Optimum Economic Design and Control of a Gas Permeation

Ind. Eng. Chem. Res. 2008, 47, 1221-1237

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Optimum Economic Design and Control of a Gas Permeation Membrane Coupled with the Hydrodealkylation (HDA) Process Gregory R. Bouton and William L. Luyben* Chemical Engineering Department, Lehigh UniVersity, Bethlehem, PennsylVania 18015

This paper studies the design and control of a modified hydrodealkylation (HDA) process that uses a membrane to reduce hydrogen losses in the methane purge stream. A dynamic, counter-current membrane module is written using Aspen Custom Modeler to capture both the steady-state and dynamic performance of the membrane. The feed to the membrane is the purge stream from the conventional HDA process without a membrane. The hydrogen-rich permeate is compressed and recycled back into the process to reduce the demand for fresh hydrogen feed. The methane-rich retentate is the new purge stream from the system. A steady-state economic analysis is performed to determine the optimum membrane area and permeate pressure. Increasing the area and decreasing the pressure result in lower hydrogen consumption; however, the capital investment and energy costs increase. The return on the incremental investment is used to select the best design. The final design reduces the required flow rate of fresh hydrogen feed by approximately one-third. This results in an estimated annual savings of almost $400 000 in hydrogen feed by investing approximately $836 000 in capital. A plantwide control structure is developed for the new process. A composition controller manipulates the flow rate of the membrane retentate, which acts as the new purge stream, to control the composition of methane in the large total gas recycle stream. A second composition controller is used to control the composition of the hydrogen being lost in the retentate purge by manipulating the power input to the permeate compressors. Dynamic simulations performed in the Aspen Dynamics environment show that the control structure is effective in rejecting disturbances in throughput and hydrogen fresh feed composition. 1. Introduction The hydrodealkylation (HDA) of toluene is a widely studied process that researchers1-3 have used to test new plant design techniques and explore the interaction between design and control. Most of this research has been focused on using the process as an example of ground-up design heuristic development and control structures. For example, researchers propose possible steady-state design alternatives of the HDA process and then choose the most economical flowsheets for dynamic investigations. This paper is not focused on methods for designing entirely new processes. Instead, the retro-fitting of an existing HDA process by installing a membrane unit is studied. An interesting design study was recently published by Konda et al.,2 which presented a modified plant design heuristic applied to the ground-up design of an HDA plant. Their approach leads to many alternatives for the HDA process, several of which include the addition of a gas permeation membrane. This was explored in their paper using a “user defined extension” in HYSYS to model the membrane at steady state and a transfer function for the dynamic model. No information was provided about what relationships were used in the “user defined extension.” They demonstrated that adding a membrane can be very beneficial to the overall process design. This paper explores the economic and dynamic factors of adding a basic membrane permeation separation unit to an existing HDA process. The membrane area and permeate pressure are varied to determine an optimal economic steadystate design, which is a tradeoff between reducing hydrogen fresh feed and the costs of capital (membrane and recycle * To whom correspondence should be addressed. Tel.: 610-7584256. Fax: 610-758-5057. E-mail address: [email protected].

compressor) and energy (compressor power). Larger membrane areas and lower permeate pressures allow more material to pass through the membrane and decrease hydrogen losses. More material and lower permeate pressures drive up the costs associated with compressing the low-pressure permeate stream back to the pressure in the gas loop so that it can be recycled. There are two overall goals of this study. The first is to show that adding a membrane separation unit to the purge stream of an existing HDA process is economically beneficial from a steady-state point of view. The economic optimum configuration of membrane size and recycle compressor power are determined based on the return on the incremental investment. Increasing the membrane area and reducing the permeate pressure result in higher capital investment, but increase the net saving up to the point of diminishing returns. The installation of a membrane in the purge stream has very little effect on the operating conditions in the remainder of the HDA plant, aside from reducing the required fresh hydrogen feed. The second goal is to develop a control structure for the process with the membrane separation unit that successfully rejects disturbances. The dynamics of the plant with the membrane unit are demonstrated to remain similar to those of the original plant when typical disturbances occur. 2. Process Description The HDA process produces benzene via the hydrodealkylation of toluene. Methane and diphenyl are also produced as byproducts. The original version of the HDA process used in this work takes the basic form of the process presented by Douglas1 and Luyben.4 The control structure used is that described in Luyben.4 The production rate of benzene is 125 kmol/h. The steady-state HDA process flowsheet for the base-case process without a membrane is given in Figure 1, which shows detailed stream properties and equipment parameters.

