An Industrial Design Control Study For Vac Monomer Process.pdf

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Computers Chem. Engng Vol. 22, No. 7—8, pp. 867—877, 1998 1998 Elsevier Science Ltd All rights reserved. Printed in Great Britain PII: S0098-1354(98)00030-1 0098—1354/98 $19.00#0.00 An industrial design/control study for the vinyl acetate monomer process Michael L. Luyben* and Bjo¨ rn D. Tyre´ us DuPont Central Research & Development, Experimental Station - Bldg 357, P.O. Box 80357, Wilmington, DE 19880-0357, USA (Received 23 April 1997; received in revised form 29 December 1997) Abstract This work presents design details of an industrial process for the manufacture of vinyl acetate monomer. Our purpose is to offer a realistic example that is uniquely suited for academic researchers pursuing simulation, design, and control studies. The vinyl acetate process has common, real chemical components. It contains many standard unit operations in a realistic flowsheet. And it illustrates the types of systems of industrial research interest in the areas of process design, optimization, simulation, and control. Vapor-phase reactions convert ethylene, oxygen, and acetic acid into vinyl acetate with water and carbon dioxide as byproducts. The process contains a packed tubular reactor, a feed-effluent heat exchanger, an absorber, a vaporizer, an azeotropic distillation column with decanter, and both gas and liquid recycle streams. All physical property, kinetic, and flowsheet data have been compiled from sources in the open literature. We detail the flowsheet information required to construct rigorous steady state and dynamic mathematical models of the process and present the process control requirements and objectives. Finally, we briefly describe the rigorous nonlinear dynamic simulation we have constructed for this process using TMODS, DuPont’s in-house dynamic simulator. Models of this process have also been developed by Aspen Technology and Hyprotech in their commercial simulators and are available directly from the vendors. 1998 Elsevier Science Ltd. All rights reserved Keywords: industrial design/control study; vinyl acetate monomer process 1. Introduction Downs and Vogel (1993) published an industrial plantwide control test problem that has proved to be a beneficial service to the academic process control community. A number of researchers have utilized this example to test their ideas and technical develop- ments. Many publications have appeared about the Eastman process, which was provided as a dynamic simulation in Fortran code. The problem has usefully served as a realistic check on the industrial and practi- cal relevance of the ever-increasing amount of process control publications in chemical engineering. We have heard of continued interest among aca- demic researchers within the process design and con- trol areas to have additional industrial examples of realistic processes that can be used in assessing new technology. We also recognize the need in the litera- ture for plantwide design, optimization, and control studies that grapple with: (1) a realistically large *Corresponding author. E-mail: [email protected]. dupont.com. process flowsheet containing standard chemical unit operations; (2) a process with the typical industrial characteristics of recycle streams and energy integra- tion; and (3) real nonideal chemical components. This paper presents design details of an industrial process for the production of vinyl acetate monomer and thus goes a step beyond the Eastman process control challenge problem. The reaction loop section of the vinyl acetate process contains a flowsheet and unit operations that are typical of many chemical plants. It has both gas and liquid recycle streams with real components. We have chosen to convey this study as if we had been assigned the task of designing the control system for a proposed new vinyl acetate process that is to be built. We have been given a particular preliminary design that has not been optimized. The design could potentially be improved with modifications to the flowsheet or design parameters. The data we provide in this paper are what would typically be available or easily obtainable: (1) kinetic reaction parameters and physical property data, (2) a flowsheet structure with stream and equipment information, and (3) the location of control valves 867 Fig. 1. Vinyl acetate monomer process flowsheet. included in the preliminary design. However, we would not be given a linear transfer function model. We certainly would not have a rigorous nonlinear dynamic simulation. Steady state and dynamic mod- els would have to be constructed by using a commer- cial software simulation package or by writing the code in some chosen programming language. As a re- sult, unlike Downs and Vogel (1993), we do not make available any code that simulates the vinyl acetate process. Based upon the information provided in this paper, models have been developed by Aspen Techno- logy and Hyprotech in their commercial simulators. We have ourselves built a rigorous nonlinear dy- namic model of the process described in this paper using TMODS, DuPont’s in-house dynamic simula- tor. This