Engineering Evaluations of a Catalytic Membrane Reactor for the

87030 Rende CS, Italy, and Department of Chemical Engineering and Materials, c/o The University of. Calabria, via P. Bucci, cubo 44/A, 87030 Rende CS,...
0 downloads 0 Views 153KB Size
Download PDF
7676

Ind. Eng. Chem. Res. 2005, 44, 7676-7683

Engineering Evaluations of a Catalytic Membrane Reactor for the Water Gas Shift Reaction Giuseppe Barbieri,*,† Adele Brunetti,†,‡ Teresa Granato,‡ Paola Bernardo,† and Enrico Drioli†,‡ Institute for Membrane Technology (ITM-CNR), c/o The University of Calabria, via P. Bucci, cubo 17/C, 87030 Rende CS, Italy, and Department of Chemical Engineering and Materials, c/o The University of Calabria, via P. Bucci, cubo 44/A, 87030 Rende CS, Italy

A study of the performance of a membrane reactor (MR) for the water gas shift (WGS) reaction is presented, also pursuing the membrane engineering approach in the logic of the Process Intensification Strategy. The MR mathematical model was developed from the design equation of traditional reactors considering a H2 high-selectivity membrane, to perform a comparison between the two reactor types and experimental literature data8 and qualitatively and quantitatively estimate the convenience of MR use. The effect of the operating conditions (temperature, reaction pressure, feed flow rate, etc.) on the catalyst efficiency was also considered in addition to their influence on the reaction from kinetic and thermodynamic points of view. A catalyst effectiveness factor was calculated considering the Thiele module. It takes into account the kinetic and diffusive resistances inside the catalytic pellet, which also depend on the pellet geometric characteristics (pore diameter, pore length, tortuosity, porosity, etc.). The obtained results confirmed the advantage of the use of a MR for the WGS reaction, in terms of conversion improvement and reduction of the necessary reaction volumes and related costs. Introduction The industrial application of the water gas shift (WGS) reaction is mainly related to hydrogen production. Currently, hydrogen is produced by reforming and/ or partial oxidation of light hydrocarbons such as natural gas. These processes produce hydrogen, carbon monoxide, carbon dioxide, water, and a small amount of a CH4 mixture. The WGS reaction reduces the CO content, simultaneously producing more H2:

CO + H2O ) CO2 + H2

∆H°298 ) -41 kJ/mol

This reaction is exothermic and is characterized by no variation in the number of moles. Thus, the CO equilibrium conversion is favored by a low temperature and is independent of the reaction pressure. The reaction rate is very low; thus, a catalyst is necessary for CO conversion. The value at which the CO concentration in the final stream must be reduced depends on the final use of the gas. In fact, after the removal of carbon monoxide, hydrogen is widely used from the petrochemical industry in hydrotreating and hydrocracking processes. New technologies such as proton exchange membrane fuel cells, requiring CO-free hydrogen (less than 10 ppm), are promoting the improvement of an innovative WGS process.1 A promising approach is the use of membrane reactors (MRs), combining reaction and H2 separation through a selective membrane. In this way, the equilibrium can be shifted, achieving a higher CO conversion value.2-6 * To whom correspondence should be addressed. Tel.: +39 0984 492029. Fax: +39 0984 402103. E-mail: g.barbieri@ itm.cnr.it. † ITM-CNR. ‡ Department of Chemical Engineering and Materials.

