A Novel Control Methodology for a Pilot Plant Azeotropic Distillation

Ind. Eng. Chem. Res. 2006, 45, 8361-8372

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A Novel Control Methodology for a Pilot Plant Azeotropic Distillation Column Lina M. Rueda, Thomas F. Edgar,* and Robert B. Eldridge Department of Chemical Engineering, College of Engineering, The UniVersity of Texas at Austin, 1 UniVersity Station C0400, Austin, Texas 78712

A fundamental dynamic model was successfully used in the implementation of multiple control methodologies via a novel inferential control strategy using HYSYS to treat missing process measurements. Results from steady state and dynamic testing of an azeotropic distillation system of methanol, normal pentane, and cyclohexane were obtained. Steady-state equilibrium and nonequilibrium models were developed and validated with experimental data from a packed distillation unit operated at finite reflux. Dynamic multicomponent distillation experiments were also carried out, and experimental process data were collected using the pilot scale experimental unit. Two different variable pairings were studied, and the results from individual control loop configurations were compared with a multivariable control strategy using the model predictive control (MPC) software Predict Pro. Introduction This work presents the results from the experimental validation of dynamic models of an azeotropic distillation system of methanol, normal pentane, and cyclohexane. The model was validated with experimental data from a pilot-scale size packed distillation unit operated at finite reflux. The approach presented in this work links the process fundamental dynamic model (HYSYS) with the control software used in the process. The model was modified online using a feedback configuration to eliminate the difference between the process and model outputs. The model was used in the implementation of different control strategies to infer process variables that could not be determined with field instrumentation. Two different variable pairings were studied, and the results from individual control loop configurations were compared with a multivariable control strategy using model predictive control (MPC). The dynamic model was developed using HYSYS from Aspen Technologies. The model was linked to Emerson Process Management’s DeltaV digital automation system. The experiments were carried out in the pilot plant of The Separation Research Program (SRP) at The University of Texas at Austin. Literature Review Distillation is the most common separation technique in the chemical industry. It consumes enormous amounts of energy, which can typically exceed 50% of the plant operating costs. Chemical mixtures of polar and nonpolar components form nonideal liquid mixtures that often result in azeotropic mixtures, and this introduces challenges to the design and operation of a separation process. Heterogeneous Azeotropic Distillation Most of the published dynamic models for nonideal multicomponent distillation separations are related to heterogeneous azeotropic distillation. This process is the most widely used to separate azeotropic mixtures with low relative volatilities. Heterogeneous azeotropic distillation uses a third component (entrainer) to form a heterogeneous azeotrope in the reflux drum. * To whom correspondence should be addressed. Tel.: (512) 4713080. Fax: (512) 471-7060. E-mail: [email protected].

One of the phases is recovered as product, and the other is sent back as reflux to the column. Although the reflux drum is used as a decanter, this process usually requires more than one column to recover the entrainer. Chien et al.1,2 compared two different models where two and three columns were used to separate a mixture of isopropyl alcohol + water with cyclohexane as entrainer. The study concluded that optimum design of the two column approach is more economical than the three column approach. Kurooka et al.3 developed a dynamic simulator to characterize a distillation column for the separation of water, n-butyl-acetate, and acetic acid. The system used in this study displayed a complex dynamic behavior, increasing the operation and control challenges. The dynamic model was used to investigate the performance of a nonlinear controller with exact input-output linearization of a simplified model. Although a dynamic simulation was developed for these works, no experimental data were presented to validate the models. Wang et al.4 performed experimental validations of dynamic and steady-state models for a mixture of isopropyl alcohol + water with cyclohexane as entrainer. The objective was the analysis of multiple steady states, parametric sensitivity, and critical reflux. The study used a laboratory scale sieve plate distillation column, 5 cm in diameter. Baur et al.5 and Springer et al.6 also carried out experiments for model validation using a lab-size column, similar to the one used in the parametric sensitivity research, but focused on multicomponent diffusion and multiphase hydrodynamics. Baur et al.5 used two systems, methanol-2-propanol-water and benzene-2-propanol-n-propanol, to examine the influence of mass transfer on the composition trajectories during distillation of mixtures that exhibit distillation boundaries. Using published experimental data, they conclude that, for reliable design and simulation, it is necessary to use a rigorous mass transfer model based on the Maxwell-Stefan diffusion equations. Springer et al.6 used equilibrium and nonequilibrium (mass transfer based on Maxwell-Stefan) models of three different systems, methanol-2propanol-water, water-ethanol-acetone, and water-methanolmethyl acetate. The study compared the models using experimental data from a lab-size column and concluded nonequilibrium models are necessary to obtain a good description of the azeotropic system, because the boundary crossing is influenced by interphase mass transfer not considered in the equilibrium

