Plant-Wide Control System Design of an Alkylation Process Using

Article pubs.acs.org/IECR

Plant-Wide Control System Design of an Alkylation Process Using Integrated Framework of Simulation, Heuristics, and Optimization Sumit Tripathi, Suraj Vasudevan,† and G. P. Rangaiah* Department of Chemical & Biomolecular Engineering, National University of Singapore, Engineering Drive 4, Singapore 117576, Republic of Singapore S Supporting Information *

ABSTRACT: In recent years, increasing concern of process economics, strict product specifications, and stringent safety and environmental regulations has resulted in increased use of material recycle and energy integration in chemical process plants. These highly integrated plants need effective control systems for smooth and optimal operation. This has led researchers to propose plant-wide control (PWC) system design methodologies. The present contribution considers the application of one such recently proposed methodology, the integrated framework of simulation, heuristics, and optimization (IFSHO) [Vasudevan, S.; Rangaiah, G. P. Integrated Framework Incorporating Optimization for Plant-Wide Control of Industrial Processes. Ind. Eng. Chem. Res. 2011, 50, 8122−8137]. This framework is applied to the autorefrigerated alkylation process for the production of high-octane C8 components, which is important in petroleum refining. The step-by-step application of IFSHO is discussed. The performance of the resulting control structure is analyzed and compared to that of the earlier control structure [Luyben, W. L. Design and Control of an Autorefrigerated Alkylation Process. Ind. Eng. Chem. Res. 2009, 48, 11081−11093], using several performance assessment criteria. controllability tools, Groenendijk et al.11 and Dimian et al.12 have presented a simulation-based methodology for evaluating the dynamic inventory of impurities, which was further used to evaluate flowsheet design and control alternatives. They have applied their approach to the vinyl chloride monomer (VCM) plant. Jorgensen and Jorgensen13 have used a mixed-integer linear programming (MILP) formulation to produce a decentralized control structure and applied their procedure to the toluene hydrodealkylation (HDA) plant. Wang and McAvoy14 have also used a MILP formulation for control structure selection and applied it to the Tennessee−Eastman (TE) challenge problem. Their approach consists of three stages, where safety issues are dealt prior to the product quality issues, and then remaining variables are considered. Kookos and Perkins15 have formulated a mixed-integer nonlinear programming (MINLP) problem to minimize the overall interaction and selectivity of closed-loop system in the face of disturbances. Solution of this MINLP problem provides manipulated variables (MVs) for regulatory control. They have considered a double effect evaporator, HDA process, and TE challenge problem as case studies. Vasbinder and Hoo16 have used a decision-based approach to decompose the process plant into smaller units. They applied their procedure to the dimethyl ether plant and found that the resulting control structure was similar to the one obtained using Luyben’s heuristic approach. Skogestad17 have proposed another promising PWC system design methodology based on self-optimizing control (SOC). In the face of disturbances,

1. INTRODUCTION A chemical process plant typically consists of a number of processing units, integrated with one another in a systematic and rational manner. The main objective of plant-wide control (PWC) is to synthesize a control structure for smooth operation of the entire plant. Because of changing production specifications and customer demands, market competition is continuously increasing. Material and energy recycles are increasingly being employed with the aim of improving economics. The presence of recycle streams hinders the smooth operation of the plant by altering their dynamics. In addition, stringent safety and environmental regulations translate to the need for more effective PWC systems. The very first study on PWC system design was presented by Buckley3 in 1964. However, PWC has increasingly become the subject of active study in the past two decades. Researchers have presented several systematic PWC system design methodologies in these years. A systematic review and classification of these methodologies can be found in work by Larsson et al.4 and Vasudevan et al.5 In these articles, PWC methodologies are classified on the basis of their approach to develop the PWC structure, such as heuristics-based, mathematics-based, optimization-based, and mixed approaches. Cao et al.6,7 and Cao and Rossister8 have presented several mathematical tools for initial screening and selection of PWC structure. Luyben et al.9 have presented a nine-step heuristicsbased methodology, which is attractive from the point of understanding and implementation. Zhu et al.10 have suggested decomposing the plant into linear and nonlinear subunits. On the basis of this idea, they have presented an optimizationbased strategy to integrate linear and nonlinear modelpredictive controllers (MPCs) and applied it to the styrene plant. By combining steady-state and dynamic simulations with © 2013 American Chemical Society

Received: Revised: Accepted: Published: 2887

March 1, 2012 January 14, 2013 January 16, 2013 January 16, 2013 dx.doi.org/10.1021/ie3005034 | Ind. Eng. Chem. Res. 2013, 52, 2887−2906

Industrial & Engineering Chemistry Research

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process. Dorneanu et al.34 have proposed a model reduction technique and combined it with control group approach to decentralize the control structure problem. They have applied their technique to develop PWC structure for the alkylation process with intermediate cooling in the reaction section. In a recent article, Luyben2 has studied the autorefrigerated alkylation process. In his work, design optimization has been performed, and a PWC structure has been developed. In the current work, operation optimization of the alkylation process is performed, and the PWC structure for it is subsequently developed using IFSHO. The performance of the resulting control structure is analyzed and compared to that of Luyben2 (named as LS) using several performance criteria. The rest of this Article is organized as follows: the next section gives a brief description of the alkylation process and its simulation. Section 3 discusses step-by-step application of IFSHO to the alkylation plant. Section 4 presents the comparative performance assessment of the control structures. Finally, the conclusions are given in section 5.

the resulting control structure shows minimal loss without the need of resetting the set points (SPs) of the selected controlled variables (CVs). Although SOC procedure is systematic and rigorous, it involves extensive computational effort. Cao and Saha18 have used an improved algorithm of branch and bound method for screening control structures by ranking all possible input and output combinations. They have used their algorithm for the selection of the best control strategy for TE process. Konda et al.19 have proposed an eight-step methodology, the integrated framework of simulation and heuristics (IFSH), in which they employed steady-state and dynamic simulation to guide the control structure design at every stage. It reduces the reliance on heuristics and requires minimal experience. Recently, Vasudevan et al.20 have presented a comparison of PWC structures for the styrene monomer plant developed using Luyben’s nine-step heuristics-based methodology, IFSH, and SOC. Their results show that IFSH and SOC are promising but there is still scope and need for a better procedure that includes mathematical/optimization tools together with heuristics and simulation. Consequently, Vasudevan and Rangaiah1 have proposed an eight-step integrated framework of simulation, heuristics, and optimization (IFSHO), in which heuristics and optimization are brought together with the use of simulation. They have applied this methodology to the styrene plant and concluded that IFSHO yields a stable control structure that performs significantly better in terms of economic performance metrics. Basically, IFSHO uses the steady-state and dynamic simulation tools to make the decision and guide the control structure at every stage. In addition, this methodology incorporates optimization/ reoptimization to decide on additional control variables, and also performs detailed study on effects of recycle, as opposed to other methodologies. Luyben’s heuristics procedure has been applied to several chemical processes such as TE challenge problem, HDA process, and vinyl acetate process.9 Besides this procedure, a few other methodologies have also been applied to chemical processes. For example, SOC and IFSH have been applied to HDA, styrene, and ammonia synthesis processes.20−24 Application of PWC methodologies to industrial processes is of interest to test the effectiveness of the proposed methodology and to compare different PWC system design methodologies. From PWC perspective, apart from HDA, styrene, and ammonia synthesis processes, researchers have studied several other processes such as biodiesel process.25−32 The focus of the present study is to apply IFSHO to another process to test its effectiveness and to compare the resulting control structure with other control structures. For this, alkylation process is chosen because of its importance, recycles and heat integration in the process, and a recent study on it by Luyben.2 The alkylation process for production of high octane C8 compounds from C4 olefins is vital in petroleum refineries. This process studied by Luyben2 comprises three continuous stirred tank reactors (CSTRs) in series, two heat exchangers, and two distillation columns. The presence of two liquid recycles and heat integration makes this process challenging for PWC study. The alkylation process has been previously studied by Mahajanam et al.,33 Dorneanu et al.,34 and Luyben2 from the PWC perspective. Mahajanam et al.33 have presented a scalingbased method to eliminate poor pairings between CVs and MVs, and to generate and rank attractive control structure alternatives, and illustrated their procedure on the alkylation

