Optimisation of azeotropic distillation columns combined with pervaporation membranes

Optimisation of azeotropic distillation columns combined with pervaporation membranes

Computers and Chemical Engineering 26 (2002) 563– 573 www.elsevier.com/locate/compchemeng Optimisation of azeotropic distillation columns combined wi...

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Computers and Chemical Engineering 26 (2002) 563– 573 www.elsevier.com/locate/compchemeng

Optimisation of azeotropic distillation columns combined with pervaporation membranes Ana M. Eliceche a,*, M. Carolina Daviou a, Patricia M. Hoch a, Inmaculada Ortiz Uribe b a

Chemical Engineering Dept., PLAPIQUI, Uni6ersidad Nacional del Sur, CONICET, Camino La Carrindanga km 7, 8000 Bahı´a Blanca, Argentina b Dpto. de Quı´mica, Uni6ersidad de Cantabria, A6da los Castros s/n, 39005 Santander, Spain

Abstract The main objective of this work is the analysis and optimisation of azeotropic distillation columns, when a liquid side stream with the distributing non-key component is treated in a pervaporation membrane and the retentate is recycled to the column. The objective is to separate the pure distributing non-key component using a pervaporation membrane, thus helping to improve the purity in the top and/or bottom products. The operating conditions of the column such as reflux ratio, product and side draw flowrates and pressure are selected optimally to minimise the operating cost of the hybrid system. The simulation of the pervaporation membrane units is implemented solving the differential– algebraic equation system of mass transport and energy balances. The optimisation of the operating conditions of the azeotropic distillation column in the hybrid distillation/pervaporation system for Methyl tert-butyl ether production is presented. Numerical results with a significant reduction in the operating cost are reported. © 2002 Elsevier Science Ltd. All rights reserved. Keywords: Azeotropic distillation; Pervaporation; Optimisation; MTBE

Nomenclature B Cc Cm,r Co,i Cp Cr Co Co,ref Co,i Co,r D E F1 F2 NE NF1

bottom flow rate (kg mol/h) condenser operating cost ($/h) cost of membrane replacement ($/membrane unit) intermediate heating operating cost ($/h) pervaporation membrane operating cost ($/h) reboiler operating cost ($/h) condenser operating cost coefficient ($/kJ) operating cost coefficient for condensing the permeate ($/kJ) operating cost coefficient for intermediate heating between modules ($/kJ) reboiler operating cost coefficient ($/kJ) distillate flow rate (kg mol/h) sidestream (kg mol/h) fresh feed flow rate (kg mol/h) retentate flow rate (kg mol/h) location of the side draw location of fresh feed

* Corresponding author. E-mail address: [email protected] (A.M. Eliceche). 0098-1354/02/$ - see front matter © 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 0 9 8 - 1 3 5 4 ( 0 1 ) 0 0 7 7 5 - X

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NF2 Qc Qi Qr Qref R recMTBE,B xMTBE,B

location of the recycle stream (retentate) heat withdrew from the condenser of the column (kJ/h) heat added between pervaporation modules heat added to the reboiler of the column (kJ/h) refrigeration needed for the pervaporation modules (kJ/h) reflux ratio MTBE recovery in the bottom product liquid composition of MTBE in the bottom product

1. Introduction Debottlenecking and azeotrope breaking are fruitful fields for hybrid membrane systems. Some studies propose a combination between distillation columns and pervaporation membranes as an interesting alternative for solving these problems in industrial processes. The original Hu¨ ls process to obtain pure Methyl tert-butyl ether (MTBE) (Fig. 1) involves several azeotropic distillation columns to obtain a high recovery and purity of MTBE as end product and methanol to be recycled to the reactor. Hybrid distillation-pervaporation processes are generally less energy-consuming than distillation, and the separation taking place through the membrane is not influenced by the equilibrium between components. Recent patents propose hybrid distillation/pervaporation technologies for azeotrope breaking processes involving the separation of alcohols and ethers (Chen, Eng, Glazer, & Wensley, 1988; Chen, Markiewickz, & Venugopal, 1989) applied to the MTBE process, replacing the Hu¨ ls process. The pervaporation membrane used shows high flux and high selectivity to the permeation of Methanol, effectively breaking the azeotrope

