Comparison of Dynamic and Static Performances of a Quaternary

Jun 3, 2010 - According to the Douglas24 onion model meth- odology, the steady state distillation train is built and designed by means of shortcut or ...
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Ind. Eng. Chem. Res. 2010, 49, 6135–6143

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Comparison of Dynamic and Static Performances of a Quaternary Distillation Sequence Gholamreza Baghmisheh, Mohammad Shahrokhi,* and Ramin Bozorgmehri Department of Chemical & Petroleum Engineering, Sharif UniVersity of Technology, P.O. Box 11365-9465, Azadi AVe., Tehran, Iran

In this work, steady state and dynamic performances of quaternary distillation column sequences designed based on steady state and dynamic cost functions have been investigated. To quantify the dynamic performance, product losses due to disturbances have been considered in the objective function. In addition, variations of operating costs such as utilities have been considered in the objective function. To separate a quaternary mixture into four products, 22 configurations have been used. It has been observed that the feed composition, disturbance frequency and magnitude affect the dynamic behavior strongly. To decrease the optimization computational load, a scheme that provides a suboptimal result has been proposed. By performing simultaneous optimization that requires much more computational time, it has been shown that the highest ranking configurations obtained by the proposed method are the same as those provided by simultaneous technique. The simulation results indicate that there is no clear pattern for configuration ranking based on column sequence specifications. 1. Introduction Design of a continuous chemical process is usually carried out under steady state conditions for a given operating range, assuming that a control system can be designed to maintain the process at the desired operating level and within the design constrains. However, favorable process static characteristics could limit the effectiveness of a control system, leading to a condition that design specifications cannot meet. Usually, alternative designs are judged on the basis of economic aspects alone, without taking controllability and dynamic behavior into account. This may lead to elimination of easily controlled, but slightly less economical alternatives in favor of slightly more economical designs that may be extremely difficult to control.1,2 Many papers have been proposed for finding the optimum design of a distillation column sequence using the superstructure approach. Mixed-integer linear programming (MILP), mixedinteger nonlinear programming (MINLP), and genetic algorithm are the most popular methods that have been utilized for optimization purposes. The MILP and MINLP techniques require a process model and are time-consuming. Also using the rigorous model may lead to a large nonconvex problem. The genetic algorithm is the most recommended technique for this purpose.3-7 Despite the interaction and conflict between design and control, complex plants have been often operated reasonably well. These plants usually have many surge tanks that reject and minimize operation dynamic interactions. Nowadays buffer surge tanks have been utilized to isolate units of a modern complex plant and prevent total shutdown. Dynamic behavior of a middle-vessel continuous distillation column (MVCC) has been studied by Barolo and Papini,8 Phimister and Seider,9 Faanes and Skogestad,10 Bezzo and Barolo,11 and Loperena et al.12 As Luyben et al. have mentioned, process design impacts the controllability far more than control algorithms do and design on the basis of steady-state economics is risky, because the resulting plants are often difficult to control (i.e., inflexible, with * To whom correspondence should be addressed. E-mail address: [email protected].

poor disturbance-rejection properties), leading to off-spec products, excessive use of fuel, and associated profitability losses.13 Some heuristics and recommendations have been reported in the literature regarding design and control effects, control philosophy, controller design, and tuning. Some of them have been reported by Luyben et al.13 and have been used in process design.14 But these rules are case dependent; therefore, rigorous analysis should be carried out to select the best alternative. To analyze controllability and dynamic resiliency of a developed process, three vital steps must be considered. These steps are selecting a control structure, tuning controller parameters, and evaluating dynamic behavior. Evaluation of dynamic behavior based on a suitable objective function and designing a test procedure are the most critical steps. Since static and dynamic behaviors of the column sequence can affect the total cost, multiobjective optimization approach can be used. In this paper, steady state and dynamic costs are incorporated in one objective function, and the best alternative has been found by minimizing this objective function. To quantify the dynamic performance, products losses due to disturbances have been considered in the objective function. 2. Problem Statement As mentioned before, traditionally, design of a process control system is postponed until the process design is completed. Nowadays, it is broadly accepted that this is not a desirable situation since this sequential design approach can lead to processes that are difficult to control. As a consequence, different ways to take controllability issues into account in the process design stage have been developed and described in the literature.15 These methods can be classified into two groups: (i) methods which are able to screen alternative designs for controllability and (ii) methods which integrate process design and the control systems.16,17 In the first approach, controllability of alternative designs is tested such that alternatives that might have acceptable steadystate economics but poor control performances are rejected in the early stage of design. Controllability is quantified using

