Design and Control of a Vapor-Phase Conventional Process and

ARTICLE pubs.acs.org/IECR

Design and Control of a Vapor-Phase Conventional Process and Reactive Distillation Process for Cumene Production Ashok S. Pathak, Sankalp Agarwal, Vivek Gera, and Nitin Kaistha* Department of Chemical Engineering, Indian Institute of Technology Kanpur, Kanpur 208016, India ABSTRACT: The economic optimum design and plantwide control of two alternative processes for cumene manufacture, a conventional process using a vapor-phase packed bed reactor and a reactive distillation (RD) process, are compared in this work. In terms of the total annualized cost (TAC), the RD process is a significant 47% cheaper than the conventional process. This is attributed to the lower capital and energy costs due to process integration. The RD process yield to desired product is also higher. Effective decentralized plantwide regulatory control structures exhibiting good load rejection characteristics are developed for the two processes. A two-point temperature inferential control structure on the RD column is found to work well. The RD process thus appears a promising alternative to the conventional process.

’ INTRODUCTION Over the past two decades, reactive distillation (RD), which combines reaction and separation in the same unit, has matured into an alternative for conventional “reaction followed by separation” processes.1-3 The technology is particularly attractive when significant reaction rates can be achieved at the tray bubble temperature and the component relative volatilities allow recycle of reactants through stripping/rectification. The process integration then yields a much more compact and significantly less expensive plant.4 On the flip side, fewer valves are available for regulating both the reaction and the separation along with pronounced nonlinear effects that may compromise control performance.5,6 Unlike conventional processes, controllability evaluation is then an integral part of the design cycle for RD technology-based processes7 where the economic process design itself may require alteration for acceptable controllability. Successful commercial applications of RD include esterification (methyl acetate,1 ethyl acetate,8 and butyl acetate9), etherification (MTBE,10 ETBE,11 and TAME12), olefin metathesis,13 and ethylene glycol.14 Sharma and Mahajani15 comprehensively review RD technology applications. RD for cumene manufacture16 is among the more industrially relevant applications of the technology, cumene being an important industrial intermediate in the production of phenolic and polycarbonate resins, epoxy, and nylon-6. It is produced by the Friedel-Crafts alkylation of benzene with propylene over acid catalyst. The cumene can further alkylate to di-isopropyl benzene (DIPB) and heavier polyisopropyl benzenes (PIPBs) as side products. Recently, plants utilizing RD technology have been commercialized by CD Tech17 as an alternative to conventional technologies where vapor- or liquid-phase alkylation occurs in a packed bed reactor. The purpose of this article is to quantitatively compare the economics and controllability of the RD process with a conventional vapor-phase alkylation process for cumene manufacture. To the best of our knowledge, a design and control study for the RD cumene process has not been performed in the open r 2011 American Chemical Society

literature. Also, a quantitative comparison of competing process technologies for cumene manufacture is missing. A recent article by Luyben18 develops a steady-state economic optimum design of a vapor-phase conventional process. The process evaluated here (described later) however differs in its use of a transalkylator to convert the PIPBs back to cumene in contrast to Luyben’s flowsheet that discards the PIPBs as a byproduct stream and does not process it further. The use of a transalkylator is standard practice in conventional cumene manufacturing process technology.17 In the following, the conventional and RD processes for cumene manufacture are briefly described. Near-optimum steady-state designs are obtained, and the two processes are compared for capital costs, energy costs, and revenue. Plantwide regulatory control structures for both processes are finally developed, and the closed loop responses to principal disturbances are compared. A summary of the findings concludes the article.

’ PROCESS DESCRIPTION Friedel-Crafts alkylation of benzene with propylene to form cumene is the most common route for industrial-scale cumene production. The main reaction is thus C6 H6 þ C3 H6 f C9 H12 ðmain reactionÞ benzene

propylene

cumene

The cumene can further alkylate to di-isopropyl benzene (DIPB) as C9 H12 þ C3 H6 f C12 H18 ðside reactionÞ cumene

propylene

DIPB

In practice, further alkylation to small amounts of heavier poly isopropyl benzenes (PIPBs) also occurs. The DIPB (and PIPBs) Received: April 1, 2010 Accepted: January 3, 2011 Revised: December 31, 2010 Published: February 09, 2011 3312

dx.doi.org/10.1021/ie100779k | Ind. Eng. Chem. Res. 2011, 50, 3312–3326

Industrial & Engineering Chemistry Research

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Figure 1. Conventional process schematic.

