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PALLAVI KUMARI
Y9227397
A Thesis Submitted in Partial Fulfillment of the
Requirement for the
B. TECH – M. TECH DUAL DEGREE
Under the supervision of
DR. NITIN KAISTHA
CONTROL SYSTEM DESIGN FOR ENERGY EFFICIENT ON-TARGET PRODUCT PURITY OPERATION OF A HIGH
PURITY PETLYUK COLUMN
DEPARTMENT OF CHEMICAL ENGINEERING
INDIAN INSTITUTE OF TECHNOLOGY KANPUR
MAY, 2014
ii
iii
Acknowledgement
My first and sincere gratitude goes to my supervisor, Prof. Nitin Kaistha, for his
continuous supervision, invaluable insight and motivational encouragement at all stages
of this thesis. I have been enriched by not only his unsurpassed knowledge, objective
and principled approach to research method, but also I have learnt the vital skill of
disciplined critical thinking.
I am deeply thankful to my lab-mates Rahul, Ojasvi, Vivek, Abhishek and Harish for
creating a cheerful and constructive environment. Specifically I would comprehend my
thanks to Rahul for his immense patience with stimulating discussions and constant
motivation to complete the work and Ojasvi for his kind assistance and encouragement.
I would like to thank my family, especially my parents for always believing in me, for
their continuous love and their supports in my decisions.
Last but not least, I would like to thank my friends for their unconditional support,
efficacious remarks and constant encouragement throughout my degree. In particular, I
truly appreciate the patience and understanding shown by my wing-mates particularly
during the last year.
Pallavi
iv
Abstract
In this work, energy efficient, on-target product purity operation of a high-purity
three product benzene-toluene-xylene ternary Petlyuk column is studied. The basic
regulatory control system consists of four temperature inferential control loops with a
fixed prefractionator vapor to fresh feed ratio. An economic control system on top of the
regulatory layer adjusts these 5 setpoints. It consists of three product purity controllers
that adjust three temperature setpoints along with a reboiler duty reduction controller
that adjusts the remaining two free setpoints in the regulatory layer. The latter makes
these adjustments to prevent the downward curvature in the prefractionator and main
column middle section temperature profiles from being too large. Closed loop results
for large feed composition changes show significant energy savings (up to 15%) are
realized via temperature profile curvature control compared to column operation for
fixed xylene and benzene impurity mol fraction in the side-draw (constant setpoint
operation). The case study highlights the need for innovative control strategies for
realizing the sustainability benefit of the integrated complex Petlyuk column during
actual operation.
Keywords: Energy efficient operation, Petlyuk column, economic control, optimum
process operation
v
Table of Contents
1. Introduction ............................................................................................................ 1
2. Petlyuk Column Optimum Design ......................................................................... 6
3. Control Structure Design ..................................................................................... 12
3.1. Regulatory Control Structure ............................................................................... 12
3.2. Control Structure for Economic Operation ......................................................... 17
3.2.1 Product Quality Control System ................................................................... 18
3.2.2. Control System for Reboiler Duty Reduction ............................................. 21
4. Dynamic Simulations and Closed Loop Results .................................................. 30
4.1. Equipment Sizing and Plumbing ......................................................................... 30
4.2. Controller Tuning ................................................................................................ 30
4.3. Closed Loop Results ............................................................................................ 31
5. Discussion ............................................................................................................ 40
6. Conclusion ........................................................................................................... 42
vi
List of Figures
Figure 1. The ternary Petlyuk column configuration
(a) Conventional configuration (b) Dividing wall configuration
Figure 2. Petlyuk column design and optimized operating conditions
Figure 3. QR variation with VP for different values of xS,X Figure 4. Petlyuk column base-case profiles (a) Temperature and (b) Composition
profile
Figure 5. Petlyuk column regulatory control structure
Figure 6. Petlyuk column tray temperature sensitivities
Figure 7. Quality control system on top of regulatory structure
Figure 8. Variation in steady state temperature profile with feed composition change for
CSCC
operation at constant setpoints and reoptimized setpoints.
Figure 9. Quantifying curvature in a temperature profile
Figure 10. Mapping curvature (C) to large downward curvature (y)
Figure 11. TS1/TS5 curvatures for the different feed composition changes for fixed and
reoptimized VP/F and xS,X
Figure 12. Petlyuk column control system for QR reduction
Figure 13. CSR transient response to (a) throughput disturbance; (b) feed composition
disturbance
Figure 14. CSCC
and CSEC
transient response to benzene composition disturbance
Figure 15. CSCC
and CSEC
transient response to toluene composition disturbance
Figure 16. CSCC
and CSEC
transient response to xylene composition disturbance
vii
List of Tables
Table 1: Prefractionator bottom benzene composition variation for feed composition
disturbances with xD,T, xS,T, xB,T, VP and xS,T constant
Table 2: Comparison of QR and QR
MIN for feed composition disturbances
Table 3: Controller tuning parameters for CSR, CS
CC ans CS
EC
Table 4: Purity of the three product streams for principal disturbances to CSR
Table 5: Comparison of QR for CSCC
, CSEC
, CSEC
with only yC1 on manual and CSEC
with only yC5 on manual
1
Chapter 1
1. Introduction
In the process industry, distillation remains the most preferred and widely used
unit operation for separating liquid mixtures
into its constituent pure (pseudo)
components 1. The basic idea is to utilize the difference in the volatility of the mixture
components by repeated flashing to purify it. This is accomplished via countercurrent
vapour-liquid contact on the trays of a simple distillation column with the reboiler
providing the vapour stream into the bottom and the condenser providing refluxed
liquid to the top of the column. The process is then naturally energy intensive with the
reboiler heat driving the separation so that distillation alone can contribute up to 53% of
plant energy costs 2. Thus, innovations towards energy efficient distillation
configurations for a given separation task has traditionally been of interest to the
process industry. The volatility in energy prices in recent years has particularly renewed
interest in the synthesis, design, operation and control of complex column
configurations that can be significantly more energy efficient than a conventional light-
out-first (direct sequence) or heavy-out-first (indirect sequence) train of simple
distillation columns.