Methanol–MTBE. The process called ‘Total Recovery Improvement for MTBE’ (TRIM™), is a combination of an organophilic pervaporation membrane and distillation, using two different layouts. One with the pervaporation membrane between the reactor and the distillation column, and the second layout with the membrane treating a sidestream of the column (Fig. 2). When the membrane is used to treat the sidestream, the required area decreases and investment costs could be reduced by 20%. The integration of the TRIM™ process to an existing one would be attractive if the production could be increased by 5%. In a recent review of Lipnizki, Hausmanns, Ten, Field, and Laufenberg (1999a) several processes of organophilic pervaporation are described. Even when the medical applications of membrane processes like dialysis are more profitable than any other industrial membrane process because of higher annual sales, in a near future, due to its high potential to separate organic–aqueous and organic–organic mixtures, it is forecast that pervaporation market share will grow at rates higher than any other membrane application. The authors also show a measure of the interest in pervapo-

Fig. 1. Schematic Hu¨ ls MTBE production process.

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565

Fig. 2. Schematic TRIM™ process.

ration with a graph showing how the number of papers on pervaporation increased over the last 20 years. Lipnizki, Field, and Ten (1999b) present an extense review of pervaporation-based hybrid processes, focusing on industrial applications and pointing out the need of optimisation of some of the analysed processes. One of the fields where there is need of optimisation is the distillation/pervaporation hybrid process. Ho¨ mmerich and Rautenbach (1998) studied the integration of pervaporation and vapour permeation into the Hu¨ ls process. They analysed the influence of the operating conditions in a hybrid distillation–pervaporation– vapour permeation system for the MTBE production and implemented the simulation of the process in ASPEN. Gonza´ lez and Ortiz Uribe (2001a,b) carried out experimental work to find a semi-empirical model for the pervaporation membrane to separate methanol and MTBE, and simulated the hybrid distillation/pervaporation process using gPROMS (PSEnterprises, 2000) performing a cost analysis. However, the formal optimisation of hybrid distillation/pervaporation process has not been reported previously. In particular, the optimisation of the debutanizer column with pervaporation membrane units to treat the side stream is reported in this work. Previous work on the optimisation of non-conventional distillation columns (Hoch & Eliceche, 1991) neither contemplate the azeotropic distillation case nor include simultaneously the rigorous simulation of pervaporation membranes. Thus the main objective of this work is the optimisation of the azeotropic distillation column in a hybrid distillation/pervaporation system using a rigorous simulation of the azeotropic distillation column and the pervaporation membrane units. Recent work (Ho¨ mmerich & Rautenbach, 1998; Gonza´ lez & Ortiz, 2001b) explored the influence of the optimisation variables

performing the simulation of the process at different operating conditions. As previously stated, the optimisation of the hybrid distillation–pervaporation process has not been attempted in former work. The formal optimisation of the hybrid system that includes an algebraic and differential equation system is described in this work. Numerical results of the optimisation are shown for the separation of a mixture of butanes, methanol and MTBE. This work was motivated by the evaluation of the feasibility of revamping the MTBE separation sector of a refinery. 2. Distillation –pervaporation process for MTBE production MTBE has been the chemical with the highest increase in its rate of production, a notorious 20%/year during the years 1985–1995 (Trevisan, 1995). MTBE is used as a high octane fuel additive. It provides the fuel with additional oxygen, decreasing the amount of CO produced as it benefits combustion completeness. The production process of MTBE consists of a reaction sector, where i-C4H10 is combined with methanol to form the ether, and a separation sector where all the MTBE must be separated from unreacted methanol and C4’s. Unreacted methanol forms azeotropic mixtures with MTBE and butanes. In the conventional Hu¨ ls process, a sequence of azeotropic distillation columns was used to break the azeotropes, thus recovering MTBE and methanol to be recycled to the reactor (Fig. 1). A hybrid distillation–pervaporation process seems as an attractive alternative, because it combines the advantages of both methods. The use of hybrid systems can improve the cost of the traditional Hu¨ ls separation sequence as reported recently (Ho¨ mmerich & Rautenbach, 1998).

