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On the non-monotonic behaviour of methane—steam reforming kinetics
Chemical Engineering Scienc-c, Vol. 45, No. 2, pp. 491-501,
1990.
ooo9-2509po
Printed in Great Britain.
0
s3.00+0.00
1990 Pergamon Press plc
ON THE NON-MONOTONIC BEHAVIOUR OF METHANE-STEAM REFORMING KINETICS S. S. E. H. ELNASHAIE,’ A. M. ADRIS, A. S. AL-UBAID and M. A. SOLIMAN Chemical Reaction Engineering Group, Chemical Engineering Department, King Saud University, PO Box 800, Riyadh 11421, Saudi Arabia (Received
7 March
1988; accepted
for publication
19 May
1989)
Abstract-A parameteric study on the rate expression recently developed by Xu and Froment (1989a, A.1.Ch.E. J. 35,88-96) is carried out over a wide range of parameters. The analysis of this rate expression has shown a non-monotonic dependence of the reaction rate upon steam partial pressure which explains the contradictions between the rate expressions available in the literature, that is the prediction of positive, as well as negative effective reaction order with respect to steam. A simplified pseudo-homogeneous model with a constant effectiveness factor, with Xu and Froment’s rate expression was used to investigate the
implications of the non-monotonic kinetics on the performance of steam reformers. The main implication was also checked using a heterogeneous model that represents very closely industrial steam reformers.
INTRODUCTION A large
number
of kinetic
rate expressions
for the
steam reforming of methane is reported in the literature (Akers and Camp, 1955; Atroshchenko et al., 1969; Bodrov et al., 1964; Ross and Steel, 1972; Munster and Gobka, 1981; Quach and Rouleau, 1975; De Deken et al., 1982). Most of these rate equations are either emperically based power law kinetics or are obtained by applying a large number of assumptions on a proposed mechanism. These facts make the rate equations obtained valid only for a certain range of reaction conditions and thus of limited use, especially that the original mechanism, even before applying the simplifying assumptions, is never certain. In addition, this approach has led to certain discrepencies such as the disappearance of certain reactants and/or products concentrations from the rate equations. When the chemisorption process is taken into consideration it is noticed in many cases that the concentrations of certain components are absent from the denominator of the Langmuir-Hinshelwood type rate equations, while these components are known to be strongly adsorbed. One of the most interesting contradictions noticed in these rate equations is the prediction of positive, as well as negative effective reaction order with respect to steam. Some investigators attributed this phenomenon to the difference in the acidity of the catalyst support (AlIJbaid, 1986). In fact this negative effective order of the reaction is a strong indication for the existence of a non-monotonic dependence of the rate of reaction upon the concentration of a specific reactant. A general rate equation based on LangmuirHinshelwood-Hougen-Watson has been developed recently
(LHHW) approach by Xu and Froment
(1989a). This rate equation has been investigated in this study and has shown a non-monotonic dependence of the rate of methane disappearance upon steam partial pressure. Comparison with previous investigations is presented and the implications of non-monotonic kinetics on the behaviour of industrial steam reformers are investigated. THE NON-MONOTONIC
OF METHANESTEAM
The kinetic rate equations developed by Xu and Froment (1989a), based on (LHHW) approach, are shown to be more general relative to the previous rate expressions available in the literature, and explain a number of contradictions in the work of previous investigators. Xu and Froment have taken into consideration the two main reactions of steam reforming together with the water-gas shift reaction: CH, + H,O c, CO + 3H, CO + H*O+-+ CO, + H, CH, + 2H,O*
CO, + 4H,.
The adsorption-surface reaction+lesorption used consists of the following 13 steps: H,O+LuO-L+H, CH, + L-
(r.d.s)
(II) (III) model (1)
CH,-L
(2)
+ Lt* CHa-L
+ H-L
(3)
CH,-L
+ Lc* CH,-L
+ H-L
(4)
CH,O-L
+ L
(5)
CHO-L
+ H-L
+ O-L-
CH,O-L (r.d.s)
(I)
CH,-L
CH,-L
(r.d.s) ‘Author to whom all correspondence should be addressed. On leave from the Chemical Engineering Department, Cairo University, Cairo, Egypt.
KINETICS REFORMING
+ Lo
CHO-L CO-L CHO-L
+ Ltt CO-L
(6)
+ H-L
(7)
+ O-L-
co,-L
+ L
(8)
+ O-L+-+
CO,-L
+ H-L
(9)
CO-L-
co
+ L
(10)
492
S.
co,-Lu
co,
2H-Lt*
S.
E. H.
ELNASHAIE
+ L
(11)
L + H,-L
(12)
H,-LeH,+L
(13)
with steps (7), (8) and (9) being the rate determining steps. Based on this mechanism the following rate equations were obtained:
P
rz=k,
. .
PHZO (p”,)“.5. PC0
(T:*)= -
‘t=k,
P co (
PHI0 -- PCOl K, >I
P P CH.‘ip,,0)2
DEN’
(pH,)o.5
-
(14)
R CH4=II
(15)
(17)
fr3
RHzO = r, + r2 + 2r, ‘pCO,
r,=k, (PHJ3.5
DEN2
>I
K,
et al.
simplest way to present the dependence of the kinetic rate equations upon the partial pressure of one component in the two-dimensional plot. The case where partial pressures of all components are varying along the length of the reactor tube is also investigated. The analysis covered a temperature range of 800-1200 K, and a total pressure range of 0.1-1.5 MPa, and has shown that rl and r2 have a non-monotonic dependence on steam partial pressure, while the dependence of r3 on steam partial pressure is a monotonic function [Fig. l(a)]. Also, since:
DEN’
(16)
Kl.K2
DEN= 1+ &oPco+KH,PH,
+ Kc,.Pc,,
+ KH~oPH~oIPH~ where r, , r2 and rS are the rates of reactions I, II and III respectively in (kg mol/kg cat h).
The increase of temperature causes the location of the point of maximum to move towards lower values of steam partial pressure.
The 13 step reaction mechanism used shows competition for the active sites between methane and steam, and thus leads to the functional dependene of the rate of reaction shown in eqs (14), (15) and (16), which can give non-monotonic dependence of the reaction rate upon the partial pressure of steam and methane. The kinetic rate constants, activation energies, adsorption constants and heats of adsorption are all given in Table 1. RATE DEPENDENCE
(18)
both R,,, ann R,,, showed a non-monotonic dependence on steam partial pressure [Fig. l(b)]. The location of the maximum rate point (zero order dependence point) and its value are highly affected by the rate equation parameters. A parametric study has shown that:
INVESTIGATION
An investigation was carried out on the dependence of each reaction rate as well as the total methane disappearance on reactants concentrations (or partial pressures). The partial pressures for all components involved in the reactions, except the one under investigation (e.g. steam), were considered to be constant. This situation does not correspond to the actual variation of the partial pressures of the reacting mixture components along the reactor tube, but it is the
‘2
L’
.
1 Steam
2
3
partial
4 pressure
5
6
(MPa
x IO)
5
6
Table 1. Pre-exponential factors for the reaction rate constants and adsorption activation constants, energies and heats of adsorption Activation
Constant k, :: Gel &H. K H.0 K “I
Pre-exponential factor
energies Ei and heats of chemisorption ( - AHi)
9.49 X 10’5 4.39 x 106 2.29x IO” 8.23x lO-5 6.65 x IO-* 1.77X 105
+240.1 +67.13 + 243.9 + 70.65 38.28 - 88.68
6.12 x 10-g
82.9
K, =[exp (-26,830.0/T+30.114)] K, =exp (4400/T-4.036).
x 10w2.
a”
I
1 Steam
2 partial
3
4 pressure
LMPa
*
x 10)
Fig. l(a). Dependence of r,, r2 and r3 on steam partial P cr,,=0.02. pressure at 900 K, P, =0.85. P,,=O.Ol. P,,, =O.Ol, P,, =0.03 (all in MPa). (b) Dependence of R,,,, and R HZ0on steam partial pressure [same conditions of Fig. l(a)].
Non-monotonic behaviour of methane-steam reforming kinetics
(2) The
increase of total pressure causes the location of the point of maximum to move towards higher values of steam partial pressure. (3) The effect of increasing H,/CH, ratio is to move the point of maximum rate towards higher values of steam partial pressure. Increasing the other products concentrations has a similar effect.
REACTION
RATE
DEPENDENCE
OBSERVED
BY
OTHER
INVESTIGATORS
Among a chosen twelve investigators who studied the kinetics of methane steam reforming reaction, four investigators (Bodrov et al., 1964; Ross and Steel, 1973; Al-Ubaid, 1984; Nikrich, 19701, reported negative order dependence of the rate of reaction upon steam partial pressure, four reported zero order (Akres and Camp, 1955; Bodrov et al., 1967a, b; Munster and Gabka, 1981), and five investigators reported positive order dependence (Al-Ubaid, 1984; Quach and Rouleau, 1975; Atroshchenko et al., 1969; Kopsel et al., 1980; De Deken et al., 1982). The recent kinetic rate expressions developed by Xu and Froment (1989a), can give both positive and negative order dependence of the rate of reaction upon steam partial pressure. The reaction rates using this new kinetic expression were compared with the corresponding rates of the expression of Bodrov et a[. (1964), which gives negative effective order and with the expression of De Deken ef al. (1982), which gives positive effective order dependence on steam. COMPARISON
WITH
BODROV
KINETICS
Bodrov rl ul. (1964), carried out their investigation in a flow reactor with recycle, on nickel foil, at atmospheric pressure and m the temperature range of
1073-l 173 K, they obtained pression: ?-=
Fig. 2. Comparison
rate ex-
kPc,, 1 +aCPH,o/PH21 +bP,,
(19)
Case (1) Bodrov et al. (1964), carried out this set of experiments at 1073 K, using a nickel surface area of 0.0775 m2, with the following reacting mixture composition: P CH4= 0.003SS MPa,
P,,
= 0.0115 MPa
P co2 = 0.00522 MPa,
P,,
= 0.055 1 MPa
the reaction rate constant at this temperature as given by Bodrov et al. is 800 (standard liters of methane/h m2 Ni atm). Steam partial pressure was changed between the minimum value used by Bodrov in this set of experiments (0.01 MPa), and the maximum value (0.0244 MPa). The same conditions were
Range
partial
the following
where r is the rate of reaction in standard liters of methane/hm’ Ni, and a and b are constants equal to 0.5 and 2.0, respectively, at 1073 K, and 0.2 and 0.0 respectively at 1173 K. The geometrical surface area of the nickel foil used in the investigation was 4.49 m’/kg. To compare the rate of reaction obtained by the above expression with that obtained by Xu and Froment (1989a), both rates were converted into mol/m’ Ni h, using the general gas law and the catalyst unit weight was converted to nickel unit area using the nickel surface area per kilogram catalyst given by Xu and Froment (9300 mz Ni/ kg cat). Two sets of experiments by Bodrov are considered here to be compared with the corresponding rates obtained by Xu and Froment rate expressions at the same conditions of the reaction.