2. OVERVIEW AND SIMULATION OF THE ALKYLATION PROCESS 2.1. Description of Alkylation Process. In the alkylation process, lower isoparaffins with ternary carbon atoms (such as isobutane) react with olefins to produce higher molecular weight isoparaffins. These isoparaffins have high octane number and are used in oil refineries for blending with petrol. Alkylation can take place at high temperature without catalysts. However, commercial processes involve low temperature alkylation conducted in the presence of HF or H2SO4 as catalysts. When HF is used as the catalyst, reaction temperature is maintained at around 100 °F, and sufficient pressure is required to keep the hydrocarbons and acid in liquid state. The process using H2SO4 as catalyst is more sensitive to temperature than is the HF process. With H2SO4, it is necessary to carry out the reactions at moderately lower temperature. There are several reasons for this. At very low temperature, the acid viscosity becomes so high that good mixing of the reactant and subsequent separation becomes difficult. At higher temperature, polymerization of olefins becomes significant and yield decreases. Because of these reasons, industrial practice is to conduct the alkylation between 30 and 70 °F.35 Under identical operating conditions, the products from the HF and H2SO4 acid alkylation processes are quite similar. However, the HF process poses more pollution risk. Hence, we have chosen to study the H2SO4 process, as in Luyben.2 The principal reaction that occurs in the alkylation process is the combination of olefins with isoparaffins: (CH3)2 CCH 2 + (CH3)3 C−H → (CH3)3 C−CH(CH3)2 (1)

An undesirable series-parallel reaction that produces high molecular weight component dodecane is (CH3)2 CCH 2 + (CH3)3 C−CH(CH3)2 → C12H 26

(2)

These reactions follow the kinetics provided in Mahajanam et al.33 Reaction 1: ⎛ ⎛ 15 356 ⎞⎞ ⎟⎟C k1 = ⎜1.663 × 109 exp⎜ − buteneC isobutane ⎝ ⎝ RT ⎠⎠

(3)

Reaction 2: 2888

dx.doi.org/10.1021/ie3005034 | Ind. Eng. Chem. Res. 2013, 52, 2887−2906


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Figure 1. Steady-state flowsheet for the alkylation plant with the optimal conditions developed in this study (all compositions are in mole fraction).

⎛ ⎛ 19 444 ⎞⎞ ⎟⎟C k 2 = ⎜4.158 × 1012 exp⎜ − buteneC isooctane ⎝ ⎝ RT ⎠⎠

Aspen HYSYS v7.2. As in Luyben,2 Chao−Seader property package has been used for predicting the properties of the components present in this process. Table 1 presents a comparison of the important steady-state process variables (prior to operation optimization) simulated in the current study and the ones reported by Luyben.2 It is clear from this table that the differences between the process conditions reported by Luyben2 and the ones simulated in this study are small, mainly due to the use of a different simulator. Later, in the process of PWC structure development, operation optimization is performed (see level 2.1 in section 3). The optimized alkylation process is shown in Figure 1, where the important design variables and stream data are also given. Before switching to dynamic mode, equipment sizing and proper plumbing need to be done. Plumbing involves placing control valves, compressors, and pumps at the right location. The standard guidelines are followed for this purpose.36

(4)

Both of the reaction rates have units of kmol/(s·m3), and the concentrations are in terms of kmol/m3. The process flowsheet considered in this study is similar to the one presented in Luyben.2 In this process (see Figure 1), the feed “fresh BB” (50% 1-butene, 25% n-butane, 20% isobutane, and 5% propane) is split into three equal parts and fed to three CSTRs in series. The isobutene recycle stream is fed to the first reactor only. Liquid products from the first and second reactors and part of the Fresh BB are fed to the second and third reactors, respectively. Liquid product from the third reactor is compressed to 150 psia and cooled in a feed-effluentheat-exchanger (FEHE) before sending to the deisobutanizer (DIB) column in the separation section. On the other hand, vapor products from the three reactors are mixed and compressed to 106 psia and subsequently condensed. This stream is further pressurized to 250 psia, cooled in another FEHE, and fed to the depropanizer (DP) column in the separation section. The unconverted isobutane is separated as the bottoms stream from DP column and as distillate from DIB column. These two streams are mixed together and recycled back to the reaction section. Propane, being an inert, is separated as the distillate from DP column. Similarly, the other inert, that is, n-butane, is removed as the side stream from DIB column. Isooctane is collected from the bottoms of DIB column. Note that the other feed stream “fresh butane” (50% butane, 45% n-butane, and 5% propane) is fed to the DIB column. This location has been selected on the basis of the study by Luyben.2 2.2. Alkylation Process Simulation. The steady-state and dynamic models of the alkylation process are developed in

3. APPLICATION OF IFSHO In IFSHO methodology, optimization has been brought together with heuristics and simulation, to reap more benefits and design a robust PWC structure. Integrating optimization for determining the economic PWC objectives to ensure optimal operation of the plant is the main feature of this methodology. In this 8-level methodology, the control problem is vertically decomposed based on objectives (see Figure 2). Each step in IFSHO methodology and its application to the alkylation process are described below. Level 1: Determine Control Degrees of Freedom and Steady-State Degrees of Freedom. In this level, control degrees of freedom (CDOF) are calculated. It is important to know this number for developing the control structure for any process. CDOF is the number of MVs available for controlling 2889



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Table 1. Selected Design Variables of the Alkylation Process in Luyben2 and in the Current Work Prior to Operation Optimization design variables feed “fresh BB” feed “fresh butane” physical size of each reactor (liquid volume in the reactor) reactor pressure temperature of first, second, and third reactors DP feed temperature DIB feed temperature feed stage in DIB column

feed stage in DP column side stream from DIB column final production rate final product composition

compressor duty DIB reboiler duty DIB condenser duty DP reboiler duty DP condenser duty reactor vapor product flow reactor liquid product flow

simulated in the current study using HYSYS v7.2

reported in Luyben2 using Aspen Plus

100 lb·mol/h 61 lb·mol/h 1000 ft3 (500 ft3)

100 lb·mol/h 61 lb·mol/h 1000 ft3 (500 ft3)

43.4 psia 67.3, 68.2, 69.2 °F, respectively 176 °F 98 °F reactor effluent at 7th stage fresh butane at 35th stage 14 52.59 lb·mol/h 49.91 lb·mol/h isobutane 0.0011 n-butane 0.0498 isooctane 0.9024 dodecane 0.0467 224 hp 16.2 × 106 Btu/h 13.5 × 106 Btu/h 0.759 × 106 Btu/h 0.649 × 106 Btu/h 498.7 lb·mol/h 1563 lb·mol/h

43.4 psia 66.5, 67.5, 68.5 °F, respectively 175.8 °F 98 °F reactor effluent at 7th stage fresh butane at 35th stage 14 52.6 lb·mol/h 49.9 lb·mol/h isobutane 0.0009 n-butane 0.0498 isooctane 0.9027 dodecane 0.0465 226 hp 16.7 × 106 Btu/h 14.3 × 106 Btu/h 0.663 × 106 Btu/h 0.553 × 106 Btu/h 500 lb·mol/h 1560 lb·mol/h

Figure 2. The eight levels in IFSHO methodology.

