkas, T., Avramenko, Y., Kraslawski, A., Lelkes, Z., Nyström, L. & Andrzej
Kraslawski and Ilkka, T. (2003) Selection of MINLP model of distillation
column synthesis by case-based reasoning. Computer Aided Chemical
Engineering. Elsevier.
Farry, M. (1998) Ethane from associated gas still the most economical. Oil and
Gas Journal, 96, 115-117.
Fasullo, P. (2008) US Ethane Outlook: Ethane: It’s Available and For Sale. 15th
Annual Petrochemical Feedstock Association of the Americas (PFAA).
Austin, Texas.
Fermeglia, M. & Pricl, S. (2009) Multiscale molecular modeling in nanostructured
material design and process system engineering. Computers and Chemical
Engineering, 33, 1701-1710.
Fissore, D. & Sokeipirim, D. (2011) Simulation and energy consumption analysis
of a propane plus recovery plant from natural gas. Fuel Processing
Technology, 92, 656-662.
Fletcher, R. & Leyffer, S. (1994) Solving mixed integer nonlinear programs by
outer approximation. Mathematical Programming, 66, 327-349.
201
Floquet, P., Pibouleau, L. & Domenech, S. (1994) Separation sequence synthesis:
How to use simulated annealing procedure? Computers and Chemical
Engineering, 18, 1141-1148.
Floudas, C. A., Aggarwal, A. & Ciric, A. R. (1989) Global optimum search for
nonconvex NLP and MINLP problems. Computers & Chemical
Engineering, 13, 1117-1132.
Floudas, C. A. & Gounaris, C. E. (2009) A review of recent advances in global
optimization. Journal of Global Optimization, 45, 3-38.
Foglietta, J. H. & Patel, S. N. (2007) Hydrocarbon recovery process utilizing
enhanced reflux streams. US Patent 7159417.
Gavrila, I. S. & Iedema, P. (1996) Phenomena-driven process design, a knowledge-
based approach. Computers and Chemical Engineering, 20, S103-S108.
Glasser, D., Crowe, C. & Hildebrandt, D. (1987) A geometric approach to steady
flow reactors: the attainable region and optimization in concentration space.
Industrial & Engineering Chemistry Research, 26, 1803-1810.
Groemping, M., Dragomir, R.-M. & Jobson, M. (2004) Conceptual design of
reactive distillation columns using stage composition lines. Chemical
Engineering and Processing, 43, 369-382.
Grossmann, I. E. & Biegler, L. T. (2004) Part II. Future perspective on
optimization. Computers & Chemical Engineering, 28, 1193-1218.
Grossmann, I. E., Caballero, J. A. & Yeomans, H. (2000) Advances in
mathematical programming for the synthesis of process systems. Latin
American Applied Research, 30, 263-284.
Grossmann, I. E. & Daichendt, M. M. (1996) New trends in optimization-based
approaches to process synthesis. Computers and Chemical Engineering, 20,
665-683.
Haselden, G. G. (1971) Cryogenic Fundamentals, Academic Press, London, 12-15.
Hedar, A. R. & Fukushima, M. (2006) Derivative-free filter simulated annealing
method for constrained continuous global optimization. Journal of Global
Optimization, 35, 521-549.
Henrich, F., Bouvy, C., Kausch, C., Lucas, K., Preuss, M., Rudolph, G. & Roosen,
P. (2008) Economic optimization of non-sharp separation sequences by
means of evolutionary algorithms. Computers & Chemical Engineering,
32, 1411-1432.
202
Hewitt, G. F. & Pugh, S. J. (2007) Approximate design and costing methods for
heat exchangers. Heat Transfer Engineering, 28, 76 - 86.
Hock, W. & Schittkowski, K. (1983) A comparative performance evaluation of 27
nonlinear programming codes. Computing, 30, 335-358.
Horn, F. J. M. (1961) Proceeding of 3rd European symposium on chemical
reaction engineering. New York: Pergamon.
Ishii, Y. & Otto, F. D. (2011) An alternate computational architecture for advanced
process engineering. Computers and Chemical Engineering, 35, 575-594.
