Production of Benzyl Chloride - ACS Publications - American

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Optimum Design and Analysis Based on Independent Reaction Amount for Distillation Column with Side Reactors: Production of Benzyl Chloride Lianghui Ding, Jihai Tang, Mifen Cui, Cuimei Bo, Xian Chen, and Xu Qiao* State Key Laboratory of Materials-Oriented Chemical Engineering, College of Chemistry and Chemical Engineering, Nanjing University of Technology, Nanjing 210009, Jiangsu, China ABSTRACT: Distillation columns with side reactors (SRCs) can be effectively employed to improve selectivity by manipulating the composition profiles of reactants and products inside the reaction zone. However, for the complex interaction between reaction and separation, it is difficult to simulate and optimize a SRC process. An independent reaction amount is introduced in simulating the SRC process to decouple the reaction kinetics from the mathematic models. Based on the concept of independent reaction amount, a systematic design approach, employing the Powell method, is developed to seek the internal synergistic effects between reaction and separation. The proposed optimum design methodology is demonstrated in a case study of benzyl chloride production. The effects of the design parameters, such as the number of separation stages, the stages between each reactor and the number of reactors on the process performance, are well-investigated. In addition, the effect of vapor boilup rate on the reaction capability is studied. Results demonstrate that, for the given vapor boilup rate, insufficient separation leads to a poor system performance, while excessive stages or reactors will not be beneficial toward improving reaction capability. Besides, by increasing the vapor boilup rate, the system performance can be improved obviously. The optimum configuration and the optimum match between separation and reaction can be achieved through the design approach.

1. INTRODUCTION Reactive distillation (RD), combining reaction and separation in a single unit, has proven its advantages, such as improved selectivity, increased conversion, and potential reduction in investment and operating costs.1 However, RD is not effective in many chemical systems, because of process conditions mismatch (for example, the optimum conditions of temperature and pressure for distillation may be far from optimal for reaction, and vice versa). In addition, RD may suffer from maintenance/design problems, such as catalyst deactivation/replacement and equipment design.2 One way to overcome these problems of RD columns, while maintaining the benefits of in situ separation with reaction, is to employ the side reactor or external reactor concept, that is, so-called a nonreactive distillation column coupled with side reactors (SRC).3,4 External side reactors are used as a substitute for reactive trays. The synergistic effects between reaction and separation lead to shift in the chemical equilibrium or preventing the side reactions, as a result of products being removed and distillation limits being exceeded because of the reaction, while, on the other hand, it is precisely these synergies that make the RD/SRC process so extraordinarily complex.2 As a result, the full potentials cannot be simply achieved, because of the complex interaction between reaction and separation.5 For example, the reflux ratio plays an important role in the reaction and separation phenomenon. For the synthesis of methyl acetate, poor reflux ratio or excessive reflux ratio that has a significant distillation effect leads to a lower conversion and produces an increase in the capital investment and energy consumption.6,7 Thus, to exploit the full advantages of the RD/SRC processes, research about synthesis and design has been performed to combine reaction and separation effectively.8,9 r 2011 American Chemical Society

Designing an optimal process requires significant effort and is a nontrivial task, especially for integrated reaction/separation process. In recent years, the significant progress in the field of optimization has contributed largely to aid the RD/SRC process design. Ciric and Gu proposed a mixed-integer nonlinear program (MINLP) technique to optimize the RD column, which was solved by a generalized Benders decomposition algorithm.10 This method was expanded upon by Cardoso, Salcedo, Azevedo, and Barbosa, by applying a simulated annealing-based MINLP algorithm.11 More recently, Gangadwala and Kienle applied the commercial optimization tool GAMS to solve the MINLP optimization for a butyl acetate RD column including side reactors.12 In addition, the sequential design approach is used where the variables are changed one at a time, to minimize the design objective.9,13,14 Technological improvement in the design has served to build a sufficient confidence in the optimization of RD/SRC to find the global solution.15,16 However, the key point is that the difficulty of solving the very large set of nonlinear and algebraic equations of the RD/ SRC process still exists, because of the complex interaction between reaction kinetics and phase equilibrium, which may even terminate the optimization. On the other hand, since most of the studies in the past have targeted equilibrium-controlled reactions in a RD column, system performance for consecutive reactions is rarely discussed in the RD/SRC process. In this study, the independent reaction amount given in the reaction term, which has determined the reaction rate of each Received: October 26, 2010 Accepted: August 19, 2011 Revised: August 11, 2011 Published: August 19, 2011 11143