10.1021/ie060112k CCC: $33.50 © 2006 American Chemical Society Published on Web 06/08/2006

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model. The experimental setup used in both sets of experiments5,6 consisted of one 5 cm diameter column operating at total reflux without the addition of an entrainer. Although Wang et al.4 also used a 5 cm diameter lab-sized column, their experimental setup was different; an entrainer was added to the accumulator where the two-phase mixture was decanted. Muller et al.7 used a 5 cm diameter lab-size column for ethanol dehydration with cyclohexane as entrainer. The objective of their study was to analyze multiple steady states and to validate equilibrium models. The equilibrium model predicted the existence of multiple steady states with the results verified experimentally. Yamamoto et al.8 presented an industrial example of heterogeneous azeotropic distillation of acetic acid + water with n-butyl-acetate as an entrainer. They investigated the column behavior by using dynamic simulation and developed a control system tested in the industrial application. The control performance was presented, but the publication omitted experimental data and information on dynamic model validation. Repke et al.9 developed a nonequilibrium steady-state model for the separation of a three-phase system in a packed distillation column and validated the results with experimental data. The study used a 7 cm diameter column, of 7.5 m height with effective packing height of 2.5 m, and investigated various heterogeneous mixtures, such as acetone-toluene-water and 1-propanol-1-butanol-water. The system’s behavior was better described by the nonequilibrium model than the equilibrium model, which at some conditions failed to predict the experimental behavior. Process Control The characteristics of highly nonideal mixtures present a challenge for process control. Several studies can be found in the literature addressing the multicomponent distillation control problem.10 In general, the main objective of distillation control is to maintain a desired product quality. However, direct composition control is complicated by the fact that online composition analyzers are expensive, difficult to maintain, and introduce significant dead time into the control system. These problems have typically been addressed by using column temperature measurements in an inferential control strategy. Luyben and Vinante11 recommend the use of multiple temperature measurements instead of the traditional approach based on just one optimal tray temperature measurement. Weber and Mosler12 at Esso Research and Engineering patented a multiple temperature controller to maintain the columns product composition. Brosilow and co-workers13,14 developed an inferential control technique using more variables than just temperature to infer composition. Patke and Deshpande15 did an experimental study in a laboratory scale distillation column to compare the different approaches of temperature control and inferential control and recommended inferential control over the temperature control scheme. Yu and Luyben16 designed a composition control system by using several temperature measurements in multicomponent distillation and recommended this approach over the traditional single temperature control and the inferential control scheme. More recently, Luyben17 presented a methodology for the selection of effective control structures for ternary distillation columns using only temperature measurements. Multivariable distillation control research has also focused on the choice of different control structures. Among others, Skogestad and Morari18 extensively studied the subject using the relative gain array (RGA) method.19-23 The RGA steadystate analysis, initially introduced by Bristol,24 has found widespread use in the industry.

Previous control studies for azeotropic distillation systems used various overhead configurations. In general, two liquid phases formed in the entrainer, and one of them was usually put back in the column as reflux and the other recovered as distillate product. Another difference between the traditional and the azeotropic distillation process configurations is an additional feed input in the overhead accumulator to make up for material imbalance and to respond to disturbances. Chien et al.25 constructed a laboratory scale sieve distillation column for the separation of water + 2-propanol using cyclohexane as entrainer to test different traditional control approaches. They concluded that a nontraditional inverse double loop temperature control scheme was necessary to maintain the desired temperature profile. This approach is different from the traditional approach in the sense that the top temperature is paired with reboiler duty while the bottom temperature is paired with reflux flow rate. Tonelli et al.26 studied the same system in a simulation environment and also found the reverse pairing less interactive. Ulrich and Morari27 included the entrainer flow as a manipulated variable and introduced a third control loop, which changed the overall feed to account for feed disturbances. Although this study used data from a real process, the validation of the control strategy was performed using simulation only. Rovaglio et al.28 presented a controllability and operability study of a heterogeneous azeotropic distillation system. The authors used the purification of the ethanol-water system with benzene as the entrainer. The configuration included two columns with the reflux drum acting as a decanter. The control configuration had four controlled variables: column average temperature, column pressure, and light and heavy phase reflux drum level. The study paired reboiler duty with column temperature and reflux flow rate with reflux drum level. Column pressure was paired with overhead vapor flow rate. Widagdo and Seider29 surveyed results from the literature on the use of theoretical models and computer simulation. They found that azeotropic distillation (homogeneous and heterogeneous) displayed highly nonlinear behavior indicated by the presence of multiple steady states. An important conclusion from this review was the necessity of clarifying the sources of the multiple steady states and showing their presence experimentally. The survey also acknowledged the application of complex graphical constructions as a basic tool for the design of separation systems of high nonideal mixtures. In their work, the authors examined maps of residue curves, distillation lines, and geometric methods for design, analysis of dynamic and steady-state behavior, and control of azeotropic systems. More recently, De Villiers et al.30 presented a review on the use of residue curve maps to analyze phase equilibrium data predicted from thermodynamic packages, and Kiva et al.31 presented a survey in azeotropic phase equilibrium diagrams comprising less-known published results mainly from Russian literature. Graphical analysis of ternary systems is possible by commercial process simulation software such as Distil from Aspentech and Chemcad from Chemstations. A residue curve represents the residue composition of a simple batch distillation column, while a distillation line represents the operating line of a distillation column at total reflux. Experimental System The chemical system selected for the experiments performed in this research was a ternary mixture of methanol, pentane, and cyclohexane. The ternary mixture diagram is presented in Figure 1, where the two azeotropes in the system are apparent. The two azeotropes divide the diagram into two distillation