is converted back to cumene via transalkylation with benzene as C12 H18 þ C6 H6 < ¼ > 2C9 H12 ðtransalkylationÞ DIPB

benzene

cumene

In view of the process chemistry, an essential feature of process design and operation is the need to suppress further alkylation of cumene to side products. This feature is captured by the DIPB formation side reaction, even as the reaction chemistry is more complicated due to PIPBs. Accordingly, DIPB is considered as the only side product in this work, and the formation of PIPBs is neglected. The conventional and RD processes for continuous cumene manufacture processing fresh benzene and fresh propylene feed (with some inert propane) to produce high-purity cumene are briefly described next. Conventional Process. Conventional processes for cumene manufacture perform benzene alkylation with propylene in a vapor- or liquid-phase packed bed reactor. In this work, vaporphase alkylation is considered. Figure 1 provides a schematic of

the conventional vapor-phase process. The fresh benzene and fresh C3 (95% propylene and 5% n-propane) streams are mixed with the recycle benzene, vaporized, and preheated in a feed effluent heat exchanger (FEHE) using the hot reactor effluent before being heated to the reaction temperature in a heat exchanger that uses a high-temperature heating medium. The heated stream is fed to a cooled packed bed reactor (PBR). The PBR is a shell and tube heat exchanger with catalyst loaded tubes and pressurized hot water circulating on the shell side. The water removes reaction heat and flashes to generate steam in a steam drum. The hot reactor effluent loses sensible heat in the FEHE and is further cooled using cooling water. The cooled stream is sent to a three-column light-out-first distillation train. The inert n-propane and small amounts of unreacted propylene are recovered as vapor distillate from the first column. The bottoms is further distilled in the recycle column to recover and recycle unreacted benzene as the distillate. The recycle column bottoms is sent to the product column to recover nearly pure cumene as 3313

dx.doi.org/10.1021/ie100779k |Ind. Eng. Chem. Res. 2011, 50, 3312–3326


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Figure 2. Reactive distillation process schematic.

Table 1. Reaction Kinetics and Other Model Detailsa reaction

conventional process

RD process

C3H6 þ C6H6 f C9H12

r1 = 2.8 10 exp(-104 181/RT)CBCP

r1 = 6.981 105 exp(-63 742/RT)CB0.96CP0.87

C3H6 þ C9H12 f C12H18

r2 = 2.32 109 exp(-146 774/RT)CCCP

r2 = 4.000 104 exp(-79 162/RT)CC0.61CP0.92

C12H18 þ C6H6 a 2C9H12

rf = 2.529 10 exp(-100 000/RT)xBxD;

Keq = 6.52 10-3 exp(27 240/RT)

7

8

rb = 3.877 10

9

exp(-127 240/RT)xC2

a

CB: Benzene composition. CP: Propyelene composition. CC: Cumene composition. CD: DIPB composition. xB: Benzene mole fraction. xD: DIPB mole fraction. xC: Cumene mole fraction. Composition units: kmol 3 m-3. Reaction rate units: kmol 3 m-3 3 s-1. R: 8.316 kJ 3 kmol-1. Thermodynamic package: Peng-Robinson.

the distillate and heavy DIPB as the bottoms. The DIPB stream is mixed with a fraction of the benzene recycle stream, heated, and fed to an adiabatic transalkylation reactor where DIPB reacts with benzene to form cumene. The transalkylator effluent is fed to the recycle column for recovering the benzene and cumene. Note that the process considered here is similar to that in Turton et al.19 with the exception of the transalkylation recycle loop. Reactive Distillation Process. Figure 2 provides a schematic of the RD process for cumene production as originally reported by Shoemaker and Jones.16 Compared to the conventional process, the flowsheet is much more compact with only two units, a reactive distillation column and an ordinary distillation column. The RD column consists of a reactive section and a stripping section below it. Fresh propylene feed (with 5% inert n-propane) is fed into the lower part of the reactive section, while fresh benzene is fed immediately above the reactive zone. The heavier benzene moves down the reaction zone, while the lighter C3s move up with reaction occurring in the liquid phase. Inert n-propane along with any unreacted propylene leaves as vapor distillate. The heavy reaction products (cumene and DIPB) leave from the column bottoms with the stripping section forcing any unreacted benzene back into the reaction zone. The RD column thus integrates reaction, unreacted benzene recycle, and light ends separation into a single unit. The cumene and heavier byproducts leaving in the bottoms are separated in the product column to recover nearly pure cumene as the distillate and heavy DIPB with some cumene as the bottoms. The DIPB-rich bottoms stream is recycled to the top of the RD column reactive zone. The heavy DIPB is allowed to build in the recycle loop to a level such that the forward and backward transalkylation

reaction rates balance each other with no net DIPB formation. The DIPB side product is thus recycled to extinction.