dx.doi.org/10.1021/ie102171r | Ind. Eng. Chem. Res. 2011, 50, 11143–11152

Industrial & Engineering Chemistry Research

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component while given by the reaction kinetics and reactive capacity in a traditional way, is innovatively introduced to model the SRC process. Furthermore, an alternative optimum design approach is set up to search for the optimum match between reaction and separation. Benzyl chloride production is chosen as a typical consecutive reaction, to illustrate this optimization procedure.

2. PROCESS DESCRIPTION Benzyl chloride is produced from the reaction of toluene and chlorine. However, the prepared benzyl chloride can further react with chlorine to produce the unwanted byproduct benzal chloride. The reactions are

Figure 1. Schematic of a distillation column coupled with side reactors (SRC).

The reactions are assumed to be elementary and the kinetics are given by the following equations: R1 ¼ k1 A and R2 ¼ k2 B where A and B are the mole fractions of toluene and benzyl chloride, respectively, and k1 and k2 are the respective first-order reaction rate constants.17 The ratio of rate constants k1/k2 is ∼6.1 at a reaction temperature of 100 °C.17 The conversion is defined as the number of moles of reactant chlorine consumed per mole of reactant chlorine fed, and the selectivity is defined as the number of moles of reactant toluene used in forming the desired product benzyl chloride, relative to the total number of moles of toluene reacted. The selectivity parameter is defined as the ratio of rates of the desired reaction to the undesired reaction, and, in the present case, it is given by (k1A k2B)/(k2B). A relatively higher selectivity parameter can be obtained by maintaining a high concentration of toluene and a low concentration of benzyl chlorine in the reactors. Thus, it is preferable to perform the reactions in the integrated reaction and separation technology, because of the large difference in volatility between the heavier products and the lighter reactant. The configuration of a distillation column coupled with side reactors for benzyl chloride production is displayed in Figure 1. The lighter toluene moves toward the top and the heavier benzyl chloride and benzal chloride move to the bottom products, which results in two different zones in the column: a reaction zone and a separation zone. Several stages in the reaction zone are linked with side reactors. The entire liquid stream leaving the special stage is completely rerouted through a reactor before it is fed back to the stage below. In addition, the column takes the toluene overhead through a reactor for recycle. The continuous chlorine with a certain proportion is introduced to the reactors, while fresh reactant toluene is given to the reactor connected with

the top condenser. The hydrogen chloride prepared in the reactions will escape from the condenser in the column. No reaction occurs anywhere in the column: reaction only occurs in the external side reactors. With continuous removal of the desired product benzyl chloride from the reaction zone, a higher selectivity may be reached.

3. MATHEMATIC MODELS AND SIMULATION 3.1. Reactor Equations. The modeling approaches based on the equilibrium stage model are capable of predicting the complex phenomenon in a traditional RD column. The equations that model equilibrium stages, which are known as the MESH equations, are derived from the mass and energy balances, as well as equilibrium and summation relations. In the material balance equations, the reaction term on the reactive tray is given by the reaction holdup with the reaction kinetics, which is a nonlinear function of the temperature and concentration. 2 The combination of reaction and separation in a single unit brings about the complex interaction between the phase equilibrium and reaction kinetics, which may produce convergence problems. Here, the reactors in the SRC process have the special function decoupling the complex in situ interaction between reaction and separation, as compared to a traditional RD column, so the operation conditions for reaction and separation can be set at their optimum values. Thus, the capacity of the reactor can be assumed large enough to promise that chlorine could be consumed completely. The given feed flow rates of chlorine to the reactors are defined as the independent reaction amount. Note that the independent reaction amount is a vector with the length equal to the number of reactors. Each reactor was assumed to be a perfectly adiabatic mixed stirred tank reactor, and, in a continuous-chlorination reaction system, the following material balance equations can be 11144

