Simulation and Thermodynamic Analysis of an Integrated Process with

simulation results, the thermodynamic analysis of the process has been ... CPO reactor, and on the thermodynamic efficiency of the integrated process,...
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Ind. Eng. Chem. Res. 2005, 44, 9191-9198

9191

Simulation and Thermodynamic Analysis of an Integrated Process with a Two-Membrane Catalytic Partial Oxidation (CPO) Reactor for Producing Pure Hydrogen Wei Feng,† Peijun Ji,*,‡ Danxing Zheng,‡ Tianwei Tan,† and Jakob de Swaan Arons§ College of Life Science and Technology and College of Chemical Engineering, Beijing University of Chemical Technology, Beijing, 100029, People’s Republic of China, and Physical Chemistry and Molecular Thermodynamics, Delft University of Technology, Julianalaan 136, 2628 BL Delft, The Netherlands

Catalytic partial oxidation (CPO) is an important technology for producing hydrogen from methane. A two-membrane CPO reactor, which has both an O2 membrane and a H2 membrane, integrates various processing steps in a single reactor. It has many advantages, compared to a conventional CPO reactor or a single-membrane reactor. The intent of this work is to simulate and investigate the thermodynamic efficiency of the process with a two-membrane reactor to produce pure hydrogen for application to fuel cells. The simulation of the two-membrane CPO reactor is based on the kinetics of the reactions and the mechanisms of membrane permeation. Other units of the process, which include a polymer electrolyte membrane (PEM) fuel cell, a catalytic burner, compressors, and heat exchangers, have also been simulated. On the basis of simulation results, the thermodynamic analysis of the process has been performed. The effect of the inlet temperature of air, the inlet pressure, the flowing mode of the sweeping gas, and the fraction of H2 recovered on the production rate of useful products (H2 and CO) of the twomembrane CPO reactor, and on the thermodynamic efficiency of the integrated process, have been discussed. 1. Introduction Because of its potential application in the future, hydrogen has been gaining more and more attention. Catalytic partial oxidation (CPO) is one of the key technologies for hydrogen production from natural gas.1,2 In a conventional CPO process, air (together with methane and steam) are fed into a conventional CPO reactor, in which some of the methane is combusted to provide the heat needed by the steam reforming reaction. The produced hydrogen is mixed with other gases such as N2 from the air, CO, CO2, steam, and unconverted CH4. Some disadvantages of applying such a hydrogen-rich gas mixture to a fuel cell are (i) the hydrogen conversion in fuel cell is limited to 85% and (ii) CO can damage a PEM fuel cell if the concentration of CO is >40 ppm.3 Generally, two stages of water-gasshift (WGS) reactors and a selective oxidization reactor are placed after the conventional CPO reactor, to convert most of the CO into H2 and reduce the concentration of CO. If a H2 membrane is applied to a CPO reactor, pure hydrogen can be produced. The process then can be simplified, and the thermodynamic efficiency of the process can be improved,4 because pure H2 can be fully converted in the fuel cell. The development of the O2 membrane5 also provides the possibility to improve the conventional CPO process. There are various advantages of an O2-membrane CPO reactor, such as the elimination of N2 contamination in * To whom correspondence should be addressed. Fax: 008610-64416406. E-mail: [email protected]. † College of Life Science and Technology. ‡ College of Chemical Engineering. § Delft University of Technology.

Figure 1. Scheme of a two-membrane catalytic partial oxidation (CPO) reactor (the sweeping gas is in a co-current mode).

the product, and control of the supply of oxygen along the reactor’s axial coordinate, mitigating the formation of “hot spots” and eliminating NOx emission. A two-membrane CPO reactor combines the characteristics of an O2-membrane CPO reactor and a H2membrane CPO reactor. The scheme of a two-membrane CPO reactor, which contains both an O2 membrane and a H2 membrane, is shown in Figure 1. In the twomembrane CPO reactor, O2 is transported across the O2 membrane to the reaction side, where it reacts with methane, which provides energy for the steam reforming reaction. The syngas is formed through the steam reforming reaction in the reaction side. The hydrogen in the gas mixture permeates through a H2 membrane, and the permeating H2 is then carried out by the sweeping gas. Minish et al.5 investigated a two-membrane CPO system for its techno-economic feasibility. Based on initial feasibility assessment, they determined that there are no technical issues that will prevent the development of the integrated two-membrane reactor. Chen et al.6 simulated a novel circulating fast fluidizedbed reactor with O2 and H2 membranes. By optimizing the number of H2 membranes, the number of O2 membranes, the oxygen feed rate, and the steam-tocarbon ratio, they determined that the hydrogen pro-