’ STEADY-STATE ECONOMIC DESIGN OPTIMIZATION Steady-state models for the two processes are built using a commercial process simulator. Unisim Design is used to simulate the conventional process, while Aspen Plus is used to simulate the RD process. In our experience, the RD solver in Aspen Plus is much more robust compared to Unisim. The reaction kinetics for the conventional process main reactor are taken from Turton et al.,19 while reasonable transalkylation reaction kinetics are inferred from literature reports20-22 with the reverse reaction kinetic parameters adjusted to match the equilibrium constant reported in Lei et al.22 In the RD process, the alkylation reactions are modeled as kinetic reactions and the transalkylation reaction is assumed to reach equilibrium on the reactive trays. The reaction kinetics and transalkylation equilibrium constant expression are taken from Lei et al.22 The Peng-Robinson equation of state is used to model the thermodynamic properties (vapor-liquid equilibrium, enthalpy etc). Table 1 summarizes the reaction kinetic and other model parameters used in this work. Near economic optimum steady-state designs are obtained for the two processes as follows. Conventional Process Design. The conventional process is to be designed to process 105.26 kmol/h of fresh C3 feed that is 95 mol % propylene. The fresh propylene component flow rate is thus 100 kmol/h. For good flowsheet convergence properties, the total (recycle plus fresh) benzene flow is specified. The design suggested by Turton et al.,19 from where the kinetic expression for 3314


Industrial & Engineering Chemistry Research the main reactions has been taken, is a good starting point for seeking a more economical design. Douglas23 points out that even as there are several design variables in any process, only a few are dominant with a significant impact on the overall plant economics. The plantwide economic optimization problem is thus significantly simplified by optimizing only the dominant design variables and using heuristic “local” design rules for the others. The flowsheet structure dictates that the reactor should be designed for nearly complete propylene conversion as the unreacted propylene is not recovered and lost as fuel gas. The single-pass propylene conversion is then directly proportional to the cumene production rate. For a given reactor feed and inlet temperature, complete propylene conversion requires an infinitely long PBR. A slight decrease in the propylene conversion causes a dramatic reduction in the reactor size (and cost) at the expense of a slight reduction in cumene production rate. There thus exists a reactor size versus production rate trade off for the process. The reactor inlet temperature is a dominant design variable with a higher temperature, resulting in higher per-pass conversion but more DIPB formation. A smaller size reactor may be used for a given conversion so that the reactor cost reduces; however, the transalkylation cost goes up, implying an economic trade off. The total benzene fed to the main reactor is another important design variable with higher feed rates, implying a greater benzene excess inside the reactor suppressing DIPB formation at the expense of higher benzene recycle (and associated cost). The reactor operating pressure may also be considered an important design variable. However, industrial practice typically favors reactor operation at maximum pressure for maximum reaction rates so that the reactor operating pressure is fixed at 25 atm as suggested in Turton et al.19 and not optimized. The number of reactor tubes is set at 1500, and the tube inner diameter is taken as 3 in. The high reactor operating pressure also allows fuel gas column operation at a higher pressure to mitigate the loss of precious benzene in the first column vent. In the separation train, the column operating pressure of the recycle and product columns is chosen to be slightly above atmospheric at 1.5 atm. The low pressure gives the greatest driving force for mass transfer for reduced energy consumption. The pressure of the first column is chosen to be 15 atm to suppress the loss of precious benzene. The 10 atm pressure difference between the reactor and the first column gives sufficient head for the cooled material to flow into the first column without a pump. Some benzene is lost in the column vapor vent for a reasonable condenser temperature that allows cooling water to be used as the cooling medium. This loss is adjusted for a condenser temperature of ∼50 °C. The number of trays in each of the columns is chosen to be 3 times the minimum trays from the Fenske equation with the relative volatility of the key components being calculated at the feed conditions. The light key component recovery in the bottoms and heavy key component recovery in the distillate is set at 0.1% for the calculation. Once the number of trays in the columns is fixed, the feed tray location of the final design is adjusted to minimize reboiler duty consumption. The column diameters are obtained using Fair’s method-based tray sizing utilities in the respective simulators. The flow rate of the product column bottom DIPB stream is low giving a small transalkylator reactor which makes only a minor contribution to the capital cost. A heursictic approach is therefore used to design it. The maximum reactor inlet temperature should not exceed 240 °C due to the possibility of cumene dealkylation. The single-pass reactor conversion is limited by the equilibrium conversion. The benzene to DIPB excess ratio, the reactor inlet operating temperature, and cumene composition determine the

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Figure 3. Transalkylation reaction equilibrium conversion variation with benzene to DIPB ratio and temperature.

