Hydrogen production from hydrogen sulfide using membrane reactor integrated with porous membrane having thermal and corrosion resistance

Journal of Membrane Science 146 (1998) 39±52

Hydrogen production from hydrogen sul®de using membrane reactor integrated with porous membrane having thermal and corrosion resistance Hirofumi Ohashi, Haruhiko Ohya*, Masahiko Aihara, Youichi Negishi, Svetlana I. Semenova1 Department of Material Science and Chemical Engineering, Yokohama National University, Hodogaya-ku, Yokohama 240-8501, Japan Received 2 December 1997; received in revised form 4 March 1998; accepted 5 March 1998

Abstract Using mathematical model and experimental method, the thermal decomposition of hydrogen sul®de in membrane reactor with porous membrane which has Knudsen diffusion characteristics was investigated. With mathematical model, the effect of characteristics of membrane reactor and operating conditions on H2 concentration in the permeate chamber, yH2 , which increases at higher reaction temperature, lower pressure and higher ratio of cross-sectional area of the permeate chamber to that of the reactor, was evaluated. The reaction experiments with ZrO2±SiO2 porous membrane were carried out under the following conditions: temperature T, 923±1023 K; pressure in the reactor pRT, 0.11±0.25 MPa absolute; pressure in the permeate chamber pPT, 5 kPa absolute and inlet ¯ow rate of H2S fH02 S , 3.210ÿ5±1.510ÿ4 mol/s. At pRT ˆ0.11 MPa and fH02 S ˆ6.410ÿ5, yH2 increased from 0.02 at Tˆ923 K to 0.15 at 1023 K. With the experimental condition, pRT ˆ0.11, Tˆ1023 K and fH02 S ˆ3.210ÿ5, yH2 was 0.22. The experimental results were compared with the results of the mathematical analysis. The agreement between both the results is found rather good at a lower reacting temperature, but not so good at a higher reacting temperature. # 1998 Elsevier Science B.V. All rights reserved. Keywords: Hydrogen; Hydrogen sul®de; Inorganic membranes; Membrane reactor; Porous membranes

1. Introduction Sulfur dioxide which is one of the components of an air pollutant is mainly produced by combustion of sulfur containing oil. Therefore, the demand for low sulfur distillates is increasing and in petroleum re®nery, gas oil, petroleum light and heavy fractions are *Corresponding author. Tel.: +81 45 339 3989; fax: +81 45 339 4012; e-mail: [email protected] 1 Now with APO Polimersintez, 77 Frunze Str. Vladimir, 600020 Russian Federation. 0376-7388/98/$19.00 # 1998 Elsevier Science B.V. All rights reserved. PII S0376-7388(98)00089-1

subjected to the hydrodesulfurization process to reduce sulfur content. As a by-product in the process, a huge amount of hydrogen sul®de has been produced. The produced H2S is partially oxidized by the Claus process, where the valuable product is only elementary sulfur and valuable hydrogen cannot be recovered and is ®nally wasted in the form of water. The H2S decomposition process, which produces hydrogen and sulfur, has become of great interest [1,2]. H2 S@H2 ‡ 1=x Sx

(1)

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H. Ohashi et al. / Journal of Membrane Science 146 (1998) 39±52

The advantages of this process are the production of hydrogen besides sulfur production. The reaction is highly endothermic and the equilibrium conversions are low even at a high temperature. Therefore, the direct decomposition of H2S can be accomplished at high temperatures, usually above 1000 K (preferably 1800 K). For the purpose of decreasing the reaction temperature, one of the proposed methods for shifting the equilibrium conditions is the removal of the products as Rectisol process, in which sulfur is removed by condensation, and the direct removal of hydrogen from the reaction zone using permselective membrane. Since H2S starts to decompose measurably above 1000 K, the membrane should not be degraded above 1000 K. The use of palladium-based membrane would be highly desirable because of their potential to cause equilibrium shift as well as the production of a pure hydrogen stream. However, its use may be restricted by temperature and the corrosion environment of the reaction as reported by Edlund and Pledger [3,4]. The use of ceramic membrane may avoid these problems, but they would allow permeation of all components resulting in the lower equilibrium shift as reported by Dokiya et al. [5] and Kameyama et al. [6,7] Recently, Zaman and Chakma [8] investigated the reaction using mathematical models for membrane reactors and recommended the use of higher temperature and reactor con®guration with high membrane surface to reactor volume and a large residence time. In this work the reaction has been investigated in a ceramic membrane reactor using mathematical model and experimentally using zirconia membrane which shows Knudsen diffusion characteristics. The objective has been to examine the predictability of the mathematical model which includes the reaction occurring in the permeate side chamber, and to check the data obtained experimentally and mathematically.

