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Fischer-Tropsch synthesis gas conversion reactor
Chemical En&eming Science, Printed in Great Britain.
Vol. 47, No.
5, pp. 959-966.
FISCHER-TROPSCH
1992.
om9-2509/92 ss.00 + 0.00 0 1992 PWgamon PI-S4plc
SYNTHESIS REACTOR ROBERT
Amoco
Chemical Company,
GAS
CONVERSION
F. BLANKS
P.O. Box 3011, Napcrville, IL 60561, USA.
(First received 3 Jury 1990; accepted in revised form 1 October
1991)
Abstract-This
paper describes the design and mathematical modeling of a catalytic reactor for the Fischer-Tropsch conversion of synthesis gas to parat%nic hydrocarbons. The interesting feature of the reactor is a series of cooling coils located within a fixed-bed of catalyst. The coils are oriented perpendicular to the direction of gas flow through the reactor. Coolant flows through the coils to remove the heat of reaction. An experimental pilot-plant reactor was built and operated to test this design. In addition, a steady-state, two-dimensional, psedo-homogeneous reactor model was developed to study the effect of cooling-coil design on reactor performance. Higher overall heat transfer coefficients were obtained with this design, compared to a typical tubular reactor design. Thus, less cooling surface area per unit volume is required. The coil reactor design was estimated to be significantly less expensive to build than a conventional tubular fixed-bed reactor.
INTRODUCTION
Currently, many of the leading oil and gas producers are trying to develop economical processes to convert remote natural gas supplies to easily transportable liquids. Most of the research has been directed toward the synthesis of liquid fuels, such as syncrude, gasoline, middle distillates or alcohols. The Fischer-Tropsch synthesis of paraffinic hydrocarbons from natural-gas-derived synthesis gas (syngas) is one possible route. Syngas, carbon monoxide and hydrogen, can be produced from natural gas via steam reforming or partial oxidation with air. When the hydrogen to carbon monoxide ratio is approximately 2: 1, the syngas is ideally suited for conversion to paraffins via Fischer-Tropsch synthesis using a cobalt-based catalyst. The highly exothermic nature of the Fischer-Tropsch reaction requires a reactor design which can adequately control the reaction temperature within a narrow operating window. However, the capital cost of such a reactor must be kept to a minimum because the sales price of the paraffinic liquids must be competitive with crude-oil prices. Since the goal of this work was to develop a low capital-cost process for converting natural gas to transportable liquid fuels, several constraints were introduced from the beginning of the project. First, the syngas was to be generated via partial oxidation of natural gas with air. Therefore, the feed to the Fischer-Tropsch reactor contains approximately 5 1% (mole basis) syngas (with a Hz/CO ratio of about 2), and 46% nitrogen, with the balance being carbon dioxide and water. Second, the process was designed to operate at low pressure, about 0.2 MPa, in order to minimize the cost of air compression when generating the synthesis gas. Third, the target for the Fischer-Tropsch synthesis was set at 56% yield, based upon an 80% conversion of syngas with a 70% selectivity to C, + hydrocarbons, at a weight hourly
space velocity of 0.55 kg syngas/kg catalyst. These targets were met with a small, isothermal laboratory reactor. When the Fischer-Tropsch reaction is conducted using a cobalt-based catalyst, the reaction product consists of a broad spectrum of linear, saturated hydrocarbon molecules containing from 1 to over 40 carbon atoms. The distribution of hydrocarbon molecules is described by the Schulz-Flory-Anderson product distribution function (Anderson, 1984). When the HJCO ratio is nearly 2 : 1, the net reaction can be simplified as follows: 5C0
+ 11H, + &HI,
+ 5H,O
(1)
Reaction (1) assumes the distribution of products can be approximated by a single compound having the same carbon-to-hydrogen mole ratio as the mean of the product distribution (pentane, in this case): Given the feed composition described above, the adiabatic temperature rise for converting 80% of the syngas via reaction (1) is in excess of 800 K. However, to simultaneously meet the activity and selectivity targets, the reaction temperature must be controlled within a relatively narrow window of 463488 K. The lower temperature is required to maintain activity while, at temperatures above 488 K, the selectivity falls be-low target due to excess methane production. There are several conventional approaches to designing commercial reactors to operate in a nearly isothermal fashion while controlling highly exothermic reactions. The most widely used approach is to contain the catalyst in long narrow tubes, while pumping a heat transfer medium across the outer surfaces of the tubes. A second approach is to recycle a portion of the reactor effluent stream, which is combined with fresh feed and acts as an inert heat sink. A third approach is to use a series of adiabatic beds in series. Temperature is controlled between the
960
ROBERT F. BLANKS
beds with various techniques, such as conventional heat exchange to heat transfer surfaces, or “cold shooting” (addition of cold feed or other gas to the reaction mixture) (Froment and Bischoff, 1979). Unfortunately, none of these approaches was found to be both technically appropriate and economically attractive for this application. Although a multitubular reactor design was investigated in detail, the capital cost was found to be prohibitively expensive. Experiments and mathematical modeling revealed that 0.025 m tubes were the largest-diameter tubes which had good temperature stability at design consitions. Larger-diameter tubes were found to be unstable, resulting in runaway reactions with excessively high temperatures. The large amount of heat transfer surface required in this design resulted in a very expensive reactor.
Our search for a low capital-cost process led us to investigate a reactor design which featured cooling coils embedded within a fixed bed of catalyst. Coolant is pumped through the coils, which are oriented perpendicular to the direction of gas flow. The coils act as internal heat transfer surfaces, removing the heat of reaction while maintaining the desired operating temperatures. This design was tested both experimentally, via a pilot-plant reactor, and mathematically, using a steady-state, two-dimensional, pseudo-homogeneous reactor model. DESIGN
OF THE
EXPERIMENTAL
COIL
REACTOR
Figure 1 shows a schematic diagram of the pilotplant coil reactor. A photograph of one of the coils is also shown. The major objective of the design was to approximate a number of adiabatic beds in series by
Fig. 1. Syngas converter.