In this work, a study of the MR performance for the WGS reaction is presented, considering a membrane engineering approach and also following the logic of Process Intensification Strategy. It is an innovative method in process and plant design, development, and implementation. It is a design philosophy for achieving significant reductions (by factors of 10-100 or more), e.g., in plant volume at the same production capacity.7 Smaller unit operations means smaller installation plant costs because 20% of plant costs is in the process equipment and the balance in structural steel, piping, etc. The MR mathematical model was developed from the design equation of traditional reactors (TRs) considering a H2 high-selectivity membrane, to perform a comparison between the two reactors and estimate in a qualitative and quantitative way the convenience of the MR use for the WGS reaction. The variables considered in the analysis were: temperature, reaction pressure, and feeding conditions. The effect of the operating conditions on the catalyst was considered, in addition to the reaction from kinetic and thermodynamic points of view. A catalyst effectiveness factor was defined considering the Thiele module. It takes into account the kinetic and diffusive resistances inside the catalytic pellet, which also depend on the pellet geometric characteristics (pore diameter, pore length, tortuosity, porosity, etc.). The mathematical model was compared with literature experimental data for TRs and MRs. In particular, MR reaction data measured with a silica membrane (on an alumina support)8 were considered. The present work was focused on the analysis of the space time (WCatalyst/FFeed CO ) for the WGS reaction applying the design equations typically used for catalytic reactors. A subtractive term (recovery factor, RF), taking into account the hydrogen permeation through the

10.1021/ie050357h CCC: $30.25 © 2005 American Chemical Society Published on Web 08/06/2005

Ind. Eng. Chem. Res., Vol. 44, No. 20, 2005 7677

membrane and the related effect on the reaction side, was added for the MR model. Mathematical Model The model used in this work is a further development of the design equation of TRs9 for a MR. It allows an analysis of the conversion as a function of WCatalyst/ up to the equilibrium for both TRs and MRs FFeed CO characterized by a different equilibrium conversion limit: TREC and MREC, respectively. The model does not report “typical” mass balance equations, i.e., as a function of time or the reactor length, but it correlates the space time with the CO conversion, taking also into account other important variables (e.g., temperature, pressure, catalyst efficiency, H2 recovery factor, etc.). Equations 1 and 2 are the design equations for catalytic packed-bed TRs and MRs, respectively, relating CO conversion and the ratio W/F. In eq 2, the term RF (defined in eq 3) considers hydrogen permeation. MREC can be calculated using eqs 10 and 11; these equations take into account further CO conversion due to hydrogen removal by means of membrane permeation.

WCatalyst ) FFeed CO Keq

∫0X

X Feed 2∫0 ηk(P ) CO

WCatalyst ) FFeed CO Keq

dXTR ) ηrCO

TREC

dXTR (1) (XTR)2(Keq - 1) - 2KeqXTR + Keq

TREC

∫0

XMRECdX

∫0

2 ηk(PFeed CO )

MR

ηrCO

pore diameter, nm

length, mm

tortuosity

pellet porosity

500

1

1.2

0.5

because of the low reaction rate limiting the hydrogen production and hence its permeation through the membrane near the entrance of a tubular MR. At a higher temperature (>250 °C), this difference is negligible because of a high permeation also in the first MR section. The influence of the catalyst efficiency, expressed as the “effectiveness factor”, was also considered:

η)

tanh φ φ

(4)

It is defined in terms of the Thiele module9 (φ), a dimensionless number that relates to the kinetic and diffusive resistances during the reaction.

φ ) Lpore

x

4kRTPFeed CO LporeDactualKeq

(5)

As shown in eq 5, the Thiele module is expressed considering the effective diffusivity, calculated according to eq 6, considering the Knudsen10 diffusion mechanism and some geometric characteristics of the catalyst such as the pore tortuosity and pellet porosity.

porositypellet ) Dactual ) DKnudsen tortuositypore

)

dXMR Keq(1 - XMR)2 - XMR(XMR - XTRRF) (2)

XMREC

The following initial and boundary conditions were introduced: (i) Only CO and H2O are fed to the reactor: almost experimental laboratory-scale studies are performed using CO/H2O mixtures, even though industrial WGS is often carried out for upgrading reformate streams. (ii) Only H2 is removed through the membrane. For instance, Pd-based and silica membranes separate H2 with a high selectivity. In particular, Pd-based membranes show an infinite selectivity versus H2 compared with other species. For the MRs and TRs, simplifying hypotheses were introduced: (i) Gas diffusion in the pores of the catalytic pellet was according to the Knudsen mechanism. (ii) There is no gas axial diffusion. (iii) The H2 permeation through the membrane was expressed by means of the lamped parameter RF.