the overall kinetics which is considered as the difference of the rates of the forward reaction of hydrogen sul®de decomposition and the reverse reaction of hydrogen sul®de synthesis from hydrogen and sulfur: rH2 S ˆ k
fpH2 S ÿ pH2
…pS2 †1=2 =K…T†g   ÿEa
fpH2 S ÿ pH2
…pS2 †1=2 =K…T†g; ˆ k0
exp R
T (2) where k0 ˆ 7:74  103 mol=…m3 Pa s†;

Ea ˆ 196 kJ=mol: (3)

K(T) is obtained from the value of the standard enthalpy of formation at 298 K and heat capacity as follows: K…T† ˆ 318:3 exp…ÿ9660 T ÿ1 ‡ 2:279 ln T ÿ 1:315  10ÿ3 T ‡ 1:228  10ÿ7 T 2 ÿ 9:845†:

(4)

When the reaction reaches equilibrium, rH2 S ˆ 0, then the relation between the pressures of each component can be expressed as follows: peH2 S ˆ peH2
…peS2 †1=2 =K…T†;

(5)

peT ˆ peH2 S ‡ peH2 ‡ peS2 :

(6)

2.2. Basic equations for reactor without membrane The schematic diagram of a reactor without membrane is shown in Fig. 1.

2. Theoretical 2.1. Kinetics Kaloidas and Papayannakos [9] proposed the following rate equation, Eq. (2), of the thermal and noncatalytic decomposition of hydrogen sul®de based on

Fig. 1. Schematic diagram of a reactor without membrane.

H. Ohashi et al. / Journal of Membrane Science 146 (1998) 39±52 Table 1 Stoichiometric number for each component in thermal decomposition of H2S H2 S ÿ1

i i

H2 1

1 ji …Mw;i
T† / p
pi : Mw;i
T

41

(13)

Eq. (13) is expressed using Knudsen number, Ki, and permeance for H2, PH2 , as follows:

S2 1 2

ji ˆ PH2
Ki
pRT



pi ; pRT

(14)

Assuming an isothermal operation and plug ¯ow in the reactor, a material balance of each gaseous component across a differential of longitudinal length l, dl of the reactor yields the following ordinary differential equation:

where s Mw;H2 : Ki ˆ Mw;i

dfi ˆ sR
i
rH2 S ; i ˆ H2 S; H2 ; S2 ; dl

Knudsen number for component i is de®ned as the ratio of the square root of the molecular weight of H2 to that of component i.

(7)

where  i is the stoichiometric number for each component shown in Table 1. It has been proved that, above 1000 K, S2 is the most abundant species of sulfur [10,11]. Eq. (7) can be non-dimensionalized as the following equations: dFi ˆ i
NRR ; dL

(8)

where Fi ˆ

fi ; fH02 S

l0 ˆ

fH02 S sR
rH0 2 S

Lˆ

l ; l0

NRR ˆ

(9) ;

(15)

2.4. Basic equations for reactor with porous membrane The schematic diagram of a reactor with membrane is shown in Fig. 2. For the membrane reactor, the following ordinary differential equation for each gaseous component can be obtained by adding membrane permeation rate term ji to Eq. (7) in the reactor. (In the reactor) dfi sR ˆ sR
i
rHR2 S ÿ ji : dl h

(16)

(10) (11)

rHR2 S fxH2 S ÿ …pRT †1=2
xH2
…xS2 †1=2 =K…T†g ˆ ; rH0 2 S fx0H S ÿ …pRT †1=2
x0H
…x0S †1=2 =K…T†g 2 2 2 (12)

where l0 means reactor length needed to react all the feed H2S, fH02 S , at the initial reaction rate, rH0 2 S . 2.3. Porous membrane Let us assume it is possible to make a membrane reactor integrated with a porous inorganic membrane which has characteristics of Knudsen ¯ow. Then, the ¯ow or permeation rate of ith component of molecular weight, Mw,i, at temperature T, ji(Mw,i,T) is expressed as follows:

Fig. 2. Schematic diagram of a reactor with membrane.