Fischer-Tropsch synthesis gas conversion reactor
961
p l a c i n g c o o l i n g coils p e r p e n d i c u l a r to the direction of the o u t e r r e a c t o r wall by a b o u t five t u b e s . In a gas flow, inside the c a t a l y s t bed. In principle, it was c o m m e r c i a l r e a c t o r of 15 ft d i a m e t e r , m a n y t u b e s d e s i r e d t h a t each zone of c a t a l y s t b e t w e e n two coils s e p a r a t e the gas and c a t a l y s t from t h e r e a c t o r w a l l . o p e r a t e s as an a d i a b a t i c bed, and each coil zone acts F o r this r e a s o n , the o u t e r r e a c t o r wall is not conas a heat e x c h a n g e z o n e , l o w e r i n g the t e m p e r a t u r e of s i d e r e d as a b o u n d a r y in o u r m o d e l i n g effort. R a t h e r , the r e a c t i o n m i x t u r e . we f o c u s on a r e g i o n c o n t a i n i n g c a t a l y s t , flowing gas, T h e r e a c t o r is not an a d i a b a t i c r e a c t o r b e c a u s e of and c o o l i n g coils, as t h o u g h this r e g i o n were e m b e d the p r e s e n c e of the heat t r a n s f e r coils c o n t a i n i n g ded in a b o u n d l e s s volume. c o o l a n t . T h e o u t e r shell of the r e a c t o r was wellIn o r d e r to o b t a i n a b e t t e r u n d e r s t a n d i n g of the insulated, but no a t t e m p t was m a d e to c r e a t e an p e r f o r m a n c e of the c o o l i n g coils w i t h i n the r e a c t o r , a a d i a b a t i c s i m u l a t i o n by c o m p e n s a t i n g heat i n p u t at m a t h e m a t i c a l m o d e l was d e v e l o p e d . T h e p u r p o s e of the o u t e r b o u n d a r y . Significant cross-flow t e m p e r this m o d e l was to d e t e r m i n e the effect of p r o c e s s a n d a t u r e g r a d i e n t s e x i s t in the c a t a l y s t b e d b e t w e e n design v a r i a b l e s , (gas flow r a t e , gas c o m p o s i t i o n , c o o l c o o l i n g coils. H o w e v e r , the c r o s s - f l o w t e m p e r a t u r e ant and i n l e t gas t e m p e r a t u r c , coil d i a m e t e r and coil g r a d i e n t s are negligible in the regions of c a t a l y s t b e d s p a c i n g ) upon the t e m p e r a t u r e a n d c o n c e n t r a t i o n not c o n t a i n i n g c o o l i n g coils, t h a t is, b e t w e e n axially profiles in the r e a c t o r . With this o p t i m i z a t i o n and p o s i t i o n e d coils, as long as the r e a c t o r is u n d e r cons c a l e - u p c o u l d be a c c o m p l i s h e d . T h e final m o d e l control and not experiencing a r u n a w a y . This will be t a i n s several p a r a m e t e r s w h i c h are not f u n d a m e n t a l d i s c u s s e d f u r t h e r in the p a p e r . p a r a m e t e r s of the s y s t e m , but are l u m p e d p a r a m e t e r s T h e p i l o t - p l a n t r e a c t o r was c o n s t r u c t e d of 0.46 m a c c o u n t i n g for s e v e r a l p h e n o m e n a , heat t r a n s f e r by (18 in.) S c h e d u l e 40 c a r b o n steel p i p e , 0 . 4 2 9 m I D c o n d u c t i o n and convection, for e x a m p l e . T h e a c t u a l (16.9 in.), 4.57 m (15 ft) l o n g , a n d c o n t a i n e d 60 c o o l i n g g e o m e t r y of the r e a c t o r c o n t a i n i n g the coils c o u l d be coils. E a c h coil was c o n s t r u c t e d of 3.35 m m (11 ft) of m o d e l e d in r a d i a l c o o r d i n a t e s u s i n g a finite-element 0.013 m m (0.5 in.) O D stainless-steel t u b i n g . This resa p p r o a c h . H o w e v e r , we c h o s e i n s t e a d to d e v e l o p a u l t e d in 0 . 1 3 4 m 2 of heat t r a n s f e r s u r f a c e per coil. m o r e simple, a p p r o x i m a t e m o d e l . This m o d e l does W i t h i n a co il, the c e n t e r - t o - c e n t e r tube s p a c i n g was not r e p r e s e n t the a c t u a l g e o m e t r y of the s y s t e m . 0.038 m (1.5 in.), w h i l e the v e r t i c a l s p a c i n g b e t w e e n R a t h e r it is a different g e o m e t r y , but one w h i c h we coils was 0 . 0 7 6 m) (3 in.). T h e c o o l i n g coils were inbelieve a d e q u a t e l y r e p r e s e n t s the b e h a v i o r of the real s t a l l e d so that each coil was offset 90 ° from the coils s y s t e m as far as o u r n e e d s are c o n c e r n e d . T h e m o d e l a b o v e and b e l o w it. This c a u s e d the c e n t e r of the t u b e s s i m u l a t e d a s m a l l r e g i o n of the r e a c t o r l o c a l i z e d in one c o o l i n g coil to be l o c a t e d d i r e c t l y u n d e r the gap a r o u n d two successive c o o l i n g coils, each f o l l o w e d by b e t w e e n t u b e s in the coil just u p s t r e a m in the r e a c t o r . an a d i a b a t i c r e a c t i o n z o n e . This v o l u m e e l e m e n t is This o r i e n t a t i o n i n c r e a s e d the likelihood that the gas e m b e d d e d in a r e a c t o r of b o u n d l e s s volume. With this w o u l d e n c o u n t e r a c o o l i n g s u r f a c e as it f l o w e d down m o d e l , we are not c o n c e r n e d with effects at the o u t e r t h r o u g h the r e a c t o r . T h e t o t a l w o r k i n g v o l u m e of the w a l l s of the r e a c t o r . F u r t h e r simplification was t h a t r e a c t o r , excluding the c o o l i n g coils, was 0.639 m 3 the cylindrical coils, b e i n g of a d i a m e t e r s i m i l a r to a (22.6 ft3). T h e v o l u m e of the r e a c t o r o c c u p i e d by the c a t a l y s t pellet, c o u l d be a p p r o x i m a t e d as fiat p l a t e s . 60 c o o l i n g coils is 0.02 m a (0.73 ft3). T h u s , the p r o b l e m c o u l d be s o l v e d in r e c t a n g u l a r At an overall s y n g a s c o n v e r s i o n of 80%, the a v e r c o o r d i n a t e s . Also, since the m o d e l s i m u l a t e d such a age c o n v e r s i o n per r e a c t i o n zone b e t w e e n coils is s m a l l v o l u m e element, the c u r v a t u r e of the c o o l i n g 1 . 