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Figure 1. Ternary map (mass basis) for cyclohexane, normal pentane, and methanol. P ) 6 psi. Property package: split from Aspen Tech.

regions. Figure 1 also identifies the feasible product region for a particular feed point using the intersections between the distillation and material balances lines. The highest pentane purity achievable in the distillate product was the azeotropic composition, which was a viable objective in both regions; however, the bottom composition objective changed from pure cyclohexane in the first region to pure methanol in the second. The column used in the SRP experiments is a 6 in. diameter stainless steel column with 27.6 ft of contacting height packed with No. 0.7 Nutter ring packing. The system is wellinstrumented with state of the art sensors and actuators from Fisher-Rosemount. The experimental plant is operated with Emerson Process Management’s DeltaV digital automation system. The simulation was implemented in HYSYS from Aspen Technologies at the application station in the DeltaV system and connected to the controllers through an interface with the digital control system. Additional details on the equipment configuration can be found at the SRP website http:// uts.cc.utexas.edu/∼utsrp/. An analytical procedure for the analysis of the samples collected from the system was developed and implemented in two HP 5890 gas chromatographs. The error in the measurement was calculated to be less than 3%. Steady-State Modeling To determine the appropriate modeling approach for predicting the behavior of the azeotropic system, results from a nonequilibrium steady-state model were compared with those from an equilibrium model. Both models used the same equipment configuration, operating conditions, and thermodynamic properties. Conditions from the two distillation regions were simulated, and their results were validated experimentally. Model Specifications The NRTL activity coefficient model was used for the liquid phase, while the Redlich-Kwong equation-of-state was used for the gas phase. Table 1 describes the column configuration used for the steady-state simulation. An important decision in this project was whether to develop a nonequilibrium (rate-based) or equilibrium model. The equilibrium models use the so-called MESH equations: material balance (M), equilibrium relations (E), summation of composi-

Table 1. Column Configuration for the Steady-State Simulation number of theoretical stages feed stage condenser type reboiler type valid phases column internals stage packing height [in.] stage vol. [ft3] diameter [in.] void fraction specific surface area [ft2/ft3] Robbins factora

24 (without condenser and reboiler) 18 total (stage 1) kettle (stage 26) vapor-liquid-liquid packed (Nutter ring metal random No. 0.7) 13.8 0.23 6.0 0.98 68.9 11.9

a Packing-specific quantity used in the Robbins correlation. The packing factor is correlated directly from dry-bed pressure-drop data. The Robbins correlation is used to predict the column vapor pressure drop. For the dry packed bed at atmospheric pressure, the Robbins or packing factor is proportional to the vapor pressure drop.33

tions (S), and enthalpy balance (H). Equilibrium models assume that the vapor phase and the liquid phase on each stage are in thermodynamic equilibrium. To account for the deviation from equilibrium, the concepts of tray efficiency (for tray columns) and HETP (for packed columns) are employed. The rate-based models do not use these concepts because the rigorous MaxwellStefan theory is used to calculate the interphase heat and mass transfer rates. Taylor et al.32 supported the use of the rate-based approach when modeling distillation column dynamics and heterogeneous azeotropic systems. They suggested that equilibrium models failed to describe column dynamics due to the fact that stage efficiencies are a function of flow rates and composition and therefore vary with time. Constant stage efficiencies are a key component of the equilibrium modeling approach. In addition, rate-based models are recommended for modeling of systems with distillation boundaries, like most azeotropic systems, because equilibrium models occasionally cross the distillation boundary, although it has been shown in practice that this boundary cannot be crossed using one column. Recently, it has been called to our attention that one explanation for the difference between the nonequilibrium and equilibrium predictions is explained by the fact that boundaries computed from an equilibrium model may be different from the boundaries computed from a nonequilibrium model. Some studies have concluded that rate-based or nonequilibrium models are necessary to obtain a good description of the