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Different configurations for the hybrid distillation/ pervaporation process can be used, locating the pervaporation membrane to treat the feed, products or side stream. In this work, the pervaporation membrane is located to treat the side stream and remove the distributing component as a permeate, helping to improve the top and bottom purity. The separation of pure MTBE as the bottom product of an azeotropic distillation column from a mixture of C4’s, methanol and MTBE is performed by means of a combined distillation column and pervaporation membrane process. The process being studied is shown in Fig. 3, where the pervaporation process is synthesized as a single unit. The azeotrope formation of methanol with both MTBE and C4 limits the purity of the products. A high purity of MTBE is required in the bottom product (B) of the column that separates a multicomponent mixture (F1) including MTBE, C4’s and methanol. A side stream (E) of the column, rich in methanol, is processed through the membrane units. The membrane selectivity allows the methanol in the column sidestream to be permeated and then condensed and recycled to the reactor (Permeate liquid stream), thus helping to improve the MTBE bottom product purity. The retentate is recycled to the column (F2). The butanes do not permeate through the membrane, and this is confirmed by some patents of the hybrid process (Chen et al., 1988) and experimental results carried out by Gonza´ lez (2000).

For a binary system, where the permeation of one of the components Eq. (1) is favoured over the other component Eq. (2), the equation system representing the mass transport and energy balances can be synthesized as (Gonza´ lez, 2000): Total flux: J(c, T)= Jtotal(c, T)= J1(c, T)+ J2(c, T), (1) where 1 refers to methanol and 2 refers to MTBE. Recently, a mathematical model based on the generalized Fick%s law and the assumption that transport through the membrane is the rate-limiting step was developed in order to describe the pervaporation flux of both components (Gonza´ lez & Ortiz Uribe, 2001a). The prediction of the flux of methanol needed a concentration-dependent diffusion coefficient whereas a simple model with concentration-independent diffusivity was sufficient for the description of the MTBE flux. Predicted results with the mathematical model and parameters agreed with experimental data obtained in a wide range of variables working with Sulzer’s Pervap2256 membranes. Further details of the pervaporation modelling can be found elsewhere (Gonza´ lez & Ortiz Uribe, 2001a). Thus, the resulting equations for the prediction of pervaporative fluxes are, J1(c, T) = [− ƒ1Do exp(~ƒ1)k2,1z1/(ln(k2,1ƒ1 + 1)(k2,1ƒ1 +1))] × dƒ1/dzp J2(c, T)= − Dz2dƒ2/dzp.

3. Pervaporation membrane model A scheme of a pervaporation module is shown in Fig. 4.

(2) (3)

Boundary conditions: At zp = 0 ƒ1 = [exp(k1x1,1/k1,1)− 1]/k2,oh

(4)

ƒ2 = k2x2,1/k1,2

(5)

Fig. 3. Schematic flowsheet for the distillation/pervaporation process.

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Fig. 4. Pervaporation membrane.

At zp =t

c%= zF

(13) (14)

ƒ1 =[exp(P2x1,2/(P v1(T)k1,1)) − 1]/k2,1

(6)

T= TF

ƒ2 =(P2x2,2/(P (T)k1,2)),

(7)

Values for fluxes and enriching factor are obtained from experimental data. The parameters were found for concentrations of methanol between 5 and 40% in a binary mixture methanol–MTBE. For different values of methanol composition in a binary mixture of methanol– MTBE, the values for fluxes were found at different temperatures ranging between 30 and 50 °C. The experimental results can be found in Gonza´ lez and Ortiz Uribe (2001a). This allows to find the necessary parameters for modelling the mass transport in the membrane. For a certain composition, the flux of component i varies with the temperature according to the expression:

v 2

where ki is the activity coefficient for component i obtained with a gE model, and ƒi the composition of component i. Global mass balance:



dm; =WJ(c, T) dzA

(8)

Component mass balance: −

dci J(c, T) =[ii (c, T) −1]ci W, dzA m;

(9)

where W is the characteristic membrane width, ci is the mole fraction of component i in the permeate, T the temperature along zA and ii is the enriching factor, defined as: ii (c, T)=

c%i ci

Energy balance:

(10) −

dT WJ(c, T)u m V (c%, T) = , dzA m; C m (c, T) pL

(11)

being uV the heat of vaporization and CpL (J/kmol K) the mass heat capacity of the liquid mixture. For Eqs. (8), (9) and (11), at zA =0, m; = F

(12)

 

Ji,T 1(c, T)= Ji,T 2(c, T)exp

Ea,i 1 1 − R T2 T1



,

(15)

where Ea,i is the apparent energy of activation, found using the experimental results at different temperatures. The value of Ea,i is independent of the temperature, thus fluxes can be slightly extrapolated to other temperatures different than the experimental, while the whole model should be used for concentrations on the retentate side lower than the maximum experimental concentration used to find the correlated values of the parameters used to describe the flux through the membrane.