model has been used to verify the feasibility of the simulation and to test the plantwide control strategy proposed in Luyben et al. (1997). We believe that this process should serve as a useful example for researchers who are interested in working on indus- trially relevant problems in simulation, design, and control. The industrial process for the vapor-phase manu- facture of vinyl acetate monomer is quite common (Daniels, 1989) and utilizes widely available raw ma- terials. Vinyl acetate is used chiefly as a monomer to make polyvinyl acetate and other copolymers. Hoechst-Celanese, Union Carbide, and Quantum Chemical are reported US manufacturers. DuPont also currently operates a vinyl acetate process at its plant in LaPorte, Texas. To protect any proprietary DuPont information, all of the physical property and kinetic data, process flowsheet information, and modeling formulation in this work come from sources in the open literature. We cite each source of data and our process flowsheet is based upon the description in Report 15B by SRI International (1994). No relation, either implied or intended, exists between this pub- lished study and the DuPont process. 2. Vinyl acetate process Figure 1 shows the eleven basic unit operations proposed for the reaction section of the vinyl acetate process, which is the focus of this study and the plant we wish to design and operate. Three raw materials, ethylene (C ` H " ), oxygen (O ` ), and acetic acid (HAc), are converted into the vinyl acetate (VAc) product. Water (H ` O) and carbon dioxide (CO ` ) are byprod- ucts. We assume that an inert component, ethane (C ` H ' ), enters with the fresh ethylene feed stream. We consider the following two reactions: C ` H " #CH ` COOH#1/2 O ` PCH ` "CHOCOCH ` #H ` O, (1) C ` H " #3O ` P2CO ` #2H ` O. (2) The exothermic reactions occur in a reactor contain- ing tubes packed with a precious metal catalyst on a silica support. Heat is removed from the reactor by generating steam on the shell side of the tubes. Water flows to the reactor from a steam drum, to which make-up water (BFW) is supplied. The steam leaves the drum as saturated vapor. The reactions are irre- versible and the reaction rates have an Arrhenius-type dependence on temperature. 868 M.L. LUYBEN and B.D. TYRE US We located plots of experimental kinetic data in Samanos et al. (1971) for a particular vinyl acetate catalyst. As summarized by Neurock et al. (1996), various mechanisms have been proposed for the formation of vinyl acetate (i.e. Samanos et al., 1971; and Nakamura and Yasui, 1970, develop completely different expressions). However, we derived the fol- lowing rate expressions that provide the best fit to the experimental data. r ¹ "0.1036 exp(!3674/¹) ; p - p # p (1#1.7p 5 ) (1#0.583p - (1#1.7p 5 )) (1#6.8p ) , (3) r ` "1.9365;10` exp(!10, 116/¹) ; p - (1#0.68p 5 ) 1#0.76p - (1#0.68p 5 ) , (4) where r ¹ has units of moles of vinyl acetate produced/ min/(g catalyst) and r ` has units of moles of ethylene consumed/min/(g catalyst). ¹ is the absolute temper- ature in Kelvin and p G is the partial pressure of com- ponent i (O is oxygen, E is ethylene, A is acetic acid, and ¼ is water) in psia. The standard state heat of reaction is !42.1 kcal/mol of vinyl acetate for r ¹ and !316 kcal/mol of ethylene for r ` . These values are cal- culated using heats of formation from the DIPPR database. Thus the reactions are quite exothermic, particularly the combustion reaction to carbon dioxi- de, which also is more sensitive to temperature be- cause of the higher activation energy. The reactor effluent flows through a process-to- process heat exchanger, where the cold stream is the gas recycle. The reactor effluent is then cooled with cooling water and the vapor (oxygen, ethylene, carbon dioxide, ethane) and liquid (vinyl acetate, water, acetic acid) are separated. The vapor stream from the separ- ator goes to the compressor and the liquid stream from the separator becomes a part of the feed to the azeotropic distillation column. The gas from the com- pressor enters the bottom of an absorber, where the remaining vinyl acetate is recovered. A liquid stream from the base is recirculated through a cooler and fed to the middle of the absorber. Liquid acetic acid that has been cooled is fed into the top of the absorber to provide the final scrubbing. The liquid bottoms prod- uct from the absorber combines with the liquid from the separator as the feed stream to the distillation column. Part of the overhead gas exiting the absorber enters the carbon dioxide removal system. This could be one of the several standard industrial CO ` removal pro- cesses. Here we simplify this system by treating it as a component separator with a certain efficiency that is a function of rate and composition. The gas stream minus carbon dioxide is split, with part going to the purge for removal of the inert ethane fromthe process. The rest combines with the large recycle gas stream and goes to the feed-effluent heat exchanger. The fresh ethylene feed stream is added. The gas recycle stream, the fresh acetic acid feed, and the recycle liquid acetic acid stream enter the vaporizer, where steam is used to