42

H. Ohashi et al. / Journal of Membrane Science 146 (1998) 39±52

Also the reaction occurs in the permeate chamber, and we can obtain the following ordinary differential equation: (In the permeate chamber) dui sR ˆ sP
i
rHP 2 S ‡ ji ; dl h

(18)

(In the permeate chamber) dUi
pi ˆ SP
i
NRP ‡ Ki
H2
R ; dL pT

(19)

where Ui ˆ

ui

fH02 S

;

(20)

rP fpP :yH S ÿ …pPT †3=2
yH2
…yS2 †1=2 =K…T†g NRP ˆ H0 2 S ˆ T 2 ; rH2 S fpRT
x0H S ÿ …pRT †3=2
x0H
…x0S †1=2=K…T†g 2 2 2 (21) s ; sR PH
p R ˆ 02 T : rH 2 S
h

SP ˆ

H 2

P

(22) (23)

Rate ratio, H2 , is the inverse ratio of the initial reaction rate, rH0 2 S , to the permeation ¯ux of H2 when only H2 exists in the reactor with zero pressure in the permeate chamber.
pi is the difference between partial pressure in the reactor, pRT
xi , and that in the permeate chamber, pPT
yi .
pi ˆ pRT
xi ÿ pRT
yi :

(24)

With Eq. (24), Eqs. (18) and (19) can be transformed into the following equations: (In the reactor) dFi …pR
xi ÿ pPT
yi † ˆ i
NRR ÿ Ki
H2
T : dL pRT

dUi …pR
xi ÿ pPT
yi † ˆ SP
i
NRP ‡ Ki
H2
T : dL pRT

(26)

(17)

where h is the ratio of the volume of the reactor to the membrane area. Substituting Eq. (14) into Eqs. (16) and (17), nondimensionalization is carried out using rate ratio, H2 , and the results are as follows: (In the reactor) dFi
pi ˆ i
NRR ÿ Ki
H2
R : dL pT

(In the permeate chamber)

(25)

2.5. Numerical analysis Numerical integration of Eqs. (8), (25) and (26) was carried out by fourth order Runge±Kutta method with the following boundary conditions: FH2 S ˆ FH0 2 S ˆ 1:0;

FH2 ˆ FH0 2 ˆ 0;

FS2 ˆ FS02 ˆ 0 at L ˆ 0;

(27)

Ui ˆ Ui0 ˆ 0;

(28)

i ˆ H2 S; H2 ; S2 at L ˆ 0:

For the purpose of calculating the arguments of Eqs. (8), (25) and (26), xi and yi can be obtained from the following equations: .X (29) Fi ; x i ˆ Fi .X (30) yi ˆ Ui Ui : At Lˆ0, yi cannot be de®ned. Therefore, y0i needs to be calculated. As a ®rst trial, assuming y1i ˆ x0i ; …1† Ui for the ®rst increment
Lˆ0.001 are calculated with Eq. (26). Second trial of y2i can be calculated using Eq. (30). Comparing y2i with y1i , if the difference between y2i and y1i is larger than a de®ned value of error; the same procedure of calculation is repeated replacing y2i in Eq. (26). If small, calculation procedure of Runge±Kutta method starts with y0i ˆ y2i . 3. Results of numerical analysis 3.1. Reactor without membrane The conversion of H2S, , is de®ned as follows, using fH2 S obtained by the numerical integration: ˆ

…fH02 S ÿ fH2 S † : fH02 S

(31)

Fig. 3 shows the increase of conversion of H2S along with the non-dimensional reactor length

H. Ohashi et al. / Journal of Membrane Science 146 (1998) 39±52

Fig. 3. Conversion profiles in the reactor without membrane at the reaction temperatures of 823, 1023 and 1223 K and the reaction pressures 0.2, 1 and 10 MPa.

at the reaction temperatures of 823, 1023 and 1223 K and at the reactor pressures 0.2, 1 and 10 MPa, respectively. The conversion increases monotonically with the increase of the reaction temperature, and with the decrease of the reaction pressure. At lower reaction temperature, the conversion reaches equilibrium values calculated from Eqs. (5) and (6) at the short dimensionless reactor length, for example Lˆ0.01 at 823 K. Even at a higher temperature of 1223 K, and lower pressure of 0.2 MPa, conversion reaches 0.125 at Lˆ0.35 and gradually increases thereafter to the equilibrium value of 0.130. 3.2. Reactor with membrane Taking account of both ¯ow of H2S in the reactor, fH2 S , and in the permeate chamber, uH2 S , the total conversion of H2S, using fH2 S , uH2 S dimensionalized values of corresponding values of numerically integrated T, is de®ned as follows: T ˆ

…fH02 S ÿ fH2 S † ‡ …u0H2 S …ˆ 0† ÿ uH2 S † : fH02 S ‡ u0H2 S …ˆ 0†

(32)

43

Fig. 4. Profile of total conversion in the reactor integrated with porous membrane at reaction temperature 1223 K and pressure in the reactor, pRT ˆ0.2 MPa and in the permeate chamber, pPT ˆ5 kPa with membrane reactor characteristics, H2 ˆ0.01 and SPˆ1.