the process. The restraining number method of Konda et al.37 is used to determine CDOFs to be 22 for the alkylation process. Out of these 22 CDOFs, 21 have been used in our control structure (as detailed below). Of these 21, 10 are steady-state degree of freedoms (DOFs): reactor pressure, compressor duty, the three feed streams to the reactors, two DOFs in DP column, and three DOFs in DIB column. Level 2.1: Identify PWC Objectives, Perform SteadyState Optimization, and Identify the Active Constraints. It is necessary to identify PWC objectives at the very beginning of PWC structure development. This is done based on the plant operational requirements in this level. The PWC objectives for the alkylation plant are: (1) nominal production rate of 49.9 lb·mol of alkylate/h, and any change in throughput should be accomplished smoothly and quickly; (2) product quality of at least 5% n-butane in alkylate (to meet the Reid vapor pressure, RVP specification); and (3) temperature in the reactors should remain in the range of 30−70 °F. In Luyben,2 steady-state optimization was performed by varying reactor sizes and numbers of trays in distillation columns, and then an alternative process flowsheet was presented, where location of the second feed stream (fresh butane feed) entry was changed. This alternative flowsheet showed reduction in operating cost, but it is not clear whether the complete process was optimized. Hence, we have performed operation optimization of the entire process in the alternate flowsheet presented by Luyben.2 The reactor volume and number of trays in distillation columns are kept the same as used by Luyben,2 and the same feed and product specifications

have also been used in this study. However, after the steadystate optimization, required sizes for a few equipments will be different, which further changes the respective capital costs. To make it apparent and to justify that the change in capital cost will be nullified by change in operating cost, we have calculated and compared the total capital cost (TCC) of the entire process for the two designs, the one presented in this study and the one in Luyben’s study.2 The capital cost calculation has been performed using the methods/formulas given in Luyben.2 The details of capital cost calculation are given in Table 2. If the capital costs of different units in Table 2 are compared individually, it can be noticed that the capital investment in the compressor has increased in the present study. As the operating pressure inside the reactor has decreased after optimization, it further increases the compressor duty. Similarly, capital cost is higher for heat exchanger FEHE2, due to increase in area. On the other hand, as flow rates inside both of the columns have decreased after optimization, a smaller diameter is required for both columns in the current study. In addition, duty requirements for both the columns are also lower, resulting in lower capital cost for reboiler and condenser units. The cumulative effect of these changes is that the total capital cost for Luyben’s design is lower by $29 412. However, the operational optimization performed in this study has shown reduction in operating cost by $387 000 that easily complements the increase in capital cost. 2890



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Table 2. Comparison of Total Capital Cost of the Alkylation Process in Luyben2 and in the Current Work Luyben’s design2

current work capital cost ($)

unit

attributes

DP distillation column

column: D = 1.23 ft, L = 38.4 ft condenser: A = 15.53 ft2, Q = 0.626 × 106 Btu/h reboiler: A = 115.32 ft2, Q = 0.731 × 106 Btu/h column: D = 5.13 ft, L = 120 ft condenser: A = 2615 ft2, Q = 9.826 × 106 Btu/h reboiler: A = 1833 ft2, Q = 11.494 × 106 Btu/h three reactors, each with D = 1.533 ft and L = 15.33 ft Q = 0.845 × 106 Btu/h; A = 135 ft2 Q = 3.496 × 106 Btu/h; A = 558 ft2 318.2 hp D = 4.26 ft, L = 8.53 ft

DIB distillation column reactor FEHE 1 FEHE 2 compressor tank TCC

44 572 43 388 34 083 509 433 259 241 205 770 745 448 37 742 94 975 837 822 50 240 2 862 716

For steady-state operation optimization, annual operating cost (AOC), given below, has been selected as the objective function.

+ PCW ×

∑ Q pump

∑ Q condenser + PCW × Q cooler

(5)

Here, Qcompressor, QR1, QR2, Qpump, and Qcondenser represent compressor duty, reboiler duty in DIB column, reboiler duty in DP column, pump power consumption, and cooling duty, respectively. Pelectricity, PHPS, PLPS, and PCW are unit costs of electricity, high pressure steam, low pressure steam, and cooling water, respectively. These costs are listed in Table 3. Table 3. Costs of Utilities Used in This Study utility cooling water low pressure steam high pressure steam electricity

cost ($/GJ) 0.354 6.08 9.83 16.8

cost ($/Btu) 3.73489772 6.41473958 1.0371199 1.77249383

× × × ×

source −7

10 10−6 10−5 10−5

column: D = 1.26 ft, L = 38.4 ft condenser: A = 172.42 ft2, Q = 0.647 × 106 Btu/h reboiler: A = 120.31 ft2, Q = 753 874 Btu/h column: D = 6.05 ft, A = 120 ft condenser: A = 3589 ft2, Q = 13.474 × 106 Btu/h reboiler: A = 2545 ft2, Q = 15.949 × 106 Btu/h three reactors, each with D = 1.533 ft and L = 15.33 ft Q = 1.021 × 106 Btu/h; A = 163 ft2 Q = 1.506 × 106 Btu/h; A = 240 ft2 224 hp D = 4.54 ft, L = 9.08 ft

capital cost ($) 45 732 44 268 35 036 607 370 318 455 254 711 745 448 42 685 54 948 628 225 56 424 2 833 304

inert in DIB column side-stream and 95 mol % of propane inert in DP column distillate.2 Prior to the optimization, feed stages for both DIB and DP columns are varied manually to obtain the optimum location for minimum reboiler duty, as HYSYS optimizer cannot handle integer variables. Optimum location for feed stage is thus found to be 14th from the top for the DP column, whereas it is third and 33rd stage from the top for the two feeds to DIB column. Next, steady-state optimization for the whole process plant is performed by automatically varying the continuous variables using the built-in optimizer in HYSYS. Several trials are required to find the best operating point. Optimal values of key process variables for the optimal operating point are given in Table 4. It can be seen from this table that AOC for the optimal process conditions is reduced by 23% as compared to that for the conditions in Luyben.2 The optimal reactor pressure is at its lower limit of 22 psia (corresponding to reactor temperature of 30 °F). To allow for possible fluctuations during operation, reactor pressure is chosen at a slightly higher value (22.5 psia) than that given by optimization. The main reason for the reduction in operating cost could be the consideration of additional decision variables and the complete process in the optimization. The reduction in the reactor operating pressure from 43.4 to 22.5 psia by optimization results in the reduction of temperatures and consequently improves selectivity. In addition, increase in temperature of inlet feed for DIB column reduces utility requirement for the desired separation in DIB column (see reboiler utilities costs in Table 4). These changes collectively result in lower AOC even though a decrease in reactor pressure increases the compressor duty (i.e., effect of increase in reaction section utility is offset by the decrease in utility requirement in the separation section). Level 2.2: Identify and Analyze Plant-Wide Disturbances. The nature of disturbances can affect the control structure selection. Therefore, IFSHO procedure recommends that the expected plant-wide disturbances should be identified and analyzed to investigate their effect. Typical disturbances for the alkylation plant are listed in Table 5. The throughput disturbances are introduced in the steady-state simulation to check their effect on the process, by changing “fresh BB” feed rate. The other feed (i.e., fresh butane) is also changed by the same proportion for throughput change. It is noticed from the results, not presented here for brevity, that all of these

annual operating cost = Pelectricity × Q compressor + PHPS × Q R1 + PLPS × Q R2 + Pelectricity ×

attributes

Turton et al.38 Luyben2 Luyben39 Luyben39

The reactor temperature can be regulated by changing the reactor pressure; therefore, reactor pressure has been chosen as one of the decision variables for the optimization. In addition, reflux ratio of the DIB column and temperature of the feeds to the two columns have been chosen as decision variables for the steady-state optimization performed using the built-in optimizer in Aspen HYSYS. The objective function (eq 5) is subject to the following constraints: (i) Reactor temperature in the range of 30−70 °F (corresponding to reactor pressure of 21−44 psia). (ii) Production rate is at least 49.9 lb·mol/h. (iii) Alkylate product should contain at least 5 mol % of nbutane to satisfy the RVP specification for the final product. (iv) To avoid any buildup in the system, it is necessary to remove the inerts, if any, from the system. Therefore, typical industrial values are specified for the streams removing inerts from the system, 95 mol % of n-butane 2891



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Level 3.1: Select Production Rate Manipulator. A key step in designing the PWC structure is the selection of throughput manipulator (TPM), which is the variable whose SP is adjusted for the desired production rate change. For this purpose, the primary process path, that is, the path from main raw material to main product, is first identified.40 Fresh BB feed to alkylate product is identified as the primary process path due to larger steady-state gain with respect to product rate. Generally, internal/implicit variables on this path (e.g., reactor temperature or pressure) are preferred over external/explicit variables (such as feed flow rate and product rate) as the TPM. However, in this study, reactor temperature has been selected as a decision variable for steady-state optimization. Hence, the next best choice, that is, fresh feed flow rate (fresh BB in this case), is selected as TPM. Note that reactor holdup has also been tried as the second choice for TPM. However, change in reactor holdup does not affect the production rate; although an increase in reactor holdup increases per-pass conversion for both the reactions, it does not affect the overall conversion (see Table 6).