10.1021/ie100169p  2010 American Chemical Society Published on Web 06/03/2010

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Table 1. Different Configurations of 22 Separation Sequences no. of sequences

separation sequence

no. of sequences

1 2 3 4 5 6 7 8 9 10 11

A/BCD f B/CD f C/D A/BCD f BC/D f B/C A/BCD f BCD f B/C f C/D ABC/D f AB/C f A/B ABC/D f A/BC f B/C AB/CD f A/B f C/D ABC/D f ABC f A/B f B/C ABCD f B/CD f A/B f C/D ABCD f BC/D f A/B f B/C ABCD f BCD f A/B f B/C f C/D ABCD f A/BC f B/C f C/D

14 13 14 15 16 17 18 19 20 21 22

indices like the relative gain array (RGA) and singular value decomposition (SVD).16-19 In the second approach, static and dynamic characteristics of a process are considered simultaneously in screening design alternatives. In this paper, 22 configurations have been considered for separation of a quaternary mixture. If the first approach is used, the best selected steady-state sequence may have a poor controllability performance. Also if the simultaneous approach is used, screening different schemes may be very timeconsuming. In the latter approach, the dynamic issues such as controller paring, controller tuning, and performance test evaluation (using load rejection criteria or set-point tracking) must be taken into account in addition to process design. Despite the fact that this approach takes into account the dynamic performance of the process, the criterion used in dynamic performance evaluation has been solely calculated based on the deviation of the controlled variables from their corresponding set points (e.g., integral of square error, integral of absolute error, etc.). However, it should be noted that such a criterion does not take into account the change in operational cost of the whole process due to the changes in loads or set points of the controllers To decrease limitations of existing methods, an approach is proposed that compares alternative designs based on an objective function that includes steady state and dynamic costs. To quantify the dynamic performance, integral of square deviations of desired specifications such as products purities has been taken as an objective function.19-23 In this work to quantify the dynamic performance of different alternatives, an objective function which includes costs due to off-spec products and utilities has been considered. 3. Distillation Column Sequences and Alternative Evaluation under Steady State Conditions In this paper, separation of a quaternary mixture using a simple distillation column without heat integration has been investigated. According to the Douglas24 onion model methodology, the steady state distillation train is built and designed by means of shortcut or rigorous techniques. Having performed steady-state analysis, alternative schemes are ranked according to their steady-state costs. To separate a quaternary mixture into four products with at least 99.5 wt % purities, 22 configurations have been used. These configurations have been developed to generate the distinct thermally coupled distillation sequences.25,26 Typically, there are two ways to perform a separation for a nonazeotropic multicomponent mixture: the sharp splits and the sloppy splits. A sharp split takes place when the two key components are adjacent and each component in the feed appears in a significant amount only in one of the two products. A sloppy split occurs when the two key components are nonadjacent, and there is at least one middle component distributed between the top and bottom products.

separation sequences ABCD ABCD ABCD ABCD ABCD ABCD ABCD ABCD ABCD ABCD ABCD

f f f f f f f f f f f

AB/C f A/B f C/D ABC f A/B f B/C f C/D A/BC f BCD f B/C f C/D A/BC f BC/D f B/C AB/C f B/CD f A/B f C/D ABC f BC/D f A/B f B/C ABC f BCD f A/B f B/C f C/D ABC f B/CD f A/B f C/D ABC f B/CD f A/B f B/C f C/D AB/C f BCD f A/B f B/C AB/C f BCD f A/B f B/C f C/D