10.1021/ie050741e CCC: $30.25 © 2005 American Chemical Society Published on Web 11/01/2005

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Table 1. Models for the Two-Membrane CPO Reactora Reaction Side gas-phase continuity equation NR H2 O2 dFi/dz ) ar(1 - B)Fcpo s ∑k)1 (ηkυikRk) - aH2Ni + aO2Ni H2 H2 O2 O2 N4 ) NH2; Ni ) 0, i * 4; N6 ) NO2; Ni ) 0, i * 6 gas-phase energy equation 6 NR dTCPO /dz ) 1/(∑i)1 FiCPI) [arFCPO (1 - B)∑k)1 (-∆HkηkRK) r s q1 - q2 - aH2NH2∆HH2 + aO2NO2∆HO2 CPO q1 ) aH2km/δsp (TCPO - TCPO - TCPO r nr ); q2 ) aO2km/δsp (Tr nr ) solid-phase equations for calculating the effectiveness factors NR 1/ξ2 d/dξ (De,iξ2 dps,i/dξ) ) 10-5 RT FCPO rs2 ∑k)1 (νi,kRs,k) s NR -5 avDe,i/rs dps,i/dξ|ξ)1 ) 10 RT ∑k (ηkυikRk) solid-phase boundary conditions ξ ) 0, dps,i/dξ ) 0 gas-phase boundary conditions z ) 0, Fi ) Fi|z)0, T ) Tin Nonreaction Side continuity equation dGH2/dz ) aH2NH2 or dGO2/dz ) -aO2NO2 energy equation CPO /dz ) 1/∑jGjCpj[q1 + aH2NH2∆HH2]; dTnrH 2 CPO dTnrO /dz ) 1/∑jGjCpj [q2 - aO2NO2∆HO2] 2

a The sweeping gas flows through the reactor in a co-current mode.

ductivity in the novel reactor is ∼8 times higher than that in typical industrial fixed-bed steam reformers. The objective of this work is to conduct the thermodynamic analysis for an integrated process that consists of the following major units: a two-membrane CPO reactor, a catalytic burner, compressors, heat exchangers, and a fuel cell. For this purpose, the two-membrane CPO reactor and other units are simulated to obtain the production rate of H2 and the work output of the integrated process under different operation conditions. The simulation of the two-membrane reactor is based on kinetic models and the permeation mechanisms of membranes. Based on the simulation results, the thermodynamic analysis of the process has been performed. 2. Simulation 2.1. Two-Membrane Catalytic Partial Oxidation (CPO) Reactor. For the simulation of a two-membrane CPO reactor that has been provided with a Ni-Al2O3 catalyst, a one-dimensional steady-state heterogeneous model is adopted. A uniform oxidation state of the catalyst is assumed. The mechanism in the reaction and nonreaction sides of the membrane is considered to be of the plug-flow type. The influence of intraparticle concentration gradients within the catalyst pellet is taken into account by solving the solid-phase continuity equation at each increment along the adiabatic fixedbed reactor coordinate. The gas-phase continuity, energy, and solid continuity equations in the reaction side, as well as the continuity and energy equations in the