In pioneering work, Petlyuk et al. 3 suggested a complex configuration
consisting of a prefractionator followed by a main column with a side draw for
separating a ternary ideal mixture into its constituent pure components, as in Figure
1(a). Compared to a conventional two-column direct or indirect sequence, the
prefractionator in the Petlyuk configuration mitigates remixing of the middle boiler,
which distributes itself between the prefractionator top and bottom products. This
reduces the inherent process irreversibility leading to potentially significant energy
savings. Literature reports (see e.g. Triantafyllou and Smith 4) indicate impressive
2
energy savings up to 40% for a Petlyuk configuration over a conventional two-column
sequence. A further innovation to the Petlyuk configuration is incorporation of the
prefractionator within the body of the main column by inserting an appropriately
positioned vertical wall as in Figure 1(b). This is appropriately referred to as the divided
wall column (DWC). It is conceptually similar to the Petlyuk configuration with the
additional benefit of reduced capital cost. Literature reports suggest that BASF has
several (60-70) operating DWCs for improved energy efficiency 5
.
Since Petlyuk’s original path-breaking article, researchers have used its basic
idea to develop other energy efficient complex column configurations 6-9
. The reader is
referred to seminal work by Agarwal and co-workers 10-12
for a generalized systematic
methodology to synthesize energy efficient complex column configurations for multi-
component mixtures.
The literature on complex distillation configurations suggests a mature
understanding of issues in their synthesis and design. Even so, the practical realization
of significant energy savings from such a configuration during actual process operation
requires a control strategy that ensures near minimum boil-up operation regardless of
disturbances, particularly in the feed composition. The available literature on minimum
energy / optimal operation and control of complex columns is however quite limited.
Most reported studies consider the operation of a ternary Petlyuk column with a
relatively impure side-product (see e.g. Kaibel et al. 13
).
In possibly the earliest work on operation and control of a high-purity ternary
Petlyuk column, Wolff and Skogestad 14
performed a steady state bifurcation analysis to
suggest that only three product compositions should be controlled and the remaining
two dofs adjusted to minimize energy consumption. To keep the column operation near-
optimal, Halvorsen and Skogestad 15
suggested holding appropriate feedback variables
3
based on steady state analysis. The candidate variables for near-optimal operation
included position of maximum composition of intermediate component in main
fractionator, temperature profile symmetry on both sides of wall, heavy key impurity in
pre-fractionator top, impurity of non-keys in both ends of pre-fractionator, pre-
fractionator flow split and temperature difference over the pre-fractionator. In both these
articles, no closed loop dynamic results were presented so that the recommendations
remain dynamically untested.
In possibly the first article on high purity Petlyuk DWC control with closed loop
dynamic results, Ling and Luyben 16
developed a control structure for a benzene-
toluene-xylene (BTX) column, where the principal impurity in the three product streams
are controlled along with the xylene spill-over from the prefractionator top. The work is
further extended to temperature inferential control of the BTX DWC 17
, where
controlling the difference between appropriately chosen tray locations in the
prefractionator top, main column rectification section, middle section and stripping
section, is shown to provide near minimum energy column operation. A closer
examination of the closed loop results in both papers however shows that the side-draw
product (toluene) purity shows small deviations from its 99% purity target.
In a very recent paper, Dwivedi et al.18
comprehensively evaluated four
decentralized control structures with appropriate composition controllers for (near)
optimal operation of a ternary Petlyuk column and showed that overrides are needed to
mitigate excessive light component leakage down the prefractionator bottom for very
large feed composition changes. In their work too, the side draw product purity deviates
from its target value as the feed composition changes.
All of the high product purity ternary Petlyuk column control studies in the
literature thus allow the side-draw product purity to float away from its target value
4
while pursuing minimum energy operation. The debatable question then is how to
control a high purity Petlyuk column for near optimal (minimum energy) operation with
on-target purity of all the three product streams. To the best of our knowledge, this has
not been studied in the extant literature and this work addresses the same. We highlight
that on-target product purity is crucial in today’s competitive markets, as overall
profitability is determined by value added product premium charged by the guarantee
of minimum product quality to the customer.
In the following, the benzene-toluene-xylene (BTX) Petyuk column design with
base-case optimum operating conditions is first described followed by a systematic
synthesis of the regulatory control system for closing the total
material/component/energy balances. We then develop the economic control system
consisting of the product quality control loops and temperature profile straightening
loops that adjust free regulatory layer setpoints for reboiler duty reduction. Closed loop
dynamic results are then presented to quantify the reboiler duty reduction benefit
compared to constant setpoint process operation. After a brief discussion of the results,
the article is concluded.
5
Figure 1. The ternary Petlyuk column configuration
(a) Conventional configuration (b) Dividing wall configuration
(b)
(a)
6
Chapter 2
2. Petlyuk Column Optimum Design
The industrially significant ternary separation of benzene, toluene, and p-xylene
(BTX) in a Petlyuk column is studied here. Hysys with the SRK property package is
used for steady state and dynamic process modelling. We want to design a ternary
Petlyuk column, which contains 6 tray sections (TS1 – TS6) as in Figure 1, to process
100 kmol/h of equimolar BTX feed into 99 mol% pure constituents. The BTX normal
boiling points are, in order, 79.8, 109.8, and 137.8 °C, respectively. A condenser
pressure of 100 kPa is then considered appropriate giving a condenser temperature of
~80 °C (nearly pure benzene distillate) for a water cooled condenser.
At atmospheric pressure, the BTX relative volatility in order, is about
5.16:2.21:1 implying that the separation is not a difficult one. To design the column, we
must choose the number of trays in each of the six sections of the column, as in Figure
1. In the prefractionator, TS1 prevents p-xylene from leaking up the top in its vapour
product (VM). Similarly, TS2 prevents benzene from leaking down the bottom in its
liquid product (LM). In the main column, TS4 prevents the benzene in the
prefractionator top product from moving down and contaminating the side-draw toluene
product (S). Similarly, TS5 prevents the xylene from the prefractionator bottom product
from moving up and contaminating the side-draw. TS3 prevents toluene leakage up the
top in the benzene distillate product (D) and TS6 prevents toluene leakage down the
bottom xylene product (B).
