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Modeling and Optimization of Membrane Reactors for Carbon Capture in Integrated Gasification Combined Cycle Units Fernando V. Lima,* Prodromos Daoutidis,* and Michael Tsapatsis Department of Chemical Engineering and Materials Science, University of Minnesota, 421 Washington Avenue SE, Minneapolis, Minnesota 55455, United States

John J. Marano JM Energy Consulting, Inc., 1065 South Lake Drive, Gibsonia, Pennsylvania 15044, United States ABSTRACT: This paper investigates the alternative of precombustion capture of carbon dioxide from integrated gasification combined cycle (IGCC) plants using membrane reactors equipped with H2-selective zeolite membranes for the water gas shift reaction. Specifically, a one-dimensional and isothermal membrane reactor model is developed. This model is used for simulation and optimization studies considering cocurrent and countercurrent modes of reactor operation. The simulation results indicate successful countercurrent cases that satisfy all of the specified targets and constraints. With use of this developed model, a novel optimization problem is formulated and solved to guide the selection of the optimal reactor design among typical scenarios of operation. The optimization results suggest as optimal solution a reactor design with a preshift followed by a membrane reactor. The obtained optimal design enables a more efficient membrane use by placing it in the optimal location. This design also results in savings of as high as 25% (in the range of 10−25%) in terms of membrane material when compared to the original membrane reactor design. For the price range of zeolite membranes considered on the order of $1000−10 000/m2 and for large-scale applications, in which the membrane surface areas are on the order of 2000 m2, 25% of savings implies cost reductions on the order of millions of dollars (as high as $5 000 000 in this case).

I. INTRODUCTION AND PRIOR WORK Carbon dioxide (CO2) emissions from the combustion of fossil fuels to the atmosphere are expected to exceed 6 billion metric tons by 2035. About one-third of these emissions originate from coal-fired electricity generation.1 These emissions will need to be mitigated in order to reduce the impact of projected climate change within this century.2 Thus, there is a need to develop new technologies for economical production of electricity from coal that minimize the release of CO2 to the atmosphere. Integrated gasification combined cycle (IGCC) power plants have emerged as a promising technology that can achieve higher efficiencies than conventional pulverized coal (PC)-fired plants; when operated with carbon capture, IGCC units enable CO2 capture with lower penalties in energy efficiency and cost of electricity than their PC counterparts.3 This capture of CO2 must be performed from the appropriate stream in the IGCC flowsheet. The precombustion capture of CO2 from IGCC plants using membrane reactors equipped with H2-selective molecular sieve (zeolite) membranes for the water gas shift (WGS) reaction is an alternative that is investigated in this work. In the IGCC process flowsheet, the WGS membrane reactor (MR) could replace the option of CO shift conversion followed by physical absorption for CO2 removal (e.g., employing the solvent Selexol).4,5 Among the advantages of MRs over this option are the following: MRs enable higher conversions than conventional packed-bed reactors due to the equilibrium shift of the WGS reaction toward the products caused by the hydrogen (H2) removal through the membrane; MRs are compact and © 2012 American Chemical Society

modular, combining two unit operations (reaction and separation) in one and can be placed at several locations in the IGCC flowsheet;4 membrane processes for CO2 removal are more environmentally friendly than absorption, as they do not require treatment and disposal of spent solvents.5 A challenge with using H2-selective membranes in the WGS section of coal-based gasification plants is their stability under high-pressure and -temperature conditions, and in the presence of steam and possibly other trace components such as hydrogen sulfide (H2S). Typical membrane materials used or proposed for H2 separations4,6 are as follows: (i) dense metals, typically Pd-based, which have nearly infinite H2 selectivity, but are expensive, poisoned by H2S even at low concentrations, and subject to H2 embrittlement; (ii) dense polymers, which are inexpensive, but have low H2 selectivity and are subject to thermal degradation; (iii) amorphous silica, which has high cost and is hydrothermally unstable; and (iv) porous carbons that have low selectivity and are subject to oxidative degradation at high temperatures. Zeolite-based, molecular sieve membranes are one promising alternative for this application, as they have potential for high selectivity and flux7 and to be hydrothermally stable. The objective of this paper is to develop a MR model for the WGS reaction using zeolite membranes for precombustion Received: Revised: Accepted: Published: 5480

