Ind. Eng. Chem. Res. 1998, 37, 2509-2515
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Hydrogen Recovery from a H2-H2O-HBr Mixture Utilizing Silica-Based Membranes at Elevated Temperatures. 2. Calculation of Exergy Losses in H2 Separation Using Inorganic Membranes Bong-Kuk Sea, Katsuki Kusakabe, and Shigeharu Morooka* Department of Materials Physics and Chemistry, Graduate School of Engineering, Kyushu University, Fukuoka, 812-8581 Japan
The separation of hydrogen in a thermochemical water decomposition process (UT-3 process) is discussed from the point of view of exergy analysis. In this process, hydrogen is produced by hydrolysis of CaBr and FeBr2, which are contained in reactors connected in series, and is separated from H2O and HBr at the outlet of the FeBr2 hydrolysis reactor at 220-560 °C. Hydrogen concentration is anticipated to be of the order of 5 mol %. On the basis of the permeation properties of H2O- and H2-selective membranes developed in the preceding study, exergy losses for the hydrogen separation are calculated for plausible cases. The total exergy loss is smallest for a two-stage separation system: Steam is separated from a H2-H2O-HBr mixture using a H2O-selective membrane with a minimum loss of pressure and is recycled to the CaBr2 hydrolysis reactor. The permeate is recompressed to the feed side of the second stage, and hydrogen is then recovered using a H2-selective membrane. 1. Introduction As described in the preceding paper (Sea et al., 1998b), the UT-3 process (Kameyama and Yoshida, 1978; Aochi et al., 1989; Sakurai et al., 1996) has great potential as a thermochemical water decomposition process in the future. Since the reactions of the UT-3 process have been explained in detail earlier (Sea et al., 1998b), the reaction scheme is only briefly reviewed in this study. As shown in Figure 1, hydrogen is produced by hydrolysis of FeBr2, and oxygen is produced by the bromination of CaO. Hydrogen is separated from the H2-H2O-HBr mixture at point A, and oxygen is recovered from the O2-H2O mixture at point B. Steam is used as the reactant for hydrolysis in reactors 1 and 4, as well as the heat carrier for the entire system. The flow rate of steam needs to be increased in reactors 1 and 4 in order to enhance the hydrolysis. Since excessive steam prevents reactions 2 and 3, the flow rate of steam in reactors 2 and 3 should be limited within the range which is required as the heat carrier. Thus, steam is recycled through reactors 1 and 4, after H2 and HBr are separated at the exit of reactor 4 (point A). On the basis of the reason described in the preceding paper, the separation of hydrogen at point A is addressed in this study. Separation properties of membranes directly affect the exergy balance of a process to which they are applied. Thundyil and Koros (1997) analyzed masstransfer efficiency for separations using hollow fiber membranes. Shindo et al. (1985) calculated the yields of single-stage separation units with different flow patterns for multicomponent gas mixtures. Perrin and Stern (1985) developed mathematical models for the separation of binary gas mixtures using polymer membranes. The numerical calculations indicate that a twostage membrane permeator with a countercurrent flow * To whom correspondence should be addressed. Fax: 8192-651-5606. E-mail:
[email protected].
Figure 1. The reactions of the UT-3 process.
is more efficient than other permeation modes. Pan (1983, 1986) calculated the efficiency of various membrane separation systems and proposed a mathematical model for multicomponent permeation using cellulose acetate hollow fiber membranes. Hinchliffe and Porter (1997) evaluated parameters which influenced the cost of membrane separation processes. Their data indicate that the separation cost is directly related to the permeability and selectivity of the membranes employed. Xu and Agrawal (1996) developed a scheme which involved a minimal exergy loss for the separation of gases. The number of compressors which are necessary to compress the permeate to the pressure of the next feed side needs to be minimized (Agrawal, 1997). Thus exergy analysis (Keenan, 1951; Hinderink, 1996) is useful for evaluating the thermodynamic efficiency of membrane separation processes. In the preceding paper (Sea et al., 1998b), we described silica-based membranes formed on a porous support tube by the thermal decomposition of tetraethoxysilane (TEOS). The membranes were modified by heat treatment with and without γ-alumina coating. In the present study, hydrogen recovery from a H2H2O-HBr mixture produced in the UT-3 process is simulated based on the H2- and H2O-permeable mem-
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2510 Ind. Eng. Chem. Res., Vol. 37, No. 6, 1998
Figure 2. Flow scheme for the membrane separator. Table 1. Dimensionless Parameters dimensionless group
definition
permeate of i component pressure ratio at first and second stages H2/H2O selectivity H2O/H2 selectivity flow rate axial position
Ki ) kiaLPf0/(mf0) Rp1, Rp2 ) Pf/Pp SH ) kH2/kH2O SW ) 1/SH M ) m/mf0 Z ) z/L
Figure 3. Profiles of flow rates and mole fractions in the membrane separator.