To fix the number of trays in each of the tray sections, we note that a divided
wall arrangement requires the number of prefractionator trays to be equal to the number
of middle section (TS4 and TS5) trays in the main column. Since, the prefractionator
split is much easier (benzene-xylene split with large relative volatility of ~5) compared
7
to the middle section splits for TS4 and TS5 (relative volatility 2.2-2.7), it follows that
TS4 and TS5 together set the prefractionator height. We then need to only obtain the
number of trays in the main column trays sections (TS3 – TS6). These are set to twice
the minimum trays necessary for achieving a principal impurity leakage of 1 mol% for
the particular tray section, which corresponds to a separation factor of ~500. This gives
11, 12, 12 and 11 trays for TS3, TS4, TS5 and TS6 respectively. The prefractionator
then has 24 trays. Trays for TS1 and TS2 are obtained similarly and 24 trays of
prefractionator are distributed in TS1 and TS2 in their ratio. Hence, the feed to the
prefractionator is chosen to be on 14th tray.
Figure 2 provides a schematic of the complex column along with the base-case
design and operating conditions optimized for minimum reboiler duty. A pressure drop
of 0.44 kPa per tray gives a bottom pressure of 120 kPa for a condenser pressure of 100
kPa. For the given feed and column pressure profile, the column steady state operating
degree of freedom (dof) is 5. The specification variables, toluene impurity in distillate
(xD,T), toluene purity of sidestream (xS,T), toluene impurity in bottom (xB,T), xylene
impurity in sidestream (xS,X) and vapour side draw to prefractionator (VP), are used to
exhaust the 5 dofs and robustly converge the flowsheet. Of these five specifications,
three get used up for fixing the three product purities at 99 mol% each. This is most
easily accomplished by setting xD,T = 1 mol%, xS,T = 99 mol% and xB,T = 1 mol%. The
remaining 2 specifications (xS,X and VP) are then manually adjusted to obtain the
minimum boil-up operating condition. This “brute-force” minimization of QR is shown
in Figure 3, which plots its variation with VP for different values of xS,X. A minimum
reboiler duty of 1619 kW is thus obtained for xS,X = 0.0092 and VP = 111 kmol/h. The
column temperature and composition profiles at this optimized base-case are shown in
Figure 4.
8
Note that any xylene (heavy component) that spills over from the prefractionator top
necessarily moves down the main column and hence contaminates the side-draw. Similarly, any
benzene (light component) that spills over from the prefractionator bottom necessarily moves up
the main column and hence contaminates the toluene side product. Of these two spill-overs, as
insightfully pointed out by Ling and Luyben 16
, heavy xylene would prefer the liquid phase
while light benzene would prefer the vapour phase. Since the toluene product stream is a liquid
side draw, the optimum impurity distribution in the toluene side draw is predominantly xylene
(0.92%) with some benzene (0.08%).
9
Figure 2. Petlyuk column design and optimized operating conditions
10
Figure 3. QR variation with VP for different values of xS,X – – : xS,X = 0.0093; ––: xS,X = 0.0092; ––: xS,X = 0.0091; – –: xS,X = 0.0090
11
Figure 4. Petlyuk column base-case profiles
(a) Temperature profile (b) Composition profile
in main fractionator (black lines) and in prefractionator (grey lines)
––: Benzene; – –: Toluene; –∙– : p-Xylene
(b)
(a)
12
Chapter 3
3. Control Structure Design
The Petlyuk column has 8 control dofs (independent control valves), discounting
the feed valve, which is set by an upstream process or equivalently, sets the processing
rate / throughput (see Figure 5). These 8 control valves must be used to effectively close
the independent overall component, material and energy balances so that all
accumulation (total material, component or energy) terms are quickly driven to zero.
This constitutes the basic regulatory control system, in which typically, fast, cheap and
reliable process variables such as flows, levels, pressures and temperatures are
controlled using dynamically fast pairings for effective closure of the material/energy
balances. The regulatory loop setpoints determine the process inventory levels and the
corresponding steady state at which it eventually settles. These setpoints may further be
adjusted to drive the process to an economically favourable steady state. The much
slower economic/supervisory layer on top of the regulatory layer performs this
adjustment.
3.1. Regulatory Control Structure
In the Petlyuk column, the regulatory control objectives include controlling the
reflux drum and main column sump levels (1st-2
nd objectives) to balance the respective
total liquid inventories. It is assumed that the liquid from the prefractionator drains
under gravity to the main column so that there is no control valve on LM. Also, the
column pressure must be controlled to balance the process total vapour inventory (3rd
objective). Further, on the prefractionator, the xylene and benzene leakage respectively,
up the top and down the bottom, must be regulated (4th
and 5th
objectives). Similarly, on
the main column, the toluene impurity in the distillate and the bottoms must be
13
regulated (6th
and 7th
objectives). Finally, the side-product toluene purity must be
regulated (8th
objective). These last 5 regulatory objectives (4th
to 8th
) correspond to
closing the independent component inventory balances on the prefractionator and the
main column. Instead of measuring composition, which is typically expensive, slow and
unreliable, we prefer to use temperature based measurements to infer the particular
component inventory.
Of the eight regulatory objectives, total liquid/vapour inventory regulation is
more important, as large drifts in the total inventory levels would necessarily lead to
safety issues such as an overflowing/dried-up surge drum or a ruptured disc due to high
pressure differential etc. Also, total inventory regulation indirectly regulates the
component inventories. We therefore pair loops for total inventory regulation first,
followed by loops for component inventory regulation.
To close the liquid and vapour inventory balances (first three objectives),
conventional “local” pairings are used. Thus, the reflux drum level is regulated by
manipulating the distillate (D), the main column sump level is regulated by
manipulating the bottoms (B) and the condenser pressure is regulated by manipulating
the condenser duty (QC).