Fig. 4 shows the increase of total conversion of H2S along with dimensionless reactor length at the reaction temperature 1223 K, the reactor pressure of 0.2 MPa, the permeate chamber pressure of 5 kPa, and with membrane reactor characteristic, H2 ˆ0.01 and SPˆ1. Comparing with the curve for the corresponding reaction conditions Tˆ1223 K, pRT ˆ0.2 MPa, in Fig. 3, the shapes of both the curves of conversion or total conversion vs. L are almost same until Lˆ0.5. But the total conversion in the reactor with membrane continuously increases after Lˆ0.5 and takes 0.135 at Lˆ10, because forward reaction of H2S decomposition continuously occurs in the reactor accompanied by the slippage from the equilibrium state by depletion of H2 and enrichment of S2, due to the fact that the H2 permeates through the membrane more selectively than S2. The concentration curves for each component in the reactor are almost same, even with or without membrane as shown in Fig. 5. With membrane, concentrations of H2, S2 and H2S are slightly lower, higher and higher, respectively, than that of without membrane by
xH2 ,
xS2 and
xH2 S , respectively. Then, the slope of the total conversion is expressed by the

44

H. Ohashi et al. / Journal of Membrane Science 146 (1998) 39±52

Fig. 5. Concentration profiles for each component in the reactor with or without membrane at reaction temperature 1223 K and reaction pressure of 0.2 MPa.

Fig. 6. Concentration profiles for each component in the permeate chamber at reaction temperature 1223 K and pressure in the reactor, pRT ˆ0.2 MPa and in the permeate chamber, pPT ˆ5 kPa with membrane reactor characteristics, H2 ˆ0.01 and SPˆ1 and equilibrium concentration at 1223 K and pressure of 5 kPa.

following equation:

! dT …pRT †1=2 e
xS2 e 1=2
xH2 ˆ
xH2 S ÿ
xH2
…xS2 †
‡ dL K…T† xeH2 2
xeS2 ( pPT …pP †1=2 e
yH2
…yeS2 †1=2 ‡ R
yH2 S ÿ T K…T† pT !)
yH2
yS2
‡ ; (33) yeH2 2
yeS2 where forward reaction of H2S decomposition in the permeate chamber is also considered as the third term of the right-hand side of the equation. In the case of the reaction condition shown in Fig. 4, dT/dL is calculated as 8.4110ÿ4, using the following set of values:
xH2 S ˆ1.7110ÿ3,
xH2 ˆÿ3.9610ÿ3,
xS2 ˆ2.1910ÿ3,
yH2 S ˆ2.4310ÿ2,
yH2 ˆ0.104 and
yS2 ˆ7.9410ÿ2. Fig. 6 shows the concentration curves of each component in the permeate chamber, and the concentration of H2 increases steeply along with reactor length until Lˆ0.01 and then gradually increases, and reaches almost constant value of 0.415 at Lˆ5.0. Let us de®ne this constant value as yCon: H2 .

The concentration of S2 also increases steeply until Lˆ0.01, taking maximum value of 0.15, then decreases to 0.076. The solid lines in Fig. 7 show the increase of Ui. The dotted lines also shown in the same ®gure correspond to the cumulative value of permeation ¯uxes of each component. The discrepancy between the solid and the dotted lines is due to the reaction occurring in the permeate chamber, the amount of which is about 15% for H2S. The solid line for S2 is 2.5 times larger than the dotted line, because the permeation ¯ux of S2 is small compared to the reaction. 3.2.1. Effect of reaction temperature and pressure Fig. 8 shows the effect of temperature and pressure on the constant H2 concentration in the permeate chamber, yCon: H2 . With the increase of the reaction temperature, and the decrease of the pressure in the reactor, pRT , yCon: H2 increases. The effect of temperature is signi®cant, particularly at low pressure operation. are within the range from 0.027 to At 823 K, yCon: H2 0.036. But, at 1223 K yCon: H2 for 0.2 MPa is 0.415 and 0.216 for 10 MPa, these values are about 11.5 and 8.0

H. Ohashi et al. / Journal of Membrane Science 146 (1998) 39±52

45

times larger than that for 0.2 and 10 MPa at 823 K, respectively. For the purpose of yielding higher yCon: H2 , reaction temperature should be high, therefore, the most important characteristics of the membrane is thermal resistivity. On the other hand, mechanical strength of the membrane and reactor is not so important because lower the pRT higher is the yCon H2 .