3 % . T h e a d i a b a t i c t e m p e r a t u r e rise is the o r d e r of 10 coils was neglected. In o r d e r to simplify the m o d e l , the to 15 K for each r e a c t i o n z o n e . T h e t o t a l heat g e n e r cooling-coils heat t r a n s f e r surfaces were r e p r e s e n t e d ated in the r e a c t o r is 34.4 k W , or 574 W p e r coil. E a c h as fiat p l a t e s o r i e n t e d p a r a l l e l to the direction of gas coil c o n t a i n s h o t oil flowing at 0.25 m a / h r at an flow. Then the m a t h e m a t i c a l p r o b l e m is one of a gas a v e r a g e t e m p e r a t u r e of 412 to 470 K. T h e oil-side flowing in a b o u n d l e s s v o l u m e b e t w e e n a l t e r n a t i n g t e m p e r a t u r e rise v a r i e s b e t w e e n 1 and 10 K. regions c o n t a i n i n g c o o l e d flat w a l l s and w i t h o u t In an a t t e m p t to s p r e a d the r e a c t i o n e v e n l y over the walls. T h e w a l l s were offset in a l t e r n a t e p l a n e s so t h a t l e n g t h of the c a t a l y s t bed, the c a t a l y s t c o n c e n t r a t i o n gas in the c e n t e r of the s p a c e b e t w e e n w a l l s c o n t a c t e d was g r a d e d from r e a c t o r i n l e t to o u t l e t . T h e m o s t the wall in the next p l a n e a f t e r the a d i a b a t i c section. A d i l u t e c a t a l y s t c o n c e n t r a t i o n was at the inlet, 4 7 % d i a g r a m of this r e g i o n is s h o w n in Fig. 2. Z o n e s 1 and c a t a l y s t plus 5 3 % i n e r t pellets, physically m i x e d to3 are the s e c t i o n s c o n t a i n i n g the c o o l i n g coils. Z o n e s 2 g e t h e r . N e a r the o u t l e t of the r e a c t o r , the bed was and 4 are the a d i a b a t i c r e a c t i o n r e g i o n s . Since only l o a d e d with c a t a l y s t p e l l e t s alone. T h e c a t a l y s t p e l l e t s a b o u t 2 % c o n v e r s i o n o c c u r r e d w i t h i n this four-zone were 0.5 x 1.3 cm cylinders, c o r r e s p o n d i n g to an e q u i m o d e l , the p h y s i c a l p r o p e r t i e s and c o m p o s i t i o n of the v a l e n t s p h e r i c a l d i a m e t e r of 0.9 cm (0.36 in.). T h u s , the gas s t r e a m were a s s u m e d to be constant. This m o d e l c a t a l y s t p e l l e t s are the s a m e o r d e r of m a g n i t u d e in size c o u l d be focused, in s n a p - s h o t f a s h i o n , on any p a r as the d i a m e t e r of the c o o l i n g coils. t i c u l a r r e g i o n of the r e a c t o r : near the e n t r a n c e , in the middle, or near the exit. MATHEMATICAL REACTOR MODELING T h e m a t h e m a t i c a l m o d e l was w r i t t e n as a steady= In the p i l o t - p l a n t r e a c t o r (refer to Fig. 1), gas and state, two-dimensional pseudo-homogeneous reactor c a t a l y s t in the c e n t e r of the r e a c t o r are s e p a r a t e d from m o d e l . Only an e n e r g y b a l a n c e was n e c e s s a r y , since
ROBERT F. BLANKS
962
Gas flow where k,-, = 5.6 x lo6 kmol CO reacted/kg catalyst
f
Zone #l
E, 2 90.004 kJ/mol
f
R = 8.3 14 J/mol K
T Zone #2
Cooling tube
b = 1.596 x lo- l3 Pae3.
-Y t Zone #3
T 1
h -T Zone #4
Lt
1
Fig. 2. Cross-flow
reactor.
the gas properties and composition did not change significantly over the four-zone, two-coil case being analyzed. The energy balance equation was written as
u=pf&,
dT dx
d2T
-
ke-dy2
- pr( -
AiYr)rA = 0. (2)
The first term in eq. (2) describes the energy convected in and out of a reactor volume by bulk gas flow in the x-direction, axially. The second term describes the dispersion of thermal energy in the y-direction, perpendicular to the direction of bulk gas flow. The third term describes the energy generated by the chemical reaction. An axial dispersion temperature term was originally included in the model. However, a number of simulations showed this to have a negligible effect on the results, so it was removed. Adiabatic boundary conditions were used at the planes of symmetry between cooling surfaces or at the edges of adiabatic reaction zones: dT
-=0
dy
sty=
a plane of symmetry.
(3)
A boundary condition describing removal of heat by transfer to a cooled wall surface is used at the coil-bed boundaries:
!g = 2(T -
T,).
0
The kinetic reaction rate model which best-fit experimental data for the Fischer-Tropsch reaction, using a cobalt-based catalyst, was obtained from Starch et al. c1951t
This rate equation fit laboratory isothermal reactor data for a temperature range 453483 K and a pressure range O-1-0.27 MPa. The reactor model was solved on a VAX computer using the DSS/2 differential equation package (Schiesser). A five-point, finite-difference scheme was selected. Second derivatives were represented by centered differences and first derivatives by a biased upwind formula. This finite-difference technique integrated the time-dependent version of eq. (2) until a steadystate solution was obtained. Solutions consisted of two-dimensional temperature profiles for two adiabatic reaction zones, each followed by a cooling coil. The model calculates cross-flow temperature profiles at a particular axial location in the reactor. Then these are volume averaged to obtain an “average” axial temperature. This is done for successive axial locations in the reactor for zones where there are coils and zones where there are no coils. Many of the reactor parameters and process conditions are fixed by experiment and some of these vary with axial position (distance down the bed in the flow direction). Fixed are: the effective cooling surface length in the flow direction, the spacing between coils, the length of an adiabatic section, and the catalyst-pellet-equivalent spherical diameter. The gas temperature and COTposition are known, both at the inlet of the reactor and as a function of reactor length based on an overall, linear, one-dimensional simulation, using the actual axial temperature profile and reaction kinetics. (The actual profile is nearly isothermal by design.) This allows calculation of gas properties; density, thermal conductivity, heat capacity and viscosity. Also superficial gas velocity may calculated_ All of these quantities are dependent on conversion and axial position. With this information, the Reynolds and Prandtl numbers are calculated and finally the bed-to-wall heat transfer coefficient from curve 1, Figure 11.7a-3 of Froment and Bischoff (1979). Also the effective bed thermal conductivity is calculated from the procedure of Dixon (et seq.). This calculation includes individual estimates of four components of the effective-bed thermal conductivity: the fluid thermal conductivity, the effective conductivity due to fluid turbulence, the solid-pellet-effective conductivity, and a dynamic component of the pellet conductivity. These all vary with axial position since the axial gas velocity varies due to changing moles of gas caused by reaction (1) and due to the effect of gas Dronerties on the Revnolds and Prandtl numbers.