10.1021/ie0711372 CCC: $40.75 © 2008 American Chemical Society Published on Web 01/16/2008

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Ind. Eng. Chem. Res., Vol. 47, No. 4, 2008

Figure 1. Detailed flowsheet of the hydrodealkylation (HDA) process without a membrane.

2.1. Conventional Reactor Section. The two main reactions that occur in the reactor section are shown in reactions 1a and 1b.

toluene + H2 f benzene + CH4

(1a)

2(benzene) T diphenyl + H2

(1b)

Luyben4 described the steady-state parameters used in the simulation. The heats of reaction for the above reactions are -18 000 Btu/lbmol and +3500 Btu/lbmol, respectively. Kinetic rate parameters are given in eq 2 (the activation energies are given in units of cal/mol).

[

R 1 ) PTPH0.5 2.4 exp

[

R 2 ) PB2 0.001 exp

(-50RT976)]

(2a)

(-50RT976)] -50 976 (2b) P P [0.0071 exp( RT )] D H

where R 1 and R 2 represent the respective overall reaction rates (expressed in units of kmol s-1 m-3); PT, PH, and PB are the partial pressures (given in pascals) of toluene, hydrogen, and benzene; R is the universal gas constant (expressed in units of cal mol-1 K-1), and T is the temperature (given in Kelvin). The base-case steady-state HDA process used in this work, as shown in Figure 1, has a fresh feed of liquid toluene entering the process at a rate of 135.9 kmol/h. The second fresh feed is a gaseous mixture of 97% hydrogen and 3% methane entering the system at a rate of 233.0 kmol/h. The toluene fresh feed is

mixed with a toluene recycle stream from the separation section of the process (33.0 kmol/h). The total liquid toluene stream then is combined with the fresh hydrogen feed and a gas recycle stream consisting of a mixture of mostly hydrogen and methane. The total stream is sent through a feed-effluent heat exchanger (FEHE) on its way to a fired furnace. The FEHE uses the hot reactor effluent to preheat the reactant mixture, reducing the energy demand in the furnace. The furnace brings the reactant stream up to 621 °C. After leaving the furnace, the stream enters the reactor. The reactor is an adiabatic plug-flow tubular reactor that contains no catalyst and measures 2.90 m in diameter with a length of 17.37 m. An excess of hydrogen is required to prevent coking in the reactor at high temperature. The minimum acceptable ratio of hydrogen to aromatics in the reactor is 5:1. The per-pass conversion of toluene is ∼72%. The reactor outlet temperature (667 °C) is higher than the inlet because of the exothermic first reaction. This hot effluent is quenched to 621 °C by adding a cold liquid stream. The quenched effluent is the hot inlet of the FEHE. The FEHE is rather large at 1489 m2 and has a low heat-transfer coefficient of 0.114 kW m-2 K-1 because both streams are gas. The temperature of the effluent leaving the FEHE is 170.9 °C. The stream is further cooled to 48.9 °C and partially condensed using a water-cooled heat exchanger. The cooled effluent is sent to a flash tank separator. Some of the liquid stream is used to quench the hot reactor effluent, as mentioned previously. The remainder of the liquid is sent to the separation section of the process. The gaseous stream from the separator has a composition of ∼40 mol % hydrogen and ∼60 mol % methane.