In total, six first splits are identified that include three sharp splits, two asymmetric sloppy splits, and one symmetric sloppy split. Table 1 presents all of the 22 functionally distinct separation sequences for quaternary mixtures. In this table, the underline is used to indicate the distributed middle key components; i.e., ABCD means that a sloppy split is performed for the submixtures, with the two middle components B and C distributed in top (ABC) and bottom (BCD) products. Among the 22 distinct separation sequences, there are 5 sequences (1, 2, 4, 5, and 6) that contain a minimum number of three individual splits; they formulate the subspace of the well-known simple column sequences with only sharp splits. There are seven sequences (3, 7, 8, 9, 11, 14, and 15) with four individual splits; each of them includes only one sloppy split. There are seven sequences (10, 13, 14, 16, 17, 19, and 21) with five individual splits. Sequences 10, 13, 14, and 17 include two sloppy splits, and the remaining sequences include only one symmetric sloppy split. There are three sequences (18, 20, and 22) containing the maximum number of six individual splits. The sequence 18 includes all sloppy splits for the submixtures with three or more components. To select the best steady state alternative, total annual cost (TAC) with plant lifetime of 10 years has been calculated. 3.1. Steady-State Design Procedure. To design a steady state scheme, two approaches have been used: a shortcut method and a rigorous technique. In the shortcut method, first the minimum reflux ratio (Rmin) and minimum number of trays (Nmin) are estimated.27,28 The number of equilibrium stages (N) is obtained using the Erbar-Maddox29 graphic method. The actual reflux ratio (R) is set to 1.2Rmin. Feed tray location has been determined using the Kirkbride30 method. The pressure drop for a single tray is obtained based on the heuristics rule (0.1 psi/tray).31 The feed thermal condition has been considered as a decision variable and is optimized based on an objective function. The HYSYS process simulator has been applied for all case studies. After “N” has been calculated, “R” has been recalculated. In many cases the recalculated R was significantly different from its initial value. To meet the desired product compositions, two design variables of each column in the sequence have been specified. These variables can be chosen from bottom product rate, reflux ratio, boilup ratio, and top or bottom composition. Our preliminary investigation results indicate that, if the calculated R and N from the shortcut method are used, the results can have significant errors for some case studies. In the rigorous design procedure, the parameters obtained via the shortcut method are used as initial guesses for optimizing the objective function. The objective function is the TAC, and the decision variables are

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Figure 1. State task network superstructure for a 4-component mixture.

Figure 2. Base unit with the applied control structure.

• number of theoretical trays • feed tray location • feed quality 3.2. Synthesis Methodology. A superstructure configuration has been built to generate 22 alternatives for the separation of a four-component mixture with a simple column sequence. This structure can be used for mixtures having more components. Generating a superstructure is straightforward using the state task network (Figure 1) scheme proposed by Yeomans and Grossmann.32 Figure 2 shows the base unit of the superstructure. This unit has been built and saved as a template in the HYSYS environment. To have a realistic model, a condenser, heat exchanger, vessel, pump, and valve are used in HYSYS instead of the shortcut method. To implement this design procedure, an application was developed by Visual Basic (VB). In VB, this application supports the ActiveX protocol to swap the information among HYSYS, Matlab, Excel, and the main application which contains a cost estimation module, steadystate optimization engine, dynamic pressure-flow module, and

process identification unit (Figure 3). HYSYS and Matlab automation have been used for model identification and controller tuning. The VB program contains all equipment cost estimation modules and reports and saves the detailed calculation in the Excel files. Figure 3 shows such a configuration schematically. To rank different alternatives the following steps are taken: (a) Using the superstructure scheme, different alternatives are generated (b) For each alternative, the corresponding HYSYS flowsheet is built. (c) The optimum steady state design of various alternatives is obtained via HYSYS and the optimization module. (d) Using the dynamic pressure-flow module, the dynamic model for each alternative is built, and through the identification unit, a process model is obtained. (e) The initial controller settings of each column are obtained by the HYSYS autotuner and are optimized by MATLAB software using the process model.

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Figure 3. Application structure.