Table 4. Optimal Operating Point for the Alkylation Process variables annual operating cost compression cost DIB reboiler duty cost DIB condenser duty cost DP reboiler duty cost reactor pressure temperature of first, second, and third reactors reflux ratio for DIB column DP feed temperature DIB feed temperature per-pass reactor conversion 1a reactor 2a reactor 3a total conversion of 1butene in the process selectivity (% of isooctane to sum of PDIB and isooctane) feed stage in DIB column

feed stage in DP column production rate alkylate product composition a

for process conditions in Luyben2

after operation optimization in this work

1 656 081 ($/yr) 88 489 ($/yr) 1 449 652 ($/yr) 44 084 ($/yr) 42 380 ($/yr) 43.4 psia 67.3, 68.2, and 69.2 °F, respectively

1 269 029 ($/yr) 124 811 ($/yr) 1 044 748 ($/yr) 32 148 ($/yr) 40 556 ($/yr) 22.5 psia 30.45, 31.5, and 32.6 °F, respectively

0.13

0.03

176 °F 98 °F 94.34 and 2.21

175.8 °F 112 °F 81.63 and 1.46

92.64 and 4.50

82.37 and 3.05

90.51 and 6.85

81.68 and 4.79

99.92

99.59

95.1

96.2

reactor effluent at 7th stage fresh butane at 35th stage 14 49.92 lb·mol/h n-butane 0.0498 isooctane 0.9024 dodecane 0.0466

reactor effluent at 3th stage fresh butane at 33th stage 14 50.21 lb·mol/h n-butane 0.0498 isooctane 0.9129 dodecane 0.0362

Table 6. Effect of Reactor Holdup on Conversion

Table 5. Disturbances Considered in This Study description

d1 d2 d3 d4 d5

+5% change in plant throughput −5% change in plant throughput +20% change in plant throughput −20% change in plant throughput “fresh BB” feed composition disturbance (mole fraction of 1butene changed from 0.5 to 0.55, and isobutane changed from 0.2 to 0.15) “fresh butane” feed composition disturbance (mole fraction of isobutane changed from 0.5 to 0.45, and propane changed from 0.05 to 0.1)

d6

50% holdup (base case)

40% holdup

60% holdup

80% holdup

alkylate flow rate overall conversion of 1-butene reaction-1, per-pass reactor 1 conversion reactor 2 reactor 3 reaction-2, per-pass reactor 1 conversion reactor 2 reactor 3

50.21 99.59 81.63 82.37 81.69 1.47 3.06 4.79

50.29 99.44 77.45 78.7 78.36 1.29 2.7 4.25

50.17 99.67 84.32 84.67 83.74 1.58 3.28 5.13

50.12 99.77 87.65 87.47 86.21 1.72 3.55 5.54

Level 3.2: Select Product Quality Manipulator. Maintaining product quality is one of the essential requirements for many processes. In this level, we find the MV to regulate the product quality, which is a local decision. In the alkylation plant, the final product is the bottoms stream from DIB column. IFSHO suggests simulation of the corresponding unit (i.e., DIB column) separately to select the appropriate manipulator. In the final product, around 5 mol % n-butane needs to be maintained to fulfill the RVP specification. Reboiler heat duty and bottoms flow are considered as the potential MVs for controlling bottom composition. It is advisable to use an inferential temperature controller to maintain the product composition, as temperature controllers are cheaper and provide faster response in comparison to composition controllers. The tray, which shows maximum changes in temperature from tray-to-tray, that is, where the temperature gradient is largest, is selected for temperature control inside the column. For this purpose, the temperature profile inside the DIB column is inspected, and it is found that tray 50 shows the largest temperature gradient. Table 7 presents the possible variables for DIB column that can be manipulated to regulate the exit stream composition specifications. Next, taking the possible MVs for tray temperature control, process gains are calculated. A 3 × 3 RGA analysis then is performed for the above-mentioned combination of CVs and MVs.41 On the basis of these analyses, reboiler duty is selected as MV for controlling the temperature of 50th tray in the DIB column.

For reactions 1 and 2, respectively.

disturbance

variable

disturbances result in negligible changes in various stream compositions in different sections of the plant. For disturbances d1, d2, d3, and d4, percentage changes in flow rates of various streams are directly proportional to that in feed flow rate change. For example, a 5% increase in fresh BB feed flow results in a 4.5−5.5% increase in the other streamflow rates. For the composition disturbances d4 and d5 also, there are no significant changes in the process. If any section of the plant is found to be more sensitive to the disturbances, controllers in those sections need to be tuned more conservatively. As we do not notice any highly sensitive section in the plant, there is no need for any special tuning considerations. 2892



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mode. Final steady-state values for the various key variables were nearly the same for temperature or pressure as the CV for reactor. However, when pressure is controlled, various key variables showed more oscillations and took longer time to settle. Hence, reactor temperature is selected as the CV. The extent of side reaction is more in the third reactor. Therefore, variation in temperature of the third reactor has more effect on the selectivity of desired product over the side product. Hence, third reactor is chosen for temperature control. (b) Additional PWC objectives identified in level 4: From the reoptimization analysis in level 4, neither significant improvement in the operating cost nor significant changes in the key process variables are observed. Only for +20% increase in throughput, reactor temperature changes from 32.6 to 35.45 °F; however, the operating cost changes by $2863 on the annual basis, and hence the impact of this temperature change is negligible on the operating cost (refer to the Supporting Information). Hence, no further action is required in this level. (c) Inventory regulation: The following inventories need to be controlled to stabilize the plant: (i) levels in reactors 1, 2, and 3, (ii) condenser pressure, reflux drum level, and sump level in DP and DIB columns, (iii) pressure of recycle stream, and (iv) liquid level and pressure in the tank. Note that the tank pressure is maintained to condense the vapor stream, using cooling water, into liquid for pumping to a higher pressure. (d) Individual unit operations: To ensure unit-level control in the plant, the following variables need to be controlled: (i) reflux ratio and fifth tray temperature of DP column, and (ii) reflux ratio, side product composition, and 50th tray temperature of DIB column. Reasons for these are outlined below. Feed composition disturbance analysis showed that single-end control will be sufficient for the DP column. Therefore, reflux ratio and temperature of tray 5 are selected for control. The tray location is selected by observing the temperature gradient over the trays inside the DP column. The procedure is similar to that described in level 3.2 for tray selection in DIB column. To avoid loss of reactant, a strict composition specification is put for the side stream, which is used for removal of n-butane (another inert) from the 48th stage of DIB column. As impurity control is easier to maintain, isobutane impurity in the side stream is controlled. Control of 50th tray temperature in DIB column has already been handled in level 3.2. Finally, for DIB column, control of reflux ratio is chosen over distillate composition for the following reasons: (i) distillate stream is recycled to the system, and so strict control of recycle stream composition is not required, (ii) when the distillate composition is taken as a specification for steady-state simulation of DIB column only, column convergence was very difficult to achieve for large throughput changes, and (iii) reflux ratio shows smaller gain than that of reflux flow, for composition disturbances in DIB column feed. Level 5.2: Select the Corresponding Manipulated Variables. In this level, appropriate MVs are selected for the CVs selected in the previous level. Here, heuristics, mathematical tools (e.g., RGA), and steady-state and/or dynamic simulation are used for selection of appropriate manipulators.