Ind. Eng. Chem. Res., Vol. 47, No. 4, 2008 1223

This gas stream is first compressed and then split into a gas recycle and a purge stream that leaves the process in the conventional HDA process. The purge stream removes most of the methane that is formed in the reaction, but a significant amount of hydrogen is lost in the purge. The gas recycle stream helps to maintain the 5:1 ratio of hydrogen to toluene. Another important feature of this recycle is that the recycled methane acts as a heat sink to help maintain a reactor outlet temperature of 25%. The final design is a 10-cell countercurrent membrane with two compressors and heat exchangers. Table 3 shows a summary of the data used to determine the optimum membrane area and permeate pressure. For a given permeate pressure, steady-state data were generated for many different membrane areas. The area that gives the highest net annual savings is the optimum for that pressure. The optimum designs over a range of pressures are then compared to select the best design. The data in Table 3 are arranged from left to right, in order of lowest capital cost to highest capital cost. Note that net annual savings also increase from left to right, but at a decreasing rate. The return on the incremental investment is used to evaluate the alternative combinations of membrane area and permeate pressure. This incremental return information is a comparison of each column with the column to the left. The results show that the configuration given in the second column requires more capital investment ($3700) but increases the net annual savings by $1500 per year, which provides a very acceptable incremental return on investment. A comparison of the configurations in the second and third columns shows that the increase in capital investment ($3000) achieves an increase in net annual savings of $1900 per year, which also provides a high incremental return on investment. The incremental return on investment decreases substantially for the other configurations as we move farther to the right in Table 3. The configuration with a membrane area

Ind. Eng. Chem. Res., Vol. 47, No. 4, 2008 1229 Table 3. Economic Summary of the 10-Cell Counter-Current Membrane with Two-Stage Compression for Various Membrane Areas Value parameter permeate pressure (bar) membrane feed (kmol/hr) permeate (kmol/h) mole fraction of H2 in permeate retentate (kmol/h) mole fraction of H2 in retentate brake horsepower (hp) compressor 1 compressor 2 heat exchanger area (ft2) heat exchanger 1 heat exchanger 2 installed cost (dollars, $) membrane compressor 1 compressor 2 heat exchanger 1 heat exchanger 2 total capital investment (dollars, $) annual energy cost ($ per year) hydrogen savings ($ per year) return on investment (%) net annual savings ($ per year) incremental return on investment (%)

membrane area ) 266.0 m2





10.5 224.1 87.11 0.8339 137.0 0.1242

10.0 222.7 86.21 0.8421 136.5 0.1208

9.5 221.3 85.34 0.8502 136.0 0.1175

9.0 220.0 84.50 0.8582 135.5 0.1142

8.5 218.7 83.71 0.8661 135.0 0.1109

102.1 95.0

105.0 98.0

107.8 100.7

111.1 103.8

114.6 107.1

78.0 71.9

78.0 72.0

78.0 73.0

78.0 73.0

78.1 73.3

146 300 300 400 283 600 26 900 27 800 785 000 71 600 562 900 37.59 295 100

135 900 307 300 290 800 26 900 27 800 788 700 73 700 567 500 37.61 296 600 40.54

126 000 313 700 297 100 26 900 28 000 791 700 75 700 572 100 37.70 298 500 63.33

116 600 321 400 304 400 26 900 28 000 797 300 78 000 576 600 37.54 299 300 14.29

107 800 329 500 312 200 26 900 28 100 804 500 80 500 581 000 37.21 299 400 7.03

of 229 m2 and a permeate pressure of 9.5 bar is selected as the most economically favorable alternative for the 10-cell countercurrent membrane with two-stage compression. The sensitivities of the results to several economic parameters, such as the capital cost of the membrane, the cost of hydrogen, and the cost of energy, were explored. The values shown in Table 3 indicate that the membrane cost is much smaller than the compressor cost, so the results would not be influenced significantly by membrane cost. Hydrogen costs vary widely from year to year and could impact the results. However, energy costs to drive the compressors would change directly with hydrogen costs, so the balance between the two is likely to not change the optimum design significantly. 5. Incorporating the Membrane Model Into the HDA Simulation Incorporating the membrane model into the HDA process was not as simple as one might expect. Many days of effort were required to achieve a successful dynamic simulation of the coupled process. The help of James Goom of Aspen Tech is gratefully acknowledged in this effort. The problems included getting “Port” types correct, initializing the state variables, and specifying free and fixed variables. A major problem was a bug in Aspen software (Version 2004), which is discussed below. After the pressure-driven membrane unit was functional and running in Aspen Custom Modeler, it was necessary to connect the module to the existing HDA simulation. Attempts were made to incorporate the membrane model into the steady-state HDA file in Aspen Plus by importing from Aspen Custom Modeler. We were unsuccessful in this approach. One procedure that was finally successful took the approach of importing the dynamic Aspen Custom Modeler membrane file directly into the Aspen Dynamics HDA file. Some of the details of the steps in this procedure and problems encountered are discussed below. The membrane section was simulated in two files. The first is an Aspen Custom Modeler file for the membrane by itself. The second file has the two-stage compression system with two compressors, two heat exchangers, and control valves on the