branes. Optimal conditions and flow systems for recovering hydrogen are proposed on the basis of exergetic analysis. 2. Modeling of Membrane Separator As shown in Figure 2, feed and permeate gases in a membrane module flow in a countercurrent fashion with a dead end on the permeate side. Separation properties of the membrane are assumed to be constant along the membrane. The permeation of HBr is neglected for simplicity, and only hydrogen (mole fraction, x) and steam (mole fraction, 1 - x) are considered. The total material balance in the membrane module is as follows:
mf0 ) mfL + mp0
(1)
where mf and mp are the total flow rates on the feed side and permeate side, respectively. The overall material balance for hydrogen is
mf0xf0 ) mfLxfL + mp0xp0
(2)
Figure 4. Relationship among parameters used in one-stage separation using a H2-selective membrane.
hydrogen on the permeate side is
d(Mpxp) + KH dZ (xf - xp/Rp) ) 0
(7)
The boundary conditions are The hydrogen flux, jH, across the membrane is
jH ) kH(Pfxf - Ppxp)
(3)
where kH is the permeance of hydrogen. Pf and Pp are the total pressures on the feed and permeate sides, respectively. The differential material balance for hydrogen on the feed side per membrane area a dz is
at Z ) 0, Mf ) 1
(8)
at Z ) 1, Mp ) 0
(9)
From eqs 5 and 7, we obtain
d(Mfxf) ) d(Mpxp)
(10)
(4)
By the same procedure, the differential material balance for water is obtained as
By introducing a dimensionless length, Z ) z/L, eq 4 can be rewritten as
d[Mf(1 - xf)] + (KH/SH) dZ [(1 - xf) - (1 - xp)/Rp] ) 0 (11)
d(Mfxf) + KH dZ (xf - xp/Rp) ) 0
The axial profiles for flow rates and partial pressures can be calculated from eqs 5-11. Figure 3 shows typical profiles formed in the membrane module under conditions Pf ) 2 MPa, Pp ) 0.1 MPa, xf0 ) 0.1, KH ) 4, and SH ) 20. The mole fraction of hydrogen at the outlet on the permeate side, xp0, increases with decreasing KH and increasing SH. Figure 4 shows the effects of KH and SH on H2 recovery and xp0 for a one-stage separation unit. Although the H2 recovery can be increased using
d(mfxf) + kHa dz (Pfxf - Ppxp) ) 0
(5)
The dimensionless parameters used in this model are defined as in Table 1. The operating line is then given as
Mf0xf0 + Mpxp ) Mfxf + Mp0xp0
(6)
The dimensionless differential material balance for
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a membrane with a high H2 permeance, the H2 fraction on the permeate side is decreased due to the permeation of water vapor. 3. Exergy Analysis for H2 Separation Sakurai et al. (1996) calculated the thermal efficiency of the UT-3 process assuming complete heat recovery in H2 and O2 separation units. However, the separation of gases requires considerable energy. When heat, Q, is supplied to a system at temperature T, the exergy of the system, E, is increased as
δE ) δQ(T - TS)/T
(12)
where TS is the temperature of the surroundings, 298.15 K. From eq 12, the exergy change due to the temperature change is given by
δET )
∫TT cP dT - TS∫TT (cP/T) dT S
S
(13)
where cP is the specific heat of the gas mixture and is represented as a function of the absolute temperature, T:
cP ) c1 + c2T + c3T2
(14)
where c1, c2, and c3 are constants for specified materials. Values of these constants for H2, H2O, and HBr are cited from a literature reference (Castellan, 1983). In the H2 separation using a membrane, we further consider exergy changes due to (i) pressure decrease across the membrane and (ii) mixing of the components. The exergy change due to compression is
∫VV (P - PS) dV
δEP ) -
(15)
S
where PS is the surrounding pressure, 0.1 MPa. H2 and HBr are described by the law of ideal gas, and the mean compressibility factor of steam, Zc ) PV/RT, is assumed to be 0.989 under the conditions in the range of 373724 K and 2 MPa (Sato et al., 1988). Equation 15 can be written as