same. Figure 3 shows the variation in the equilibrium conversion with respect to the benzene to DIPB excess ratio for no inlet cumene and reactor inlet temperatures of 200, 220, and 240 °C. The equilibrium conversion tends to flatten out beyond an excess ratio of 2, so that increasing it further only increases the cost associated with recirculating more benzene in the transalkylation loop without a commensurate equilibrium conversion benefit. Accordingly the transalkylator feed benzene to DIPB excess ratio is fixed at 2. To prevent the reactor size from blowing up, its singlepass conversion is fixed at 75%, which is sufficiently below the equilibrium conversion (>90%). The transalkylator inlet temperature is fixed at 240 °C for the smallest possible reactor size and associated capital cost. The main reactor length (or volume), feed inlet temperature, and total benzene feed rate are then the three design variables adjusted for economic optimization. For a given fresh propylene feed rate (105.26 kmol/h corresponding to 100 kmol/h of propylene), these design variables are optimized to minimize the economic objective function J defined as J ¼ total annualized cost - revenue where the total annualized cost (TAC) is given by TAC ¼ capital cost=3 þ operating costs and the revenue is revenue ¼ product sale - raw material cost The revenue term is added to the objective function to account for production loss due to unreacted propylene loss as fuel gas. The price data and cost correlations used here are summarized in Table 2. The main reaction is highly exothermic, and a hot spot occurs in the PBR. To avoid irreversible catalyst activity loss due to coke deposition, etc., the hot-spot temperature is constrained to not exceed a maximum limit of 400 °C. The optimum values of the design variables are obtained using the fmincon optimization subroutine in Matlab with Unisim as the background flowsheet solver. At the optimum solution, the reactor inlet temperature is 342.8 °C, the total benzene flow rate is 157.5 kmol/h, and the reactor length is 7.164 m (volume 47.5 m3). Of the three design variables, only two are independent 3315



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Table 2. Equipment Sizing, Cost Correlations, and Unit Price Dataa tower sizing and costing

diameter

tray sizing utility (Fair’s method)

height

ordinary trays with 2 ft spacing reactive trays with 4 ft spacing 20% extra height for sump

condenser sizing and costing

reboiler, preheater

$17 640(D)1.066(L)0.802 (D,L in m) 0.852 kW/(K 3 m2)

capital cost heat transfer coefficient differential temperature

13.9 °C

capital cost

$7296 (area)0.65

heat transfer coefficient

0.568 kW/(K 3 m2)

differential temperature

30.0 °C

capital cost

$7296 (area)0.65

FEHE

heat transfer coefficient

0.065 kW/(K 3 m2)

reactor costing

capital cost catalyst costb

$7296 (area)0.65 $10 kg-1

bulk density

1000 kg/m3

pump

porosity

0.5

capital cost

$Cp(1.8 þ 1.51Fp2.4) log(CP) = 3.5793 þ 0.3208 log(P) þ 0.0285 log(P)2 Fp = 0.1682 þ 0.3466 log(Q) þ 0.4841 log(Q)2 outlet pressure (P) in barg, duty (Q) in kW

raw material

utilities

propylene (5% impure) benzene

$9 kmol-1 $25 kmol-1

cumene product

$65 kmol-1

steam

$9.83 GJ-1

cooling water

$0.16 GJ-1

electricity or high-temperature heating medium

$16.8 GJ-1

steam credit

$6.67 GJ-1 (from PBR) $4.83 GJ-1 (from HX2)

a

18

Taken from Luyben and Turton et al.

19 b

2

Catalyst price included in capital cost. All areas in m .

Figure 4. Variation in economic criterion for a conventional process with the main reactor length at different reactor inlet temperatures.

near the optimum with the third one being adjusted to satisfy the active hot-spot temperature constraint. To better understand the design trade offs, consider the reactor inlet temperature and reactor length as the two independent variables with the total benzene reactor feed being adjusted for a reactor hot-spot temperature of 400 °C. Figure 4 plots the variation in J with reactor length for different reactor inlet

temperatures. The minimum in the curve for each reactor inlet temperature is due to the reactor cost versus cumene production trade off described earlier. As the temperature is increased above the optimum value, the minimum in the corresponding cost curve moves up as the total benzene flow to reactor must be increased to maintain the hot-spot temperature at its maximum limit. This is accomplished by a higher benzene recycle flow, and the capital/energy cost of all equipment in the benzene recycle loop increases. Upon decreasing the reactor inlet temperature below its optimum value, even as the benzene recycle cost goes down, the hot-spot constraint becomes inactive and the propylene conversion decreases due to the reduced temperature, reducing the cumene production rate. This is clearly illustrated in Figure 5, which plots the variation in propylene conversion and total benzene flow to the main reactor with reactor inlet temperature. The slight dip in the conversion at higher temperatures is attributed to the dilution effect at higher total benzene flow. The optimized process design thus balances the reactor cost, cumene production loss penalty, and benzene recycle cost. The salient design and operating conditions for the conventional cumene process are noted in the process flowsheet in Figure 1. Reactive Distillation Process. As with the conventional process, the RD cumene process is designed to process 105.26 kmol/h of C3 feed (100 kmol/h propylene). The process design requires optimizing the design variables for the two columns including the steady-state specifications (two for each column, excluding P). The operating pressure of the RD column is arguably the most crucial design variable. A higher pressure 3316