Xu and
Steam
493
pressure
of
Froment
experiments
(MPa
by
Bodrov
et
al.
x 10)
bctwecn Bodrov and Xu and Froment rate expression (case 1) at 1073 K, P,,, -0.00355. P,,=O.O115, P co.-0 00522, P,, ~0.0551 (all in MPa).
S. S. E.
494
H.
applied on Xu and Froment rate equations to produce the corresponding reaction rates over a wide range of steam partial pressure. The two curves shown in Fig. 2 were obtained. Case (2) This set of experiments was carried out at 1173 K, using a nickel surface area of 0.00575 m’, with the following reacting mixture composition:
P ,-,=0.016 MPa,
P,,
= 0.0119
MPa
P co*-000261
P,, = 0.0462
MPa
MPa,
Xu and
/ portiot
DE DEKEN
KINETICS
~P,,o~(P,,)~--P,oIK,,I
Kc0 c pc,,
rco2=
(20)
Cl + K,,Pc,12 )2/(~H,~4--Pco*/KP,l Kz02CPC”4~(PH*0 (I+ &o~,oY
(21)
where rco and rco2 are the rates of formation of CO and CO, respectively in (kmol/kg cat h), and the rate of disappearance of methane is the sum of the rates of formation of CO and CO,. Reaction rates were expressed in terms of (moles of methane/m’ Ni h) in both cases to bring the cornparison to an equal basis using the value of 680 m2 Ni/kg cat, given by De Deken et al. (1982). The reaction rates generated by the above expressions, using a reacting mixture composition within the range of this experimental work is compared with the rates obtained by Xu and Froment expression with steam partial pressure varried over a wider range. The reaction mixture composition used in the comparison is as follows:
P CH4=0.2 P coI=0.05
MPa,
P,, = 0.05 Pa
MPa,
P,, = 0.2 MPa.
The generated rates from the two expressions are represented by the two curves shown in Fig. 4. Qualitatively, as can be seen from this figure, the behaviour
Froment
Bodrav
et
al x
0.2
0.1
Steom
WITH
De Deken et al.(1982), carried out their investigation in an integeral reactor, packed with a commercial (Ni/Al,O,) catalyst having 12 wt% Ni. The temperature range used is 823-953 K, and pressure range is 0.5-1.5 MPa, the range of the steam to methane molar ratio is 3-5, and the range of hydrogen to methane molar ratio is l&3.25. They reached the following rate expression:
I
271
Fig. 3. Comparison
COMPARISON
rco =
the reaction rate constant at this temperature as given by Bodrov et al. is 4200 (standard liters of methane/h m2 Ni atm). The steam partial pressure was changed between minimum and maximum values by Bodrov in this set of experiments (O.OlHl.023 MPa). The same conditions were applied on Xu and Froment’s rate equations with varying steam partial pressure over a wider range. The results are shown in Fig. 3. Figures 2 and 3 shows clearly that the limited range of reaction conditions in which Bodrov carried out his investigation is most probably responsible for hiding the positive order dependence region. The higher reaction rate per unit nickel area in the case of supported catalyst, in comparison with the case of pure nickel, may be due to the way in which catalyst material interacts with the support material to form a crystal structure with a certain nature, which in turn affect the activity/selectivity properties. Vance and Bartholomew (lY83), reported thus fact. It was shown that the nickel-support interactions significantly influence the adsorption of reactants and reaction intermediates on nickel as well as the activity/selectivity properties of nickel in CO, hydrogenation.
L
et al.
ELNASHAIE
pressure
.
(MPa x IO)
between Bodrov and Xu and Froment rate expressions (case 2) at 1173 K, PcH, = 0.016, 0 .00261, P,, =0.0462 (all in MPa). P ‘,=0.0119, P_=
Non-monotonic
behaviour
of methane-steam
OF THE NON-MONOTONIC FIXED BED REACTORS
Analysis
of simulation results constancy of the partial pressures of the various components other than the one under investigation is imposed by any artificial means, a reaction rate profile along the tube length which is the inverse of the rate dependence curve for the said component is to be obtained. Thus, in such a case the rate of methane disappearance will increase along the length of the reactor tube for a certain length, after which the rate of reaction reaches a maximum value then starts to decrease. This is, of course, not the case in a real (isothermal) reactor tube in which the partial pressure of the other components (other than steam) are changing along the length of the reactor tube, giving rise to a different rate dependence curve along the length of the tube. The reactions rate profiles along the tube length for the case of Table 2 and Fig. 5 are shown in Figs 6(a) and (b). For rI, r3, RCH4 and RHZO the profiles are monotonically decreasing while the behaviour of the water-gas shift reaction rate, r2, along the tube length is non-monotonic. If the
KINETICS ON
The simple isothermal pseudo-homogeneous model The use of a very simple model to investigate the implications of this non-monotonic kinetics will give the opportunity to study its effect away from the combined complex effect of other phenomena which will interfere if a more sophisticated
model
is used. Xu
(1989a) rate equations were used in a one-dimensional isothermal model for the catalyst tube, with a constant effectiveness factor, taken from Soliman et al’s (1988) work, just to bring the actual reaction rates down to reasonable values. The model equations are as follows: and Froment’s
dx,
ldl =
dx,ldl=
~cn.,
vnzo. &,c.
Table 2. Reacting steam feed partial
(22)
. &be. &HJFcH~
(23)
R,,olF,,o
mixture compositions and reaction rates at different points along the reactor tube for the case of pressure lies on the negative order branch of the rate dependence curve (temperature=900 K, total
pressure
= 2.105
MPa,
S/M
= 6.0)
At tube
Curve No.
RCH.
length (m)
1
0.0
2 3
0.00 I
4 5 6 7 8
495
kinetics
where x1 and x1 are the conversions of CH, and H,O respectively, qcH, = flnzo= constant effectiveness factor, given a value of 0.001 (Soliman et al., 1988). RCH4 are functions of PC-., PHzO, PC,, Pco2, PHI and &O and temperature. These two non-linear differential equations were solved using a fourth order Runge-Kutta routine with variable step size to ensure accuracy. The first feed introduced to the model is a typical industrial reformer feed composition (Hyman 1968), which is given by the first row in Table 2. After each reactor tube zone the reactions produce a new set of reacting mixture composition, these sets are listed in Table 2 along a 5 m length of the reactor tube, the catalyst tube diameter used is 0.127 m and the catalyst bulk density is 1225 kg/m3, the methane molar flow rate is 3 kmol/h (Hyman, 1968). The rate of methane disappearance profiles vs steam partial pressure is drawn at each point along the reactor as shown in Fig. 5. The dashed line gives the change of the rate of reaction along the reactor.
rates of both investigators are matching within the range of De Deken et al. (1982) experimentation. The extension of the Xu and Froment rate dependence: curve out of this region generates a negative effective order dependence. This shows that the hiding of negative order is most probably a result of the limited range of reaction conditions used in the investigation. Of course the qualitative difference in the behaviour of the two rate expressions may be due to the difference between the catalysts used. Experimental work in this laboratory is being carried out in order to find the relation between catalyst composition and the non-monotonic behaviour of the rate equations and the location of the maximum rate point for a number of catalysts of different compositions and different support materials. In conclusion it is clear that for the work of Bodrov et al. the, choice of carrying out the investigation at atmospheric pressure and using a limited range of steam partial pressure is most probably the reason for hidding the effective positive order dependence. Also in the work of De Deken et al., the high steam to methane ratio as well as the range of the hydrogen to methane ratio has most probably led to the shift of the point of maximum rate to high values of steam partial pressure, so that it appeared as if the addition of steam has, unconditionally, a positive effect on the reaction rate. of the reaction
IMPLICATIONS
reforming
0.05 0.10 0.50 1.00 2.50 5.00
0.3
0.2977
0.2830 0.277 1 0.2546 0.2395 0.2134 0.1889
(kmol/kg cat h)
PH,O (MPa)
PC0 (MPa)
1.80
0.0
0.0
0.005
2.700
0.0014 0.0023 0.007 1 0.0 102 0.0128 0.0124
0.0018 0.0118 0.0155 0.0283 0.0368 0.0546 0.0740
0.0122 0.0563 0.0739 0.1392 0.1827 0.2614 0.3369
0.715 0.076 0.05 1 0.020 0.013 0.007 0.004
1.7933
1.7524 1.7362 1.6759 1.6357 1.5628 1.4918
0.0006
S. S. E. H. ELNASHAIE et’nl.
496
3Xu
Froment
ond
i----
l Negotrve order / dependence repion
,_
;-
4
5
Steam Fig. 4. Comparison
between
6 partial
7
9
pressure
( MPo
10 x IO)
De Deken and Xu and Froment rate expressions =0.05, PC,,= 0.05, P,,=0.2 (all in MPa).
at 850 K, Pc,,=O.2,
P,
The monotonic decrease of rl and r3, the steam reforming reactions, is mainly caused by the effect of methane depletion and production of products which tends to decrease the reaction rate, despite the negative effective order of the reactions, as discussed in the parametric study. It is to be noticed here that the other two important parameters affecting the rate dependence behaviour which are temperature and total pressure are kept constant in this simplified model. In Fig. 6(c) the non-monotonic behaviour of the shift reaction along the length of the reactor is illustrated on the family of rate profile curves at each point along the tube length. It is clear that the influence of the negative effective reaction order reflects itself in the same manner as to be expected from the rate of reaction profile. This is due to the fact that a reactant of one of the reactions is a product of another reaction, and therefore the change in composition along the reactor tube does not destroy the rate of reaction increase with steam pressure decrease in the negative effective order region as was the case for rl and r3_
2.0
a04 THE
IMPLICATIONS SELECTION
a02
1
3 Steam
6 partiat
9
12
pressure
15
18
IMP0
x IO)
Fig. 5. Methane disappearance rate dependence protiles upon steam at different points along the reactor tube for the case of Table 2.