September 29, 2011 March 1, 2012 March 8, 2012 March 8, 2012 dx.doi.org/10.1021/ie202234u | Ind. Eng. Chem. Res. 2012, 51, 5480−5489

Industrial & Engineering Chemistry Research

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Figure 1. Integration of MR into IGCC process (adapted from ref 38).

problems were formulated and solved using genetic algorithms.37 Specifically, the following objective functions were considered in this analysis: maximize the H2 production rate, maximize the H 2 recovery yield, minimize the sweep gas flow rate, and minimize the required membrane area. A set of reactor operating and dimensional parameters was used as decision variables in this case. Therefore, all of the optimization studies reported so far were carried out with the objective of improving H2 production by SMR. Moreover, none of these studies performed a MR cost optimization as they considered only performance variables in their analysis. This paper contributes with modeling and optimization studies associated with WGS MRs for carbon capture in coal-based gasification plants. For such an application, it provides a set of constraints for the MR that enables the feasibility evaluation of a selected reactor design. Also, a cost optimization problem is formulated by assigning cost parameters to MR performance and design variables, such as H2 recovery and membrane area. The outline of the rest of this paper is as follows. First, the MR modeling approach and corresponding assumptions are described. Then, the simulation results obtained using the developed model, for cocurrent and countercurrent modes of operation, are shown. These simulations are performed with the objective of finding successful configurations that satisfy all of the specified targets and constraints. Finally, a novel optimization problem is introduced to determine the optimal reactor design among typical scenarios of operation.

carbon capture from IGCC plants. The developed model will be used for stand-alone simulation and optimization studies and will ultimately be integrated into an IGCC system model as shown in Figure 1. These studies aim to determine the membrane characteristics necessary to achieve the U.S. Department of Energy (DOE) research and development goal of 90% CO2 capture4 and to obtain the desired H2 recovery value of 95%. The desired targets should be reached without violating the constraints reported by the DOE8 for the reactor outlet streams, such as the retentate stream (rich in CO2) for capture and sequestration and the permeate stream (rich in H2) for power generation. To guide the selection of the optimal MR design in terms of maximizing reactor performance, represented by H2 recovery, and minimizing reactor cost, represented by the membrane surface area required, a novel optimization problem is formulated and solved to address typical scenarios of operation. The design alternatives to be analyzed include the following: (i) preshift, membrane separator, and WGS reactor; (ii) preshift and WGS membrane reactor; (iii) WGS reactor and membrane separator; and (iv) stand-alone WGS membrane reactor. Regarding the modeling task, several MR models for the WGS reaction of different levels of complexities have been proposed in the literature. Specifically, in order of complexity, these models can be classified as follows: 1-D and isothermal;5,9−13 1-D and nonisothermal;14−18 2-D and isothermal;19 and 2-D and nonisothermal.9,20,21 MR models using H2-selective membranes for other applications have also been presented. Among such applications are steam22−24 and autothermal25 methane reforming, both for H2 production, dry reforming of methane with carbon dioxide,26 dehydrogenation reactions of cyclohexane,27,28 ethylbenzene to produce styrene,29,30 and benzene.31 A report on modeling of Pd-based MRs for WGS and steam methane reforming (SMR) can be found in ref 32. Also, an overview on modeling of catalytic MRs for several applications is presented in ref 33 (Chapter 5). Regarding optimization studies associated with packed-bed MRs equipped with H2-selective membranes available in the literature, an optimization problem for a staged membrane reactor with a fixed number of stages was formulated.34,35 This problem was solved to determine the optimal stage length distribution that maximizes either methane (CH4) conversion, H2 recovery factor, or yield of the SMR process for H2 production using Pd-based membranes. For the same application and membrane type, two constrained optimization problems were posed considering models of different complexities.36 These problems used reactor operating conditions as decision variables and were solved by different nonlinear optimization techniques, to maximize the sum of CH4 conversion and H2 recovery. Also for H2 production via SMR, but now considering a porous ceramic MR, multiobjective optimization

II. MEMBRANE REACTOR MODEL In this section, a one-dimensional membrane reactor model for the WGS reaction is introduced for simulation and optimization studies. The model assumes a shell and tube reactor in which the catalyst is packed in the tube side, a thin membrane layer is placed on the surface of the tube wall, and the sweep gas flows in the shell side to lower the H2 partial pressure of this side. Both cocurrent and countercurrent flow configurations are analyzed as depicted in Figure 2. The model