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As seen from the equations, the pervaporation membrane is modelled in terms of a differential/algebraic system involving lumped and distributed parameters. The differential equations through the membrane must be discretized in the direction of zp, and an integration package for Initial Value Problems (IVPs) is used to solve the equations along zA. As a simplification, it is assumed that only two components permeate through the membrane, while the rest of the components remain at the retentate side and do not permeate. This simplification was experimentally tested, and holds with the pervaporation membrane Pervap2256 used to find the experimental data. The membrane favoured the permeation of methanol over MTBE so that Eqs. (1)– (15) could be used. The remaining components do not permeate through the membrane, so the assumption of binary fluxes is hold. Experimental data were available for the system being studied, so there was information regarding the values of the flux and retentate concentration (Gonza´ lez, 2000), which allowed the implementation of this model.

The pervaporation takes place when a vacuum of 15–20 torr is maintained at the permeate side. For the start-up a vacuum pump is needed, but when steady state is reached, vacuum is maintained by the permeate condensation. The distillation column has 24 theoretical stages plus a condenser (stage 0) and a reboiler (stage 25). The membrane can be purchased in modules of 30 m2, so several modules are needed to perform the separation task. The number of modules required is automatically selected by fixing the required composition of the permeant in the retentate, thus allowing the introduction of as many intermediate heaters as required. For the integration, it was assumed a characteristic width of the module (W) of 50 m, and the integration proceeds up to zA = 0.6 m for each module. Intermediate heating is provided, and the retentate stream is heated until the temperature reaches 83 °C. The purpose of the intermediate heating is to avoid the decrease of the flux across the membrane.

5. Formulation of the optimisation problem

4. Simulation of the hybrid distillation/pervaporation system The hybrid process of an azeotropic distillation column combined with several membrane modules to treat the side draw was simulated with HYSYS (1999). Each membrane module was rigorously modelled using Eqs. (1)–(15). The software gPROMS was used to implement the differential– algebraic system, then the whole model was translated into Fortran language, to allow the implementation of a user extension unit in HYSYS. The differential– algebraic equation solver DASOLV (Jarvis & Pantelides, 1992) was used to integrate the IVP along zA, while the differential equations in the direction of zp were approximated using first order backwards finite differences for the derivatives in 40 finite elements, thus obtaining a differential–algebraic non-linear equation system. The choice of using an IVP integrator was made because this allows to predict the required membrane area in order to achieve a desired separation, by means of fixing the desired composition of the permeant in the retentate stream or by letting it free as optimisation variable. This is the main difference between the implementation of the proposed model and the model shown in Gonza´ lez and Ortiz Uribe (2001a). For the simulation, thermodynamic properties for the distillation column and the pervaporation membrane were predicted using Wilson equation with user provided binary interaction parameters, taken from Espinosa, Aguirre, and Pe´ rez (1995). This method allowed to accurately predict the thermodynamic behaviour of the mixture being analysed.

The optimum operating conditions of the distillation column, such as reflux ratio, side draw and product flow rates and pressure are obtained solving an optimisation problem to minimise the operating cost of the hybrid distillation/pervaporation system. The operating cost is calculated as the summation of column and membrane units costs: Co = Ccolumn + Cmemb = (Cc + Cr + Cp)

[$/h]

(16)