vaporize the liquid. The gas stream from the vapori- zer is further heated to the desired reactor inlet tem- perature in a trim heater using steam. Fresh oxygen is added to the gas stream from the vaporizer just prior to the reactor to keep the oxygen composition in the gas recycle loop outside the explosivity region. The azeotropic distillation column separates the vinyl acetate and water from the unconverted acetic acid. The overhead product is condensed with cooling water and the liquid goes to a decanter, where the vinyl acetate and water phases separate. The organic and aqueous products are sent for further refining to another distillation section. Here we ignore the addi- tional separation steps required to produce vinyl acet- ate of sufficient purity because there is no recycle from the refining train back to the reaction loop. The bot- tom product from the distillation column contains acetic acid, which recycles back to the vaporizer along with fresh make-up acetic acid. Part of this bottoms stream is the wash acid used in the absorber after being cooled. 3. Physical property data The vapor—liquid equilibrium (VLE) data for the three nonideal component pairs are given in Table 1. These data come from the vapor-liquid equilibrium data collection in the Chemistry data series published by DECHEMA. VLE calculations are performed as- suming an ideal vapor phase and a standard Wilson liquid activity coefficient model. This takes the form GH " » H » G exp(!a GH /R¹), (5) where ¹ is the absolute temperature in K, R is the gas constant (1.987 cal/mol K), and » G is the molar vol- ume of component i given in DECHEMA and listed in Table 1. The Wilson parameters we use for the VAc—H ` O pair are assumed to be the same as the parameters for ethyl acetate and water. The reason for this assump- tion is that no VLE data are presented in DECHEMA for vinyl acetate and water, but ethyl acetate and vinyl acetate are quite similar species and should behave essentially identically. The liquid-liquid equilibrium solubility data for the VAc—H ` O pair in the column decanter come from Smith (1942) extrapolated to the decanter temperature of 40°C. Acetic acid dimerizes in the vapor phase. The Wil- son parameters listed in DECHEMA for the H ` O—HAc pair assume the effect of dimerization is modeled. Without considering the vapor-phase asso- ciation, the DECHEMA parameters predict the exist- ence of an azeotrope close to pure water. Such an Study for the vinyl acetate monomer process 869 Table 2. Pure component physical properties (c N in cal/(g °C)) Component Molecular Specific Latent Liquid Vapor weight gravity heat ht capacity ht capacity (cal/mol) a—b a—b O ` 32 0.5 2300 0.3—0 0.218—0.0001 CO ` 44.01 1.18 2429 0.6—0 0.23—0 C ` H " 28.05 0.57 1260 0.6—0 0.37—0.0007 C ` H ' 30.05 0.57 1260 0.6—0 0.37—0.0007 VAc 86.09 0.85 8600 0.44—0.0011 0.29—0.0006 H ` O 18.02 1 10684 0.99—0.0002 0.56—!0.0016 HAc 60.05 0.98 5486 0.46—0.0012 0.52—0.0007 Table 1. Wilson parameters a GH and molar volumes » G a GH VAc H ` O HAc » G (ml/mol) VAc 0 1384.6 !136.1 93.1 H ` O 2266.4 0 670.7 18.07 HAc 726.7 230.6 0 57.54 From DECHEMA vapor—liquid equilibrium data collection Vol. 1. VAc—H ` O: Part 1b, p. 236. VAc—HAc: Part 5, p. 90. H ` O—HAc: Part 1, p. 127. azeotrope does not exist for this system. The VLE behavior close to pure acetic acid is acceptable with- out a model of dimerization. Since we operate in the process where the VLE behavior is acceptable, we have used the parameters in Table 1 without special provisions for vapor-phase association. Table 2 shows the pure component physical prop- erty data, which we obtained from the DIPPR database. These data include the molecular weight M¼, the liquid specific gravity (based on the density of water at 0°C), the latent heat of vaporization H T at 0°C (in cal/mol), and the liquid cJ N and vapor cT N heat capacity parameters. The heat capacity expressions we use have the following temperature dependence: c N "a#bt, (6) where c N is in cal/(g°C) and t is the temperature in°C. Component vapor pressures PQ in psia (Table 3) are calculated using the Antoine equation, with the Anto- ine coefficients listed in the DECHEMA volumes. ln PQ"A#B/(t#C), (7) where t is the temperature in °C. For the four gas components, the A parameters of the Antoine equa- tion were estimated based upon the vapor pressure at the operating conditions in the absorber. We removed the temperature dependence to facilitate the dynamic simulation. However, in the case of ethylene and ethane, we found that we needed to include a small Table 3. Component vapor pressure antoine coefficients !ln PQ"A#B/(t#C), where PQ in psia and t in °C Component A B C O ` 9.2 0 273 CO ` 7.937 0 273 C ` H " 9.497 !313 273 C ` H ' 9.497 !313 273 VAc 12.6564 !2984.45 226.66 H ` O 14.6394 !3984.92 233.426 HAc 14.5236 !4457.83 258.45 temperature dependence for the bubble point calcu- lations to function properly. 