Received8 November 2002; receivedin revisedform 29 August 2003; accepted5 September 2003
Abstract
This work analyzes the tradeo3 between steady-state economics and dynamic controllability for heat-integrated recycle plants. The process consists of one reactor, two distillation columns, andtwo recycle streams 4rst studiedby Tyreus andLuyben (Ind. Eng. Chem. Res. 32 (1993) 1154) andfurther exploredby Cheng andYu (A.I.Ch.E. J. 49 (2003) 682) and, in this work, the two distillation columns are heat integrated. The design problem di3ers from typical column sequencing and heat-integration design, because we can design the reactor composition. Optimal trajectories for heat-integratedrecycle plants with direct andindirect sequences are analyzedas the reactor composition of C (zC) varies. Provided with correct direction for heat integration, at any given zC, the >owsheet is establishedfor both
sequences. It turns out the heat-integratedrecycle plant with direct sequence is economically optimal throughout the entire range of zC.
For dynamic controllability, the reachable production range is identi4ed as the recycle ratios (recycle >ow rate/production rate) vary. Results show that the steady-state controllability deteriorates gradually as the degree of heat integration increases and, to the extreme, at the 50% energy saving line, we have lost one control degree of freedom. However, if the recycle plant is optimally designed (zC≈ 0:6),
acceptable turndown ratio is observed and little tradeo3 between steady-state economics and dynamic operability may result. Finally, rigorous nonlinear simulations are usedto test control performance of di3erent process con4gurations (with andwithout heat integration). The results reveal that improvedcontrol can be achievedfor well-designedheat-integratedrecycle plants (comparedto the plants without energy integration). More importantly, better performance is achievedwith up to 40% energy saving andclose to 20% saving in total annual cost.
? 2003 Elsevier Ltd. All rights reserved.
Keywords: Heat integration; Recycle process; Plantwide control; Design and control
1. Introduction
Last decade has seen signi4cant progress in the design of plantwide control systems and most of the work addresses the issue of control structure design or the e3ects of mate-rial recycle on overall process dynamics. The timely book
of Luyben et al. (1999) andthe review of Larsson and
Skogestad(2000)provide an updated summary.
On the other hand, we have seen extensive literature on the design andcontrol of heat-integrateddistillation systems. Tyreus andLuyben (1976) examine the control issue of double-e3ect distillation and an auxiliary reboiler is suggestedfor improvedcontrol performance. Chiang
andLuyben (1988) study the control for three
di3er-ent heat-integration con4gurations: feed-split, light-split ∗Corresponding author. Tel.: 3365-1759; fax:
+886-2-2362-3040.
E-mail address:[email protected](C.C. Yu).
forward(integration), andlight-split reverse. They con-clude that the light-split reverse is the most controllable scheme. Weitz andLewin (1996) study the same sys-tem using the disturbance cost as a controllability mea-sure andsame conclusion is drawn. Han andPark (1996)
use nonlinear model-based control to eliminate interac-tion for double-e3ect columns and good performance can be achievedfor high-purity speci4cation. Wang andLee
(2002)explore nonlinear PI control for binary high-purity
heat-integratedcolumns with light split/reverse con4gura-tion.Yang et al. (2000)use simpli4ed model derived from state space equation to evaluate disturbance propagation for double-e3ect column under feed-split con4guration. Interaction between design and control for heat-integrated and/or thermally coupled distillation systems are studied by
Rix andGelbe (2000)andBildea and Dimian (1999)using
dynamic RGA as a controllability measure. An optimiza-tion approach is taken by Bansal et al. (2000) to investi-gate the interaction of design and control for double-e3ect
0009-2509/$ - see front matter ? 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.ces.2003.09.019
distillation. Rev et al. (2001) provide a comprehensive study on the energy saving for ternary systems. Separa-tion con4guraSepara-tions, internal thermal coupling andexternal heat-integration are explored.
However, much less work has been done on the prac-tically important process: heat-integratedrecycle plants where both material andenergy recycles exist simultane-ously. This work analyzes the tradeo3 between steady-state economics anddynamic controllability for heat-integrated recycle plants. The process consists of one reactor, two distillation columns, and two recycle streams 4rst studied
by Tyreus andLuyben (1993) andfurther exploredby
Cheng andYu (2003)and, in this work, the two distillation
columns are heat integrated. 2. Steady-state economics 2.1. Process con2gurations
The process studied is a ternary system with the following reaction: A+B → C (Tyreus andLuyben, 1993;Cheng and
Yu, 2003). Two reactants A andB are fedto a CSTR which
is operatedisothermally. The reaction is secondorder and the rate can be expressedas
R = kVRzAzB; (1)
where R is the reaction rate, k is the rate constant, zAand zB
are the mole fractions for reactants A andB, andVR is the
reactor holdup. The reactor eJuent is assumed to be a satu-ratedliquidandcontains a ternary mixture of A, B, andC, because some A andB remain unreacted. Here, A is the light component (LK), B is the heavy component (HK), andthe product C is an intermediate boiler (IK) and relative volatil-ities are: A= 4, B= 1, and C= 2 at atmospheric pressure.
Table 1 gives physical properties of the reaction/separation system. To separate the intermediate boiler (C) from the
Table 1
Basic physical properties for the reaction andseparation system Molecular weight (MW) MWA= 50, MWB= 50, MWC= 100 Averageddensity ( avg) 75 (lbm=ft3)
Heat of vaporization (LH) 50000/3 (Btu/lbmol)
Reaction A + B → C
Rate expression R = kVRzAzB (lbmol/h) Rate constant k = 1 (h−1) for nominal case
Relative volatility A=C=B= 4=2=1 for low-pressure column
A=C=B= 3:24=1:8=1 for high-pressure column
Temperatures Computedfrom Clausius–Clapeyron equation 1 T − 1 T0 = R LHln ixi ix0;i
Assuming normal boiling point of A of 200◦F andtemperature driving force for
heat integration is 30◦F XD1,A=0.99 XD1,C=0.01 XD2,A=0.01 XD2,B=0.01 XD2,C=0.98 D2=100 lb-mol/h XB2,B=0.99 XB2,C=0.01
Fig. 1. Process >owsheet andspeci4cations for the recycle plant with direct separation sequence.
high andlow boiling reactants (A andB), we needtwo dis-tillation columns with two possible disdis-tillation sequences, direct and indirect sequences. Fig.1shows the process >ow-sheet with the direct sequence (D) where reactant A (LK) is recycledfrom the top of the 4rst column back to the reactor andreactant B (HK) is recycledfrom the bottom of the sec-ondcolumn back to the reactor. Product speci4cations are also given in Fig.1.