Jackson, S. R., Finn, A. J. & Tomlinson, T. R. (2006) New challenges for UK
natural gas. 85th Annual GPA Convention. Grapevine, Texas, USA.
Jaksland, C. & Gani, R. (1996) An integreated approach to process/product design
and synthesis based on properties-process relationship. Computers and
Chemical Engineering, 20, S151-S156.
Jaworski, Z. & Zakrzewska, B. (2011) Towards multiscale modelling in product
engineering. Computers and Chemical Engineering, 35, 434-445.
Jibril, K. L., Al-Humaizi, A. I., Idriss, A. A. & Ibrahi, A. A. (2005) Simulation of
turbo-expander processes for recovering of natural gas liquids from natural
gas. Saudi Aramco Journal of Technology, 9-14.
Julka, V. & Doherty, M. F. (1990) Geometric behaviour and minimum flows for
non-ideal multicomponent distillation. Chemical Engineering Science, 45,
1801-1822.
Khoury, F. M. (2005) Rigorous Equilibrium Methods. Multistage Separation
Processes, Third Edition. CRC Press.
King, C. J. (1980) Separation Processes, New York, McGraw-Hill.
Kirkpatrick, S., Gelatt, C. D. & Vecchi, M. P. (1983) Optimization by simulated
annealing. Science, 220.
Kisala, T. P., Trevino-Lozano, R. A., Boston, J. F., Britt, H. I. & Evans, L. B.
(1987) Sequential modular and simultaneous modular strategies for process
flowsheet optimization. Computers & Chemical Engineering, 11, 567-579.
Kister, H. Z. (1992) Distillation Design, New York., McGraw-Hill.
Knight, J. R. & Doherty, M. F. (1986) Design and synthesis of homogeneous
azeotropic distillations. 5. Columns with non-negligible heat effects.
203
Knuth, D. E. (1981) The art of computer programming, 2nd Edition, Addison-
Wesley, London.
Koehler, J., Poellmann, P. & Blass, E. (1995) A review on minimum energy
calculations for ideal and nonideal distillations. Industrial and Engineering
Chemistry Research, 34, 1003-1020.
Konukman, A. E. S. & Akman, U. (2005) Flexibility and operability analysis of a
HEN-integrated natural gas expander plant. Chemical Engineering Science,
60, 7057-7074.
Koolen, J. L. A. (2001) Design of Simple and Robust Process Plants, Wiley-VCH.
Leboreiro, J. & Acevedo, J. (2004) Processes synthesis and design of distillation
sequences using modular simulators: a genetic algorithm framework.
Computers & Chemical Engineering, 28, 1223-1236.
Lee, G. C. (2001) Optimal design and analysis of refrigeration systems for low
temperature processes. PhD Thesis, Department of Process Integration, The
University of Manchester, Manchester, U.K.
Levy, S. G. & Doherty, M. F. (1986) Design and synthesis of homogeneous
azeotropic distillations. 4. Minimum reflux calculations for multiple-feed
columns. Industrial and Engineering Chemistry Fundamentals, 25, 269-
279.
Levy, S. G., Van Dongen, D. B. & Doherty, M. F. (1985) Design and synthesis of
homogeneous azeotropic distillations. 2. Minimum reflux calculations for
nonideal and azeotropic columns. Industrial and Engineering Chemistry
Fundamentals, 24, 463-474.
Li, X. & Kraslawski, A. (2004) Conceptual process synthesis: Past and current
trends. Chemical Engineering and Processing: Process Intensification, 43,
589-600.
Linnhoff, B. & Boland, D. (1982) A user guide on process integration for the
efficient use of energy.
Lu, M. D. & Motard, R. L. (1985) Computer-aided total flowsheet synthesis.
Computers and Chemical Engineering, 9, 431-445.
Mak, J. (2009) Ethane recovery methods and configurations for high carbon
dioxide content feed gases. United States Patent US2009/0301133. Fluor
Technologies.
204
Malone, M. F., Marquez, F. E., Douglas, J. M. & Glinos, K. (1985) Simple
Analytical Criteria for the Sequencing of Distillation Columns AIChE
Journal, 31, 683-689.