Fig. 7. Profiles of dimensionless flow rate in the permeate chamber, Ui, and cumulative value of permeation fluxes for each component at reaction temperature 1223 K and pressure in the reactor, pRT ˆ0.2 MPa and in the permeate chamber, pPT ˆ5 kPa with membrane reactor characteristics, H2 ˆ0.01 and SPˆ1.

Fig. 8. Effect of reaction temperature and pressure in the reactor on the constant concentration of H2 in the permeate chamber, yCon: H2 , at pressure in the permeate chamber, pTP ˆ5 kPa with membrane reactor characteristics, H2 ˆ0.01 and SPˆ1.

3.2.2. Effect of rate ratio (ratio of permeation rate to reaction rate) Fig. 9 shows the effect of rate ratio, H2 , on the H2 concentration in the permeate chamber, yH2 . With the decrease of H2 , yH2 increases. From the de®nition of Eq. (23), H2 is the ratio of the amount of permeation to the amount of reaction. Decrease of H2 means that a few amount of the reactant is withdrawn from the reactor, and that component of reactant gas reaches almost equilibrium, as shown in Fig. 5. Therefore, concentration of H2S, H2 and S2 in the permeate are 0.6, 0.36 and 0.04, respectively. The permeated H2S decompose to H2 and S2 soon in the permeate chamber, and then the concentrations of H2S, H2 and S2 in the permeate reach almost constant values, 0.54, 0.42 and 0.07, respectively. It is interesting that the shape of the

Fig. 9. Effect of rate ratio, H2 , on the concentration of H2 in the permeate chamber, H2 , at reaction temperature 1223 K and pressure in the reactor, pRT ˆ0.2 MPa and in the permeate chamber, pPT ˆ0.5 kPa with membrane reactor characteristic, SPˆ1.

46

H. Ohashi et al. / Journal of Membrane Science 146 (1998) 39±52

of yCon: H2 as shown in Fig. 8. For the reaction scheme expressed by Eq. (1), reverse reaction of synthesis of P R H2S increases with the increase of yCon: H2 . At the pT =pT Con: corresponding to the maximum yH2 reverse reaction rate becomes almost equal to the forward reaction and thereafter, exceeds the forward reaction.

Fig. 10. Effect of pressure in the permeate chamber, pPT , on the constant concentration of H2 in the permeate chamber, yCon: H2 , at reaction temperature 1223 K with membrane reactor characteristics, H2 ˆ0.01 and SPˆ1.

yH2 curves takes clearly the maximum value at Lˆ1.0 for H2 ˆ0.1, 0.5, 1.0 and 2.0. For H2 ˆ0.01, it seems yH2 is constant after Lˆ1.0. With large H2 , almost all the reactant permeates through the membrane. Therefore, the curves are discontinued at Lˆ2.0 for H2 ˆ 2.0, at Lˆ3.0 for H2 ˆ1.0 and at Lˆ7.0 for H2 ˆ0.5. 3.2.3. Effect of pPT (total pressure in the permeate chamber) Fig. 10 shows the effect of pressure in the permeate chamber, pPT , on the constant concentration of H2 in the P permeate chamber, yCon: H2 which increases at lower pT. From the Le Chatelier Brown's rule, H2S decomposition reaction which is a molecular number increasing one, proceeds when total pressure decreases. At higher pPT , with the increase of the ratio of pPT to the pressure in the reactor pRT, pPT =pRT , yCon: H2 slightly increases and passes through the maximum value and then, slightly decreases. The difference between the maximum value and the smallest is not so large as 0.02 for pPT ˆ 0.5 MPa, 0.03 for 0.10 MPa and 0.05 for 0.05 MPa. At lower pPT ˆ0.005, with the increase of pPT =pRT , yCon: H2 increase from 0.215 for pRT ˆ10 MPa to 0.43 for pRT ˆ 0.1 MPa. With pPT kept constant, increasing pPT =pRT means decreasing pRT , which results in the increase

3.2.4. Effect of SP (ratio of cross-sectional area of permeate chamber to that of the reactor) Fig. 11 shows the effect of SP on the constant concentration of H2 in the permeate chamber, yCon: H2 . With the increase of SP, which means the increase of cross-sectional area of the permeate chamber, ¯ow rate of permeated gas in the chamber decreases, resulting in the increase of residence time in the chamber. Therefore, the degree of reaction approaches almost equilibrium. In the region L larger than 5, NRP s, the non-dimentionalized reaction rate in the permeate chamber are 6.610ÿ3, 2.210ÿ3, 2.910ÿ4 and 3.010ÿ5 for SPˆ0.01, 0.1, 1 and 10, respectively. The values of NRP s for SP larger than 1.0 are very small and there essentially no reaction occurs. Therefore, approaches equilibrium concentration, 0.415, yCon: H2 and it is not necessary to increase SP larger than 1.0.