Most of the operating cost of the recycle plant in Fig. 1
comes from the energy cost in distillation columns. It is com-mon to reduce the energy cost by heat integration of these two columns. For the direct separation sequence, two con4g-urations exist: direct sequence with forward heat-integration (DF) anddirect sequence with backwardheat-integration (DB) as shown in Fig.2A. Similarly, we have two possible con4gurations for the indirect separation sequence: indirect sequence with forwardheat-integration (IF) andindirect se-quence with backwardheat-integration (IB) (Fig.2B). The energy saving can be evaluatedbasedon the vapor rate. For systems with heat integration, the total vapor rate is simply:
VTOT= V1+ V2; (2)
where V1 and V2 are the vapor rates for the 4rst andthe
secondcolumn, respectively, andVTOT is the total vapor
rate. For all four con4gurations in Fig. 2, the total energy requirement relates directly to
VTOT= max(V1; V2): (3)
Therefore, percent of energy saving can be computedandthe incentives for heat integration (versus increasedcomplex-ity in control andoperation) can be evaluatedimmediately
(Chiang andLuyben, 1983). This is the typical situation in
the design of heat-integrated distillation systems. However, in the design of recycle plants, we face a very di3erent sce-nario andthe reason is that the feedto the separation section (i.e., reactor composition) can be designed. The role heat integration plays in the design of the entire plant is not clear andpossible tradeo3s between energy saving andoperation have not been explored.
Fig. 2. Heat-integratedrecycle plant with: (A) direct separation sequence (forwardandbackwardintegration); and(B) indirect separation sequence (forward/backward integration).
2.2. Generation of process 4owsheet and total annual cost Before getting to the steady-state design, the following assumptions are made. Using the direct sequence as an ex-ample (Fig.2A), the assumptions are
(1) The process components have constant density. (2) The >ow rate of the product stream D2 is 4xedat
100 lbmol=h.
(3) The product speci4cation is xD2;C= 0:98.
(4) There is no component A leaving the bottom of the secondcolumn (xB2;A= 0). Therefore, the composition
of the heavy recycle stream B2is speci4edto be xB2;B=
0:99, and xB2;C= 0:01.
(5) There is no component B leaving the top of the 4rst column (xD1;B= 0). Therefore, the composition of the
light recycle stream D1 is speci4edto be xD1;A= 0:99,
and xD1;C= 0:01.
(6) The relative volatility of the high-pressure column is assumedto be 90% of the lower pressure one (i.e., i;HP= 0:9i;LP;Chiang andLuyben, 1983).
With given speci4cations, we can complete the steady-state design for any given reactor product composition (zC)
and reactant distribution with di3erent direction of heat integration. The steady-state conditions of all streams in the ternary recycle system are calculatedfrom balance equations (Cheng andYu, 2003). The low-pressure col-umn is assumedto be at atmospheric andthe pressure for the high-pressure column can be computedfrom the
Clausius–Clapeyron equation Psat
i = Pi;0satexp
−LHi R 1 T − 1 T0 ; (4)
where Psatis the vapor pressure, LH is the heat of
vaporiza-tion, and R is the gas constant. The temperatures are inferred from the following expression (Glinos, 1984):
1 T − 1 T0 = R LH ln ixi ix0;i; (5)
where the subscript 0 stands for a reference temperature. In this work, we assume the normal boiling point for the light component (A) is 200◦F andtemperature driving force for
heat transfer is 30◦F. With this assumption, we can compute
the temperature on each tray.
Next, standard column shortcut approach is taken for the heat-integratedcolumns. First, the Fenske equation is ap-pliedto 4ndthe minimum number of trays (NT;min) andtotal
number of trays is set to twice of NT;minandthe feedtray is
located with the Kirkbride equation. Next, provided with as-sumed physical properties, the column is sized, tray holdup is computed, andliquidhydraulic time constant is computed as shown in the appendix. The heat transfer areas for the re-boiler andcondenser are also computedfrom the vapor >ow rates (see the appendix). The reactor is also sized assuming an aspect ratio of 2. From steady-state design, we can de-termine all the process >ow rates andthe equipment sizes. Before leaving the design section it should be emphasized that a standard column design procedure (NT = 2NT;min)
is adapted here for the design of heat-integrated columns. As pointed out by one of the reviewer that an additional
Fig. 3. Optimal TAC trajectories (the reactant distribution showing min-imum TAC for a given zC) for recycle plant with direct (solid) and in-direct (dashed) sequence and the boundary (thick solid) giving the same TAC for both sequences.
energy saving can be achievedby varying the numbers of trays such that Vsupply=Vdemandandthis will be useful when
the heat-integratedcolumns of the recycle plant are not de-signedat 50% energy saving point (i.e., V1= V2).
In order to select the best steady-state design for direct or indirect sequence, we employ economic assessment to evaluate di3erent designs. The capital cost and operation cost of the entire plant are estimatedusing the correlation given inDouglas (1988)andthe operating cost (primarily energy cost) is also obtainedfrom vapor boilup. Provided with column base temperature, corresponding steam costs can be computed(appendix). Assuming payback years of 3 years, the total annual cost (TAC) model can be expressedas
TAC =capital cost3 + operating cost: (6)
The TAC can be used to discriminate di3erent process designs.
Provided with design speci4cations and economic mea-sure (TAC), optimization is performednext. Given a spe-ci4c separation sequence, we have two design degrees of freedom for the recycle plant. One is the reactant distri-bution zA=zB andthe other is the conversion (or reactor
composition of C, zC). The optimization is carriedout
se-quentially. First, the optimal reactant distribution is located for di3erent zC. These optimum reactant distributions are
denoted as the optimal TAC trajectory. Fig.3shows the op-timal reactant distribution for the direct (D) as well as the indirect (I) separation sequences when zC varies from 0 to
1 (Malone et al., 1985; Glinos andMalone, 1988). Next,
the TACs along the optimal trajectories are comparedfor
Fig. 4. 50% energy saving line (V1= V2) for given zC with direct (left) andindirect (right) sequences.
di3erent zC’s andthe optimal design for each sequence can
be obtained. Finally, the results of two di3erent separation sequences are comparedandthe true optimal design is thus obtained. The last step can be made easy by drawing a boundary (indicated by thick solid line) which de4nes where the indirect (left-hand side) sequence and the direct sequence (right-hand side) are favored. Therefore, the true optimal design may be obtained by inspection of the optimality for each sequence.Cheng andYu (2003)give detailed deriva-tion for this boundary. For the >owsheet without energy in-tegration, the results indicate that, for both sequences, the optimal paths start from the corner of heavy reactant (B) when zC is low (zC → 0) and, as the zC increases, they
con-verge towardthe center line which means equally distributed reactants (i.e., zA= zB). This coincides with one’s intuition,
because, at low zC, the operating cost of distillation columns
dominants and excess heavy component reduces the vapor rate. At high zC, the reactor cost dominates and a 50/50
dis-tribution of reactants (i.e., zA=zB= 1) is preferred, because
zA= zB gives the smallest reactor volume when zC is 4xed.
