[Computer Aided Chemical Engineering] Integrated Design and Simulation of Chemical Processes Volume 35 || Dynamic Simulation

CHAPTER

DYNAMIC SIMULATION 44.1 INTRODUCTIONDynamic simulation is an advanced process simulation activity that integrates in the same simulation

environment the design, operation and control. Compared to steady-state simulation, both modelling

and software technology are much more demanding. This is valid also for users, because insufficiently

prepared simulations can easily fail or produce unreliable results. It is important to note that some ele-

ments usually optional in steady state are required for dynamic simulations, such as the sizing character-

istics of units and pressure/flow relations. For example, a simple flash cannot be seen only as a ‘generic’

multi-phase equilibrium unit, but needs the specification of the vessel type and geometry, as well as the

relations between flow and pressures for inlet and outlet lines. In addition, key operating variables – such

as levels, temperatures or pressures – should be kept at the desired values by means of controllers.

Therefore, dynamic simulation without process control implementation has little practical sense.

This chapter begins with a general discussion. By means of an introductory example, concepts im-

portant for dynamic modelling are introduced (conservation laws and constitutive equations, use of

extensive and intensive variables, the index of a Differential-Algebraic Equations (DAE) system, pro-

cess control, flow- and pressure-driven simulation). The model is solved in Matlab. Then, the dynamic

model of a continuous-stirred tank reactor (CSTR) with phase equilibrium is developed and solved by

means of a dynamic simulator (Aspen Dynamics (AD)). The following section considers dynamic

modelling of distillation units. A benzene–toluene column is used to illustrate the main issues of de-

veloping control schemes, implementation and tuning process controllers. The final section is devoted

to dynamic flowsheeting, focusing on the entire plant rather than on stand-alone units.

4.2 DYNAMIC MODELSDynamic simulation uses mathematical models that describe how various properties of a given system

are changing in time. The unsteady-state conservation of a certain property can be expressed by the

following general equation:

accumulation

rate

� �¼ input

flows

� �� output

flows

� �+

generation

rate

� �� consumption

rate

� �(4.1)

Computer Aided Chemical Engineering. Volume 35. ISSN 1570-7946. http://dx.doi.org/10.1016/B978-0-444-62700-1.00004-8

© 2014 Elsevier B.V. All rights reserved.127

http://dx.doi.org/10.1016/B978-0-444-62700-1.00004-8

In general, the models used for dynamic flowsheeting consist of mass, energy and momentum conser-

vation equations.When chemical reactions take place, it is useful to work with number of moles instead

of mass. Because the momentum (Navier–Stokes) equations are difficult to solve, they are usually

replaced by a flow hypothesis, for example perfect mixing or plug flow.

When perfect mixing is assumed (lumped-parameter systems), the properties are time dependent,

but uniform in space. The system is described by equations in which only time derivatives appear

(ordinary differential equations, ODE, or differential and algebraic equations, DAE). Solution of

the model equations requires specification of the initial conditions. If the system properties are space

dependent due to imperfect mixing (distributed-parameter systems), derivatives with respect to spatialcoordinates are non-zero. The system is described by partial differential equations. Both initial and

boundary conditions are necessary for a complete problem formulation.

In addition to equations reflecting the mass, energy and momentum conservation laws, dynamic

models also include system-dependent constitutive equations. The constitutive equations define rela-tionships between intensive variables (e.g. P–V–T equation of state, x–y equilibrium relationships) or

the rate at which transport phenomena and chemical reactions occur.

Writing rigorousdynamicmodels are rather difficult. In general, it is a goodmodellingpractice towrite

the conservationequations using extensive variables and to introduce the intensive variables as requiredbythe constitutive equations. The essential features of dynamic modelling will be presented bymeans of the

following examples, which also include recommendations useful for developing robust dynamic models.

4.3 INTRODUCTION TO DYNAMIC MODELLING AND DYNAMIC SIMULATIONIn this section, the dynamic model of a butane/butene alkylation reactor is developed. This exercise lets

us introduce the main particularities of dynamic modelling and simulation.

The alkylation of iso-butane with butene to form iso-octane is a widely used method for producing

high-octane blending component for gasoline.

The main reaction is the combination of iso-butane and butene to iso-octane. The reaction is cat-

alysed by strong acids, for example H2SO4.

C4H8 + i�C4H10 ! i�C8H18

Að Þ + Bð Þ ! Pð Þ

However, there is an undesirable consecutive reaction of butane with iso-octane giving heavier com-

ponents, modelled here as dodecane:

C4H8 + i�C8H18 !C12H26

Að Þ + Pð Þ ! Rð Þ

The actual chemistry is more complex, but for this demonstration it captures sufficiently the essentials

of the overall chemistry. These exothermic reactions are irreversible and occur in liquid phase. Good

contact between the hydrocarbon and the H2SO4 (catalyst) phase is required; therefore, continuous-

stirred reactors are used. Note that the activation energy of the second reaction is larger than of the

first. Since low temperature favours the desired first reaction, the process is carried out at low temper-

ature (e.g.�5 �C). The second reaction is also suppressed by keeping the concentration of butene low.This is achieved by a large excess of iso-butane fed to the reactor.

128 CHAPTER 4 DYNAMIC SIMULATION

4.3.1 BALANCE EQUATIONS/CONSERVATION LAWSThe dynamic model of the alkylation reactor (Figure 4.1, left) consists of component mole balance

equations for reactants (A, B), products (P, R) and catalyst (K). Note that energy and momentum equa-

tions are replaced by the assumptions of constant temperature (T¼368 K) and perfect mixing,

respectively.

dNA

dt¼FA, in�FA,out +RA (4.2)

dNB

dt¼FB, in�FB,out +RB (4.3)

dNP

dt¼�FP,out +RP (4.4)

dNR

dt¼�FR,out +RR (4.5)

dNK

dt¼FK, in�FK,out (4.6)

The following initial conditions are assumed:

NA,0 ¼ 10kmol; NB,0 ¼ 100kmol; NP,0 ¼NR,0 ¼ 0kmol; NK,0 ¼ 100kmol (4.7)

It should be remarked that we choose to represent the state of the system by the component holdups, Nj,

which are extensive quantities. These variables are called state variables and will be denoted by x(Figure 4.1, right). The left side of the balance equations contains the rates of change of the state vari-

ables, dx/dt, while the right side consists of non-linear functions which specifie how the rate of change

can be calculated. In the first place, the rates of change are determined by variables which are exterior

NA

NB

NP

NR

NK

FA,in

FK,in FB,in

FA,out FB,out FP,out FR,out FK,out

Fout

V

u(t) y(t)

dx(t)

0 = g (x,z,u)

y = h(x,z,u)

f (x,z,u)dt

=

x(t), z(t)

(vol)

y = [FA,out FB,out FP,out FR,out FK,out]T

z = [r1 r2 rA rB rP rR cA cB cP cR cK FA,out FB,out FP,out FR,out FK,out V ]T

u = [FA,in FB,in FK,in Fout ]T

x = [NA NB NP NR NK ]T

(vol)

FIGURE 4.1

Alkylation reactor. Physical model (left) and systemic representation (right).