OF
THE
OF FEED
PHENOMENON
ON
THE
CONDITIONS
Different feeds were introduced to the model with different steam partial pressures while the feed partial pressures of the other components are kept constant, which means, of course, a change of the total pressure. The steam reformer tube chosen for simulation is 5 m long to illustrate the kinetic effets rather than the thermodynamic equilibrium effect since the assumption of constant temperature along the tube causes a
S. S. E. H. ELNASHAIE
498
fast approach
to the thermodynamic
equilibrium
of
et al.
o.32r
the mixture.
The methane conversion reformer tube was obtained versus
the corresponding
at the exit of the 5 m for each feed and plotted steam
partial
pressure
in
feed as shown in Fig. 7. In this figure it is clear that an optimum methane overall conversion can be obtained at a steam feed partial pressure of 0.9 MPa (which corresponds to S/M = 3 and P(tota1) = 1.205 MPa), although this feed composition is not the one that gives maximum reaction rate at the entrance. To explain the above results two more cases are chosen to be analyzed the same way as the case presented in Table 2, the case which gives optimum overall methane conversion is presented in Table 3, and a case of lower steam to methane ratio (S/M =-l.O), is presented in Table 4. This low steam to methane ratio may cause carbon deposition in an industrial reformer. However, carbon formation is neglected in this simulation study for the purpose of focusing on the implications of the phenomenon of non-monotonic kinetics. Comparison between Tables 3 and 4 shows that the rate of reaction for the case of lower steam to methane ratio (Table 4) is higher than that for the case of higher steam to methane ratio (Table 3) up to a half meter in the reactor, after which the contrary is true. The reason for this change, which is responsible for the lower methane conversion produced by the case of Table 4 compared with that produced by the case of
I
0.20 Steam
5 feed
15
10
partrol
pressure
20
(MPa
x10)
Fig. 7. Methane conversion at the exit of the reformer tube at different steam partial pressures in the feed (using the isothermal model), partial pressure of methane in feed = 0.3 MPa, temperature = 900 K, Fca, = 3.0 kmol/h.
Table 3, was found to be due to the fact that the reaction rate for the case of Table 4 after 0.5 m of the tube entered the positive effective order dependence region, while the reaction rate for the case of Table 3, the optimum feed conditions case, stays in the negative order dependence region up to the end of the reactor tube. Comparing the three Tables 2,3 and 4 it is clear by comparing Tables 2 and 3 that the decrease in S/M causes an increase in the outlet conversion while a further decrease in S/M to 1.0 as shown in Table 4 causes the exit conversion to decrease.
Table 3. Reacting mixture compositions and reaction rates at different points along the reactor tube for the case of optimum steam feed partial pressure (temperature = 900 K, total pressure = 2.105 MPa, S/M = 3.0)
Curve
At tube length
No.
Cm)
0.0 0.001 0.05 0.10 0.50 1.00 2.50 5.00
R CH.
(kmol/kg 0.3 0.2972 0.2795 0.272 1 0.2445 0.2268 0.1983 0.1755
0.9
0.8936 0.8548 0.8393 0.7821 0.7442 0.6789 0.6270
0.0 O.oool
0.0026
0.0043 0.0116 0.0150 0.0161 0.0174
0.0 0.0017 0.0111 0.0143 0.0255 0.0339 0.05 18 0.0658
0.005 0.0123 0.0570 0.0750 0.1413 0.1851 0.2599 0.3194
cat h)
2.750 0.731 0.082 0.056 0.022 0.014 0.007 0.004
Table 4. Reaction mixture compositions and reaction rates at different points along the reactor tube for the case of low steam feed partial pressure (temperature = 900 K, total pressure = 0.605 MPa, S/M = 1.0)
Curve No. 1 2 3 4 5 6 7 8
At tube length
PH,O
04
0.0 0.001 0.050 0.100 0.500 1.000 2.500 5.ciX-J
0.3 0.296 1 0.2698 0.2590 0.2232 0.2049 0.1841 0.1759
PC0
&Ii,
PC02
WW
NW
(MW
0.3 0.2945 0.2609 0.2481 0.2036 0.1785 0.1496 0.1397
0.0 0.0003 0.0063 0.0096 0.0190 0.0212 0.0238 0.0260
0.0 0.0016 0.0089 0.0110 0.0 I96 0.0265 0.0344 0.0362
(kmol/kg 0.005 0.0125 0.059 1 0.0773 0.1396 0.1739 0.2131 0.2271
cat h)
2.862 0.790 0.097 0.065 0.022 0.012 0.003 0.0006
Non-monotonic behaviour of methane-steam reforming kinetics From the above discussion it can be concluded that, the too close an approach to the maximum rate point on the rate dependence curve at the enterance of the reformer tube, gives higher initial rate of reaction but at the same time gives faster approach to the positive order region where the rate of reaction drops sharply. This means that there is always an optimum steam feed partial pressure that gives maximum reactor performance (expressed in terms of methane conversion) and this optimization problem is a result of the non-monotonic dependence of the rate of reaction upon steam partial pressure. The non-monotonic functional dependence of kinetic rate expressions is well known in gas-solid catalytic reactions, and was reported in the literature for many other systems. Takahashi et al. (1986) reported the non-monotonic behaviour for the hydrogenation of benzene, Cordova and Gau (1983) reported the phenomenon for benzene oxidation to maleic anhydride, which was also reported by Yue and Olaofe (1984) for the catalytic dehydrogenation of alcohols over zeolites, and by Das and Biswas (1986) for the vaporphase condensation of aniline to diphenylamine. However, the non-monotonic dependence was not recognized for the steam reforming kinetics, although it manifests itself by the presence of both negative and positive order dependence of the rate of reaction upon steam concentration. The implications of the non-monotonic behaviour phenomenon was studied on a lumped parameter system, Bykov and Yablonskii (1981), Luss (1986), Elnashaie and Yates (1973), and found to give a multiplicity of the steady state. However, in this work more practical implication for the phenomenon on the fixed bed reactor is investigated. THE
NON-ISOTHERMAL
+ Ud,(
499
T, - VI
$ n, c,,.
(24)
i=l
Equation (24) is solved simultaneously with eqs (22) and (23) using the same technique used for the isothermal model. The heat transfer coefficient U is calculated by the relation, Xu and Froment (1989b): l/U =d,J2i,,
In (d,,/d,i)+
(25)
l/r,
where C(~is the convective heat transfer coefficient the packed bed and is obtained from the correlation Leva (1951): r,d,,/&=0.813
(d,G/p)“.9
exp (-6d,/d,).
in of (26)
The model was used to obtain the change of methane conversion at the exit from the reformer tube at different partial pressures of steam in feed to determin the optimum steam feed partial pressure as shown in Fig. 8. This optimum value was found at a steam partial pressure of 0.6 MPa (S/M=2.0): this shift in the point of maximum rate towards lower
PSEUDO-HOMOGENEOUS MODEL
A simple non-isothermal model that takes the temperature variation along the length of the reactor tube is used in this section. An energy balance on the reformer tube element, assuming constant tube skin temperature, gives the following differential equation:
Steam
feed
partial
pressure (MPa x10)
Fig. 8. Methane conversion at the exit of the reformer tube at different steam feed partial pressures (using the nonisothermal model), partial pressure of methane in feed = 0.3 MPa, feed temperature = 900 K, tube skin temperature = 1300 K, Fc,,, = 3.0 kmol/h (case of Table 5).
Table 5. Reacting mixture compositions and reaction rates at different points along the reactor tube for the ease of optimum steam feed partial pressure (non-isothermal model) (feed temperature =900 K, tube skin temperature = 1300 K, total pressure =0.905 MPa, S/M = 2.0) Curve
At tube length
No.