Marcoulaki, E. C. & Kokossis, A. C. (1999) Scoping and screening complex
reaction networks using stochastic optimization. AIChE Journal, 45, 1977-
1991.
Markowski, M., Trafczynski, M. & Urbaniec, K. (2007) Energy expenditure in the
thermal separation of hydrocarbon mixtures using a sequence of heat-
integrated distillation columns. Applied Thermal Engineering, 27, 1198-
1204.
Marshall, R. (2011) Economic indicators: Chemical Engineering Plant Cost Index
(CEPCI). Chemical Engineering, 118, 80.
Martin, M. (2009) Synthesis of heat integrated gas separation systems
incorporating absorption. PhD Thesis, Chemical Engineering and
Analytical Sciences, The University of Manchester, Manchester, U.K.
McMahon, D. (2004) Navigating the technical minefield of gas processing options.
London, GPA Europe Meeting.
Mehra, Y. R. & Gaskin, T. K. (1999) Guidelines offered for choosing cryogenics
or absorption for gas processing. Oil and Gas Journal, 97, 62-69.
Mehrpooya, M., Gharagheizi, F. & Vatani, A. (2006) An optimization of capital
and operating alternatives in a NGL recovery unit. Chemical Engineering
and Technology, 29, 1469-1480.
Mehrpooya, M., Gharagheizi, F. & Vatani, A. (2009) Thermoeconomic analysis of
a large industrial propane refrigeration cycle used in NGL recovery plant.
International Journal of Energy Research, 33, 960-977.
Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H. & Teller, E.
(1953) Equation of state calculations by fast computing machines. The
Journal of Chemical Physics, 21, 1087-1092.
Metzger, M. J., Glasser, D., Hausberger, B., Hildebrandt, D. & Glasser, B. J.
(2009) Use of the attainable region analysis to optimize particle breakage in
a ball mill. Chemical Engineering Science, 64, 3766-3777.
Mitchell, M. (2009) An Introduction to Genetic Algorithms, Cambridge, MA, MIT
Press.
205
Mokhatab, S., Poe, W. A., Speight, J. G., Saeid, M., William, A. P. & James, G. S.
(2006) Natural gas liquids recovery. Handbook of Natural Gas
Transmission and Processing. Burlington, Gulf Professional Publishing.
Montolio-Rodriguez, D. & Linke, P. (2011) Conceptual screening of reactive
extraction processing options. Chemical Product and Process Modeling, 5.
Nasir, P., Sweet, W. C., Elliot, D., Chen, R. & Lee, R. J. (2003) Enhanced NGL
recovery process selected for Neptune gas plant expansion. Oil & Gas
Journal, 101, 52-+.
Ohara, S., Yamaguchi, S., Yamamori, Y. & Evelyne, J. (2008) Process and
apparatus for separation of hydrocarbons. US Patent, 7,357,003.
Ortloff (2011) http://www.ortloff.com/files/GasPPLicAll.pdf Acessed 12/6/2011.
Patel, S. N. & Foglietta, J. H. (2010) Multiple reflux stream hydrocarbon recovery
process. UNITED STATES PATENT AND TRADEMARK OFFICE
GRANTED PATENT. US, ABB Lummus.
Paules, G. E. & Floudas, C. A. (1992) Stochastic programming in process
synthesis: A two-stage model with MINLP recourse for multiperiod heat-
integrated distillation sequences. Computers and Chemical Engineering,
16, 189-210.
Peter, M. S. & Timmerhaus, K. D. (2008) Plant Design and Economics for
Chemical Engineers. McGraw Hill Publication.
Pitman, R. N., Hudson, H. M., Wilkinson, J. D. & Cuellar, K. T. (1998) Next
generation processes for NGL/LPG recovery. Proceedings, Annual
Convention - Gas Processors Association.
Poling, B. E., John M. Prausnitz & O'Connell, J. P. (2001) The Properties of Gases
and Liquids, McGraw-Hill.
Prayoonyong, P. (2009) Synthesis and design of ternary heterogeneous azeotropic
distillation processes including advanced complex column configurations.
PhD Thesis, Chemical Engineering and Analytical Sciences, The
University of Manchester, Manchester, U.K.