nonreaction side, are presented in Table 1, in which the corresponding inlet and boundary conditions are also listed. The energy equations in Table 1 take into consideration the heat of reaction, the heat exchanged between the nonreaction zone and the reaction zone, and the heat carried by the diffusing O2 or H2. The decrease in pressure is not taken into consideration. The simulation of a two-membrane CPO reactor is based on the kinetics of the methane combustion reaction, the kinetics of steam reforming to CO and CO2, and the kinetics of the WGS reaction.7 The influence of carbon deposition and that of the cracking of methane on the catalyst activity were neglected. The rate equations, as well as the kinetic parameters applied in the calculations of the reaction rate, are summarized in Tables 2-4. In the reaction side, the subscript i represents a gas species (that is, CH4, H2O, CO, H2, CO2, O2, or N2). In the solid-phase continuity equation, the effective diffusivity of component i is related to the molecular and Knudsen diffusivities. The effective diffusivities are calculated according to the method in the literature.8 The physical chemical properties Cip,9 equilibrium constants,10 and diffusivities11 are each considered to be a function of temperature. The solidphase continuity equation in Table 1 is solved by difference methods. The number of collocation points defined is dependent on the effect on the final calculation results. Normally, 10 collocation points are defined. The resulting difference equations are solved at each increment of the axial reactor coordinate. In each reactor increment, the intraparticle concentration gradients of the previous step are used as the initial value of the next step to solve the solid-phase continuity equations; thus, rapid convergence is obtained. 2.2. Permeation Mechanism of the H2 Membrane. The permeability of hydrogen through the H2permeable membrane is calculated according to eq 1:

NH2 )

Pm exp[- EA/(RT h )] high ( pH 2 δH2

x

xp

low H2 )

The apparent activation energy (EA) and pre-exponential factor (Pm) of the membrane are 29.73 kJ/mol and 7.71 × 10-4 mol m/(s m2 bar0.5), respectively.2 2.3. Permeation Mechanism of the O2 Membrane. In the simulation, the composition of the perovskite membrane for O2 permeation is La0.2Ba0.8Fe0.8Co0.2O3-δ. The permeability of oxygen through this membrane is calculated from eq 2:

( )

high pO A1 exp[- Ea/(RT h )] 2 ln low NO2 ) δO2 pO2

reaction number

reaction

kinetics of reactiona

1

CH4 + 2O2 f CO2 + 2H2O

2 3 4

CH4 + H2O f CO + 3H2 CO + H2O f H2 + CO2 CH4 + 2H2O f CO2 + 4H2

0 0 R1 ) k1,axCH4xO2/(1 + KCH xCH4+KO xO2)2 + k1,bxCH4xO21/2/ 4 2 0 0 x (1 + KCH CH4+KO xO2) 4 2 R2 ) (k2/pH22.5)(pCH4pH2O - pH23pCO/Keq2)/DEN2 R3 ) (k3/pH2)(pCOpH2O - pH2pCO2/Keq3)/DEN2 R4 ) (k4/pH23.5)(pCH4pH2O2 - pH24pCO2/Keq4)/DEN2

DEN ) 1 + KCOpCO + KH2pH2 + KCH4pCH4 + KH2OpH2O/pH2.

(2)

The activation energy Ea and the pre-exponential factor A1 are 63 kJ/mol and 7.34 × 10-7 mol/(m s K), respec-

Table 2. Reaction Rate for the Reactions in the Two-Membrane CPO Reactor

a

(1)

Ind. Eng. Chem. Res., Vol. 44, No. 24, 2005 9193 Table 3. Parameter Values for the Expression kk ) k0k exp[-Ea,k/(RT)] for the Reaction Rate Constant reaction 1 1 2 3 4

k1,a k1,b k2 k3 k4

k0k [mol-1 kgcal-1 s-1]

Ea,k [J/mol]

3.14 × 10-4 2.64 × 10-4 1.17 × 1015 bar0.5 5.43 × 105 bar-1 2.83 × 1014 bar0.5

240.1 × 103 67.13 × 103 243.9 × 103

Table 4. Parameters Values for the Expression Ki ) K0i exp[-∆Hads,i/(RT)] for the Adsorption Coefficients adsorption coefficient

K0i

0 KCH 4 0 KO 2 KCH4 KCO KH2 KH2O

6.67 × 10-2 4.34 × 10-5 6.65 × 10-4 bar-1 8.23 × 10-5 bar-1 6.12 × 10-9 bar-1 1.77 × 105

∆Hads,i [kJ/mol]

( )

FtRT0 P ln ηcp P0

-38.28 -70.65 -82.90 88.68

(3)

ηburner

3

+ ∆H|TTfg0 + ∆H|TT0end +

WFC LHV ηfFH2(-∆HH ) 2

(5)

In eq 5, FH2 and ηf represent the feeding rate of H2 and the fraction of H2 converted in the fuel cell, respectively. The work output of the fuel cell is calculated by eq 6:

(6)