dx.doi.org/10.1021/ie102171r |Ind. Eng. Chem. Res. 2011, 50, 11143–11152


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found:

y ðA0 AÞFR ¼ V 0 k1 A ¼ FCl2 x þ 2

ð3Þ

ðB B0 ÞFR ¼ V 0 ðk1 A k2 BÞ ¼ FCl2 x

ð4Þ

ðC C0 ÞFR ¼ V 0 k2 B ¼ FCl2

y 2

ð5Þ

where A, B, and C are the mole fractions of toluene, benzyl chloride, and benzal chloride at the reactor exit, and A0, B0, and C0 are the mole fractions of toluene, benzyl chloride, and benzal chloride at the reactor inlet. FR is the liquid flow rate fed to the reactor containing abundant reactant toluene; V0 represents the reaction volume (which is assumed to be sufficiently large); FCl2 is the feed flow rate of chlorine; and x and y are the mole fractions of chlorine used to form benzyl chloride and benzal chloride, respectively. The right-hand sides of eqs 35 represent the absolute reaction extents of toluene, benzyl chloride, and benzal chloride. Dividing eq 5 by eq 4, and introducing the rate-constants ratio (k1/k2 = ω) then gives B B0 k1 A k2 B ωA B 2x ¼ ¼ ¼ k2 B B y C C0

ð6Þ

Figure 2. Schematic of the equilibrium stage j: (a) Ij = 0 and (b) Ij = 1.

leaving the reactor for the column with their corresponding compositions, are achieved through a standard adiabatic flash calculation with known values of FR, A, B, and C. 3.2. Column Equations. The distillation column can be modeled just as a simple column with several side streams. The activity coefficients of the liquid phase are calculated using the Wilson model. The required thermodynamic data for phase equilibrium in this system are given in Appendix A. Note that the hydrogen chloride contributes its partial pressure to the total value and takes part in the energy balance, but it has no effect on the vaporliquid equilibrium. A schematic diagram of an equilibrium stage is shown in Figure 2. The equations that model equilibrium stages, which are known as the MESH equations, are shown as follows:

where ω = 6.1 at 100 °C with the blue light as the source light.17 On the other hand, A and B can be evaluated by shifting eqs 3 and 4 as follows: FCl2 y x þ ð7Þ A ¼ A0 2 FR FCl2 B¼ x þ B0 FR

Mj, i ¼ Ij RLj Zj, i þ Ij RV j ZY j, i þ ð1 Ij ÞLj1 Xj1, i Lj Xj, i þ Vjþ1 Yjþ1, i Vj Yj, i

Ej, i ¼ Yj, i

ð8Þ

Sj ¼

Substituting A and B with the relations described by eqs 7 and 8 into eq 6 produces rA0 ωFCl2 =FR x þ y=2 FCl2 =FR x þ B0 2x ¼ y FCl2 =FR x þ B0

ð10Þ

For the given information of the stream entering the reactor (FCl2, FR, A0, B0), the unknown x, y can be resolved from the relations described by eqs 9 and 10 with the product distribution (A, B, C) obtained from the relations described by eqs 7 and 8. It can be seen that the production rates and product distribution could be determined by the specified independent reaction amount with the rate-constants ratio (ω), avoiding the direct use of reaction kinetics. It should be noted that the relations described by eqs 310 are derived under the condition that the reaction temperature is 100 °C. To simplify the simulation, the effect of the temperature on ω is neglected. Since the reactor is adiabatic, the reactor temperature rises and some vapor is produced because the reactions are exothermic. The real reactor temperature, and the quantities of the vapor and liquid streams

P

c

∑ Xj, i 1 i¼1

Hj ¼ Ij RLj HRLj þ Ij RV j HRV j þ Ij RHClj HR HClj þ ð1 Ij ÞLj1 HLj1 Lj HLj þ Vjþ1 HV jþ1 Vj HV j þ VGjþ1 HVGjþ1 VGj HVGj