1294.3 INTRODUCTION TO DYNAMIC MODELLING AND DYNAMIC SIMULATION

to the modelled system, called input variables, u. The set of input variables contains the reactor-inletcomponent flow rates, Fj,in and the total reactor-outlet volumetric flow rate, Fout

(vol). The input variables

can be further classified as manipulated inputs and disturbances.Specification of the input variables is necessary for solving the dynamic model. We assume that

only reactants and catalyst are fed to the reactor and set the following constant flow rates (in kmol/h):

FA, in; FB, in; FK, in½ � ¼ 71; 710; 390½ �

The outlet flow rate is also assumed constant, and set equal to the inlet volumetric flow rate:

Fvolð Þout ¼F�

out ¼FA, inVm,A +FB, inVm,B +FK, inVm,K ¼ 118:8m3=h (4.8)

with the molar volumes (in m3/kmol):

Vm,A; Vm,B; Vm,P; Vm,R; Vm,K½ � ¼ 0:222; 0:089; 0:098; 0:158; 0:222; 0:11½ �

4.3.2 CONSTITUTIVE EQUATIONSIn general, a dynamic model is correctly written (a solution is possible) if, given the state and input

variables, the rates of change (right side of the differential equations) can be calculated. For the alkyl-

ation reactor, the following constitutive equations can be used:

Total volume:

V¼NAVm,A +NBVm,B +NPVm,P +NRVm,R +NKVm,K (4.9)

Concentrations:

cA ¼NA

V;cB ¼NB

V;cP ¼NP

V;cR ¼NR

V;cK ¼NK

V(4.10)

Reaction rates (Mahajanam et al., 2001):

r1 ¼ k1cAcB; k1 ¼ 1:62�109exp �65,133

8:31T

� �m3=kmol=s (4.11)

r2 ¼ k2cAcP; k2 ¼ 4:16�1012exp �81,417

8:31T

� �m3=kmol=s (4.12)

Component net generation rates:

RA ¼� r1 + r2ð ÞV; RB ¼�r1V; RP ¼ r1� r2ð ÞV; RR ¼ r2V (4.13)

Outlet flow rates:

FA,out ¼Fvolð Þout cA;FB,out ¼F

volð Þout cB;FP,out ¼F

volð Þout cP;FR,out ¼F

volð Þout cR;FK,out ¼F

volð Þout cK (4.14)

It can be seen that rate of change calculation introduces some auxiliary variables, z (Figure 4.1, right),and new algebraic equations (4.9)–(4.14). It is important to emphasize that, given the state and input


variables, x and u, the auxiliary variables z can be found by solving the algebraic part of the model. If

this is not possible, either some constitutive equations are missing or we are dealing with a DAE system

of an index larger than 1 (see also the next section).

Finally, we remark that, from the multitude of model variables, only a subset y is of interest. Theseare called outputs. For the alkylation problem, one could choose the outlet flow rates, Fj,out, as model

outputs. Other choices, such as outlet concentrations, reactant conversion, transformation yield and

selectivity, are also possible.

In conclusion, the dynamic models of lumped-parameter systems can be represented in the follow-

ing condensed form:

dx tð Þdt

¼ f x tð Þ,z tð Þ,u tð Þð Þ (4.15)

0¼ g x tð Þ,z tð Þ,u tð Þð Þ (4.16)

y tð Þ¼ h x tð Þ,z tð Þ,u tð Þð Þ (4.17)

Initial condition : x 0ð Þ¼ x0 (4.18)

4.3.3 DEGREES OF FREEDOMThe degrees of freedom (DOF) are defined as the variables that must be specified to define the process.

DOF analysis is an important issue in dynamic simulation. In principle, the number of DOF can be

determined by examining the model and applying the rule ‘variables minus equations’. This procedure

is practical for simple units, but less convenient for complex units. These can be solved, however, as

assembly of simpler devices, or smaller flowsheets.

The concept of control degrees of freedom, defined as the valves available for control purposes

(Luyben, 1996), is very useful for variable specification in dynamic simulation. It turns out that, most

of the time, the number of dynamic DOF equals the number of control DOF. As a result, a practical

method to determine the dynamic DOF consists of ‘counting the valves’ available on the process

streams, plus the heat duties for heaters/coolers, as well as the mechanical power of compressors

and pumps.

4.3.4 SOLUTION TOOLSThe set of differential and algebraic equations can be solved numerically. Simple models can be solved

by implementing the Euler method in Microsoft Excel (office.microsoft.com). General-purpose math-

ematical software as Mathworks Matlab (www.mathworks.com), Maplesoft Maple (www.maplesoft.

com), Wolfram Research Mathematica (www.wolfram.com) asks the user to write the mathematical

model and to call an ODE or DAE solver. For more difficult problems, one can use a high level

programming language such as FORTRAN or C++ together with appropriate numerical libraries, such

as Rogue Wave IMSL (www.roguewave.com), Numerical Algorithm Group (NAG) (www.nag.co.uk)

or available from free sources such as Netlib repository (www.netlib.org). More specialized dynamic

process modelling software packages are PSE gPROMS (www.psenterprise.com), AspenTech Aspen


http://office.microsoft.com

http://www.mathworks.com

http://www.maplesoft.com

http://www.maplesoft.com

http://www.wolfram.com

http://www.roguewave.com

http://www.nag.co.uk

http://www.netlib.org

http://www.psenterprise.com

Dynamics, Aspen CustomModeller and HYSYS (www.aspentech.com). These packages provide com-

prehensive facilities for developing, validating and executing dynamic models of chemical processes.

Activities such as steady-state and dynamic simulation, optimization and parameter estimation can be

performed. Libraries of models for the most common unit operations are included, as well as support

for calculating physical properties. The modelling languages are object oriented. Thus, the user defines

classes ofModels which are instantiated by Units. The Units are connected by Streams and can be ag-gregated to form complexModels. This facilitates model development and maintenance and enhances

reusability.

4.3.5 THE INDEX PROBLEMDAE systems can be solved in a computationally efficient manner by converting them into ODE sys-

tems (this is done automatically by the DAE solvers). Thus, Equation (4.16) is differentiated once

(index-one DAE, Pantelides and Barton, 1992) and the time derivatives of the auxiliary variables

are obtained as:

dz tð Þdt

¼ @g

@z

� ��1 @g

@x

dx

dt+@g

@u

du

dt

� �(4.19)

The initial conditions for the auxiliary variables, z(0)¼ z0, are found by solving the algebraic equa-

tions (4.16), where the initial values of the state variable x0 and the inputs u(0) are known. This is calledinitialization and is the first step of a dynamic simulation. Initialization might fail if a good approx-

imation for z0 is not available. For this reason, the recommended approach is to use a known steady state

as the initial condition for the dynamic simulation.

Equation (4.19) can be used only when the matrix @g/@z is nonsingular, which is equivalent to re-

quiring that the algebraic equations (4.16) are solvable with respect to the auxiliary variables z. If this isnot the case, Equation (4.19) must be differentiated again. The DAE system has an index larger than

one and the solvers fail.

In the practical context of a process simulation involving a large number of variables, the diagnosis

of a high-index problem is not trivial. When high-index is found, both gPROMS and Aspen Custom

Modeller suggest changes in specifications. However, the user can prevent such troubles by choosing

the correct set of input variables. In the alkylation example, the reaction volume V is a legitimate

steady-state specification, while the outlet flow rate Fout(vol) is a result of steady-state simulation. How-

ever, this leads to a high-index DAE system. Therefore, in a dynamic model the outlet flow rate Fout(vol)

must be specified, while the reaction volume V is obtained as a result.

Another example is found in modelling and simulation of distillation columns: for steady-state

purposes, it is usual to set the purity of top and bottom products and to find the required reflux and

vapour flow rates as simulation results. This specification is not acceptable in dynamic mode be-

cause it leads to a high-index problem. Therefore, if certain purities are required, the dynamic dis-

tillation models must include composition controllers manipulating, for example, the reflux and the

reboiler duty.

An additional element of difficulty arises when the input variables are suddenly changed, for ex-

ample in a stepwise manner. Then, the derivative du/dt from Equation (4.19) becomes infinite and

re-initialization is necessary. If this step fails, ramping of the input from the initial to the final value

in a finite time might provide a solution.


http://www.aspentech.com

4.3.6 COMPUTATION OF PHYSICAL PROPERTIES (LOCAL MODELS)While solving the dynamic model of a process system, it should be kept in mind that most of the com-

puting time is spent for evaluating physical properties. Very non-linear thermodynamic models require

iterative calculations at each step of the integration procedure. Therefore, using simpler models can

appreciably reduce the computing time. This is achieved by means of local models for physical prop-

erties, valid over a limited interval of temperature, pressure and composition. In the above example, we

assumed the additivity of the (constant) molar volumes. When calculating the phase equilibrium, the

following linear relation may approximate the variation of K-factors:

lnKi ¼Ai +Bi=T (4.19a)

Sometimes, this approach decreases the robustness of simulation and the user must restore the rigorous

thermodynamics option.