(ml
1 2 3 4 5 6 7 8
0.0 0.00 I 0.05 0.10 0.50 1.00 2.50 5.00
Reacting
&A, 0.3 0.297 0.276 0.268 0.234 0.211 0.166 0.113
(ZK, 0.6 0.594 0.557 0.541 0.484 0.443 0.363 0.282
PC0
(M Pa) 0.0 0.001 0.004 0.006 0.016 0.02 1 0.03 1 0.057
PC,,
(Mf’a)
0.0 0.003 0.011 0.013 0.024 0.033 0.049 0.056
(LFa) 0.005 0.012 0.058 0.076 0.147 0.197 0.296 0.397
R (kmol/iL’cat 2.78 0.747 0.088 0.06 1 0.0266 0.0194 0.0146 0.0123
h)
mixture temperature 900 900.2 901.2 902.3 911.3 922.7 956.9 1007.7
(K)
S. S. E. H.
500
, 0.70
30,
iz2ooa50 10
0
Steam
ELNASHAIE
feed
partial
30
20
pressure
(MPa
x 10 1
Fig. 9. Profile of rate of methane disappearance
dependence upon steam feed partial pressure and the corresponding exit methane conversion predicted by a one-dimensional heterogeneous modei, operating conditions are given as follows: tube length/O.D./I.D.= 11.95/0.102/0.0795 m; feed composition for point a (mole %) CH,= 12.98%. C,H,=2.14%,
C3H,=0.42%,C,H,, =0.05%, H,O =8X73%, N,=0.34%, H, =0.34%; total molar feed rate =4085.7 kmol/h; inlet conditions: feed temperature = 853 K, feed pressure = 2.44 MPa (number
of catalyst
tubes=
176).
values of steam partial pressure compared with the isothermal case is due to the increase of temperature along the reactor length. A compIete mapping of reaction rate dependence profiles along the reactor tube length for this optimum feed case, is shown in Table 5. HETEROGENEOUS MODEL
FOR INDUSTRIAL
STEAM
REFORMERS
In addition to the above results a relatively rigorous heterogeneous model which has been successfully checked against a large number of industrial steam reformers (Soliman et al., 1988; Elnashaie et al., 1989), has been used to check the existence of this maximum conversion point. The results of this simulation is shown in Fig. 9, and it is clear that this maximum conversion point does exist for industrial steam reformers. Detailed analysis of this phenomenon in industrial steam reformers is given elsewhere (Elnashaie et al., 1989). CONCLUSIONS
The steam reforming kinetics developed by Xu and Froment (1989a), is obviously a more general form than previous steam reforming kinetics and it explains a number of contradictions existing in the literature. The comparison with Bodrov (1964) kinetics and with De Deken et al. (1982) kinetics reveals clearly the limited nature of their kinetic rate equations. The kinetic rate equations of Xu and Froment predict well both positive and negative effective reaction orders
et al.
with respect to steam. The non-monotonic nature of this kinetics gives rise to an interesting optimization problem with respect to the feed partial pressure of steam. This optimization problem is demonstrated using a one-dimensional pseudo-homogeneous model with constant effectiveness factor for both isothermal and non-isothermal cases. It is also demonstrated using a detailed heterogeneous model which was verified successfully against a large number of industrial steam reformers. It is shown that the optimum feed partial pressure of steam that gives maximum output conversion is higher than that giving maximum rate of reaction at the entrance. The non-isothermal case gives optimum steam feed partial pressure which is lower than the isothermal case. It is also shown that this optimum feed partial pressure of steam does exist for industrial steam reformers. Work is underway in this department to verify the non-monotonic kinetics of this reaction experimentally and, for different types of steam reforming catalysts, the results of this detailed kinetic investigation will be published shortly. Acknowledgement-The authors would like to record their appreciation to Prof. Froment, for providing the authors with his more general kinetics for steam reforming prior to publication and for very stimulating discussions during exchange of visits between the two departments.
NOTATION
A cpi d d:;
4 Ei Fi G
(-A&i) (-AHi) Kl K2 k,, k
k, K CH.3 Kc,, K L ni
PT pi
K Hz It20
reformer tube cross-sectional area, m2 heat capacity of component i, J/kg K reformer tube outside diameter, , reformer tube inside diameter, m catalyst particle diameter, m activation energy for reaction i, kJ/mol molar feed rate of component i, kmoljh process gas mass velocity, kg/h m2 heat of reaction for reaction i, kJ/mol heat of chemisorption for component i, kJ/mol equilibrium constant for reaction I, MPa2 equilibrium constant for reaction II rate coefficients for reactions I and III respectively, kmol MPa/kg cat h rate coefficient for reaction II, kmol/kg cat h MPa adsorption constants for CH,, CO, H,, MPa-’ dissociation adsorption constant for H,O, MPa-’ reformer tube coordinate, m number of moles for component i in the reaction mixture, kmol/h total pressure, MPa component i partial pressure, MPa
Non-monotonic r1, r21 I3 R
CH4
R Hz0 T T, u
rates of reactions I, II and III respectively, kmol/kg cat h rate of CH, disappearance, kmol CH,/kg cat h H,O disappearance, kmol rate of H,O/kg
cat h
temperature of the reacting mixture, K tube skin temperature, K overall
heat transfer
Xl
conversion
x2
conversion
peared/CH,
ZICH.
fl&O
Pbr
W/m2 K CH, moles disap-
coefficient,
of methane,
moles in feed of
H,O moles in feed transfer coefficient,
steam,
disappeared/H,0 ai
behaviourof methane-steam reforming
moles
convective heat W/m’ K effectiveness factor of CH, diappearance rate effectiveness factor of H,O disappearance rate constant average effectiveness factor viscosity of the reacting gas mixture, kg/m h process gas and tube metal thermal conductivities, W/m K catalyst bulk density, kg cat/m’ REFERENCES
W. and Camp, D. P., 1955, Kinetics of Akres, W methane-steam reactions, A.1.Ch.E. J. 1, 471475. Al-Ubaid, A. S., 1986, Steam reforming of hydrocarbons catalyzed over nickel supported catalysts. Arabian J. Sci. Engng 12, 189. Al-Ubaid, A. S., 1984, Methane steam reforming activity, stability and characterization of nickel supported catalysts. Ph.D. Thesis, University of Notre Dame, Indiana, U.S.A. Atroshchenko, V. I., Raman, Sh. K. and Zryagintsev. G. I., 1969, Kinetics of conversion of natural gas by steam under pressure. J. Appl. Chem. USSR 42, 149&1503. Bodrov, N. M., Apel’baum, L. 0. and Temkin M. I., 1964, Kinetics of the reactions of methane with steam on the surface of nickel. Kinetica Karaliz 5, 696-705. Bodrov, N. M., Apcl’baum, L. 0. and Temkin, M. I., 1967, Kinetics of the reaction of methane with water vapour, catalyzed by nickel on a porous carrier. Kinetic0 Kotaliz 8, 821-828. Bodrov, N. M., Apel’baum, L. 0. and Temkin, M. I., 1967b, Kinetics of the reaction of methane with steam on the surface of nickel at 4CP36OO”C. Kinet. Catal. 9, 1065-1071. Bykov, V. I. and Yablonskii, C. S., 1981, Steady-state multiplicity in heterogeneous catalytic reactions. Int. Chem. Engng 21, 142-155. Cordova, V. R. and Gau, G., 1983, Redox kinetics of benzene oxidation to maleic anhydride. Can. J. Chem. Engng 61, 200-207. Das, G. and Biswas, A. K., 1986, Initial rate study on the
kinetics
501
vanor-chase condensation of aniline to diphenylamine. _ _ Cdn. J: Chem. Engng 64.473477. De Deken. J. C.. Devos. E. F. and Froment. G. F., 1982. Steam reforming of natural gas. Chem. Reaction Engng ACS Symp. Ser. 196. Elnashaie, S. and Yates, J., 1973, Multiplicity of the steady state in fluidised bed reactors-I. Steadv state consideration. Chem. Engng Sci. 28, 515-520. Elnashaie, S. S. E. H.. Al-Ubaid, A. S.. Soliman. M. A. and Adris, A. M., 1988, On the kinetics and reactor modelling for the steam reforming of methane-a review. J. ~nyny Sci. (King Saud University)14, No. 2, 247-273. Elnashaie,S. S. E. H., Aaris, A. M.. Soliman, M. A. and AlUbaid, A. S., 1989, Parametric investigation of industrial steam reformers (submitted for publication). Hyman, M. H., 1968, Simulate methane reformer reactions. Hyd. Car. Pro. 49, 13 1. Kopsel, R., Richter, A. and Meyer, B., 1980, Catalyst deactivation and kinetics of methane steam reforming. Chem. Tech. 32, 460. Leva, M., Winstrub, M., Grummer, M.. Pollchik, M. and Stroch, H. H., 1951, Fluid flow through packed and fluidized systems. U.S. Bur. Mines, Bull. 504. Luss, D., 1986, Steady-state multiplicity features of chemically reacting systems. Chem. Engng Educ. Award lecture, pp. 12-56. Munster, P. and Gabka, H. J., 1981, Kinetics of the steam reforming of methane with iron, nickel, and iron-nickel alloys as catalysts. J. Catal. 72, 279-287. Nikrich, E. M., 1970, Kinetics of partial oxidation of natural gas by a small amount of steam. J. Appl. Chem. USSR 43, 372. Paloumbis. S. and Petersen, E. E., 1982, Coke deposition on a commercial nickel oxide catalyst during the steam reforming of methane. Chem. React. Engng, Am. Chew Sot. 38,489495. Quach, P. T. and Rouleau, U. D., 1975, Kinetics of the methane-steam reaction over nickel catalyst in a continuous stirred tank reactor. J. Appl. Chem. Biotech. 25, 445-459. Ross, J. R. H. and Steel, M. C. F., 1972, Mechanism of the steam reformina of methane over a CODreCiDitated nickelalumina cataly;t. J. Chem. Sot. Faraday T&s. 1, 69. Soliman, M. A., Elnashaie, S. S. E. H., Al-Ubaid, A. S. and Ad&, A. M., 1988, Simulation of steam reformers for methane. Chem. Engng Sci. 43, 8. Takahashi, T., Yamashita, K., Kai, T. and Fujiyoshi, I., 1986, Hydrogenation of benzene, mono-, di-, and trimethylbenzenes over nickel catalysts supported on porous glass. Can. J. Chem. Engng 64, 1008-1013. Vance, C. K. and Bartholomew, C. H., 1983, Hydrogenation of carbon dioxide on group VIII metals--III. Effect of support on activity/selectivity and adsorption properties of nickel. Appl. Catal. 7, 169-177. Xu, I. and Froment, G. F., 1989a, Methane-steam reforming, methanation, and water-gas shift-I. Intrinsic kinetics. A.1.Ch.E. J. 35, 88-96. Xu, J. and Froment, G. F., 1989b, Methane-steam reforming-11. Diffusion limitation and reactor simulation. A.I.Ch.E. J. 35, 97-103. Yue, P. L. and Olaofe, 0.. 1984, Kinetic analysis of the catalytic dehydrogenation of alcohols over zeolites. Chem. Engng Res Des. 62, 81-91.