(f) Having the optimal controller settings, various alternatives are ranked based on the proposed objective function. 4. Dynamic Simulation and Alternative Resiliency 4.1. Dynamic Model Construction. Dynamic simulations of alternatives are carried out using the HYSYS software. To consider the pressure-flow concept in dynamic simulation when transferring to dynamic mode, extra valves and pumps (Figure 2) between equipment have been utilized. Pressure drop in the valves and pressure rise in the pumps have been set, based on the pressure-flow concept. The expert class prepared in VB has been used to implement the pressure flow setting in HYSYS. The prepared program contains valve, vessel, pump, tray, and heat exchanger sizing modules. Also the following assumptions have been made in dynamic simulation modeling: • For all pumps, a template centrifugal pump curve characteristic with a usual revolutions per minute has been used. • Equal percentage valves with 60% opening at the normal operating flow rate have been considered for control valves. • Condenser holdup is neglected compared to reflux drum holdup; reboiler holdup is incorporated in column sump; pipe holdup is neglected. • Liquid residence time of vessels is considered to be 15 min, and the normal operating level is set to 50%. Also, the columns sump liquid residence time has been set to 20 min. • Tray spacing is 2 ft; the weir height is set to 2 in.; the tray downcomer area to total tray area is set to 10%. These rules of thumb settings are based on Ludwig’s31 recommendations. • Pressure drop in the control valves is set to 2 bar and in the heat exchangers to 0.5 bar. The following control philosophy has been used in this study: Control of column top pressure was carried out by manipulating the cooling water flow rate (Figure 2). The reflux drum level has been controlled by the distillate flow rate, and the bottom flow rate has been used to control the column bottom sump level (Figure 2). The main controlled variables are top and bottom compositions. The corresponding manipulated variables are the liquid reflux flow rate and vapor boilup, respectively, the so-called LV configuration (Figure 2). This configuration is insensitive to level tuning, but for the other configurations the level control tuning is very important.33 It is assumed that product compositions are measured without time delay. Feed temperature is controlled by the suitable utility stream. 4.2. Dynamic Plus Steady State Performance Index. To quantify the dynamic performance, product losses due to

disturbances have been considered in the objective function. In addition, operating costs, such as utility cost, have been also included in the dynamic part of the objective function. The total objective function used for ranking the alternatives is given below. objective function ) steady state total annual cost + off-spec and operating costs due to disturbances (1) The steady state total annual cost has been defined by the following equation: steady state total annual cost ) no._of_columns

[

∑

fi(NC, DC, PC, GC,S&T, HC, ...) i)1 no._of_heat_exchangers

∑

+

gi(AHX, PHX, GHX,S&T, ...)] +

i)1

no._of_vessels

∑

hi(HV, DV, PV, GV, ...)]/lifetime + (CcoldQcold +

i)1

ChotQhot) (2) where the fi, gi, and hi are functions reflecting the capital cost of columns, heat exchangers, and vessels, respectively, obtained by the method proposed by Guthrie.34 Furthermore, Qcold and Qhot imply the condenser and reboiler duties. Also, Ccold and Chot are the cooling water and steam utility costs. The rest of variables are defined in the Nomenclature. The main disturbance in practice is variation of the feed composition, and this is considered to be the main load in this study. The log sheet and data historian of 3 y of three units, aromatic fractionation and natural gas fractionation of the Bandar Imam Petrochemical Company (BIPC) and natural gas liquids fractionation of the South Pars Gas Company (SPGC) have been studied. As mentioned above, the dominant identified disturbances were variations of feed composition. In the present work, variation of the feed flow rate has been also studied for one case. The other disturbances such as failures of cooling water, the steam and power supplier system, and instrument air have been ignored in this study. Type, magnitude, and frequency of the load can change the value of the performance index, and therefore, they should be fixed. Two methods have been used to account for product losses (off-spec products). In the first approach which is used for high purity products, product compositions are measured online and product streams are switched to off-spec tanks when composition falls below the

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Table 2. Feed Specifications of the Case Studies feed mole fractions feed condition feed flow rate ) 1900 kmol/h inlet temperature ) 30 °C inlet pressure ) 1 bar product purity ) 99.5 wt %

aromatic

case no.

