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Ind. Eng. Chem. Res. 1998, 37, 4222-4230
MTG Process in a Fluidized Bed with Catalyst Circulation: Operation and Simulation of an Experimental Unit Jose´ M. Ortega,* Ana G. Gayubo, Andre´ s T. Aguayo, Martı´n Olazar, and Javier Bilbao Departamento de Ingenierı´a Quı´mica, Universidad del Paı´s Vasco, Apartado 644, 48080 Bilbao, Spain
The simulation of the MTG process has been studied in a fluidized bed with circulation of the catalyst (prepared based on a HZSM-5 zeolite). The simulation has been carried out by taking into account the activity distribution of the catalyst particles in the bed and by using experimentally determined kinetic models for the reaction at zero time on stream and for the catalyst deactivation. The results of the simulation have been proven in an experimental laboratory unit by operating in the range between 380 and 420 °C, with different values of space time and of average residence time of the catalyst. Introduction The design of the reactor for the transformation of methanol into gasoline (MTG) is conditioned by the high exothermicity of the reaction and by the rapid deactivation of the catalyst (prepared based on a HZSM-5 zeolite). Although the reactor of the sole industrial unit in operation (in New Zealand) is of an adiabatic fixed bed and operates in cycles of reaction-regeneration, this operation strategy was adopted at a time when the knowledge about the technology of the fluidized bed with catalyst circulation was so limited that its industrial implementation was somewhat adventurous.1-3 Subsequent studies have revealed the great advantages of the fluidized bed, and so this technology has proven to be the most suitable for this process.3,4 The operating conditions and the results of the studies carried out by Mobil have been published in the literature.5-7 They correspond to fluidized-bed units with catalyst circulation, first to a 4 barrel/day unit and subsequently to a 100 barrel/day unit. These studies are mainly based on the knowledge of the intrinsic aspects of fluidization (particle design, baffle design, circulation of the solid between reactor and regenerator, etc.), and on the optimization of the heat transfer for obtaining an isothermal regime. In this paper an attempt is made to contribute to the development of the MTG process in a fluidized bed with catalyst circulation by using, in the simulation, the kinetic models recently determined for zero time on stream (fresh catalyst) and for catalyst deactivation.8 The simulation results have been proven by operating in a laboratory unit. The reactor simulation requires taking into account catalyst particles activity distribution. Weng and Chen explained theoretically how the population balance and residence time distribution function should be applied to calculate the catalyst activity distribution function in fluidized-bed reactors with catalyst circulation when the catalyst is subjected to deactivation.9 Residence time distribution of particles was taken into account in a noncatalytic gas-solid reaction by Heesink et al.10 The general basis in order to take the residence time distribution into account on the average conversion of * To whom correspondence should be addressed.