Fig.3 also shows the optimal trajectories always lie in the composition space where the heavy reactant is greater or equal to the light reactant. A question naturally arises: Do these results also apply to heat-integratedsystems? 2.3. Energy saving
2.3.1. Maximal percentage of energy saving and trajectory of minimal energy consumption
For heat-integrateddistillation columns, the incentives for integration can best be seen in Fig.4where the line of equal vapor rate is drawn (i.e., V1 = V2). These lines (Fig. 4)
correspondto 50% of energy saving. For the direct sequence (Fig. 4A), the 50% energy saving line lies on the region where the direct sequence is favored(e.g., thick solidline in Fig.3), but, for the indirect sequence (Fig.4B), the maximal possible energy saving line also lies in the region where the indirect sequence is not favored. That implies that, for the indirect sequence, percentage-wise, the 50% energy saving line may be attractive, but the total energy requirement may not be minimal.
Fig. 5 shows the optimal energy consumption path as zC changes from zero to one. For the direct sequence, the
Fig. 5. Minimal energy consumption (minimum VTOT) paths for a given zCwith heat-integratedrecycle plant with direct andindirect sequences.
optimal path coincides with the 50% energy saving line (Figs.4A and5), but for the indirect sequence, the trajec-tory for the minimal energy usage is completely di3erent from the 50% energy saving line (Fig.4B). The reason is quite obvious, for the indirect sequence, for total energy re-quirement (e.g., V1 + V2) is less in the region where
in-direct sequence is favored (Fig. 3). This means that less substantial heat-integration is expectedfor the recycle plant with indirect separation sequence and a higher degree of heat-integration will occur for the direct sequence.
2.3.2. Direction of heat integration
Next, we explore the e3ects of the direction (e.g., forward or background) of heat integration on the total annual cost. Two cases are considered: one is the case of V1 = V2, and
the other is V1= V2.
Let us use the direct sequence to illustrate the e3ect of heat-integration direction. First, consider the case of V1¡ V2. From thermodynamics perspective, the forward
heat-integration con4guration (DF) should be avoided, be-cause this will leadto a higher pressure in the high-pressure column (the pressure in the low-pressure column is 1 atm). However, the requiredvapor rate for DF is sim-ply VTOT= V2;LP (Eq. (3)). On the other hand, if the DB
con4guration is employed, we have a lower pressure in the high-pressure column, but the vapor rate becomes: VTOT = V2;HP. Note that relative volatility, generally,
de-creases with a pressure increase. Therefore, we expect V2;HP¿ V2;LP and, thus a higher energy requirement with
DB con4guration. Unless, the di3erence in the steam pressure (from pressure andsubsequently temperature dif-ference) can o3set this increase in the vapor rate, DF con4guration is favoredin this case for its lower energy consumption. Therefore, the general rule is: integrate from the column with a smaller vapor rate (Vsmall) to the column
Fig. 6. Total annual costs with di3erent directions in heat integration for recycle plant with direct separation sequence with di3erent reactant distribution when zC= 0:6.
with a larger vapor rate (Vlarge). Fig.6 shows the TAC for the direct sequence with di3erent directions of heat integra-tion. The results show the suggestedintegration direction, Vsmall → Vlarge, gives lower TAC throughout the entire
range of reactant distribution.
For the case of V1= V2, either the forwardintegration
or the backgroundintegration will give the same energy consumption. The backwardintegration (DB) has a small advantage because of a lower pressure and, thus, lower steam temperature. However, the di3erence in TAC is less than 1% over the entire range of zC.
2.3.3. Optimal TAC trajectory and corresponding process 4owsheet
Fig. 7 show the optimal TAC trajectory for the direct sequence as zC varies from 0 to 1. Unlike the case of
non-integratedrecycle plant (e.g., Fig. 3), it follows the 50% energy saving line at low zC(zC¡ 0:5) andconverges
towardthe center line (zA=zB = 1) at high product
com-position (zC → 1). The reason for that is, at low zC, the
operating cost of distillation columns dominates and high degree of heat integration reduces the vapor rate by half. At high zC, the reactor cost dominates and a 50/50 distribution
of reactants is favored. As for the direction of heat integra-tion, at low zC, either backwardor forwardheat integration
can be chosen, but at high zC, forwarddirection is preferred
(DF) as shown in Fig.7.
A very di3erent trajectory is observed for the indirect se-quence as shown in Fig. 8. It looks quite similar to that of non-integratedsystem (cf. Fig. 3), but at a lower TAC
Fig. 7. Optimal TAC trajectory (x) and corresponding direction(s) for heat integration for recycle plant with direct separation sequence (minimal energy consumption trajectory (circle) also shown).
Fig. 8. Optimal TAC trajectory and corresponding direction for heat integration for recycle plant with indirect separation sequence.
as the result of heat integration. But the optimal trajectory is far away from the 50% energy saving line, and, there-fore, a lesser degree of heat integration is encountered. The optimal path starts from the corner of heavy reactant (B) andconverges towardthe center line for the same reason as explainedearlier. Since this is the region where V1¿ V2
(Fig. 4B), backwardintegration (IB) is the optimal one throughout the entire range of zC.
Fig. 9A compares the TACs for three di3erent cases: without heat integration, direct sequence with heat inte-gration, andindirect sequence with heat integration. As expected, the heat-integrated plant with direct sequence gives the lowest TAC. Fig. 9B shows the percent saving on TAC. For the direct sequence, it ranges from 5% to 20% andfor the indirect sequence it is within 12%. At true optima (zC ≈ 0:6), a further 18% saving in TAC
Fig. 9. Optimal TACs for non-heat-integratedplant andheat-integrated recycle plants with direct and indirect sequences (A); and percent TAC saving for heat-integratedplants (B).
is expectedfor the direct sequence with forwardheat integration.