4. Process data and constraints 4.1. Design requirements The process design that we use is based upon the flowsheet shown in SRI Report 15B. We assume that the production basis of our process with new catalyst is 785 mol/min VAc and at the given conditions 85 mol/min CO ` is also produced. For a plant with 90% operating utility, this corresponds to an annual production rate of 32;10' kg/yr, if the VAc rate is sustained over the life of the catalyst. We assume that the catalyst lifetime is one year. The ethylene and oxygen feed streams come from supply headers. Acetic acid comes from a storage tank. The carbon dioxide is released to the atmo- sphere. The gas purge stream is sent to a thermal converter. The vinyl acetate and water products from the decanter are fed to other distillation columns in a refining train. Available on the plant are the follow- ing utilities: cooling tower water at a supply temper- ature of 30°C, steam at supply pressures of 50 and 200 psia, refrigeration at !25°C, and electricity and process water. Economic data for raw material and energy costs are listed in Table 4. Any capital equip- ment and vessel cost data can be found in Guthrie (1969). The costs should be updated to current prices. Also, the appropriate material of construction factors should be used. Cost correlations for some equipment are given in Douglas (1988). 870 M.L. LUYBEN and B.D. TYRE US Table 5. Process stream data Table I Reactor Reactor Absorber Absorber Absorber Purge in out vapor in vapor out liquid out flow Stream Number 1 2 3 4 5 6 Flow (mol/min) 19250 18850 16240 15790 1210 3 Temperature (°C) 148.5 158.9 80 40.4 47.7 40.4 Pressure (psia) 128 90 128 128 128 128 O ` (mol frac) 0.075 0.049 0.057 0.058 0.001 0.059 CO ` 0.007 0.011 0.013 0.014 0.001 68 C ` H " 0.583 0.551 0.642 0.658 0.025 0.667 C ` H ' 0.216 0.221 0.256 0.263 0.010 0.266 VAc 0 0.043 0.021 0.002 0.255 0.002 H ` O 0.009 0.055 0.007 0.001 0.129 0.001 HAc 0.110 0.070 0.004 0.004 0.579 0.005 moles/million. Pressure drop in gas loop assumed to be in reactor. Table 6. Process stream data Table II Column Column Organic Aqueous Fresh feed bottoms product product HAc feed Stream number 7 8 9 10 11 Flow (mol/min) 3820 2160 826 831 785 Temperature (°C) 42.5 137.2 40 40 30 Pressure (psia) 84 30 18 18 150 VAc (mol frac) 0.206 11 0.950 0.002 0 H ` O 0.281 0.093 0.050 0.998 0 HAc 0.513 0.907 370 370 1 moles/million. Table 4. Economic data for vinyl acetate process Item Cost/price Acetic acid $0.596/kg Oxygen $0.044/kg Ethylene $0.442/kg Vinyl acetate $0.971/kg 200 psia steam $11/1000 kg 50 psia steam $8.8/1000 kg Cooling tower water $0.02/1000 l Process water $0.15/1000 l !25°C refrigeration $0.12/h, ton Electricity $0.065/kwh Tables 5—7 contain the flow, temperature, pressure, and composition data for selected streams in the pro- cess. The corresponding stream numbers are shown in Fig. 1. In our simulation, all gas is removed in a com- ponent separator prior to the distillation column. This involves the liquid from the separator and the absorb- er. The gas is sent back and combines with the vapor product from the separator to form the vapor feed to the absorber. Tables 8—10 contain certain vessel data that are required to size the equipment and construct the simulation. These data come from our TMODS dynamic simulation and not from a commercial steady-state simulation package. The reactor contains 622 tubes packed with cata- lyst. The tube diameter is 3.7 cm and length 10 m. Steam is generated on the shell side of the reactor to remove the heat of reaction. We have modeled the reactor in 10 sections in the axial direction. The reac- tor temperature profile is shown in Fig. 2. The flow- sheet design conditions are for a new catalyst with an activity of 1. However, the catalyst does deactivate over the course of operation. This deactivation via sintering is a nonlinear function of operating time (t WP ) and temperature, since higher temperatures within the tubes (t RS@C ) promote deactivation. We assume that the activity (a) decays exponentially with time from 1.0 to 0.8 after 1 yr according to a"f (t RS@C ) exp(!t WP /0.621). (8) Study for the vinyl acetate monomer process 871 Table 7. Process stream data Table III Fresh Fresh CO ` CO ` C ` H " feed O ` feed purge Removal in flow Stream number 12 13 14 15 Flow (mol/min) 831 521 85 6411 Temperature (°C) 30 30 40.4 40.4 Pressure (psia) 150 150 128 128 O ` (mol frac) 0 1 0 Same CO ` 0 0 1 as C ` H " 0.999 0 0 stream C ` H ' 0.001 0 0 4 Table 8. Reactor and vaporizer equipment data Catalyst weight 2590 kg Catalyst porosity 0.8 Catalyst bulk density 0.385 kg/l Catalyst heat capacity 0.23 cal/g °C Overall heat transfer coefficient 150 kcal/h °C m` Number of tubes 622 Tube length 10 m Tube diameter 3.7 cm Circumferential heat transfer area 725 m` Shell side temperature 133°C Reactor heat duty 2.8;10' kcal/h Steam drum volume 2 m` BFW to steam drum 79.5 kg/min Reactor feed heater duty 5.3;10` kcal/h Vaporizer duty 1.3;10' kcal/h Vaporizer total volume 17 m` Vaporizer working level volume 4 m` Vaporizer temperature 119°C If the tube temperature has not exceeded 180°C, then f (t RS@C )"1. Above this temperature, then f (t RS@C )"exp[!