∫PP (1/P) dP - ZcRTSPS∫PP (1/P2) dP
δEP ) ZcRTS
S
S
) ZcRTS[ln(P/PS) - (1 - PS/P)]
(16)
The entropy change by mixing is given by
δSM )
1
nk
∑
Ni)1
niR ln(N/ni) )
nk
R
[N ln N -
N
ni ln ni] ∑ i)1
(17)
where N is the total number of moles in the system and ni is the number of moles of the i component. Thus, the exergy change due to mixing is then given by nk
δEM ) TS δSM ) RTS
xi ln xi ∑ i)1
(18)
where xi is the mole fraction of the i component in the mixture. The exergy loss due to mixing is decreased by the membrane separation. The total exergy of the feed or retentate is the sum of δET, δEP, δEM, and the
Figure 5. Scheme for a one-stage separation using a H2-selective membrane (case I).
chemical exergies of the components. The chemical exergies of H2(g), H2O(g), and HBr(g) are 235.34, 8.58, and 98.58 kJ mol-1, respectively, at 298.15 K and 0.1 MPa. The exergy loss by H2 separation is then calculated from
(exergy loss) ) (exergy in feed) (exergy in retentate) + (exergy of unrecovered H2) (exergy of recovered H2) (19) Case I. Figure 5 shows the conditions for a one-stage separation using a H2-selective membrane. The following assumptions are made for simplication: (1) The chemical exergy of hydrogen in the retentate is assumed to be zero because the unrecovered hydrogen is consumed in the oxygen formation reactors. (2) H2 and H2O are fed at 450 °C and 2.0 MPa (Sakurai et al., 1996). (3) The temperature remains unchanged in the separation unit. (4) The total pressure on the permeate side is 0.1 MPa. (5) The permeate is separated into water and hydrogen at 25 °C. (6) The latent heat of steam is completely recovered. (7) The partial pressure of steam at 25 °C and 0.1 MPa is neglected. (8) Steam in the permeate is condensed at 25 °C and 0.1 MPa and is heated again to 450 °C and 2 MPa. The mole fraction of hydrogen at the inlet, xf0, and the H2/H2O selectivity, SH, are varied, and the exergy loss per mole of recovered hydrogen is calculated. Figures 6 and 7 show the total exergy loss per mole of recovered hydrogen. When xf0 is 0.01, the minimum total exergy loss appears at a H2 recovery of 70-90%, and the total exergy loss is strongly dependent on SH. The total exergy loss for xf0 ) 0.01 exceeds the chemical exergy of hydrogen even when a membrane of SH ) 100 is used. Figures 8 and 9 show the contribution of exergy losses for the membrane with a H2/H2O selectivity of 20 and 100 for xf0 ) 0.05. On one hand, when hydrogen recovery is low, the exergy loss due to unrecovered hydrogen is large. On the other hand, when hydrogen recovery is high, a considerable amount of steam is transferred to the permeate side. The total exergy loss at higher hydrogen recoveries is largely caused by the compression and heating of the steam which is permeated through the membrane and condensed in the trap. When xf0 is 0.05, the minimum total exergy loss is 121 and 72 kJ mol-1 when a H2-selective membrane of SH ) 20 and 100, respectively, is used. When xf0 is larger than 0.1, it is possible to reduce the total exergy loss to 71 kJ mol-1 using a membrane of SH ) 20, which may be attained as described later. Thus, it is preferable that the H2 mole fraction in the feed of the H2 separation
2512 Ind. Eng. Chem. Res., Vol. 37, No. 6, 1998
Figure 6. Total exergy loss for one-stage separation (case I). xf0 ) 0.01 and 0.03. Figure 8. Distribution of exergy losses for one-stage separation (case I). xf0 ) 0.05, SH ) 20. Exergy changes: ", due to pressure rise of trapped steam from 0.1 to 2 MPa; #, due to temperature rise of trapped steam from 25 to 450 °C; 0, due to unrecovered H2; 9, due to mixing entropy.