With the total liquid balance controllers in place, we focus attention on
component inventory regulation. On the prefractionator, we have two independent
component balances. Of these, regulating the xylene spillover up the top is critical as
this sets the principal impurity level in the liquid side-draw product (xS,X). Accordingly,
a sensitive prefractionator enriching tray temperature is controlled for tight regulation of
the same. On the other hand, loose regulation of the benzene spillover down the bottom
may be acceptable as benzene prefers the vapour phase and is therefore the minor
impurity in the side-draw. Given that the prefractionator is highly overdesigned in terms
14
of the number of trays for the easy benzene-xylene split, regulating the top xylene
spillover indirectly regulates the bottom benzene spillover. This may be inferred from
the steady state simulation results in Table 1, which show that even for large changes in
the feed composition (feed rate remains fixed at base-case value), the prefractionator
bottom benzene composition changes negligibly with xD,T, xS,T, xB,T, VP and xS,X chosen
as the 5 convenient column specifications and fixed at their respective base-case values.
Note that xS,X indirectly fixes the prefractionator top xylene spillover. The data in Table
1 suggests that at fixed feed rate, maintaining xS,X constant at constant VP provides tight
self-regulation of the benzene spillover down the bottom. Accordingly, we hold VP in
ratio with the fresh feed rate (F), the ratio being necessary for handling large throughput
changes. Maintaining a sensitive enriching section tray temperature and VP/F thus
closes the two independent component balances on the prefractionator.
On the main column, the three independent component balances to be regulated
correspond to toluene leakage in the distillate and the bottoms, and maintaining the
side-draw toluene purity. To accomplish the same, sensitive tray temperatures in the
enriching, middle and stripping sections are controlled by adjusting, respectively, the
reflux rate (R), side-draw rate (S) and reboiler duty (QR).
The basic regulatory control structure discussed above is schematically depicted
in Figure 5 and is labelled CSR for convenient reference. To obtain the sensitive control
tray temperature locations, sensitivity analysis with respect to the four manipulated
variables, namely, LP, R, S and QR is performed. Figure 6 plots the temperature
sensitivities. From the plot, prefractionator tray 7 (TP7), main column rectification
section tray 7 (TM7), middle section tray 33 (TM33) and stripping section tray 40 (TM40)
are candidate control tray locations. The Niederlinksi Index (NI) for the 3x3 main
column temperature control system however is close to zero implying unfavourable
15
multivariable interaction. Subsequent dynamic simulations exhibited extreme difficulty
in getting the column to settle at a steady state with these four tray temperatures being
controlled. For a better NI, we choose to control tray 16 temperature (TM16) instead of
TM33, which gives a positive NI closer to 1. Note from the base-case temperature profile
(Figure 4), that TM16 is in the region where the temperature profile is still sharp. It is
then an appropriate location for sensing the movement of the separation zone due to
accumulation/depletion of toluene in the column middle section and adjusting the side-
draw rate for closing the toluene component balance.
Table 1. Variation in prefractionator bottom benzene
spill-over for feed composition disturbances
with xD,T, xS,T, xB,T, VP and xS,T constant
Disturbance (mol%) xB in LM
Base Case 0.0010
B 27 0.0015
B 39 0.0012
T 27 0.0009
T 39 0.0013
X 27 0.0013
X 39 0.0014
16
Figure 5. Petlyuk column regulatory control structure
17
Figure 6. Petlyuk column tray temperature sensitivities
TM Sensitivity to R TP Sensitivity to LP
TM Sensitivity to S TM Sensitivity to QR
18
3.2. Control Structure for Economic Operation
The regulatory control structure CSR closes the material/energy balances and
drives the process to a steady state. Of the 8 regulatory layer setpoints, the liquid level
setpoints have only a transient effect and do not affect the final steady state at which the
process settles. We also assume the pressure controller setpoint is kept fixed at its
design value to avoid pressure compensation of temperature controller setpoints. The
remaining five setpoints, namely, VP/F SP
, TP7SP
, TM7SP
, TM16SP
and TM40SP
, then
determine the final steady state at which the process settles. It is desirable that this
steady state be such that the process profitability is maximized. This requires
appropriate adjustment of the regulatory setpoints, which is accomplished by the
economic control system.
For the Petlyuk column, the first and foremost economic operation requirement
is that the purity of the three products be on-target at 99 mol% each. These would
consume three regulatory layer setpoints leaving two free setpoints that may be further
adjusted to reduce / minimize the reboiler duty and hence the energy consumption per
kmol feed processed. The economic control system thus consists of the product quality
control system and the reboiler duty reduction control system. These are developed in
the following.
3.2.1 Product Quality Control System
On-target product quality control requires that the impurity leakage in the
product streams be tightly controlled. This is accomplished by cascade composition
controllers that manipulate appropriate regulatory layer temperature setpoints, as shown
in Figure 7. The distillate product composition controller adjusts TM7SP
to maintain the
toluene impurity at 1 mol%. The distillate contains no xylene so that the distillate purity
19
then is 99 mol% benzene. Similarly, the bottoms product composition controller adjusts
TM40SP
to maintain its toluene impurity at 1 mol% for a 99 mol% pure xylene product.
The side-draw stream contains xylene as the principal impurity (0.92 mol%) with some
benzene impurity (0.08 mol%). For on-target 99% pure toluene side-draw, the most
convenient option is to maintain both the xylene and benzene impurities in the side-
draw at their base-case values. This is accomplished by a side draw xylene impurity
controller which adjusts TP7SP
, and a toluene purity controller which adjusts TM16SP
.
Note that adjusting TP7SP
changes the prefractionator top xylene spillover, which
achieves tight control of the principal xylene impurity in the side draw. With the xylene
impurity controlled tightly, controlling the side-draw toluene purity is equivalent to
controlling its benzene impurity since xS,B = 1% - xS,X for xS,T = 99%. For convenience,
we have chosen to control xS,T instead of xS,B as then the toluene purity controller
setpoint, xS,TSP
, remains constant at 99%, regardless of the choice of the xylene impurity
setpoint, xS,XSP
.