benzene (A)

toluene (B)

o-xylene (C)

biphenyl (D)

case 1 case 2 case 3 case 4 case 5 case 6 case 7 case 8

0.40 0.10 0.10 0.30 0.17 0.25 0.33 0.39

0.30 0.20 0.10 0.30 0.44 0.25 0.36 0.24

0.20 0.30 0.40 0.30 0.22 0.25 0.16 0.23

0.10 0.40 0.40 0.10 0.17 0.25 0.15 0.14

feed mole fractions feed flow rate ) 1900 kmol/h inlet temperature ) 30 °C inlet pressure ) 1 bar product purity ) 98.5 wt %

paraffinic

case no.

n-pentane (A)

n-hexane (B)

n-heptane (C)

n-octane (D)

case 9 case 10 case 11 case 12

0.10 0.10 0.40 0.30

0.10 0.20 0.30 0.30

0.40 0.30 0.20 0.30

0.40 0.40 0.10 0.10

desired value. In the second approach, switching to off-spec tanks is based on offline measurements which are performed two or three times per day. This strategy can be used for low purity products. In this paper, for the high purity product case, an online analyzing approach has been utilized. But for the low purity product case, the off-line approach has been used. In the off-line approach, an intermediate tank with 8 h residence time for each product has been considered. If the composition of the mixture in the off-spec tank fulfills the quality requirement of the products after 8 h, the tank content is transferred to the monthly or weekly main product tanks; otherwise, their contents are transferred to an off-spec tank or returned to the feed tanks for reuse. For the low purity case, a purity of 97.5 wt % has been considered. In this study, feed composition is assumed to change stepwise around its nominal value with magnitudes of (10%-(15% of the nominal value. Frequencies of composition variations have been assumed to be 2, 4, 8, 12, 18, and 24 times/y for low frequency loads and 82, 110, 165, and 330 times/y for high frequency loads. At the first step, the initial values of single loop controller tuning parameters have been obtained using an autotuning variation (ATV) test.35 To consider the loop interaction, the controller detuning technique proposed by Tyreus and Luyben36 has been used. In this tuning method, the controller parameters are modified according to the following formulas: KC ) KATV C /FT

(3)

τC ) τATV C FT

(4)

where KCATV and τCATV are ATV controller settings, FT is the detuning factor, and KC and τC are recommended controller settings. In the second step, each single distillation column has been modeled according to the following equation:

[

] [

][ ]

Q11 Q12 reflux topcomp ) comp Q21 Q22 steam bottom

(5)

where the Qi j are the transfer functions (second-order model plus lag) relating top and bottom compositions to reflux and reboiler steam flow rates. Distillation towers usually have wellbehaved open-loop characteristics. The open-loop eigenvalues are negative and real. This results in open-loop dynamics that decay exponentially without oscillation. Therefore the secondorder plus lag models are suitable.

Composition controller settings have been optimized based on the process model using the Matlab software environment by object link embedding (OLE) automation. The integral of the absolute errors (IAE) has been selected as the objective function for loop tuning in each column. A series of set-point changes have been applied to the model for optimization purposes. Using the initial controller settings obtained from the ATV method decreased the optimization runtime considerably. According to the described procedure, controllers’ settings for each column have been obtained. The final controller tunings of trains, containing 3, 4, 5, or 6 distillation columns, may be obtained by three different approaches. In the first approach, all composition control loops are tuned simultaneously using an initial setting obtained for each single column. In the second approach, one detuning factor is used for all columns and its optimal value is found through optimizing the objective function. In the third approach, each column has its own detuning factor obtained through the optimization. In all approaches, controller settings are obtained based on minimization of the performance index given by eq 1. In this study, the third approach has been used. Dynamic losses have been calculated through dynamic simulation runs for a specified period of time considering an external disturbance acting on the system. To make the results independent of disturbance direction, a combination of eight random disturbances has been used. 5. Results and Discussion 5.1. Case Study. Two sets of four-component mixtures have been considered. One set is an aromatics mixture (benzene, toluene, o-xylene, and biphenyl), and the other one is a hydrocarbon mixture (n-pentane, n-hexane, n-heptane, and n-octane). To evaluate the effect of feed composition, different mixtures have been tested (Table 2). 5.2. Steady-State Optimization. The steady-state results for case 7 are shown in the Table 3. This case reflects the operating condition of aromatic plant in Bandar Imam Petrochemical Company (BIPC) when the hydrodealkylation (HDA) unit is not in service and toluene is one of the final products. Table 3 shows that if the rigorous optimization approach is used, the best configuration will be sequence 8, but if the sequences are built by the shortcut method the best case will be sequence 1. Differences of TAC of the shortcut and optimization methods have also been presented. As can be seen, the differences are noticeable. In most case studies, the best case of the shortcut and optimization method are the same, but this cannot be