Fig. 11. Effect of SP on the constant concentration of H2 in the permeate chamber, yCon: H2 , at reaction temperature 1223 K and pressure in the reactor, pRT ˆ0.2 MPa and in the permeate chamber, pPT ˆ0.5 kPa with membrane reactor characteristic, H2 ˆ0.01.

H. Ohashi et al. / Journal of Membrane Science 146 (1998) 39±52

4. Experimental and experimental results 4.1. Membrane preparation Via the metal alkoxide method reported earlier [12,13], a thin microporous ZrO2±SiO2±Y2O3 layer was coated on the surface of a porous ceramic tubing, the dimensions of which were 5.5 mm o.d. and 3.5 mm i.d. and average pore diameter was 0.5 mm (supplied by ToTo). The molar ratio of Zr(OC3H7)4:Si(OC2H5)4:Y(CH3COO)3
4H2O:i-C3H7OH in the coating solution was 0.9:0.1:0.054:20.0. More details of the preparation procedure of the composite membrane was reported earlier [14]. 4.2. Membrane integrated reactor A schematic ¯ow diagram of the experimental apparatus is shown in Fig. 12. All tubing were made of 316 stainless steel and the cell was made of 310s stainless steel. Temperature in the reactor is controlled so as to make ¯at distribution in the range of 7.0 cm on the surface of membrane by

47

temperature controller (DB-1000, Chino) and also adjusting the winding density of heating wire in the furnace. Cut-view of the reactor cell is shown in Fig. 13. A typical example of temperature distribution of the center of reactor is also shown in Fig. 13, from which the effective length of the reactor, le, is de®ned as considering reaction rate written in Eq. (2): R lT le ˆ

exp‰ÿEa =fR
T…l†gŠdlg ˆ 9:0 cm: expfÿEa =…R
Tmemb: †g

0

The cross-sectional area of the reactor and the permeated chamber are sRˆ5.92 cm2, and sPˆ 0.096 cm2, respectively. The effective length of the membrane and the reactor are 70 and 90 mm, respectively, and hˆVreactor/Smemb.ˆ(1.429.0)/ (0.557.0)ˆ4.6 cm. 4.3. Permeance of pure gas The measuring method of permeation of pure gas was already reported earlier [12].

Fig. 12. A schematic flow diagram of the experimental apparatus.

48

H. Ohashi et al. / Journal of Membrane Science 146 (1998) 39±52

Fig. 13. A cut-view of the reactor cell. s R ˆ5.92 cm 2 , s Pˆ0.096 cm 2 , S PˆsP /sRˆ0.016 (dimensionless), l eˆ9.0 cm, hˆVreactor/Smemb.ˆ4.6 cm.

Fig. 14(a) shows the dependence of permeance of H2 and H2S on temperature. The correlation of permeance of H2 on 1/T shows one straight line. But, the correlation for H2S is made of two lines. Assuming the permeation mechanism of gas through this membrane as Knudsen ¯ow mechanism, the permeance for H2 p and H2S are replotted against 1= Mw;i
T in Fig. 14(b) and Pi found seems to be well correlated by Eq. (35) based on Knudsen ¯ow mechanism. The solid lines in Fig. 14(a) are taken from Fig. 14(b). It was found that the permeance of H2S is slightly higher than that predicted at lower temperature and slightly lower at higher temperature: ji ˆ Pi

pi ;

p Pi ˆ 1:2  10ÿ7 Mw;i
T :

(34) (35)

4.4. Reaction experiment Reaction experiment for the thermal decomposition of H2S was carried out under the condition as follows: reaction temperature 923±1023 K, operating pressure in the reactor 0.11±0.25 MPa absolute and that in the permeate chamber 5.3 kPa absolute and the inlet ¯ow

Fig. 14. (a) 1/T vs. Pi; (b) 1/(Mw,iT)1/2 vs. Pi.

rate of H2S, fH02 S ˆ3.210ÿ5±1.510ÿ4 mol/s. A product sulfur was removed continuously using a trap cooled by an ice at the outlet of the reactor and permeate chamber. The composition of gaseous mixture at the exit of the reactor and the permeate chamber were analyzed with gas chromatography (GC-8A, Shimadzu) using Poropak Q column (GL Science).