Table 7. MVs Considered for DIB Column CVs

MVs

bottoms composition side-stream composition reflux ratio (for distillate composition)

bottoms flow; reboiler heat duty side streamflow; reboiler heat duty reflux flow; distillate flow

Level 4: Optimize the Plant for Throughput Changes and Determine Additional Economic PWC Objectives. In this level, additional variables (other than those specified in level 2.1) that have direct impact on optimal operation of the plant in the face of throughput changes are identified. When the throughput is changed, steady-state values for various process variables change. Next, the base case values of key process variables are compared to the final values after throughput change. The variables that show significant change are identified, and these are candidate variables to be considered for control. Optimal operation is always desirable, irrespective of changes in throughput or in the face of disturbance(s). Hence, reoptimization of the plant at the changed throughput is suggested in this level to check whether any other variables need to be adjusted to achieve optimum operation in case of a throughput change. For every throughput change, the process is again optimized using the same objective function, decision variables, and constraints considered in level 2.1. Next, the reoptimized values of process variables are compared to the ones achieved after throughput is changed (i.e., without reoptimization). The variables showing significant changes are considered as additional variables to be controlled, and their SPs are readjusted to achieve optimal operation at the new throughput. The expected throughput disturbances are introduced one by one into the process, and reoptimization is done at the changed throughput conditions. The values of key variables for changed throughput before and after reoptimization can be found in the Supporting Information; these results are for disturbances d1, d2, d3, and d4. Analysis of these results indicates that most of the process variables are not significantly different before and after reoptimization. Only compositions of feed streams to columns (in other words, reactor effluents) show slight variations. The vapor and liquid equilibrium inside the reactors can be significantly affected by changes in reactor temperatures. Therefore, slight variations in reactor temperatures might be the reason for changes in the compositions of column feed streams. This further justifies control of reactor temperatures. However, we did not rely on this alone and subsequently tested to control the feed compositions to the columns to see its effect on the control system performance; these details are given later in level 8. In summary, for throughput changes in the alkylation process, reoptimization does not yield any significant improvement in AOC. Hence, it can be concluded that reoptimization in this level does not suggest changing the SP of any variable in case of a throughput change. Level 5.1: List/Select the Controlled Variables. (a) Process constraints listed in level 2.1: Reactor pressure (and corresponding reactor temperature) is found to be at the lower bound after optimization, and so the constraint related to the reactor pressure (or temperature) is active and must be controlled. The selection between pressure and temperature control is done by simulating the reactor part alone in HYSYS dynamic 2893



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(a) Process constraints listed in level 2.1: Temperature of the third reactor is controlled by manipulating compressor duty. (b) Inventory regulation: Heuristics recommend that the control structure should be self-consistent for the selected TPM.42 Accordingly, for the selected TPM (fresh feed flow of BB), levels along the primary process path need to be controlled in the direction of flow. Therefore, each of the reactor levels is controlled by manipulating the respective reactor effluent flow. Similarly, based on the self-consistency heuristic for the side path, tank level is controlled by manipulating the tank effluent flow. Tank pressure is controlled by manipulating the duty of the cooler placed before the tank. Pressure of the recycle stream has been controlled by manipulating the opening of the recycle stream valve. If the reflux ratio is beyond the range of 0.1−10 (as in the current case for DP column with reflux ratio of 12.09), it is recommended to control condenser level by manipulating the larger stream.43 Therefore, DP column condenser level is controlled by manipulating reflux flow. Reboiler levels in both DP and DIB columns are controlled by manipulating the respective bottoms flow rates. Condenser level in the DIB column is controlled by manipulating the “fresh butane” feed flow. Condenser pressure in each of the distillation column is controlled by the most obvious choice, that is, condenser duty. (c) Individual unit operations: (i) As reflux flow has already been used to control condenser level in the DP column, distillate flow is the manipulator for controlling reflux ratio. (ii) For inferential control of bottoms composition in DP column, tray 5 temperature is controlled using reboiler duty as the manipulator. (iii) DIB column reflux ratio is controlled by manipulating reflux flow, based on the heuristic that the smaller flow between distillate and reflux should be used as the manipulator for reflux ratio control. (iv) On the basis of RGA results for DIB column, side product composition is controlled using side product flow rate. To conclude this level, all of the CVs selected along with the corresponding MVs are summarized in Table 8. Level 6: Check Component Material Balances. In this level, it has been suggested to check and ensure whether the plant-wide inventory is regulated and overall material balance for all components has been accounted for. For this purpose, a “Downs Drill” table is prepared, which lists input, output, consumption, and generation of every chemical species present in the system (Table 9). After the pairing selection of CVs and MVs, controller parameters are tuned in this level. All of the flow, pressure, and level controllers are tuned using the guidelines in Luyben.36 The autotuner present in HYSYS is used for tuning temperature and composition controllers. As the autotuner gives aggressive settings, controller parameters are then finetuned to give satisfactory performance. Next, dynamic simulation is run without connecting the recycle to check the accumulation (if any) of all components and units. Accumulation tables are prepared using the “Spreadsheet” object available in HYSYS. It is observed that the accumulation of each

Table 8. CVs with Their Corresponding MVs in IFSHO Control Structure CVs (selected in level 5.1) process constraints listed in level 2.1 inventory regulation

individual unit operations

temperature of third CSTR liquid levels in all three CSTRs pressure of recycle stream tank level tank pressure recycle stream pressure DIB condenser pressure DIB condenser level DIB reboiler level DP condenser pressure DP condenser level DP reboiler level DIB side stream composition (isobutane) DIB reflux ratio fifth stage temperature DP reflux ratio

MVs (selected in level 5.2) compressor duty liquid effluent flow of the corresponding CSTR recycle stream valve opening tank outlet (liquid) flow cooling duty valve opening in recycle stream condenser duty fresh butane feed flow bottoms flow condenser duty reflux flow bottoms flow side stream product flow reflux flow reboiler duty distillate flow rate

component in the plant is negligible. Therefore, the present control system is sufficient to regulate component inventory. Level 7: Analyze Effects Due to Integration. The analysis in all of the previous levels is performed without attaching the recycle. Konda et al.19 concluded that, due to inherent interlink between component inventory regulation and recycle introduction, recycle and integration effects should be analyzed in a later step. Therefore, this level deals with analysis of the severity of recycle(s) effect on the process. Once the component balances have been satisfied in the previous level, recycle is connected, and the dynamic simulation is run to compare performance of the control structure to the one without recycle connected. It is observed that the effect of integration is not severe in the alkylation process. Therefore, no further modifications are required to the control structure already developed. Level 8: Any Other Considerations. The main purpose of this level is to meaningfully use the remaining CDOFs, if any, for improving the performance of the PWC structure, if needed. For the alkylation process, 1 CDOF is left unused that can be used for this purpose. As some variations are noticed in the feed compositions of the column feeds in the face of disturbances in level 4, a composition controller is installed to control the composition of either DP feed or DIB feed. This composition loop is cascaded with the third reactor temperature controller. The procedure for connecting this composition controller is as follows. (a) Case 1: In this case, DIB column feed composition is controlled by manipulating SP of third reactor temperature controller. Recall that third reactor temperature is controlled using compressor duty with a fixed SP. But now, SP for the third reactor temperature controller comes from the composition controller. (b) Case 2: In this case, CV for the composition controller is replaced by composition of DP column feed. The rest of the procedure is similar to that in case 1. 2894



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Table 9. “Downs Drill” Table Showing Component Material Balances component isobutane 1-butene iso-octane dodecane n-butane propane

input fresh fresh 0 0 fresh fresh

feed feed

feed feed

generation

output

consumption

accumulation controlled by

0 0 reaction 1 reaction 2 0 0

propane purge traces of n-butane, alkylate alkylate alkylate n-butane, alkylate propane purge

reaction 1 reactions 1 and 2 reaction 2 0 0 0

fresh BB feed flow control, side product composition control fresh BB feed flow control DIB tray temperature control DIB tray temperature control side product composition control DP reflux ratio control

Figure 3. Transient profiles of reactor pressure (pressure in all three reactors is overlapping), composition (mole fraction of major component) of liquid and vapor products from the reactor system, DIB distillate, and DP bottom stream flow rates (in lb·mol/h) due to each of the disturbances d3 (+20%), d4 (−20%), d5 (fresh BB), and d6 (fresh butane) in Table 5, introduced at time 1 h. The horizontal axis in each plot is time in hours. 2895



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Figure 4. Control structure developed by applying IFSHO.