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Table 3. Comparison of Estimated Fixed Capital and Operating Costs for 22 Distillation Sequences under Steady-State Conditions for Case 7

no. of sequences

fixed capital investment ($)

operating cost ($/y)

total annual cost ($/y) with optimization

1 2 3 4 5 6 7 8 9 10 11 14 13 14 15 16 17 18 19 20 21 22

4,966,616 6,473,676 5,660,030 7,600,960 7,314,533 5,432,070 7,581,844 5,920,587 6,660,272 6,422,635 6,579,764 6,927,754 7,075,383 6,613,686 6,769,152 7,344,328 7,579,209 7,397,637 6,769,527 7,447,776 7,905,770 7,488,257

3,276,779 3,406,352 3,887,889 3,709,182 3,392,679 3,353,438 3,660,032 3,178,534 3,223,111 3,542,799 4,204,992 4,523,405 4,304,089 3,669,750 3,371,352 3,734,268 3,559,185 3,938,604 3,360,721 3,596,154 3,704,530 3,707,793

3,773,440 4,053,720 4,453,892 4,469,278 4,143,932 3,896,645 4,418,217 3,770,593 3,889,139 4,185,063 4,862,969 5,216,180 5,011,627 4,331,119 4,048,267 4,468,701 4,317,106 4,678,368 4,037,673 4,340,932 4,495,108 4,456,619

total annual cost ($/y) with shortcut method

relative differences of shortcut and optimization methods

relative differences of sequences from the best case (optimization method)

relative differences of sequences from the best case (shortcut method)

4,307,398 4,414,820 4,991,579 4,959,099 4,554,623 4,500,658 5,092,232 4,361,595 4,463,428 4,803,541 5,335,922 5,818,454 5,615,314 4,808,303 4,453,262 4,961,637 4,722,199 5,187,119 4,394,483 4,891,408 5,092,267 4,856,804

-14 -9 -14 -11 -10 -16 -15 -16 -15 -15 -10 -14 -14 -11 -10 -11 -9 -11 -9 -13 -13 -9

0.1 7.5 18.1 18.5 9.4 3.3 17.2 0.0 3.1 11.0 29.0 38.3 32.9 14.9 7.4 18.5 14.5 24.1 7.1 15.1 19.2 18.2

0.0 2.5 15.9 15.1 5.7 4.5 18.2 1.3 3.6 11.5 23.9 35.1 30.4 11.6 3.4 15.2 9.6 20.4 2.0 13.6 18.2 14.8

Table 4. Steady-State Ranking of 22 Configurations for Eight Case Studies

considered as a rule for all cases. Table 4 shows the steady state ranking of 22 configurations for 8 case studies, obtained by rigorous optimization method. As can be seen, the highest ranking sequence is changed by changing the feed composition. From the sequence rankings obtained in these case studies, the following results can be concluded: (1) None of the sequences containing more than four distillation columns is the best case, i.e., sequences that have more than one sloppy distillation column are not in the top ranks. (2) Having more than one intermediate component, it is impossible or very difficult to predict the ranking of sequences heuristically.