Figure 7. Total exergy loss for one-stage separation (case I). xf0 ) 0.05 and 0.1.
cell is equal to or higher than 0.05. The experimental results for H2 production by the UT-3 process (Aochi et al., 1989) indicates that the mole fraction of H2 can be increased to 0.05 by optimizing reaction conditions. Case II. When the H2 fraction in the feed is low, it should be increased by a two-stage membrane system, as shown in Figure 10. Water is removed with a H2Oselective membrane in the first stage, and hydrogen is recovered with a H2-selective membrane in the second stage. The removed water is returned to the hydrogen formation reactors, as indicated in Figure 1, bypassing the oxygen formation reactors where excessive water hinders the oxygen-producing reactions. The recycle of steam is desirable from the chemical equilibria in reactions 1-4. The total pressure on the permeate side of the H2O-separating unit is assumed to be 0.1 MPa (Rp1 ) 20) or 1.0 MPa (Rp1 ) 2) and is increased to the system pressure, 2.0 MPa, before being introduced to the feed side of the H2-separating unit. The exergy change due to this compression is calculated by eq 16. All assumptions (1)-(8) for case I, except assumption (4), are applied. The total pressure on the permeate side of the H2-separation unit is fixed at 0.1 MPa (Rp2 ) 20).
Figure 9. Distribution of exergy losses for one-stage separation (case I). xf0 ) 0.05, SH ) 100. Keys are the same as in Figure 8.
When the total pressure on the first-stage permeate side is reduced to 0.1 MPa (Rp1 ) 20), the calculated exergy loss required by the recompression of steam to 2 MPa, to return to the inlet of reactor 1, exceeds the exergy of recovered hydrogen. Thus, the total pressure on the first-stage permeate side is fixed at 1.0 MPa (Rp1 ) 2) in the following calculation. Figure 11 shows the total exergy loss calculated for the two-stage separation unit as functions of xf0, SW, and SH. When the H2 mole fraction in the initial feed is 0.01 and 0.03, the exergy loss is greatly reduced using the two-stage separation unit but is still very high. However, it is possible to decrease the exergy loss to a value much smaller than the chemical exergy of hydrogen if the H2 fraction in the initial feed is 0.05. Figures 12
Ind. Eng. Chem. Res., Vol. 37, No. 6, 1998 2513
Figure 10. Scheme for a two-stage separation using H2- and H2Oselective membranes in series (case II). RP1 ) 2.
Figure 12. Distribution of exergy losses for two-stage separation (case II). xf0 ) 0.05, SW ) 200, SH ) 20, and RP1 ) 2. Exergy changes: !, due to pressure rise of the first-stage permeate from 1 to 2 MPa; ", due to pressure rise of trapped steam from 0.1 to 2 MPa; #, due to temperature rise of trapped steam from 25 to 450 °C; 0, due to unrecovered H2; 9, due to mixing entropy.
Figure 11. Total exergy loss for two-stage separation (case II).
and 13 show the contribution of exergy losses for the two-stage membrane separator with a H2/H2O selectivity of 20. Since approximately the half of steam is recovered at the first stage, the exergy loss due to the permeation of steam at the second stage is decreased. The minimum total exergy loss for the two-stage separation is calculated to be 78 and 57 kJ mol-1 under the conditions xf0 ) 0.05, SW ) 200, and SH ) 20 and 100, respectively. Case III. Figure 14 represents a two-stage separation, where two H2-selective membranes are used in series. The permeate side is operated at 0.1 MPa for both stages, and the permeate from the first stage is compressed to 2.0 MPa and completely introduced into the feed side of the second stage. The other assumptions are the same as shown for case II. Figure 15 shows the contribution of exergy losses in case III under the conditions xf0 ) 0.05 and SH ) 20. The minimum value of the total exergy loss is 127 kJ mol-1, which is much larger than that calculated for the two-stage separation using H2O- and H2-selective membranes in series (case II). In case III, the retentate of the first stage is compressed entirely to the feed side of the second stage, which requires a substantial exergy loss.