purge and cooling water streams. The compression system was created in Aspen Plus as a steady-state model and then exported into Aspen Dynamics as a pressure-driven dynamic file. Both the dynamic compression system file and the custom membrane model were then imported into the Aspen Dynamics HDA plant simulation file. The Aspen Dynamics HDA simulation file is opened. Selecting the File menu at the top of the screen brings up a menu from which Import Types is selected. A window opens and asks for the type of file to be opened. There is a dropdown box in the window that includes the choice Aspen Custom Modeler Language file type. After selecting that option, the appropriate filename for the membrane model is chosen for import. After the type is imported, the flowsheet itself may be imported. Back at the file menu, there is another option called Import Flowsheet. This option brings up another window where the drop-down menu is used to select the Aspen Custom Modeler Language file type. The filename of the membrane is once again selected and imported. This time, the flowsheet from the membrane file should appear next to the HDA process diagram. After this procedure is followed, the next step is to ensure that the file with the coupled units will be initialized and run. Because of a bug in Aspen Dynamics, it would not initialize. The correction of this problem, provided by James Goom, is to go to the top left of the explorer pane, click the icon marked Globals and select DynamicOptions. A window opens that contains several parameters. The parameter of interest is GlobalPDriVen. The parameter is either set as True or as False. The HDA simulation is designed to be pressure-driven, but when the membrane file is imported from the custom modeling software, the pressure-driven option is incorrectly set to False. It must be reset to True to be able to initialize and run the simulation. Once this bug was corrected, the simulation was successfully run with the main process and the membrane unconnected on the same flowsheet. Before connecting the membrane to the HDA process, the composition controller on the original purge stream is disconnected, and the original purge stream is deleted. The membrane

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Figure 5. Basic flowsheet comparison of the HDA process and the HDA process with a membrane.

feed stream that is imported with the membrane model will now take the place of the deleted purge stream. The retentate will serve as a new purge stream. In the initial coupling of the two flowsheets, the permeate is not connected and simply leaves the system. Eventually, it will be recycled back into the process. The next task is to import the compression system from its dynamic file to the HDA with a membrane file. The same procedure is required as for the membrane unit. The only exception is the default dynamic file type is selected instead of the custom modeler language file type. After importing the types and the flowsheet, the entire compression system is in the process window next to the HDA process with a membrane. At this point, the first compressor is attached to the permeate stream. The remainder of the compression section is deleted. The file is initialized and run in dynamic mode with the membrane and single compressor on the permeate stream. Then other portions of the compression system are added one at a time. This is done until both compressors and heat exchangers have been attached to the permeate stream and a control valve is located on the retentate stream. Once the membrane and compression unit are assembled in the file, the compressed permeate recycle loop must be closed, i.e., the permeate gas must be fed back into the total gas recycle stream. If the full permeate stream is suddenly recycled, it will introduce such a large disturbance that the control system cannot handle it. To avoid this problem, a homotopy-type procedure was use to gradually introduce permeate back into the gas recycle stream. With the loop still not closed, the membrane area is decreased a few square meters at a time from the initial value of 229 m2 to 1 m2. After each area change, the simulation is reinitialized and run in dynamic mode until a new steady state is determined. Decreasing the area to a very small value causes the bulk of the membrane feed to leave the system in the retentate. Very little material passes through the membrane and enters the permeate stream. After the membrane area becomes small, the compressed permeate recycle loop is closed by adding the permeate stream to the gas recycle stream. The model can be initialized and run in dynamic mode with this small change. The membrane area then can be slowly increased back up to