ð9Þ x þ y¼1

rj, i Xj, i Pj,S i

ð11Þ

ð12Þ ð13Þ

ð14Þ

Here, the variable Ij determines if a stage j is a feedback stage from a reactor (Ij = 1). (See Figure 2.) A value of vapor boilup rate VN is first given for the simulation. The stages and reactors are numbered from top to bottom, respectively. In the column, stage 1 represents the uppermost column tray and N is the partial reboiler. The steady-state solution of the MESH equations is achieved using the NewtonRaphson method with numerical evaluation of the Jacobian matrix. In addition, the initial values of Vj and Lj are generated from the constant molar flow assumption. The initial column composition profile X is guessed according to the distribution rule of the components, with toluene decreasing from top to bottom while benzyl chloride and benzal chloride both increase. The initial stage temperature (Tj) is set to be the boiling point of toluene at the given pressure. The simulation of the SRC process was completed using Matlab software. The employment of the independent reaction amount has avoided direct use of the reaction kinetics to compute the reaction rate and decoupled the reaction kinetics from the 11145



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Figure 3. (a) Composition profiles. (b) Temperature profile.

Figure 4. Effect of the feed flow rate of chlorine (FCl2) and the distributed ratio to the reactor connected with the condenser (fb)(1) on the selectivity.

mathematic models, which supplies a simplified way of simulating the SRC process. 3.3. Simulation Results. The simulated base case can be described as follows: 2 reactors are linked to a 10-stage column, which has 7 stripping stages and 2 intermediate stages placed between the two reactors. The bottom vapor boilup rate is fixed at 10 kmol/h. In the simulation for the base case, the feed rate of chlorine is set to 6 kmol/h and chlorine is introduced evenly into the two reactors. The feed flow rate of toluene is set to be the net production rate of benzyl chloride and benzal chloride calculated in the reactor model, which changes with iteration until a steady-state solution is achieved. Thus, the feed flow rate of toluene mainly decided by the feed flow rate of chlorine is treated as a dependent variable. The simulation results are displayed in Figures 3a and 3b, which give the composition and temperature profiles in the column, respectively. It can be seen that there is a high concentration of toluene and a low concentration of benzyl chloride in the reaction zone, which is beneficial for the selectivity. This is proved by the small presence of byproduct benzal chloride in the column shown in Figure 3a. With the continuous removal of benzyl chloride from the reaction zone, a benzyl chloride purity of 0.9533 is obtained in the bottoms and a high selectivity of 0.95 can be achieved. 3.4. Effect of the Feed Flow Rate and the Distributed Ratios of Chlorine. The feed flow rate of chlorine is direct to the production rate of the process, and a larger production rate is

Figure 5. Effect of the feed flow rate of chlorine (FCl2) on the composition profiles of benzyl chloride.

always attractive in the chemical industry. The effects of the feed flow rate of chlorine FCl2 and the distributed ratios of chlorine to the reactors (fb) on the selectivity are discussed, respectively, for the base case. Figure 4 shows that there exists an optimum distributed ratio of chlorine to the reactor connected with the condenser corresponding to the maximum selectivity for a specified feed flow rate. There is a higher composition of toluene in the top reactor, and increasing the ratio of chlorine to this reactor is effective for improving the selectivity. But increasing the ratio too much will lead to an excessive increase in the composition of benzyl chloride, which results in the formation of the undesired byproduct benzal chloride and leads to a lower selectivity. On the other hand, the effect of feed flow rate of chlorine on the composition of benzyl chloride with the uniform distribution is shown in Figure 5. It can be found that, as the feed flow rate of chlorine increases, the concentration of benzyl chloride in the reaction zone increases, while it favors the side reaction and induces a decrease in the selectivity of benzyl chloride, as shown in Figure 4. Hence, to obtain better selectivity under similar operating conditions, a lower feed rate of chlorine with a good distribution is recommended.

4. OPTIMUM DESIGN 4.1. Economic Analysis. As described above, a lower feed rate of chlorine with a proper distribution leads to a higher selectivity. However, reduced flow rate may be impossible to implement, since this decision is associated with the desired production rate. For the 11146



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Figure 6. (a) Effect of feed flow rate of chlorine on TC. (b) Tradeoff of operation costs, capital costs, other costs, and raw materials costs.