In this work, an ηf value of 100% is assumed for the humidified pure H2.16,17

2.6. Catalytic Burner. A catalytic burner is used to heat the reactants to the inlet temperature. The remaining H2, CO, CO2, N2, H2O, and CH4 in the exhaust gas of the membrane reactor or the fuel cell are introduced into the furnace. The temperature of the after-combustion gas mixture leaving the furnace (Tend) is calculated by solving eq 4:

∆Hheating

ηFC )

LHV WFC ) ηFCηfFH2(-∆HH ) 2

tively. The oxygen permeation rate equation, and the coefficients, have been obtained from the literature.12,13 2.4. Heat Exchanger. By solving the energy balance equation, the heat exchangers are simulated; 20% of heat loss in the units is assumed. 2.5. Compressor. The electric power used in the compressor is calculated by assuming the compressor exergy efficiency (ηcp) to be 50% (see eq 3).14

Wcp )

H2 (the heat released by burning of H2 to steam at LHV , as shown in standard state, -241.83 kJ/mol) ∆HH 2 15 eq 5:

Fburner ∆Hcom )0 ∑ l l l)1

(4)

∆Hheating represents the heat required for heating the reactants to the inlet temperature (Tin) of the twomembrane CPO reactor. ηburner is the heating efficiency of the catalytic burner. Fburner and ∆Hcom represent the l l molar flow rate and the heat of combustion of the combustible component l in the rejected fuel gas mixture at T0, respectively. The combustible components in the rejected fuel gas mixture include CH4, CO, and H2. ∆H|TT0end represents the heat required to elevate the temperature of all after-combustion species (CO2, H2O, and N2) from T0 to Tend. Tfg represents the temperature of the fuel gas mixture before introducing it into the burner. ∆H|TTfg0 is the heat released by the fuel gas mixture when cooled from Tfg to T0. In this work, a 20% heat loss in the furnace and heat exchangers is assumed. 2.7. Polymer Electrolyte Membrane Fuel Cell (PEMFC). The efficiency of fuel cell (ηFC) is usually defined as the ratio of electrical power output WFC to the rate of H2 converted and the lower heating value of

3. Simulation of the Two-Membrane CPO Reactor At a given methane conversion, the production rate of useful products of a CPO reactor increases as the inlet temperature of reactants increases.18,19 However, it is difficult for industry to increase the temperature of methane and steam above 800 K. Therefore, in this work, the inlet temperature of methane and steam for the two-membrane CPO reactors is set at 800 K. In a two-membrane CPO reactor, H2 is transported to the permeate side of the H2 membrane, mainly driven by the difference in the square root of the partial pressure over the membrane. Using a sweeping gas, lower H2 partial pressures at the permeate side of the membrane can be achieved; thus, a higher fraction of H2 recovered can be obtained. Normally, pure argon, nitrogen, or steam is used as sweeping gas for H2 separation.6,20 In this work, the separated H2 is to be fed into the PEM fuel cell, which requires pure H2 (or humidified pure H2) to achieve 100% H2 conversion; therefore, steam is chosen as the sweeping gas. After the temperature cools to the operation temperature of the fuel cell, the separated H2 becomes humidified pure H2; thus, the separated H2 can be fully converted to electricity in the fuel cell.16,17 Factors such as the inlet pressure, the inlet temperature of air, the flowing mode of the sweeping gas, and the fraction of H2 recovered will affect the production rate of useful products (which include H2 and CO). In the following sections, based on the simulation results, the effects of these factors are discussed. 3.1. Definition of the Fraction of H2 Recovered. Figure 2a shows the profile of the mole fraction of each component in a two-membrane CPO reactor. The CH4 conversion rate is slow near the entrance of the reactor, because of a gradually feeding of O2 through an O2 membrane. The removal of hydrogen through a H2 membrane drives the steam reforming reaction and the WGS reaction toward a higher CH4 conversion and a higher CO conversion; therefore, the mole fraction of CO2 is much higher than that of CO. Because of the continuous removal of hydrogen from the reactor, the mole fraction of hydrogen does not change so much along the reactor axial coordinate. In addition, the production rate of separated H2 increases along the reactor length, as shown in Figure 2b.