the initial value, while the simulation runs in dynamic mode. The final steady-state conditions are achieved when the membrane area is at its design value. 6. Steady-State Operation A comparison between the original HDA process and the HDA process with a membrane is shown in Figure 5, including stream values for the hydrogen feeds and process purges. There are several minor variations in stream variables between the HDA file and the HDA with a membrane file. For example, the HDA with a membrane file requires a slightly increased (0.22%) amount of toluene to obtain the same overall production rate of benzene. Figures 1 and 6 contain detailed information on streams throughout each process. The main difference, as expected, occurs in the fresh hydrogen feed flow rate. With an equivalent production level of 125 kmol/h of benzene, the normal HDA process requires a fresh hydrogen feed of 233.0 kmol/h, whereas the membranecontaining process requires only 156.0 kmol/h. This results in a savings of 77.0 kmol/hr, which represents a 33% reduction in the original amount of fresh hydrogen feed. The additional process equipment (two compressors, two heat exchangers, and the membrane) requires an additional capital investment of $835 800. The cost to run the compressors, based on an average electricity cost of 5¢/kW-h, is $79 800 per year. As calculated from the steady-state conditions observed in the final Aspen Dynamic simulation, the final savings achieved from the addition of the membrane and compression unit is approximately $400 000 per year for a capital investment of $835 800. The reduction in hydrogen feed, and the associated economics, are shown in Table 4. There are two reasons why these results differ slightly from those presented in the steady-state economic section. The first, as previously mentioned, is that the economics were performed on the membrane and compression system before they were attached to the entire HDA process. However, the main reason is that the economic design was performed using a steady-state benzene production rate of 94.5 kmol/h. However, to be consistent with other studies,3 the target production rate was


Figure 6. Detailed flowsheet of the HDA process with a membrane.

Table 4. Dynamic Simulation Results

Table 5. Detailed Controller Listing for Both Processes

parameter

value

typical HDA hydrogen feed membrane HDA hydrogen feed reduction in hydrogen feed savings in hydrogen feed total energy cost capital cost membrane compressor 1 heat exchanger 1 compressor 2 heat exchanger 2 total capital investment annual savings return on investment

233.0 kmol/h 156.0 kmol/h 77.04 kmol/h $688 300/yr $79 800/yr $126 000 $374 300 $37 300 $260 700 $37 500 $835 800 $399 600 47.81%

changed to 125 kmol/h of benzene during the later stages of the dynamic testing. 7. Control Structure and Dynamic Tests The control structure for the conventional HDA configuration has been previously described. The addition of the membrane unit requires only two changes in the reaction/membrane section of the plant. The separation section is unchanged. A composition controller on membrane feed stream controls the composition of methane in this stream by manipulating the retentate flow rate, which is the new purge stream. A second composition controller is added to control the composition of hydrogen in the retentate by manipulating the work of the first compressor. The purpose of the controller is to ensure that hydrogen losses are kept small. If the hydrogen composition increases, the compressor power is increased, which reduces permeate pressure and increases the permeate flow rate.

controller

setpoint

gain

τI (min)

action

PCR TCQ TCR TCC LC

Common Controllers for Reactor Section 33 atm 2.0 10 621.1 °C 0.2 1.8 621.1 °C 0.5 9.0 48.89 °C 0.5 5.0 1.524 m 2.0 60 000

reverse direct reverse reverse direct

PC1 TC1 LC11 LC12 PC2 TC2 LC21 LC22 PC3 TC3 LC31 LC32

Common Controllers for Separation Section 10.2 atm 2.0 20 50 °C 1.0 20 2.12 m 2.0 60 000 0.284 m 2.0 60 000 2.04 atm 1.0 20 124.4 °C 5.0 20 2.404 m 2.0 60 000 2.292 m 2.0 60 000 2.041 atm 1.0 10 235 °C 0.20 7.5 1.14 m 2.0 60 1.162 m 10 60

direct reverse direct direct reverse reverse direct direct reverse reverse direct direct