Figure 7. Simplified diagram of the optimization procedure.

given operating conditions, the optimum feed flow rate of chlorine and the distributed ratios now should be obtained from the effects on the economic costs. The evaluated total cost (TC) is composed of raw materials costs, operation costs, capital costs, and other costs for the salaries of workers, which are calculated based on the mass production rate of benzyl chloride. The operation costs include the costs of steam and cooling water, and the capital costs cover the cost of the column, stages, and external reactors. Appendix B gives detailed steps for computing the TC value. Figure 6 shows the effects of feed flow rate of chlorine on the costs for the base case with chlorine obeying the uniform distribution. Note that the feed flow rate of toluene also changes accordingly. Figure 6b shows the fact that the raw materials costs are orders-of-magnitude larger than the operation costs or capital costs are decisive toward the total cost; thus, the feed rates have more significant effects on the costs than the number of column stages or reactors. In addition, the raw materials costs increase as the feed rate increases, while

the capital costs, operation costs, and other costs decrease steeply, initially because of the increasing production rate of desired benzyl chloride. However, when the feed rate of chlorine is further increased, the capital investment, operation cost, and other costs decrease slightly, because of the tradeoff between the larger dimensions of the equipments and the increasing production rate. Therefore, the increasing raw materials costs become more dominant and the TC begins to increase. Thus, there is a minimum in the TC curve at a certain feed rate of chlorine, as shown in Figure 6a. Besides, a poor distribution of chlorine, which decreases the selectivity, will increase the costs attributed to the reduced yield of benzyl chloride. The objective of this paper is to search for the optimum values of F Cl 2 and fb under the given conditions, which denotes the maximum reaction capability corresponding to the minimum cost. The Powell method is applied to optimize F Cl 2 and fb simultaneously, because of its great efficiency for finding the minimum of a function without derivatives. The objective function and constraints are described 11147



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Figure 8. (a). Effect of NS on the composition profiles of toluene in the reaction zone. (b). Effect of NS on the composition profiles of benzyl chloride in the reaction zone. (NR = 3, NRS = 1, VN = 10 kmol/h, FCl2= 7 kmol/h, fb(1) = 0.34, fb(2) = 0.33, fb(3) = 0.33.)

Figure 9. Effect of NS on the optimum reaction capability. (NR = 3, NRS = 1, VN = 10 kmol/h). Note: fb°m denotes the optimum distributed ratio of chlorine to the mth reactor.

Figure 10. Effect of NRS on the composition profiles of benzyl chloride in the reaction zone. (NR = 3, NS = 9, VN = 10 kmol/h, FCl2 = 7 kmol/h, fb(1) = 0.34, fb(2) = 0.33, fb(3) = 0.33.)

as follows. minðTCÞ ¼ f ðNS, NRS, NR, FCl2 , fbÞ

ð15Þ

subject to FCl2 > 0 0 < fbðkÞ < 1 NR

∑ fbðkÞ ¼ 1

k¼1

k¼1 k¼1

,..., ,...,

NR NR

MESH and reactor equations

4.2. Optimization Procedure. It is assumed that the same number of separation stages between each reactor is employed. Thus, there are mainly five independent design parameters to be optimized with the given boilup rate: the number of stripping stages in the separation zone (NS), the number of stages between each reactor in the reaction zone (NRS), the number of reactors (NR), the feed flow rate of chlorine (FCl2), and the distributed ratios of chlorine to the reactors (fb). There are three discrete variables (NS, NRS, NR) and two continuous variables (FCl2, fb) to be optimized. The multistep sequential optimization procedure is shown in Figure 7. It was observed that either the number of reactors (NR) or the number of stages between each reactor changes (NRS), when the mole fraction of benzyl chloride in the

Figure 11. Effect of NRS on the optimum reaction capability (NR = 3, NS = 9, VN = 10 kmol/h).

stage between the reaction zone and the separation zone is >0.3; consequently, the selectivity will decrease steeply. However, when the value is 2, a negligible

Figure 12. Effect of NR on the optimum reaction capability (NS = 9, NRS = 2, VN = 10 kmol/h).