3. Operability and control 3.1. Operability
Any 10–20% reduction in TAC certainly provides incen-tive for energy integration for the recycle system. The next question then becomes: Are these plants operable? In this work steady-state operability measure is employed. Follow-ing the approach originally proposedby Subramanian and
Georgakis (2001)andfurther extendedby Cheng andYu
(2003), we use the recycle ratio (recycle >ow rate/product
>ow rate, e.g., RRi) to evaluate the production rate handling
Fig. 10. Available input spaces (spannedby RR1 andRR2) andcorre-sponding reachable output space (turndown ratio) for non-heat-integrated (A); heat-integrateddirect sequence (B); andheat-integratedindirect sequence (C).
capability of the recycle plant. First, we let the recycle ratios to be halvedanddoubledto explore the reachable produc-tion rate. Fig. 10A shows the achievable production rates for the non-integrated system under indirect sequence. Cer-tainly, the input space is the entire square de4ned by RR1
andRR2, because they are two independent variables and
we have two degrees of freedom. For the direct sequence with forwardheat integration (DF), an auxiliary reboiler is installedto provide necessary heat input to the low-pressure column (e.g., Fig.7) for the case of V1= V2. It is reasonably
assumedthat the auxiliary reboiler can provide up to twice of its nominal steady-state heat input. Therefore, the input
space is a subset of the square as the result of heat integra-tion as shown in Fig.10B. Fig.10B also shows that at low zC (e.g., zC¡ 0:5), the distillation system is design along
the 50% energy saving line (V1= V2). This is a complete
heat-integratedsystem andno auxiliary reboiler is required, and we are left with only one degree of freedom (Fig.7). Thus, the input space becomes a line in the two-dimensional space as shown in Fig.10B. Therefore, some degree of free-dom is lost as the result of heat integration and its severity depends on the degree of heat integration (it becomes most severe at the 50% energy saving line). The input space for the indirect sequence is shown in Fig. 10C and the input al-most spans the entire square because the optimal TAC path is far away from the 50% energy saving line (Fig.4B).
The available input space does indicate the tradeo3 be-tween energy saving andoperability (Fig.10) as a result of loss of degree of freedom. As expected, the non-integrated system gives the largest turndown ratio over the entire range of zC along the optimal path (Fig.10A) andthe indirect
se-quence with backwardintegration (IB) shows a little smaller but also goodturndown ratio. However, for the most eco-nomical direct sequence with backward/forward heat inte-gration results in very small reachable production range at low zC(e.g., zC¡ 0:2) andbecomes acceptable at higher zC
(e.g., zC¿ 0:5) and, fortunately, the optimal TAC trajectory
does not coincide with the 50% energy saving line. Therefore, tradeo3 between steady-state economic (i.e., lower TAC via heat integration) andoperability is encoun-teredfor recycle plant at low zC (i.e., if the process has to
be operatedat low zC). But at true economic optima (zC ≈
0:6), all three con4gurations give acceptable turndown ra-tios. Table2 show the operating conditions at true optima for all three con4gurations (DF, IB, andD, i.e., direct se-quence without heat integration).
3.2. Control
3.2.1. Control structure
As pointedout byCheng andYu (2003), no single con-trol structure works well over the entire composition space. The principle is to determine the variable handling in the production rate variation. For example, when the reactor composition is used to accommodate production change, we shouldalways let the smaller reactant composition >oat. In turns of recycle ratio or recycle >ow rate, this implies that we shouldlet the smaller >ow or >ow ratio >oat by 4xing the larger one.
From optimal operating condition for the DF con4gura-tion has the following reactor composicon4gura-tion zA= 0:22, zB=
0:18, and zC=0:60. This means we should4x the recycle
ra-tio of the 4rst column (recycling component A). In order to ensure expectedamount of A recycle back to the reactor, the distillate composition of A in the 4rst column is control as shown in Fig.11. Furthermore, ratio schemes are employed throughout to provide better throughput handling capability
(e.g., a balancedscheme of Wu andYu, 1996). Once the basic strategy is set, the 11 control degrees of freedom are arrangedas follows (Fig.11):
1. The production rate is set by the fresh feed of B (F0B).
2. The reactor holdup is held constant by controlling reactor eJuent >ow rate (F).
3. The recycle ratio of the 4rst column (RR1= D1=D2) is
4xed.
4. The top composition of the 4rst column (xD1;A) is
con-trolledby changing re>ux ratio (R1=D1).
5. The top level of the 4rst column is controlledby manip-ulating the fresh feedof reactant A (F0A).
6. The boilup ratio of the 4rst column (V1=B1) is 4xed.
7. The bottom level of the 4rst column is controlledby changing the bottom >ow rate (B1).
8. The product composition (xD2;C) is heldby manipulating
the re>ux ratio of the secondcolumn (R2=D2).
9. The boilup ratio of the secondcolumn (V2=B2) is 4xed.
10. The top level of the secondcolumn is controlledby ma-nipulating the production rate (D2).
11. The bottom level of the secondcolumn is controlledby changing the bottom >ow rate (B2).
The optimal reactant composition (Table2) for the IB is: zA = 0:14, zB = 0:24, and zC = 0:62. Therefore, the
recy-cle >ow (or recyrecy-cle ratio) relatedto component B should be 4xed. With this basic strategy, a control structure can be constructedandit is almost the mirror image of the DF con4guration as shown in Fig.12. Note that the true optima for both heat-integratedsystems are locatedat region where V1= V2and auxiliary reboilers are required to provide
addi-tional heat to meet the total energy requirement. Therefore, similar to the system without heat-integration, both con4g-urations have 11 control degrees of freedom. For the pur-pose of comparison, the optimal design for the recycle plant without heat integration is also shown in Table2. This cor-responds to the direct sequence (D) and the control structure is exactly the same as Fig.11except that the separators are not heat integrated.