Controllers with Variations for HDA (1) and Membrane (2) FCT(1) 168.92 kmol/h 2.0 5.0 reverse FCT(2) 168.89 kmol/h 2.0 5.0 reverse CC(1) 58.8 mol % CH4 2.0 99 999 direct CC(2) 40.34 mol % H2 2.987 62.568 reverse CCM PCM TC4 TC5

Controllers for Membrane Section Only 11.7 mol % H2 1.707 27.984 19.64 atm 2.74685 1.0 49.85 °C 4.103 2.112 49.95 °C 5.593 3.564

direct direct direct direct

To handle the two-stage compression setup, a pressure controller is used to control the pressure of the stream leaving the first compressor by manipulating the work of the second compressor. Two temperature controllers are installed that control the outlet temperatures of the compressed gas streams

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leaving the heat exchangers by manipulating the cold water flows. Setpoints and tuning parameters for these controllers and others can be found in Table 5. Dead times of 3 min are used in all composition loops, and dead times of 1 min are used in all temperature loops. Relay-feedback tests were performed to obtain Tyreus-Luyben controller settings. Figure 5 gives an overview of the main differences between the typical HDA control structure and the HDA with a membrane control structure. Figure 6 is a detailed flowsheet of the entire HDA process with a membrane, including stream properties and the full control scheme implemented in Aspen Dynamics.

Both the HDA process and the HDA process with a membrane are tested in dynamic mode to compare the responses to a few typical disturbances. The first disturbance is a 5% increase in the fresh feed of toluene entering the process. This disturbance is achieved by changing the setpoint of the total toluene flow controller. For the HDA process, the setpoint of the controller was taken from 168.9 kmol/h with a corresponding fresh toluene feed of 135.9 kmol/h to a setpoint of 175.1 kmol/h with a fresh toluene feed of 142.7 kmol/h, which results in a 5.03% increase in fresh toluene feed. The HDA with membrane file starts with a total toluene flow rate of 168.8 kmol/h with a fresh toluene feed of 136.1 kmol/h and is stepped to a setpoint

Figure 7. Increase of 5% in fresh toluene feed for the HDA process with a membrane.

Figure 8. Comparison of responses to a 5% increase in fresh toluene feed for (- - -) the HDA process and (s) the HDA process with a membrane.


Figure 9. Increase of 2.77 °C in the reactor inlet temperature for the HDA process with a membrane.

Figure 10. Comparison of responses to a 2.77 °C increase in the reactor inlet temperature for (- - -) the HDA process and (s) the HDA process with a membrane.

of 174.9 kmol/h total toluene flow with a corresponding fresh toluene flow rate of 143.0 kmol/h for a 5.05% increase in fresh toluene. The results of this test are shown in Figure 7 for the HDA process with a membrane. A comparison between the HDA process and the HDA process with membrane is given in Figure 8. The second disturbance is an increase in the reactor inlet temperature. For both processes, the setpoint of the reactor inlet controller was increased by 2.77 °C (from 621.11 °C to 623.88 °C). Responses to this disturbance are shown in Figure 9 for the membrane process. Figure 10 compares the responses of the HDA process and the HDA process with a membrane.

The last variable to be changed is the purity of the fresh hydrogen feed. The initial purity of the fresh hydrogen is 97% hydrogen and 3% methane. The purity is first increased to 99% hydrogen and 1% methane. This is done by selecting the hydrogen fresh feed stream and using the Manipulate form to alter the stream compositions. The results of this disturbance can be observed in Figure 11 for the membrane process, while the comparison between the two processes is shown in Figure 12. Possibly the most difficult disturbance for the membrane is the decrease in hydrogen fresh feed purity to 95% hydrogen and 5% methane. This is expected to be difficult because more

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Figure 11. Responses to 2% increase in fresh hydrogen feed purity for the HDA process with a membrane separation unit.