(3) Despite the extra distillation column, the sequences with one sloppy distillation column can be the best ones. 5.3. Dynamic Evaluation. To evaluate dynamic performances of different column trains, dynamic simulations of these sequences considering feed composition variations have been performed. As mentioned in section 3.2, square wave disturbances with different frequencies have been used. To make the dynamical results independent of disturbance direction, the average result obtained from eight random disturbances has been used instead of a single random disturbance. Figure 4 shows such disturbances for case study 7. Dynamic simulations have been done for 14 cases for 2 feed component types. For eight cases with aromatic feed the online off-spec detection and for four cases with paraffinic feed the off-line off-spec tank strategy have been utilized. The results (Table 5) indicate that, in general, the steady state of alternatives ranking is different from the dynamic one, but there are some cases where the best alternatives are the same. As can be seen from Table 5, for case 3, alternatives ranking is effectively dependent on the load frequency. For example, case 11 whose steady-state rank is 13, has been promoted to the third rank for high frequency loads. Also it is observed that configuration 21 which has the second rank for the load frequency of 2-8, has fallen to low rank sequences for higher frequencies. In this case study, the best case for frequencies between 2 and 12 times per year is the sequence 5 and for frequencies above 18 is the sequence 1. Simulation results for case 4 (not shown) indicate that the first three high ranking configurations are independent of load

Figure 4. Feed composition disturbances (case 7).

Ind. Eng. Chem. Res., Vol. 49, No. 13, 2010 Table 5. Alternatives Ranking for Loads with Different Frequencies for Case 3

Table 6. Alternatives Ranking for Loads with Different Frequencies for Case 10

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The questions which arise are how high above the desired product purity should the composition set point be chosen and what is its optimum value. To find the optimum composition set point, the total costs (steady state plus dynamic) are calculated for different values of the composition set point. Having these data, the total cost is plotted versus composition set point, and the set point corresponding to the minimum value of the total cost is selected as the optimum composition set point. It should be noted that the optimum set point also depends on the load frequency. For the system under consideration, for the low frequency loads the optimum set point is 98.5% while it is 99.0% for the high frequency loads. Table 6 illustrates the results of case 10. As can be seen for this case, sequence 11 is the best alternative for all frequencies. In the Table 7 the highest ranking configurations of the aromatic component set have been shown for two disturbances with different amplitudes ((10% and ( 15%) at all frequencies. As shown in this table, configurations 1 (known as the direct sequence) and 5 (known as the indirect sequence) are often the best alternatives. From the simulation studies, the following results can be obtained: (1) The heuristic screening rules that can be used for steady state design are not applicable for the dynamic case. (2) Ranking of distillation configurations is effectively changed by changing the load frequency or magnitude. (3) Configurations that contained more than five distillation columns are never the best alternative. (4) In some cases, the best steady configuration has a poor dynamic performance. (5) Configuration 1 and 5 are often the best alternatives. (6) Products prices change the sequences ranking effectively. 6. Simultaneous Optimization Approach

frequency. For case 2 (not shown), sequence 5 is independent of load frequency and it is the best scheme for all load frequencies except the frequency 330 times/y, but in general, alternatives ranking is changed as load frequency changes. For the offline composition measurement strategy, case 10 has been considered. To investigate the load type, the feed flow rate has been chosen as the main disturbance. As mentioned before, the acceptable product purity for this case is 97.5%.

In the previous section, the steady state and dynamic performance evaluations have been carried out separately. For the steady state case, the total annual cost is optimized versus feed quality, feed tray location, and number of trays. For dynamic case, using the optimized steady state model, a dynamic performance index is optimized using controller settings as decision variables. To check the accuracy of this strategy, a simultaneous approach that optimizes the dynamic performance index with respect to all aforementioned decision variables has been applied to two cases. Using genetic algorithm, some top ranking sequences obtained by the proposed scheme have been optimized based on this approach. Each column has seven decision variables namely feed tray location, feed quality, number of trays, and two proportional-integral (PI) controllers setting. For each decision variable reflecting a design variable, 4 bits and, for controllers’ settings, 6 bits have been allocated in the binary chromosome. Therefore chromosomes’ length for