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Figure 3. Temperature profiles of air, the reaction gas mixture, and the separated H2 of the two-membrane CPO reactor when Tair ) 800 and 1200 K. The CH4 conversion is 95%, and the fraction of H2 recovered is 90%. Tin ) 800 K; Pin ) Pair ) 2 bar; PH2 ) 1 bar; and the inlet rates of CH4 and H2O are 1.0 and 1.5 mol/s, respectively.

Figure 2. Plots of (a) molar fractions of the different species and (b) the production rate of separated H2, each versus the dimensionless axial coordinate of the two-membrane CPO reactor (at Tin ) 800 K, Pin ) Pair )10 bar, and PH2 ) 1 bar; the inlet rates of CH4 and H2O are 1.0 and 1.5 mol/s, respectively). The inlet rate of O2 (the air) into the nonreaction side of the two-membrane reactor is 0.35 mol/s, and the inlet rates of CH4, H2O, and O2 are 1.0, 1.5, and 0.35 mol/s, respectively. The H2 and O2-membrane areas are 5 and 14 m2, respectively. Steam is the sweeping gas, flowing at a rate of 5 mol/s.

The ratio of separated H2 to all the useful products is defined as the fraction of H2 recovered (σ):

σ)

S FH 2 S R FH + FRCO + FH 2 2

(7)

R where FH and FRCO are the flow rates of H2 and CO 2 S is remaining in the reaction region, respectively. FH 2 the flow rate of separated H2, and all the H2 and CO produced are called the useful products in this work. The fraction of H2 recovered is a very important parameter, which is frequently used in the following discussion, because the amount of H2 that is recovered will have a great effect on the thermodynamic efficiency of the integrated process. 3.2. Effect of the Inlet Temperature of Air on the Useful Products. Figure 3 shows the temperature profiles of the reaction gas mixture, the separated H2 together with the sweeping gas (steam), and the air flowing along the reactor axial coordinate. The solid lines and the dashed lines represent the results for the inlet temperatures of air at temperatures of 800 and 1200 K, respectively. From the temperature profiles, we know that, at the inlet temperature of air (Tair ) 1200 K), the air provides heat to the CPO reaction region. Because of the heat from the air, the amount of CH4 required for combustion is reduced and more methane can be converted to useful

Figure 4. Production rate of useful products of the two-membrane CPO reactor versus the fraction of H2 recovered at Tair ) 1200 and 800 K, respectively. The CH4 conversion is 95%. Tin ) 800 K; Pin ) Pair ) 2 bar; PH2 ) 1 bar; and the inlet rates of CH4 and H2O are 1.0 and 1.5 mol/s, respectively.

products. Therefore, the production rate of useful products increases as the inlet temperature of air Tair increases, as shown in Figure 4. 3.3. Effect of the Fraction of H2 Recovered on the Useful Products. If the type and thickness of the H2 membrane is fixed, the fraction of H2 recovered (σ) can be adjusted by changing the H2-membrane area applied, the molar flow rate of the sweeping gas, and the pressure at the permeate side or the reaction side. In a conventional CPO reactor, the heat released by the methane combustion reaction is used to provide heat for the methane steam reforming reaction, increasing the temperature of the gas mixture to achieve a given methane conversion. In a two-membrane CPO reactor with a H2 membrane, the steam reforming reaction is not only driven by the methane combustion, but also by the removal of H2 through a H2 membrane (the removal of H2 changes the composition of the reaction gas mixture and, thus, moves the gas mixture in the reaction zone away from the equilibrium). Therefore, the steam reforming reaction can achieve a given methane conversion at a lower temperature, which requires the combustion of less methane. Therefore, for a given methane conversion and a given inlet condition, more inlet methane can be converted to useful products; i.e.,

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Figure 5. Production rate of useful products of the two-membrane CPO reactor versus the inlet pressure. The CH4 conversion is 95%. Tin ) 800 K; Tair ) 1200 K; Pin ) Pair; PH2 ) 1 bar; and the inlet rates of CH4 and H2O are 1.0 and 1.5 mol/s, respectively. Table 5. Effect of Pressure on the Required H2-Membrane Areaa pressure, P [bar]

H2-membrane area [m2]

9 16

2.28 1.59

The production rate of separated H2 is 2.9 mol/s. Tin ) 800 K; Tair ) 1200 K; PH2 ) 1 bar; the inlet rates of CH4 and H2O are 1.0 and 1.5 mol/s, respectively. Steam is the sweeping gas, at a flow rate of 10 mol/s.