Cc = Co,cQcon, Cr = Co,rQreb, n

Cp = Co,pQperv + % Cc,i Qint,i + Cm,

(17)

i=1

where Qcon is the heat (kJ/h) withdrew from the condenser of the column, Qreb (kJ/h) is the heat added to the reboiler of the column, Qperv (kJ/h) is the heat withdrew in the pervaporation unit to condense the permeate, Qint,i is the heat added after the stage i, n is the number of pervaporation modules used and Cm is the cost of replacing the membrane. The operating cost of replacing the membrane modules is included in the objective function considering that they must be replaced every 2 years. For the operation of the condenser in the pervaporation membranes, a refrigerant fluid is needed, because the methanol condenses at very low temperatures (− 5 °C at the permeate pressure, usually 0.02 bar). The refrigeration cost to condense the permeate is a function of this temperature. Details on the operating cost are presented in Appendix A. The optimisation problem for the hybrid distillation/pervaporation system is formulated as:

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Table 3 Cost results for the example shown

Table 1 Feed to the column Component

Flow rate (kg mol/h)

Cost ($/h)

Optimum

i-butene MTBE Methanol F1 (kg mol/h) Temperature (K) Pressure (kPa)

325.82 155.00 32.96 512.78 334.30 685.00

Condenser Reboiler Refrigerant Heating between PV modules Membrane replacement

2.10 127.94 4.53 4.77 5.36

1.45 88.42 3.13 3.30 3.70

Total

144.70

100.00

min x

s.t.

Co(x) g(x)50

b L 5x5 b U,

(18)

where the optimisation variables x are the reflux ratio (r), a product flow rate (B), the side draw flow rate (E) and the column pressure (P), b L and b U are lower and upper bounds on the variables x. The separation objectives like minimum composition or recovery in the products and operating constraints related with the maximum sidedraw flowrate are formulated as inequality constraints g(x). The simulation of the hybrid system and the solution of problem Eq. (18) is implemented in HYSYS. The membrane modules are modelled in a user extension unit in HYSYS. For each set of x variables provided by the HYSYS optimisation code, a rigorous simulation of the hybrid system is carried out including the solution of the differential equations to model the pervaporation membranes. HYSYS is a sequential modular simulator, therefore the equality constraints modelling the processes are not explicitly formulated as equality constraints in problem Eq. (18). This includes the differential equations used to model the membrane units. The software developed allows the incorporation of different membrane models as user extension units in HYSYS. Thus the optimisation of similar technologies like the production of ethyl tert-butyl ether (ETBE) or other hybrid separation processes combining distillation columns with pervaporation membranes in different

Percentage

configurations and combinations of units can be implemented adapting the software developed. Once the rigorous simulation of the pervaporation membrane module is generated and interfaced automatically in HYSYS, the optimisation of different systems is feasible by modifying the membrane models and implementing a solution strategy for the system of differential equations.

6. Numerical results A mixture of iso-butene, MTBE and methanol has to be separated to obtain MTBE as a bottom product of the column. A hybrid distillation/pervaporation process is analysed to perform this task. The liquid side draw is located above the fresh feed and the retentate from the membrane is recycled to the column in the stripping section. The distillation column has 26 stages, the liquid side draw is located in stage 4, the fresh feed in stage 9 and the permeate from the membrane modules is recycled in stage 20. The composition, temperature and pressure of the fresh feed (F1) are shown in Table 1. For the sake of clarity, the mixture of butanes of the original process is replaced by one component, isobutene, which forms azeotrope with methanol, so a ternary mixture is considered instead of the original multicomponent mixture. MTBE also forms an azeotropic mixture with methanol at the working pressure.

Table 2 Optimisation results for the example shown

Side stream (kg/h) Reflux ratio Pcondenser (kPa) Bottom flow rate (kgmol/h) Bottom specification (wt.%) MTBE recovery (%) E/Liq ratio (%) Number of PV modules Cost ($/h)

Initial point

Optimum point

Lower bound

Upper bound

4900 1.22 600 162.98 98.02 99.62 27.31 26 160.26

5542 0.9515 572.5 161.96 98.02 99 40.93 22 144.7

3000 0.9 300 160 98.02 99 –

7500 1.25 1200 170 – – 41

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In this work, the objective is to obtain grade gasoline MTBE 98 wt.% with a recovery of 99% in the column. The inequality constraints g(x) of problem Eq. (18) are: recMTBE,B

Minimum MTBE recovery in the bottom product Minimum MTBE composition in the bottom product Maximum value of sidedraw