Figure 2. Water gas shift membrane reactor representations for cocurrent (solid line) and countercurrent (dashed line) configurations.

also assumes constant pressure and temperature and plug-flow operation and neglects axial dispersion. The reactor operates in 5481

dx.doi.org/10.1021/ie202234u | Ind. Eng. Chem. Res. 2012, 51, 5480−5489


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to calculate steady-state concentration profiles for the primary species (CO, H2O, CO2, H2, and N2) present in the tube and shell with respect to reactor length. These profiles are used to obtain steady-state compositions for these species in the retentate and permeate streams. This section reports simulation results for several case studies assuming different membrane characteristics (permeance and selectivity). For each case study, the values of the membrane reactor parameters, such as CO conversion, H2 recovery/productivity, and CO2 capture, are calculated; and the reactor stream purities, such as the CO2 purity in the retentate and H2 purity in the permeate, are computed. Target values for these parameters as well as constraints for these streams are defined on the basis of data reported by the DOE.8 As briefly mentioned above, the objective of these case studies is to obtain a MR configuration that is able to achieve the DOE target goal of 90% CO2 capture and to reach the desired H2 recovery value of 95%.8 In addition to satisfy the MR stream purity constraints, these desired values should be reached without violating transportation safety constraints of the CO2 capture stream,8 such as a low CO concentration, obtained by reaching the desired CO conversion value of 98%, and a H2 molar fraction below the flammability limit of 2%. The simulation setup considers WGS reactor operating conditions (such as feed composition, reactor dimensions, diameter of catalyst, and membrane characteristics) consistent with IGCC specifications that are either taken from the literature or based on expected conditions of our laboratory facilities. Specifically, the following reactor feed composition in mole percentage is assumed: CO, 24.43%; H2O, 48.86%; CO2, 5.68%; H2, 19.33%; N2, 1.70%. This composition corresponds to a syngas stream from the gasifier after steam injection.8 It is also assumed in this analysis that sulfurous compounds and other impurities from the original syngas stream have been removed using warm gas cleanup processes that are currently under development by the DOE/NETL42−44 and located upstream of the membrane reactor. Regarding the reactor and catalyst dimensions, the diameters of the tube and shell assumed in this study, dt = 1.02 cm and ds = 6.12 cm, respectively, are based on literature values5 and the reasonable equipment size of our laboratory facilities. A diameter of the catalyst particle, dcat. = 250 μm, is considered to eliminate internal diffusion resistance.40 Also, the reactor length, L = 30 cm, is selected so that a reasonable residence time (τ = 3.68 s) for plug-flow operation in the reaction side is obtained. These given dimensions also result in a large enough axial aspect ratio (L/dcat. ≥ 30) to enable neglecting the axial dispersion component in the reaction side.45 Moreover, the mass of catalyst used in the simulations, mcat. = 20 mg, corresponds to the approximate minimum amount of catalyst necessary to reach the reaction equilibrium and was determined by performing simulations without the membrane (QH2 = 0). Finally, the membrane characteristics and their respective ranges assumed, based on expected values for the zeolite membrane that is currently under tests in our laboratory facilities, are as follows: H2/other gases selectivity:

steady state, and the ideal gas law is assumed to hold. The following mole balances represent the membrane reactor model:

mole balance, tube (reaction side): dFi,t

= riA t − Ji πd t

dz

(1)

in which ri = rCO for i = CO, H2O; ri = −rCO for i = CO2, H2; and ri = 0 for i = N2 (see Notation for definition of model variables and subscripts);

mole balance, shell (permeation side): (±)

dFi,s dz

= Ji πd t

(2)

in which the symbols (+) and (−) are associated with the cocurrent and countercurrent modes, respectively. The flux through the zeolite membrane is assumed to be dictated by Fickian activated diffusion. Thus, this flux is proportional to the corresponding component partial pressure difference across the membrane39 and is given by Ji = Q iΔPi

(3)

For the WGS reaction, the following reaction rate expression40 associated with a Cu/ZnO/Al2O3 catalyst is considered: ⎛ PCO2P H2 ⎞ mcat. ⎟ rCO = −K ⎜⎜PCOP H2O − K eq ⎟⎠ A t L ⎝