Table 7. Alternatives Ranking of First Component Set with Different Species Composition for Disturbance Amplitudes of (10% and (15% Steady State Plus Dynamic Ranking load amplitude ) 10% case number

steady state ranking

1 2 3 4 5 6 7 8

1 4 4 1 8 1 8 1

low frequency load (times/y) 2 1 5 5 1 6 1 1 1

4 1 5 5 1 6 1 1 1

8 1 5 5 1 6 1 1 1

14 1 5 5 1 6 1 1 1

load amplitude ) 15%

high frequency load (times/y) 18 1 5 1 1 6 1 1 1

24 1 5 1 1 6 1 1 1

82 1 5 1 1 6 1 1 1

110 1 5 1 1 6 1 1 1

165 1 5 1 1 6 2 1 1

low frequency load (times/y) 330 1 11 1 1 6 2 1 1

2 1 5 5 1 6 1 1 1

4 1 5 5 1 6 1 1 1

8 1 5 5 1 6 1 1 1

14 1 5 5 1 6 1 1 1

high frequency load (times/y) 18 1 5 1 1 6 1 1 1

24 1 5 1 1 6 1 1 1

82 1 5 1 1 1 2 1 2

110 2 5 1 3 1 2 1 2

165 2 5 1 3 1 2 2 2

330 2 11 1 3 4 2 2 2

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Table 8. Comparison of Alternatives Ranking Obtained from Simultaneous and the Proposed Methods for Case 6 steady state plus dynamic ranking case no.

low frequency load (times/y)

applied approach

6 simultaneous approach

proposed approach

relative error from the best case

high frequency load (times/y)

low frequency load (times/y)

high frequency load (times/y)

4 1 2 5 6 22 11

12 1 2 22 5 6 11

24 1 2 22 5 11 6

82 1 2 22 5 11 6

165 2 1 22 5 11 6

330 2 1 22 5 11 6

4 0 2 13 13 18 27

12 0 2 20 22 35 42

24 0 2 23 35 65 68

82 0 1 36 93 169 214

165 0 0 53 166 298 397

330 0 2 82 288 512 700

1 2 6 5 22 11

1 2 22 5 6 11

1 2 22 5 6 11

1 2 22 5 11 6

2 1 22 5 11 6

2 1 22 5 11 6

0 2 13 14 18 29

0 2 21 25 36 49

0 2 24 42 69 79

0 1 41 117 212 216

0 1 62 211 379 400

0 3 98 365 650 701

trains with 3, 4, 5, and 6 columns will be 108, 144, 188, and 216 bits, respectively. The initial values of decision variables have been set to those obtained by the proposed approach. The result of sequences ranking for case 6, using the simultaneous optimization technique and the proposed method, is presented in Table 8. As can be seen for the high frequency loads, all top six sequences are the same for the two approaches, and for low frequency loads, the differences are minor. 7. Conclusions In this work, optimization of a quaternary mixture separation using simple distillation sequences has been considered. In the first step, the total cost has been minimized under steady-state conditiona. Since process loads such as feed composition variations can affect the system performance, the transient behavior should be also taken into account. Therefore in the second step, optimization is carried out based on a dynamic performance index that also includes transient behavior of the sequence. To decrease the optimization computational load, a suboptimal strategy has been proposed that uses steady state optimal results and only considers the controllers setting as decision variables. To check the accuracy of proposed approach (onion optimization strategy), the results are compared with those obtained from simultaneous optimization approach. It has been shown that the first ranking schemes are the same for both approaches for two case studies, but the computational time required for the simultaneous approach is approximately 15 times more than that of the proposed scheme. Therefore the proposed suboptimal technique can be used with a relatively high confidence, for choosing the best distillation column sequence with much less computational load. Nomenclature A ) area bottomcomp ) column bottom composition C ) column D ) diameter FT ) detuning factor G ) genus H ) height HX) heat exchanger KCATV ) autotuning variation controller gain KC ) controller gain N ) number of stages

P ) pressure Qi j ) transfer functions relating top and bottom compositions to reflux and reboiler steam flow rates topcomp ) column top composition V ) vessel τC ) controller integral time τCATV) autotuning variation controller integral time S&T ) shell and tube or tray

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ReceiVed for reView January 25, 2010 ReVised manuscript receiVed April 11, 2010 Accepted May 20, 2010 IE100169P