] 0.99 xMTBE,B ] 0.98 E50.41 * Lj−1

being j the stage from where the side draw is extracted and Lj − 1 the liquid flow rate of stage ( j −1). Optimisation results with the initial and final solution points, upper and lower bounds used in problem Eq. (18) are shown in Table 2. An important reduction in the reflux ratio of 22% and a significant reduction of 9.7% in the operating cost have been achieved by selecting the optimum operating conditions. The operating cost of the distillation column is nearly 90% of the total cost and the membrane cost is nearly 10% as reported in Table 3. Thus the optimisation of the operating conditions of the distillation column has a great impact in reducing the energy consumption and operating cost. The minimum composition and recovery are active constraints. The constraints related to the minimum composition and recovery of MTBE in the bottom product of the column are active because the cost of the column increases with higher composition and recovery, requiring a higher reflux ratio. A fixed composition of methanol in the retentate of 6% wt C4-free basis (equivalent to 15% mole-basis) is

assumed to perform the pervaporation process, while Gonza´ lez and Ortiz Uribe (2001b), Ho¨ mmerich and Rautenbach (1998) have used 5 wt.% The number of pervaporation modules required to perform this separation is calculated. The HYSYS selected optimisation option to solve problem Eq. (18) is the Mixed method. It starts the optimisation with the Box method using a very loose convergence. After convergence, an SQP method is then used to locate the final solution using the desired tolerance. The optimisation variables selected were the side draw flow rate, the reflux ratio and the pressure of the column. It is assumed that cooling water is used to condense the distillate of the column and low pressure steam is used to heat the bottom of the column and to provide interstage heating between the membrane modules. For this example, 22 modules are required to obtain the specified composition of methanol in the retentate. The temperature profile for the pervaporation modules is shown in Fig. 5. The retentate methanol molar composition decreases from 40 to 15% (C4-free basis), while the permeate composition remains above 99% throughout the membranes. Composition profiles in the membrane are shown in Fig. 6a and b. It is considered that only MTBE and methanol permeate through the membrane, while the iso-butene remains at the retentate side (Chen et al., 1988). Liquid composition profiles for the distillation column, when a side stream is withdrawn and the retentate is recycled to the column, are shown in Fig. 7. Fig. 8 shows in detail the methanol composition profile considering the ternary system, with a clear

Fig. 5. Temperature profiles in the pervaporation modules.

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Fig. 6. (a) Composition profiles of the permeate. (b) Composition profiles of the retentate.

reference to the stages where the fresh feed, recycle and side stream are located. There is no formal exploration of other alternatives for the location of these streams, as the purpose of this work is to optimise the operating conditions only, with no structural changes involved. The extraction stream is optimally located, in the maximum value of the methanol composition profile in the rectification section. The location of fresh feed, recycle and side draw have not been modified during the optimisation, as the

objective of this work is to improve the operating cost without changes in these variables, although the placement of the fresh feed, side stream extraction and retentate recycle locations can be modified to improve the objective function, while maintaining the total number of stages fixed. The procedure developed by Hoch and Eliceche (1991) treat the number of stages as continuous optimisation variables, allowing the simultaneous selection of feed and side stream locations with the flowrates in a non-linear programming problem

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formulation. The implementation of this option is currently being studied, as it is not possible to do it within the HYSYS environment in an algorithmic fashion. Instead, a trial-and-error procedure can be performed and was initially used to locate the side draw, fresh feed and recycle from the membranes reported in Table 2. The cost of the process has been improved from 156 to 148 $/h, representing a reduction of approximately

10% on the total cost of the process. It was not the purpose of this work to compare the hybrid system cost with the cost of the original Hu¨ ls process, but from the data in Table 3 it can be seen that the operating cost of the reboiler of the column represents almost 90% of the total cost, thus replacing a distillation column with the pervaporation membrane seems to be economically attractive.

Fig. 7. Column liquid composition profile.

Fig. 8. Methanol liquid composition profile.