Saad, Y. (2003) Iterative Methods for Sparse Linear Systems. 2nd edition, Boston,
MA.
Sargent, R. A., Barbosa, P. & Matos, H. (2004) Process systems engineering - A
retrospective view with questions for the future. Computer Aided Chemical
Engineering. Elsevier.
206
Seader, J. D. & Henley, E. J. (1998) Separation Process Principles, Wiley, New
York.
Seuranen, T., Hurme, M. & Pajula, E. (2005) Synthesis of separation processes by
case-based reasoning. Computers & Chemical Engineering, 29, 1473-1482.
Shah, P. B. & Kokossis, A. C. (2002) New synthesis framework for the
optimization of complex distillation systems. AIChE Journal, 48, 527-550.
Shah, V. & Gilbert, J. R. (2004) Sparse matrices in MATLAB : Design and
implementation. Lecture Notes in Computer Science (including subseries
Lecture Notes in Artificial Intelligence and Lecture Notes in
Bioinformatics).
Sharratt, P. N., Hernandez-E.A. & Flores T.A. (2008) Modeling of an industrial
NGL-recovery unit considering environmental and economic impacts. 2008
AIChE Spring National Meeting, Conference Proceedings.
Siirola, J. J. (1996) Strategic process synthesis: Advances in the hierarchical
approach. Computers and Chemical Engineering, 20, S1637-S1643.
Sinnott, R. K. (2003) Coulson and Richardson's Chemical Engineering: Chemical
Engineering Design v. 6.
Smith, R. (2005) Chemical Process: Design and Integration, John Wiley & Sons,
Ltd.
Smith, R. & Linnhoff, B. (1988) Design of separators in the context of overall
processes. Chemical Engineering Research and Design, 66, 195-228.
Smith, R. & Varbanov, P. (2006) What's the price of steam? Chemical Engineering
Progress, 101, 29-33.
Sorensen, H. H. B. & Asterby, O. (2009) On one-point iterations and DIIS. AIP
Conference Proceedings.
Suphanit, B. (1999) Design of complex distillation system. PhD Thesis,
Department of Process Integration, University of Manchester Institute of
Science and Technology (UMIST), Manchester, U.K.
Tahouni, N., Hassan Panjeshahi, M. & Ataei, A. (2010) Comparison of sequential
and simultaneous design and optimization in low-temperature liquefaction
and gas separation processes. Journal of the Franklin Institute.
The MathWorks, I. (2010) http://www.mathworks.com/products/matlab/.
207
Thong, D. Y. C. & Jobson, M. (2001) Multicomponent homogeneous azeotropic
distillation 2. Column design. Chemical Engineering Science, 56, 4393-
4416.
Turton, R., Bailie, R. C., Whiting, W. B. & Shaeiwitz, J. A. (2008) Analysis,
Synthesis, and Design of Chemical Processes, Prentice Hall.
Ulrich, G. D. & Vasudevan, P. T. (2006) How to estimate utility costs. Chemical
Engineering, 113, 66-69.
vanLaarhoven, P. J. M. & Aarts, E. H. L. (1987) Simulated Annealing, Theory and
Applications, D. Reidel Publishing Co.
Walas, S. M. (1985) Phase Equilibria in Chemical Engineering, Butterworth-
Heinemann
Walas, S. M., Fair, J. R. & Couper, J. R. (2005) Chemical Process Equipment -
Selection and Design 2nd ed., Gulf Professional Publishing.
Wang, J. (2004) Synthesis and optimisation of low temperature gas separation
processes. PhD Thesis, Department of Process Integration, University of
Manchester Institute of Science and Technology (UMIST), Manchester,
U.K.
Wang, J. & Smith, R. (2005) Synthesis and optimization of low-temperature gas
separation processes. Industrial and Engineering Chemistry Research, 44,
2856-2870.
Wang, K., Salhi, A. & Fraga, E. S. (2004) Process design optimisation using
embedded hybrid visualisation and data analysis techniques within a
genetic algorithm optimisation framework. Chemical Engineering and
Processing: Process Intensification, 43, 663-675.