Figure 14. Effect of VN on the optimum reaction capability (NR = 4, NS = 9, NRS = 2).

Figure 13. (a) Effect of VN on the composition profiles of toluene. (b) Effect of VN on the composition profiles of benzyl chloride. (Conditions for both panels: NR = 4, NS = 9, NRS = 2, FCl2 = 7 kmol/h, fb(1) = fb(2) = fb(3) = fb(4) = 0.25.) 11149


Industrial & Engineering Chemistry Research decrease in the compositions of benzyl chloride in the reaction zone is observed. Figure 11 shows the influence of different NRS values on their optimum reaction capability. Results demonstrate that two intermediate stages between each reactor are sufficient to achieve the best reaction performance. Further increases in the number negligibly influence the optimum reaction capability, because the separation performance is hardly increased. Furthermore, slight changes in the distributed ratios of chlorine are observed from Figure 11 by increasing the number of separation stages between reactors. 4.3.3. Effect of the Number of Reactors (NR). The effect of the number of reactors on the system performance is discussed here. For this analysis, the optimum values of NS and NRS (NS = 9 and NRS = 2) are selected. Figure 12 reveals that the reaction capability is improved when the number of reactors is changed from 1 to 5. As the number of reactors increases, the distillation effect is also enhanced, because the total number of stages is increased correspondingly with the fixed values of NS and NRS. Hence, increasing the number of the reactors increases the optimum reaction capability, but an asymptotic limit is also approached. This is because the separation driving force given by the separation stages is always restricted to the reboiler duty. In addition, the feed ratios of chlorine to the reactors should strictly obey the distribution rule of toluene in the column, decreasing from top to bottom. It can be shown that the process with four reactors can display the most satisfactory system performance.

5. EFFECT OF VAPOR BOILUP RATE (VN) Under the optimum SRC configuration, an increase in the vapor flow rate pulls the desired product down from the reaction zone, making it rich in reactant toluene and deficient in benzyl chloride, as shown in Figure 13. A poor separation of removing benzyl chloride from the reaction section leads to an increased tendency for forming benzal chloride. Since the raw materials cost dominates the total cost, the optimum reaction capability shows a linear increase with the vapor boilup rate in Figure 14. It also can be found that, for a given feed flow rate of chlorine, at least the same quantity of vapor boilup rate should be provided to promise efficient system performance. 6. CONCLUSION The internal effects of reaction and separation on the system performance in the SRC process have been discussed for the production of benzyl chloride. Insufficient separation, which cannot provide efficient separation driving force, will limit the reaction capability greatly. Increasing the feed flow rate could yield a larger production rate, but further increases in the feed flow rate leads to a lower selectivity. To exploit the full advantages of the coupled reaction and separation technology, a systematic procedure has been set up to search for the optimum match between reaction and separation. It has been proven that better performance can be reached toward the separation efficiency of removing benzyl chloride from the reaction zone by increasing the number of separation stages between reactors, the number of stripping stages, and the number of reactors. Excess separation stages and reactors above optimal values provide negligible improvement in the separation performance, which would not be advantageous for reaction capability but may lead to difficulties to the process operation, along with rising capital investment. The maximum reaction

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Table A.1. Antoine Coefficients A

component

B

C

Vi (cm3/mol)

toluene (1)

9.58

3215.10

47.71

106.61

benzal chloride (2)

9.95

4429.46

41.16

129.07

benzyl chloride (3)

9.67

3759.38

63.32

115.84

Table A.2. Wilson Parameters Wilson Parameter, Aij (cal/mol)a toluene (1) benzal chloride (2) benzyl chloride (3) toluene (1)

a

0

benzal chloride (2)

30.83

benzyl chloride (3)

6.22

65.82

10.56

0

95.46

62.90

0

Note that Aij = 0 implies ideality.

capability for the given vapor boilup rate can be exploited when the harmonious relationship between separation and reaction is achieved. Moreover, by increasing the vapor boilup rate, the reaction capability can be increased linearly.