the particle is similar to that of catalytic reactions under deactivation, in which activity is the property of the solid changing with residence time. Azkoiti et al. calculated the activity distribution functions in a bubbling fluidized-bed reactor under several operating conditions, for the dimerization of acetaldehyde to chrotonaldehyde on a SiO2/Al2O3, both when catalyst activity at the inlet was uniform or distributed because it came from a regenerator that was operating under partial regeneration.11,12 Arandes et al. explain the design of a fluidized-bed regenerator for this reaction when the catalyst is fed with activity distribution.13 Bilbao et al. studied the activity distribution of a SiO2/ Al2O3 catalyst used in the polymerization of gaseous benzyl alcohol in a spouted bed where the regime was a perfect mix for the catalyst and by feeding it with uniform activity (fresh).14 Khang and Lee use the residence time distribution function to calculate the particle size distribution function and activity distribution of a Ziegler-Natta catalyst used in the polymerization of ethylene, either when there is perfect mix regime for the solid or when there are deviations from ideal flow.15 Bos et al. used the residence time distribution function of a (SAPO-34) catalyst in the MTO (methanol to olefins) process to calculate the coke content distribution function, either when a bubbling fluidized bed or a pneumatic conveying reactor was used.16 Schoenfelder et al. take into account the residence time distribution of a (ZSM-5) catalyst in the MTO process by adopting a four-stage model in the simulation of a pneumatic conveying reactor, under conditions in which catalyst deactivation is negligible.17 Experimental Section Catalyst. The catalyst has been prepared from a HZSM-5 zeolite, synthesized by following the methods proposed by Mobil.18 The zeolite has been subjected to an agglomeration process with bentonite (Exaloid), using fused alumina (Martinswerk) as the inert charge. The properties of the HZSM-5 zeolite and the catalyst are set out in Table 1. The Bronsted/Lewis ratio has been measured by FTIR spectrometry from the intensity of the adsorption bands at 1550 and 1455 cm-1. Prior
10.1021/ie9709291 CCC: $15.00 © 1998 American Chemical Society Published on Web 10/03/1998
Ind. Eng. Chem. Res., Vol. 37, No. 11, 1998 4223 Table 1. Properties of the HZSM-5 Zeolite and the Catalyst HZSM-5 zeolite Si/Al ratio Bronsted/Lewis ratio crystallinity crystal size, µm particle size, mm apparent density, g‚cm-3 BET surface area, m2‚g-1 pore volume, cm3‚g-1 micropore volume, cm3‚ g-1 (99% of diameter < 0.7 nm) pore volume distribution of the catalyst, vol % dp < 10-3 µm 8.1 10-3 to 10-2 µm 14.7 10-2 to 2 µm 77.2
catalysta
24 2.9 97% 6.3 0.94 420 0.65 0.17
0.3-0.5 1.21 124 0.43
zeolite acidity measurements
NH3
tert-butylamine
total acidity, (mmol of base)‚g-1 temperature peaks in the TPD
0.51 422 °C
0.46 304 °C
a Composition: zeolite, 25 wt %; bentonite, 30 wt %; alumina, 45 wt %.
to use, the catalyst is calcined at 570 °C for 2 h (in order for the experimental results to be reproducible under reaction-regeneration cycles).19 Reaction Equipment. The components of the reaction equipment are shown in Figure 1.20 The reactor, Figure 2, is cylindrical and of stainless steel 316, with a total length of 0.672 m. It is provided with a porous plate of 3-µm diameter holes for gas distribution, which is located 0.115 m above the reactor base. The reaction
Figure 1. Outline of the reaction equipment.