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Table 2. Experimental Steady-State Composition Data [wt %] feed no. MeOH 1 2 3 4 5 6 7 8

4.06 3.96 3.27 3.67 2.95 3.28 3.02 4.06

distillate

bottom

C5

C6

MeOH

C5

C6

MeOH

C5

C6

49.34 51.52 43.65 44.15 41.77 51.10 48.06 52.11

46.60 44.52 53.09 52.18 55.29 45.62 48.92 43.83

6.74 6.85 8.92 8.66 8.75 4.34 6.33 5.99

93.08 92.96 90.83 91.29 90.92 95.26 93.64 93.84

0.18 0.19 0.25 0.06 0.33 0.40 0.03 0.17

1.58 0.63 0.48 0.86 0.84 2.22 0.43 2.10

8.97 3.78 20.41 17.63 23.89 6.93 12.24 9.64

89.45 95.58 79.11 81.50 75.27 90.85 87.33 88.26

azeotropic system,34,35 while others have validated azeotropic distillation equilibrium models experimentally,36,37 which suggests that the equilibrium approach can perform very well in modeling of azeotropic distillation systems. In this work, two different steady-state models were developed; one used the equilibrium modeling approach and the other the nonequilibrium approach. These models provided an initial understanding of the process and allowed the two different modeling methods to be compared with the experimental data. The steady-state data for each condition are presented in Table 2. Number of Stages/Segments Validation The number of stages in the equilibrium model was determined using the HETP provided by the packing vendor and the total height of packing in the column. Initially, the number of segments in the rate-based model was selected to match the number of stages used in the equilibrium model. To validate the choice of number of stages/segments, simulations were performed adjusting the number of equilibrium stages and

segments. The results, presented in Table 3, correspond to the analysis of the steady-state condition #2. The results indicated the selected number of equilibrium stages was correct, because fewer stages gave less agreement with the experimental data and more stages did not improve the model performance as compared with the experimental data. Increasing the number of segments to 52 in the rate-based model improved the model performance when compared with the experimental data, matching the predicted composition to that of the equilibrium model in five of the eight conditions studied. If the number of segments equals the number of stages, the separation predicted by the rate-based model is always going to be lower than the prediction from the equilibrium model. This statement is explained by Peng,38 who derived a relationship between the equilibrium model and the nonequilibrium model. The relationship established that when the number of segments in the rate-based model is the same as the number of stages in the equilibrium model, the solution of both models is identical if the interfacial area is infinite. Because for a real packed column the area in the rate-based model is finite, the separation predicted by the equilibrium model is always going to be better than that predicted by the rate-based model where the number of stages and segments is the same. Therefore, the number of segments in the rate-based model must be set to a higher value than the number of equilibrium stages, otherwise the model underpredicts the separation. Column Temperature Profile The following section includes the results obtained after analyzing the temperature profiles in three different steady-state conditions. Figure 2 indicates that the equilibrium model gives

Figure 2. Equilibrium and nonequilibrium models comparison with experimental data for steady-state condition #1. First distillation region. Table 3. Composition [wt %] Results after Variation in the Number of Equilibrium Stages Used in the Equilibrium Model and the Number of Segments Used in the Rate-Based Model (First Distillation Region; Steady-State Condition #2) product

comp.

13 stages EQ model

13 stages RB model

26 stages EQ model

26 stages RB model

52 stages RB model

52 stages EQ model

exp.

distillate

MeOH C5 C6 MeOH C5 C6

7.40 90.60 2.01 0.00 6.50 93.50

8.244 85.421 6.335 0.01 20.23 79.77

7.397 92.566 0.037 0.000 4.232 95.768

8.250 89.739 2.011 0.000 16.241 83.759

7.397 92.566 0.037 0.000 4.232 95.768

8.250 90.346 1.404 0.000 15.681 84.319

6.85 92.96 0.19 0.635 3.782 95.583

bottoms


Figure 3. Equilibrium and nonequilibrium models comparison with experimental data for steady-state condition #5. First distillation region.