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7. Conclusions

maintain vacuum,

The optimisation of the operating conditions of an azeotropic distillation column in a hybrid distillation/ pervaporation system has been presented. A rigourous modelling of the pervaporation membrane units has been implemented. Numerical results are reported for MTBE production, and the main improvements that can be expected by optimising the operating conditions of the debutanizer column are shown. A reduction of 9.7% in the operating cost of the distillation/pervaporation process has been achieved. Although in this work the option of treating the side stream with pervaporation membranes has been analysed, the same approach can be used to study different configurations, for example pre-treatment of the feed or end products purification with pervaporation membranes. The methodology can be extended to similar technologies like the production of ETBE or other hybrid separation process combining distillation and pervaporation, where similar reductions in the operating cost can be expected.

Cheat = Co,i Qi, is the interstage heating operating cost, and

(A.6)

Cm = nCm,ra,

(A.7)

Acknowledgements This work was carried out under research grant PICT 14-04065 from ANPCyT, Argentina.

Appendix A. Operating cost evaluation The operating cost of the process is calculated as the sum of operating costs for the condenser and reboiler of the column plus the operating costs of the pervaporation membrane, Co =Cc + Cr +Cp +Cm,

(A.1)

where Cc =Co,c

Qcond , DTw

(A.2)

is the operating cost of the condenser of the column, Cr = Co,rQreb,

(A.3)

is the operating cost of the reboiler of the column, Cp =Cref + Cheat,

(A.4)

is the operating cost of the pervaporation module, Cref = Co,refQref, (A.5) is the cost of condensing the permeate in order to

is the cost of membrane replacement, with n, number of pervaporation modules, Cm,r the replacing cost of each module. The annuity a is calculated considering an inflation rate of 10% a year. Cost coefficients can be found in Seider, Seader, and Lewin (1999).

References Chen, M. S., Eng, R. M., Glazer, J. L., & Wensley, C. G. (1988). Pervaporation process for separating alcohols from ethers, U.S. Patent 4774365. Chen, M. S., Markiewickz, G. S., & Venugopal, K. G. (1989). Development of membrane pervaporation TRIM™ process for methanol recovery from CH3OH/MTBE/C4 mixtures. American Institute of Chemical Engineering Symposium Series, 85, 82–88. Espinosa, J., Aguirre, P. A., & Pe´ rez, G. A. (1995). Product composition regions of single feed reactive distillation columns: mixtures containing inerts. Industrial and Engineering Chemistry Research, 34, 853 – 861. Gonza´ lez Gonza´ lez, B. PhD. Thesis, Universidad de Cantabria (2000). Gonza´ lez, Gonza´ lez B., & Ortiz Uribe, I. (2001a). Mathematical modelling of the pervaporative separation of Methanol –Methyl tert-Butyl Ether mixtures. Industrial and Engineering Chemistry Research, 40, 1720 – 1731. Gonza´ lez, Gonza´ lez B., & Ortiz Uribe, I. (2001b). Modelling and simulation of a hybrid process (pervaporation – distillation) for the separation of azeotropic mixtures of alcohol – ether. Journal of Chemical Technology and Biotechnolgy, 76, 1 – 14. Hoch, P. M., Eliceche, A. M. (1991). Optimal design of non-con6entional distillation columns, Process Technology Proceedings vol. 10, Computer Oriented Process Engineering, pp. 369 – 374. Ho¨ mmerich, U., & Rautenbach, R. (1998). Design and optimization of combined pervaporation/distillation processes for the production of MTBE. The Journal of Membrane Science, 146, 53–64. Hyprotech, HYSYS User Manual (1999). Jarvis, R. B., Pantelides, C. C. (1992). DASOLV: a differential –algebraic equation solver, CPSE report series. Lipnizki, F., Hausmanns, S., Ten, P. K., Field, R. W., & Laufenberg, G. (1999a). Organophilic pervaporation: prospects and performance. Chemical Engineering of Journal, 73, 113 – 129. Lipnizki, F., Field, R. W., & Ten, P. K. (1999b). Pervaporation-based hybrid process: a review of process design, applications and economics. Journal of Membrane Science, 153, 183 – 210. PSEnterprises (2000). gPROMS v. 1.8.4 User Guide. Seider, W.D., Seader, J.D., Lewin D.R. (1999). Chapter 10: Profitability analysis. Process design principles, John Wiley and Sons (ed.). Trevisan, M. (1995). Lead-free thanks to MTBE, Sulzer Technical review, 1, pp. 35 – 37.