zone (0.363 m from the porous plate) has an internal diameter of 30 mm and an external diameter of 39 mm. The upper zone of the reactor has an internal diameter of 65 mm and an external diameter of 74 mm, which attenuates particle entrainment. The lid of the reactor is provided with holes for the catalyst inlet, gas outlet, refrigeration pipe, and thermocouples. The reactor is placed in a convection oven made of stainless steel and heated by a 2500-W electric resistance, which permits a temperature of 600 °C to be reached. Temperature is measured with three K type thermocouples located at three longitudinal positions: base of the reactor (1.0 cm), upper half (3.0 cm), and bed outlet (4.0 cm). The temperature at the base of the reactor is controlled by means of the electric resistance of the oven with a digital PID PM-2820. Given the considerable dimensions of the reactor and the chamber, thermal inertia of the unit requires a cooling device in order to rapidly adjust the temperature. This device is a sealed-end tube introduced in the catalyst bed (Figure 2) with pressurized air as the cooling fluid, which operates when the temperature is 1 °C above the set point. Methanol flow is regulated by means of a computercontrolled Iwaki metering pump, which allows for working in a range of flow rates between 0.20 and 4.00 g‚min-1. Subsequently, methanol is vaporized and preheated to 180 °C. The flow rates of inert gas (N2) and air (for regeneration) are controlled by Brooks 5850 mass flowmeters, which are controlled by the unit’s software. The maximum flow rate that both controllers can regulate is 15.0 cm3‚s-1. At the reactor outlet, the gas stream passes through a filter of 7-µm mesh, where
4224 Ind. Eng. Chem. Res., Vol. 37, No. 11, 1998
flame ionization, FID) and by following the methodology explained in previous papers.19,21-23 Product separation is carried out using an arrangement of three columns: (1) Semicapillary HP-1, of 0.53-m diameter and 5.0-m length. It splits the sample into two fractions: (a) volatile (C1-C4) and polar (methanol, water, and DME); (b) the remaining products. (2) Semicapillary SUPEL-Q Plot, of 0.53-m diameter and 30.0-m length, for complete separation of volatile and polar components, which will be analyzed using TCD and FID. (3) Capillary PONA of 0.20-mm diameter and 50.0-m length, for separation of the remaining products, which will be analyzed by FID. A detailed identification of the components analyzed by chromatography was performed by means of GCFTIR (Hewlett-Packard 5890 II-Nicolet 740) and by means of GC-MS (Hewlett-Packard 5890 II-Engine from Hewlett-Packard). The identification of the components (isoparaffins, olefins, aromatics, and naphthenes) was carried out using PIANO standard samples for chromatography from Air Liquide. The calibration of the areas corresponding to the chromatographic peaks was carried out using specific factors for each component.24 These factors were contrasted using commercial mixtures from Air Liquide and methanol-water mixtures at given proportions. Kinetic Modeling of the MTG Process
Figure 2. Reactor in detail.
solids are retained and so do not reach the 10-port sampling valve, which sends samples of gaseous product stream to the chromatograph for analysis. All the reaction product pipes are thermostated (180 °C) to avoid condensation of heavier products. The condenser consists of 0.5-m length concentric tubes and uses water as the cooling fluid, which circulates along the external annular zone. The condensed liquid is collected in a small vessel and discharged from here by means of a pneumatic valve. The monitoring of the liquid quantity is carried out using a charge cell. The gaseous phase that is not condensed at room temperature (light gases) passes through a volume meter before it is released to the atmosphere. System pressure is regulated with a Brooks 5866 pressure controller. The catalyst stored in a hopper is fed by means of a Retsch adjustable vibratory device. The control of the catalyst flow allows for establishing the average residence time of the catalyst in the reactor. The introduction of the catalyst into the reactor takes place through a lock for solids, whose function is to maintain the reactor sealed. Catalyst circulation is helped by a small stream of N2. The two valves placed at the catalyst outlet also have the function of keeping the reactor sealed. A N2 stream at high temperature eliminates the products adsorbed on the catalyst, which avoids solid caking and the resulting problems of outlet pipe blockage. Product Analysis. Product analysis is carried out by gas chromatography (Varian Star 3400 CX provided with detectors of thermal conductivity, TCD, and of