Wang, L. & Sunden, B. (2001) Design methodology for multistream plate-fin heat
exchangers in heat exchanger networks. Heat Transfer Engineering, 22, 3-
11.
Wang, X. H. & Li, Y. G. (2010) Stochastic GP synthesis of heat integrated
nonsharp distillation sequences. Chemical Engineering Research and
Design, 88, 45-54.
Westerberg, A. W. (2004) A retrospective on design and process synthesis.
Computers and Chemical Engineering, 28, 447-458.
Wilkinson, J., Hudson, H., Cuellar, K. & Pitman, R. (2002) Next generation
processes for NGL/LPG recovery. Hydrocarbon Engineering, 7, 77-84.
208
Yan, W., Bai, L., J., Y., Chen, R. & Elliot, D. (2008) Optimum design of turbo-
expander ethane recovery processes. Chevron Energy Technology
Company.
Yaws, C. L., Li, K. Y. & Fang, C. S. (1981) How to find the minimum reflux for
binary systems im multiple feed columns. Chemical Engineering (New
York), 88, 153-156.
Yiqing, L., Xigang, Y. & Fenglian, D. (2009) Synthesis and heat integration of
thermally coupled complex distillation system. International Journal of
Energy Research, 34, 626-634.
Zhong, W. A. & Gang, X. Y. (2009) A simulated annealing-based approach to the
optimal synthesis of heat-integrated distillation sequences. Computers and
Chemical Engineering, 33, 199-212.
209
Appendix A: MATLAB-HYSYS Interface for physical properties
and Vapour-liquid equilibrium data
External software can be used to access Aspen HYSYS using a method called
automation (HYSYS 2006.5 Customization Guide1). Automation allows the user to
interact with an application through objects exposed by developers of that
application. By using an automation client such Visual Basic, the end user can
write the code to access these objects and interact with HYSYS.
Aspen HYSYS v 2006.5 is employed in this work to calculate the physical
properties and vapour-liquid equilibrium data. The procedure to link MATLAB
and HYSYS is not provided directly in the customization guide. Therefore an
interface is developed between MATLAB and HYSYS. The interface is explained
with the aid of an example below:
Example: Dew point calculation of a ternary mixture.
The example illustrates the calculation of the dew point of a saturated vapour
mixture having 60 mol% n-Hexane, 25 mol% n-Heptane and 15 mol% n-Nonane.
The method involves the following steps:
1. Start HYSYS with only one active file and flowsheet. Specify the
components in HYSYS and select fluid property package (Peng-Robinson
in this example)
2. Create a material stream (named ‘DEW’). The pressure, vapour fraction,
temperature and composition of this stream is provided by MATLAB.
1 Available from:
http://support.aspentech.com/Public/Documents/Engineering/Hyprotech/2006.5/As
penHYSYS2006_5-Cust.pdf
210
3. Create a spreadsheet (named ‘SPRDSHT’). This spreadsheet is used for
receiving mole fractions of the stream from MATLAB and sending them to
the material stream created in the previous step.
a) The mole fractions of the stream sent from MATLAB will be stored
in cells A1 (for n-Hexane), A2 (for n-Heptane) and A3 (for n-
Nonane).
b) Define the values in cells B1, B2 and B3 to be equal to those in cells
A1, A2 and A3, respectively.
c) Make connections between cells B1, B2 and B3 and mole fractions
of the material stream created in step 2 using ‘Exported Variables’
in ‘Connections’ tap of the spreadsheet.