(4)

in which ⎛ −47400 ⎞ ⎟ K = 82.2 exp⎜ ⎝ RT ⎠ ⎛ 4577.8 ⎞ K eq = exp⎜ − 4.33⎟ ⎝ T ⎠

Also, the factor multiplying the right-hand side of eq 4 is necessary to convert the reaction rate to the appropriate model units. The developed model was validated using published simulation data from the literature10 as a benchmark. The simulation results showed good agreement with the published data. Specifically, the molar flow rates in the tube and shell along the reactor length were compared for different values of Damköhler and permeation numbers calculated at feed conditions. The introduced model suffices for the purpose of screening MR configurations with the aim of finding successful and optimal reactor designs. The analysis of the nonisothermal reactor operation, as well as optimization and control studies associated with this operation, will be further examined in a future publication. The developed model is simulated next to determine the membrane characteristics necessary to achieve the DOE target goal of 90% of carbon capture4,8,41 and to obtain desired H2 recovery and CO conversion values. Remark 1. Although the developed model uses the f lux expression for zeolite membranes and the reaction rate for a Cu/ Zn-based catalyst, in eqs 3 and 4, respectively, this model could also be applied to dif ferent membrane materials and catalyst types by simply replacing the given appropriate flux and rate expressions.

α H2 /all = 10−1000

H2 permeance through the membrane:

III. RESULTS: MEMBRANE REACTOR SIMULATIONS The reactor model described in the previous section is simulated by considering cocurrent and countercurrent flow configurations

Q H = 0.01−10 mol/(s· m 2· atm) 2

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A. Cocurrent Configuration. The simulation results for the cocurrent configuration are presented in Tables 1 and 2.

Remark 2. The presence of sulf urous compounds would not be an issue for the considered zeolite membrane but could cause activity problems to the Cu/Zn-based catalyst used in this work.46 The selected reactor operating temperatures9 and pressures8 for the tube and shell are also consistent with the specifications of an IGCC unit. Specifically, the temperatures of the reaction and permeation zones are assumed constant with the value of 598 K (325 °C). This value is within the inlet temperature ranges of typical WGS reactor4 and warm gas cleanup processes42,43 that are present in the IGCC unit, and also consistent with the operation temperature of the Cu/Zn-based catalyst.47 Moreover, the selected pressure in the shell (permeate) corresponds to the required inlet pressure of the IGCC gas turbine8 (see Table 1 for pressure values used in the simulations). In this case, the permeate stream (rich in H2) from the membrane reactor could be directly fed into the turbine without the need of stream recompression.4 The definitions of the membrane reactor parameters considered as well as their target values3,8,9 are the following: CO conversion (XCO):

Table 1. MR Simulation Results for Cocurrent Configuration: Pressures and Compositions of Reactor Streams compositions (%)

FH2,p H2 in permeate = ≥ 95% (H2 + CO) in feed FH2,f + FCO,f

H2O

CO2

H2

N2

feed retentate sweep permeate

47.63 47.63 25.86 25.86

24.43 0.81 0 0.02

48.86 35.78 100 64.35

5.68 41.83 0 0.32

19.33 19.18 0 35.29

1.70 2.41 0 0.02

value (%)

target (%)

XCO R H2

97.62 68.02

98 95

CCO2

99.04

90

purityCO2,r

41.83

95

purityH2,p

35.29

44

Also, the concentration profiles for the reacting species in this case are plotted in Figure 3. Specifically, Table 1 shows the assumed pressures and the calculated compositions (in mole percent) for each MR stream. Moreover, Table 2 presents the calculated parameter values, including the CO2 purity in the retentate and the H2 purity in the permeate, and their specified targets. In this and the remaining tables of the paper, the entries in boldface and italics indicate whether a target specification/ constraint is reached or violated, respectively. Note that for this case study, the constraint on the H2 molar fraction in the retentate (yH2,r ≤ 2%) is violated. Also, none of the parameter targets are reached, except the one corresponding to the CO2 capture. B. Countercurrent Configuration. Similarly to those for the cocurrent case, the simulation results for the countercurrent configuration are presented in Tables 3 and 4. Also, the concentration profiles for this mode are plotted in Figure 4. Note that, for this case study, all of the specified problem targets and constraints are satisfied, except the one associated with the CO2 purity in the retentate. However, the table entries related to this purity, such as purityCO2,r and the compositions of CO2 and H2O in the retentate, are still in boldface and with footnotes ”a” indicating that the percentage sum of CO2 and H2O in the retentate is greater than 95% (96.31%). Because CO2 could be easily separated from H2O by cooling, this case is considered as successful. Thus, in the remaining tables of the paper, the purity obtained by the sum of these two compositions will be presented instead of the one associated with only the CO2 percentage. The simulation results showed a better performance of the countercurrent configuration when compared to the cocurrent mode for the same set of conditions. This conclusion is justified by a more uniform driving force for H2 permeation along the reactor length for the countercurrent case in comparison with the cocurrent mode.19 Specifically, for the cocurrent mode, the driving force along the reactor length tends to zero as both H2 concentrations in the tube and shell approach the same value at