Fischer-Tropsch COMPARING
THE MODEL
TO PILOT-PLANT
synthesis gas conversion reactor
DATA
The mathematical model of the coil reactor was compared with experimental data obtained in the pilot plant. The model was first focused on a section near the inlet of the reactor. All of the parameters in eqs (2)-(5) were known except for the effective radial thermal conductivity of the bed, k, and the bed-towall heat transfer coefficient, h,. The value of h, was obtained from a Prandtl number and Reynolds number plot of Coberly and Marshall (1951). The value of k, was determined from a procedure developed by Dixon (1978). These were later reevaluated using more recent information (Dixon, 1987). Next, the model was focused on a section near the exit of the reactor. Once again, all of the parameters in the model, excluding the two heat transfer variables, were directly measured or calculated from pilot-plant data. The values of the two heat transfer parameters used for the top section of the reactor, k, and h, were modified, because the Reynolds and Prandtl numbers for the exit of the reactor were substantially different from those for the reactor inlet. Without any further adjustment, the model generated a temperature profile which agreed with the measured data at both inlet and outlet. We felt that this validated the model’s predictions as well as the values used for the heat transfer parameters. The predicted axial and radial temperature profiles for these two cases are shown in Figs 3-6. The predictions are quite sensitive to the values chosen for k, and h,. The model was also used to predict the effect of
219 218 ”
217
-
8
216
-
g
215
-
ii
214
-
s
213
-
5
212-
6
211
-
210
-
_________o_____
Horizontalspacing Fig. 4. Top of pilot-plant cross-Bow temperature profile. at first coil, (0) outlet temperature from first coil, (0) initial temperature at second coil, (0) outlet temperature from second coil, (a) initial temperature at third coil. ( x ) Initial temperature
215 0
(u
g
214
:[
213
t
R
8
B Ea 212
219
Ii 0 ii 211 ,Q ii g 210 g & 20s
217
e L g
216
208
g 207 206 Axial position 214
Gas Row c
Fig. 5. Axial temperature profile for pilot-plant bottom of reactor.
213
I
I
I
4
I
Axial position Gas flow
m
Fig. 3. Axial temperature profile for pilot-plant top of reactor.
increasing the concentration of carbon monoxide in the reactor feed from 36% to 40%. The model predicted that such an increase would result in a runaway reaction. This prediction was confirmed experimentally. We have concluded that the mathematical model, represented by eqs (2)-(5), is an effective simulation of
ROBERT F. BLANKS
964
63 ,
if
Single
Coil/Pilot
Plant
209
0’
3
E f! f P
207 205
A
79
126
200
316
501
Reynolds number
199
Fig. 7. Overall heat transfer coefficients. (0) l/2 in. coils-stream, (El) I/2 in. coils-water, (0) literatureh, for tubes, (D) l/4 in. coils-water, (EY)pilot plant. Horizontal spacing
Fig. 6. Bottom of pilot-plantcross-flow temperatureprofile. ( x ) Initial temperatureat first coil, (0) outlet temperature from first coil, (0) initial temperatureat second coil, (0) outlet temperature from second coil, (A) initial temperature at third coil.
reality. This is based upon comparisons of predicted axial temperature profiles with experimental data from the pilot plant for sections near both the top and the bottom of the reactor, when the pilot plant was operating satisfactorily at steady state. Further substantiation is the match of a predicted runaway reaction, an uncontrollable axial temperature profile, with an actual runway in the pilot-plant experimental reactor. Here the terms axial temperature profile refer either to the volume-averaged cross-flow temperature calculated at each axial position from the model, or the experimental average of several thermocouples placed in various positions in the pilot plant at one axial location. In this operation, with the pilot plant under control at steady state, the adiabatic section always evens out the cross-flow, horizontal, variations in temperature. It will be seen in a later section, however, that this is not the case for an improperly designed reactor, as when the process demands an excessive conversion per unit length. HEAT
TRANSFER
COEFFICIENTS COIL
FOR TUBULAR
AND
GEOMETRCRS
The packed-bed heat transfer parameters, h, and k,, have been studied in tubular geometry by a number of investigators (Froment and Bischoff, 1979; Coberly and Marshall, 1951; Dixon, et seq.). In tubutar reactors, these parameters may be combined to give an overall heat transfer parameter: 1
1
R
U
h,
4k,
-=-+---. A comparison
_.
(6)
was made between the overall heat
transfer coefficients obtained from this study, using the coil reactor design in both reacting and nonreacting systems, and those predicted for tubular geometries (Froment and Bischoff, 1979; Coberly and Marshall, 1951; Dixon, et seq.) (Fig. 7). Shown in Fig. 7 are the measured overall coefficients, U, from this work and literature values for h, versus Reynolds Number. As eq. (6) illustrates the only way U and h, could be equivalent is the case when k, approaches infinity. Since this is not the case here we conclude that the values of U for our geometry are larger than values of U for tubular systems. (Heat fluxes during the experiments which generated the data of Fig. 7 are comparable. In the reacting system, the heat flux was 4.3 kW/m’. In the nonreacting experiments the heat flux ranged from 1.6 to 15 kW/m2. Typical tubular reaction heat Aux is 2-5 kW/m2.) We believe the overall heat transfer coefficient, U, for the coil reactor geometry is higher than that of a tubular reactor geometry, given the same Reynolds and Prandtl numbers. The exact reasons for this are not quantitatively understood. The higher values may be caused by enhanced convective heat transfer due to increased gas mixing which, in turn, is caused by the presence of the cooling coils. Heat transfer may be increased because of decreased boundary-layer thickness on the upstream side of the cooling surfaces. Also, the staggered nature of the cooling coils causes the disruption of peaks in the radial temperature profiles, preventing them from propagating axially downstream. Each of these factors may account for the enhanced heat transfer observed in the coil reactor design, compared to a conventional tubular design. COMMERCIAL
REACTOR
DESIGNS
The mathematical model of the coil reactor was used to predict the performance of several different
96.5
Fischer-Tropsch synthesis gas conversion reactor commercial coil reactor designs. The results for both a controllable and an uncontrollable designs are shown in Figs 8-11. This design was based upon a 4.57 m diameter reactor. Either 0.025 or 0.051 m diameter cooling coils were found to be sufficient to control the reactor temperature. However, the axial and radial spacing between coils was found to be the difference
210
c! 209
B :e ;
208
Axialposition Gas flow
*
Fig. 10. Axial temperature profile For commercial reactor.
240
,
,
,
I
I
Axial position 230 Gas flow w
Fig. 8. Axial temperature profile for commercial reactor.
210
220
210
200
q90
160 Horizontal spacing
Fig. 11. Cross-flow temperature profile for commercial reactor. ( x ) Initial temperature at first coil, (0) outlet temperature from first coil, (0) initial temperature at second coil, (1) outlet temperature from second coil, (A) initial temperature at third coil.