recovery factor ) RFH2 )

Table 1. Catalyst Characteristics Assumed

Permeate (Qy)H 2 Permeate Retentate (Qy)H + (Q y)H 2 2 (3)

In the following, RF will be used instead of RFH2. The validation of the latter hypothesis has been verified considering the comparison reported in Figure 9. The figure shows a difference between the model prediction and experimental datum at T e 220 °C,

4850dpore

x

T porositypellet (6) M tortuositypore

The kinetic equation considered in this paper as a reference is that proposed by Moe (Amadeo-Laborde11) considering a low-to-medium-temperature catalyst and valid in the temperature range 180-250 °C; in addition, it also includes a pressure reaction dependence.

[

rCO ) kPCOPH2O 1 -

PH2PCO2 PH2OPCOKeq

]

(7)

k ) ψ × 1.85 × 10-5e12.88-1855.5/T; ψ ) 0.86 + 0.14PReaction (8) The commercial catalyst (copper/zinc oxide; Haldor Topsoe LK821-2) considered in the model also used in the experiments8 showed a reaction rate lower than that of Amadeo-Laborde. Therefore, a lower catalyst active phase was assumed, and the factor 1/2 reported in eq 9 reflects this condition. More accurate tuning is not possible because the catalyst composition is not available. The catalytic pellet diameter considered in eq 6 is

1 k ) ψ × 1.85 × 10-5e12.88-1855.5/T 2

(9)

3 mm, as in the commercial one; the pellets were crashed into smaller particles before carrying out the laboratory-scale experiments. The other catalyst geometric characteristics assumed in the model are reported in Table 1. No measurement of these parameters was carried out, respecting an agreement with the

7678

Ind. Eng. Chem. Res., Vol. 44, No. 20, 2005

Table 2. MR Equilibrium Analysis state initial reaction TR equilibrium permeation nonequilibrium reaction MR equilibrium MR equilibrium

CO

H2O

CO2

H2 n0XTR n0XTREC -RFn0XTREC n0XTREC(1 - RF) Rn0(1 - XTREC) n0[XTREC(1 - RF) + R(1 - XTREC)] n0(XMREC - XTRECRF)

n0 -n0XTR n0(1 - XTREC)

mn0 -mn0XTR mn0(1 - XTREC)

n0XTR n0XTREC

n0(1 - XTREC) -Rn0(1 - XTREC) n0(1 - XTREC)(1 - R) n0(1 - XMREC)

mn0(1 - XTREC) -Rmn0(1 - XTREC) mn0(1 - XTREC)(1 - R) n0(1 - XMREC)

n0XTREC Rn0(1 - XTREC) n0[XTREC + R(1 - XTREC)] n0XMREC

catalyst supplier. Therefore, the most common values were adopted; they were not determined by a fitting in order to optimize the agreement of the mathematical model with the experimental data. Table 2 presents the reaction stages (initial/reactive/ permeation) for reaching the equilibrium. In particular, the MR equilibrium is considered as a step following the TR equilibrium condition after hydrogen permeation through the membrane. In this approach, two steps in a series are proposed: the first represents what happens in a TR up to the equilibrium; the second considers in addition the hydrogen permeation through the membrane. In particular, XTR and XMR indicate the CO conversion, while TR and MR equilibrium conversions are indicated as XTREC and XMREC, respectively. The H2 permeation through the membrane modifies the equilibrium condition already achieved in TR (TREC, TR equilibrium conversion), further pushing the reaction toward product formation. The R term (eqs 10 and 11 and Table 2) takes into account this CO extra conversion in order to reach the MR equilibrium condition (MREC, MR equilibrium conversion), starting from the TR equilibrium condition, once a certain hydrogen fraction (RF) is removed by the membrane. When the MR equilibrium conditions are achieved, it is possible to use eq 10 to calculate the R value indicating the CO extra conversion with respect to TREC. Equation 11 allows the calculation of the MREC value for the unitary value of the feed molar ratio (m ) H2O/CO).