MATLAB Code
%Specify molar composition of mixture
XF = [0.6 0.25 0.15];
%Start the MATLAB-HYSYS communication
hy = actxserver ('HYSYS.Application');
% Active the HYSYS document and flowsheet
hyActive = hy.ActiveDocument;
hFlowsheet = hyActive.Flowsheet;
% Connect to HYSYS solver
hSolver = hyActive.Solver;
% Link to the material stream 'DEW'
hDEW = hFlowsheet.Streams.Item('DEW');
% Link to the spreadsheet 'SPRDSHT'
hSprd = hFlowsheet.Operations.Item('SPRDSHT');
%Link to cells A1 to A3 in 'SPRDSHT'
211
hCellA1 = hSprd.Cell('A1');
hCellA2 = hSprd.Cell('A2');
hCellA3 = hSprd.Cell('A3');
% Set the pressure of 'STREAM' to be 1 atm
hDEW.Pressure.SetValue(1, 'atm');
% Set the vapour fraction of 'STREAM' as saturated vapour
hDEW.VapourFraction.SetValue(1);
% Turn HYSYS Solver off
hSolver.CanSolve = 0;
% Delete the current values in cells A1 to A3
hCellA1.Erase;
hCellA2.Erase;
hCellA3.Erase;
% Set the mole fraction of components as given by XF
hCellA1.CellValue = XF(1);
hCellA2.CellValue = XF(2);
hCellA3.CellValue = XF(3);
% Turn HYSYS Solver on (HYSYS automatically determines phase equilibrium)
hSolver.CanSolve = 1;
% Define ‘hDpl_DEW’ to use for retrieving phase equilibrium data
hDupl_DEW = hDEW.DuplicateFluid;
Get the molar enthalpy of given phase (kJ/kmol)
H_V = hDupl_DEW.MolarEnthalpyValue
% Get the composition of liquid phase in equilibrium with xF
x = hDupl_DEW.lightliquidPhase.MolarFractionsValue
212
% Get the molar enthalpy of liquid phase (kJ/kmol)
H_L = hDupl_DEW.lightliquidPhase.MolarEnthalpyValue
% Get the dew point temperature (oC)
T = hDupl_DEW.TemperatureValue
Results
Composition Feed (saturated vapour) Liquid phase
n-Hexane 0.6 0.23
n-Heptane 0.25 0.21
n-Nonane 0.15 0.56
Molar enthalpy -1.6794x105 -2.255x105
Dew-point 105.1 oC
213
Appendix B: Cost Estimation
The quantitative synthesis methodology developed in this work uses capital and
operating costs to establish a comparison between design options and to enable the
systematic optimisation of the problem.
A number of sources of equipment sizing and capital cost correlations are available
in the open literature (Peter and Timmerhaus, 2008, Walas et al., 2005, Turton et
al., 2008). Published capital cost data often derive from various sources of different
times. Such data need to be up to date and expressed on a common basis using cost
indexes.
The operating cost is assumed to be based solely on the utility requirement. After
the capital and operating costs are calculated, the total annualised cost of the
flowsheet can be determined from the sum of annualised capital cost and operating
cost. The total annualised cost is used for calculating the annual profit which is
used as an indicator for comparison among different flowsheets and quantitatively
analyse the optimisation results.
B.1 Capital cost estimation
The first step in the equipment cost estimation is to calculate the equipment size.
Once the equipment is sized, the capital cost can be estimated using correlations or
cost data from literature as appropriate.
In this study, the capital cost of flowsheet units is calculated by applying the
Module costing technique (Turton et al., 2008). The bare module cost, which is the
sum of direct and indirect cost for a unit is given by:
BMopBM FCC = (B.1)
214
where
BMC is the bare module equipment cost
opC is the purchased cost at ambient pressures using carbon steal as the material
of construction
BMF is the bare module cost factor, dependent on the material of construction
and operating pressure
Eq. B.1 can be further written as:
( )PMopBM FFBBCC 21 += (B.2)
where FM and FP are the material and pressure factor respectively.
The values of B1 and B2 are provided in the following table.
Table B.1 Constants for Bare module factor
Equipment Type B1 B2
Fixed tube Heat exchanger 1.63 1.66
Process vessel 2.25 1.82
The purchased cost of the equipments at ambient operating pressure and using
carbon steel as the material of construction is given by:
( ) ( )[ ]2103102110 AlogKAlogKKClogop ++= (B.3)
where A is the capacity or size parameter for the equipment. The data for K1, K2
and K3 along with maximum and minimum values used in the above correlation is
given in Table B.2.