Kinetic Modeling for Zero Time on Stream (Fresh Catalyst). In previous papers, the suitability of different kinetic models proposed for the MTG process was studied.8,22 From the analysis of the results in a fluidized bed (which guarantees bed isothermicity), the suitability in the 320-420 °C range was determined for a kinetic scheme with the following single steps:8 k1
A 98 C k2
2C 98 D k3
A + C98 D k4
C + D 98 D This kinetic scheme takes into account, in the third step, the reaction of oxygenates, A, with light olefins (ethene and propene), C, rather than with the heaviest products, D, as is proposed in the model of Schipper and Krambeck.25 This one also fitted well to the results of an isothermal fixed bed in the 320-380 °C temperature range.26 The values of the kinetic parameters are 8
k1 ) 24.72 exp[-15720/R(1/T - 1/673)]
(1)
k2 ) 1.681 exp[-6050/R(1/T - 1/673)]
(2)
k3 ) 63.56 exp[-13500/R(1/T - 1/673)]
(3)
k4 ) 3.353 exp[-5000/R(1/T - 1/673)]
(4)
Deactivation Kinetic Model. In previous papers the suitability was proven for the following kinetic model corresponding to a deactivation which is nonselective and dependent on the concentrations of the three
Ind. Eng. Chem. Res., Vol. 37, No. 11, 1998 4225
lumps of the kinetic scheme that are in the reaction medium:8,22,23,27
-
da ) (kdAXA + kdCXC + kdDXD)a dt
(5)
In eq 5, catalyst activity, a, is defined as the relative disappearance reaction rate of the lump of oxygenates and of the formation of the lumps of products compared to their respective reaction rates for the fresh catalyst:
a)
(
(
dXA
) ( ) (
d(W/FM0) dXA
d(W/FM0)
t
t)0
)
dXC
) ( ) (
d(W/FM0) dXC
d(W/FM0)
t
t)0
)
dXD
)
d(W/FM0) dXD
d(W/FM0)
)
t
t)0
(6) The values determined in the 360-420 °C temperature range for the kinetic parameters of eq 5 are8
kdA ) 0.326 exp[-23700/R(1/T - 1/673)]
(7)
kdC ) 0.097 exp[-14570/R(1/T - 1/673)]
(8)
kdD ) 0.176 exp[-24130/R(1/T - 1/673)]
(9)
Results Hydrodynamics and Solid Flow Pattern in the Reactor. Several aspects of this study are detailed in a previous paper.28 The catalyst was diluted with alumina (Martinswerk), which was calcined at 1000 °C in order to ensure it being inert. Thus, several objectives are achieved: (1) improvement of fluidization quality and of solid circulation along the pipes; (2) bed isothermicity; (3) attainment of a constant bed height and, consequently, constant gas flow rate in the feed. Space time is changed by modifying the proportion of the catalyst in the feeding mixture catalyst-alumina, which corresponds to the border between groups A and B of Geldart. By segregation studies being carried out, a mixing degree near unity was determined for an alumina particle in the range between 0.09 and 0.12 mm. The catalyst particle size is between 0.3 and 0.5 mm. The segregation study consisted of measuring along the bed (taking out samples of successive layers of the stagnant bed by aspiration) the percentage of each component of the mixture catalyst-alumina. The range of particle sizes chosen allows for total separation of the catalyst from the alumina, simply by sizing. A hydrodynamic study was carried out using beds made up of alumina and of mixtures of the alumina and catalyst. For this purpose, a glass column of 3.0-cm internal diameter was used. The value of the minimum fluidization velocity experimentally determined was 1.05 cm‚s-1, which is almost independent of the bed composition (up to 20 wt % catalyst). The experimentally determined minimum velocity for complete fluidization was 3.2 cm‚s-1 for alumina, and it increases with the catalyst content up to a value of 4.5 cm‚s-1 for the mixture with 20 wt % catalyst. Residence time distribution of the solid in the reactor was studied by means of using the stimulus-response technique, at 350 °C, and using air as a fluidizing agent
Figure 3. Comparison of the experimental results of the C curve (response to the injection of a solid tracer stimulus) in the fluidizedbed reactor (points) and the C curve calculated assuming a perfect mix for the solid flow pattern (lines).