Figure 4. Equilibrium and nonequilibrium models comparison with experimental data for steady-state condition #6. First distillation region.

a better approximation of the experimental data than does the nonequilibrium model. The similarities between the equilibrium model and the experimental data suggest that the vapor pressure model was accurate. Because the vapor pressure model was the same for equilibrium and nonequilibrium models, the differences obtained from the rate-based model may be caused by errors in the mass transfer and heat transfer coefficient predictions, which may not be accurate for this particular system. The results from steady-state condition #5 are presented in Figure 3. The feed composition was modified inside the same distillation region, but the material balance was maintained. Figure 3 indicates that again the temperature profile is best described by the equilibrium model. However, the experimental data do not reflect the temperature changes displayed by both models around the feed point (stage 18) between stages 16 and

21. These changes could actually take place in the column but were not detected in the experiments because the column did not have temperature measurements in these stages. The equilibrium model and experimental data in Figure 3 displayed a flat temperature profile between stages 8 and 15, which was not exhibited by the nonequilibrium model. Although the composition predicted by both models was roughly the same, the temperature profile in this particular case was important because it indicated the approximation to the azeotropic region. The results from steady-state condition #6 are presented in Figure 4. The temperature profile given by the nonequilibrium model in Figure 4 again failed to indicate the constant temperature response starting in stage 6. In contrast, the equilibrium model gave a very close temperature profile, and, given that the

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Figure 5. Nonequilibrium model column temperature profile for steady-state condition #6.

Figure 6. Experimental and predicted distillate normal pentane composition. First distillation region.

compositions predicted by both models were very similar, it was concluded that the vapor pressure model used was accurate. Figures 3 and 4 illustrate the temperature profile of conditions 5 and 6, which actually have a higher composition of methanol than condition 2, presented in Table 3. The presence of methanol changes the mixture conditions. The equilibrium separation predicts higher content of C6 but also a higher concentration of MeOH, which results in a lower temperature than the prediction from the nonequilibrium model. In general, the equilibrium model predictions were closer to experimental data, with traces of methanol in the bottom stream, while the nonequilibrium model did not predict methanol traces at the bottom. Because increasing the number of segments in the rate-based model improved the composition prediction for some of the steady-state conditions studied, the temperature profile was studied using different numbers of segments. The results for condition #6 are presented in Figure 5. The agreement between the experimental temperature profile and the rate-based model changes when the number of segments is modified because the separation tends to increase with the number of segments and so does the temperature difference between the top and bottom segments. In this particular

simulation, the prediction of the equilibrium model was closer to the experimental data than that predicted by the rate-based model even after the number of segments was modified. Mass Transfer Correlation Evaluation To improve the rate-based model, the mass and heat transfer models have to be adapted to this particular system. The mass transfer model used in the rate-based model in Aspen Plus (RateFrac) calculates the mass transfer coefficients and the interfacial area available for mass transfer using the correlations developed by Onda et al.39 In an attempt to find a more suitable mass transfer model for the system, a study was performed using the correlation of Billet and Schultes.40 The Billet and Schultes correlation was added to the Aspen Plus model using a FORTRAN subroutine.41 The results were compared with the experimental data and the predictions from the equilibrium model and the rate-based model with the Onda et al. correlation. Figure 6 illustrates the predicted compositions from all of the different models. The model based on the Billet and Schultes correlation gave the same prediction as the Onda et al. correlation model for five of the eight conditions studied. For the other three conditions, the model containing the Onda et al. correlation gave a closer agreement to the experimental data.


Figure 7. Column temperature profile for steady-state condition #5.

Figure 8. Experimental and predicted distillate normal pentane composition. First distillation region. All models.

Heat Transfer Correlation The effect of the heat transfer correlation was studied by initially assuming the temperatures of the liquid and vapor phases to be same, therefore eliminating the interfacial heat transfer effect. Aspen Plus calculates the heat transfer coefficients for the rate-based model using the Chilton-Colburn analogy.42 The analogy, eq 1, relates the mass transfer coefficients, kav, heat transfer coefficients, htc, and Schmidt (Sc) and Prandtl, Pr, numbers.

kav(Sc)2/3 )

htc (Pr)2/3 Cpmix

(1)

where Cpmix ) molar heat capacity [J/kg mol/K]. The nonequilibrium models were modified using a FORTRAN subroutine to compare the model predictions with and without interfacial heat transfer. The temperature profile predicted by the model with no interfacial heat transfer was the same as the temperature of the liquid phase in the model with the interfacial heat transfer calculations (Figure 7). However, there was a slight difference in the composition prediction; after

the heat transfer calculations in the interface were eliminated, the rate-based models predicted a higher separation. Figure 8 compares the normal pentane distillate composition predictions from all of the different models and the experimental data. The results indicated that the equilibrium models gave the best agreement with the experimental data for the composition and temperature predictions. The rate-based models gave good agreement with the experimental data and improved the composition prediction as the number of segments was increased. However, increasing the number of segments also moved the temperature profile away from the experimental data. The predictions from the rate-based models also improved after the heat transfer in the interface was neglected. The rate-based model with the Billet and Schultes correlation improved more than the model with the Onda et al. correlation after heat transfer in the interface was neglected. Packing Size Different packing parameters were modified in the rate-based models to determine if it was possible to obtain a better agreement between the temperature profiles predicted by the