only to the catalyst (see eqs 4 and 5) and they are not influenced by the membrane presence. Results and Discussion The model results and some experimental data for the TR were compared as a function of the temperature, WCatalyst/FFeed CO , etc. (Figures 2-4). They are also reported in order to validate the model and the assumption of the factor 1/2 in eq 9 and to discuss the differences presented afterward for the MR. As shown in Figure 2, the TR CO conversion as a function of WCatalyst/FFeed CO initially increases exponentially and then reaches a plateau given by the TREC at the corresponding temperature. Each continuous line represents the CO conversion calculated as a function of WCatalyst/FFeed CO at a fixed temperature (250, 280, and 320 °C). These nearly coincide for low WCatalyst/FFeed CO values; when WCatalyst/FFeed CO increases, they diverge and tend toward the corresponding equilibrium conversion. In addition, when the temperature is increased, the

Keq ) [XTREC + R(1 - XTREC)][XTREC(1 - RF) + R(1 - XTREC)] [(1 - XTREC)(1 - R)][(1 - XTREC)(1 - R)m]

(10) Figure 1. Effectiveness factor (eq 4) and Thiele module (eq 5) as a function of temperature at different reaction pressures.

XMREC ) [XTREC + R(1 - XTREC)]

) [XTREC + R(1 - XTREC) + (1 - XTREC)(1 - R)] XTREC + R(1 - XTREC) (11) The effectiveness factor and Thiele module behavior as a function of the temperature are reported in Figure 1 at different reaction pressures. The Thiele module increases exponentially with the temperature, while the catalyst efficiency has an opposite trend. In this analysis, a MR with the catalyst packed in an annulus was considered, because this MR configuration has a better thermal performance because of the better energy transfer from the furnace to the reaction side (Marigliano et al.12). The effectiveness factor and Thiele module in a (packed-bed inert-membrane reactor) MR are the same as those in the TR because they are parameters related

Figure 2. TR CO conversion as a function of WCatalyst/FFeed CO . Experimental data at 250 °C (2) and 280 °C (4). Solid lines: model results. Dashed lines: TREC values.

Ind. Eng. Chem. Res., Vol. 44, No. 20, 2005 7679

Figure 3. TR CO conversion as a function of WCatalyst/FFeed CO . Experimental data at 1 bar (2) and 2 bar (4). Solid lines: model results. Dashed line: TREC value at 250 °C.

Figure 4. TR CO conversion as a function of temperature. PReaction ) 1 bar. Experimental data at 1300 gcatalyst min/mol (2) and 1900 gcatalyst min/mol (4). Solid lines: model results. Dashed line: TREC value.

catalyst efficiency diminishes (Figure 1); because the diffusive resistances in the catalytic pellet become more important, as a consequence the curves move toward the right. A lower CO conversion is reached when the operating temperature increases because the reaction is exothermic, and therefore the equilibrium constant is a decreasing function of temperature. However, the plateau is reached at a lower space time and at a higher temperature. Some experimental data8 measured at 250 and 280 °C showing a good agreement with the mathematical model previsions are also reported. The effect of the reaction pressure on the TR CO conversion is reported in Figure 3. The TR CO conversion calculated as a function of WCatalyst/FFeed CO has the same trend when different reaction pressures are considered. However, the plateau conversion (representing the TREC value) is reached at a higher reaction pressure at low WCatalyst/FFeed CO . Therefore, the pressure has a positive effect on the reaction kinetics (eq 8), although there is no effect on the thermodynamics (no mole variation for WGS) and the catalyst efficiency gets worse (Figure 1). Also in this case there is a good agreement between the TR mathematical model and the experimental data. The TR CO conversion as a function of the temperature was calculated for three WCatalyst/FFeed CO values (500, 1300, and 1900 g min/mol) in order to estimate the reaction rate-determining steps (Figure 4). The calculated TR CO conversion initially shows an increasing trend (T < 250 °C), although less evident than the