(t RS@C !180)/50], where t RS@C is in °C. Two parameters define the performance of the cata- lyst: selectivity (SEL) and space-time yield (STY). Catalyst selectivity determines the fraction of the ethylene consumed that makes the desired vinyl acet- ate product. SEL"100 mol/min VAc mol/min VAc#0.5 mol/min CO ` . (9) For conditions at the design basis with fresh catalyst, the selectivity is 94.8%. At a catalyst activity of 0.8, higher reactor temperatures are required to achieve about the same VAc production rate, increasing the production rate of CO ` to 126 mol/min and reducing the selectivity to 92.4%. The space—time yield quan- tifies the activity of the catalyst by volume. STY"g VAc/h/liter catalyst. (10) Table 9. FEHE, separator, and absorber equipment data FEHE duty 4.4;10` kcal/h FEHE hot outlet temperature 134°C FEHE ºA 6800 kcal/h °C Separator cooler duty 2.7;10' kcal/h Separator volume 15 m` Separator working level volume 8 m` Gas loop volume 170 m` Approximate compressor size 350 kW Absorber base volume 8 m` Absorber bottom section 2 theoretical stages Absorber top section 6 theoretical stages Absorber stage efficiency 50% Absorber tray holdup 14 kmol Absorber liquid recirculation 15 kmol/min Absorber cooler duty 6.5;10` kcal/h Absorber wash acid feed 756 mol/min Absorber wash acid cooler duty 1.3;10` kcal/h Table 10. Column and decanter equipment data Theoretical stages 20 Feed stage 15 from bottom Stage efficiency 50% Tray holdup 2.3 kmol Reboiler duty 4.0;10' kcal/h Condenser duty 3.9;10' kcal/h Base working level volume 6 m` Decanter working level volume 5 m` For conditions at the design basis, the STY is 603 since the total volume of catalyst (tube volume) is 6724 l. The CO ` removal system is assumed to be a com- ponent separator that removes just carbon dioxide at a certain efficiency, which is the fraction in the feed leaving in the CO ` purge. This efficiency (Eff) is a function of the feed rate (F ''` in mol/min) and composition (x ''` in mole fraction). At the design conditions, the efficiency is 0.995 for a feed rate of 6410 mol/min at 0.014 mol fraction CO ` . The 872 M.L. LUYBEN and B.D. TYRE US Fig. 2. Reactor temperature profile. maximum allowable feed rate to the CO ` removal systemis 8000 mol/min set by its capacity. The follow- ing correlation determines the system efficiency Eff"0.995!3.14;10'(F ''` !6410) !32.5(x ''` !0.014), (11) where the efficiency must lie between 0 and 1. Two key safety constraints exist in the process. First, the oxygen composition must not exceed 8 mol % anywhere in the gas recycle loop to remain outside the explosivity envelope of ethylene (Coward and Jones, 1952). Continuous and reliable O ` analyzers will be installed in the process at the inlet of the reactor to monitor oxygen composition. Second, the pressure in the gas recycle loop and distillation col- umn cannot exceed 140 psia because of the mechanical construction limit of the process vessels. Pressure measurements are readily available and will be instal- led at appropriate locations. Exceeding either the oxy- gen concentration or pressure limits will shut down the process via interlocks. Several other operational constraints must also be satisfied during process operation. The peak reactor temperature along the length of the tube must remain below 200°C, otherwise mechanical damage occurs to the catalyst requiring shutdown. Liquid levels in the vaporizer, separator, absorber base, distillation col- umn base, and decanter must operate within the limits of 10—90%. The vessel volumes listed have been pro- posed for the working liquid inventories between the level taps. Reactor inlet temperature must exceed 130°C to prevent condensation of liquid in the reactor. The hot side exit temperature from the feed-effluent heat ex- changer (FEHE) must remain above 130°C to avoid condensation in the exchanger, which has been designed to handle only vapor-phase flow. In the azeotropic distillation column, the acetic acid in the decanter organic phase must not exceed 600 mol/mil- lion to prevent product contamination. A decanter composition analysis for acetic acid is available from the laboratory every 4 h. Also, the vinyl acetate com- position in the bottoms stream must remain below 100 mol/million to minimize polymerization and foul- ing in the column reboiler and vaporizer. The column temperature profile is plotted in Fig. 3. 4.2. Control requirements Figure 4 shows the location of the 26 control valves that have been proposed in the preliminary design. Flow, temperature, pressure, and level measurements are readily available and can be installed in any loca- tion needed for control. The O ` analyzers at the reactor inlet are specialized instruments that are fast and reliable. However, if additional composition measurements are used, they must be conventional chromatographic analyzer types that are character- ized by sampling frequency and reliability problems. It must be assumed that any chromatographic ana- lyzer used in this process has a 10 min sampling fre- quency and 10 min deadtime. Also, this analyzer has a 90% utility. The remainder of the time the instru- ment is off-line for maintenance or calibration. Hence, when an analyzer is not on line, the plant must be able to continue producing vinyl acetate. Further, it must be demonstrated how the control system functions when an analyzer is down and one of the disturbances listed below occurs. The control system which we are asked to design for this process must be able to operate in the face of several known disturbances and changes we antici- pate a priori. 