Figure 6. Effect of flowing mode on the amounts of steam (as the sweeping gas) required at different inlet pressure. The fraction of H2 recovered is 90%. The CH4 conversion is 95%. Tin ) 800 K; Tair ) 1200 K; Pin ) Pair; PH2 ) 1 bar; the inlet rates of CH4 and H2O are 1.0 and 1.5 mol/s, respectively.

electricity, or heat. The overall exergy efficiency ηEx for the process is defined as given in eq 8:

ηEx )

a

the production rate of useful products increases as σ increases, as shown in Figures 4 and 5. 3.4. Effect of the Inlet Pressure on the Useful Products. Figure 5 shows the effect of inlet pressure on the production rate of useful products for the twomembrane CPO reactor at different σ values. At higher inlet pressure, less useful products are produced. However, at higher inlet pressure, the H2-membrane area required by the two-membrane CPO reactor is reduced, as shown in Table 5. 3.5. Effect of the Flowing Mode of Sweeping Gas. For the two-membrane CPO reactor, the sweeping gas of steam can be used to carry the separated H2 out, either in a counter-current mode or in a co-current mode. The reactor with a counter-current mode has been modeled by a stepwise numerical procedure. It begins with a fixed production rate of separated H2 for a hypothetical flowing rate of sweeping gas at z ) 0 on the permeate side. The outlet temperature of separated H2 must be assumed. Repeating the calculation until the convergence is achieved, the molar rate of separated H2 is zero at the end of the reactor. Figure 6 shows the comparison between countercurrent mode and co-current mode, in terms of the amounts of steam required. Flowing in a countercurrent mode for the sweeping gas is better than in a co-current model, because lesser amounts of steam are needed. 4. Thermodynamic Analysis of the Integrated Process The thermodynamic efficiency (ηEx) is an important parameter for a process.21,22 It reflects the fate of the original work (Exinput) put into the process as fuel,

Wnet Exinput

(8)

where

Wnet ) WFC - Wcp

(9)

The exergy input Exinput includes the exergy of methane used as reactant in the two-membrane CPO reactor, the exergy of the methane added as additional fuel in the catalytic burner, and the exergy from some cooling water. The net work output (Wnet) of each process is equal to the work output of the fuel cell (WFC) minus the work used in the compressors (Wcp), as expressed in eq 9. 4.1. Exergy Flows of the Process. Figure 7 illustrates the scheme of the integrated process with a two-membrane CPO reactor, in which heat recovery and heat integration have been taken into consideration, using a catalytic burner and heat exchangers. Compressors to compress the air are indicated, with the input work needed. The energy of the fuel gas mixture rejected from the two-membrane reactor is recovered by introducing the gas mixture into the catalytic burner, where the combustion heat of the remaining fuel gas is utilized to heat the reactants. Heat exchangers are used to recover the heat from the hot streams used to make steam as the sweeping gas, and they are used to heat the air that is introduced into the reactor and the fuel cell. Corresponding to the temperature of each stream, the exergy flows have been indicated in the process scheme. 4.2. Exergy Depletion of the Process. Based on the exergy flows shown in Figure 7, the exergy balance of the process has been obtained and is presented in Figure 8, including the work lost in each step and the fractions of work lost for some key steps. The results show that the work loss of the process mainly occurs in the fuel cell. Other contributors are in the sequence of the catalytic burner, the two-membrane CPO reactor, and the heat exchangers. Because of the work loss

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Figure 7. Exergy flows in an integrated process. Pin ) 2 bar, and the CH4 conversion is 95%; the air inlet temperature is 1200 K. “HE” denotes the heat exchanger.

Figure 8. Exergy balance of the process, corresponding to a fraction of H2 recovered of σ ) 85%. The number, which is expressed as a percentage, is the ratio of the work loss of some key steps to the total work lost.

throughout the process, the overall exergy efficiency is not higher than 40%. 4.3. Thermodynamic Efficiency of the Process. In Figure 9, the effects of the flowing mode of sweeping gas and the fraction of H2 recovered on the overall exergy efficiency of the process are presented. The sweeping gas flowing in a counter-current mode makes the process have a higher thermodynamic efficiency than in a co-current mode, because less steam is needed in the counter-current mode. For a fraction of H2 recovered that is