The control structure developed up to level 7 is found to perform better than these alternative control structures (cases 1 and 2) in the face of disturbances. Further, the two alternative control structures show more oscillations and take longer time to stabilize larger disturbances. Therefore, it is concluded that no further modification is required at this level. As mentioned earlier, both reactor 3 temperature and recycle stream pressure (at a value equal to the reaction section pressure) are controlled. One reason to keep the recycle pressure at the considered value is that the streams from distillation columns are at higher pressures and they have to be brought down to around the operating pressure in the reaction section. The other reason is that maintaining the recycle pressure at the desired value in the reaction section will further help reactor regulation. To confirm, profiles of reactor pressure are observed in the presence of each of the considered disturbances. Reactor pressures are found to be maintained (besides reactor temperature, which is controlled by changing compressor duty), and the reactor composition changes slightly for regulating the reactor temperature (see Figure 3). However, this change in reactor composition is not much to further affect the performance of the control system. Note that DIB distillate and DP bottoms constitute the recycle. Both of these streams along with DIB reflux stream (ratioed to DIB distillate stream) will change in the presence of disturbances; these streams will also be affected when recycle valve tries to maintain the pressure of the recycle stream. The flow rate profiles of these streams in Figure 3 show that changes in these streams are similar to those in the recycle stream flow rate. The transient profiles of the recycle stream and DIB reflux flow rates are given in Figures 8 and 9.

The developed control structure contains 21 controllers and is shown in Figure 4. The corresponding CVs and MVs with controller parameter values are shown in Table 10. Under the initial steady-state conditions, control valves are designed for 50% opening. Controlling the recycle stream pressure instead of recycle flow and the reflux ratio instead of distillate composition control in DIB column are the main differences in the control structure developed using IFSHO as compared to LS presented in Luyben.2 When the dynamic simulations were started, the final product (alkylate) composition settled at different values for both of the control structures, that is, at around 7% instead of desirable 5% of n-butane in it. To examine it, the internal profiles of both the columns, DP and DIB columns, were compared to the profiles obtained in steady-state mode and dynamic simulation. It was found that pressure profiles were different from what was achieved in steady-state mode. To avoid these differences and to get similar pressure profiles, the column diameters were increased for dynamic simulations. The final column diameter was 8.8 and 2 feet for DIB and DP columns, respectively. These changes have been applied for dynamic simulation for both control structures. Our group has previously faced this kind of problem, where column diameter needs to be altered when switching from steady-state mode to dynamic mode in HYSYS. Fine-tuning of the controllers has been done for the simulated LS control structure for fair performance. In general, tuning parameters for the composition and temperature loops have been adjusted by fine-tuning with the aid of autotuner. These tuning parameters are slightly more aggressive than those reported by Luyben.2 In addition, P-only controller has 2896



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Table 10. Controllers with Their Parameters in IFSHO Control Structure CV

MV

Reaction Section fresh BB feed valve opening (TPM) BB feed split ratio to second BB feed flow to second CSTR reactor BB feed split ratio to third BB feed flow to third CSTR reactor temp of third CSTR compressor duty liquid levels in all three CSTRs liquid effluent flow of the reactor recycle pressure recycle stream valve opening Deisobutanizer Column (DIB) condenser pressure condenser duty condenser level fresh butane feed flow reboiler level bottoms flow 50th stage temperature reboiler duty reflux ratio reflux flow side stream composition side stream product flow (isobutane) Depropanizer Column (DP) condenser pressure condenser duty condenser level reflux flow reboiler level bottoms flow 5th stage temperature reboiler duty reflux ratio distillate flow Tank tank level tank (liquid) outlet flow tank pressure cooling duty fresh BB feed flow

Table 11. Controllers with Their Parameters in LS (Used in This Study)

Kc (%/%), τi (min)

CV

MV

Reaction Section fresh BB feed valve opening (TPM) BB feed split ratio to second fresh BB feed flow to second CSTR reactor BB feed split ratio to third fresh BB feed flow to third CSTR reactor temp of third CSTR compressor duty liquid levels in all three liquid effluent flow of the CSTRs reactor recycle flow recycle stream valve opening Deisobutanizer Column (DIB) condenser pressure condenser duty condenser level fresh butane feed flow reboiler level bottoms flow 49th stage temperature reboiler duty distillate composition reflux flow side stream composition side stream product flow (isobutane) Depropanizer Column (DP) condenser pressure condenser duty condenser level reflux flow reboiler level bottoms flow fourth stage temperature reboiler duty reflux ratio distillate flow Tank tank level tank (liquid) outlet flow tank pressure cooling duty

Kc (%/%), τi (min)

fresh BB feed flow

0.5, 0.3 0.5, 0.3 0.5, 0.3 8.5, 5 2 1.8, 25

5, 0.5 2.5 2 4, 1.5 0.5, 0.3 4, 20

5, 2.5 3.5 2 8, 7.5 0.05, 0.3 1.75 2.5, 5

been used for reflux-drum level control for DP column. In this study, proportional gain (Kc) of 2.8 is used for the DP column reflux-drum level controller instead of 5 used in Luyben.2 A possible reason for these differences is the use of different simulators. The final tuning parameters used in the current study for LS control structure are listed in Table 11.

0.5, 0.3 0.5, 0.3 0.5, 0.3 8, 8 2 0.5, 0.3 4.75, 5 1.9 2 4, 6 6, 25 4.2, 15

3.5, 1 2.8 2 5.2, 6.5 0.1, 0.1 1.75 2, 10

of its final value and is calculated on the basis of the production rate and slowest control loop. Settling time based on absolute accumulation has been defined differently. Accumulation is assumed to be settled, when it reaches a cutoff value of 1.5% of nominal production rate. Dynamic Disturbance Sensitivity (DDS). Konda and Rangaiah45 have proposed this measure, defined as the time integral of absolute accumulation. They have suggested that component accumulation and overall control system performance are strongly correlated as accumulation is nonzero until the control system attenuates the disturbance. Absolute accumulation is considered because neither a positive nor a negative value is desirable. Mathematically, DDS measure is defined as

4. PERFORMANCE ASSESSMENT OF PWC SYSTEMS The alkylation process with both the control structures is simulated for a long time to achieve stable condition. Once steady state is achieved in the respective case, the process is subjected to the throughput and feed composition disturbances listed in Table 5, one at a time. Different methodologies have different overall objectives to design a PWC structure. Hence, selecting a single measure to compare the performance of control structures developed from different methodologies is not justifiable. Therefore, a few performance measures should be used to make an overall conclusion based on the results. Hence, on the basis of the recommendations of Vasudevan and Rangaiah,44 settling time, dynamic disturbance sensitivity (DDS), deviation from the production target (DPT), and total variation (TV) in the MVs are used for evaluation and comparison of the control structures. In addition, profiles of key variables are shown in Figures 3, 5−8 for the comparison. Settling Time. The time required for the process variable to settle within acceptable range is called settling time. It can be based on any of the following variables: production rate, product quality, overall absolute component accumulation, and slowest control loop.44 In this study, settling time is considered as the time when the concerned process variable is within ±1%

DDS =

ts

n

∫0 (∑ absolute accumulation of component i) dt i=1

(6)

where i is the number of components, and absolute accumulation is defined as: absolute accumulation = |inflow − outflow + generation − consumption| (7)

In the current study, 1.5% of nominal production rate has been considered as the cutoff for DDS calculation. Deviation from the Production Target (DPT). Production rate is one of the most important objectives. Any deviation of the production rate from its target can directly affect profitability. Hence, Vasudevan and Rangaiah44 have proposed 2897



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Figure 5. Transient profile of CSTR 1 temperature (in °F) due to disturbances d3 and d4 introduced at time 1 h. The horizontal axes are time (in hours).

Figure 6. Transient profile of CSTR 2 temperature (in °F) due to disturbances d3 and d4 introduced at time 1 h. The horizontal axes are time (in hours).

Figure 7. Transient profile of feed composition to the DP column due to disturbances d3 and d4 introduced at time 1 h. The horizontal axes are time (in hours).

DPT, which is an indirect measure of economic performance during the transient period. DPT is expressed as: DPT =

∫0

ts

disturbance, the control structure that performs better is shown in bold in these tables.

5. DISCUSSION From Table 12, it can be noticed that DDS values are comparable for both of the control structures for the throughput disturbances. However, LS control structure shows better performance in terms of DDS for the composition disturbances. As for DPT, positive value indicates overproduction, whereas negative value indicates underproduction; both of these are undesirable from an operational point-of-view. Therefore, a smaller (absolute) value of DPT is desirable. Absolute DPT values (in Table 12) are generally comparable for both control structures. In LS control structure, recycle flow has been controlled at a fixed ratio with the fresh feed. This could be a reason for the reactor temperatures taking longer time to stabilize in the face of disturbances (see Figures 5 and 6). Variations in reactor temperatures affect the reaction section performance and lead to variations in the compositions of feed streams to the columns (see Figure 7). These variations are translated to the separation section also, which further affect the performance of the control system. The overall effect of this can be seen from the larger control effort required for most disturbances in LS control structure (see Table 12).