with a velocity of 5.0 cm‚s-1. The stimulus was the instantaneous injection of a quantity of the solid tracer (the catalyst), m0 ) 1.0 g, into the flow of the solid fed into the reactor (alumina), Qs. Starting from the injection time, solid samples which contain a catalyst mass, ∆m, are collected at the outlet. Point flow rates corresponding to these catalyst quantities are ∆m/∆t. The normalized response, ∆m/∆tm0, is calculated throughout time and this corresponds to the C or E curve:29
C(t) ) E(t) )
∆m ∆tm0
(10)
In Figure 3, the experimental results (points) of the E curve corresponding to two solid flow rates are plotted. Figure 3a corresponds to Qs ) 21.0 g‚h-1 and Figure 3b to Qs ) 76.2 g‚h-1. These flow rates correspond to extreme values within the range in which experimental runs were carried out. The lines of both plots in Figure 3 correspond to the C curve for a regime of a perfect solid mix,
C(t) ) E(t) )
t 1 exp t τ
( )
(11)
where τ is the average residence time of the solid in the reactor:
τ)
S W ) QS QC
(12)
4226 Ind. Eng. Chem. Res., Vol. 37, No. 11, 1998 Table 2. Operating Conditions T, °C: 380, 400, 420 W/FM0, (g of catalyst)‚h‚(g of methanol)-1: 0.022, 0.033, 0.040 τ, h: 0.308, 0.533, 0.705, 0.866
The adequate fitting of the experimental results in Figure 3 to the C curve corresponding to a perfect mix regime shows that the assumption of a perfect mix for the solid is valid for the whole range of solid flow rates used. This aspect was also proven by feeding intermediate solid flow rates between those of Figure 3a and Figure 3b and several mixtures of alumina + catalyst. In all the cases the regime was of a perfect mix for the solid. Operation in the Experimental Unit. Effect of Operating Conditions. Experiments in a fluidizedbed reactor with catalyst circulation have been carried out by feeding fresh catalyst; that is, all the particles fed to the reactor have the same activity, which is equal to unity. The operating conditions corresponding to the 36 runs are set out in Table 2. Space time was varied by controlling the catalyst weight fraction in the alumina + catalyst mixture in the feed. Average residence time of the catalyst in the reactor, eq 12, set by controlling the solid flow rate. Unfortunately, the catalyst used in the experimental unit undergoes attrition, which follows a first-order kinetics for weight loss with a kinetic constant value of 0.02752 h-1.20 In the experimental procedure, the attrition corresponding to the average residence time of the catalyst in the reactor has been taken into account and a higher catalyst flow has been fed to compensate for the catalyst lost by attrition. Although attrition will be smaller in industrial operation, by means of a suitable catalyst preparation to minimize the problem, it cannot be totally avoided and must consequently be taken into account in the design. The experiments have been carried out with the following sequence: once the conditions corresponding to a given value of space time and to an average residence time are set, heating of the reactor (containing alumina in order to avoid empty reactor heating) is started, which continues until the predetermined reaction temperature is reached. In this moment, heating of the mixture of the catalyst and alumina begins. By on-line analysis of the reaction products, the composition corresponding to the steady state (stable value of reaction product composition) is determined. With the aim of economizing in experimentation, once a steady state is reached, the reaction temperature is increased, while the remaining operating conditions are maintained fixed, up to a new steady state corresponding to the new reaction temperature; this procedure is followed for the subsequent steady states. As an example of the results, the evolution with time of the water-free base mass fraction of each lump is shown in Figures 4-6, until the successive steady states corresponding to three temperatures are reached when experiments were carried out using several values of space time and of average residence time. In Figures 4-6 it is observed that the mass fractions of the lumps of olefins and gasoline increase and the ones for oxygenates decrease up to the first steady state, whereas the evolution of the concentration of the lumps is opposed while the following steady states are reached. This different evolution is caused by the fact that the first steady state is reached with an increasing catalyst content in the bed, and so conversion of oxygenates
Figure 4. Evolution of the mass fraction of each lump, on a waterfree basis, until the steady state is reached, for three values of temperature. Space time, 0.040 (g of catalyst)‚h‚(g of methanol)-1; average residence time, 0.866 h.
Figure 5. Evolution of the mass fraction of each lump on a waterfree basis until the steady state is reached, for three values of temperature. Space time, 0.033 (g of catalyst)‚h‚(g of methanol)-1; average residence time, 0.308 h.