1. The process will operate at a catalyst activity of 0.8 (or lower based upon reactor temperature) at the end of 1 yr. The control system must still function for the changed conditions. 2. Process operation must be regulated automatically to reflect changes in raw material and operating costs so that the process always runs close to the ecomomic optimum. Fig. 3. Azeotropic distillation column profile. Study for the vinyl acetate monomer process 873 Fig. 4. Location of control valves. 3. The control system must be able to change produc- tion rate (as measured by steady organic flow from the decanter) by at least 20% (both up and down) over the course of 6 h. This is due to limits on tank storage. 4. The plant needs to run at half the VAc production design rate but at maximum selectivity. This is the result of an occasionally precipitous drop in the price of vinyl acetate to a third its normal value. 5. In-line (but not operating) spare pumps will be installed for the fresh acetic acid supply line and for the distillation column feed stream. However, it must be demonstrated what the control system does during the course of a 5 min loss of either fresh acetic acid or column feed pump. 6. The control system must handle a step change in the composition of ethane in the fresh ethylene feed stream from 0.001 to 0.003 mol fraction. 7. The control system must not shut down the pro- cess due to the loss of fresh oxygen feed flow. Instead, this should result in the process going into ‘‘hot recycle’’ mode. 5. Nonlinear dynamic model 5.1. Background In this section we provide a brief description of the nonlinear dynamic modules used in TMODS. These modules have been constructed following the practi- cal philosophy toward dynamic simulation outlined in Luyben (1990). Our purpose is to provide a ‘‘feel’’ for the level of detail we use in our dynamic simulations without divulging exactly how our simu- lator is implemented. We would like to point out that the kind of dy- namic models we use strike a balance between simula- tion efficiency and rigor of representation. We have found that simulation speed is of vital importance and we always strive to keep our user interactive simula- tions running between 10 and 60 times real time. There are basically two ways to meet this goal. We can either limit the scope of the simulation to a few process units that are rigorously simulated or limit the complexity of most units within a plantwide scope. Since we have found the plantwide perspective to be most important for control simulations, we generally opt for the second alternative. This nonlinear dynamic model has been utilized to confirm the feasibility of the simulation. It is the basis for the data presented in the stream and equipment tables. We also have used the simulation to test the control strategy described in Luyben et al. (1997), which was derived following the plantwide control design procedure. 5.2. Physical property calculations TMODS is implemented in an object-oriented framework (Tyreus, 1992). It consists of a number of generic classes that can be instantiated into objects in the simulation. The objects are given appropriate parameters to reflect the actual piece of equipment they represent. The objects are also connected to- gether by the end user of the simulation to create a flowsheet. The most important aspect of the object- oriented representation is the use of fluid objects. The 874 M.L. LUYBEN and B.D. TYRE US fluid objects are instances of the fluid system pertain- ing to the simulation. The fluid system contains all the physical property constants described earlier includ- ing the kinetic parameters. Each fluid object is then able to perform a number of services based upon these parameters. For homogeneous (single phase) fluids these services amount to calculating thermodynamic state variables from the knowledge of two intensive state variables and the composition of the fluid. In TMODS these services are implemented to be explicit functions of the known state variables. Examples are º"º(P, ¹, n ¹ , n ` , 2 ), h"h(P, ¹, x ¹ , x ` , 2 ), ¹"¹(P, u, x ¹ , x ` , 2 ), v"v(P, ¹, x ¹ , x ` , 2 ), where P is the total pressure; ¹ is the temperature; n G is the number of moles of component i; x G is the mole fraction of component i (x G "n G /n G ); º is the total internal energy; v is the specific volume, u is the specific internal energy; and h is the specific enthalpy. In many cases the fluid object represents a hetero- geneous equilibrium system. Examples are the fluid objects in vaporizers, partial condensers, decanters, and on the trays of a distillation column. Here the thermodynamic state is completely specified by two extensive state variables and the number of moles of each component. The only difference to a homogene- ous system is that the unknown intensive state vari- ables are no longer explicit functions of the known entities. For example, to determine the pressure and temperature of a fluid in vapor—liquid equilibrium, we have to solve the following three nonlinear implicit algebraic equations: , G¯¹ (K G !1)(n G /n) 1#(K G !1) "0, (12) »/n!