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Figure 9. Experimental and predicted temperature profile using different packing sizes in the nonequilibrium model.

rate-based model and the ones obtained from experimental data. The parameters modified were: packing size, packing factor, void factor, surface area, and critical surface tension. Changes in the packing and void factors did not generate changes in the temperature prediction, while changes in the surface area and critical surface tension deviated even more the temperature predictions from the experimental values. Figure 9 illustrates the different temperature profiles obtained when the packing size is changed from 0.05 to 0.28 ft in increments of 0.01 ft. The value given by the packing manufacturer is 0.1 ft. From the figure, it is observed that increasing the packing size from the recommended value (0.1 ft) increases the temperatures from the rectifying section but decreases the temperatures from the stripping section. On the other hand, decreasing the packing size from the recommended value decreases the temperatures from the rectifying section while increasing the temperatures from the stripping section. It is concluded that modifying the packing size did not improve the rate-based model temperature profile predictions. There are two important remarks related to the temperature response given by the equilibrium and nonequilibrium models. First, the temperature difference between the experimental data and the equilibrium model changed between distillation regions but remained roughly constant to the predictions of the nonequilibrium model. Second, the slope of the temperature profile obtained from the experiments outside the azeotropic condition was closer to the slope in the profile predicted by the nonequilibrium model than the one predicted by the equilibrium model. The fact that the temperature profile from the equilibrium model in the azeotropic region gave a better agreement with experimental data than with the nonequilibrium model may suggest that more segments need to be added to the rectifying section of the column in the nonequilibrium model. This conclusion is based on the composition prediction in the first distillation region, where the nonequilibrium model did not always predict the separation obtained in the experiments. The equilibrium approach was selected to study the system behavior and to develop further work on online modeling reconciliation because it showed good agreement with the

experimental data. In addition, less CPU resources were needed to implement this simulation. Initially, steady-state results from the HYSYS equilibrium simulation were matched with steady-state equilibrium simulation results in Aspen Plus, and then the dynamic simulation was developed in HYSYS using the steady-state simulation as the starting point. Control Study The dynamic model was intended to be used as a tool to determine process parameters that could not be measured directly in the field, such as composition, a variable needed to implement the control strategies. For this reason, the model predictions had to be accurate and track the process behavior throughout the entire operating region. A reconciliation module was used to calculate the model parameters that minimize the error between plant measurement and model variables. The algorithm used in the reconciliation module is based on the gradient approach for model-reference adaptive control.43 The method modifies the parameters in the model so that the error between the outputs of process and reference model is driven to zero. In the gradient approach, the parameter is obtained as the output of an integrator. A more rapid convergence could also be achieved by adding a proportional adjustment to the integral action. The control law then takes the form of eq 2, which can be implemented in the plant using PI controller software, where the constants γ1 and γ2 represent the proportional and integral gains respectively.43

u(t) ) γ1e(t) + γ2

∫0t e(τ) dτ

(2)

Initially, the model parameters selected to be updated online were the overall column heat transfer coefficient and HYSYS dynamic efficiency.44 Given that the packing HETP value was obtained from experimental data, the efficiency value should not change much from the value of unity. However, it was expected to have some variations for different flooding conditions, mainly due to the system’s nonideal behavior. The model efficiency value was modified to match the process distillate


C5 composition. Because the error in the measurement was about 3%, the parameter was modified if the model output was off by more than 3% from the process output. After data from the experiments were analyzed, it was concluded that the efficiency value was fairly constant at a value of 0.7 in the distillation region rich in cyclohexane and pentane and 0.5 in the distillation region rich in methanol and normal pentane. Although the reconciliation module was used to determine these values, the efficiency parameter was not modified online to reconcile the model online. The column’s external surface heat transfer coefficient directly influences the heat loss experienced by the column. The model developed in this work used a simple heat loss equation, where the heat loss is calculated from the parameters specified by the user: overall heat transfer coefficient U and ambient temperature Tamb. The heat transfer area A and the fluid temperature Tf are calculated for each stage by the model. The heat loss is calculated using eq 3.