4.3.7 SIMULATION SCENARIOS AND RESULTSDynamic simulation requires that the input variables are specified over a time interval of interest. We

start the investigation of the alkylation reactor by assuming that, during 20 h, all the inputs are kept

constant. Results obtained by solving the dynamic model in Matlab are presented in Figure 4.2.

Figure 4.2 shows the evolution in time of reaction volume and concentrations (left) and reactor-

outlet flow rates (right). The most noteworthy result is that the reactor is unstable: as time passes,

the reaction volume decreases and eventually drops to zero, which means an empty vessel. Negative

values for physical quantities as volume, concentration or flow rate are obtained and therefore the

model ceases to represent the reality.

Monitoring all variables of a model describing a complex plant is impractical. For this reason, the

dynamic simulators require the definition of variable types and bounds specification that are enforced

during the dynamic simulation.

The reason for instability is obvious: although in Equation (4.8), the inlet and outlet volumetric flowrates are set equal, this does not ensure the equality of inlet and outlet mass flow rates. Therefore, de-

pletion occurs. It should be remarked that a specification of the outlet flow rate which perfectly

0

5

10

15

20

25

0

1

2

3

4

5

6

0 5 10 15 20

c (k

mo

l/m3 )

F (

kmo

l/h)

V (

m3 )

t (h) t (h)

cB

cK

cA cP cR

V

0

20

40

60

80

0

200

400

600

800

0 5 10 15 20

FB,out

FA,out

FP,out

FR,out

FK,out

FIGURE 4.2

Alkylation reactor: dynamic simulation results.


balances the inlet flow is impossible, as it would require infinite calculation precision and would not be

applicable when disturbances are present. Therefore, an important conclusion of this section is that the

inventory must always be controlled. In practice, this is achieved by implementing control loops which

manipulate inlet or outlet streams in order to keep levels and pressures at required values. This brings us

to the next particularity of dynamic simulation, namely, process control.

4.3.8 PROCESS CONTROLIn dynamic simulation, the liquid and gas holdups are stabilized by using level and pressure controllers,

respectively. Typically, the controller changes a manipulated input variable in such a way that a con-trolled output variable is as close as possible to a specified set point (SP). The necessary control actionis obtained by means of a control algorithm. For the alkylation example, we will include a level con-

troller manipulating the outlet flow rate (Figure 4.3).

The following control algorithm will be applied:

Fvolð Þout ¼ max 0,F�

out +K V�VSP� ��

(4.20)

where

F�out ¼ 118:8m3=h; K¼ 10

m3=h

m3

In the new model, the SP becomes an input variable, while the outlet flow rate is an auxiliary one.

Results of dynamic simulation are presented in Figure 4.4, for the following scenario: initially, the vol-

ume SP is set to VSP¼30 m3. Then, at time 0.5, 1 and 1.5 h, VSP is modified to 15, 45 and 30 m3, re-

spectively. The system is stabilized, as the level controller adjusts the outlet flow rate such that the

reaction volume stays close to the required value despite SP changes.

NA

NB

NP

NR

NK

VLC

VSPV

voloutF

FA,inFK,in FB,in FA,in

FK,in FB,in

NA

NB

NP

NR

NK

VLC

VSPV

voloutF

a

P1 P2

FIGURE 4.3

Alkylation reactor with level control. Flow-driven (left) and pressure-driven (right) simulations.


We also note that using process control allows setting an output variable (the reaction volume, V) tothe required value, without running into high-index problems. A similar approach is applicable to a

distillation column, where two concentration controllers might change the reflux and boilup rates in

order to meed distillate and bottoms specifications.

4.3.9 FLOW- AND PRESSURE-DRIVEN DYNAMIC SIMULATIONSThe model used during previous simulations assumed that the outlet flow rate can be set to any desired

value, without any concern regarding how this is achieved. This simulation mode is called flow drivenand it has the key advantage of an easy setup.

A more realistic model would consider a pump and a valve, with the outlet flow rate determined by

the valve type (Cv), valve opening (a), the fluid density (r) and the pressure difference between the

pump outlet and the vessel receiving the flow (DP¼P1�P2):

Fvolð Þout ¼Cvk að Þ

ffiffiffiffiffiffiffiDPr

s(4.21)

Moreover, the dynamics of the valve could be included in the model. This simulation mode is called

pressure driven. It is more realistic but also more demanding, because all pumps and valves must be

taken into account.

4.4 CSTR WITH VAPOUR–LIQUID EQUILIBRIUMThis section will present the dynamic model of a CSTR, including vapour–liquid equilibrium. If only

one phase is considered, the well-known CSTR model is obtained. On the other hand, by setting the

reaction rates to zero, the dynamic model of a Flash (single-stage distillation) is obtained. The Flash is

an important model in flowsheeting because distillation columns can be modelled as a set of Flash op-

erations interconnected by liquid and vapour flows.

0

10

20

30

40

50

0

50

100

150

200

250

300

V (

m3 )

Fo

ut (

m3 /

h)

t (h)

Fout

V

VSP

0

0.1

0.2

0.3

0.4

0.5

0.6

0

1

2

3

4

5

6

0 0.5 1 1.5 2 0 0.5 1 1.5 2

c (k

mo

l/m3 )

t (h)

cB

cK

cA

cP

cQ

FIGURE 4.4

Alkylation reactor: results of closed-loop dynamic simulation.

1354.4 CSTR WITH VAPOUR–LIQUID EQUILIBRIUM

4.4.1 DYNAMIC MODELFigure 4.5 depicts the layout of a CSTRwith vapour–liquid equilibrium. Amulti-component feed of the

composition zi is split in vapourV and liquid L, with the compositions yi and xi, respectively. In the liquidphase, several chemical reactions take place. Optionally, heat may be added or removed. The problem is

to study the dynamic response at various disturbances, as changes in throughput or composition.

The key to successful development of the CSTR with vapour–liquid equilibrium dynamic model is

using extensive variables and writing the total mass balance equation for each component together with

enthalpy balance. This leads to the following:

Differential equations (mass and energy balance)

dnidt

¼Fzi�Vyi�Lxi +Ri (4.22)

dU

dt¼HF�VhV �LhL +Q (4.23)

With initial conditions : ni 0ð Þ¼ ni,0, U 0ð Þ¼U0 (4.24)

The algebraic equations allow calculation of the right hand side of the system (4.22)–(4.23), as follows.

The component holdups are split between the two phases:

ni ¼ nV, i + nL, i NC equationsð Þ (4.25)

Introduce mole fractions, necessary for constitutive relationships:

xi ¼ nL, iXknL,k

NC equationsð Þ (4.26)

yi ¼nV, iXknV,k

NCequationsð Þ (4.27)

Vapour and liquid phases are in equilibrium:

P’i y, T, Pð Þyi ¼ gi x, Tð ÞxiPvapi Tð Þ NC equationsð Þ (4.28)

Liquid and vapour fill the vessel:Xi

nV, i ¼VVrV y, T, Pð Þ 1 equationð Þ (4.29)

Xi

nL, i ¼VLrL x, T, Pð Þ 1 equationð Þ (4.30)

Vtotal ¼VV +VL 1 equationð Þ (4.31)


V , yi

F , Zi

L , Xi

Q

nV

nL

P

P1

P2

a1

a2

a0

T

HV

HL

FIGURE 4.5

CSTR with vapour–liquid equilibrium. The following notation will be used:

i¼1. . .NC: components;

k¼1. . .NR: chemical reactions;

ni, nV,i, nL,i: component i molar holdup in the vessel, vapour and liquid phases, respectively (kmol);

F, V, L: feed, vapour and liquid flow rates (kmol/s);

zi, xi, yi: feed, liquid and vapour mole fractions;

n: matrix of stoichiometric coefficient;

rk: reaction rates (kmol/m3/s);

Ri: component reaction rate (kmol/s);

UF, UL, UV: feed, liquid and vapour internal energy (J);

Q: heat duty (W);

hV, hL: vapour- and liquid-specific energy (J/kmol);

gi: activity coefficients;

’i: fugacity coefficients;

Pivap: component vapour pressure (Pa);

Vtotal, VL, VV: vessel, liquid and vapour volume (m3);

rL, rV: liquid and vapour molar densities (kmol/m3);

T: temperature (K);

P, P0, P1, P2: pressures (Pa);

a0, a1, a2: valve opening (%);

f: function of valve opening in pressure–flow relationships.