Figure 5. Variation in propylene conversion and total benzene feed to reactor with reactor inlet temperature (conventional process).

results in a higher reactive zone temperature due to the increase in reactive tray bubble point temperature giving higher reaction rates. The total catalyst requirement then goes down. Also, for a reasonable water-cooled condenser temperature (∼50 °C), the loss in precious benzene in the distillate vent reduces as the pressure is increased. On the flip side, increasing the operating pressure reduces the benzene-cumene relative volatility so that the reboiler duty must increase to maintain the benzene leakage down the RD column bottoms for on-specification product cumene purity. Also, the DIPB formation rate goes up (higher reaction temperature). Since raw materials and products are much more expensive than energy, minimizing benzene loss is likely to be the dominant effect in the optimization (Douglas’s doctrine).23 The RD column should therefore be operated at as high a pressure as possible. The use of high-pressure steam as a cheap heat source however imposes a maximum limit on the RD column pressure. Assume a 30 °C reboiler temperature driving force so that the process fluid temperature is 225 °C (highpressure steam at 255 °C). The process fluid in the reboiler is essentially a cumene-DIPB mixture (negligible benzene). The pure DIPB boiling pressure at 225 °C is 4.66 atm, which reduces to 4 atm for 20 mol % DIPB. An RD column operating pressure of 4 atm thus appears reasonable, allowing for sufficient (up to 20%) DIPB build-up to recycle it to extinction without compromising the reboiler temperature driving force. After fixing the RD column operating pressure at 4 atm, the number of stripping trays is fixed at 10 for sufficient fractionation capacity to prevent benzene leakage down the bottoms which would necessarily contaminate the cumene product. The location of the two fresh feeds must be chosen for achieving high reactant composition in the reactive zone so that all of the loaded catalyst is utilized to the fullest extent. Since benzene is significantly heavier than the C3s, it would flow down the column and should therefore be fed immediately above the reactive zone as a liquid. The C3s being the lightest would tend to move up the column so that the C3 stream should be fed toward the bottom of the reactive zone for proper catalyst utilization. Since at 25 °C and 4 atm (column pressure) the C3 feed is about 75% liquid, which would flow down, it is fed immediately above the lowest reactive tray. A C3 feed location immediately below the reactive zone is suboptimal with the reboiler duty increasing similar to an ordinary distillation column with a lower down light feed location.

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The fresh benzene feed flow rate is chosen as 100 kmol/h to exactly match the fresh propylene flow rate as dictated by the stoichiometry of the main reaction. The choice is appropriate as any excess is either lost in the RD distillate vent stream or in the bottoms stream contaminating the product. Also, reducing the benzene feed would imply a loss in the excess propylene, again a precious raw material. As in the conventional process, the operating pressure of the product column is chosen to be slightly above atmospheric at 1.5 atm and the number of trays is set to 3 times the minimum trays from the Fenske equation. The remaining design variables for the process are the four steady-state specifications for the two columns (two for each column) and the reactive tray hold up, which are continuous variables, along with the discrete design variables, namely, the number of reactive trays and the product column feed tray location. The two steady-state specification variables for the RD column are chosen as the reflux rate and the distillate rate. The distillate rate should be chosen slightly above the inert propane flow rate entering with the C3 feed to allow it an exit route along with any unreacted propylene and small amounts of benzene (for a reasonable condenser temperature). In the product column, the reflux ratio and the bottoms rate are chosen as the specification variables. The latter directly sets the DIPB recycle stream rate for fast and reliable recycle tear convergence. As an initial guess, the feed to the product column is fed on Tray 13 (total 17 trays) for a long rectification section (about twothirds of the column), providing enough fractionation capacity to prevent DIPB leakage in the distillate product stream. An initial converged flowsheet is first obtained for 5 reactive trays and a large reactive tray hold-up (for sufficient reaction capacity) by manually adjusting the four column specifications. In particular, the bottoms flow specification for the product column (DIPB recycle) is adjusted so that negligible DIPB is lost with the cumene product, and the RD column distillate vent specification is adjusted to maintain a particular vent benzene mole fraction (0.09 at 4 atm operating pressure) for a condenser temperature of about 50 °C. The built-in Aspen Plus optimizer is then used to minimize the total reboiler duty with the four column specifications and the reactive tray holdup as the design variables. Equality constraints for 99.9 mol % product purity and the vent benzene mole fraction in the RD column overhead vapor distillate stream are imposed in the optimization. To better understand the dominant effect of RD column operating pressure on the process economics, Table 3 reports the total reboiler duty, the total catalyst loading, and the vent benzene loss of RD process designs with the four column specifications and the catalyst loading optimized as described above at RD column operating pressures between 2 and 4 atm. The total number of reactive trays is kept fixed at 5. The TAC, revenue, and economic criterion J of the designs is also reported in the table. As expected, the catalyst loading and benzene loss decrease with pressure while the total reboiler duty increases. Notice the increase in the revenue as pressure is increased due to reduced benzene loss in the RD column vent. The increased revenue causes the economic criterion for the 4 atm RD column operating pressure design to be the best, verifying Douglas’s doctrine. The 4 atm RD column operating pressure design obtained above has a hold up per reactive tray of about 3.4 m3. The stripping section RD column diameter using the tray sizing utility is approximately 1.6 m. For a catalyst density of 1000 kg/m3, assuming a spacing of 4 ft between two reactive trays with a catalyst loading height of 2 ft (2 ft free space between two reactive 3317