Horizontal spacing
Fig. 9. Cross-flow temperature profile for commercial re-
actor. ( x ) Initial temperature at first coil, (0) outlet temperature from first coil, (0) initial temperature at second coil, (0) outlet temperature from second coil, (A) initial temperature at third coil.
between the controllable and the uncontrollable designs. Although a commercial-scale version of the coil reactor design was never constructed, pilot-plant data and economic analyses suggest it is a cheaper alternative to conventional multitubular reactor designs. An analysis was done for a world-scale plant, processing 2.5 million standard cubic meters per day of
ROBERT F. BLANKS
966
natural gas. The result was that the ratio of the capital cost of a bank of conventional tubular reactors, capable of controlling the FT reaction at design conditions, to the capital cost of a bank of coil reactors was four. CONCLUSIONS
NOTATION
AH, h,
sK
effective J/msK
bed
radial
TW u uX X Y Greek Pb Pf
reaction parameter defined in eq. (5), kmol/kg h partial pressure, Pa reaction rate defined in eq (S), kmol/kg h characteristic length, m; or gas constant, 8.314 J/mol K temperature, K wall temperature, K overall heat transfer coefficient, J/m’ s K gas velocity in axial direction, m/s axial dimension, m radial dimension, m letters catalyst bulk density, kg/m’ fluid density, kg/m’ REFERENCES
Anderson, R. B., 1984, 7’he Fischer-Tropsch Synthesis, Academic Press, Orlando, FL. Coberly, C. A. and Marshall, W. P., 1951, Chem. Engng Prog. 47, 141. Dixon, A. G., 1978. Ifeat Transfm in Packed Beds, p. 238. Chemical Reaction Engineering, Houston. Dixon, A. G., 1986. Effective heat transfer parameters f&r transient packed bed models. A.I.Ch.E. J. 32, 1978, 809; Heat Trctnsjer in Packed Beds, p. 238. Chemical Reaction Engineering, Houston; 1979, Theoretical prediction of effective heat transfer parameters in packed beds. A.I.Ch.E. J. 25, 663; 1985, Thermal resistance models of packed bed effective heat transfer parameters. A.I.Ch.E. J., 31, 826; 1985, Wall to fluid coefficients for fixed bed heat and mass transfer. Int. J. Heat Mass Transfer 28, 879; 1985, Solid conduction in low d Jd beds of spheres, pellets, and rings. Int. J. Heat Mass Transfer 28, 383; 1984, Fluid phase radial transport in packed beds of low tube to particle diameter ratio. Int. J. Heat Mass Transfer 27,
1701.
reaction parameter defined in eq. (5), l/Pa fluid-phase heat capacity, J/kg/ K reaction parameter defined eq. (5), kJ/mol heat of reaction, J/km01 heat transfer bed-to-wall coefficient, J/m*
k,
P rA R T
A reactor design was developed to control the temperature of a highly exothermic gas-phase reaction. In this design, cooling coils are placed directly inside a fixed bed of catalyst pellets. The cooling coils are oriented perpendicular to the direction ofbulk gas flow and serve to remove the heat of reaction while maintaining a narrow distribution of temperatures within the reactor. The coil reactor design was examined both experimentally, via a pilot-plant reactor, and mathematically using a two-dimensional pseudo-homogeneous reaction model. The model was found to predict the performance of the pilot-plant reactor. Heat transfer coefficients for the coil reactor design were found to be greater than those for tubular reactor designs. The increased values of the heat transfer coefficients are probably due to enhanced fluid mixing, a reduction in the fluid boundary layer near the upstream surface of the cooling_coils, and improved placement of the cooling surfaces within the reactor. The enhanced heat transfer coefficients of the coil reactor design resulted in lower capital cost estimates for commercial-scale coil reactors, compared to conventional multitubular designs.
b c E,’
ko
thermal
conductivity,
Dixon, A. G., 1987, Private communication. Froment, G. F. and Bischoff, K. B., 1979, Chemical Reactor Analysis and Design. Wiley, New York. Kulkarni, B. D. and Doraiswamy, L. K., 1980, Estimation of effective transDort orooerties in oacked bed reactors. Cakal. Rev. Sci Engig &3), 431. Schiesser. W. E.. DSSM Manual. Lehiah Universitv. _, Bethlehem, PA. Starch, H. N., Golumbic, N. and Anderson, R. B., 1951, The Fischer-Tropsch and Related Syntheses. Wiley, New York.
Vol. 47, No.
5, pp. 959-966.
FISCHER-TROPSCH
1992.
om9-2509/92 ss.00 + 0.00 0 1992 PWgamon PI-S4plc
SYNTHESIS REACTOR ROBERT
Amoco
Chemical Company,
GAS
CONVERSION
F. BLANKS
P.O. Box 3011, Napcrville, IL 60561, USA.
(First received 3 Jury 1990; accepted in revised form 1 October
1991)
Abstract-This
paper describes the design and mathematical modeling of a catalytic reactor for the Fischer-Tropsch conversion of synthesis gas to parat%nic hydrocarbons. The interesting feature of the reactor is a series of cooling coils located within a fixed-bed of catalyst. The coils are oriented perpendicular to the direction of gas flow through the reactor. Coolant flows through the coils to remove the heat of reaction. An experimental pilot-plant reactor was built and operated to test this design. In addition, a steady-state, two-dimensional, psedo-homogeneous reactor model was developed to study the effect of cooling-coil design on reactor performance. Higher overall heat transfer coefficients were obtained with this design, compared to a typical tubular reactor design. Thus, less cooling surface area per unit volume is required. The coil reactor design was estimated to be significantly less expensive to build than a conventional tubular fixed-bed reactor.