3.2.2. Controller design
Nonlinear simulation is carriedout to test the dynamics andcontrol of the recycle plant. The column model is sim-ilar to the ideal distillation model ofLuyben (1990)except this is a multicomponent version. It consists of NC ordinary di3erential equations (ODEs) for the reactor, NC(NTi+ 2)
for the ith column. It was programmedin FORTRAN which is available upon request. For the purpose of control, 4 min of analyzer deadtime is assumedfor composition measurement. Let us use the direct sequence with forward integration (DF) in Fig. 11 to illustrate the controller de-sign. The process consists of two composition loops, 4ve level loops, andfour >ow (or ratio) loops. Typically, >ow controller can be set directly and, in this work, perfect >ow
Fresh composition of B (mole fraction) 1 1 1
Reactor holdup (VR) (lb mol) 2475 2917 3200
Reactor eJuent (F) (lb mol=h) 164.4 159.0 151.6
Reactor composition of A (zA) (mole fraction) 0.22 0.14 0.16
Reactor composition of B (zB) (mole fraction) 0.18 0.24 0.19
2. Distillation 1
Distillate >ow rate (lb mol=h) 35.53 121.5 23.38
Distillate temperature (◦F) 310.2 228.6 200.2
Composition of A in distillate (mole fraction) 0.99 0.183 0.99
Composition of B in distillate (mole fraction) ∼ 0 0.008 ∼ 0
Composition of C in distillate (mole fraction) 0.01 0.809 0.01
Bottom >ow rate (lb mol=h) 128.9 37.54 128.1
Bottom temperature (◦F) 361.8 280.2 244.2
Composition of A in bottom (mole fraction) 0.008 ∼ 0 0.008
Composition of B in bottom (mole fraction) 0.229 0.99 0.225
Composition of C in bottom (mole fraction) 0.763 0.01 0.767
Relative volatility (A=C=B) 3.24/1.8/1 4/2/1 4/2/1
No. of trays 32 27 27
Feedtray 15 17 12
Vapor >ow rate (lb mol=h) 243.4 293.3 179.9
3. Distillation 2
Distillate >ow rate (lb mol=h) 100 21.48 100
Distillate temperature (◦F) 238.7 310.2 237.8
Composition of A in distillate (mole fraction) 0.01 0.99 0.01
Composition of B in distillate (mole fraction) 0.01 ∼ 0 0.01
Composition of C in distillate (mole fraction) 0.98 0.01 0.98
Bottom >ow rate (lb mol=h) 28.882 100 28.078
Bottom temperature (◦F) 280.2 353.5 280.2
Composition of A in bottom (mole fraction) ∼ 0 0.01 ∼ 0
Composition of B in bottom (mole fraction) 0.99 0.01 0.99
Composition of C in bottom (mole fraction) 0.01 0.98 0.01
Relative volatility (A=C=B) 4/2/1 3.24/1.8/1 4/2/1
No. of trays 27 32 27
Feedtray 18 13 19
Vapor >ow rate (lb mol=h) 258.6 198.5 256.8
4. Cost
Reactor cost ($) 3.11E+05 3.43E+05 3.79E+05
Column cost ($) 3.29E+05 3.67E+05 3.65E+05
Heat exchanger cost ($) 6.43E+05 6.77E+05 7.84E+05
Operating cost ($) 1.38E+05 1.48E+05 1.85E+05
Pay-back years 3 3 3
TAC ($) 5.65E+05 6.11E+05 6.95E+05
control is assumed. In the 4ve level loops, four of them are column reboiler or re>ux drum holdups and one is the reac-tor holdup. Perfect level control is assumed for the column inventory andthe reactor level PI controller is tunedby set-ting the closed-loop time constant 1/10th of the residence
time with a damping coeQcient of 0.707 and this only requires steady-state operating data. So, in practice, only the two composition loops require plant testing andiden-ti4cation. Relay feedback test (Yu, 1999) is carried out on this multivariable system (Fig. 13) andit takes
Fig. 11. Control structure for DF con4guration.
Fig. 12. Control structure for IB con4guration.
Fig. 13. Relay feedback tests of composition loops for DF con4guration.
approximately 4:5 h to complete the 4rst roundas shown in Fig. 13. Once the ultimate gain (Ku) andultimate
period(Pu) becomes available, the PI controller
parame-ters, controller gain Kcandreset time I, are obtainedusing
Tyreus andLuyben tuning rule (Kc= Ku=3 and I = 2Pu).
The same controller design procedure is applied to all three con4gurations.
3.2.3. Production rate changes
Before getting into the details of simulation results, it shouldbe emphasizedthat these optimal designs (DF, IB, andD) correspondto di3erent steady states (Table2). For 20% production rate changes, simulation results show that the DF con4guration gives the best performance andthe product composition returns to set point in 8 h (xD2;C in
Fig. 14A) as opposedto 16 h for the IB con4guration (xB2;C in Fig. 14B) andfor con4guration without heat
xD2,A R2 zA zB D2 xD2,C xB2,C B2 rr2 rxn xB1,C xB2,C B1 B2 br2 rxn xB2,B V2 FOA rr1 xB1,B xB2,A V1 V2 FOB br1 VR F zB D2 D1 F 0 50 100 0 50 100 0 50 100 0 50 100 0 50 100 0. 005 0. 01 0. xD1,A xD2,A R1 R2 zA VR 015 0 50 100 0. 979 0. 98 0. 981 0 50 100 0. 8 0. 9 1 0 50 100 0 0. 1 0. 2 0 50 100 100 200 300 0 50 100 50 100 150 0 50 100 0 200 400 0 50 100 0 50 0 50 100 0. 2 0. 25 0 50 100 0 0. 2 0. 4 0 50 100 50 100 150 0 50 100 1. 5 2 2. 5 0 50 100 49 50 51 Time 0 50 100 100 200 300 Tim e 0 50 100 5 6 7 Tim e 0 50 100 1 1. 5 2 Time 0 50 100 0 0. 2 0. 4 0 50 100 0. 75 0. 8 0. 85 0 50 100 0. 98 1 0 50 100 0. 005 0. 01 0. 015 0 50 100 100 200 300 0 50 100 0 100 200 0 50 100 0 200 400 0 50 100 20 40 60 0 50 100 0. 8 0. 9 0.1 0 50 100 0 0. 1 0. 2 0 50 100 0. 008 0. 01 0. 012 0 50 100 0. 979 0. 98 0. 981 0 50 100 100 200 300 0 50 100 0 20 40 0 50 100 0 200 400 0 50 100 50 100 150 0 50 100 0. 1 0. 15 0. 2 0 50 100 0. 2 0. 3 0 50 100 50 100 150 0 50 100 1 2 3 0 50 100 49 50 51 Tim e 0 50 100 100 200 300 Tim e 0 50 100 0 2 4 Tim e 0 50 100 1 2 3 Tim e ∆ F0A = + 20% ∆ F0A= -20% (A) (B) xD1,C xD2,C
Fig. 14. Closed-loop responses for +20% throughput changes with: (A) DF con4guration; (B) IB con4guration; and (C) direct sequence without heat integration (D).
xB1,C xB2,C B1 B2 rr2 rxn xB1,B xB2,B V1 V2 FOA rr1 zB D2 D1 xD1,C xD2,C F xD1,A xD2,A R1 R2 zA VR 0 50 100 0. 99 0 50 100 0. 008 0. 01 0. 012 0 50 100 0 0. 2 0. 4 0 50 100 0. 6 0. 8 1 0 50 100 100 200 300 0 50 100 0 20 40 0 50 100 100 200 300 0 50 100 0 100 200 0 50 100 0.008 0. 01 0. 012 0 50 100 0. 979 0. 98 0. 981 0 50 100 0. 8 0. 9 1 0 50 100 0 0. 1 0. 2 0 50 100 100 200 300 0 50 100 50 100 150 0 50 100 0 200 400 0 50 100 0 50 0 50 100 0. 1 0. 15 0. 2 0 50 100 0. 15 0. 2 0. 25 0 50 100 50 100 150 0 50 100 1 1. 5 2 0 50 100 49 50 51 Tim e 0 50 100 100 200 300 Tim e 0 50 100 6 7 8 Tim e 0 50 100 1 2 3 Tim e ∆ F0B = + 20% ∆ F0B= -20% (C) Fig. 14. continued.