1990.
ooo9-2509po
Printed in Great Britain.
0
s3.00+0.00
1990 Pergamon Press plc
ON THE NON-MONOTONIC BEHAVIOUR OF METHANE-STEAM REFORMING KINETICS S. S. E. H. ELNASHAIE,’ A. M. ADRIS, A. S. AL-UBAID and M. A. SOLIMAN Chemical Reaction Engineering Group, Chemical Engineering Department, King Saud University, PO Box 800, Riyadh 11421, Saudi Arabia (Received
7 March
1988; accepted
for publication
19 May
1989)
Abstract-A parameteric study on the rate expression recently developed by Xu and Froment (1989a, A.1.Ch.E. J. 35,88-96) is carried out over a wide range of parameters. The analysis of this rate expression has shown a non-monotonic dependence of the reaction rate upon steam partial pressure which explains the contradictions between the rate expressions available in the literature, that is the prediction of positive, as well as negative effective reaction order with respect to steam. A simplified pseudo-homogeneous model with a constant effectiveness factor, with Xu and Froment’s rate expression was used to investigate the
implications of the non-monotonic kinetics on the performance of steam reformers. The main implication was also checked using a heterogeneous model that represents very closely industrial steam reformers.
INTRODUCTION A large
number
of kinetic
rate expressions
for the
steam reforming of methane is reported in the literature (Akers and Camp, 1955; Atroshchenko et al., 1969; Bodrov et al., 1964; Ross and Steel, 1972; Munster and Gobka, 1981; Quach and Rouleau, 1975; De Deken et al., 1982). Most of these rate equations are either emperically based power law kinetics or are obtained by applying a large number of assumptions on a proposed mechanism. These facts make the rate equations obtained valid only for a certain range of reaction conditions and thus of limited use, especially that the original mechanism, even before applying the simplifying assumptions, is never certain. In addition, this approach has led to certain discrepencies such as the disappearance of certain reactants and/or products concentrations from the rate equations. When the chemisorption process is taken into consideration it is noticed in many cases that the concentrations of certain components are absent from the denominator of the Langmuir-Hinshelwood type rate equations, while these components are known to be strongly adsorbed. One of the most interesting contradictions noticed in these rate equations is the prediction of positive, as well as negative effective reaction order with respect to steam. Some investigators attributed this phenomenon to the difference in the acidity of the catalyst support (AlIJbaid, 1986). In fact this negative effective order of the reaction is a strong indication for the existence of a non-monotonic dependence of the rate of reaction upon the concentration of a specific reactant. A general rate equation based on LangmuirHinshelwood-Hougen-Watson has been developed recently
(LHHW) approach by Xu and Froment
(1989a). This rate equation has been investigated in this study and has shown a non-monotonic dependence of the rate of methane disappearance upon steam partial pressure. Comparison with previous investigations is presented and the implications of non-monotonic kinetics on the behaviour of industrial steam reformers are investigated. THE NON-MONOTONIC
OF METHANESTEAM
The kinetic rate equations developed by Xu and Froment (1989a), based on (LHHW) approach, are shown to be more general relative to the previous rate expressions available in the literature, and explain a number of contradictions in the work of previous investigators. Xu and Froment have taken into consideration the two main reactions of steam reforming together with the water-gas shift reaction: CH, + H,O c, CO + 3H, CO + H*O+-+ CO, + H, CH, + 2H,O*
CO, + 4H,.
The adsorption-surface reaction+lesorption used consists of the following 13 steps: H,O+LuO-L+H, CH, + L-
(r.d.s)
(II) (III) model (1)
CH,-L
(2)
+ Lt* CHa-L
+ H-L
(3)
CH,-L
+ Lc* CH,-L
+ H-L
(4)
CH,O-L
+ L
(5)
CHO-L
+ H-L
+ O-L-
CH,O-L (r.d.s)
(I)
CH,-L
CH,-L
(r.d.s) ‘Author to whom all correspondence should be addressed. On leave from the Chemical Engineering Department, Cairo University, Cairo, Egypt.
KINETICS REFORMING
+ Lo
CHO-L CO-L CHO-L
+ Ltt CO-L
(6)
+ H-L
(7)
+ O-L-
co,-L
+ L
(8)
+ O-L+-+
CO,-L
+ H-L
(9)
CO-L-
co
+ L
(10)
492
S.
co,-Lu
co,
2H-Lt*
S.
E. H.
ELNASHAIE
+ L
(11)
L + H,-L
(12)
H,-LeH,+L
(13)
with steps (7), (8) and (9) being the rate determining steps. Based on this mechanism the following rate equations were obtained:
P
rz=k,
. .
PHZO (p”,)“.5. PC0
(T:*)= -
‘t=k,
P co (
PHI0 -- PCOl K, >I
P P CH.‘ip,,0)2
DEN’
(pH,)o.5
-
(14)
R CH4=II
(15)
(17)
fr3
RHzO = r, + r2 + 2r, ‘pCO,
r,=k, (PHJ3.5
DEN2
>I
K,
et al.
simplest way to present the dependence of the kinetic rate equations upon the partial pressure of one component in the two-dimensional plot. The case where partial pressures of all components are varying along the length of the reactor tube is also investigated. The analysis covered a temperature range of 800-1200 K, and a total pressure range of 0.1-1.5 MPa, and has shown that rl and r2 have a non-monotonic dependence on steam partial pressure, while the dependence of r3 on steam partial pressure is a monotonic function [Fig. l(a)]. Also, since:
DEN’
(16)
Kl.K2
DEN= 1+ &oPco+KH,PH,
+ Kc,.Pc,,
+ KH~oPH~oIPH~ where r, , r2 and rS are the rates of reactions I, II and III respectively in (kg mol/kg cat h).
The increase of temperature causes the location of the point of maximum to move towards lower values of steam partial pressure.
The 13 step reaction mechanism used shows competition for the active sites between methane and steam, and thus leads to the functional dependene of the rate of reaction shown in eqs (14), (15) and (16), which can give non-monotonic dependence of the reaction rate upon the partial pressure of steam and methane. The kinetic rate constants, activation energies, adsorption constants and heats of adsorption are all given in Table 1. RATE DEPENDENCE
(18)
both R,,, ann R,,, showed a non-monotonic dependence on steam partial pressure [Fig. l(b)]. The location of the maximum rate point (zero order dependence point) and its value are highly affected by the rate equation parameters. A parametric study has shown that:
INVESTIGATION
An investigation was carried out on the dependence of each reaction rate as well as the total methane disappearance on reactants concentrations (or partial pressures). The partial pressures for all components involved in the reactions, except the one under investigation (e.g. steam), were considered to be constant. This situation does not correspond to the actual variation of the partial pressures of the reacting mixture components along the reactor tube, but it is the
‘2
L’
.
1 Steam
2
3
partial
4 pressure
5
6
(MPa
x IO)
5
6
Table 1. Pre-exponential factors for the reaction rate constants and adsorption activation constants, energies and heats of adsorption Activation
Constant k, :: Gel &H. K H.0 K “I
Pre-exponential factor
energies Ei and heats of chemisorption ( - AHi)
9.49 X 10’5 4.39 x 106 2.29x IO” 8.23x lO-5 6.65 x IO-* 1.77X 105
+240.1 +67.13 + 243.9 + 70.65 38.28 - 88.68
6.12 x 10-g
82.9
K, =[exp (-26,830.0/T+30.114)] K, =exp (4400/T-4.036).
x 10w2.
a”
I
1 Steam
2 partial
3
4 pressure
LMPa
*
x 10)
Fig. l(a). Dependence of r,, r2 and r3 on steam partial P cr,,=0.02. pressure at 900 K, P, =0.85. P,,=O.Ol. P,,, =O.Ol, P,, =0.03 (all in MPa). (b) Dependence of R,,,, and R HZ0on steam partial pressure [same conditions of Fig. l(a)].
Non-monotonic behaviour of methane-steam reforming kinetics
(2) The
increase of total pressure causes the location of the point of maximum to move towards higher values of steam partial pressure. (3) The effect of increasing H,/CH, ratio is to move the point of maximum rate towards higher values of steam partial pressure. Increasing the other products concentrations has a similar effect.
REACTION
RATE
DEPENDENCE
OBSERVED
BY
OTHER
INVESTIGATORS
Among a chosen twelve investigators who studied the kinetics of methane steam reforming reaction, four investigators (Bodrov et al., 1964; Ross and Steel, 1973; Al-Ubaid, 1984; Nikrich, 19701, reported negative order dependence of the rate of reaction upon steam partial pressure, four reported zero order (Akres and Camp, 1955; Bodrov et al., 1967a, b; Munster and Gabka, 1981), and five investigators reported positive order dependence (Al-Ubaid, 1984; Quach and Rouleau, 1975; Atroshchenko et al., 1969; Kopsel et al., 1980; De Deken et al., 1982). The recent kinetic rate expressions developed by Xu and Froment (1989a), can give both positive and negative order dependence of the rate of reaction upon steam partial pressure. The reaction rates using this new kinetic expression were compared with the corresponding rates of the expression of Bodrov et a[. (1964), which gives negative effective order and with the expression of De Deken ef al. (1982), which gives positive effective order dependence on steam. COMPARISON
WITH
BODROV
KINETICS
Bodrov rl ul. (1964), carried out their investigation in a flow reactor with recycle, on nickel foil, at atmospheric pressure and m the temperature range of
1073-l 173 K, they obtained pression: ?-=
Fig. 2. Comparison
rate ex-
kPc,, 1 +aCPH,o/PH21 +bP,,
(19)
Case (1) Bodrov et al. (1964), carried out this set of experiments at 1073 K, using a nickel surface area of 0.0775 m2, with the following reacting mixture composition: P CH4= 0.003SS MPa,
P,,
= 0.0115 MPa
P co2 = 0.00522 MPa,
P,,
= 0.055 1 MPa
the reaction rate constant at this temperature as given by Bodrov et al. is 800 (standard liters of methane/h m2 Ni atm). Steam partial pressure was changed between the minimum value used by Bodrov in this set of experiments (0.01 MPa), and the maximum value (0.0244 MPa). The same conditions were
Range
partial
the following
where r is the rate of reaction in standard liters of methane/hm’ Ni, and a and b are constants equal to 0.5 and 2.0, respectively, at 1073 K, and 0.2 and 0.0 respectively at 1173 K. The geometrical surface area of the nickel foil used in the investigation was 4.49 m’/kg. To compare the rate of reaction obtained by the above expression with that obtained by Xu and Froment (1989a), both rates were converted into mol/m’ Ni h, using the general gas law and the catalyst unit weight was converted to nickel unit area using the nickel surface area per kilogram catalyst given by Xu and Froment (9300 mz Ni/ kg cat). Two sets of experiments by Bodrov are considered here to be compared with the corresponding rates obtained by Xu and Froment rate expressions at the same conditions of the reaction.