The decentralized quality control structure on top of the regulatory control
system is shown in Figure 7, and is labelled CSCC
for convenient reference. The
setpoints xD,TSP
, xB,TSP
, xS,TSP
, xS,XSP
and VP/F SP
correspond to the five steady state
operating dofs. Of these, the first three setpoints are fixed for on-target product quality.
The last two setpoints are then adjustable for reducing the reboiler duty (QR) towards
enhanced process energy efficiency.
We can operate the column using CSCC
at fixed base-case optimum values for
the two free setpoints, VP/F SP
and xS,XSP
. The control system should provide on-target
quality control regardless of changes in the feed composition. However, since the two
unconstrained setpoints are kept fixed post-disturbance and not re-optimized, QR is
likely to be sub-optimal, i.e. more than the minimum achievable reboiler duty (QRMIN
)
20
for the altered feed composition. To get a quantitative feel for the suboptimality in QR
with fixed setpoint operation, Table 2 compares QRMIN
with QR for ~6 mol% feed
composition change in either direction for each component, with the other two
components remaining equimolar. The Table data suggests that the degree of QR
suboptimality depends strongly on the direction of the feed composition disturbance. It
is most severe when the benzene mol fraction in the feed increases from 33% to 39%,
for which QR is a significant 16% more than QRMIN
. Less severe suboptimality with QR
being ~ 12% more than QRMIN
, is observed for a toluene lean feed. For a xylene lean
feed, QR is about 8% more than QRMIN
. For the other composition disturbances, the QR
increase over QRMIN
is no more than 3%. This suggests that for particular feed
composition disturbances, fixed setpoint operation can result in significant energy
inefficiency. There then exists incentive to adjust the two unconstrained setpoints, xS,XSP
and VP/F SP
to reduce QR towards QRMIN
.
Table 2. Comparison of QR using CS
CC and QR
MIN for feed composition disturbances
Disturbance (mol%) QR QRMIN
QR - QR
MIN % suboptimality
B 39 1859 1600 259 16.19
B 27 1740 1690 50 2.95
T 39 1736 1704 32 1.88
T 27 1758 1576 182 11.55
X 39 1651 1615 36 2.23
X 27 1798 1664 134 8.05
21
3.2.2. Control System for Reboiler Duty Reduction
The conceptually simplest way of ensuring near minimum reboiler duty
operation is to adjust VP/FSP
and/or xS,X to control appropriate process variable(s) that
remain invariant (or close to invariant) at the QRMIN
solution. Luyben refers to such
control structures as eigenstructures 19
while Skogestad refers to them as self-optimizing
Figure 7. Quality control system on top of regulatory structure
22
15. What constitutes such a process variable is however not straightforward. For the
present case, we avoid process variables that require tray composition measurements
and limit ourselves to appropriate combinations of tray temperatures. This is a
reasonable assumption as today’s columns are quite well instrumented with multiple
tray temperatures across the entire column being available, whereas composition
measurements remain cumbersome, expensive, unreliable and delayed.
To obtain the appropriate self-optimizing process variable(s), we compare the
column final steady state temperature profiles for the feed composition disturbances for
(a) fixed VP/F and xS,X and (b) VP/F and xS,X adjusted to minimize QR. In our
simulations, we found that the temperature profiles obtained in Hysys steady state mode
simulations and pressure-driven dynamic mode simulations were noticeably different.
This is likely because in the steady state mode, Hysys assumes a fixed column pressure
profile regardless of column internal flows, whereas in dynamics mode, the local tray
pressure drops vary with column internal flows. This variation in the column pressure
profile can cause the temperature profile to be different between the two modes. Since
we are interested in operating the column in dynamics, we compare the temperature
profiles obtained in dynamics mode and use differences between the optimal profile and
the profile for fixed setpoint operation to extract an appropriate temperature based
process variable for driving QR towards QRMIN
.
Figure 8 compares the final optimum steady state temperature profiles of the
prefractionator enriching section (TS1) and the main column middle section below side-
draw (TS5) for the feed composition disturbances with the corresponding profile for
fixed VP/F and xS,X (i.e. no reoptimization of free setpoints). The base-case optimum
temperature profile is also shown for reference. All the optimum temperature profiles
are relatively straight and the QR suboptimality due to fixed VP/F and xS,X operation is
23
most clearly visible in the large downward curvature of the temperature profiles. For the
case of a benzene rich feed, the TS5 temperature profile is curved significantly
downwards. For a benzene lean feed on the other hand, the TS1 profile curves
significantly downwards. A careful evaluation of the temperature profiles also shows
that at constant setpoint operation, a large downward curvature occurs in either TS1 or
TS5 for a toluene rich/lean feed and a xylene lean feed but not a xylene rich feed. This
then suggests that preventing downward curvature in the TS5/TS1 temperature profiles
by adjusting the two free setpoints should help drive QR towards QRMIN
, for most of the
feed composition changes, including the most severe disturbance (in terms of degree of
suboptimality due to fixed setpoints) of a benzene rich feed.
We now need a convenient metric for TS1/TS5 temperature profile downward
curvature. The simplest method is to draw a straight line between two appropriate fixed
tray locations and obtain the curvature as the deviation of the actual profile around this
line. As shown in Figure 9, when the actual tray temperatures are all above / below the
straight line, the curvature magnitude would be large. On the other hand, in case some
of the actual temperatures are above and others below the straight line, cancellations
would occur and the curvature magnitude would be small.
More specifically, let TM and TN be the chosen lower and higher tray temperature
locations, respectively. Then, the straight-line interpolated temperature of the ith
tray
above TM (i = 1 to N-M-1) is
ti = TM + i*(TN-TM)/(N-M+1)
The curvature (summed deviation) of the actual tray temperatures around this line then
is
24
Since we want to make adjustments only when the profile moves significantly
downwards, i.e. the curvature becomes large negative, the process variable to be
controlled, y, is defined as
As shown in Figure 10, this ensures y is zero for positive or slightly negative (>-α)
curvatures. When we control y with ySP
= 0, control action gets taken only when y
becomes large negative i.e. the temperature profile curves significantly downwards. The
parameter α may be used as a controller tuning parameter for enhanced reboiler duty
reduction while avoiding limit cycles due to the on-off switch inherent in the definition
of y.