Component reaction rates:

Ri ¼VL

Xk¼1,NR

ni,krk x, Tð Þ NC equationsð Þ (4.32)

The total energy is split between the two phases:

U¼UL +UV 1 equationð Þ (4.33)

UL ¼ nLhL x, T, Pð Þ 1 equationð Þ (4.34)

UV ¼ nVhV y, T, Pð Þ 1 equationð Þ (4.35)

Pressure–flow relationships:

F¼ f 0 a0ð ÞffiffiffiffiffiffiffiffiffiffiffiffiffiP0�P

p1 equationð Þ (4.36)

V¼ f 1 a1ð Þ ffiffiffiffiffiffiffiffiffiffiffiffiffiP�P1


L¼ f 2 a2ð Þ ffiffiffiffiffiffiffiffiffiffiffiffiffiP�P2


The specified inputs are: feed composition (zi), pressures (P0, P1, P2), duty (Q) and valve openings

(a0, a1, a2).The user must specify the constitutive equations for vapour pressure Pi

vap, reaction rates (rk), fugac-ity and activity coefficients (’, g), densities (rL, rV), liquid- and vapour-specific energies (hL, hV) andthe valve characteristics (f ).

There are (5NC+9) unknowns in the algebraic equations: component number of moles in liquid and

vapour phase (nV,i, nL,i), component mole fractions in liquid and vapour phase (xi, yi), component re-

action rates (Ri), liquid and vapour volume (VL, VV), pressure (P), temperature (T), flow rates (F, L, V),liquid and vapour energy (UL, UV). These unknowns are found by solving Equations (4.25)–(4.38).

The above system of equations can be solved following using general-purpose software or process

simulation tools. The next section shows the use of Aspen Dynamics for solving the problem of phase

equilibrium coupled with a chemical reaction.

4.4.2 APPLICATION: OLEFIN METATHESIS IN A CSTR WITH VAPOUR–LIQUIDEQUILIBRIUMOlefin metathesis is used in the petrochemical industry. In this section, we consider the metathesis of

2-pentene to form the two products 2-butene and 3-hexene:

2C5H10>C4H8 +C6H10

Að Þ Bð Þ Cð Þ

This reaction has been the subject of several studies concerning reactive distillation (Okasinski and

Doherty, 1998; Chen et al., 2000; Al-Arfaj and Luyben, 2002).


The reaction rate is given by the following relationship:

r¼ kctot x2A�xBxCKeq

� �(4.39)

where ctot is the total mole concentration (kmol/m3).

k¼ 9:594�105exp�3321:2

T

� �kmol=m3=h and Keq ¼ 0:25

A steady-state simulation is built in Aspen Plus (Figure 4.6). The reaction takes place in a 20 m3 CSTR,

in which the liquid holds 10 m3. The reaction temperature and pressures are set to 80 �C and 4 bar,

respectively. The feed consists of 2-pentene, at 10 bar and 25 �C. The pressure of vapour and liquid

products is 1 bar. Table 4.1 presents the results of steady-state simulation. The conversion of

2-pentene is about 52%. The heavy component 2-hexene and 2-pentene are found mainly in the liquid

product. 2-Butene is distributed almost equally between the vapour and liquid phases. After getting

steady-state convergence, the pressure-driven dynamic simulation file is exported.

Then, the dynamic simulation continued in AD. Figure 4.7 shows the flowsheet. All the necessary

equations are built in the library models. The parameters of the physical properties are taken from the

appropriate database. Moreover, the simulator adds level, temperature and pressure controllers. Setting

the controllers is based on the information available, as follows: temperature range of 100 �C, level andpressure ranges of 0 – twice the steady-state values. The correct mode of control action (direct or re-

verse, see Section 4.6.1) and initial values for the gain and integral time are also set (Table 4.2).

Dynamic simulation was carried out considering the following scenario (Figure 4.8): starting from

the steady state, the opening of the feed valve is changed from 50% to 60%, at time t¼1 h. The feed

Feed

L-out

Reactor

V-out

V1

V2

V0

F-in

Vapour

Liquid

FIGURE 4.6

Olefin metathesis reactor: Aspen Plus steady-state simulation.


flow rate increases almost instantaneously (this is expected, because the valve dynamics was

neglected). In order to keep the pressure and level at their SPs, the controllers open the valves V1

and V2 and the vapour and liquid flow rates increase. The change of product compositions is small.

Then, at time t¼7 h, the SP of the temperature controller is reduced from 80 to 70 �C. The duty

Table 4.1 Olefin Metathesis Reactor: Stream Results

F-in Feed L-out Liquid V-out Vapour

Temperature (�C) 25 25 80 80 80 80

Pressure (bar) 4 10 4 1 4 1

Vapour (Frac) 0 0 0 0 1 1

Mole flow (kmol/h) 50 50 34.306 34.306 15.694 15.694

Mass flow (kg/h) 3506.7 3506.7 2472.5 2472.5 1034.3 1034.3

Volume flow (m3/h) 5.432 5.432 4.184 4.184 115.21 460.82

Mole flow (kmol/h)

Pentene 50 50 17.103 17.103 7.129 7.129

Butene 0 0 6.232 6.232 6.652 6.652

Hexene 0 0 10.971 10.971 1.914 1.914

Mole (Frac)

Pentene 1 1 0.499 0.499 0.454 0.454

Butene 0 0 0.182 0.182 0.424 0.424

Hexene 0 0 0.32 0.32 0.122 0.122

FIGURE 4.7

Olefin metathesis reactor: Aspen Dynamics dynamic simulation.


decreases and the newSPof temperature is quickly reached. As a result of the temperature decrease, only

liquid phase products are obtained. The pressure drops, the vapour valve V1 is completely closed and

control of the pressure is no longer possible (saturation of the control valve). Asmore liquid is produced,

the liquid valve V2 opens. For about 2 h, valve V2 is also saturated (100% open). Changes of mole frac-

tions in both liquid and vapour phases can be observed. A new steady state is reached after about 5 h.

4.5 DYNAMIC DISTILLATION COLUMNA dynamic model of a distillation column can be assembled from simpler units, such as trays, heat

exchangers (condenser, reboiler), reflux drum, valves and pumps (Figure 4.9). Tray modelling has

to answer two issues: (1) accurate description of material and energy holdup, and (2) accurate pressure

drop calculation.

Dynamic model of distillation column illustrates the relationship between dynamic and design

DOF: dynamic (control) DOF (distillate, reflux, bottoms, steam and cooling water flow rates)¼ steady

state (design) DOF (pressure, distillate and bottoms purity)+number of non-reactive levels (reflux

drum, column sump).

4.5.1 TRAY MODELLINGThe dynamic model of a single tray is similar to the dynamic model of the CSTR with vapour–liquid

equilibrium, discussed in previous section. The model of a distillation column can be built by assem-

bling the models of trays, condenser, reflux drum and reboiler. However, the solution of the resulting

model is a much more difficult problem.

For a single tray k (Figure 4.10), the material and energy balance equations are:

dnk, idt

¼ Lk�1, i�Lk, i +Vk + 1, i�Vk, i (4.40)

dUk

dt¼ Lk�1hL,k�1�LkhL,k +Vk + 1hV,k + 1�VkhV,k (4.41)

Table 4.2 Olefin Metathesis Reactor: Controller Settings

TC PC LC

Controlled variable Temperature Pressure Liquid level

Controlled variable range 30–130 �C 0–8 bar 0–4.5 m

Manipulated variable Duty Opening of valve V1 Opening of valve V2

Manipulated variable range 0–3�106 kcal/h 0–100% 0–100%

Control action Reverse Direct Direct

Kc (%/%) 2.5 20 10

Ti (min) 6 12 60

1414.5 DYNAMIC DISTILLATION COLUMN

Feed

Time (h)

Blo

cks(

"V0"

).P

os %

Str

eam

s("f

eed"

).F

(km

ol/h

r)

Feed

0.0 2.5 5.0 7.5 10.0 12.5 15.0

25.0

50.0

75.0

100.0

20.030.040.050.060.070.080.0

Flow rate

Valve position

Vapour

Str

eam

s("v

apou

r").