INTRODUCTION
Currently, many of the leading oil and gas producers are trying to develop economical processes to convert remote natural gas supplies to easily transportable liquids. Most of the research has been directed toward the synthesis of liquid fuels, such as syncrude, gasoline, middle distillates or alcohols. The Fischer-Tropsch synthesis of paraffinic hydrocarbons from natural-gas-derived synthesis gas (syngas) is one possible route. Syngas, carbon monoxide and hydrogen, can be produced from natural gas via steam reforming or partial oxidation with air. When the hydrogen to carbon monoxide ratio is approximately 2: 1, the syngas is ideally suited for conversion to paraffins via Fischer-Tropsch synthesis using a cobalt-based catalyst. The highly exothermic nature of the Fischer-Tropsch reaction requires a reactor design which can adequately control the reaction temperature within a narrow operating window. However, the capital cost of such a reactor must be kept to a minimum because the sales price of the paraffinic liquids must be competitive with crude-oil prices. Since the goal of this work was to develop a low capital-cost process for converting natural gas to transportable liquid fuels, several constraints were introduced from the beginning of the project. First, the syngas was to be generated via partial oxidation of natural gas with air. Therefore, the feed to the Fischer-Tropsch reactor contains approximately 5 1% (mole basis) syngas (with a Hz/CO ratio of about 2), and 46% nitrogen, with the balance being carbon dioxide and water. Second, the process was designed to operate at low pressure, about 0.2 MPa, in order to minimize the cost of air compression when generating the synthesis gas. Third, the target for the Fischer-Tropsch synthesis was set at 56% yield, based upon an 80% conversion of syngas with a 70% selectivity to C, + hydrocarbons, at a weight hourly
space velocity of 0.55 kg syngas/kg catalyst. These targets were met with a small, isothermal laboratory reactor. When the Fischer-Tropsch reaction is conducted using a cobalt-based catalyst, the reaction product consists of a broad spectrum of linear, saturated hydrocarbon molecules containing from 1 to over 40 carbon atoms. The distribution of hydrocarbon molecules is described by the Schulz-Flory-Anderson product distribution function (Anderson, 1984). When the HJCO ratio is nearly 2 : 1, the net reaction can be simplified as follows: 5C0
+ 11H, + &HI,
+ 5H,O
(1)
Reaction (1) assumes the distribution of products can be approximated by a single compound having the same carbon-to-hydrogen mole ratio as the mean of the product distribution (pentane, in this case): Given the feed composition described above, the adiabatic temperature rise for converting 80% of the syngas via reaction (1) is in excess of 800 K. However, to simultaneously meet the activity and selectivity targets, the reaction temperature must be controlled within a relatively narrow window of 463488 K. The lower temperature is required to maintain activity while, at temperatures above 488 K, the selectivity falls be-low target due to excess methane production. There are several conventional approaches to designing commercial reactors to operate in a nearly isothermal fashion while controlling highly exothermic reactions. The most widely used approach is to contain the catalyst in long narrow tubes, while pumping a heat transfer medium across the outer surfaces of the tubes. A second approach is to recycle a portion of the reactor effluent stream, which is combined with fresh feed and acts as an inert heat sink. A third approach is to use a series of adiabatic beds in series. Temperature is controlled between the
960
ROBERT F. BLANKS
beds with various techniques, such as conventional heat exchange to heat transfer surfaces, or “cold shooting” (addition of cold feed or other gas to the reaction mixture) (Froment and Bischoff, 1979). Unfortunately, none of these approaches was found to be both technically appropriate and economically attractive for this application. Although a multitubular reactor design was investigated in detail, the capital cost was found to be prohibitively expensive. Experiments and mathematical modeling revealed that 0.025 m tubes were the largest-diameter tubes which had good temperature stability at design consitions. Larger-diameter tubes were found to be unstable, resulting in runaway reactions with excessively high temperatures. The large amount of heat transfer surface required in this design resulted in a very expensive reactor.
Our search for a low capital-cost process led us to investigate a reactor design which featured cooling coils embedded within a fixed bed of catalyst. Coolant is pumped through the coils, which are oriented perpendicular to the direction of gas flow. The coils act as internal heat transfer surfaces, removing the heat of reaction while maintaining the desired operating temperatures. This design was tested both experimentally, via a pilot-plant reactor, and mathematically, using a steady-state, two-dimensional, pseudo-homogeneous reactor model. DESIGN
OF THE
EXPERIMENTAL
COIL
REACTOR
Figure 1 shows a schematic diagram of the pilotplant coil reactor. A photograph of one of the coils is also shown. The major objective of the design was to approximate a number of adiabatic beds in series by
Fig. 1. Syngas converter.
Fischer-Tropsch synthesis gas conversion reactor
961
p l a c i n g c o o l i n g coils p e r p e n d i c u l a r to the direction of the o u t e r r e a c t o r wall by a b o u t five t u b e s . In a gas flow, inside the c a t a l y s t bed. In principle, it was c o m m e r c i a l r e a c t o r of 15 ft d i a m e t e r , m a n y t u b e s d e s i r e d t h a t each zone of c a t a l y s t b e t w e e n two coils s e p a r a t e the gas and c a t a l y s t from t h e r e a c t o r w a l l . o p e r a t e s as an a d i a b a t i c bed, and each coil zone acts F o r this r e a s o n , the o u t e r r e a c t o r wall is not conas a heat e x c h a n g e z o n e , l o w e r i n g the t e m p e r a t u r e of s i d e r e d as a b o u n d a r y in o u r m o d e l i n g effort. R a t h e r , the r e a c t i o n m i x t u r e . we f o c u s on a r e g i o n c o n t a i n i n g c a t a l y s t , flowing gas, T h e r e a c t o r is not an a d i a b a t i c r e a c t o r b e c a u s e of and c o o l i n g coils, as t h o u g h this r e g i o n were e m b e d the p r e s e n c e of the heat t r a n s f e r coils c o n t a i n i n g ded in a b o u n d l e s s volume. c o o l a n t . T h e o u t e r shell of the r e a c t o r was wellIn o r d e r to o b t a i n a b e t t e r u n d e r s t a n d i n g of the insulated, but no a t t e m p t was m a d e to c r e a t e an p e r f o r m a n c e of the c o o l i n g coils w i t h i n the r e a c t o r , a a d i a b a t i c s i m u l a t i o n by c o m p e n s a t i n g heat i n p u t at m a t h e m a t i c a l m o d e l was d e v e l o p e d . T h e p u r p o s e of the o u t e r b o u n d a r y . Significant cross-flow t e m p e r this m o d e l was to d e t e r m i n e the effect of p r o c e s s a n d a t u r e g r a d i e n t s e x i s t in the c a t a l y s t