CO2 capture (CCO2): FCO,r + FCO2,r carbon in retentate = ≥ 90% carbon in feed FCO,f + FCO2,f

Other constraints associated with the reactor streams are8

CO2 purity in the retentate: purityCO ≥ 95% 2,r

H2 molar fraction in the retentate: yH ,r ≤ 2% 2

H2 purity in the permeate: purityH ,p ≥ 44% 2

As mentioned previously, both the cocurrent and countercurrent modes of reactor operation are considered in the work. Mathematically, the cocurrent case corresponds to an initial value problem that was solved using the MATLAB subroutine “ode15s”. This subroutine uses a variable-order solver based on numerical differentiation formulas.48 On the other hand, the countercurrent case corresponds to a boundary value problem49 that was solved using the MATLAB subroutine “bvp4c”. This subroutine is based on a fourth-order collocation method.50 Both the cocurrent and countercurrent cases are simulated in the next subsection for the following initial set of conditions: Q H = 0.1 mol/(s·m 2·atm) 2

α H2 /all = 1000 vs = 400 cm3/min;

CO

parameter

H2 recovery/productivity (RH2):

CCO2 =

pressure (atm)

Table 2. MR Simulation Results for Cocurrent Configuration: Calculated Parameter Values and Specified Targets

FCO,f − (FCO,r + FCO,p) CO converted XCO = = ≥ 98% CO in feed FCO,f

R H2 =

stream

vt = 400 cm3/min

sweep gas composition: pure steam 5483



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-

Figure 3. Cocurrent case: concentration profiles for reacting species (mol/cm3) in tube (solid blue line) and shell (dashed red line) vs reactor length.

permeate more through the membrane. This permeation especially affects CO2 capture performance and H2 purity in the permeate. Specifically, the values for these two parameters gradually decrease with selectivity and even violate their constraints in some cases, such as the CO2 capture for αH2/all = 10 and the H2 purity for both αH2/all = 100 and 10. To determine the smallest selectivity value for which all of the constraints are satisfied, simulations are carried out by gradually decreasing the value of αH2/all by increments of 10 and checking the constraints for each case. As the result of these simulations, the value of αH2/all = 320 is obtained as the successful case with the smallest selectivity value that does not violate any of the parameter restrictions imposed. Lower selectivity values could be obtained if these restrictions were relaxed, but then other downstream units would have to be added to achieve all goals. Finally, for the selected case, αH2/all = 1000, simulations for different values of H2 permeance within the defined range, QH2 = 0.01, 1, and 10 mol/(s·m2·atm), were also performed (in addition to the already reported results for QH2 = 0.1 mol/(s·m2·atm)). These additional case studies are not presented here as none of them were successful (i.e., they violated at least one of the specified targets or constraints) for the given reactor dimensions. The analysis of whether the successful countercurrent case, αH2/all = 1000, QH2 = 0.1 mol/(s·m2·atm), can be improved, by optimizing the membrane reactor design, is carried out next.

Table 3. MR Simulation Results for Countercurrent Configuration: Pressures and Compositions of Reactor Streams compositions (%)

a

stream

pressure (atm)

CO

H2O

CO2

H2

N2

feed retentate sweep permeate

47.63 47.63 25.86 25.86

24.43 0.04 0 0.02

48.86 43.49a 100 55.40

5.68 52.82a 0 0.30

19.33 0.66 0 44.27

1.70 2.98 0 0.02

(%CO2 + %H2O)r ≥ 95%.