Zn(

"hex

") (

kmol

)

Str

eam

s("v

apou

r").

Zn(

"pen

") (

kmol

)

Str

eam

s("v

apou

r").

Zn(

"but

") (

kmol

)

Str

eam

s("v

apou

r").

F (

kmol

/h)

0.25

0.5

0.75

1.0

Time (h)

0.0 5.0 10.0 15.0

0.0

20.0

40.0

Flow rate BUT

PEN

HEX

Liquid

Str

eam

s("l

iqui

d").

Zn(

"hex

") (

kmol

/k)

Str

eam

s("l

iqui

d").

Zn(

"pen

") (

kmol

/k)

Str

eam

s("l

iqui

d").

Zn(

"but

") (

kmol

/k)

Str

eam

s("l

iqui

d").

F (

kmol

/h)

0.5

1.0

Time (h)

0.0 5.0 10.0 15.020.0

30.0

40.0

50.0

60.0

70.0

Flow rate

BUT

PENHEX

Temperature controller

Set

poi

nt C

Con

trol

ler

outp

ut M

Mkc

al/h

r

Pro

cess

var

iabl

e (C

)

Time (h)

0.0 2.5 5.0 7.5 10.0 12.5 15.0

0.05

0.10.15

0.20.25

0.3

65.0

70.0

75.0

80.0

85.0

OP

PV

Pressure controller

Set

poi

nt b

ar

Con

trol

ler

outp

ut %

Pro

cess

var

iabl

e (b

ar)

25.0

50.0

75.0

100.0

Time (h)

0.0 2.5 5.0 7.5 10.0 12.5 15.0

3.0

3.5

4.0

PVOP

Level controller

Time (h)

Set

poi

nt (

m)

Con

trol

ler

outp

ut %

Pro

cess

var

iabl

e m

25.0

50.0

75.0

100.0

0.0 2.5 5.0 7.5 10.0 12.5 15.0

2.2

2.25

2.3

2.35

2.4

2.45

PVOP

FIGURE 4.8

Olefin metathesis reactor: dynamic simulation results.

Then, the right side of the differential equations can be calculated as follows:

• Perform a UV-flash for each tray k. This gives the phase split (nk,iL ,nk,i

V ), phase compositions (xk,i,yk,i), temperature (Tk), pressure (Pk), and specific energies (hk

L,hkV);

• Compute the liquid flow rate from tray hydraulics (Francis weir formula):

Lk, i ¼ Lkxk, i (4.42)

Lk ¼ 1:839rLkWh1:5ow (4.43)

Column

Ref-drum

Cond

Reboiler

V3 V2

V1

V4

V5

FIGURE 4.9

Dynamic model of a distillation column.

Lk-1

Vk+1Lk

Vk

hw

how

FIGURE 4.10

Tray modelling.


where how is the height over the crest given by:

how ¼ hl�hw (4.44)

hl is the liquid height, which in turn is related to the liquid holdup nkL as:

hl ¼ nLk= AtrayrLk� �

(4.45)

• Compute the vapour flow rate, which is related to pressure difference:

Vk, i ¼Vkyk, i (4.46)

DPk ¼DPdry +DPliq +DPres (4.47)

where

DPdry ¼C0V2k is the dry plate pressure drop (4.48)

DPliq ¼ hLrLg is the static pressure drop (4.49)

DPres accounts for superficial tension effects, froth, etc.

The solution of the resulting set of DAE is highly non-linear and stiff. Different assumptions may fa-

cilitate the integration, depending on physical situation, modelling scope and numerical solver. The

most common assumptions are:

• At pressures below 10 bar, the vapour holdup can be neglected. This implies that a change in vapour

flow at the bottom of the column immediately change the vapour flow at the top (Skogestad, 1997).

Moreover, the UV-flash is no longer necessary and can be replaced by a bubble point calculation.

• Fixed plate pressure drop.

• Fixed top column pressure, but variable plate pressure drop. Note that vapour flow from reboiler,

reflux flow and condenser pressure are set. The pressure drop profile is computed by an iterative

procedure within a time interval. The vapour composition yk,i is found from bubble point calculation

(Px flash). This also gives the temperature T and the specific enthalpies hL,k, hV,k.

If the change of liquid enthalpy from plate to plate is very small, and if the molar enthalpies of vapour-

ization of components are close, then we may safely assume that:

Vk ¼Vk�1 (4.50)

In this case, the energy balance is not needed.

Taking into account the above elements the following models may be formulated, ordered by in-

creasing complexity (Grassi, 1992):

• Model 1a. Assumptions: equimolar vapour flow, negligible vapour holdup, constant liquid holdup,

constant pressure. Remark: Energy balance and overall mass balance are neglected. The only

dynamic element is the tray composition. Consequently, this model might be useful for some


dynamic studies, when the composition dynamics is relevant but the process itself is rather slow.

This model is not suitable for control, where an accurate description of the initial response is

required.

• Model 1b. Assumptions: equimolar vapour flow, negligible vapour holdup, constant pressure.

Remark: If the energy balance is disregarded, the dynamics is dominated by material balance and

liquid flow rate.

• Model 2a. Assumptions: negligible change of specific liquid enthalpy, negligible vapour holdup,

constant pressure or tray pressure drop.

• Model 2b. Assumptions: negligible change of specific liquid enthalpy, significant but constant

vapour holdup, constant tray pressure drop.

• Model 3. Assumptions: significant specific liquid enthalpy change, negligible vapour holdup,

variable tray pressure drop. Remark: Model 3 is suitable for most dynamic studies where the

pressure variation is moderate.

• Model 4. Assumptions: significant specific liquid enthalpy change, significant vapour holdup,

variable tray pressure drop. Remark: Model 4 is suitable for high pressure, where the contribution of

gas phase is significant. Downcomer modelling might be necessary.

4.5.2 EXAMPLE: DYNAMIC SIMULATION OF A BENZENE–TOLUENE DISTILLATIONCOLUMNConsider the separation of a benzene/toluene mixture by distillation in a tray column. Study the build-

ing of a dynamic model and explore the behaviour of the separation without purity control.

Solution. This time we will make use of a flow-driven simulation. We consider 100 kmol/h of equi-

molar mixture benzene/toluene. The distillate purity is moderate of 98.5%. Steady-state design gives

16 plates plus condenser and reboiler with the feed on the plate 10. The hydraulic sizing at 80% from

flooding gives the following tray characteristics: diameter 1 m, tray spacing 0.6096 m, and weir height

0.05 m. The reflux drum is a vertical cylindrical vessel with elliptical head and 2.3 m height�1.15 m

diameter. Similarly, the sump has a height of 3 and 1.15 m diameter.

The flowsheet is completed with P-type controllers for level in the reflux drum and bottoms, and PI

controller for pressure. These controllers ensure the basic inventory control, but are not sufficient for

quality control. Figure 4.11 presents simulation results for the following scenario: starting from the

Distillate

Time (h)

Stre

ams(

"2")

.Zn(

"ben

zene

") (k

mol

/k)

stre

ams(

"2")

.F (k

mol

/h)

0.85

0.9

0.95

1.0

35.0

40.0

45.0

50.0

55.0

60.0

65.0Feed

Time (h)

Stre

ams(

"1")

.Zn(

"ben

zene

") (k

mol

/k)

Stre

ams(

"1")

.F (k

mol

/h)

0.4

0.5

0.6

0.7

0.8

80.0

100.