Q ) UA(Tf - Tamb)

(3)

During the model validation phase, U was modified until the mass balance in the model matched the experimental mass balance; that is, distillate and bottoms flow rates were the same in the model and the experiment when all of the other conditions in the model were set to match the conditions in the experiment. Tamb was based on the conditions of the experiment, but was not continuously upgraded. The heat transfer coefficient was updated online using the reconciliation module during the control experiments described in the next section. Its value increased up to 5% as the liquid flow in column decreased and vice versa. The heat transfer coefficient is dependent upon the physical properties of the fluid and the physical conditions of the experiment, which varied with the operating region. The heat transfer coefficient was also impacted by variations in the ambient temperature. These variations were not measured continuously nor automatically upgraded during the experiments. Although this variation was found to be small, it shifted the model from the process outputs. Composition Control Composition inferred by temperature measurements is a common practice in distillation control. Although temperature has been the measurement of choice in monitoring and controlling the separation due to its fast response and low cost, for highly nonideal systems holding the temperature constant does not imply that composition will also be constant. In such cases, direct measurements of composition using online analyzers should be considered. However, online analyzers involve high capital and maintenance cost and slow response, especially for multiplexed sample points. To overcome these issues, this work introduced the use of a high fidelity dynamic model as a soft sensor for product composition. During the study, the main control objective was to maximize throughput while maintaining distillate product within specification (that is, maximize C5 concentration). It was also desired to minimize cost of column operation (operational cost of reboiler and condenser) while maintaining adequate disturbance rejection. Stabilizing the basic operation of the column was achieved by inventory (level), flow, and pressure controls. The control loops in this level were configured with independent PID controllers (see Table 4).

Table 4. Basic Column Control Configuration manipulated variable feed flow valve position preheater steam flow valve position reflux flow valve position distillate flow valve position bottom flow valve position reboiler steam flow valve position nitrogen flow splitter valve position

controlled variable feed flow rate feed temperature reflux flow rate distillate flow rate bottom flow rate steam/duty flow rate column pressure

Table 5. Composition Manipulated and Controlled Variable Configurationsa manipulated variable 1

reflux flow rate (R) steam flow rate (Q) distillate flow rate (D) steam flow rate (Q)

2 a

controlled variables DC - R BC - Q DC - Q BC - D

λ (RGA) 0.972 0.028 -0.004 1.004

0.028 0.972 1.004 -0.004

DC ) distillate composition; BC ) bottom composition.

To control the product composition in the column, two different configurations were considered on the basis of the relative gain array analysis (RGA). The RGA was used to obtain an initial understanding on how to pair variables for inventory and separation control. The gain matrix was calculated using the step responses from the dynamic model developed in HYSYS. Step changes were performed in the manipulated variables, using different magnitudes and directions, and the results were averaged. The analysis indicated that both configurations were viable (see Table 5). The results from the RGA analysis were consistent with the traditional control configuration used in ordinary distillation (pairing 1) and the results from studies in azeotropic distillation where the opposite pairing (pairing 2) gave less loop interaction than the traditional variable pairing used in distillation.25,26 As mentioned previously, the process had two feasible distillation regions. The data presented in this paper include experimental data only from region one (feed composition with high concentration of cyclohexane and normal pentane). The control objective was to maintain the pentane/methanol azeotrope in the distillate and maximum recovery of cyclohexane in the bottom stream. For this reason, the key components selected for control were normal pentane for the distillate stream and cyclohexane for the bottom stream. The manipulated variables were selected between the same options as for inventory control: distillate, reflux, steam, and bottom flow rate. The level in the reflux drum was paired with the distillate flow rate in the first configuration (pairing 1) and with the reflux flow rate in the second configuration (pairing 2). The column level was paired with the bottom flow in the two control configurations. The dynamic model was connected online to the DCS and provided estimates for variables where instrumentation was not available. Because the plant did not have an online measurement of composition, this configuration provided the controlled variable estimates. During experimentation, samples of distillate and bottom products were collected after mass balance was achieved in the process and compared with the values provided by the simulation. The difference between measured and estimated values was within (3%. Samples of the feed were collected every half hour, and the values were introduced in the model. Model-Based Control Linear MPC was implemented using the commercial advanced control module Predict Pro from DeltaV. The process model used by the controller was identified online using the

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Table 6. MPC Step Response Modelsa

reflux flow rate steam flow rate feed temperature feed flow rate

distillate C5 composition

bottom C6 composition

κ ) 3.8 θ ) 16 s τ ) 689.23 s κ ) -3.2 θ ) 48 s τ ) 1828.95 s κ ) -0.2 θ ) 16 s τ ) 344.62 s κ ) 0.4 θ ) 24 s τ ) 689.23 s

κ ) -1.4 θ)8s τ ) 172.31 s κ ) 3.5 θ ) 40 s τ ) 1899.86 s κ ) 0.2 θ ) 88 s τ ) 190.67 s κ ) -0.2 θ ) 16 s τ ) 221.54 s

a κ ) gain. θ ) dead time. τ ) first-order time constant. Time to steady state ) 5600 s.

process model identification tool included in the module. DeltaV PredictPro uses step response modeling for the generation of the MPCPro controller. The step responses are generated using two types of models: finite impulse response (FIR) and autoregressive (ARX). The FIR model is used to identify the process delay used in the ARX model. The identified step responses are presented in Table 6. The MPC variables were selected on

the basis of results from the PID study. The gain (κ) is dimensionless because it is normalized by the transmitter range. The controller in the MPC algorithm is designed as an online-horizon optimization problem that is solved subject to the given constraints. For MPC based on linear process models, both linear and quadratic objective functions can be used.45 Equation 4 represents the control law that minimizes a quadratic objective function.