Figure 6. Evolution of the mass fraction of each lump on a water free basis until the steady state is reached, for three values of temperature. Space time, 0.022 (g of catalyst)‚h‚(g of methanol)-1; average residence time, 0.533 h.
increases until a steady catalyst mass is reached. However, the subsequent steady states are reached in a different way, as in the bed there is a catalyst that has been carrying out the reaction at lower temperatures and consequently subjected to lower deactivation. The increase in temperature for a constant value of space time and of average residence time implies more severe catalyst deactivation, which explains the conversion of oxygenates’ decrease until the corresponding steady state is reached.
Ind. Eng. Chem. Res., Vol. 37, No. 11, 1998 4227
Figure 7. Catalyst activity distribution function for several values of average residence time. Temperature, 400 °C; space time, 0.033 (g of catalyst)‚h‚(g of methanol)-1.
Figure 8. Catalyst activity distribution function for several values of space time. Temperature, 400 °C; average residence time, 0.866 h.
Activity Distribution Function. In the operation with catalyst circulation, the activity of each catalyst particle is determined by its residence time and, consequently, the residence time distribution (RTD) of the particles in the bed must be ascertained in order to calculate the activity distribution function. Thus, when a catalyst with uniform activity is fed, once the steady state is reached, a particle with a residence time between t and t + dt will have an activity between a and a + da, that is,
-f(a) da ) E(t) dt
(13)
where the negative sign indicates activity loss as residence time increases. The activity distribution function is
f(a) )
E(t) -da/dt
(14)
Equation 14 is solved by using eq 11 as the E(t) curve and eq 5 for the deactivation. To take into account the effect of the reaction medium composition on the deactivation, a mass conservation equation for each i lump in the reactor (assuming plug flow for the gas) must also be solved at the same time:
∂Xi (1 - ) RT m u ∂Xi ) F ri0 a ∂t PM mt Z ∂ξ
(15)
where the formation rate of each i lump at zero time on stream, ri0, corresponds to the kinetic model previously described for the MTG process. In previous papers the methodology for solving eq 15 was detailed.8,22 To solve the set of differential equations, a calculation program written in FORTRAN and the DGEAR subroutine from the IMSL library are used. Following this reactor design methodology, the catalyst past history at each reactor position is taken into account.30-35 As an example, in Figures 7-9 the distribution functions calculated for certain systems studied are shown. These results correspond to a state of low catalyst deactivation, and the values of average activity of the distributions are between 0.95 and 0.74. In Figures 7-9 it is observed that the profiles of this activity distribution flatten and they shift to the left (lower activity) as the residence time and temperature increase and as space time decreases, corresponding to more severe conditions of catalyst deactivation.
Figure 9. Catalyst activity distribution function for several values of temperature. Space time, 0.033 (g of catalyst)‚h‚(g of methanol)-1; average residence time, 0.533 h.
Simulation of the Experimental Unit and Verification. The conversion at the reactor outlet (expressed as a mass fraction of each i lump in the product stream) is the average value obtained as the contribution of catalyst particles with different activity to the reaction:
Xi )
∫01Xi(a) f(a) da
(16)
The values of the water free-base mass fraction of the lumps corresponding to each value of activity, Xi(a), have been calculated by simultaneously solving the equations of mass conservation, eq 15, and the equation of deactivation, eq 5. To show the validity of the simulation routine and of the kinetic models used, the experimental values (points) of the water-free base mass fractions of the lumps are compared in Figures 10-12 with the values calculated (lines) with the simulation routine. Each figure corresponds to one reaction temperature. Conclusions The validity of the kinetic models for the MTG process, both for zero time on stream and for deactivation, used in the simulation of the operation in a fluidized-bed reactor with catalyst circulation has been proven in an experimental unit. With the methodology followed in the reactor design, the activity distribution of the catalyst particles in the reactor has been rigorously calculated. For this calculation, the residence time distribution function (E(t) curve)
4228 Ind. Eng. Chem. Res., Vol. 37, No. 11, 1998
Figure 10. Experimental (points) and calculated values (lines) of the average mass fraction of each lump on a water-free basis for several values of the average residence time and space time. 380 °C.