Figure 13. Distribution of exergy losses for two-stage separation (case II). xf0 ) 0.05, SW ) 200, SH ) 100, and RP1 ) 2. Keys are the same as in Figure 12.
4. Discussion It is possible to separate hydrogen from the steamcontaining mixture by condensation. When the H2H2O-HBr mixture is cooled to 87 °C under 2.0 MPa, the mole fraction of steam in the gas phase is reduced to approximately 0.03, equal to the value obtained at 25 °C under 0.1 MPa. After hydrogen is separated, the condensate is vaporized and again heated to the reaction temperature. When xf0 ) 0.05, the sensible heat required for heating the steam to 450 °C at 2.0 MPa is 87 kJ/mol of recovered hydrogen. This value is larger than the minimum total exergy loss shown in Figures 12 and 13, but this heat is compensated by the sensible
2514 Ind. Eng. Chem. Res., Vol. 37, No. 6, 1998
exergy losses much smaller than the chemical exergyof hydrogen. To attain these values for a feed of xf0 ) 0.05, SW for a H2O-selective membrane and SH for a H2selective membrane are required to be 100 and 20, respectively. As described in the preceding study (Sea et al., 1998b), silica membranes modified with a boehmite sol may meet the requirement of SW ) 100 by further optimizing the preparation conditions. However, the H2-selective membrane showed SH of 7-15 and was somewhat unstable in steam at 400 °C. The SH of H2-selective membranes may be increased by producing membranes using hydrophobic materials, such as siliconcarbide (Sea et al., 1998a) and fluorocarbons. The improvement of H2-selective membranes is the target of a future study. 5. Conclusions Figure 14. Scheme for a two-stage separation using two H2selective membranes in series (case III).
On the basis of the permeation properties of H2- or H2O-selective Si-based membranes, the exergy balance for hydrogen separation in the UT-3 process was analyzed and a hydrogen recovery system involving a minimized exergy loss was proposed. To reduce exergy losses due to temperature and pressure changes, a twostepped H2 separation unit using H2O- and H2-selective membranes in series was suitable for a feed of xf0 ) 0.05. The increase in efficiency of the heat-exchanger systems was also important for the reduction of the exergy loss. Acknowledgment This work was supported by the Ministry of Education, Science, Sports and Culture, Japan (Grant-in-Aid for Scientific Research on Priority Area “Principle of Exergy Regeneration”) and by the New Energy and Industrial Technology Development Organization (NEDO). Nomenclature
Figure 15. Distribution of exergy losses for two-stage separation (case III). xf0 ) 0.05, SH ) 20, and RP1 ) 20. Exergy changes: !, due to pressure rise of the first-stage permeate from 0.1 to 2 MPa; ", due to pressure rise of trapped steam from 0.1 to 2 MPa; #, due to temperature rise of trapped steam from 25 to 450 °C; 0, due to unrecovered H2; 9, due to mixing entropy.
heat which is recovered from the cooling step, provided no exergy is lost during the heat exchange. In the UT-3 process, however, the HBr concentration in the steam recycled to reactor 1 should be low, since the hydrolysis of CaBr2 is controlled by the chemical equilibrium, as described in the preceding paper. Thus, steam is separated from HBr before being recycled to reactor 1. The exergy required by the H2O-HBr separation should be added to the total exergy loss by the condensation method. The H2O-selective membranes developed in the preceding study rejected HBr at a H2O/HBr selectivity of 300-1000. The steam separated at point A using the H2O-selective membrane can be returned without further purification steps. As shown in Figure 11, the two-stage separation using H2O- and H2-selective membranes (case II) gives total
a ) membrane area per unit length, m cP ) molar heat capacity, J mol-1 K-1 δEM ) exergy change due to mixing, J mol-1 δEP ) exergy change due to compression, J mol-1 δET ) exergy change due to temperature change, J mol-1 jH ) hydrogen flux, mol m-2 s-1 ki ) permeance of i component, mol m-2 s-1 Pa-1 L ) membrane length, m m ) molar flow rate, mol s-1 N ) total number of moles in the system ni ) number of moles of i component nk ) number of components P ) total pressure, Pa PS ) reference pressure, Pa Q ) molar heat input, J mol-1 R ) gas constant, J mol-1 K-1 δSM ) entropy change due to mixing, J mol-1 K-1 T ) temperature of system, K TS ) reference temperature, K V ) volume, m3 mol-1 VS ) reference volume, m3 mol-1 x ) hydrogen mole fraction Zc ) mean compressibility factor of steam, PV/RT z ) axial position, m Suffixes H, W ) hydrogen and water, respectively
Ind. Eng. Chem. Res., Vol. 37, No. 6, 1998 2515 f, p ) feed and permeate sides, respectively 0, L ) values at z ) 0 and L, respectively
Sakurai, M.; Bilgen, E.; Tsutsumi, A.; Yoshida, K. Adiabatic UT-3 thermochemical process for hydrogen production. Int. J. Hydrogen Energy 1996, 21, 865-870.