Figure 5. XMREC - XTREC and MREC as a function of temperature at different RF values. PReaction ) 1 bar. Solid lines: model results. Dashed line: TREC. Table 3. Operating Conditions for the Reaction Used in the MR Mathematical Model Calculations variable

range

temperature, °C H2O/CO feed molar ratio (m) reaction pressure, bar recovery factor (RF) RF ) 0 for TR

210-350 1 1-5 0-1

experimental data, and then a decreasing behavior close to the thermodynamic equilibrium. However, the three lines are quite different. The maximum CO conversion is more evident in the case of the lowest WCatalyst/FFeed CO (500 gcatalyst min/mol) value, i.e., high space velocity; in addition, the conversion is far from the achievement of the equilibrium conversion. At a low temperature, in fact, the reaction kinetics is slower and becomes the process rate-determining step. At a temperature higher than 250 °C, the reaction is faster but close to the thermodynamic equilibrium, and this induces a decrement in the TR conversion that follows the TREC in an asymptotic way. In particular, the mathematical model CO conversions calculated at WCatalyst/FFeed CO of 1300 and 1900 g min/mol are reported in order to make a comparison with some experimental data measured under the same conditions. The model well agrees with the experimental data at temperatures higher than 250 °C. At a temperature lower than 250 °C, the model overestimates the conversion. To fit the experimental data, the kinetics equation (eq 7) was divided by 2 (eq 9) and used in all calculations (Figures 1-12). MR experimental data8 measured with a microporous silica membrane using a commercial catalyst (copper/ zinc oxide; Haldor Topsoe LK821-2) were used for the comparison. The reaction conditions used in experimental tests and also applied in the mathematical model are reported in Table 3. The MREC calculated by eqs 10 and 11 as a function of the temperature and for different RF values is reported in Figure 5. The MREC (solid lines) decreases when the temperature increases as for the TR; however, the MREC is always higher than the TREC. This decreasing trend is less evident at higher RF values. When hydrogen is removed from the reaction side, the reaction is pushed toward the formation of a new product and therefore the CO conversion becomes higher. Figure 5 also reports the difference (MREC - TREC) at different RF values (0.1, 0.5, and 0.9). The advantage

7680

Ind. Eng. Chem. Res., Vol. 44, No. 20, 2005

Figure 6. MR CO conversion as a function of WCatalyst/FFeed CO at different temperatures and different RF values (at 210 °C). PReaction ) 1 bar. Solid lines: model results. Dashed lines: TREC values.

Figure 7. MR CO conversion as a function of WCatalyst/FFeed CO . Experimental data at T ) 210 °C and RF ) 0.3 (O) and at T ) 250 °C and RF ) 0.9 (b). PReaction ) 1 bar. Solid lines: model results. Dashed lines: TREC values.

of using a MR is more evident at a higher RF and increases when the temperature is increased at a fixed RF. The MREC tends to the unitary value in the whole temperature range because much more hydrogen (RF f1) is removed from the reaction side. Therefore, the MREC is almost complete for a RF of 0.9, even at a low temperature (210 °C). At a lower temperature, the MREC - TREC difference is low because TREC f 1; when the temperature is increased, the difference increases, showing MR advantages. The advantage of the use of a MR for the WGS reaction is easily recognized considering Figure 6, where the conversion calculated is reported as a function of WCatalyst/FFeed CO , as was already done for the TR in Figure 2. In particular, the temperature effect (210, 280, and 320 °C) was analyzed for RF ) 0.5. The CO conversion trend is similar to that reported for a TR (Figure 2): the curves are very close at low WCatalyst/FFeed CO values, and then the conversion increases up to the plateau, in this case higher than the TREC. In addition, the effect of the RF increase (0, 0.5, and 0.9) is analyzed at 210 °C. The curve at RF ) 0 reaches the TREC, whereas at the other RF, this limit is overcome and the curves tend toward a higher value. The agreement between the mathematical model and the MR experimental data can be observed in Figure 7, in which two calculated curves at 210 and 250 °C at two RF (0.3 and 0.9, respectively) values are also reported. The RF values were calculated from experimental data taking into account the flow rate and