b e d b e t w e e n design v a r i a b l e s , (gas flow r a t e , gas c o m p o s i t i o n , c o o l c o o l i n g coils. H o w e v e r , the c r o s s - f l o w t e m p e r a t u r e ant and i n l e t gas t e m p e r a t u r c , coil d i a m e t e r and coil g r a d i e n t s are negligible in the regions of c a t a l y s t b e d s p a c i n g ) upon the t e m p e r a t u r e a n d c o n c e n t r a t i o n not c o n t a i n i n g c o o l i n g coils, t h a t is, b e t w e e n axially profiles in the r e a c t o r . With this o p t i m i z a t i o n and p o s i t i o n e d coils, as long as the r e a c t o r is u n d e r cons c a l e - u p c o u l d be a c c o m p l i s h e d . T h e final m o d e l control and not experiencing a r u n a w a y . This will be t a i n s several p a r a m e t e r s w h i c h are not f u n d a m e n t a l d i s c u s s e d f u r t h e r in the p a p e r . p a r a m e t e r s of the s y s t e m , but are l u m p e d p a r a m e t e r s T h e p i l o t - p l a n t r e a c t o r was c o n s t r u c t e d of 0.46 m a c c o u n t i n g for s e v e r a l p h e n o m e n a , heat t r a n s f e r by (18 in.) S c h e d u l e 40 c a r b o n steel p i p e , 0 . 4 2 9 m I D c o n d u c t i o n and convection, for e x a m p l e . T h e a c t u a l (16.9 in.), 4.57 m (15 ft) l o n g , a n d c o n t a i n e d 60 c o o l i n g g e o m e t r y of the r e a c t o r c o n t a i n i n g the coils c o u l d be coils. E a c h coil was c o n s t r u c t e d of 3.35 m m (11 ft) of m o d e l e d in r a d i a l c o o r d i n a t e s u s i n g a finite-element 0.013 m m (0.5 in.) O D stainless-steel t u b i n g . This resa p p r o a c h . H o w e v e r , we c h o s e i n s t e a d to d e v e l o p a u l t e d in 0 . 1 3 4 m 2 of heat t r a n s f e r s u r f a c e per coil. m o r e simple, a p p r o x i m a t e m o d e l . This m o d e l does W i t h i n a co il, the c e n t e r - t o - c e n t e r tube s p a c i n g was not r e p r e s e n t the a c t u a l g e o m e t r y of the s y s t e m . 0.038 m (1.5 in.), w h i l e the v e r t i c a l s p a c i n g b e t w e e n R a t h e r it is a different g e o m e t r y , but one w h i c h we coils was 0 . 0 7 6 m) (3 in.). T h e c o o l i n g coils were inbelieve a d e q u a t e l y r e p r e s e n t s the b e h a v i o r of the real s t a l l e d so that each coil was offset 90 ° from the coils s y s t e m as far as o u r n e e d s are c o n c e r n e d . T h e m o d e l a b o v e and b e l o w it. This c a u s e d the c e n t e r of the t u b e s s i m u l a t e d a s m a l l r e g i o n of the r e a c t o r l o c a l i z e d in one c o o l i n g coil to be l o c a t e d d i r e c t l y u n d e r the gap a r o u n d two successive c o o l i n g coils, each f o l l o w e d by b e t w e e n t u b e s in the coil just u p s t r e a m in the r e a c t o r . an a d i a b a t i c r e a c t i o n z o n e . This v o l u m e e l e m e n t is This o r i e n t a t i o n i n c r e a s e d the likelihood that the gas e m b e d d e d in a r e a c t o r of b o u n d l e s s volume. With this w o u l d e n c o u n t e r a c o o l i n g s u r f a c e as it f l o w e d down m o d e l , we are not c o n c e r n e d with effects at the o u t e r t h r o u g h the r e a c t o r . T h e t o t a l w o r k i n g v o l u m e of the w a l l s of the r e a c t o r . F u r t h e r simplification was t h a t r e a c t o r , excluding the c o o l i n g coils, was 0.639 m 3 the cylindrical coils, b e i n g of a d i a m e t e r s i m i l a r to a (22.6 ft3). T h e v o l u m e of the r e a c t o r o c c u p i e d by the c a t a l y s t pellet, c o u l d be a p p r o x i m a t e d as fiat p l a t e s . 60 c o o l i n g coils is 0.02 m a (0.73 ft3). T h u s , the p r o b l e m c o u l d be s o l v e d in r e c t a n g u l a r At an overall s y n g a s c o n v e r s i o n of 80%, the a v e r c o o r d i n a t e s . Also, since the m o d e l s i m u l a t e d such a age c o n v e r s i o n per r e a c t i o n zone b e t w e e n coils is s m a l l v o l u m e element, the c u r v a t u r e of the c o o l i n g 1 . 3 % . T h e a d i a b a t i c t e m p e r a t u r e rise is the o r d e r of 10 coils was neglected. In o r d e r to simplify the m o d e l , the to 15 K for each r e a c t i o n z o n e . T h e t o t a l heat g e n e r cooling-coils heat t r a n s f e r surfaces were r e p r e s e n t e d ated in the r e a c t o r is 34.4 k W , or 574 W p e r coil. E a c h as fiat p l a t e s o r i e n t e d p a r a l l e l to the direction of gas coil c o n t a i n s h o t oil flowing at 0.25 m a / h r at an flow. Then the m a t h e m a t i c a l p r o b l e m is one of a gas a v e r a g e t e m p e r a t u r e of 412 to 470 K. T h e oil-side flowing in a b o u n d l e s s v o l u m e b e t w e e n a l t e r n a t i n g t e m p e r a t u r e rise v a r i e s b e t w e e n 1 and 10 K. regions c o n t a i n i n g c o o l e d flat w a l l s and w i t h o u t In an a t t e m p t to s p r e a d the r e a c t i o n e v e n l y over the walls. T h e w a l l s were offset in a l t e r n a t e p l a n e s so t h a t l e n g t h of the c a t a l y s t bed, the c a t a l y s t c o n c e n t r a t i o n gas in the c e n t e r of the s p a c e b e t w e e n w a l l s c o n t a c t e d was g r a d e d from r e a c t o r i n l e t to o u t l e t . T h e m o s t the wall in the next p l a n e a f t e r the a d i a b a t i c section. A d i l u t e c a t a l y s t c o n c e n t r a t i o n was at the inlet, 4 7 % d i a g r a m of this r e g i o n is s h o w n in Fig. 2. Z o n e s 1 and c a t a l y s t plus 5 3 % i n e r t pellets, physically m i x e d to3 are the s e c t i o n s c o n t a i n i n g the c o o l i n g coils. Z o n e s 2 g e t h e r . N e a r the o u t l e t of the r e a c t o r , the bed was and 4 are the a d i a b a t i c r e a c t i o n r e g i o n s . Since only l o a d e d with c a t a l y s t p e l l e t s alone. T h e c a t a l y s t p e l l e t s a b o u t 2 % c o n v e r s i o n o c c u r r e d w i t h i n this four-zone were 0.5 x 1.3 cm cylinders, c o r r e s p o n d i n g to an e q u i m o d e l , the p h y s i c a l p r o p e r t i e s and c o m p o s i t i o n of the v a l e n t s p h e r i c a l d i a m e t e r of 0.9 cm (0.36 in.). T h u s , the gas s t r e a m were a s s u m e d to be constant. This m o d e l c a t a l y s t p e l l e t s are the s a m e o r d e r of m a g n i t u d e in size c o u l d be focused, in s n a p - s h o t f a s h i o n , on any p a r as the d i a m e t e r of the c o o l i n g coils. t i c u l a r r e g i o n of the r e a c t o r : near the e n t r a n c e , in the middle, or near the exit. MATHEMATICAL REACTOR MODELING T h e m a t h e m a t i c a l m o d e l was w r i t t e n as a steady= In the p i l o t - p l a n t r e a c t o r (refer to Fig. 1), gas and state, two-dimensional pseudo-homogeneous reactor c a t a l y s t in the c e n t e r of the r e a c t o r are s e p a r a t e d from m o d e l . Only an e n e r g y b a l a n c e was n e c e s s a r y , since
ROBERT F. BLANKS
962
Gas flow where k,-, = 5.6 x lo6 kmol CO reacted/kg catalyst
f
Zone #l
E, 2 90.004 kJ/mol
f
R = 8.3 14 J/mol K
T Zone #2
Cooling tube
b = 1.596 x lo- l3 Pae3.