Xu and
Steam
493
pressure
of
Froment
experiments
(MPa
by
Bodrov
et
al.
x 10)
bctwecn Bodrov and Xu and Froment rate expression (case 1) at 1073 K, P,,, -0.00355. P,,=O.O115, P co.-0 00522, P,, ~0.0551 (all in MPa).
S. S. E.
494
H.
applied on Xu and Froment rate equations to produce the corresponding reaction rates over a wide range of steam partial pressure. The two curves shown in Fig. 2 were obtained. Case (2) This set of experiments was carried out at 1173 K, using a nickel surface area of 0.00575 m’, with the following reacting mixture composition:
P ,-,=0.016 MPa,
P,,
= 0.0119
MPa
P co*-000261
P,, = 0.0462
MPa
MPa,
Xu and
/ portiot
DE DEKEN
KINETICS
~P,,o~(P,,)~--P,oIK,,I
Kc0 c pc,,
rco2=
(20)
Cl + K,,Pc,12 )2/(~H,~4--Pco*/KP,l Kz02CPC”4~(PH*0 (I+ &o~,oY
(21)
where rco and rco2 are the rates of formation of CO and CO, respectively in (kmol/kg cat h), and the rate of disappearance of methane is the sum of the rates of formation of CO and CO,. Reaction rates were expressed in terms of (moles of methane/m’ Ni h) in both cases to bring the cornparison to an equal basis using the value of 680 m2 Ni/kg cat, given by De Deken et al. (1982). The reaction rates generated by the above expressions, using a reacting mixture composition within the range of this experimental work is compared with the rates obtained by Xu and Froment expression with steam partial pressure varried over a wider range. The reaction mixture composition used in the comparison is as follows:
P CH4=0.2 P coI=0.05
MPa,
P,, = 0.05 Pa
MPa,
P,, = 0.2 MPa.
The generated rates from the two expressions are represented by the two curves shown in Fig. 4. Qualitatively, as can be seen from this figure, the behaviour
Froment
Bodrav
et
al x
0.2
0.1
Steom
WITH
De Deken et al.(1982), carried out their investigation in an integeral reactor, packed with a commercial (Ni/Al,O,) catalyst having 12 wt% Ni. The temperature range used is 823-953 K, and pressure range is 0.5-1.5 MPa, the range of the steam to methane molar ratio is 3-5, and the range of hydrogen to methane molar ratio is l&3.25. They reached the following rate expression:
I
271
Fig. 3. Comparison
COMPARISON
rco =
the reaction rate constant at this temperature as given by Bodrov et al. is 4200 (standard liters of methane/h m2 Ni atm). The steam partial pressure was changed between minimum and maximum values by Bodrov in this set of experiments (O.OlHl.023 MPa). The same conditions were applied on Xu and Froment’s rate equations with varying steam partial pressure over a wider range. The results are shown in Fig. 3. Figures 2 and 3 shows clearly that the limited range of reaction conditions in which Bodrov carried out his investigation is most probably responsible for hiding the positive order dependence region. The higher reaction rate per unit nickel area in the case of supported catalyst, in comparison with the case of pure nickel, may be due to the way in which catalyst material interacts with the support material to form a crystal structure with a certain nature, which in turn affect the activity/selectivity properties. Vance and Bartholomew (lY83), reported thus fact. It was shown that the nickel-support interactions significantly influence the adsorption of reactants and reaction intermediates on nickel as well as the activity/selectivity properties of nickel in CO, hydrogenation.
L
et al.
ELNASHAIE
pressure
.
(MPa x IO)
between Bodrov and Xu and Froment rate expressions (case 2) at 1173 K, PcH, = 0.016, 0 .00261, P,, =0.0462 (all in MPa). P ‘,=0.0119, P_=
Non-monotonic
behaviour
of methane-steam
OF THE NON-MONOTONIC FIXED BED REACTORS
Analysis
of simulation results constancy of the partial pressures of the various components other than the one under investigation is imposed by any artificial means, a reaction rate profile along the tube length which is the inverse of the rate dependence curve for the said component is to be obtained. Thus, in such a case the rate of methane disappearance will increase along the length of the reactor tube for a certain length, after which the rate of reaction reaches a maximum value then starts to decrease. This is, of course, not the case in a real (isothermal) reactor tube in which the partial pressure of the other components (other than steam) are changing along the length of the reactor tube, giving rise to a different rate dependence curve along the length of the tube. The reactions rate profiles along the tube length for the case of Table 2 and Fig. 5 are shown in Figs 6(a) and (b). For rI, r3, RCH4 and RHZO the profiles are monotonically decreasing while the behaviour of the water-gas shift reaction rate, r2, along the tube length is non-monotonic. If the
KINETICS ON
The simple isothermal pseudo-homogeneous model The use of a very simple model to investigate the implications of this non-monotonic kinetics will give the opportunity to study its effect away from the combined complex effect of other phenomena which will interfere if a more sophisticated
model
is used. Xu
(1989a) rate equations were used in a one-dimensional isothermal model for the catalyst tube, with a constant effectiveness factor, taken from Soliman et al’s (1988) work, just to bring the actual reaction rates down to reasonable values. The model equations are as follows: and Froment’s
dx,
ldl =
dx,ldl=
~cn.,
vnzo. &,c.
Table 2. Reacting steam feed partial
(22)
. &be. &HJFcH~
(23)
R,,olF,,o
mixture compositions and reaction rates at different points along the reactor tube for the case of pressure lies on the negative order branch of the rate dependence curve (temperature=900 K, total
pressure
= 2.105
MPa,
S/M
= 6.0)
At tube
Curve No.
RCH.
length (m)
1
0.0
2 3
0.00 I
4 5 6 7 8
495
kinetics
where x1 and x1 are the conversions of CH, and H,O respectively, qcH, = flnzo= constant effectiveness factor, given a value of 0.001 (Soliman et al., 1988). RCH4 are functions of PC-., PHzO, PC,, Pco2, PHI and &O and temperature. These two non-linear differential equations were solved using a fourth order Runge-Kutta routine with variable step size to ensure accuracy. The first feed introduced to the model is a typical industrial reformer feed composition (Hyman 1968), which is given by the first row in Table 2. After each reactor tube zone the reactions produce a new set of reacting mixture composition, these sets are listed in Table 2 along a 5 m length of the reactor tube, the catalyst tube diameter used is 0.127 m and the catalyst bulk density is 1225 kg/m3, the methane molar flow rate is 3 kmol/h (Hyman, 1968). The rate of methane disappearance profiles vs steam partial pressure is drawn at each point along the reactor as shown in Fig. 5. The dashed line gives the change of the rate of reaction along the reactor.
rates of both investigators are matching within the range of De Deken et al. (1982) experimentation. The extension of the Xu and Froment rate dependence: curve out of this region generates a negative effective order dependence. This shows that the hiding of negative order is most probably a result of the limited range of reaction conditions used in the investigation. Of course the qualitative difference in the behaviour of the two rate expressions may be due to the difference between the catalysts used. Experimental work in this laboratory is being carried out in order to find the relation between catalyst composition and the non-monotonic behaviour of the rate equations and the location of the maximum rate point for a number of catalysts of different compositions and different support materials. In conclusion it is clear that for the work of Bodrov et al. the, choice of carrying out the investigation at atmospheric pressure and using a limited range of steam partial pressure is most probably the reason for hidding the effective positive order dependence. Also in the work of De Deken et al., the high steam to methane ratio as well as the range of the hydrogen to methane ratio has most probably led to the shift of the point of maximum rate to high values of steam partial pressure, so that it appeared as if the addition of steam has, unconditionally, a positive effect on the reaction rate. of the reaction
IMPLICATIONS
reforming
0.05 0.10 0.50 1.00 2.50 5.00
0.3
0.2977
0.2830 0.277 1 0.2546 0.2395 0.2134 0.1889
(kmol/kg cat h)
PH,O (MPa)
PC0 (MPa)
1.80
0.0
0.0
0.005
2.700
0.0014 0.0023 0.007 1 0.0 102 0.0128 0.0124
0.0018 0.0118 0.0155 0.0283 0.0368 0.0546 0.0740
0.0122 0.0563 0.0739 0.1392 0.1827 0.2614 0.3369
0.715 0.076 0.05 1 0.020 0.013 0.007 0.004
1.7933
1.7524 1.7362 1.6759 1.6357 1.5628 1.4918
0.0006
S. S. E. H. ELNASHAIE et’nl.
496
3Xu
Froment
ond
i----
l Negotrve order / dependence repion
,_
;-
4
5
Steam Fig. 4. Comparison
between
6 partial
7
9
pressure
( MPo
10 x IO)
De Deken and Xu and Froment rate expressions =0.05, PC,,= 0.05, P,,=0.2 (all in MPa).
at 850 K, Pc,,=O.2,
P,
The monotonic decrease of rl and r3, the steam reforming reactions, is mainly caused by the effect of methane depletion and production of products which tends to decrease the reaction rate, despite the negative effective order of the reactions, as discussed in the parametric study. It is to be noticed here that the other two important parameters affecting the rate dependence behaviour which are temperature and total pressure are kept constant in this simplified model. In Fig. 6(c) the non-monotonic behaviour of the shift reaction along the length of the reactor is illustrated on the family of rate profile curves at each point along the tube length. It is clear that the influence of the negative effective reaction order reflects itself in the same manner as to be expected from the rate of reaction profile. This is due to the fact that a reactant of one of the reactions is a product of another reaction, and therefore the change in composition along the reactor tube does not destroy the rate of reaction increase with steam pressure decrease in the negative effective order region as was the case for rl and r3_
2.0
a04 THE
IMPLICATIONS SELECTION
a02
1
3 Steam
6 partiat
9
12
pressure
15
18
IMP0
x IO)
Fig. 5. Methane disappearance rate dependence protiles upon steam at different points along the reactor tube for the case of Table 2.