Figure 8. MR CO conversion as a function of WCatalyst/FFeed CO . Experimental data (symbols) at 2 bar. T ) 280 °C; RF ) 0.5. Solid lines: model results. Dashed line: TREC value at 280 °C.

composition of both retentate and permeate streams. The important effect of RF can also be observed: although the TREC at 210 °C is higher than that at 250 °C, a higher conversion is obtained at 250 °C and RF ) 0.9. Therefore, a high RF overcomes the negative effect of the temperature. One of the more interesting aspects of MR use is the positive effect that the reaction pressure has on the process, also for reactions that happen without mole number variation (e.g., WGS) or with an increasing mole number. In a MR, a pressure increase allows the attainment of higher conversion values (Figure 8) at a fixed space time. In fact, a high pressure on the reaction side facilitates the permeation and therefore pushes the reaction toward product formation. Figure 8 reports the effect of the reaction pressure (1, 2, and 3 bar) on the MR CO conversion for a fixed RF. The mathematical model agrees quite well with the experimental data measured. The positive effect of the pressure, already observed in a TR (Figure 3), is much more evident for the MR (Figure 8). In fact, a high reaction pressure not only influences the kinetics but also promotes hydrogen permeation through the membrane. The achievement of the CO conversion plateau is possible in a shorter space-time when the reaction is carried out at a higher pressure. For instance, at 280 °C and 1 bar, a WCatalyst/FFeed CO of 5000 gcatalyst mol/min necessary in a TR reduces to 2500 gcatalyst mol/min or only 400 gcatalyst mol/min at a pressure of 3 bar (280 °C) in a MR to achieve the MREC. However, the difference between the curves calculated at 1 and 2 bar is more evident than that between the curves calculated at 2 and 3 bar; a further increment of the driving force does not add any other improvement to the permeation process because, according to the model, a higher RF is required for giving higher hydrogen permeate flow rate. Figure 9 reports the MR CO conversion as a function of the temperature calculated for two RF values (0.6 and 0.9). The conversion trend is similar to that already seen for a TR; however, the positive effect of the membrane on the CO conversion can be appreciated, and conversion exceeds the TREC in a wide temperature range for both cases considered. At the lowest RF value (0.6), the MR conversion is closer to the TREC at a high temperature.

Ind. Eng. Chem. Res., Vol. 44, No. 20, 2005 7681

Figure 9. MR CO conversion as a function of temperature. WCatalyst/FFeed CO ) 2000 g min/mol. Experimental data at RF ) 0.6 (O) and 0.9 (b). Solid lines: model results. Dashed line: TREC.

Figure 11. Membrane area as a function of WCatalyst/FFeed CO at different RF and temperature values. PReaction ) 1 bar. Solid lines: model results. Table 4. Assumed Conditions for the Membrane Area Calculationa FFeed CO (mmol/ min)

QFeed CO (cm3(STP)/ min)

FCatalyst (kg/m3)

ODMembrane (mm)

IDMR (cm)

AAnnulus (cm2)

4

100

3,250

1.6

1.7

2.35

a

STP ) 25 °C and 1013 bar.

Table 5. Sievert’s Law Parameter Values Obtained on a Pd-Based Membrane13

TREC WCatalyst/FFeed CO X

Figure 10. and space time ratio between MR and TR as a function of temperature at different RF values. PReaction ) 1 bar. Solid lines: model results.

In the following equation, the space time ratio is defined: Catalyst Feed MR /FCO ) (Ffluid/FCatalyst)MR τMR (W ) TR τTR (WCatalyst/FFeed (Ffluid/FCatalyst)TR CO ) TREC WCatalyst/FFeed CO X

(12)

In Figure 10, as a function of temperature is shown. As the temperature increases, the time necessary to obtain the equilibrium value decreases rapidly because the kinetics are faster. In addition, the space time ratio of MR and TR is reported in Figure 10. This ratio allows one to see immediately the advantage of the use of a MR for the WGS and to estimate the required dimensions of a MR with respect to a TR, under the same operating conditions, to reach a specific conversion value. For instance, the MR volume to reach the equilibrium conversion is about 1/3 of the TR volume required under the same operating conditions (1 bar and 280 °C) when RF is equal to 0.5 (i.e., 50% of the produced hydrogen is removed from the reaction side). This also affects the required catalyst amount and implies significant advantages in terms of reduced equipment costs. The last part of the present work reports an analysis about the membrane area required in order to carry out the WGS reaction in a MR, for set feeding conditions and reactor geometry (Table 4). This analysis refers to membranes characterized by a high H2 selectivity, such as Pd-based, where the only permeating species is H2.