’ APPENDIX A: THERMODYNAMIC DATA FOR BENZYL CHLORIDE SYSTEM Antoine coefficients are presented in Table A.1, and Wilson parameters are presented in Table A.2. The vapor saturation pressure (PS) can be defined as B ðA1Þ lnðPs Þ ¼ A T þ C where Ps is expressed in units of bar and temperature (T) is given in Kelvin. The activity coefficient can be defined as ln ri ¼ 1 lnð

where Λij ¼

Z

Z

∑ Λij xjÞ k∑¼ 1 j¼1

Vj L Aij exp Vi L RT

Λki xk Z

∑ Λkj xj j¼1

ðA2Þ

ðA3Þ

’ APPENDIX B: TC CALCULATION The total cost (TC), which is based on the mass production rate of benzyl chloride in the bottoms, consists of the raw materials costs, operation costs, capital costs, and other costs for the salaries of workers. Detailed cost functions determining the equipment cost (viz, the cost of column shell, column internals, heat exchangers and reactors) and the operation costs involving the cost of hot and cold utilities are described. The capital investment is estimated using specific equations.18 A CE index of 521.9 is applied in the calculation. The equipment is sized as follows: (1) Column diameter (D) rffiffiffiffiffiffiffi 4VS ðB1Þ D ½m ¼ πu 11150



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where VS is the maximum vapor flow rate in the column (expressed in units of m3/s) and u is the gas flow velocity in empty tower (expressed in units of m/s). (2) Column height (L) L ½m ¼ 1:2NS

(2) Heat-exchanger cost (CH) CH ½$=ðton=hÞ ¼

CE expð7:5048 þ 0:16 ln AÞ 394Mb

ðB9Þ

ðB2Þ (3) Reactor cost (CR)

where NS is the number of column stages. (3) Column weight (We) We ½kg ¼ πDðL þ 0:8DÞδF

ðB3Þ

Qr Kr ΔT

C1 ½$=ton ¼

þ1304D0:63316 L0:80161 þ 220πD2 L

ðB8Þ

ðB12Þ

Cc Q c Mb Cpc Δtc

ðB13Þ

where Cc is the cooling water price (expressed in units of $/kg), Cpc the mass-specific heat capacity of the cooling water (expressed in units of kJ/(kg K)), and Δtc the rising temperature of the cooling water (given in Kelvin). Note that, here, the reboiler duty Qr and condenser duty Qc should be expressed in units of kJ/h. (5) Raw materials cost (CF) CF ½$=ton ¼

19:3FCl2 þ 87:4F Mb

ðB14Þ

As for other costs, an expenditure of $220 000 per year is assumed. (6) Other costs (CS)

where E denotes the reaction extent of toluene (expressed in units of kmol/h), d̅ R the mean density of the reaction mixture (expressed in units of kg/m3), and M ̅ R the molecular weight of the reaction mixture (expressed in units of kg/kmol). The liquid fraction in the reactor θ is assumed to be 65%. The mass production rate of benzyl chloride Mb (expressed in units of ton/h) is calculated as follows: ðB7Þ Mb ½ton=h ¼ LN XN, 3 126:58 103

CE h exp 7:1977 þ 0:21915 ln We þ 0:02297ðln We Þ2 394Mb

Cs Q r Mb q r

cooling water cost ½$=ton ¼

ðB6Þ

CC ½$=ðton=hÞ ¼

ðB11Þ

where Cs is the saturated steam price (expressed in units of $/kg) and qr is the latent heat of the steam, which is dependent on the bottom temperature (expressed in units of kJ/kg).

ðB5Þ

where LN is the bottom rate of benzyl chloride (expressed in units of kmol/h) and XN,3 denotes the mole fraction of benzyl chloride. The basic capital costs, which include the column, heat exchanger, and reactors, are calculated according to (1) Column cost (CC)

CC þ CH þ CR 7 300 24

steam cost ½$=ton ¼

where Qc is the condenser duty (expressed in units of J/s), the overall heat-transfer coefficient (Kc) is assumed to be equal to 250 J/(s m2 K), and the log-mean temperature driving force (ΔTc, given in Kelvin) is dependent on the dew points and bubble points for a total condenser. (6) Reactor volume (Vr) E Vr ½m3 ¼ θk1 d̅ R =M ̅ R