integration (D) (xD2;C in Fig. 14C). Nonlinear responses were observedas one compares the positive andnega-tive changes. For production rate increase, most of the variables are heldat the vicinity of nominal steady state. However, for a production decrease, the recycle stream with composition uncontrolledshowing signi4cant devi-ation from nominal values (xB2;B in Fig. 14A, xD2;B in
Fig.14B, and xB2;B in Fig.14C). These responses indicate
that some of the product C is recycled back to the reactor to make the term kzAzB (rxn in Fig.14) less than the nominal
value.
3.2.4. Feed composition variations
At nominal cases, the fresh feeds are assumed to be pure A andB (100 mol%). Fig. 15 shows the responses when the fresh feedof A (F0A) contains some impurity C and z0A
becomes 92% and89%, respectively. Results shown that, for DF andIB con4gurations, product compositions (xD2;C
in Fig.15A and xB2;C in Fig.15B) return to nominal
val-ues andmost of the variables settle down in 100–200 h as shown in Fig.15A andB. However, for the direct sequence without heat integration (D) with a −11% composition change, the control system fails to maintain product purity andsome of the internal >ows simply take o3 as shown in Fig.15C.
Similarly, feedcomposition variations of fresh feedB (z0B) are investigatedandC is assumedto be the
impu-rity. Fig. 16A shows, for the DF con4guration, the prod-uct composition xD2;C returns to the set point in less than
100 h. Oscillatory responses were observedfor −11% feed composition disturbance, but the magnitude of deviation is reasonably small (e.g., LxD2;C¡ 0:001). For the IB
con4g-uration, goodcontrol can be achievedfor −8% feedcompo-sition change. However, for −11% feedcompofeedcompo-sition distur-bance, the system becomes unstable as shown in Fig.16B andthe potential instability cannot be observedqualitatively until 700 h (almost 30 days) after the step load change. For the direct sequence without heat integration (D con4gura-tion), smooth loadresponses can be achievedfor −8% feed composition change (Fig. 16C). However, for −11% feed composition disturbance, a limit cycle is observedandall process variables show sustainedoscillation. The reason for the limit cycle is explainedas follows. First, a signi4cant decrease in the total amount of B leads to the stoichiometric imbalance andexcess amount of A goes over to the second column. The composition loop tries to re-establish product composition by increasing re>ux >ow (R2, t = 50–80 in
Fig. 16C), this results in increasedvapor boilup andbase >ow (V2and B2, t =50–80) and, subsequently, excess
prod-uct C is recycledback to the reactor. An increase in zCslows
down andreaction rate anddecrease the amount of A excess andthis eventually leads to a smaller internal traQc in the secondcolumn anda decreasedamount of recycledprod-uct C (B2; t = 80–120). But again, the problem of A excess
xB2,C B2 rr2 rxn xB1,C xB2,C B1 B2 rr2 rxn xB2,B V2 FOA rr1 xB1,B xB2,B V1 V2 FOA rr1 zB D2 xD2,C xD1,C xD2,C F zB D2 D1 F xD2,A R2 zA VR xD1,A xD2,A R1 R2 zA VR 0 200 40 0 0 0. 005 0. 01 0 200 40 0 0. 979 0. 98 0. 981 0 200 400 0. 98 1 0 200 400 0 0. 01 0. 02 0 200 40 0 150 200 250 0 200 40 0 100 110 120 0 200 400 250 300 350 0 200 400 20 40 60 0 200 40 0 0 0. 2 0. 4 0 200 40 0 0 0. 2 0. 4 0 200 400 90 100 110 0 200 400 1. 8 1. 9 2 0 200 40 0 50 50. 05 Tim e 0 200 40 0 160 180 200 Tim e 0 200 400 5 10 15 Tim e 0 200 400 1. 5 2 2. 5 Tim e 0 200 400 0.99 0 200 400 0.008 0.01 0.012 0 200 400 0.2 0.3 0.4 0 200 400 0.6 0.7 0.8 0 200 400 200 250 300 0 200 400 20 30 40 0 200 400 200 300 400 0 200 400 100 150 200 0 200 400 0 0.005 0.01 0 200 400 0.979 0.98 0.981 0 200 400 0.98 1 0 200 400 0 0.01 0.02 0 200 400 150 200 250 0 200 400 100 110 120 0 200 400 250 300 350 0 200 400 20 40 60 0 200 400 0 0.2 0.4 0 200 400 0 0.2 0.4 0 200 400 90 100 110 0 200 400 1.8 1.9 2 0 200 400 50 50.05 Time 0 200 400 160 180 200 Time 0 200 400 5 10 15 Time 0 200 400 1.5 2 2.5 Time ∆ z0A =-11% ∆ z0A=-8% (A) (B)
Fig. 15. Closed-loop responses for −8% and −11% feedcomposition (z0A) changes with: (A) DF con4guration; (B) IB con4guration; and(C) direct sequence without heat integration (D).
reappears. The scenario continues anda limit cycle results. In summary, the tolerable composition variation is around 10% and, again, the DF con4guration gives better
distur-bance rejection capability. More importantly, the improved performance is obtainedusing heat-integratedsystem with a 20% lesser TAC.