Figure 11. Experimental (points) and calculated values (lines) of the average mass fraction of each lump on a water-free basis for several values of the average residence time and space time. 400 °C.
has been combined with the consideration of the past history of each catalyst particle from the time it enters the reactor (by solving the mass conservation equation of each lump in the reactor). It is noteworthy that the deactivation kinetic model is especially important in the simulation and that the model proposed, eq 5, takes the effect of the concentration of the lumps of the kinetic scheme into account. This consideration is important in the MTG process on HZSM-5 zeolites. The methodology and the kinetic models here proposed will be useful in future papers in order to determine the operating conditions (temperature, space time) and, particularly, the average residence time of the catalyst that maximizes the yield of gasoline and of light olefins, in a system of an interconnected reactorregenerator in a fluidized bed. For simulation of this system, which is the proper unit at industrial scale, knowledge of the reactivation kinetics is required for the design of the regeneration unit. Both the reaction step and the catalyst regeneration step (both highly exothermal) are the potential cause
of irreversible deactivation, which takes place by catalyst dealumination. The importance of irreversible deactivation in the MTG process carried out in an adiabatic fixed bed under reaction-regeneration cycles is attenuated when both steps are carried out in a fluidized bed, where temperature is uniform and temperature profiles are avoided. In this system the only potential cause of irreversible deactivation is the steam produced in the reaction and this problem may be minimized by following a suitable catalyst preparation. Nevertheless, in the optimization of the interconnected reactor-regenerator system, catalyst attrition must be taken into account by incorporating additional fresh catalyst. Attrition must be especially taken into account in catalyst preparation as it is of great importance in the global economy of the process. Acknowledgment This work was carried out with financial backing of the Ministry of Education and Culture of the Spanish Government (Project DGICYT PB93-0505).
Ind. Eng. Chem. Res., Vol. 37, No. 11, 1998 4229 ri0 ) reaction rate of lump i formation for the fresh catalyst, (g of lump i)‚(g of total mass)‚h-1‚(g of catalyst)-1‚(g of water-free products)-1 S ) solid mass, g T ) temperature, K t ) time on stream, h u ) gas linear velocity, m‚h-1 W ) catalyst mass, g Xi ) weight fraction of lump i on a water-free basis Xi ) weight fraction of lump i at the reactor outlet on a water-free basis, eq 16 Z ) total length of the reactor, m z ) longitudinal coordinate of the reactor, m Greek Letters ∆m ) catalyst mass collected for a time ∆t, g ) bulk porosity F ) catalyst density, g‚L-1 ξ ) dimensionless longitudinal coordinate of the reactor (z/Z) τ ) average residence time of the solid in the reactor, h
Literature Cited
Figure 12. Experimental (points) and calculated values (lines) of the average mass fraction of each lump on a water free basis for several values of the average residence time and space time. 420 °C.
Nomenclature A, C, D ) lump of oxygenates (methanol and dimethyl ether), of light olefins (ethene and propene), and of the remaining products, respectively a ) remaining catalyst activity due to coke deposition, referred to the reaction rate, eq 6 C(t), E(t) ) response of a tracer instantaneous stimulus and distribution function of residence time in the reactor dp ) pore diameter, µm FM0 ) mass flow of methanol in the feed, (g of methanol)‚h-1 kdi ) kinetic constant for deactivation by coke formation for lump i, h-1 k1, k2, k3, k4 ) kinetic constants for the different individual steps of the kinetic scheme, h-1 M ) average molecular weight of the water-free products, g‚mol-1 m, mt ) mass flow of water-free products and total mass flow, g‚h-1 m0 ) amount of solid tracer (catalyst), g P ) partial pressure of water-free products, atm R ) constant of the gases, cal mol-1 K-1 (atm m3 mol-1 K-1 in eq 15)
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Received for review December 18, 1997 Revised manuscript received July 20, 1998 Accepted July 21, 1998 IE9709291