OF
THE
OF FEED
PHENOMENON
ON
THE
CONDITIONS
Different feeds were introduced to the model with different steam partial pressures while the feed partial pressures of the other components are kept constant, which means, of course, a change of the total pressure. The steam reformer tube chosen for simulation is 5 m long to illustrate the kinetic effets rather than the thermodynamic equilibrium effect since the assumption of constant temperature along the tube causes a
S. S. E. H. ELNASHAIE
498
fast approach
to the thermodynamic
equilibrium
of
et al.
o.32r
the mixture.
The methane conversion reformer tube was obtained versus
the corresponding
at the exit of the 5 m for each feed and plotted steam
partial
pressure
in
feed as shown in Fig. 7. In this figure it is clear that an optimum methane overall conversion can be obtained at a steam feed partial pressure of 0.9 MPa (which corresponds to S/M = 3 and P(tota1) = 1.205 MPa), although this feed composition is not the one that gives maximum reaction rate at the entrance. To explain the above results two more cases are chosen to be analyzed the same way as the case presented in Table 2, the case which gives optimum overall methane conversion is presented in Table 3, and a case of lower steam to methane ratio (S/M =-l.O), is presented in Table 4. This low steam to methane ratio may cause carbon deposition in an industrial reformer. However, carbon formation is neglected in this simulation study for the purpose of focusing on the implications of the phenomenon of non-monotonic kinetics. Comparison between Tables 3 and 4 shows that the rate of reaction for the case of lower steam to methane ratio (Table 4) is higher than that for the case of higher steam to methane ratio (Table 3) up to a half meter in the reactor, after which the contrary is true. The reason for this change, which is responsible for the lower methane conversion produced by the case of Table 4 compared with that produced by the case of
I
0.20 Steam
5 feed
15
10
partrol
pressure
20
(MPa
x10)
Fig. 7. Methane conversion at the exit of the reformer tube at different steam partial pressures in the feed (using the isothermal model), partial pressure of methane in feed = 0.3 MPa, temperature = 900 K, Fca, = 3.0 kmol/h.
Table 3, was found to be due to the fact that the reaction rate for the case of Table 4 after 0.5 m of the tube entered the positive effective order dependence region, while the reaction rate for the case of Table 3, the optimum feed conditions case, stays in the negative order dependence region up to the end of the reactor tube. Comparing the three Tables 2,3 and 4 it is clear by comparing Tables 2 and 3 that the decrease in S/M causes an increase in the outlet conversion while a further decrease in S/M to 1.0 as shown in Table 4 causes the exit conversion to decrease.
Table 3. Reacting mixture compositions and reaction rates at different points along the reactor tube for the case of optimum steam feed partial pressure (temperature = 900 K, total pressure = 2.105 MPa, S/M = 3.0)
Curve
At tube length
No.
Cm)
0.0 0.001 0.05 0.10 0.50 1.00 2.50 5.00
R CH.
(kmol/kg 0.3 0.2972 0.2795 0.272 1 0.2445 0.2268 0.1983 0.1755
0.9
0.8936 0.8548 0.8393 0.7821 0.7442 0.6789 0.6270
0.0 O.oool
0.0026
0.0043 0.0116 0.0150 0.0161 0.0174
0.0 0.0017 0.0111 0.0143 0.0255 0.0339 0.05 18 0.0658
0.005 0.0123 0.0570 0.0750 0.1413 0.1851 0.2599 0.3194
cat h)
2.750 0.731 0.082 0.056 0.022 0.014 0.007 0.004
Table 4. Reaction mixture compositions and reaction rates at different points along the reactor tube for the case of low steam feed partial pressure (temperature = 900 K, total pressure = 0.605 MPa, S/M = 1.0)
Curve No. 1 2 3 4 5 6 7 8
At tube length
PH,O
04
0.0 0.001 0.050 0.100 0.500 1.000 2.500 5.ciX-J
0.3 0.296 1 0.2698 0.2590 0.2232 0.2049 0.1841 0.1759
PC0
&Ii,
PC02
WW
NW
(MW
0.3 0.2945 0.2609 0.2481 0.2036 0.1785 0.1496 0.1397
0.0 0.0003 0.0063 0.0096 0.0190 0.0212 0.0238 0.0260
0.0 0.0016 0.0089 0.0110 0.0 I96 0.0265 0.0344 0.0362
(kmol/kg 0.005 0.0125 0.059 1 0.0773 0.1396 0.1739 0.2131 0.2271
cat h)
2.862 0.790 0.097 0.065 0.022 0.012 0.003 0.0006
Non-monotonic behaviour of methane-steam reforming kinetics From the above discussion it can be concluded that, the too close an approach to the maximum rate point on the rate dependence curve at the enterance of the reformer tube, gives higher initial rate of reaction but at the same time gives faster approach to the positive order region where the rate of reaction drops sharply. This means that there is always an optimum steam feed partial pressure that gives maximum reactor performance (expressed in terms of methane conversion) and this optimization problem is a result of the non-monotonic dependence of the rate of reaction upon steam partial pressure. The non-monotonic functional dependence of kinetic rate expressions is well known in gas-solid catalytic reactions, and was reported in the literature for many other systems. Takahashi et al. (1986) reported the non-monotonic behaviour for the hydrogenation of benzene, Cordova and Gau (1983) reported the phenomenon for benzene oxidation to maleic anhydride, which was also reported by Yue and Olaofe (1984) for the catalytic dehydrogenation of alcohols over zeolites, and by Das and Biswas (1986) for the vaporphase condensation of aniline to diphenylamine. However, the non-monotonic dependence was not recognized for the steam reforming kinetics, although it manifests itself by the presence of both negative and positive order dependence of the rate of reaction upon steam concentration. The implications of the non-monotonic behaviour phenomenon was studied on a lumped parameter system, Bykov and Yablonskii (1981), Luss (1986), Elnashaie and Yates (1973), and found to give a multiplicity of the steady state. However, in this work more practical implication for the phenomenon on the fixed bed reactor is investigated. THE
NON-ISOTHERMAL
+ Ud,(
499
T, - VI
$ n, c,,.
(24)
i=l
Equation (24) is solved simultaneously with eqs (22) and (23) using the same technique used for the isothermal model. The heat transfer coefficient U is calculated by the relation, Xu and Froment (1989b): l/U =d,J2i,,
In (d,,/d,i)+
(25)
l/r,
where C(~is the convective heat transfer coefficient the packed bed and is obtained from the correlation Leva (1951): r,d,,/&=0.813
(d,G/p)“.9
exp (-6d,/d,).
in of (26)
The model was used to obtain the change of methane conversion at the exit from the reformer tube at different partial pressures of steam in feed to determin the optimum steam feed partial pressure as shown in Fig. 8. This optimum value was found at a steam partial pressure of 0.6 MPa (S/M=2.0): this shift in the point of maximum rate towards lower
PSEUDO-HOMOGENEOUS MODEL
A simple non-isothermal model that takes the temperature variation along the length of the reactor tube is used in this section. An energy balance on the reformer tube element, assuming constant tube skin temperature, gives the following differential equation:
Steam
feed
partial
pressure (MPa x10)
Fig. 8. Methane conversion at the exit of the reformer tube at different steam feed partial pressures (using the nonisothermal model), partial pressure of methane in feed = 0.3 MPa, feed temperature = 900 K, tube skin temperature = 1300 K, Fc,,, = 3.0 kmol/h (case of Table 5).
Table 5. Reacting mixture compositions and reaction rates at different points along the reactor tube for the ease of optimum steam feed partial pressure (non-isothermal model) (feed temperature =900 K, tube skin temperature = 1300 K, total pressure =0.905 MPa, S/M = 2.0) Curve
At tube length
No.