ðB10Þ

(4) Operation cost (CV)

ðB4Þ

where Qr is the reboiler duty (expressed in units of J/s), the overall heat-transfer coefficient (Kr) is assumed to be equal to 1000 J/(s m2 K), and the temperature driving force in the reboiler (ΔT, given in Kelvin) is dependent on the steam temperature. (5) Condenser heat-transfer area (Ac) Qc Ac ½m2 ¼ Kc ΔTc

CE 4908:2Vr 0:32 394Mb

A payback period of 7 years with 300 work days per year is assumed.

where the thickness of the column shell (δ) is assumed to be 0.008 m, and the density of the construction materials (F) is 7850 kg/m3. (4) Reboiler heat-transfer area (Ar) Ar ½m2 ¼

CR ½$=ðton=hÞ ¼

CS ½$=ton ¼

220000=300=24 Mb

ðB15Þ

The total cost (TC), expressed in units of $/ton, is defined as TC ½$=ton ¼ CV þ CF þ CS þ C1

ðB16Þ

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT This work is supported by Jiangsu Province Higher Education Natural Science Foundation (09KJA530004) and China Postdoctoral Science Foundation (20100471325). 11151



’ NOMENCLATURE A0 = composition of toluene in stream entering the external reactor [mole fraction] A = composition of toluene in stream leaving the external reactor [mole fraction] B0 = composition of benzyl chloride in stream entering the external reactor [mole fraction] B = composition of benzyl chloride in stream leaving the external reactor [mole fraction] C0 = composition of benzal chloride in stream entering the external reactor [mole fraction] C = composition of benzal chloride in stream leaving the external reactor [mole fraction] fb = distributed ratios of chlorine to the reactors fb°m = the optimum distributed ratio of chlorine to the mth reactor F = feed flow rate of toluene [kmol/h] FCl2 = feed flow rate of chlorine [kmol/h] FR = flow rate leaving the external reactor [kmol/h] HLj = enthalpy of liquid stream on stage j [MJ/kmol] HRHClj = enthalpy of hydrogen chloride leaving the reactor for stage j [MJ/kmol] HRLj = enthalpy of liquid stream leaving the external reactor for stage j [MJ/kmol] HRVj = enthalpy of vapor stream leaving the external reactor for stage j [MJ/kmol] HVj = enthalpy of vapor stream on stage j [MJ/kmol] HVGj = enthalpy of hydrogen chloride on stage j [MJ/kmol] Ij = switch (1 or 0) for feedback stage j from the external reactor k = reaction rate constant [1/h] Lj = liquid flow rate from stage j [kmol/h] N = number of stages in the column including the reboiler NR = number of external side reactors NRS = number of stages between each reactor in the reaction zone NS = number of stripping stages in the separation zone Rj = reaction rate of reaction j [1/h] RHClj = flow rate of hydrogen chloride leaving the reactor for stage j [kmol/h] RLj = liquid flow rate leaving the reactor for stage j [kmol/h] RVj = vapor flow rate leaving the reactor for stage j [kmol/h] PSj,i = vapor saturation pressure of component i on stage j [kPa] P = column pressure [kPa] rj,i = activity coefficient of component i on stage j Tj = column temperature on stage j [K] TC = total cost [$/ton] V0 = reaction holdup [kmol] VGj = flow rate of hydrogen chloride from stage j [kmol/h] Vj = vapor flow rate from stage j [kmol/h] VN = vapor boilup rate [kmol/h] x = mole fraction of chlorine used to form benzyl chloride Xj,i = composition of component i in the liquid on stage j [mole fraction] y = mole fraction of chlorine used to form benzal chloride Y j,i = composition of component i in vapor on stage j [mole fraction] Z j,i = composition of component i in the liquid stream leaving the external reactor for stage j [mole fraction] ZY j,i = composition of component i in the vapor stream the leaving external reactor for stage j [mole fraction]

ARTICLE

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Greek Symbol

ω = rate-constants ratio 11152


Production of Benzyl Chloride - ACS Publications - American

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