012

0.0 Bottoms

Time (h)

Stre

ams(

"3")

.Zn(

"tolu

ene"

) (km

ol/k

)

Stre

ams(

"3")

.F (k

mol

/h)

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.00.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0

0.85

0.9

0.95

1.0

35.0

40.0

45.0

50.0

55.0

60.0

65.0

Mole fractionMole fraction

Mole fraction

Flow rate

Flow rateFlow rate

FIGURE 4.11

Dynamic response of a distillation column in open loop.


steady state, the feed flow rate is increased from 100 to 110 kmol/h (at time t¼1 h), and then decreased

to 90 kmol/h (at time t¼3 h). Then (at time t¼5 h), the flow rate is restored to its initial value, but the

amount of benzene in feed is increased to 60%, and then decreased to 40% (at time t¼7 h). We are

interested in distillate and bottoms flow rates and purities. It can be observed that larger feed rate leads

to a sharp decrease of bottoms purity, while smaller feed rate results in low distillate purity. Similarly,

when more benzene if fed to the column (higher mole fraction in feed at the same flow rate), the bot-

toms purity is lower, while less benzene in feed degrades the distillate purity. These results are

expected: the reboiler duty is kept constant; therefore, the changes in distillate rate are small. Conse-

quently, the purities of the products are directly influenced by the amount of light component in feed.

The need for quality control in a distillation column is obvious.

4.6 PROCESS CONTROL TOOLS4.6.1 IMPLEMENTATION OF CONTROLLERSThe majority of controllers in industry are based on single input single output (SISO) loops. The im-

plementation of controllers in a dynamic simulation consists of a succession of operations, as follows:

• Select the process variable (PV) that has to be controlled. This may be a stream or unit variable,

usually pressure, temperature, concentration, mass or volumetric flow rates, as well as the liquid

level. Specify the variation range, PVmin�PVmax. The desired value of the PV is called setpoint

(SP). Usually, the SP is positioned close to the midrange.

• Define the controller output (OP) as the manipulated variable. This is usually a stream flow rate or

heat duty. The steady-state design supplies the nominal value. The maximum output OPmax may be

taken as twice the nominal value. The minimum output OPmin may be set to zero or to a non-zero

safe value.

• Implement controller. The PID (proportional-integral-derivative) controllers are mostly used in

practice. A PID controller modifies the manipulated variable following the algorithm:

OP¼OPss +Kc e tð Þ + 1

tI

ðt0

e tð Þdt+ tD de tð Þdt

� �(4.51)

In the above relation, OPss is the steady-state value, or the bias of the manipulated variable, and eis the error defined as difference between PV and SP:

e¼ SP tð Þ�PV tð Þ (4.52)

A PID controller has three adjustable parameters Kc tI and tD that define the proportional (P),

integral (I) and derivative (D) actions. The most important is the controller gain Kc. Usually, Kc is

dimensionless and is expressed in (% OP range)/(% PV range). Higher gain gives faster response,

but also more oscillatory behaviour. P-controller always has a steady-state error. The error is

removed by integration over a time, with the controller parameter tI known as reset time. Thederivative component may be considered for faster response, the parameter tD being known as ratetime. Determining the above parameters implies a tuning procedure, as discussed later in this

section.


• Define the mode of action. In direct action, when the PV is above the SP (negative error), the

controller output/manipulated variable (OP) is increased. For instance, consider level control by

outlet flow. When the level rises above the SP, the outlet flow must increases. In reverse action,when PV is above SP, the manipulated variable decreases. Here, we may give as example the

control of purity by reflux: when the purity of the product increases above the SP, the reflux flow

rate must diminish. In general, the control action is determined by the process, negative/positive

gain requiring direct/reverse action. Incorrect control action leads to instability.

• Prepare the controller view and recorder settings.

4.6.2 TUNING OF PI CONTROLLERSPI is the most used control algorithm. Tuning of PI controllers aims to find the parameters of the algo-

rithm such that the tightest control is achieved. However, the risk of destabilizing the system due to too

aggressive controller actionmust be avoided. Therefore, the controller gain leading to instability (called

ultimate gain, KU) is found by gradually increasing the controller gain until sustained oscillations of

period PU occur. In another method, called auto-tune variation (ATV), the controller is replaced by

a relay of amplitude h. Each time the controlled variable crosses the SP, the controller OP is reversed.

Sustained oscillation of amplitude a occurs. Then, the ultimate gain can be calculated as:

KU ¼ 4h

pa(4.53)

By knowing KU and PU, the parameters of a PI controller can be calculated with simple relations as

given in Table 4.3, according to Ziegler–Nichols (ZN) or Tyreus–Luyben (TL). It is considered that

the ZN tuning is somewhat aggressive, while TL is more appropriate for chemical processes. Note that

the values of tuning parameters determined as above should be seen only as initial values. The tuning

should continue up to the point where the performance of controller is satisfactory.

Another problem is the use of the tuning parameters for SISO loops in a multi-input multi-output

environment. The interactions between loops can be reduced in some cases only by ‘detuning’ the pa-

rameters, usually by diminishing the gains and increasing the reset times.

4.6.3 EXAMPLE (CONTINUED): CONTROL OF THE BENZENE–TOLUENE DISTILLATIONCOLUMN4.6.3.1 Control structureControl structure selection is the first step in designing the control system of a given flowsheet. The

control system must achieve the following objectives:

Table 4.3 Tuning Rules for PI Controllers

Tuning Rule Kc (%/%) PU (min)

Ziegler–Nichols (ZN) KU/2.2 PU/1.2

Tyreus–Luyben (LT) KU/3.2 PU/2.2

1474.6 PROCESS CONTROL TOOLS

1. Safe operation (inventory control). Safety features are always implemented during process design

(inherently safe design). For example, a relief valve would protect the column from high pressure

due to failure of the condenser cooling. However, the control system takes care of less critical

situations. A pressure increase of smaller magnitude can be handled by increasing the condenser

duty (PC, Figure 4.12). Control of levels in reflux drum and column sump (LC1 and LC2) by means

of distillate and bottoms rates achieve liquid inventory containment. Moreover, keeping a certain

level in these vessels avoid that the pumps lose suction. Therefore, these loops also have equipment

protection function.

2. Deliver the required product (quality control). It is important that the distillation column delivers

the distillate and bottom products at the required purities (otherwise, the products cannot be sold).

However, composition measurements are expensive and often unreliable, being also characterized

by large time delays. The solution is employing the inferential control: as there is a direct

relationship between boiling point and composition, controlling two temperatures in the top and

bottom of the distillation column (TC1, TC2) by means of reflux and boilup rates (hopefully)

ensures composition control. There are various techniques which allow selection of the trays with

controlled temperature. A practical rule is to choose the trays where the temperature profile is most

sensitive. By looking at the temperature profile obtained from steady-state simulation, we choose

the 3rd and 16th stage. The dynamics of the temperature measurements is modelled by two first-

order elements with time constants of 1 min (Lag1, Lag2). If composition measurements are

available, composition controller can be used to give, in a cascade fashion, the SP of temperature

controller. This solution is implemented at the bottom of the distillation column (XC). The

‘Discretize’ model from AD library simulates the measurement: it takes 10 min to perform the

analysis; therefore a sample is taken every 10 min.

3. Achieve economic profitability (optimization). The SPs of the controllers implemented in steps 1

and 2 above (together known as regulatory control) are given by a supervisory control layer. For

example, one could take into account market conditions (price products vs. their purity, steam and

cooling water costs) and decide the product purity which gives the maximum profit. This objective

will not be considered in this chapter.

4.6.3.2 Controller tuningA quick-and-dirty method for estimating the controller gain relies on the following observation: a gain

Kc¼1%/%means that the maximum control action is taken when the controlled variable is at the bound

of its variation range. Therefore, if the ranges for the controlled and manipulated variables are well

specified based on process knowledge and engineering judgement, Kc¼1%/% often works. Moreover,

the direct synthesis method (Luyben and Luyben, 1997) specifies the desired closed-loop response for a

given input. Then, with the model of the process known, the required form and the tuning of the feed-

back controller are back calculated. It can be shown (Luyben and Luyben, 1997) that the direct syn-

thesis method requires that the reset time of a PI controller is equal to the time constant of the process,

which can result from an ‘educated guess’. This method was applied for tuning the level, pressure and

bottom temperature controllers (Table 4.4).