We are interested in regulating the temperature profile downward curvature of
the prefractionator enriching section (TS1), yTS1, and middle section below side-draw
(TS5), yTS5. In this example, yTS1 is defined taking the tray immediately above the feed
tray as the lower tray (TM) and the prefractionator top tray as the higher tray (TN). For
the TS5 downward curvature, yTS5, TM is taken as tray 36 (middle section bottom tray)
and TN is taken as tray 29 (5 trays below side-draw). This choice of tray locations allows
for easier temperature profile curvature based distinction in the fresh feed composition.
This is evident from Figure 11, which plots the curvatures, CTS1 and CTS5 for the
different feed composition changes with fixed / reoptimized VP/F and xS,X. The large
negative curvatures in either CTS1 or CTS5 for fixed setpoint operation correlate to
changes in the feed composition (except a xylene rich feed). The absence of the large
negative curvature in the corresponding optimum profiles implies that curvature may be
used to infer suboptimality in QR and make appropriate adjustments in the available free
setpoints to drive the operation towards optimality (QRMIN
).
25
The QR reduction control system then consists of manipulating the two free
setpoints, VP/F and xS,X, to maintain yTS1 and yTS5. The straightforward decentralized
pairing is to maintain yTS1 by manipulating VP/F SP
and regulate yTS5 by adjusting xS,XSP
.
Since the xS,XSP
controller is likely to be slow due to large lags associated with
composition measurements, a dynamic improvement is to let the yTS5 controller bypass
the xS,X controller and directly manipulate the prefractionator tray temperature controller
setpoint, TP7SP
. This completes the overall control system with the regulatory control
loops, the quality control loops and the reboiler duty reduction loops. The full control
system for economic operation is shown in Figure 12 and labelled CSEC
(economic
control) for convenient reference.
26
Figure 8. Variation in steady state temperature profile with feed composition change for
CSCC
operation at constant setpoints (dashed lines) and reoptimized setpoints (solid
lines).
–●–: Base case profile; Black : Composition increase; Grey: Composition decrease
TM Sensitivity to QR
27
Figure 10. Mapping curvature (C) to large downward curvature (y)
Figure 9. Quantifying curvature in a temperature profile
28
α
Figure 11. TS1/TS5 curvatures for the different feed composition changes for fixed and
reoptimized VP/F and xS,X
α
29
Figure 12. Petlyuk column control system for QR reduction
30
Chapter 4
4. Dynamic Simulations and Closed Loop Results
To test the proposed control system, a rigorous dynamic simulation is built in
Hysys and closed loop results are obtained for principal disturbances, namely large
changes in the fresh feed composition and a ±20% step change in the fresh feed rate
(throughput). Feed composition changes are tested for each component (B, T or X)
changing as a step from 33 mol% (base-case) to 39 mol% or 27 mol% with the other
two components remaining equimolar.
4.1. Equipment Sizing and Plumbing
The equipment are sized using heuristics to fix hold-ups and hence the
equipment dynamic time constants. The prefractionator and main-column inner
diameter (ID) are chosen for a 0.6 m/s maximum vapour superficial velocity assuming
20% coverage by the tray downcomers. The condenser and reboiler are sized for ~10
min liquid residence time at 50% level at the base-case conditions in Figure 2. For a
pressure driven simulation, the tray resistance to vapour flow is calculated at the base-
case steady state vapour flow – pressure profile and used. Appropriate plumbing (pumps
and valves) is provided on the distillate, side-draw and bottoms lines. Note that Hysys
allows direct setting of the reflux rate and the vapour/liquid rate to the prefractionator so
that no plumbing is configured on these lines.
4.2. Controller Tuning
After appropriate sizing / plumbing modifications for a pressure driven
simulation, the regulatory and economic layer controllers are installed and tuned. A 2
min lag is applied in all temperature loops to account for sensor dynamics. The
composition measurements have a 5 min delay and are sampled every 5 mins. The PI
pressure controller uses a large gain and small time constant for tight column pressure
31
control. The two level controllers are P only with a gain of 2. The feed flow controller is
PI and tuned for a fast but non-oscillatory servo response. The four temperature
controllers are PI and tuned sequentially using the Hysys autotuner with further
refinement of the tuning for a slightly underdamped servo response. First, the
prefractionator temperature loop (TP7-LP) is tuned (all other temperature loops on
manual) followed by the main column loops in bottom-up sequence, i.e., TM40-QR, TM16-
S, TM7-R, in that order, with previously tuned loops on automatic. The composition
controllers are PI and tuned individually by first setting the reset time to approximately
the 2/3rd
response completion time and the controller gain to the inverse of the process
gain. These tuning parameters are then further refined for a slightly underdamped servo
response. The two temperature profile downward curvature controllers (yTS1-VP/F and
yTS5-xS,X) are PI and tuned by hit-and-trial for a fast and not-too-oscillatory regulatory
response to the principal disturbances. The curvature offset, α, described previously, is
chosen based on Figure 8 so that the y for the optimal conditions map to 0. To avoid a
limit cycle due to the on-off non-linearity in the definition of y, the α for yTS1 is relaxed
a bit. The controller parameters of the salient loops used in this work are reported in
Table 3.
4.3. Closed Loop Results
Closed loop dynamic simulation results for the principal disturbances are now
presented and discussed. To better appreciate the incremental improvement by the use
of additional loops on top of the regulatory control system, results are presented for
each of the three control structures CSR, CS
CC and CS
EC.
Figure 13 plots the transient response of salient process variables to the
throughput and feed composition disturbances, obtained for the basic regulatory control
system, CSR. The response curves suggest that the four-point temperature inferential
32
control structure, CSR, robustly handles the throughput/feed composition changes in
either direction with smooth changes in the manipulated process flow and the transient
response completing in about 6 h. Nonlinearity is evident in the response to feed
composition changes with the total change in QR and LP, which set the column internal
flows, exhibiting asymmetry.