xB1,C xB2,C B1 B2 rr2 rxn xB1,B xB2,B V1 V2 FOA rr1 zB D2 D1 xD1,C xD2,C F xD1,A xD2,A R1 R2 zA VR (C) 0 200 400 600 800 0.989 0.9895 0.99 0 200 400 600 800 0.01 0.0105 0.011 0 200 400 600 800 0.4 0.6 0 200 400 600 800 0.4 0.6 0 ×10-3 ×10-3 200 400 600 800 200 250 300 350 0 200 400 600 800 15 20 0 200 400 600 800 200 250 300 350 0 200 400 600 800 150 200 250 0 200 400 600 800 2 4 6 8 0 200 400 600 800 0.979 0.98 0.981 0 200 400 600 800 0.99 0.995 0 200 400 600 800 5 10 0 200 400 600 800 200 400 600 800 0 200 400 600 800 100 105 110 0 200 400 600 800 200 400 600 800 0 200 400 600 800 50 100 150 0 200 400 600 800 0.06 0.08 0.1 0.12 0.14 0 200 400 600 800 0.2 0.4 0 200 400 600 800 100 105 0 200 400 600 800 1.45 1.5 0 200 400 600 800 50 50.05 Time 0 200 400 600 800 150 200 250 Time 0 200 400 600 800 10 15 20 Time 0 200 400 600 800 2 4 6 8 10 12 Time ∆ z0A =- 11% ∆ z 0A=-8% Fig. 15. continued. 4. Conclusion
This work analyzes the tradeo3 between steady-state economics anddynamic control for heat-integratedrecycle plants. Optimal TAC trajectories for heat-integratedrecycle plants with direct and indirect sequences are derived as zC
varies. The results indicate that, for the direct sequence, the trajectory follows the 50% energy saving line at low zC
andconverges to the line where the reactants are equally distributed at high zC. For the indirect sequence, the
tra-jectory locates far away from the 50% energy saving line which also indicates a lesser degree of heat integration is expected. Provided with correct direction for heat inte-gration, the >owsheet is establishedfor both sequences. It turns out the heat-integratedrecycle plant with direct se-quence is economically optimal andbackwardintegration (DB) is preferredat low zC while the forwardintegration
(DF) shouldbe usedfor zC¿ 0:5. For steady-state
con-trollability, the reachable production range is identi4ed as the recycle ratios vary. From the available input space, it is clear that controllability deteriorates gradually as the degree of heat integration increases and, at the 50% energy saving line, one control degree of freedom is lost. How-ever, if the recycle plant is optimally designed (zC ≈ 0:6),
acceptable turndown ratio is observed and little tradeo3 between steady-state economics and dynamic operability may result. Finally, rigorous nonlinear simulations are used to test control performance of di3erent process con4gura-tions (with andwithout heat integration). The results reveal that improvedcontrol can be achievedfor well-designed heat-integratedrecycle plants (comparedto the plants with-out energy integration) with up to 40% energy saving and close to 20% saving in total annual cost.
Notation
Bi bottom >ow rate from ith column
D recycle process with direct separation sequence (without heat integration)
DB recycle process with direct separation sequence under backward heat integration
DF recycle process with direct separation sequence under forward heat integration
Di distillate >ow rate from ith column
F >ow rate out of the reactor
xB2,C B2 rr2 rxn xB1,C xB2,C B1 B2 rr2 rxn zB D2 xD2,C xD1,C xD2,C F zB D2 D1 F xD2,A R2 zA VR (A) xD1,A xD2,A R1 R2 zA VR (B) xB2,B V2 FOA rr1 xB1,B xB2,A V1 V2 FOB rr1 0 50 100 200 0 50 10 0 30 0 50 100 200 0 50 10 0 120 0 50 100 0 0. 01 0. 02 0 50 10 0 0. 979 0. 98 0. 981 0 50 100 0. 5 1 0 50 10 0 0 0. 5 0 50 100 150 200 250 0 50 10 0 95 100 105 0 50 100 250 300 350 0 50 10 0 20 40 60 0 50 100 0. 22 0. 23 0. 24 0 50 10 0 0. 1 0. 15 0. 2 0 50 100 80 90 100 0 50 10 0 1. 6 1. 8 2 0 50 100 49 .8 50 50 .2 Tim e 0 50 10 0 150 200 250 Tim e 0 50 100 5 5. 5 6 Tim e 0 50 10 0 1. 5 2 2. 5 Tim e 0 200 400 600 800 0. 2 0. 25 0 200 400 600 800 0. 75 0. 8 0 200 400 600 800 0. 988 0. 99 0. 992 0 200 400 600 800 0. 008 0. 01 0. 012 0 200 400 600 800 180 200 0 200 400 600 800 130 140 150 0 200 400 600 800 300 350 0 200 400 600 800 25 30 35 0 200 400 600 800 0. 99 0. 995 0 200 400 600 800 5 10 0 200 400 600 800 0. 012 0. 014 0. 016 0 200 400 600 800 0. 979 0. 98 0. 981 0 200 400 600 800 200 250 300 0 200 400 600 800 25 30 35 0 200 400 600 800 200 250 300 0 200 400 600 800 100 105 110 0 200 400 600 800 0. 15 0. 2 0 200 400 600 800 0. 16 0. 18 0. 2 0. 22 0 200 400 600 800 100 105 110 0 200 400 600 800 1. 62 1. 64 1. 66 1. 68 0 200 400 600 800 50 50.02 50.04 Tim e 0 200 400 600 800 160 165 170 Tim e 0 200 400 600 800 1 1. 5 2 2. 5 Tim e 0 200 400 600 800 2 2. 5 3 Tim e ∆ z0B =- 11% ∆ z0B=- 8%
Fig. 16. Closed-loop responses for −8% and −11% feedcomposition (z0B) changes with: (A) DF con4guration; (B) IB con4guration; and(C) direct sequence without heat integration (D).
xB1,C xB2,C B1 B2 rr2 rxn zB D2 D1 xD1,C xD2,C F xD1,A xD2,A R1 R2 zA VR (C) xB1,B xB2,B V1 V2 FOA rr1 0 100 200 0. 99 0 100 200 0. 009 0. 01 0. 011 0 100 200 0. 15 0. 2 0. 25 0 100 200 0. 75 0. 8 0. 85 0 100 200 150 200 250 0 100 200 20 30 40 0 100 200 150 200 250 0 100 200 100 150 200 0 100 200 0 0. 05 0 100 200 0. 975 0. 98 0. 985 0 100 200 0 0. 5 1 0 100 200 0 0. 5 1 0 100 200 0 500 1000 0 100 200 95 100 105 0 100 200 0 500 1000 0 100 200 0 50 100 0 100 200 0. 15 0. 2 0 100 200 0. 1 0. 15 0. 2 0 100 200 80 90 100 0 100 200 1. 2 1. 4 1. 6 0 100 200 49. 8 50 50. 2 Tim e 0 100 200 150 200 250 Tim e 0 100 200 5 6 7 Tim e 0 100 200 0 5 10 Tim e ∆ z0B = -11% ∆ z0B=- 8% Fig. 16. continued.