H. Ohashi et al. / Journal of Membrane Science 146 (1998) 39±52

Fig. 15. Effect of temperature on total conversion, H2 concentration in the reactor, xH2 , and in the permeate chamber, yH2 , at pressure in the reactor, pRT ˆ0.11 MPa and in the permeate chamber, pPT ˆ5 kPa with membrane reactor characteristic, SPˆ0.016.

4.4.1. Effect of the reaction temperature Fig. 15 shows the effect of the reaction temperature on T, xH2 and yH2 . With the increase of temperature, T, xH2 and yH2 increase. 4.4.2. Effect of the pressure in the reactor, pRT Fig. 16 shows the effect of pRT on total conversion, T, H2 concentration at the exit of the reactor, xH2 , and H2 concentration at the exit of the permeate chamber, yH2 . At pRT ˆ0.11 MPa, yH2 was 0.15. With the increase of pRT ; T ; xH2 and yH2 decrease. 4.4.3. Effect of the dimensionless distance along with the reactor, L Using Eqs. (10) and (11), non-dimensional reactor length, L can be rewritten as follows: Lˆ

l
rH0 2 S
sR : fH02 S

(36)

49

Fig. 16. Effect of the pressure in the reactor, pRT , on total conversion, H2 concentration in the reactor, xH2 , and in the permeate chamber, yH2 , at reaction temperature 1023 K and pressure in the permeate chamber, pPT ˆ5 kPa with membrane reactor characteristics, H2 ˆ0.08 and SPˆ0.016.

Therefore, we can change the value of L by changing inlet ¯ow rate of H2S, fH02 S . Fig. 17 shows the effect of L on T, xH2 and yH2 . With the increase of L, T increases from 0.045 to 0.06, and yH2 from 0.15 to 0.22. 5. Analysis of experimental results Table 2 shows a list of Ki and H2 at 923, 973 and 1023 K, using Eqs. (15),(23) and (35). The value of l0 can be calculated using Eq. (10). For example, Tˆ1023 K, pRT ˆ0.11 MPa, fH02 S ˆ6.410ÿ5 mol/s, sRˆ 5.910ÿ4 m2, lˆ0.09 m, rH0 2 S ˆ0.0885 mol/(m3 s), l0 ˆ fH02 S =…sR
rH0 2 S †ˆ1.23 m. Therefore, Lˆl/l0ˆ0.073. Because the initial reaction rate, rH0 2 S , de®ned by Eq. (2) depends on temperature, the value of L changes with temperature as shown in Table 3.

50

H. Ohashi et al. / Journal of Membrane Science 146 (1998) 39±52

Fig. 17. Effect of dimensionless distance along with reactor, L, on total conversion, H2 concentration in the reactor, xH2 , and in the permeate chamber, yH2 , at reaction temperature 1023 K and pressure in the reactor, pRT ˆ0.11 MPa and in the permeate chamber, pPT ˆ5 kPa with membrane reactor characteristics, H2 ˆ0.08 and SPˆ0.016.

Table 2 Rate ratio and Knudsen number T (K)

H2 (dimensionless)

KH2 S (dimensionless)

KS2 (dimensionless)

923 973 1023

1.01 0.27 0.08

0.243

0.177

Table 3 Initial reaction rate, rH0 2 S (at pRT ˆ0.11 MPa), l0 and dimensionless distance, L T (K) 923 973 1023

rH0 2 S (mol/(m2 s)) ÿ3

7.3210 2.7110ÿ2 8.8510ÿ2

l0 (m)

L (m)