(actual production rate

− target production rate) dt

(8)

Total Variation (TV) in the MVs. Vasudevan and Rangaiah44 have recommended this measure to evaluate the performance of the control structure with respect to control valve movement. Mathematically, TV is defined by: TV =

ts

n

∞

∫0 (∑ ∑ |uj,(i+1) − uj,i|) dt j=0 i=0

(9)

where uj(i+1) and uj,i are jth valve opening at time i+1 and time i, respectively, and n is the total number of control valves in PWC system. TV is a measure of control effort required, and so a smaller value is preferred. Results for DDS, DPT, and TV for the alkylation process with IFSHO and LS control structures are summarized in Table 12. Settling times for both of the control structures are also calculated and listed in Table 13. For each measure and 2898



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Figure 8. continued

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Figure 8. continued

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Figure 8. Transient profiles of selected variables due to disturbances d3 and d4 introduced at time 1 h. The horizontal axes are time (in hours).

Table 12. Assessment of the PWC Systems for Alkylation Process: DDS, DPT, and TV DDS (lb·mol) disturbance d1 d2 d3 d4 d5 d6 a

(production rate) (production rate) (production rate) (production rate) (fresh BB composition) (fresh butane composition)

DPT (lb·mol)

TV

LS

IFSHO

LS

IFSHO

LS

IFSHO

51 56 >195a 192 51 30

54 55 198 212 100 61

−2.97 2.97 −12.2 13.1 240 −1.15

−3.46 3.5 −13.7 13.4 232 −0.48

305 307 1110 1068 250 393

203 191 607 603 372 226

Until 3000 min, overall accumulation was oscillating around the cutoff value.

Table 13. Assessment of PWC Systems for Alkylation Process: Settling Time in Minutes for production rate disturbance d1 d2 d3 d4 d5 d6

(production rate) (production rate) (production rate) (production rate) (fresh BB composition) (fresh butane composition)

for overall accumulation

for slowest control loop

LS

IFSHO

LS

IFSHO

LS

IFSHO

87 92 170 181 140 0.0b

128 133 183 174 147 0.0b

1772 1550 >3000a 2447 1280 833

1050 1423 1347 1865 1470 1200

2137 2723 2787 2970 1535 1539

1288 1178 1951 1978 1556 1315

Until 3000 min, overall accumulation was oscillating around the cutoff value. bFor d5, alkylate flow rate remains within ±0.5% for both of the control structures. a

The alkylate production rate, fresh butane feed rate, and side stream product flow, their compositions, and several other variables’ transient profiles for d3, d4, d5, and d6 disturbances are shown in Figures 8 and 9 for both of the control structures. The variables and the respective units are shown together. All of the horizontal axes are time with unit of hours. For some of the transients, time range has been intentionally increased to make sure that the variable has settled. If we compare various flow rates for both control structures, the transients are quite smooth. However, IFSHO settles slightly slower than LS. The reason could be fixing the recycle

In the case of settling time (listed in Table 13), LS control structure shows marginally faster settling in terms of production rate. However, if the two control structures are compared on the basis of accumulation attenuation, IFSHO shows faster settling. Again, if these two control structures are compared on the basis of slowest control loop, IFSHO shows better performance. The performance of IFSHO’s “slowest settling control loop” is also related to the fact that IFSHO shows smaller TV values. Therefore, it can be concluded that IFSHO shows comparatively better inventory regulation and dynamic performance. 2901



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Figure 9. continued

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Figure 9. continued

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Figure 9. Transient profiles of selected variables due to disturbances d5 and d6 introduced at time 1 h. The horizontal axes are time (in hours).

For the fresh BB composition disturbances, transients are different for both control structures. The reason is again recycle flow control in LS, which forces other flows, like feed to the reactors, reactor effluents, and further the feed to the columns, etc., to settle faster than that in IFSHO. For the fresh butane composition disturbance, both control structures show similar behavior.

at a constant ratio to the fresh feed in the LS. As the throughput is changed, recycle is also fixed at a value ratioed with fresh feed, which forces other related streams to settle immediately. Yet, fixing this recycle has an undesirable effect on the overall system. According to Luyben,39 feed flow rate change can immediately affect reflux-drum level even though it is not introduced into the drum. Therefore, if the throughput is changed, the impact should appear as changes in DIB refluxdrum level immediately in the same direction. As DIB refluxdrum level is controlled by manipulating the fresh butane stream, the fresh butane stream should change immediately in the opposite direction. This behavior is evident for IFSHO in Figure 8a for fresh butane flow. For throughput increases (i.e., d3 disturbance), IFSHO produces initial increase in “fresh butane” flow, in contrast to decrease under LS. On the other hand, for throughput increase (d4 disturbance), “fresh butane” flow initially decreases in IFSHO, whereas it increases in LS. The reason for this opposite behavior is fixing of the recycle flow in LS. In case of LS, recycle flow comprises DIB distillate and DP bottoms flow, and it is ratioed with fresh BB feed. Hence, if the fresh feed is decreased, SP for recycle flow decreases. This forces DIB distillate flow to decrease immediately and results in increased reflux-drum level. This behavior of DIB reflux-drum is so intense that fresh butane valve shuts for a while. On the other hand, when fresh feed is increased, reflux-drum level decreases due to sudden increase in recycle. Hence, “fresh butane” flow has to increase immediately to overcome it. The intensity of fixing the recycle at some ratio to the fresh feed can be assumed with the fact that the control valve has to be sized differently for it. If we start with 50% opening of valve for fresh butane in the nominal case, for the 20% throughput increase this valve saturates immediately. To avoid the valve saturation, the PV range of fresh butane has to be increased. It is evident in Figure 8a that starting with fresh butane flow of about 60 lb·mol/h in base case, it has increased to 150 lb·mol/h in case of 20% throughput increase.

6. CONCLUSIONS A PWC structure has been developed for the autorefrigerated alkylation process by step-by-step application of the recently proposed IFSHO methodology. The performance of the developed control structure has then been compared to that of the control structure reported by Luyben,2 using various performance measures. There are two main differences between the two control structures: Pressure of recycle stream and DIB column reflux ratio have been controlled in IFSHO in the place of recycle flow and DIB distillate stream composition, respectively, in LS. The dynamic performance of both these control structures is found to be comparable based on DPT. For the composition disturbances, LS control structure shows better performance than the one developed using IFSHO in terms of DDS. However, both the control structures show similar performance for throughput changes, if compared based on just DDS; and IFSHO performs better in terms of TV for the throughput changes. Dynamic performances of both control structures are debatable based on settling times, as LS control structure shows faster settling for production rate and IFSHO shows faster response in terms of accumulation and slowest control loop.