Although the previous method led to quite good results, the top temperature controller was tuned

using the TL setting. Thus, the ATV method for finding the stability limit is applied using the facility

offered by the PID controller model as implemented in AD. Figure 4.13 shows the onset of sustained

oscillations, whose magnitude and period are used for finding the ultimate gain and the ultimate period


FIGURE 4.12

Control of the benzene–toluene distillation column.

Table 4.4 Benzene–Toluene Distillation Column: Controller Settings

LC1 LC2 PC TC1 TC2 XC

Controlled variable Level Level Pressure Temperature on

tray 3

Temperature Toluene mole

fraction

Controlled variable

range

0–2.8 m 0–3.6 m 0.9–1.1 bar 70–100 �C 100–130 �C 0–0.03

Manipulated variable Distillate

flow

Bottoms

flow

Condenser duty Reflux Reboiler duty Set point of TC2

Manipulated variable

range

0–7800 kg/h 0–9200 kg/h �2.2–0�106 kcal/h 0–16,000 kg/h 0–3�106 kcal/h 100–130 �C

Control action Direct Direct Reverse Direct Reverse Direct

Kc (%/%) 10 10 2 42.27 1 0.138

Ti (min) 60 60 12 2.64 20 87.12

(Figure 4.14, left). Then, the gain and integral time are calculated according to the tuning rules

(Table 4.3 and Figure 4.14 right).

Tuning of the composition controller is the most difficult. There is dead time associated with the

temperature measurement and the control action can be updated only when new measurements are

available (once every 10 min). Here, the ATVmethod and the TL tuning rules really show their power.

Table 4.4 presents the controller settings.

4.6.3.3 Dynamic simulation resultsDynamic simulation results are presented in Figure 4.15. The same disturbance scenario as described in

Section 4.5.2 was also employed. A dramatic improvement of the column performance is observed.

Compared to Figure 4.11, deviations from the specified purities are much smaller. Notably, distur-

bances are rejected with small changes of the manipulated variables.

Unexpectedly, despite the complex control employed at the bottom of the column (composition-

temperature cascade), control of the top product looks better. This is due to the difference in the tuning

of two temperature controllers (ATV+TL for TC1, heuristics for TC2). Comparing the gains and reset

times (Table 4.4), it appears that the simulation model, which does not include the dynamics of the

control valve and assumes high precision of the temperature measurement, allows a very aggressive

tuning of the top temperature controller TC1.

In practice, such good control performance cannot be always attained. Indeed, adding to the temper-

aturemeasurements aGaussian noisewith standard deviation of only 2� induces extremely fast and large

changes (between the minimum and maximum allowed values) of the manipulated variables

(Figure 4.16, left), while more realistic results are obtained for the bottom controller TC2. Similarly,

other assumptionsmight make the control tasks appear easier than in reality. For example, direct manip-

ulation of the reboiler duty leads to instantaneous change of the vapour flow along the entire column.

TC1

Time (h)

Set

poi

nt C

Con

trolle

r out

put (

kg/h

)

Pro

cess

var

iabl

e C

2.275 2.325 2.375 2.425 2.475

7500

.080

00.0

8500

.090

00.0

81.8

81.9

82.0

82.1

82.2

OP

PVSP

FIGURE 4.13

Benzene–toluene column. Finding the stability limit by ATV technique.

1514.6 PROCESS CONTROL TOOLS

In conclusion, the user must be aware that dynamic simulations assume high measurement preci-

sion, which is seldom achievable and neglects some important practical dynamic features. As a result,

controller settings obtained by simulation might be applicable only within a simulation environment!

4.7 DYNAMIC FLOWSHEETINGDynamic flowsheeting consists of performing the dynamic simulation of the whole process plant

rather than of a single unit. Commercial software for dynamic flowsheeting may be classified into

equation-oriented (EO) and modular. In the EO approach (Barton and Pantelides, 1993), the models

of single units are combined into one big DAE system, which is solved by standard numerical tech-

niques. In a modular approach, the unit models are solved individually. An iterative coordination

algorithm ensures the convergence at the flowsheet level (Hillestad and Hertzberg, 1986; Kulikov

et al., 2005). In a simultaneous-modular simulation, the streams (couplings) between units are torn

(guessed) and each unit model is integrated over one time interval. Then, the error is computed for

each tear stream, over the entire interval. If the convergence criteria are not met, the couplings and/or

the integration interval are updated. The strategy can be executed in parallel on several computers,

but the convergence properties depend on availability of good initial guesses of all flowsheet

couplings. In the sequential-modular approach, tearing is applied to only few streams. The units con-

nected by untorn streams are integrated sequentially, accordingly to the flowsheet topology. Then, the

convergence of the tear streams is checked and the tear streams are updated if necessary. To proceed

to the next integration interval, the evolution of the tear streams is estimated by extrapolation

(Kulikov et al., 2005).

FIGURE 4.14

Benzene–toluene column. Controller tuning using the stability limit results.


Stre

ams(

"1")

.Zn(

"ben

zene

") (

kmol

/k)

0.4

0.5

0.6

0.7

0.8

Stre

ams(

"1")

.F k

mol

/h)

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.010.0

0.4

0.5

0.6

0.7

0.8 Feed

Time (h)

0.4

0.5

0.6

0.7

0.8

80.0

100.

012

0.0

Flow rate

Mole fraction

Distillate

Time (h)

Stre

ams(

"2")

.Zn(

"ben

zene

") (

kmol

/k)

Stre

ams(

"2")

.F (

kmol

/hr)

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0

0.98

0.99

1.0

35.0

40.0

45.0

50.0

55.0

60.0

65.0

Flow rate Molefraction

Bottoms

Time (h)

Stre

ams(

"3")

.Zn(

"tolu

ene"

) (km

ol/k

)

Stre

ams(

"3")

.F (

kmol

/h)

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0

0.98

0.99

1.0

35.0

40.0

45.0

50.0

55.0

60.0

65.0

Flow rate

Molefraction

TC1

Time (h)

Set

poi

nt C

Con

trolle

r out

put (

kg/h

)

Pro

cess

var

iabl

e C

0.0 2.5 5.0 7.5 10.0

8000

.090

00.0

1000

0.0

81.9

81.9

582

.0

OP PV

XC

Time (h)

Set

poi

nt (

kmol

/km

ol)

Con

trolle

r ou

tput

C

Pro

cess

var

iabl

e (k

mol

/km

ol)

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0

114.

011

5.0

116.

0

0.00

50.

00:

0.01

50.

020.

025

OP

PV

TC2

Tim e (h)

Set

poi

nt C

Con

trol

ler

outp

ut M

M(k

cal/h

)

Pro

cess

var

iabl

e C

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0

1.05

1.1

1.15

1.2

1.25

112.

011

3.0

114.

011

5.0

116.

0

OP

PV

SP

FIGURE 4.15

Benzene–toluene distillation column: closed-loop dynamic simulation results.

Initialization is an important issue in dynamic simulation. In theory, for index-one problems, pro-

viding the initial values for the state variables and the inputs is sufficient to calculate the initial values

of all variables. In practice, this is more difficult because the solution of the algebraic part may fail to

converge. Therefore, guesses for the initial values can be taken from a steady-state solution obtained by

SM or EO approach.

Despite the progress in software technology in the last years, solving a dynamic flowsheet simu-

lation problem is still not an easy task. A working procedure may be formalized as follows.

Problem analysis

– Define the dynamic flowsheeting problem, specifying the variables of interest (control objectives),

the measurements, the available manipulated variables (including their allowed range of variation)

and the simulation scenario (expected disturbances).

– Solve the steady-state flowsheeting problem.

– Check that, at steady state, the disturbances can be rejected with the manipulated variables within the

allowed range. If necessary, modify the design to ensure that the manipulated variables are effective

for control purposes.

– Decide about slow and fast dynamic units. Slow units need dynamic models, while steady-state

models can be applied in the latter case of fast units.

– Size the units with significant dynamics. Analyse the modelling of the key units (chemical reactor,

separation units).