∆U(k) ) (STQS + R)-1STQEˆ 0(k + 1) Eˆ 0(k

The vector + 1) corresponds to the predicted deviations from the reference trajectory when no further control action is taken; this vector is known as the predicted unforced error vector. The matrices Q and R are weighting matrices used to weight the most important components of the predicted error and control move vectors, respectively.46 In DeltaV Predict Pro, the elements of Q are known as penalty on error, while the entries of R are the “penalty on move”. The MPC controller is tuned by modifying the values of the matrixes Q and R. R offers convenient tuning parameters because increasing the values of its elements reduces the magnitude of the input moves, providing a more conservative controller.

Figure 10. Experimental composition control using linear MPC. Feed flow rate configured as manipulated variable.

Figure 11. Experimental MPC behavior using different tuning parameters.

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Figure 10 illustrates the linear MPC performance in the experiment after a series of step changes in the distillate and bottoms composition set points. Both output errors were assigned a penalty of one. The penalty on move was set to 25 for the steam flow rate and 20 for the reflux flow rate. In the experiment, the optimizer was also configured to maximize the concentration of C5 in the distillate. The SP was allowed to change 0.5% for both controlled variables. Given that the system is nonlinear,47 the tuning parameters in the multivariable controller were set up to provide robustness and eliminate oscillation in the response. The main difficulty occurred due to changing gains in the process. The gains related to the distillate composition were smaller when the azeotropic composition was reached in the distillate composition than in other regions with lower pentane recovery in the overhead product. Figure 10 illustrates MPC responses inside and outside the azeotropic region with different tuning parameters. Controller tuning 1 has a higher penalty on move (PM) for both manipulated variables than controller tuning 2. The parameters used in controller tuning 2 were the values suggested by DeltaV Predict Pro. These values are calculated on the basis of the assumption that the system is linear. A higher penalty on move improved system stability in the region with higher gains. The penalty on error was set to 1 for both controlled variables. From Figure 11, it is observed that tuning 2 produces an unstable closed loop response. Conclusions Open and closed loop experiments were carried out in a pilot scale azeotropic distillation system of methanol, normal pentane, and cyclohexane. The experimental data were used to validate steady state and dynamic equilibrium and nonequilibrium models. It was concluded that equilibrium models accurately described the process steady-state behavior. Although the process displayed a highly nonideal and nonlinear behavior, multiple steady states were not observed in the simulations nor found experimentally. Contrary to some reports on rate-based models, it was concluded that the results predicted by the equilibrium model were similar to those predicted by the nonequilibrium model. Analysis of the process steady state and dynamic models indicated that equilibrium models accurately predict the distillation column behavior. In multicomponent azeotropic distillation, temperature measurements do not offer accurate indications of composition; hence commercial dynamic simulation software was used to obtain an inferential control solution. Linear MPC gives excellent performance when the composition is used directly as a controlled variable and the appropriate tuning is used. Literature Cited (1) Chien, I.-L.; Chao, H.-Y.; Teng, Y.-P. Design and control of a complete heterogeneous azeotropic distillation column system. Comput.Aided Chem. Eng. 2003, 15B (Process Systems Engineering 2003, Part B), 760-765. (2) Chien, I.-L.; Zeng, K.-L.; Chao, H.-Y. Design and control of a complete heterogeneous azeotropic distillation column system. Ind. Eng. Chem. Res. 2004, 43, 2160-2174. (3) Kurooka, T.; Yamashita, Y.; Nishitani, H.; Hashimoto, Y.; Yoshida, M.; Numata, M. Dynamic simulation and nonlinear control system design of a heterogeneous azeotropic distillation column. Comput. Chem. Eng. 2000, 24, 887-892. (4) Wang, C. J.; Wong, D. S. H.; Chien, I.-L.; Shih, R. F.; Liu, W. T.; Tsai, C. S. Critical reflux, parametric sensitivity, and hysteresis in azeotropic

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ReceiVed for reView January 25, 2006 ReVised manuscript receiVed April 27, 2006 Accepted May 1, 2006 IE060112K

A Novel Control Methodology for a Pilot Plant Azeotropic Distillation

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