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ASSOCIATED CONTENT

S Supporting Information *

Table showing the values of key process variables. This material is available free of charge via the Internet at http://pubs.acs.org. 2904



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Optimization and Self-Optimizing Control. Control Eng. Pract. 2007a, 15, 1222. (22) Araujo, A. C. B.; Hori, E. S.; Skogestad, S. Application of PlantWide Control to the HDA Process. II - Regulatory Control. Ind. Eng. Chem. Res. 2007b, 46, 5159. (23) Araujo, A. C. B.; Skogestad, S. Control Structure Design for the Ammonia Synthesis Process. Comput. Chem. Eng. 2008, 32, 2920. (24) Zhang, C.; Vasudevan, S.; Rangaiah, G. P. Plantwide Control System Design and Performance Evaluation for Ammonia Synthesis Process. Ind. Eng. Chem. Res. 2010, 49, 12538. (25) Bildea, C. S.; Kiss, A. A. Dynamics and Control of a Biodiesel Process by Reactive Absorption. Chem. Eng. Res. Des. 2011, 89, 187. (26) Zhang, C.; Rangaiah, G. P.; Kariwala, V. Design and Plant-wide Control of a Biodiesel Plant. In Plant-Wide Control: Recent Developments and Applications; Rangaiah, G. P., Kariwala, V., Eds.; Wiley: New York, 2011. (27) Araujo, A. C. B.; Shang, H. Enhancing a Smelter Off-Gas System Using a Plant-Wide Control Design. Ind. Eng. Chem. Res. 2009, 48, 3004. (28) Araujo, A. C. B.; Brito, R. P.; Shang, H. Mitigation of Energy Intensity of an Industrial Off-Gas Cleaning System Using Process Engineering Solutions. J. Cleaner Prod. 2009, 17, 1512. (29) Shang, H.; Scott, J. A.; Araujo, A. C. B. Modeling and Control of Industrial Off-gas Systems. In Plant-Wide Control: Recent Developments and Applications; Rangaiah, G. P., Kariwala, V., Eds.; Wiley: New York, 2011. (30) Ward, J. D.; Yu, C. C.; Doherty, M. F. Plant-Wide Operation of Processes with Crystallization. AIChE J. 2007, 53, 2885. (31) Ward, J. D.; Yu, C. C.; Doherty, M. F. Plant-Wide Dynamics and Control of Processes with Crystallization. Comput. Chem. Eng. 2010, 34, 112. (32) Ward, J. D.; Yu, C. C.; Doherty, M. F. Analytical Design and Operation of Systems with Crystallization, Filtration, and Recycling. Ind. Eng. Chem. Res. 2011, 50, 1196. (33) Mahajanam, R. V.; Zheng, A.; Douglas, J. M. A Shortcut Method for Controlled Variable Selection and Its Application to the Butane Alkylation Process. Ind. Eng. Chem. Res. 2001, 40, 3208. (34) Dorneanu, B.; Bildea, C. S.; Grievink, J. On the Application of Model Reduction to Plantwide Control. Comput. Chem. Eng. 2009, 33, 699. (35) Gary, J. H.; Handwerk, G. E.; Kaiser, M., J. Petroleum Refining Technology and Economics, 5th ed.; CRC Press Taylor & Francis Group: New York, 2007. (36) Luyben, W. L. Plant-Wide Dynamic Simulators in Chemical Processing and Control; Marcel Dekker: New York, 2002. (37) Konda, N. V. S. N. M.; Rangaiah, G. P.; Krishnaswamy, P. R. A Simple and Effective Procedure for Control Degrees of Freedom. Chem. Eng. Sci. 2006, 61, 1184. (38) Turton, R.; Bailie, R. C.; Whiting, W. B.; Shaeiwitz, J. A. Analysis, Synthesis, and Design of Chemical Processes; Prentice Hall: NJ, 2009. (39) Luyben, W. L. Design and Control of the Cumene Process. Ind. Eng. Chem. Res. 2010, 49, 719. (40) Price, R. M.; Lyman, P. R.; Georgakis, C. Throughput Manipulation in Plant-Wide Control Structures. Ind. Eng. Chem. Res. 1994, 33, 1197. (41) Svrcek, W. Y.; Mahoney, D. P.; Young, B. R. A Real-Time Approach to Process Control, 2nd ed.; John Wiley & Sons, Ltd.: New York, 2006. (42) Price, R. M.; Georgakis, C. Plant-Wide Regulatory Control Design Procedure Using a Tiered Framework. Ind. Eng. Chem. Res. 1993, 32, 2693. (43) Fruehauf, P. S.; Mahoney, D. P. Distillation Column Control Design Using Steady-State Models: Usefulness and Limitations. ISA Trans. 1993, 32, 157. (44) Vasudevan, S.; Rangaiah, G. P. Criteria for Performance Assessment of Plant-Wide Control Systems. Ind. Eng. Chem. Res. 2010, 49, 9209.

AUTHOR INFORMATION

Corresponding Author

*Fax: 65-67791936. E-mail: [email protected]. Present Address †

School of Chemical and Biomedical Engineering, Nanyang Technological University, 62 Nanyang Drive, Singapore 637459. Notes

The authors declare no competing financial interest.

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REFERENCES

(1) Vasudevan, S.; Rangaiah, G. P. Integrated Framework Incorporating Optimization for Plant-Wide Control of Industrial Processes. Ind. Eng. Chem. Res. 2011, 50, 8122. (2) Luyben, W. L. Design and Control of an Auto-refrigerated Alkylation Process. Ind. Eng. Chem. Res. 2009, 48, 11081. (3) Buckley, P. S. Techniques of Process Control; Wiley: New York, 1964. (4) Larsson, T.; Skogestad, S. Plant-Wide Control - A Review and a New Design Procedure. Model., Identif. Control 2000, 21, 209. (5) Vasudevan, S.; Konda, N. V. S. N. M.; Rangaiah, G. P. Plant-Wide Control: Methodologies and Applications. Rev. Chem. Eng. 2009a, 25, 297. (6) Cao, Y.; Biss, D.; Perkins, J. D. Assessment of Input-Output Controllability in the Presence of Control Constraints. Comput. Chem. Eng. 1996, 20, 337. (7) Cao, Y.; Rossiter, D.; Owens, D. Input Selection for Disturbance Rejection under Manipulated Variable Constraints. Comput. Chem. Eng. 1997, 21, 403. (8) Cao, Y.; Rossiter, D. An Input Pre-Screening Technique for Control Structure Selection. Comput. Chem. Eng. 1997, 21, 563. (9) Luyben, W. L.; Tyreus, B. D.; Luyben, M. L. Plant-Wide Process Control; McGraw-Hill: New York, 1998. (10) Zhu, G. Y.; Henson, M. A.; Ogunnaike, B. A. A Hybrid Model Predictive Control Strategy for Non-Linear Plant-Wide Control. J. Process Control 2000, 10, 449. (11) Groenendijk, A. J.; Dimian, A. C.; Iedema, P. D. Systems Approach for Evaluating Dynamics and Plant-Wide Control of Complex Plants. AIChE J. 2000, 46, 133. (12) Dimian, A. C.; Groenendijk, A. J.; Iedema, P. D. Recycle Interaction Effects on the Control of Impurities in a Complex Plant. Ind. Eng. Chem. Res. 2001, 40, 5784. (13) Jorgensen, J. B.; Jorgensen, S. B. Towards Automatic Decentralized Control Structure Selection. Comput. Chem. Eng. 2000, 24, 841. (14) Wang, P.; McAvoy, T. Synthesis of Plant-Wide Control Systems Using a Dynamic Model and Optimization. Ind. Eng. Chem. Res. 2001, 40, 5732. (15) Kookos, I. K.; Perkins, J. D. Heuristic-Based Mathematical Programming Framework for Control Structure Selection. Ind. Eng. Chem. Res. 2001, 40, 2079. (16) Vasbinder, E. M.; Hoo, K. A. Decision-Based Approach to PlantWide Control Structure Synthesis. Ind. Eng. Chem. Res. 2003, 42, 4586. (17) Skogestad, S. Control Structure Design for Complete Chemical Plants. Comput. Chem. Eng. 2004, 28, 219. (18) Cao, Y.; Saha, P. Improved Branch and Bound Method for Control Structure Screening. Chem. Eng. Sci. 2005, 60, 1555. (19) Konda, N. V. S. N. M.; Rangaiah, G. P.; Krishnaswamy, P. R. Plant-Wide Control of Industrial Processes: An Integrated Framework of Simulation and Heuristics. Ind. Eng. Chem. Res. 2005, 44, 8300. (20) Vasudevan, S.; Rangaiah, G. P.; Konda, N. V. S. N. M.; Tay, W. H. Application and Evaluation of Three Methodologies for Plantwide Control of the Styrene Monomer Plant. Ind. Eng. Chem. Res. 2009b, 48, 10941. (21) Araujo, A. C. B.; Govatsmark, M.; Skogestad, S. Application of Plant-Wide Control to the HDA Process. I - Steady-State 2905



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(45) Konda, N. V. S. N. M.; Rangaiah, G. P. Performance Assessment of Plant-Wide Control Systems of Industrial Processes. Ind. Eng. Chem. Res. 2007, 46, 1220.

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Plant-Wide Control System Design of an Alkylation Process Using

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