Figure 12. Comparison of responses to a 2% increase in fresh hydrogen feed purity for (- - -) the HDA process and (s) the HDA process with a membrane.

material must be forced through the existing membrane cells to purge enough methane to prevent a buildup in the system. When initially trying to introduce this change, there was a numerical integration error in the program. This problem was solved by changing the purity to 96% hydrogen and 4% methane and manually stepping the simulation for two integration steps. The purity then was changed to the target of 95% hydrogen and 5% methane. The integrator was able to handle this change. The two steps represent a total of 0.002 h (7.2 s) of simulation time, so the overall effect of the intermediate step should be minimal. Results of this disturbance can be observed in Figure 13 for the HDA process with a membrane. The flow rates of the retentate, the permeate, and the hydrogen fresh feed all increase. The retentate hydrogen composition is maintained at the desired

value by increasing compressor work, which decreases permeate pressure. The control system handles this difficult upset quite well. A comparison of the responses of the HDA process with a membrane and the typical HDA process is included in Figure 14. These dynamic tests illustrate that the proposed control structure for the HDA process with a membrane provides effective dynamic control of the system. 8. Conclusion This paper demonstrates that the addition of a gas permeation membrane can potentially provide a large economic benefit for an existing HDA plant. The $836 000 capital investment in membrane and compression equipment generates a net annual


Figure 13. Responses to a 2% decrease in fresh hydrogen feed purity for the HDA process with membrane separation unit.

Figure 14. Comparison of responses to a 2% decrease in fresh hydrogen feed purity for (- - -) the HDA process and (s) the HDA process with a membrane.

savings of $400 000. These savings result from a 30% reduction in the flow rate of the fresh hydrogen feed required to produce the same amount of benzene. The net savings reflect the capital cost of the additional equipment and the cost of compressor energy. The optimum economic design has two design variables: membrane area and permeate pressure. The return on incremental capital investment is used to determine the best combination of these two design degrees of freedom.

A control structure is developed for the membrane unit that provides effective dynamic control. The composition of the gas recycle is controlled by manipulating the methane-rich retentate stream. The loss of hydrogen in the retentate purge stream is controlled by manipulating the power to the permeate recycle compressor. The control structure and dynamics of the remainder of the process (reaction section and separation section) are not affected by the addition of the membrane.

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Appendix The following text is the program for the final 10-cell counter-current gas permeation membrane:


Acknowledgment James Goom from Aspen Technology contributed valuable assistance in successfully transferring models from Aspen Custom Modeler to Aspen Dynamics. Financial support for this work was provided by the Zisman Family Fund. Literature Cited (1) Douglas, J. M. Conceptual Design of Chemical Processes; McGrawHill: New York, 1988; p 601. (2) Murthy Konda, N. V. S. N.; Rangaiah, G. P.; Lim, D. K. H. Optimal Process Design and Effective Plantwide Control of Industrial Processes by a Simulation-Based Heuristic Approach. Ind. Eng. Chem. Res. 2006, 45, 5955-5970. (3) de Arau´jo, A. C. B.; Hori, E. S.; Skogestad, S. Application of Plantwide Control to the HDA Process. IIsRegulatory Control. Ind. Eng. Chem. Res. 2007, 46, 5159-5174.

(4) Luyben, W. L. Plantwide Dynamic Simulators in Chemical Processing and Control; Marcel Dekker: New York, 2002; p 429. (5) Membrane Handbook; Kluwer Academic Publishers: Dordrecht, The Netherlands, 1992; p 954. (6) Economic Indicators. Chem. Eng. 2007, (April 1). (7) Baker, R. W. Future Direction of Membrane Gas Separation Technology. Ind. Eng. Chem. Res. 2002, 41, 1393-1411. (8) Smith, O. J., III. Private communication, 2007. (9) Peters, M. S.; Timmerhaus, K. D.; West, R. E. Plant Design and Economics for Chemical Engineers, Fifth Edition; McGraw-Hill: New York, 2003; p 988. (10) Seider, W. D.; Seader, J. D.; Lewin, D. R. Process Design Principles: Synthesis, Analysis and EValuation; Wiley: New York, 1999.

ReceiVed for reView August 20, 2007 ReVised manuscript receiVed November 1, 2007 Accepted November 2, 2007 IE0711372

Optimum Economic Design and Control of a Gas Permeation

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