Table 4 reports the purity of the three product streams for the principal
disturbances using CSR. Noticeable product purity deviations are evident for the feed
composition change disturbances. This is expected since a change in the feed
composition requires a readjustment in the prefractionator and middle-section split
requiring the temperature profiles to shift, as in Figure 8, which is prevented by holding
TP7 and TM16 constant. Quality deviations are also observed for throughput changes.
This is attributable to variability in the column pressure profile at the altered internal
flows so that the composition of the tray, whose temperature is controlled, is slightly
different implying a slightly altered split and hence product purity deviations. Since the
column top pressure is controlled, the effect is naturally more pronounced towards the
ends of the column, which show larger “local” tray pressure deviations. The product
purity controllers in CSCC
and CSEC
should appropriately adjust the temperature
setpoints for zero-offset in the product purities at the final steady state.
The transient response of CSCC
and CSEC
to benzene, toluene and xylene
composition step changes in the fresh feed is shown in Figure 14, Figure 15 and Figure
16 respectively. The solid and dashed lines correspond to CSCC
and CSEC
responses,
respectively, while the black and grey lines are for a composition increase and decrease,
respectively. In all cases, the response completes in about 20 hrs with the final total
impurity in each of the product streams settling at 1 mol% for on-target product purity
of 99 mol% each. The QR responses show that the final steady state QR using CSEC
33
(dashed lines) is always less than CSCC
implying that the temperature profile curvature
control helps improve the process energy efficiency. The savings in QR are particularly
significant for a benzene rich (Figure 14, black dashed line) and a toluene lean feed
(Figure 15, grey dashed line) with marginal savings for the other feed composition
changes. The transient responses also show that the curvature controllers, through their
manipulation of VP/FSP
and TP7SP
and the consequent nested action of the product purity
controllers, cause the appropriate “shift” in the prefractionator and middle section
temperature profiles for QR reduction. This is evident in the mostly large differences
between the final steady state TP7 and TM16 values for CSEC
(dashed lines) and CSCC
(solid lines).
For a quantitative comparison of the energy savings by using the temperature
profile downward curvature controllers, Table 5 compares QR for CSCC
, CSEC
, CSEC
with the yTS1 (TS1 downward curvature) controller on manual (i.e. VP/F SP
kept fixed at
base-case value) and CSEC
with yTS5 (TS5 downward curvature) controller on manual
(i.e. xS,XSP
is kept fixed at base-case value with xS,X controller manipulating TP7SP
). The
quantitative data shows that the two curvature controllers together help significantly
reduce QR towards QRMIN
for the benzene rich and toluene lean feed composition
disturbances with marginal improvement for the other feed composition disturbances.
The results also suggest that a substantial fraction of the QR reduction benefit can be
attained from only the yTS5 controller with the yTS1 controller achieving only marginal
improvements in QR. For the system studied, downward curvature in the temperature
profile of the middle tray section below side-draw product (TS5) thus appears to have a
more significant impact on QR reduction.
To explain the same, consider regulating only yTS5 by directly adjusting TP7SP
holding VP/FSP
constant. A large negative yTS5 indicates substantial suboptimality in QR.
34
To bring yTS5 back towards zero, the direct acting yTS5 controller would reduce TP7SP
which alters the prefractionator top xylene spillover and hence the side-draw purity. The
deviation in the side draw purity is detected by its purity controller, which would adjust
TM16SP
. It is then expected that the final steady state at which the column settles would
have an altered impurity mix in the side-draw. Thus e.g., for the benzene rich feed
composition disturbance, at the final steady state with only yTS5 regulated, xS,X changes
from 0.92 mol% to 0.88 mol% (xS,X + xS,B = 1 mol% for 99 mol% pure toluene side
product). This re-adjustment of the product impurity distribution corresponds to QR
reducing from 1859 kW to 1652 kW, which is quite close the QRMIN
value of 1600 kW.
Even as the absolute change in the benzene and toluene impurity mol fractions appears
small, the relative change in the impurity distribution is quite substantial with the
xS,B:xS,X ratio changing from 0.087 to 0.133. This then suggests that the side-product
impurity distribution (which is constrained by the side-product purity target) is a key
determinant of the reboiler energy consumption. Its proper adjustment with feed
composition is then critical towards energy efficient operation and any meaningful
control strategy must necessarily address the same to realize the energy efficiency
benefit of the complex column configuration, particularly when large changes in the
feed composition are expected.