Q0 (nmol/m s Pa0.5)

Ep (kJ/mol)

Q0e-Ep/RT (nmol/m s Pa0.5) for T ) 400 °C

242

16.3

13.2

For the calculation of the membrane area, with it being necessary to know the hydrogen flux through it, the permeation parameters for Sievert’s law (Table 5) calculated by Bernardo et al.13 for a tubular membrane of Pd/Ag (60 µm thick) with a transmembrane ∆P of 1.05 bar were assumed. Pd JH ) 2

Q0 -Ep/RT Retentate e ( PH 2 δ

x

xP

Permeate ) H2

(13)

Figure 11 reports the MR membrane area as a function of WCatalyst/FFeed CO . In particular, a RF increment requires a higher membrane area because the hydrogen amount to be removed from the reaction side is greater. Moreover, when the temperature is increased, the membrane area reduces at the same WCatalyst/FFeed CO and RF values. In fact, both the reaction kinetics and the permeation are facilitated by a high temperature and, therefore, a smaller membrane area is required for the same conversion. This last concept appears more clearly in Figure 12, in which the CO conversion as a function of the membrane area is reported. In a MR, CO conversion increases linearly with the membrane area. The conversion overcomes the TREC value, reaching the MREC. In Figure 12, all of the reported lines show a linear relationship between the MR conversion and the required membrane area. Moreover, for a fixed conversion value, the membrane area required increases as the hydrogen RF increases. Conclusions This work gives an engineering evaluation of the WGS reaction in a MR by means of a mathematical model

7682

Ind. Eng. Chem. Res., Vol. 44, No. 20, 2005

List of Symbols A ) area, cm2 D ) diameter, m D ) diffusivity, cm2/s F ) molar flow rate, mol/min Keq ) equilibrium constant k ) kinetic constant, gcatalyst min/mol bar2 L ) length, mm m ) H2O/CO feed ratio P ) pressure, bar Q ) volumetric flow rate, m3(STP)/min R ) gas constant, bar L/mol °C T ) temperature, °C WCatalyst ) catalyst weight, g Figure 12. CO conversion as a function of membrane area at different RF and temperature values. PReaction ) 1 bar. Solid lines: model results. Dashed line: connection among TREC values located over the solid lines calculated at the corresponding temperature.

for the CO conversion analysis. The model takes into account the influence of the operating conditions (temperature, pressure, etc.) and also the catalyst efficiency expressed in terms of the Thiele module. In addition, a specific approach was developed to evaluate the MREC and its dependence on the temperature and RF, a parameter indicating hydrogen subtraction from the reaction side. The MR model results give a satisfactory agreement when compared to the experimental literature data and a TR performance; in addition, the MR conversion is higher than the TREC, the upper limit imposed by thermodynamics for the TR conversion. The influence of the reaction pressure, temperature, RF, etc., on the MR CO conversion was also studied. A pressure increase allows the attainment of a higher conversion at the same space time. In fact, the pressure acts in a TR only on kinetics, while in a MR it facilitates hydrogen permeation through the membrane, which induces a further product formation, having a positive effect on thermodynamics. Furthermore, a RF increase implies a higher difference between the MR conversion and TREC; a high RF overcomes the temperature negative effect on the MR conversion. The space time analysis gives an estimation of the advantage of a MR. In particular, a very low space time ratio (1/3; see Figure 10) between the MR and TR means that the volume required by a MR is significantly lower than that required by a TR for achieving the same conversion, with clear advantages, e.g., in plant dimension reduction. The membrane area was also evaluated as a function of WCatalyst/FFeed CO , temperature, and RF; it increases with RF but decreases significantly with the temperature. Finally, the obtainment of a H2-rich or pure stream (if a high or infinite selective membrane, respectively, is used) must not be forgotten. Acknowledgment This work was performed also with the contribution of the Italian Ministry for Foreign Affairs, Direzione Generale per la Promozione e la Cooperazione Culturale, Rome, Italy.