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Table 3. Variation in Process and Economic Parameters with RD Column Pressure RD column pressure (atm) f process performance parameters

economic performance

2

3

4

benzene loss (kmol h-1)

1.346

0.810

0.55

catalyst ($106)

2.8371

1.1120

0.683

QTotal (MW)

2.921

2.929

3.463

TAC ($106 yr-1)

2.1529

1.5776

1.6007

revenue ($106 yr-1)

21.3474

21.6001

21.7218

-J ($106 yr-1)

19.1945

20.0225

20.1211

Figure 6. Optimized RD column details. (a) Design and operating parameters. (b) Temperature profile. (c) Composition profile.

trays), accommodating 3400 kg of catalyst on a reactive tray would require a reactive zone diameter of about 2.7 m3. For a practical RD tower with a single-diameter cross-section across all its height, the design is further refined by incrementally increasing the number of reactive trays and reoptimizing the four column specifications and the reactive holdup per tray until the reactive zone diameter calculated as above and the stripping section diameter are reasonably close. For this design, there are a total of 11 reactive trays with a catalyst loading of 1275 kg per reactive tray (14 ton total catalyst) and the RD column diameter is 1.66 m. This design is considered the final near optimum design. Its salient conditions are shown in Figure 2. The RD column is separately shown in Figure 6 along with the temperature and composition profiles. Economic Comparison. The capital/energy cost and equipment size details of the major equipment in the optimized design of

the conventional process are provided in Table 4. The catalyst purchase is assumed to be a one-time investment and therefore treated as a capital cost. For convenience, the conventional process is partitioned into the reaction section, the separation section, and a miscellaneous section as in the table for convenience. The TAC of the conventional process is $2.8610 106 yr-1 with the three sections contributing, respectively, about 54%, 41%, and 5% to the TAC. The main reactor capital cost (including catalyst) contribution to the TAC is more than one-third at $1.0293 106 yr-1 and is by far the most significant one by a single piece of equipment. It is therefore not surprising that the reactor size and operating conditions (inlet temperature and total benzene flow) turn out to be the dominant design variables for the process. The total energy cost contribution to the TAC is about 40% at $1.1404 106 yr-1. The reaction section, separation section, 3318



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Table 4. Cost and Size Details of Optimized Conventional Process Designa capital cost, $106

equipment size

energy, kW

energy cost,

total capital

total energy cost,

$106 yr-1

cost, $106

$106 yr-1

0.2605

0.2718

0.4936

0.1579

0.4601

0.3438

1.2142

0.7735

separation section fuel gas recovery column

recycle column

product column

height

10.97 m

0.1291

diameter

1.067 m

reboiler

53.89 m2

0.0974

1065.19

0.2713

condenser

10.71 m2

0.0341

126.85

0.0005

height

16.82 m

0.2377

diameter

1.372 m

reboiler condenser

29.91 m2 150.1 m2

0.0664 0.1895

height

14.63 m

0.1874

diameter

1.219 m

reboiler

67.15 m2

0.1124

1327.29

0.3381

condenser

116.1 m2

0.1605

1374.378

0.0057

591.2 1777.35

0.1506 0.0074

total reaction section reactor1

volume area

47.474 m3 2532 m2

catalyst

weight

47.45 tons

1.8980

vaporizer

area

137.7 m2

FEHE

1.1900

(-)2721.41

(-)0.4705

0.1792

2722.42

0.6937

1.1900

(-)0.4705 1.8980 0.1792

0.6937

area

78.52 m2

0.1244

500.27

2

HX1

area

48.54 m2

0.0910

959.49

0.4178

0.0910

0.4178

HX23

area

121.1 m2

0.1649

(-)2394.09

(-)0.2997

0.1649

(-)0.2997

3.6475

0.3413

0.0110 0.2577

0.0095 0.0158

0.1244

total miscellaneous HX3 pump

area

1.891 m2

0.0110 0.2577

trans reactor

volume

0.7069 m3

0.0023

area

37.70 m2

weight

0.707 tons

catalyst

37.38 36.26

0.0095 0.0158

0.0023

0.0283

0.0283

total grand total

steam cooling water electricity high-temperature heating medium

627.95

0.6932

3278.59

0.0136

36.26 959.49

0.0158 0.4178

TAC a

-1

-1

-1

-1.