(1!) v*!v4"0, (13) º/n!(1!)u*!u4"0, (14) where N is the number of components in the system, n is the total number of moles in the fluid object ( n G ), K G is the K-value for component i (K G "y G /x G ), x G is the mole fraction i in the liquid phase, y G is the mole fraction i in the vapor phase, is the fraction of n in the vapor phase; v is the specific volume; and u is the specific internal energy. The known state variables are total internal energy and total volume that follow from the dynamic energy balance and the equipment size. The total moles of each component follow from the dynamic material balances. The K-values are calculated from the equi- librium requirement that the chemical potential of each component is equal in both phases 4 G "* G , or equivalently that the partial fugacities of each com- ponent are equal across the phases f 4 G "f * G . In TMODS we assume that the vapor phase is ideal such that f 4 G "y G P. The liquid-phase partial fugacity is calculated with an activity model according to f * G "x G G PQ G where G is the liquid-phase activity coefficient of com- ponent i and PQ G is the vapor pressure of component i. To reduce the computational burden of iteratively solving the three nonlinear equations, we frequently make simplifying assumptions around two-phase sys- tems. For example, in vapor—liquid equilibria we of- ten assume that the vapor holdup is negligible ("0). This eliminates one of the three equations. The re- maining variables can be solved for by making either of the following assumptions. We can solve for ¹ and P explicitly based on the fact that the n G ’s and the total º pertain to a single phase (the liquid). Or we can assume that the pressure is known along with the n G ’s of the liquid, and we can solve for temperature and vapor compositions via a bubble point calculation. The role of the unit operations is greatly simplified by the use of fluid objects. The unit operations contain one fluid object for each fluid holdup in the equip- ment. For example, a vaporizer contains one fluid object and a distillation tray section has a fluid object on each tray. The unit operation is responsible for managing the accumulation of mass and energy into the fluid objects. With the knowledge of the total internal energy, the total volume, and the number of moles of each component, the thermodynamic state is fixed. The fluid objects are then responsible for calcu- lating all other relevant state variables pertaining to the current state. The equipment equations for accumulation of mass and energy depend upon whether the system is lumped or distributed. 5.3. Lumped equipment models Material balances: dn G dt "FGLxGL G !FMSR xMSR G #R G . (15) Energy balance: dº dt "FGLhGL!FMSRhMSR#Q#HR. (16) Auxiliary relations: FMSR"f (n G , P, ¹, equipment configuration), (17) where FGL is the molar flow of all streams entering the vessel, xGL G is the mole fraction i in entering streams, FMSR is the molar flow of exit streams, xMSR G is the mole Study for the vinyl acetate monomer process 875 fraction i in exit streams, R G is the net production of i from all chemical reactions, hGL is the specific en- thalpy of entering streams, hMSR is the specific enthalpy of exit streams, Q is the heat input to the vessel, and HR is the total heat from reactions. 5.4. Distributed equipment models Material balances: *c G *t "! *J G *z ! *(c G v) *z # H GH r H !N G . (18) Energy balance: *(u K ) *t "! *J O *z ! *(h K v) *z ! H H H r H ! G N G h G !q. (19) Momentum balance: *(v) *t "! *P *z ! *(vv) *z # G G FC G . (20) Auxiliary relations: N G "k E a(p G !p * G ), (21) q"h U a(¹!¹ U ), J G "!D G *c G *z , J O "!k 2 *¹ *z , where c G is the molar concentration of i; J G is the diffusion flux of component i; v is the bulk velocity of fluid; v GH is the stoichiometric coefficient for compon- ent i in reaction j; r H is the specific rate of reaction; N G is the molar flux of component i; is the fluid density; u K is the specific internal energy (mass based); J O is the heat flux due to conduction; h K is the specific enthalpy (mass based); H H is the heat of reaction for reaction j; q is the external heat flux per unit volume; FC G is the external force acting on component i; k E is the overall mass transfer coefficient; a is the surface to volume ratio for heat and mass transfer; p G is the partial pressure for component i; p * G is the interface partial pressure for component i; ¹ U is the interface temper- ature; D G is the molar diffusivity coefficient of compon- ent i; and k 2 is the conductivity coefficient. 