Greek Letters φ ) Thiele module η ) catalyst effectiveness factor F ) density, kg/L  ) porosity yi ) molar fraction of the ith species X ) CO conversion τ ) space time, min Superscripts Feed ) membrane module inlet stream Permeate ) membrane module outlet stream on the permeation side Retentate ) membrane module outlet stream on the feed side Acronyms MR ) membrane reactor MREC ) membrane reactor equilibrium conversion RF ) recovery factor STP ) standard temperature (25 °C) and pressure (1 atm) TR ) traditional reactor TREC ) traditional reactor equilibrium conversion WGS ) water gas shift

Literature Cited (1) Li, Y.; Fu, Q.; Flytzani-Stephanopoulos, M. Low-temperature water-gas shift reaction over Cu- and Ni-loaded cerium oxide catalysts. Appl. Catal., B 2000, 27, 179. (2) Kikuchi, E.; Uemiya, S.; Sato, N.; Inoue, H.; Ando, H.; Matsuda, T. Membrane reactor using microporous glass-supported thin film of palladium. Application to the water-gas shift reaction. Chem. Lett. 1989, 489. (3) Uemiya, S.; Sato, N.; Inoue, H.; Ando, H.; Kikuchi, E. The water-gas shift reaction assisted by palladium membrane reactor. Ind. Eng. Chem. Res. 1991, 30, 585. (4) Basile, A.; Violante, V.; Santella, F.; Drioli, E. Membrane integrate system in the fusion reactor cycle. Catal. Today 1995, 25, 321. (5) Violante, V.; Basile, A.; Drioli, E. Composite catalytic membrane reactor analysis for the water gas shift reaction in the tritium fusion fuel cycle. Fusion Eng. Des. 1995, 30, 217. (6) Criscuoli, A.; Basile, A.; Drioli, E. An analysis of the performance of membrane reactors for the water-gas shift reaction using gas feed mixtures. Catal. Today 2000, 56, 53. (7) Stankiewicz, A.; Moulijn, J. A. Process Intensification. Ind. Eng. Chem. Res. 2002, 41, 1920. (8) Barbieri, G.; Bernardo, P. Experimental evaluation of hydrogen production by membrane reaction. In Carbon Dioxide Capture for Storage in Deep Geologic FormationssResults from the CO2 Capture Project; Elsevier: New York, 2004; Vol. 1, Chapter 22, pp 385-408. (9) Levenspiel, O. Ingegneria delle Reazioni Chimiche; Casa Editrice Ambrosiana: Milano, Italy, 2000. (10) Cussler, E. L. Diffusion; Cambridge University Press: Cambridge, U.K., 1997.

Ind. Eng. Chem. Res., Vol. 44, No. 20, 2005 7683 (11) Amadeo, N. E.; Laborde, M. A. Hydrogen production from the low-temperature water gas shift reaction: kinetics and simulation of the industrial reactor. Int. J. Hydrogen Energy 1995, 20, 949. (12) Marigliano, G.; Barbieri, G.; Drioli, E. Effect of energy transport on a palladium membrane reactor for methane steam reforming process. Catal. Today 2001, 67, 85. (13) Bernardo, P.; De Rango, S.; Barbieri, G.; Drioli, E. Permeation properties of a Pd-based tubular membrane. Proceedings

of the 1st Italy-Russia Workshop on Membrane Processes for a Sustainable Industrial Growth, Cetraro (CS), Italy, Sept 17-20, 2003.

Received for review March 17, 2005 Revised manuscript received June 22, 2005 Accepted June 27, 2005 IE050357H