Steam cost: $9.83 GJ . Cooling water cost: $0.16 GJ . Electricity cost: $16.8 GJ . (1) Steam credit: $6.67 GJ medium cost: $16.8 GJ-1. (3) Steam credit: $4.83 GJ-1.

and miscellaneous energy cost contributions are, respectively, about 30%, 68%, and 2%. Expectedly, the separation energy cost is the most significant contributor. The reaction section energy cost is much lower due to the recovery of reaction heat as steam, preheating of the cold feed with the hot reactor effluent in a process-to-process feed effluent heat exchanger, and steam generation in the effluent cooler. The optimized RD process equipment size and capital/energy cost details are provided in Table 5. The TAC for the process is $1.5025 106 yr-1, which is about 47% lower than the conventional process. The RD process thus costs almost half the conventional process. The TAC contribution of the RD column (including catalyst), the product column, and pumping costs as indicated in the table is, respectivel,y about 66%, 31%, and 3%. The RD column (including catalyst) is the most expensive piece

0.2993

0.0253

5.1607

1.1404

$2.8610 106 yr-1

(2) High-temperature heating

of equipment (capital cost $1.4194 106) in the process, constituting about 70% of the total capital investment. The energy cost contribution to the TAC is a substantial 55% at $0.8338 106 yr-1. Compared to the conventional process, the RD process energy cost is about 27% lower, which is significant. The propylene feed rate to both processes is the same. The cumene production rates are however different at 98.88 and 99.46 kmol/h for the conventional and RD processes, respectively. The yield to desired product (selectivity) of the optimized conventional process is thus lower. One can increase the cumene production rate to exactly match the RD process production rate by increasing the reactor length to reduce the unreacted propylene loss. A design degree of freedom is then lost with the main reactor propylene conversion (or size) being adjusted for the desired cumene production rate. The 3319



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Table 5. Cost Details of the Optimized Reactive Distillation Processa capital cost, $106

size

energy, kW

energy cost,

total capital

total energy

$106 yr-1

cost, $106

cost, $106 yr-1

reactive distillation reactive distillation column

catalyst

height

23.04 m

diameter

1.657 m

0.3741

0.8584

reboiler

174.17 m2

0.2088

1978.60

0.5041

condenser

266.79 m2

0.2755

3159.49

0.0131

weight

14.03 tons

0.5610

0.5172

0.5610

total

1.4194

0.5172

0.4669

0.3096

product recovery product column

height

12.44 m

diameter

1.312 m

0.1778

reboiler

60.07 m2

0.1045

1187.42

0.3025

condenser

143.97 m2

0.1845

1704.99

0.0071

miscellaneous pump

0.1120

grand total

16

0.007

0.1120

0.007

steam

3166.02

0.8066

2.006

0.8338

cooling water

4864.48

0.0202

16

0.007

electricity

$1.5025 106 yr-1

TAC a

-1

-1

-1

Steam cost: $9.83 GJ . Cooling water cost: $0.16 GJ . Electricity cost: $16.8 GJ .

Table 6. Process and Economic Performance Comparison between the Conventional and the RD Process conventional process parameter product and raw material

optimum -1

product cumene (kmol 3 h ) cumene purity (mol fraction)

98.88 0.9990

fresh C3 (kmol 3 h-1)

economic performance

a

99.46 0.9990

RD Process 99.46 0.9990

105.26

105.26

105.26

98.94

99.52

100.0

yielda

0.9888

0.9994

0.9946

kg steam/ton cumene

95.07

99.76

476.66

kWh electricity/ton cumene

3.05

3.11

1.338

kWh high-temp. heating/ton cumene

80.71

80.78

0

revenue ($)/ton cumene energy cost ($)/ton cumene

252.88 13.32

253.33 13.46

252.39 9.69

fresh benzene (kmol 3 h-1)

process performance

alternative

capital cost ($106 yr-1)

5.1607

5.7504

2.006

TAC ($106 yr-1)

2.8610

3.0761

1.5025

-J ($106 yr-1)

18.7855

18.7367

20.2240

On the basis of propylene.

remaining two design variables may then be adjusted to minimize the TAC. The key process/economic performance metrics of such an alternative design and the optimum conventional process design are compared with those of the final RD process design in Table 6. As expected, the RD process is significantly cheaper than both the conventional process designs in terms of the TAC. Specifically, its TAC is $1.3585 106 and $1.5736 106 yr-1 lower than, respectively, the optimum and alternative conventional process designs due to the substantially lower capital and energy costs, a consequence of the process integration. The economic criterion, -J, for the RD process is $1.4385 106 and 1.4873 106 yr-1 more

than the optimal and alternative process designs, amounting to a non-negligible improvement in the yearly plant cash flow. Even as the yearly energy cost of the RD process is lower, the steam consumption (including steam credit) is approximately five times the conventional process. The RD process however scores in not requiring a hightemperature heating source (or alternatively an expensive furnace) and lower pumping costs (electricity).