Table 4. MR Simulation Results for Countercurrent Configuration: Calculated Parameter Values and Specified Targets parameter

a

value (%)

target (%)

XCO R H2

99.84 99.06

98 95

CCO2

98.97

90

purityCO2,r

52.82a

95

purityH2,p

44.27

44

(%CO2 + %H2O)r ≥ 95%.

z ≈ 12 cm (see Figure 3). On the other hand, the average driving force for permeation is significantly larger for the countercurrent case (see Figure 4). The constant removal of H2 through the membrane along the reactor length results in CO conversion values of almost 100% (see Table 4). To analyze the effect that changing the membrane selectivity, αH2/all, has in the performance of the countercurrent configuration, several case studies are performed considering different values of selectivity between 10 and 1000. The simulation results for a few of these case studies, αH2/all = 1000, 100, and 10, are shown in Table 5. Note that as αH2/all decreases, species other than H2

IV. MEMBRANE REACTOR OPTIMIZATION In this section, a novel optimization problem is formulated and solved using the membrane reactor model to systematically determine the optimal reactor design among typical operating scenarios. The design alternatives analyzed include the following sequence of units:4,38 (i) preshift, membrane separator, packedbed WGS reactor; (ii) preshift, WGS membrane reactor; (iii) packed-bed WGS reactor, membrane separator; (iv) stand-alone WGS membrane reactor. 5484



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Figure 4. Countercurrent case: concentration profiles for reacting species (mol/cm3) in tube (solid blue line) and shell (dashed red line) vs reactor length.

Table 5. Countercurrent Simulation Results: Parameter Values for Different Selectivities

credit H2 = FH2,pHHVH2$H2 Op

and

value (%) αH2/all = 1000

αH2/all = 100

αH2/all = 10

XCO R H2

99.84 99.06

99.34 99.00

95.02 97.21

98 95 90

parameter

Sm = πdt (l4 − l3 + L − l5)

target (%)

CCO2

98.97

90.15

29.07

purityCO2+H2O,r

96.31

96.62

98.30

95

purityH2,p

44.27

43.14

34.05

44

yH2,r

0.66

0.51

0.01

(≤)2

where, regarding the last expression, the first term in the parentheses, (l4 − l3), is denoted by Lm1 and the last term in the parentheses, (L − l5), is denoted by Lm2. Specifically, the term costm represents the estimation of the membrane cost as a function of surface area required. On the basis of current estimates, the price range for zeolite membranes, $m, assumed here is between $1000 and $10 000/m2. We assumed a nondiscounted capital charge for the membrane due to the relatively short duration of time considered in the optimization problem. Also, the creditH2 term is associated with H2 recovery, which is a function of the amount of H2 in the permeate stream. This term is calculated using a H2 higher heating value, HHVH2, of 269.38 Btu/mol,51 a credit associated with H2 as the fuel entering the gas turbine for power generation in terms of its HHV of $H2 = $13.21/(106 Btu), and the annual operating period in seconds, Op. By converting to the appropriate units, this credit corresponds to a H2 fuel value of $1.78/kg. The vector of the decision variables, x, that corresponds to the lengths associated with the reaction (l1 and l2) and permeation zones (l3, l4, and l5), is defined as follows:

To address all of these design possibilities in one formulation, the decision variables considered in the problem are specified as the lengths associated with the reaction and permeation zones. The optimization problem is solved with the objectives of maximizing reactor performance, represented by H2 recovery (RH2), while minimizing the amount of membrane material used as a function of membrane surface area required (Sm). To perform the optimization, cost parameters are associated with RH2 and Sm. This problem is also subject to the target specifications for the membrane reactor parameters and constraints in the retentate and permeate streams, which were defined in the previous section. A. Problem Formulation. On the basis of the cost objectives described above, the following problem is mathematically formulated for optimal membrane placement:

x = [l1 l2 l3 l4 l5 ]′

In addition to the constraints on the membrane reactor parameters (XCO, RH2, CCO2) and streams (purityCO2,r, yH2,r, purityH2,p), the decision variables for each zone must satisfy the following set of dimensional restrictions: reaction zone:

Φ = min[cost m − credit H2] x

subject to:

MR target specifications and constraints

(5)

in which the terms “costm” and “creditH2” are given by

l1 > 0,

cost m = Sm$m 5485

l2 ≥ l1,

l2 ≤ L



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permeation zone: l3 ≥ 0,

l4 ≥ l3 ,

l5 ≥ l4 ,

This solution corresponds to a minimum objective function with the following terms: costm = $72.97 and creditH2 = $310.97. Figure 6 shows a schematic diagram for this optimal

l5 ≤ L

Specifically, the constraint on the first reaction zone, l1 > 0, ensures that this zone is always present for all of the design alternatives analyzed. On the basis of these restrictions, the lengths of each reaction, Lrz, and membrane, Lm, zone are within the following ranges: Lrz1, 0−l1; Lrz2, l2−L; Lm1, l3−l4; Lm2, l5−L. Figure 5 shows a schematic representation of the

Figure 6. Schematic diagram of membrane reactor optimal solution.

Table 6. MR Optimization Results for Countercurrent Configuration: Calculated Parameter Values and Specified Targets parameter

value (%)

target (%)

Figure 5. Schematic representation of MR optimization problem.

XCO R H2

99.75 97.86

98 95

formulated problem. Note that the proposed formulation addresses all of the typical WGS reactor designs mentioned above. For example, a stand-alone WGS MR, scenario iv, corresponds to l1 = l2, l3 = 0, and l4 = l5. Finally, the preceding optimization problem (5) is characterized by a nonlinear objective function with a nonlinear set of constraints and can be solved using the MATLAB subroutine “fmincon”. The active-set (medium-scale) optimization algorithm uses a sequential quadratic programming method (SQP) (see ref 52 for an overview of SQP). The next section focuses on studies associated with the countercurrent configuration with the aim of satisfying all of the defined target specifications and constraints, as done in the preceding successful case study, but with the minimal amount of membrane used for the highest possible performance. Remark 3. The proposed optimization problem formulation specif ically focuses on WGS reactor designs. However, design alternatives for other applications of interest, such as the autothermal coupling of methane steam reforming and methane catalytic combustion,53 could be considered by incorporating more reaction or separation zones into the optimization problem accordingly. B. Results: Case Studies. To verify whether the length of the membrane layer can be successfully reduced for the MR countercurrent configuration, the optimization problem initial guess, x0, chosen for the first case study, corresponds to the stand-alone MR configuration:

CCO2

99.23

90

purityCO2+H2O,r

95.41

95

purityH2,p

44.00

44

yH2,r

1.54

(≤)2

solution, and Table 6 presents the parameter values obtained for this successful case. Note that this solution suggests that the optimal reactor design should be a short preshift reactor (length of catalyst bed of about 5.5 cm), followed by a long WGS MR (catalyst and membrane layers of lengths of about 22 cm), i.e., scenario ii discussed earlier. This optimal design is not obvious if the countercurrent concentration profiles in Figure 4 for the permeation zone, including H2, are analyzed separately. This design, however, can be justified by the fact that most of the CO conversion occurs in the beginning of the reaction zone (z ≤ 6 cm) as shown in Figure 4, where the equilibrium conversion of CO has not yet been reached. As the WGS reaction approaches the equilibrium, the membrane will be needed to shift this equilibrium and enable a higher conversion. The really short reaction zone at the end of the reactor probably occurs due to the high-activity catalyst used that is able to achieve some CO conversion even for really short residence times. Once the optimization problem is solved, this short second zone can be eliminated by fixing the optimal design of a preshift followed by a membrane reactor. The obtained optimal solution also shows that the total length of the membrane layer (Lm1 + Lm2) required to satisfy all the specified targets and constraints is of approximately 22.7 cm, which is about 25% shorter than the original MR length of 30 cm. This result indicates savings in membrane material of about 25% when compared to the successful MR configuration presented previously. Thus, for the zeolite price considered, significant savings could be obtained in a scenario in which large-scale commercialization is pursued. For such a case, in which membrane surface areas38 are on the order of 2000 m2, 25% savings implies total cost reductions on the order of millions of dollars (as high as ≈$5 000 000 in this case).

x0 = [ L L 0 L L ]′

Also, to initially focus on determining the highest possible savings in terms of membrane material that could be obtained for an optimal design, the problem is solved by considering the upper bound value of zeolite membrane price, $m = $10 000/m2. The following optimal solution is obtained for this set of conditions: x = [27.07 28.92 5.35 27.31 29.19]′ 5486



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formulation introduced in this paper can help in guiding the membrane experimental research by determining the necessary characteristics that such a membrane must have for the purpose of carbon capture in IGCC units.