I recycle process with indirect separation sequence
IB recycle process with indirect separation sequence under backward heat integration IF recycle process with indirect separation
sequence under forward heat integration k speci4c reaction rate
Li liquid>ow rate in the column
NC number of component NFi feedtray number in column i
NTi total number of trays in column i
Psat vapor pressure
rri re>ux ratio of ith column
rxn total reaction rate (Eq. (1)) RRi recycle ratio in column i
T temperature
TAC total annualizedcosts
Vi vapor boilup in column i
VR reactor holdup in moles
xBk;j bottom composition in kth column (mole
fraction of component j)
xDk;j distillate composition in kth column (mole
fraction of component j)
z;j reactor composition (mole fraction of
component j)
z;oj fresh feedcomposition (mole fraction of
component j)
Greek letters
j relative volatility of component j
LH heat of vaporization
Subscripts
HP high-pressure column
LP low-pressure column
Acknowledgements
Financial support of the National Science Council of Taiwan is gratefully acknowledgedandwe also thank Vin-cent Chang for performing some simulation runs for the recycle plants. FORTRAN programs for the recycle plants are available upon request.
AppendixA.
Shortcut design, equipment sizing, and TAC calculation
1. Use twice of the minimum number of trays (Fenske equa-tion) for column design and the Kirkbride equation for
2. Compute reactor diameter in ft (assume an aspect ratio of 2 andan averagedmolecular weight of 66.7) DR= 2 " VRMW avg 1=3 : (A.3)
3. Calculate column diameter in ft and assuming tray spac-ing of 2:4 ft DC;i= 1 900" MWRgasT P 1=2 Vi1=2; (A.4)
LC;i= 2:4NT;i; (A.5)
where Rgas= 1545=144 psia ft3=lb-mol◦R, T is the
aver-agedcolumn temperature in◦R, P is the column pressure
in psia, Vjis the vapor >ow rate in lbmol/h.
4. Use Francis weir formula to 4ndthe height over weir (how;i) in ft how;i= LiMW 9600 avgDc;i 2=3 : (A.6)
5. Compute liquidtray holdup (Mn;i) in lbmol assuming a
wier height of 1 inch Mn;i=(how;i+ (1=12))("D
2 c;i=4) avg
MW : (A.7)
6. Compute liquidhydraulic time constant ('i) in h from
'i=57600(h"Dc;i
ow;i)1=2: (A.8)
7. Compute heat transfer areas for reboiler andcondenser AR;i=UViLH RLTR; (A.9) Ac;i=UViLH CLTC: (A.10) Assuming UR= 250 Btu=(h◦Fft2), LTR= 30◦F, UC = 150 Btu=(h◦Fft2), andLT C= 20◦F.
8. Use M& S index of 950 to compute capital costs and the formula taken fromDouglas (1988)
reactor cost =M&S280 101:9D1:066 R L0:802R
×(2:18 + (3:67 × 1:2)); (A.11)
×(2:29 + (1:35 + 0:1)3:75);
(A.14) 9. Compute steam (LHsteam comes from steam table) and
cooling water cost (assuming LTCW= 30◦F) from
steam cost = CS(LH Vi) LHsteam ; (A.15) cooling-water cost =CW(LH Vi) CP;CWLTCW : (A.16)
Utilities cost Price
Saturatedsteam CS (per 1000 lb)
600 psig $4.52
250 psig $3.72
150 psig $3.4
50 psig $2.8
Cooling water CW (per 1000 gal)
90◦F-water $0.03
References
Bansal, V., Ross, R., Perkins, J.D., Pistikopoulos, E.N., 2000. The interaction of design and control: double-e3ect distillation. Journal of Process Control 10, 219.
Bildea, C.S., Dimian, A.C., 1999. Interaction between design and control of a heat-integrateddistillation system with prefractionator. Transactions of the IChem 77, 597.
Cheng, Y.C., Yu, C.C., 2003. Optimal region for design and control of ternary systems. A.I.Ch.E. Journal 49, 682.
Chiang, T.P., Luyben, W.L., 1983. Comparison of energy consumption of 4ve heat-integrated distillation con4gurations. Industrial and Engineering Chemistry Process Design andDevelopment 22, 175. Chiang, T.P., Luyben, W.L., 1988. Comparison of the dynamic
performance of three heat-integrateddistillation con4gurations. Industrial and Engineering Chemistry Research 27, 99.
Douglas, J.M., 1988. Conceptual Design of Chemical Processes. McGraw-Hill, New York.
Glinos, K., 1984. Global approach to the preliminary design and synthesis of distillation trains. Ph.D. Dissertation, University of Massachusetts, Amherst.
Glinos, K., Malone, M.F., 1988. Optimality regions for complex column alternatives in distillation systems. Chemical Engineering Research and Design 66, 229.
Han, M., Park, S., 1996. Multivariable control of double-e3ect distillation con4gurations. Journal of Process Control 6, 247.
Larsson, T., Skogestad, S., 2000. Plantwide control: a review and a new design procedure. Modeling Identi4cation and Control 21, 209. Luyben, W.L., 1990. Process Modeling Simulation and Control for
Luyben, W.L., Tyreus, B.D., Luyben, M.L., 1999. Plantwide Process Control. McGraw-Hill, New York.
Malone, M.F., Glinos, K., Marquez, F.E., Douglas, J.M., 1985. Simple, analytical criteria for the sequencing of distillation columns. A.I.Ch.E. Journal 31, 683.
Rev, E., Emtir, M., Szitkai, Z., Mizsey, P., Fonyo, Z., 2001. Energy saving of integratedandcoupleddistillation systems. Computers and Chemical Engineering 25, 119.
Rix, A., Gelbe, H., 2000. On the impact of mass andheat integration on design and control of distillation column systems. Transactions of the IChem 78, 542.
Subramanian, S., Georgakis, C., 2001. Steady-state operability characteristics of idealize reactors. Chemical Engineering Science 56, 5111.
Tyreus, B.D., Luyben, W.L., 1976. Dynamics andcontrol of heat-integrateddistillation columns. Chemical Engineering Progress 72 (9), 59.
Tyreus, B.D., Luyben, W.L., 1993. Dynamics andcontrol of recycle systems. 4. Ternary systems with one or two recycle streams. Industrial andEngineering Chemistry Research 32, 1154.
Wang, S.J., Lee, E.K., 2002. Nonlinear control of high-purity heat-integrateddistillation system. Journal of Chemical Engineering of Japan 35 (9), 848.
Weitz, O., Lewin, D.R., 1996. Dynamic controllability andresiliency diagnosis using steady state process >owsheet data. Computers and Chemical Engineering 20, 325.
Wu, K.L., Yu, C.C., 1996. Reactor/separator processes with recycle-1. Candidate control structure for operability. Computers and Chemical Engineering 20, 1291.
Yang, Y.H., Lou, H.H., Huang, Y.L., 2000. Steady state disturbance propagation modelling of heat integrated distillation processes. Chemical Engineering Research andDesign 78 (A2), 245.