14.8 4.00 1.23

6.0810ÿ3 2.2510ÿ2 7.3010ÿ2

Solid lines shown in Figs. 15±17 are the numerically analyzed values; total conversion, T, xH2 and yH2 are de®ned by Eqs. (32), (29) and (30), respectively. The agreement between the experimental values and the numerical analyzed is good in Fig. 15. Large difference is found for T, xH2 and yH2 in Fig. 16, which shows the effect of the pressure. Observed values are smaller than the calculated values, except yH2 , at low pressure. The reason might be due to the inadequate design of the reactor or the fact that it is impossible to design an ideal reactor. The temperature of the reactant gas decreases from the reaction temperature to the room temperature as shown in Fig. 13. During the course of decreasing temperature, reverse reaction may occur because the activation energy of the reverse reaction, 105 kJ/mol, is lower than that of the forward reaction, 196 kJ/mol [9]. Therefore, in the region from the exit of the reactor to the sampling port, the reverse reaction exceeds the forward reaction, resulting in the reduction of the experimental values of xH2 . As for yH2 , H2 concentration in the permeate chamber, the observed yH2 is larger at lower pRT, but with the increase of pRT , yH2 is smaller than the calculated one. The permeated gas might also be subjected to further reaction. From the temperature pro®le in Fig. 13, the residence time in the permeate chamber after reaction zone is almost the same as that in the reaction zone. Therefore, further forward reaction occurs, and reverse reaction occurs during the course of temperature decreasing. At lower pRT, the amount of permeate is small. On the contrary, with the increase of pRT , the amount increases. Hence, residence time during the course of temperature decreasing is shorter at low pRT and longer at high pRT because the pumping capacity of the vacuum pump is limited. At higher pRT, the reverse reaction is larger than the forward reaction in the region from the exit of the permeated chamber to the sampling port. Therefore, with the increase of pRT , the amount of the reverse reaction increases, and then the experimental values of yH2 is smaller than the calculated value. In Fig. 17, it was found that the experimental values of yH2 is higher than the calculated one. The reason might be due to the fact that ¯ux of H2S was smaller than that predicted on Knudsen ¯ow mechanism as mentioned in Fig. 14(a) and ¯ux of H2 was same as predicted, resulting in the increase of yH2 .

H. Ohashi et al. / Journal of Membrane Science 146 (1998) 39±52

6. Conclusion 1. Theoretical equations for the thermal decomposition of H2S without and with porous membrane which has Kundsen diffusion characteristics are obtained. 2. In the results of numerical analysis for the reactor integrated with porous membrane, high value of H2 concentration in the permeate chamber can be obtained at higher reaction temperature, lower pressure, lower rate ratio and higher SP . 3. It was found that the permeation mechanism for H2 and H2S through the membrane is based on Knudsen diffusion. 4. Membrane reactor was constructed integrating ZrO2±SiO2 composite membrane and thermal decomposition of H2S was carried out using membrane reactor in the temperature range 923±1023 K, pressure in the reactor 0.11±0.25 MPa absolute, and that in the permeate chamber 5 kPa absolute and inlet flow rate of H2S 3.210ÿ5±1.510ÿ4 mol/s. 5. It was found that the reactor integrated with ZrO2± SiO2 composite membrane gave 0.22 of H2 concentration in the permeate chamber in maximum, and this value was higher than the equilibrium one in the reactor by about four times under the temperature condition 1023 K, pressure in the reactor 0.11 MPa absolute, that in the permeate chamber 5 kPa absolute and inlet flow rate of H2S 3.210ÿ5 mol/s. 6. The agreement between the experimental results and the numerical analysis was relatively good. 7. Symbols fi h ji k k0 l l0

flow rate of component i in the reactor (mol/s) ratio of the volume of the reactor to the membrane area (m) gas permeation flux through the membrane of component i (mol/(m2 s)) reaction rate constant (mol/(m3 Pa s)) frequency factor corresponding to the reaction rate constant (mol/(m3 Pa s)) length along with the reactor zone (m) reactor length needed to react all the feed H2S at the initial reaction rate as defined by Eq. (10) (m)

p
p rH2 S s ui xi yi Ea Fi Ki K(T) L Mw,i NR Pi R Smemb. SP T Ui Vreactor

H 2 i 

pressure (Pa) trans-membrane pressure (Pa) reaction rate (mol/(m3 s)) cross-sectional area (m2) flow rate of component i in the permeate chamber (mol/s) mol fraction of component i in the reactor (dimensionless) mol fraction of component i in the permeate chamber (dimensionless) apparent activation energy of H2S decomposition reaction (J/mol) dimensionless flow rate of component i in the reactor as defined by Eq. (9) (dimensionless) Knudsen number as defined by Eq. (15) (dimensionless) thermodynamic equilibrium constant (Pa1/2) dimensionless distance along with the reactor as defined by Eq. (11) (dimensionless) molecular weight of component i (kg/mol) dimensionless reaction rate (dimensionless) permeance of component i (mol/(m2 Pa s)) gas constant (J/(mol K)) surface area of membrane (m2) ratio of cross-sectional area of permeate chamber to that of reactor (dimensionless) absolute temperature (K) dimensionless flow rate of component i in the permeate chamber as defined by Eq. (20) (dimensionless) volume of the reactor (m3) rate ratio as defined by Eq. (23) (dimensionless) stoichiometric coefficients of component i (dimensionless) conversion (dimensionless)

Superscripts 0 R P

feed condition in the reactor in the permeate chamber

Subscripts i T

51

reactants total

52

H. Ohashi et al. / Journal of Membrane Science 146 (1998) 39±52

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