Typically, membrane reactor designs for large-scale applications consist of several concentric membrane tubes installed in parallel within the shell.9,14,20,38 It is worth mentioning that different optimal solutions are obtained for different values of assumed zeolite membrane prices. As this price is reduced, the magnitude of the term costm in eq 5 is also reduced when compared to the creditH2 term. This reduction results in a minimization of the membrane cost with a comparatively smaller weight in the optimization problem, and, thus, smaller savings are expected. Specifically, for the case considering the lower bound price of zeolite membranes, $m = $1000/m2, in which the costm term is 1 order of magnitude lower than when $m = $10 000/m2, savings of approximately 10% in terms of membrane material are obtained. Using the obtained optimal design, it is now possible to check whether a case with a selectivity value lower than αH2/all = 320 obtained in the previous section for the original MR design could also be successful. Specifically, a new design is built by adding the approximate amount of membrane saved, Lm = 7.5 cm, to the end of the membrane reactor so that this design corresponds to a preshift reactor of length of 7.5 cm, followed by a MR with the total original length of 30 cm. Once again, the selectivity value is gradually decreased by increments of 10 and the constraints are checked. As the result of these simulations, the case with αH2/all = 270 is identified as the successful case with the smallest selectivity value for the specified design. The parameter values for this case are presented in Table 7.

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Corresponding Author

*E-mail: [email protected] (F.V.L.); [email protected] (P.D.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors acknowledge the financial support from DOE through Award No. DE-FE0001322.

Table 7. Simulation Results for Countercurrent Configuration with Optimal Design and αH2/all = 270: Calculated Parameter Values and Specified Targets parameter

value (%)

target (%)

XCO RH2

99.85 99.35

98 95

CCO2

96.12

90

purityCO2+H2O,r

96.58

95

purityH2,p

44.00

44

yH2,r

0.44

(≤)2

AUTHOR INFORMATION

NOTATION A = cross-sectional area (cm2) d = diameter (cm) F = molar flow rate (mol/s) HHV = higher heating value (Btu/mol) K = reaction rate constant [mol/(gcat.·s·atm2)] Keq = reaction equilibrium constant l = zone length (cm) L = reactor length (cm) m = mass (gcat.) J = flux through the membrane [mol/(s·cm2)] Op = reactor operating cycle (s) P = pressure (atm) Q = permeance [mol/(s·cm2·atm)] r = reaction rate [mol/(s·cm3)] R = ideal gas constant [J/(mol·K)] S = surface area (cm2) T = reaction temperature (K) v = volumetric flow rate (cm3/min) x = vector of decision variables (cm) z = reactor axial coordinate (cm) $ = cost or credit (dollars)

Acronyms

CCS = carbon capture and sequestration IGCC = integrated gasification combined cycle MR = membrane reactor NETL = National Energy Technology Laboratory SMR = steam methane reforming SQP = sequential quadratic programming WGS = water gas shift

This value, αH2/all = 270, corresponds to a selectivity reduction of about 15% when compared to the previous case, αH2/all = 320. Therefore, this new design enables a more efficient membrane use by placing it in the optimal location.

V. CONCLUSIONS A one-dimensional, isothermal membrane reactor model for the WGS reaction was developed for simulation and optimization studies. The simulation case studies performed indicated successful countercurrent configurations that reach all the specified targets and satisfy the constraints posed. A novel optimization problem was formulated and solved to systematically guide the selection of the optimal MR design for WGS reaction and to determine whether the original MR design could be improved for optimal membrane use, without violating any of the restrictions imposed. The optimization results showed as optimal solution a reactor design with a preshift followed by a MR and savings of as high as 25% (in the range of 10−25%) in terms of membrane material when compared to the original membrane reactor design. For industrial-scale reactors, these savings represent an amount of as high as $5 000 000. Finally, the membrane reactor model and optimization

Greek Letters

Φ = objective function ($) α = selectivity ΔP = partial pressure difference across the membrane (atm) τ = residence time (s)

Subscripts

cat. = catalyst f = feed i = species index m = membrane m1, m2 = membrane zones p = permeate r = retentate rz1, rz2 = reaction zones s = shell t = tube 5487



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