215
Table B.2 Equipment cost data for Equation B.1
Equipment Type K1 K2 K3 Capacity Min
size
Max
size
Centrifugal
Compressor
2.2897 1.3604 -1.027 Fluid power,
kW
450 3000
Fixed tube Heat
exchanger
4.3247 -0.303 0.1634 Area, m2 10 1000
Process vessel 3.4974 0.4485 0.1074 Volume, m3 0.3 520
Tray column 3.4974 0.4485 0.1074 Volume, m3 0.3 520
Sieve trays 2.9949 0.4465 0.361 Area, m2 0.07 12.3
The cost obtained from Eq. B.2 is at the ambient pressure. To account for a higher
pressure in the pressure vessel the following equation is employed (Turton et al.,
2008):
( )( )[ ]
00630
0031501608502
1
.
.P.
DP
F vessel,p
++−
+
=
(B.4)
where D is the vessel diameter in meters, P the operating pressure in barg based on
ASME code for pressure vessel design (ASME 2000).
For other equipments, Eq. B.5 gives the pressure factor
( )2103102110 PlogCPlogCCFlog p ++= (B.5)
Table B.3 Pressure factors for process equipments (Turton et al., 2008)
Equipment Type C1 C2 C3 Pressure range (barg)
Centrifugal
Compressor
0.038 -0.112 0.082 5<P<140
Fixed tube Heat exchanger 0 0 0 5<P<140
216
Turton et al., (2008) obtained the data for the purchased cost of different
equipments in 2001. In order to account for inflation and to obtain current cost
estimates, it is necessary to update the original estimates with the adequate
economic indexes. This relationship is given by Eq. B.6
1
2
12I
ICC =
(B.6)
where C2 is the purchased cost at current time
C1 is the purchased cost at base time
I2 is the cost index at current time
I1 is the cost index at base time
Typical cost indexes for the chemical industry include the Chemical Engineering
Plant Cost Index (CEPCI), published monthly in Chemical Engineering magazine.
The Marshall & Swift Economic Index is also of general use for equipment
costing. In this work, CEPCI is used to account for inflation. A value of 397 for
CEPCI was used for year 2001 (Turton et al., 2008) while a value of 560.4 is used
December 2010 for this work which is obtained from Chemical Engineering
Magazine (Marshall, 2011).
B.1.1 Annualised capital cost
In this work, we assume that the capital is borrowed over a fixed period n (3 years)
at a fixed rate of interest i (5%). Capital cost is then expressed on an annual basis
according to
( )( )( )11
1
−+
+×=
n
n
i
iiCCAC
(B.7)
where AC is the annualised cost, CC is the capital cost, n is the number of years,
and i is an interest rate per year.
217
B.1.2 Capital cost estimation for distillation columns
The capital cost of a column consists of the costs of the shell, trays and installation
cost of equipment. The shell cost is proportional to the weight of column which
depends on the column diameter, height and material of construction. The cost of
trays is a function of column diameter, number of stages and column internals.
Sieve trays are assumed in this work, while the material of construction is carbon
steel. The height of a column is estimated based on the actual number of stages.
The height of the column (H) is given by Eq.B.8 (Peter and Timmerhaus, 2008).
( ) HHNH sact ∆+−= 1 (B.8)
where Nact is the actual number of stages, Hs is the trays spacing and H∆ is the
additional height for vapour and liquid disengagement at the top and bottom of the
column.
A tray spacing of 0.5 m and an efficiency of 100% is employed in this work. H∆ is
assumed to be 10% of the column height. To avoid flooding, the vapour velocity
must be operated below the flooding velocity, and the velocity will normally be
between 70 to 90 percent of the flooding velocity. The diameter of the column is
given by:
u.
VD
π
4=
(B.9)
where V is the volumetric vapour flow rate, and u is the vapour velocity, which is
is assumed to be 80% of flooding velocity (uf) in the column. The flooding velocity
is calculated from Equation B.10 (Sinnott, 2003):
v
vLf Ku
ρ
ρρ −= 1
(B.10)
where Lρ is the density of liquid, Lρ the density of vapour and K1 is a coefficient
dependent on the vapour liquid flowrates. The value of K1 is obtained from
Sinnott (2003).
218
The column diameter and the height of the column are used to determine the
volume of the column, which is then used in Eq. B.3 for estimating the purchased
cost of the column.