35
Table 3. Controller tuning parameters for CSR, CS
CC and CS
EC
Supervisory Layer
CV MV KC Ti (min) Set Point PV Span MV Span
CS
CC CS
EC CS
CC CS
EC
xD,T TM7 0.2 0.25 60 60 0.01 0.0001-0.0200 77.3-107.3°C
xS,T TM16 0.11 0.2 90 90 0.99 0.9600-1.0000 96.5-126.5°C
xB,T TM40 0.1 0.15 60 60 0.01 0.0001-0.0200 119.5-149.5°C
xS,X TP7 0.12 - 90 - 0.0092 0.0001-0.0300 83.5-113.5°C
yTS1* VP/F - 0.05 - 75 0 -20 - +20 0-2.26
yTS5**
TP7 - 0.1 - 35 0 -20 - +20 83.5-113.5°C
Regulatory Layer
TM7 R 2.5 30 94.6 77.3-107.3°C 0-225 kmol/h
TM16 S 3.5 70 115.2 96.5-126.5°C 0-66 kmol/h
TM40 QR 0.3 40 141.3 119.5-149.5°C 0-3333 kW
TP7 LP 1.4 20 101.3 83.5-113.5°C 0-75 kmol/h
*Reverse action; **Direct action
Table 4. Purity of the three product streams for principal disturbances to CSR
Disturbance (mol%) xD,B xS,T xB,X
B 27 0.9928 0.9869 0.9893
B 39 0.9859 0.9758 0.9910
T 27 0.9875 0.9866 0.9891
T 39 0.9916 0.9863 0.9909
X 27 0.9885 0.9831 0.9917
X 39 0.9912 0.9936 0.9882
F -20 0.9921 0.9961 0.9916
F +20 0.9885 0.9739 0.9879
Table 5. Comparison of QR for different operating strategies
Disturbance
(mol%)
CSCC
CSEC
CS
EC: yTS1
manual
CSEC
: yTS5
manual
QR % sub
optimality QR
% sub
optimality QR
% sub
optimality QR
% sub
optimality
B 39 1859 16.2 1652 3.3 1652 3.3 1863 16.4
B 27 1740 3.0 1690 0.0 1740 3.0 1690 0.0
T 39 1736 1.9 1712 0.5 1736 1.9 1714 0.6
T 27 1758 11.5 1608 2.0 1608 2.0 1760 11.7
X 39 1651 2.2 1650 2.2 1650 2.2 1650 2.2
X 27 1798 8.1 1735 4.3 1735 4.3 1800 8.2
36
Figure 13. CSR transient response to (a) throughput disturbance; (b) feed composition
disturbance
––: F +20%; ––: F -20%; ––: B 39 mol%; ––: B 27 mol%;
– –: T 39 mol%; – –: T 27 mol%; –∙–: X 39 mol%; –∙–: X 27 mol%
(a)
(b)
37
Figure 14. CSCC
and CSEC
transient response to benzene composition disturbance
––: B 39 mol%; ––: B 27 mol%
38
Figure 15. CSCC
and CSEC
transient response to toluene composition disturbance
––: T 39 mol%; ––: T27 mol%
39
Figure 16. CSCC
and CSEC
transient response to xylene composition disturbance
––: X 39 mol%; ––: X 27 mol%
40
Chapter 5
5. Discussion
Based on the results presented, some comments on the operability of a ternary
Petlyuk column vis-à-vis a conventional direct / indirect sequence are in order. The
basic argument in favour of a Petlyuk column is that an optimized design for a given
throughput and feed composition is significantly more energy efficient and less capital
intensive compared to an optimized direct/indirect sequence. The energy efficiency of
the optimized high-purity Petlyuk column design however deteriorates significantly (up
to 16% for the example case study), unless the two free setpoints (unconstrained dofs)
are readjusted to appropriately rebalance the prefractionator / middle section splits
towards minimum energy consumption. This rebalancing in an automated feedback
arrangement is, however, not a straightforward task. For the commonly applied constant
setpoint operating policy in the industry (CSCC
for the studied example), the Petlyuk
column energy efficiency may then deteriorate significantly due to large feed
composition changes. Since the split rebalancing readjusts the impurity distribution in
the side-draw, the deterioration in energy efficiency may be mitigated if small
deviations in the side-draw product purity from its target are allowed i.e. the side draw
product purity is allowed to float. From the operational standpoint, it then stands to
reason that a high-purity Petlyuk column would be preferable over a conventional
distillation train when (a) large changes in the feed composition are not expected or (b)
relatively “loose” side-draw product purity control is acceptable. Alternatively, the
Petlyuk configuration may also be preferred when the side-draw product purity target is
not too stringent (e.g. 90 mol% pure instead of 99 mol%).
We note that the current study has considered a conventional Petlyuk column
where the liquid/vapour flow rate to the prefractionator is directly adjustable. In the
41
DWC arrangement however, typically only the liquid split ratio (and not flowrate) is
adjustable with the vapour split ratio not being adjustable, as it is fixed by the dividing
wall partitioning of the column cross-sectional flow area. Control system design for
optimal operation with on-target product purity control of a DWC must then account for
the loss in a control dof. In particular, the feasibility of the desired product impurity
targets becomes an issue, which is also referred to as the black-hole problem 20
. We are
currently researching control strategies for on-target product purity control with reboiler
duty reduction for the ternary Petlyuk DWC arrangement and hope to report the
findings shortly.
Lastly, we highlight the prefractionator and middle section temperature profiles
shift quite a bit for handling the feed-composition disturbances (see e.g. Figure 8). If the
product composition measurements are very infrequent (e.g. once a shift / day), the
composition based updates in the temperature setpoints would be very infrequent. The
column would then, in-effect, operate at constant temperature setpoints for prolonged
durations (until the next update). Holding a prefractionator/middle section tray
temperature constant necessarily prevents the respective profiles from shifting. This
would significantly degrade product purity and reboiler duty reduction control. In such
situations, we recommend the use of differential temperature difference in temperature
of two trays in a section 17
or double differential temperature 21
, instead of absolute
temperature, to infer the tray section splits to mitigate the economic control
performance degradation. We also highlight that differential temperature measurements
would also mitigate inadvertent changes in the tray section splits due to variability in
the column pressure profile.
42
Chapter 6
6. Conclusion
In conclusion, this work has systematically developed and evaluated the
performance of a control system for energy efficient on-target product purity operation
of a high purity BTX Petlyuk column. Results show that four-point temperature control
at constant prefractionator vapour to fresh feed ratio provides effective column
regulation for large throughput and feed composition changes. The adjustment of these
temperature setpoints, as in CSCC
, to maintain the four principal impurities (toluene in
distillate and bottoms; xylene and benzene in side-draw) in the product streams results
in significant energy inefficiency. For feed composition changes, the reboiler duty is
noticeably higher than the minimum duty possible with on target product purities. The
suboptimality is particularly severe (~16%) for a benzene rich feed. It is shown that
large downward curvature in the temperature profile of the prefractionator enriching
section and the middle section below side-draw can be used to infer the suboptimality.
By preventing large downward curvature in these profiles by manipulating the vapour to
the prefractionator and the prefractionator control tray temperature setpoint, as in CSEC
,
the suboptimality is significantly mitigated. The worst-case reboiler energy
consumption penalty is then only 4,26% more than the minimum possible. The work
highlights the need for innovative control solutions for realizing the energy-efficiency
benefit of the ternary Petlyuk column for large disturbances.
43
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