’ REGULATORY PLANTWIDE CONTROL SYSTEM To compare the operability of the two processes, decentralized plantwide regulatory control structures are synthesized and their 3320



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Figure 7. Conventional process plantwide control structure.

closed loop dynamic response to load disturbances compared. Salient features of control structure applied to each process, its tuning, and closed loop dynamic response results obtained are described next. Control Structures. Figure 7 shows the regulatory control structure for the conventional process. Auctioneering control is used to maintain the main reactor hot-spot temperature by manipulating the steam drum pressure set point. In the simulation, this is emulated by the temperature controller adjusting the coolant inlet temperature with a 2 min lag on the controller output to account for cooling circuit dynamics. As in practice, the coolant circulation rate is set to a high value so that the reactor shell side temperature does not show an appreciable change (99.9 mol %). The reboiler duty maintains a sensitive stripping tray (Tray 14) temperature. The reflux is maintained in ratio with the feed with the ratio set point being adjusted to maintain another sensitive tray temperature (Tray 10) in the stripping section. Controlling two tray temperatures in the stripping section mitigates variation in the benzene leakage down the bottoms for tight cumene product purity control. In the product column, the bottoms rate is very small due to low DIPB formation so that it cannot be used for bottom sump level control. Accordingly, the reboiler duty is adjusted to maintain the 3321



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Figure 8. Reactive distillation process plantwide control structure.

sump level. The material balance for this column is highly skewed with more than 97% of the feed being recovered as distillate and the remaining as bottoms. The DIPB-cumene separation is an easy one, and loose purity regulation of the bottoms stream is acceptable as it is recycled through the transalkylator. The very simple L/F-B control structure is therefore implemented where the reflux is maintained in ratio with the feed and the bottoms is flow controlled. The feed to reflux ratio is implemented for feedforward compensation of the reflux rate to mitigate the product purity deviation for a throughput change. The ratio set point may be adjusted to maintain the product purity, which would usually be available from an online analyzer or a laborious laboratory analysis protocol. The bottoms flow set point is fixed slightly above the maximum expected DIPB rate to prevent DIPB from accumulating inside the column. The benzene flow to the transalkylator is flow controlled, and its set point is set at twice the bottoms flow set point to always maintain a large benzene excess. With this arrangement, the bottoms DIPB recycle stream cumene composition floats and regulates itself. Of the two fresh feeds, the C3 (limiting reactant) feed rate is flow controlled and its set point acts as the throughput manipulator to effect a change in the production rate. The fresh benzene feed rate is adjusted to maintain the total benzene flow to the reactor. It is thus fed as a makeup stream. The arrangement prevents a slow benzene build up/depletion in the main recycle loop and ensures stoichiometric balancing of the fresh feeds. Figure 8 shows the regulatory plantwide control structure for the RD cumene process. In the RD column, the reflux drum level is maintained by adjusting the reflux rate as the column operates at total liquid reflux. The column pressure is maintained using the vent rate with the condenser duty being adjusted to hold the condenser temperature. The bottom sump level is controlled using the bottoms. The reboiler duty maintains a sensitive stripping tray temperature (Tray 14) to prevent unreacted benzene from dropping down the column. One of the fresh feeds can be used as

Table 7. Controller Tuning Parametersa reset time

derivative

(min)

time (min)

set point, °C

controller

gain

TC3

0.25

20.0

TC4

0.5

8.0

TC5

0.2

40.0

116.9

TC6

0.3

15.0

168.3

TC1

0.16

15.8

200.6

TC2

0.52

5.5

149.3

TC3

0.85

7.92

190.9

conventional process 4

400 227

RD process

a

All level controllers are P only with gain 2. Temperature sensor span 50 °C.

the throughput manipulator with the other being adjusted to hold an appropriate reactive tray temperature for maintaining stoichiometric feed balance. We found the tray temperature response to a change in the C3 feed to be much more well behaved than a change in the benzene feed rate. Accordingly, the C3 feed is used for tray temperature control, and the fresh benzene flow set point acts as the throughput manipulator. From sensitivity analysis, reactive Tray 9 was found to be the most appropriate with a reasonable sensitivity to the C3 feed and an acceptable Niederlinski Index (∼0.4). The RD process product column material balance is relatively much less skewed than its counterpart in the conventional process with ∼20% of the feed dropping down the bottoms. The much lower reboil ratio (

Design and Control of a Vapor-Phase Conventional Process and

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