5.5. Specific implementations Catalytic plug flow reactor: The catalytic plug flow reactor is modeled according to equations (18)—(21) on the tube side and equations (15)— (17) on the shell side. Simplifying assumptions are J G "0, J O "0, and *(v)/*t"0. The time-independent momentum equa- tion (20) sets the pressure profile in the reactor. We assume that the entire gas loop pressure drop is repre- sented by the reactor pressure drop. A simple back- ward discretization scheme is used for the spatial derivatives. Gas Separator: This generic flash calculation can be implemented in a number of different ways. In TMODS this unit is implemented with two fluid ob- jects on the process side and a single-phase liquid object on the shell side. In our implementation the process side fluid objects are not in equilibrium with each other. The vapor object determines the system pressure. The shell side fluid determines the static flash temperature. This allows us to use equation (12) to solve for the partition of incoming feeds into the vapor and liquid objects. The vapor object in the gas separator defines the pressure level of the gas recycle loop. As mentioned above, the reactor determines the pressure drop in the loop. Absorber: The gas absorber is implemented as two countercurrent versions of equations (18), (19), and (21). Each node, or stage, contains a liquid phase and a vapor phase that are not in equilibrium with each other. Instead, the single-phase state is determined by the integration of equations (18) and (19). The auxili- ary equations (21) then use the partial pressure and temperature differences between the two phases to determine the mass and heat transfer rates. »aporizer: The vaporizer is implemented as a lum- ped system with a single fluid object. The vapor hold- up is assumed negligible compared to the liquid inventory. Distillation Column: Each tray is a lumped system and contains a fluid object. The holdup in the vapor phase is ignored. The pressure on each tray is assumed known, which reduces the flash calculation to a bubble point calculation. The energy balance deriv- ative (16) is approximated numerically, which allows us to solve for the vapor rate from stage to stage. This is done to reduce system stiffness. Decanter: The TMODS decanter contains two fluid objects: one for the light phase and one for the heavy phase. The partition coefficients (K-values) are assumed constant and independent of temperature. This allows us to use equation (12) to determine the distribution of the two liquid phases. Again, this is done to save simulation time. Heat Exchangers: Heat exchangers are calculated statically with the effectiveness method. This allows for an explicit calculation of the exit temperatures based upon the exchanger effectiveness and the inlet temperatures and heat capacities. The exchanger ef- fectiveness depends on the effective ºA, the ratio of stream heat capacities, and the exchanger config- uration. The exit temperatures are time-lagged to introduce some realistic dynamics (usually very fast compared to the overall recycle loop dynamics). 6. Conclusions In this work we have presented design details of an industrial process for the manufacture of vinyl acetate 876 M.L. LUYBEN and B.D. TYRE US monomer. The design is preliminary and has not been optimized. We have conveyed the study as if we had been assigned the task of devising a control strat- egy for this plant that is to be built. We have sum- marized the design requirements for process opera- tion and the control objectives that must be achieved for various disturbances. A brief description was also provided on the nonlinear dynamic modules in our simulation. The purpose of this paper is to offer a real- istic system that can be used by academic researchers who are interested in working on an industrially rel- evant study in the areas of design, simulation, and control. Complete models for this vinyl acetate process have been made available by Aspen Technology and Hy- protech. These models can be obtained electronically from the following web sites: (1) The application file for the vinyl acetate process can be obtained from Aspen Technology’s example library Web site: http://www.aspentec.com/tspsd/example/ example.htm Search for ‘‘Vinyl Acetate’’ to find and download the application file. (2) The case is made available at Hyprotech www.hyprotech.com on the FTP site (Papers/VinylAcetateProcess/VA – files. zip). To download the file directly, users may type the following into their Web browser: ftp: //ftp.hyprotech.com/pub/Papers/ VinylAcetateProcess/VA – files.zip Acknowledgements We want to thank Dr W.D. Smith, Jr, DuPont, for his support and help in making it possible to publish this work. Also, we are grateful to Prof. W.L. Luyben, Lehigh University, for his suggestions on the scope of the paper and his careful review of the manuscript. References Coward, H.F. and Jones, G.W. (1952) Limits of flammability of gases and vapors. Bulletin 503, Bureau of Mines. Daniels, W.E. (1989) Vinyl ester polymers. In: Encyclopedia of polymer science and engineering, 2nd ed. New York: Wiley. Vol. 17, (pp. 393—425). Downs, J.J. and Vogel, E.F. (1993) A plant-wide industrial process control problem. Computers in Chemical Engineer- ing 17, 245—255. Douglas, J.M. (1988) Conceptual design of chemical processes. New York: McGraw-Hill. Guthrie, K.M. (1969) Capital cost estimating. Chemical En- gineering 76, 114—142. Mar. 24. Luyben, M.L., Tyreus, B.D., and Luyben, W.L. (1997) Plantwide control design procedure AIChE J. 43, 3161—3174. Luyben, W.L. 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New York: Van Nostrand Reinhold. Study for the vinyl acetate monomer process 877