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Agrawal, R. A Simplified method for the synthesis of gas separation membrane cascades with limited numbers of compressors. Chem. Eng. Sci. 1997, 52, 1029-1044. Aochi, A.; Tadokoro, T.; Yoshida, K.; Kameyama, H.; Nobue, M.; Yamaguchi, T. Economical and technical evaluation of UT-3 thermochemical hydrogen production process for an industrial scale plant. Int. J. Hydrogen Energy 1989, 14, 421-429. Castellan, G. W. Physical Chemistry; Addison-Wesley: Reading, MA, 1983; p 140. Hinchliffe, A. B.; Porter, K. E. Gas separation using membranes. 1. Optimization of the separation process using new cost parameters. Ind. Eng. Chem. Res. 1997, 36, 821-829. Hinderink, A. P.; Kerkhof, F. P. M.; Lie, A. B. K.; de Swaan Arons, J.; van der Kooi, H. J. Exergy analysis with a flowsheeting simulatorsI. Theory; calculating exergies of material streams. Chem. Eng. Sci. 1996, 51, 4693-4700. Kameyama, H.; Yoshida, K. Br-Ca-Fe water decomposition cycles for hydrogen production. Proc. 2nd World Hydrogen Energy Conf. Zurich 1978, 829-850. Keenan, J. H. Availability and irreversibility in thermodynamics. Br. J. Appl. Phys. 1951, 2, 183-192. Ohya, H.; Nakajima, H.; Togami, N.; Aihara, M.; Negishi, Y. Separation of hydrogen from thermochemical process using zirconia-silica composite membrane. J. Membr. Sci. 1994, 97, 91-98. Pan, C.-Y. Gas separation by permeators with high flux asymmetric membranes. AIChE J. 1983, 29, 545-553. Pan, C.-Y. Gas separation by high flux, asymmetric hollow-fiber membranes. AIChE J. 1986, 32, 2020-2027. Perrin, J. E.; Stern, S. A. Modeling of permeators with two different types of polymer membranes. AIChE J. 1985, 31, 1167-1177.
Sea, B.-K.; Ando, K.; Kusakabe, K.; Morooka, S. Separation of hydrogen from steam using a SiC-based membrane formed by chemical vapor deposition of triisopropylsilane. J. Membr. Sci. 1998a, in press. Sea, B.-K.; Watanabe. M.; Kusakabe, K.; Morooka, S.; Kim, S. S. Hydrogen recovery using membranes from a H2-H2O-HBr mixture at elevated temperatures. 1. Preparation of H2O- and H2-selective membranes. Ind. Eng. Chem. Res. 1998b, 37, 2502-2508. Shindo, Y.; Hakuta, T.; Yoshitome, H.; Inoue, H. Calculation methods for multicomponent gas separation by permeation. Sep. Sci. Technol. 1985, 20, 445-459. Thundyil, M. J.; Koros, W. J. Mathematical modeling of gas separation permeators for radial cross-flow, countercurrent, and cocurrent hollow fiber membrane modules. J. Membr. Sci. 1997, 125, 275-291. Xu, J.; Agrawal, R. Gas separation membrane cascades. I. Onecompressor cascades with minimal exergy losses due to mixing. J. Membr. Sci. 1996, 112, 115-128.
Received for review October 20, 1997 Revised manuscript received March 5, 1998 Accepted March 11, 1998 IE980173L