B.1.3 Capital cost estimation for heat exchangers
The purchase cost of shell and tube heat exchangers is estimated by the module
costing technique. However, the cost factors were not available for the multistream
plate fin heat exchangers. So the cost of plate-fin heat exchangers is obtained from
Peters and Timmerhaus (2003, Figure 14-27) for compact heat exchangers.
A preliminary area may be obtained from the heat exchanger load, Q, the inlet and
outlet temperatures and an approximate overall heat transfer coefficient, U, using
the following equation.
LMTU
QA
∆=
(B.11)
Where LMT∆ represents the logarithmic mean temperature of the heat exchanger.
The temperature of cooling water is taken to be 25oC. A minimum temperature
difference of 10oC is assumed. The overall heat transfer coefficient (U) is
estimated to be 600 W/m2 K for a shell and tube heat exchanger with the cooling
water in the tube side and light organics in the shell side (Peter and Timmerhaus,
2008). For the reboiler using steam, a value of 800 W/m2 K is used. For all other
heat exchangers using process streams U is assumed to be 400 W/m2 K.
B.2 Operating cost estimation
The consideration of utility cost is quite important as it projects the energy trade-
offs onto the synthesis process. In this work, operating costs are assumed to be the
equivalent of utility costs. The different process utilities used in the demethaniser
process flowsheet synthesis include the electricity, process steam, refrigerants and
cooling water. The calculation of the utility costs is a complex problem as the
utility prices can not be estimated from the conventional inflationary indexes
(Ulrich and Vasudevan, 2006). Moreover, the cost of utilities fluctuates due to the
219
volatility of energy costs and utility tariffs being determined on individual plant
basis.
The method presented by Ulrich and Vasudevan (2006) to estimate utility costs is
employed in this study. This method is based on empirical correlations. According
to this method, the cost of any utility may be correlated to the cost of fuel through
an equation of the form:
( ) fu bCCEPCIaC += (B.12)
Where
Cu is the cost of the utility, Cf is the price of fuel in $/GJ, CEPCI is the Chemical
Engineering Plant Cost Index, and coefficients a and b are functions of certain
utility specific variables are available from Ulrich and Vasudevan (2006).
B.2.1 Steam cost
Smith and Varbanov (2006) discussed that it is difficult to attribute a single
economic value for steam at a certain level. The cost of steam is dependent on the
cost of fuel utilised in the boiler. They discussed that the steam price depends on
the fuel price, fuel heat content, boiler efficiency, price of electricity and driver
mechanical efficiency.
In this study we only require steam at low pressure conditions for the demethaniser
column reboiler. Steam at 6 bar is assumed to be available for heating. The cost of
the steam is calculated based on steam generation in a boiler using natural gas as a
fuel. The boiler is assumed to have an efficiency of steam generation of 80%.
Boiler feed water is available at 100oC. The costs of steam at each pressure
determined from Equation (B.13).
efficiencyBoilerfeedwaterboilersteam
ofEnthalpyofEnthalpytcosFuelsteamofCost ×
−×=
(B.13)
220
For an average cost of natural gas at 5.0 $/GJ, the LP steam cost from this equation
is about 500 $/kWyr.
B.2.2 Electricity Cost
Equation B.10 is used to estimate the cost of electricity. For the electricity
purchased from outside the plant, a = 0.00013 and b = 0.010.
Based on the cost of natural gas for electric power generation of $5.6 /ft3($5.0/GJ)
(from U.S. Energy Information Administration, www.eia.doe.gov), gross calorific
value of 40 MJ/m3 and CEPCI of 560.4 in Dec. 2010 (Marshall, 2011), the cost of
electricity calculated from equation (B.12) is $ 0.123/kWh.
B.2.3 Cooling water cost
Cooling water is assumed to be available at 25oC with a target temperature of 30
oC. The cost of cooling water ($/m3) is also based on the Eq. B.11 where the
coefficient a and b are given by Ulrich and Vasudevan (2006):
15100300010 −−×+= q..a and 0030.b =
where q is the cooling water volumetric flowrate.
Solving the Eq. B.11 for an assumed capacity of 1 m3/sec comes out at $ 0.088/m3
($130/kWyr).