(ml
1 2 3 4 5 6 7 8
0.0 0.00 I 0.05 0.10 0.50 1.00 2.50 5.00
Reacting
&A, 0.3 0.297 0.276 0.268 0.234 0.211 0.166 0.113
(ZK, 0.6 0.594 0.557 0.541 0.484 0.443 0.363 0.282
PC0
(M Pa) 0.0 0.001 0.004 0.006 0.016 0.02 1 0.03 1 0.057
PC,,
(Mf’a)
0.0 0.003 0.011 0.013 0.024 0.033 0.049 0.056
(LFa) 0.005 0.012 0.058 0.076 0.147 0.197 0.296 0.397
R (kmol/iL’cat 2.78 0.747 0.088 0.06 1 0.0266 0.0194 0.0146 0.0123
h)
mixture temperature 900 900.2 901.2 902.3 911.3 922.7 956.9 1007.7
(K)
S. S. E. H.
500
, 0.70
30,
iz2ooa50 10
0
Steam
ELNASHAIE
feed
partial
30
20
pressure
(MPa
x 10 1
Fig. 9. Profile of rate of methane disappearance
dependence upon steam feed partial pressure and the corresponding exit methane conversion predicted by a one-dimensional heterogeneous modei, operating conditions are given as follows: tube length/O.D./I.D.= 11.95/0.102/0.0795 m; feed composition for point a (mole %) CH,= 12.98%. C,H,=2.14%,
C3H,=0.42%,C,H,, =0.05%, H,O =8X73%, N,=0.34%, H, =0.34%; total molar feed rate =4085.7 kmol/h; inlet conditions: feed temperature = 853 K, feed pressure = 2.44 MPa (number
of catalyst
tubes=
176).
values of steam partial pressure compared with the isothermal case is due to the increase of temperature along the reactor length. A compIete mapping of reaction rate dependence profiles along the reactor tube length for this optimum feed case, is shown in Table 5. HETEROGENEOUS MODEL
FOR INDUSTRIAL
STEAM
REFORMERS
In addition to the above results a relatively rigorous heterogeneous model which has been successfully checked against a large number of industrial steam reformers (Soliman et al., 1988; Elnashaie et al., 1989), has been used to check the existence of this maximum conversion point. The results of this simulation is shown in Fig. 9, and it is clear that this maximum conversion point does exist for industrial steam reformers. Detailed analysis of this phenomenon in industrial steam reformers is given elsewhere (Elnashaie et al., 1989). CONCLUSIONS
The steam reforming kinetics developed by Xu and Froment (1989a), is obviously a more general form than previous steam reforming kinetics and it explains a number of contradictions existing in the literature. The comparison with Bodrov (1964) kinetics and with De Deken et al. (1982) kinetics reveals clearly the limited nature of their kinetic rate equations. The kinetic rate equations of Xu and Froment predict well both positive and negative effective reaction orders
et al.
with respect to steam. The non-monotonic nature of this kinetics gives rise to an interesting optimization problem with respect to the feed partial pressure of steam. This optimization problem is demonstrated using a one-dimensional pseudo-homogeneous model with constant effectiveness factor for both isothermal and non-isothermal cases. It is also demonstrated using a detailed heterogeneous model which was verified successfully against a large number of industrial steam reformers. It is shown that the optimum feed partial pressure of steam that gives maximum output conversion is higher than that giving maximum rate of reaction at the entrance. The non-isothermal case gives optimum steam feed partial pressure which is lower than the isothermal case. It is also shown that this optimum feed partial pressure of steam does exist for industrial steam reformers. Work is underway in this department to verify the non-monotonic kinetics of this reaction experimentally and, for different types of steam reforming catalysts, the results of this detailed kinetic investigation will be published shortly. Acknowledgement-The authors would like to record their appreciation to Prof. Froment, for providing the authors with his more general kinetics for steam reforming prior to publication and for very stimulating discussions during exchange of visits between the two departments.
NOTATION
A cpi d d:;
4 Ei Fi G
(-A&i) (-AHi) Kl K2 k,, k
k, K CH.3 Kc,, K L ni
PT pi
K Hz It20
reformer tube cross-sectional area, m2 heat capacity of component i, J/kg K reformer tube outside diameter, , reformer tube inside diameter, m catalyst particle diameter, m activation energy for reaction i, kJ/mol molar feed rate of component i, kmoljh process gas mass velocity, kg/h m2 heat of reaction for reaction i, kJ/mol heat of chemisorption for component i, kJ/mol equilibrium constant for reaction I, MPa2 equilibrium constant for reaction II rate coefficients for reactions I and III respectively, kmol MPa/kg cat h rate coefficient for reaction II, kmol/kg cat h MPa adsorption constants for CH,, CO, H,, MPa-’ dissociation adsorption constant for H,O, MPa-’ reformer tube coordinate, m number of moles for component i in the reaction mixture, kmol/h total pressure, MPa component i partial pressure, MPa
Non-monotonic r1, r21 I3 R
CH4
R Hz0 T T, u
rates of reactions I, II and III respectively, kmol/kg cat h rate of CH, disappearance, kmol CH,/kg cat h H,O disappearance, kmol rate of H,O/kg
cat h
temperature of the reacting mixture, K tube skin temperature, K overall
heat transfer
Xl
conversion
x2
conversion
peared/CH,
ZICH.
fl&O
Pbr
W/m2 K CH, moles disap-
coefficient,
of methane,
moles in feed of
H,O moles in feed transfer coefficient,
steam,
disappeared/H,0 ai
behaviourof methane-steam reforming
moles
convective heat W/m’ K effectiveness factor of CH, diappearance rate effectiveness factor of H,O disappearance rate constant average effectiveness factor viscosity of the reacting gas mixture, kg/m h process gas and tube metal thermal conductivities, W/m K catalyst bulk density, kg cat/m’ REFERENCES
W. and Camp, D. P., 1955, Kinetics of Akres, W methane-steam reactions, A.1.Ch.E. J. 1, 471475. Al-Ubaid, A. S., 1986, Steam reforming of hydrocarbons catalyzed over nickel supported catalysts. Arabian J. Sci. Engng 12, 189. Al-Ubaid, A. S., 1984, Methane steam reforming activity, stability and characterization of nickel supported catalysts. Ph.D. Thesis, University of Notre Dame, Indiana, U.S.A. Atroshchenko, V. I., Raman, Sh. K. and Zryagintsev. G. I., 1969, Kinetics of conversion of natural gas by steam under pressure. J. Appl. Chem. USSR 42, 149&1503. Bodrov, N. M., Apel’baum, L. 0. and Temkin M. I., 1964, Kinetics of the reactions of methane with steam on the surface of nickel. Kinetica Karaliz 5, 696-705. Bodrov, N. M., Apcl’baum, L. 0. and Temkin, M. I., 1967, Kinetics of the reaction of methane with water vapour, catalyzed by nickel on a porous carrier. Kinetic0 Kotaliz 8, 821-828. Bodrov, N. M., Apel’baum, L. 0. and Temkin, M. I., 1967b, Kinetics of the reaction of methane with steam on the surface of nickel at 4CP36OO”C. Kinet. Catal. 9, 1065-1071. Bykov, V. I. and Yablonskii, C. S., 1981, Steady-state multiplicity in heterogeneous catalytic reactions. Int. Chem. Engng 21, 142-155. Cordova, V. R. and Gau, G., 1983, Redox kinetics of benzene oxidation to maleic anhydride. Can. J. Chem. Engng 61, 200-207. Das, G. and Biswas, A. K., 1986, Initial rate study on the
kinetics
501
vanor-chase condensation of aniline to diphenylamine. _ _ Cdn. J: Chem. Engng 64.473477. De Deken. J. C.. Devos. E. F. and Froment. G. F., 1982. Steam reforming of natural gas. Chem. Reaction Engng ACS Symp. Ser. 196. Elnashaie, S. and Yates, J., 1973, Multiplicity of the steady state in fluidised bed reactors-I. Steadv state consideration. Chem. Engng Sci. 28, 515-520. Elnashaie, S. S. E. H.. Al-Ubaid, A. S.. Soliman. M. A. and Adris, A. M., 1988, On the kinetics and reactor modelling for the steam reforming of methane-a review. J. ~nyny Sci. (King Saud University)14, No. 2, 247-273. Elnashaie,S. S. E. H., Aaris, A. M.. Soliman, M. A. and AlUbaid, A. S., 1989, Parametric investigation of industrial steam reformers (submitted for publication). Hyman, M. H., 1968, Simulate methane reformer reactions. Hyd. Car. Pro. 49, 13 1. Kopsel, R., Richter, A. and Meyer, B., 1980, Catalyst deactivation and kinetics of methane steam reforming. Chem. Tech. 32, 460. Leva, M., Winstrub, M., Grummer, M.. Pollchik, M. and Stroch, H. H., 1951, Fluid flow through packed and fluidized systems. U.S. Bur. Mines, Bull. 504. Luss, D., 1986, Steady-state multiplicity features of chemically reacting systems. Chem. Engng Educ. Award lecture, pp. 12-56. Munster, P. and Gabka, H. J., 1981, Kinetics of the steam reforming of methane with iron, nickel, and iron-nickel alloys as catalysts. J. Catal. 72, 279-287. Nikrich, E. M., 1970, Kinetics of partial oxidation of natural gas by a small amount of steam. J. Appl. Chem. USSR 43, 372. Paloumbis. S. and Petersen, E. E., 1982, Coke deposition on a commercial nickel oxide catalyst during the steam reforming of methane. Chem. React. Engng, Am. Chew Sot. 38,489495. Quach, P. T. and Rouleau, U. D., 1975, Kinetics of the methane-steam reaction over nickel catalyst in a continuous stirred tank reactor. J. Appl. Chem. Biotech. 25, 445-459. Ross, J. R. H. and Steel, M. C. F., 1972, Mechanism of the steam reformina of methane over a CODreCiDitated nickelalumina cataly;t. J. Chem. Sot. Faraday T&s. 1, 69. Soliman, M. A., Elnashaie, S. S. E. H., Al-Ubaid, A. S. and Ad&, A. M., 1988, Simulation of steam reformers for methane. Chem. Engng Sci. 43, 8. Takahashi, T., Yamashita, K., Kai, T. and Fujiyoshi, I., 1986, Hydrogenation of benzene, mono-, di-, and trimethylbenzenes over nickel catalysts supported on porous glass. Can. J. Chem. Engng 64, 1008-1013. Vance, C. K. and Bartholomew, C. H., 1983, Hydrogenation of carbon dioxide on group VIII metals--III. Effect of support on activity/selectivity and adsorption properties of nickel. Appl. Catal. 7, 169-177. Xu, I. and Froment, G. F., 1989a, Methane-steam reforming, methanation, and water-gas shift-I. Intrinsic kinetics. A.1.Ch.E. J. 35, 88-96. Xu, J. and Froment, G. F., 1989b, Methane-steam reforming-11. Diffusion limitation and reactor simulation. A.I.Ch.E. J. 35, 97-103. Yue, P. L. and Olaofe, 0.. 1984, Kinetic analysis of the catalytic dehydrogenation of alcohols over zeolites. Chem. Engng Res Des. 62, 81-91.