– Examine plantwide control problems, such as the input of reactants, the manipulation of the

production rate, and the control of waste and impurities. Develop a plantwide control structure.

– Prepare the dynamic run.

Dynamic flowsheeting

– Initialize the dynamic simulation, for example using the steady-state results. Failure of this step is

often very difficult to solve. One can change the reporting options in order to identify the problematic

unit. The warnings issued during exporting the dynamic simulation should be carefully checked.

In some cases, changing the convergence tolerance of the unit models and tear streams to a lower

TC2

Time (h)

Set

poi

nt

Con

trolle

r out

put M

M(k

acl/h

)

Pro

cess

var

iabl

e

TC1

Time (h)

Set

poi

nt

Con

trolle

r out

put (

kg/h

)

Pro

cess

var

iabl

e

4000

.080

00.0

1200

0.01

6000

.0

0.0 0.2 0.4 0.6 0.8 1.0

0.8

1.6

2.4

100.

011

0.0

120.

013

0.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.060.0

90.0

120.

0 OP

PV

OP

PV

FIGURE 4.16

Benzene–toluene column: closed-loop dynamic simulation results including noisy temperature measurements.


value might help. Removing the unused components and correct selection of ‘valid phases’ are also

recommended (use single phase option where possible). For plug-flow reactors, increasing the

number of discretization elements will reduce the difference between steady-state and dynamic

models. Also note that AD takes into consideration the parameters specified in the input form and not

the results of Aspen Plus Design Specification, Calculator and Optimization blocks. Therefore, it is

recommended to ‘reconcile’ the steady-state simulation, remove or hide Design Specifications, run

the steady-state simulation again and export the dynamic simulation.

– Implement the inventory control of all units (levels and pressures). Check that the inventory control

is plantwide consistent, namely, the control loops can avoid accumulation/depletion of all chemical

species. Check the stability of the plant (levels and pressures are constant, flow rates have reasonable

values, no reaction extinction/ignition occurs, etc.).

– Implement the quality control loops.

– Execute closed-loop dynamic simulation.

Analysis of results

– Study the plant performance in closed loop faced to different disturbances.

– Perform refinement of design and control, and finally optimization.

4.8 FURTHER READINGAs a general reference for mathematical modelling in chemical engineering, we recommend the newest

edition of the acclaimed textbook of Bird et al. (2006). A classical guide for writing equations for de-

terministic systems is the book of Himmelblau and Bishoff (1968), probably now rather difficult to

find. A refreshing retrospective of mathematical modelling has been revealed by Aris (2001). Non-

linear dynamics is becoming an important topic in design, since it is implied not only in safety aspects

but also in design for flexibility. An advanced treatment of non-linear dynamics can be found in the

book of Bequette (1998). More complex dynamic phenomena, such as the occurrence of multiple

steady states and chaotic behaviour, are presented in an accessible but rigorous manner. Numerous

examples built in Matlab illustrate the mathematical issues.

Mathematical formulation of dynamic models and their linearization are treated in books dealing

with process dynamics and control, for example Stephanopoulos (1984), Luyben (1989), Ogunnaike

and Ray (1994), Luyben and Luyben (1997) and Marlin (1995).

Very useful theoretical and practical insights in dynamics and control of distillation processes, with

many implications in dynamic simulation, can be found in Luyben (1992) with contributions from spe-

cialists in different areas. Dynamics and control of distillation are presented: Luyben (2006, conven-

tional distillation), Luyben and Chien (2010, azeotropic distillation) and Kiss (2013, advanced

distillation units).

A useful presentation of process dynamics from a practical viewpoint can be found in the book of

Ingham et al. (1994). Luyben (2002) illustrates the techniques and fundamentals to develop, design,

and test plantwide regulatory control schemes with commercial dynamic simulation packages.

In Dimian and Bildea (2008) and Luyben (2011), several case studies of complete process flow-

sheets are developed, starting with conceptual and ending with dynamics and plantwide control

studies.

1554.8 FURTHER READING

REFERENCESAl-Arfaj, M.A., Luyben, W.L., 2002. Design and control of an olefin metathesis reactive distillation column.

Chem. Eng. Sci. 57, 715–733.

Aris, R., 2001. Modelling Principles. Academic Press, New York.

Barton, P.I., Pantelides, C.C., 1993. Equation-oriented dynamic simulation—current status and future perspec-

tives. Comp. Chem. Eng. 17 (S1), S263–S285.

Bequette, R.W., 1998. Process Dynamics, Modelling, Analysis and Simulation. Prentice Hall, New Jersey.

Bird, R., Lightfoot, W., Stewart, E., 2006. Transport Phenomena. John Wiley & Sons, New York.

Chen, F., Huss, R.S., Malone, M.F., Doherty, M.F., 2000. Simulation of kinetic effects in reactive distillation.

Comp. Chem. Eng. 24, 2457–2472.

Dimian, A.C., Bildea, C.S., 2008. Chemical Process Design—Computer-Aided Case Studies. Wiley-VCH,

Weinheim.

Grassi, V.G., 1992. Rigorous modelling and conventional simulation. In: Luyben, W. (Ed.), Practical Distillation

Control. Van Nostrand Reinhold, New York.

Hillestad, M., Hertzberg, T., 1986. Dynamic simulation of chemical engineering systems by the sequential mod-

ular approach. Model. Ident. Control 7 (3), 107–127.

Himmelblau, D., Bishoff, K., 1968. Process Analysis and Simulation. Deterministic Systems. Wiley, New York.

Ingham, J., Dunn, I.J., Heinzle, E., Prenosil, J.E., 1994. Chemical Engineering Dynamics. Modelling with PC Sim-

ulation. VCH-Wiley, Weinheim.

Kiss, A.A., 2013. Advanced Distillation Technologies: Design Control and Applications. Wiley-VCH, Weinheim.

Kulikov, V., Briesen, H., Grosch, R., Yang, A., vonWedel, L., Marquardt, W., 2005. Modular dynamic simulation

for integrated particulate processes by means of tool integration. Chem. Eng. Sci. 60, 2069–2083.

Luyben, W., 1989. Process Modelling, Simulation and Control. McGraw Hill, New York.

Luyben, W., 1992. Practical Distillation Control. Van Nostrand Reinhold, New York.

Luyben, W.L., 1996. Design and control design of freedom. Ind. Eng. Chem. Res. 35, 2204–2214.

Luyben, W.L., Luyben, M.L., 1997. Essentials of Process Control. McGraw Hill, NewYork.

Luyben, W., 2002. Plantwide Dynamic Simulators in Chemical Processing and Control. Dekker, New York.

Luyben, W., 2011. Principles and Case Studies of Simultaneous Design. John Wiley & Sons, New Jersey.

Luyben, W.L., 2006. Distillation Design and Control Using Aspen Simulation. John Wiley & Sons – AIChE,

New York.

Luyben, W., Chien, L., 2010. Design and Control of Distillation Systems for Separating Azeotropes. JohnWiley &

Sons, New Jersey.

Mahajanam, R.V., Zheng, A., Douglas, J.M., 2001. A shortcut method for controlled variable selection and its

application to the butane alkylation process. Ind. Eng. Chem. Res. 40, 3208–3216.

Marlin, T.E., 1995. Process Control. McGraw Hill, New York.

Ogunnaike, B.A., Ray, W.H., 1994. Process Dynamics, Modelling and Control. Oxford University Press,

New York.

Okasinski, M.O., Doherty, M.F., 1998. Design method for kinetically controlled, staged reactive distillation col-

umns. Ind. Eng. Chem. Res. 37, 2821–2834.

Pantelides, C.C., Barton, P.I., 1992. Equation-oriented dynamic simulation. Comp. Chem. Eng. 18, S263–S285.

Skogestad, S., 1997. Dynamics and control of distillation columns—a critical survey. Model. Ident. Control

18, 177–217.

Stephanopoulos, G., 1984. Chemical Process Control. An Introduction to Theory and Practice. Prentice-Hall

International, New Jersey.


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[Computer Aided Chemical Engineering] Integrated Design and Simulation of Chemical Processes Volume 35 || Dynamic Simulation