-Y t Zone #3
T 1
h -T Zone #4
Lt
1
Fig. 2. Cross-flow
reactor.
the gas properties and composition did not change significantly over the four-zone, two-coil case being analyzed. The energy balance equation was written as
u=pf&,
dT dx
d2T
-
ke-dy2
- pr( -
AiYr)rA = 0. (2)
The first term in eq. (2) describes the energy convected in and out of a reactor volume by bulk gas flow in the x-direction, axially. The second term describes the dispersion of thermal energy in the y-direction, perpendicular to the direction of bulk gas flow. The third term describes the energy generated by the chemical reaction. An axial dispersion temperature term was originally included in the model. However, a number of simulations showed this to have a negligible effect on the results, so it was removed. Adiabatic boundary conditions were used at the planes of symmetry between cooling surfaces or at the edges of adiabatic reaction zones: dT
-=0
dy
sty=
a plane of symmetry.
(3)
A boundary condition describing removal of heat by transfer to a cooled wall surface is used at the coil-bed boundaries:
!g = 2(T -
T,).
0
The kinetic reaction rate model which best-fit experimental data for the Fischer-Tropsch reaction, using a cobalt-based catalyst, was obtained from Starch et al. c1951t
This rate equation fit laboratory isothermal reactor data for a temperature range 453483 K and a pressure range O-1-0.27 MPa. The reactor model was solved on a VAX computer using the DSS/2 differential equation package (Schiesser). A five-point, finite-difference scheme was selected. Second derivatives were represented by centered differences and first derivatives by a biased upwind formula. This finite-difference technique integrated the time-dependent version of eq. (2) until a steadystate solution was obtained. Solutions consisted of two-dimensional temperature profiles for two adiabatic reaction zones, each followed by a cooling coil. The model calculates cross-flow temperature profiles at a particular axial location in the reactor. Then these are volume averaged to obtain an “average” axial temperature. This is done for successive axial locations in the reactor for zones where there are coils and zones where there are no coils. Many of the reactor parameters and process conditions are fixed by experiment and some of these vary with axial position (distance down the bed in the flow direction). Fixed are: the effective cooling surface length in the flow direction, the spacing between coils, the length of an adiabatic section, and the catalyst-pellet-equivalent spherical diameter. The gas temperature and COTposition are known, both at the inlet of the reactor and as a function of reactor length based on an overall, linear, one-dimensional simulation, using the actual axial temperature profile and reaction kinetics. (The actual profile is nearly isothermal by design.) This allows calculation of gas properties; density, thermal conductivity, heat capacity and viscosity. Also superficial gas velocity may calculated_ All of these quantities are dependent on conversion and axial position. With this information, the Reynolds and Prandtl numbers are calculated and finally the bed-to-wall heat transfer coefficient from curve 1, Figure 11.7a-3 of Froment and Bischoff (1979). Also the effective bed thermal conductivity is calculated from the procedure of Dixon (et seq.). This calculation includes individual estimates of four components of the effective-bed thermal conductivity: the fluid thermal conductivity, the effective conductivity due to fluid turbulence, the solid-pellet-effective conductivity, and a dynamic component of the pellet conductivity. These all vary with axial position since the axial gas velocity varies due to changing moles of gas caused by reaction (1) and due to the effect of gas Dronerties on the Revnolds and Prandtl numbers.
Fischer-Tropsch COMPARING
THE MODEL
TO PILOT-PLANT
synthesis gas conversion reactor
DATA
The mathematical model of the coil reactor was compared with experimental data obtained in the pilot plant. The model was first focused on a section near the inlet of the reactor. All of the parameters in eqs (2)-(5) were known except for the effective radial thermal conductivity of the bed, k, and the bed-towall heat transfer coefficient, h,. The value of h, was obtained from a Prandtl number and Reynolds number plot of Coberly and Marshall (1951). The value of k, was determined from a procedure developed by Dixon (1978). These were later reevaluated using more recent information (Dixon, 1987). Next, the model was focused on a section near the exit of the reactor. Once again, all of the parameters in the model, excluding the two heat transfer variables, were directly measured or calculated from pilot-plant data. The values of the two heat transfer parameters used for the top section of the reactor, k, and h, were modified, because the Reynolds and Prandtl numbers for the exit of the reactor were substantially different from those for the reactor inlet. Without any further adjustment, the model generated a temperature profile which agreed with the measured data at both inlet and outlet. We felt that this validated the model’s predictions as well as the values used for the heat transfer parameters. The predicted axial and radial temperature profiles for these two cases are shown in Figs 3-6. The predictions are quite sensitive to the values chosen for k, and h,. The model was also used to predict the effect of
219 218 ”
217
-
8
216
-
g
215
-
ii
214
-
s
213
-
5
212-
6
211
-
210
-
_________o_____
Horizontalspacing Fig. 4. Top of pilot-plant cross-Bow temperature profile. at first coil, (0) outlet temperature from first coil, (0) initial temperature at second coil, (0) outlet temperature from second coil, (a) initial temperature at third coil. ( x ) Initial temperature
215 0
(u
g
214
:[
213
t
R
8
B Ea 212
219
Ii 0 ii 211 ,Q ii g 210 g & 20s
217
e L g
216
208
g 207 206 Axial position 214
Gas Row c
Fig. 5. Axial temperature profile for pilot-plant bottom of reactor.
213
I
I
I
4
I
Axial position Gas flow
m
Fig. 3. Axial temperature profile for pilot-plant top of reactor.
increasing the concentration of carbon monoxide in the reactor feed from 36% to 40%. The model predicted that such an increase would result in a runaway reaction. This prediction was confirmed experimentally. We have concluded that the mathematical model, represented by eqs (2)-(5), is an effective simulation of
ROBERT F. BLANKS
964
63 ,
if
Single
Coil/Pilot
Plant
209
0’
3
E f! f P
207 205
A
79
126
200
316
501
Reynolds number
199
Fig. 7. Overall heat transfer coefficients. (0) l/2 in. coils-stream, (El) I/2 in. coils-water, (0) literatureh, for tubes, (D) l/4 in. coils-water, (EY)pilot plant. Horizontal spacing
Fig. 6. Bottom of pilot-plantcross-flow temperatureprofile. ( x ) Initial temperatureat first coil, (0) outlet temperature from first coil, (0) initial temperatureat second coil, (0) outlet temperature from second coil, (A) initial temperature at third coil.
reality. This is based upon comparisons of predicted axial temperature profiles with experimental data from the pilot plant for sections near both the top and the bottom of the reactor, when the pilot plant was operating satisfactorily at steady state. Further substantiation is the match of a predicted runaway reaction, an uncontrollable axial temperature profile, with an actual runway in the pilot-plant experimental reactor. Here the terms axial temperature profile refer either to the volume-averaged cross-flow temperature calculated at each axial position from the model, or the experimental average of several thermocouples placed in various positions in the pilot plant at one axial location. In this operation, with the pilot plant under control at steady state, the adiabatic section always evens out the cross-flow, horizontal, variations in temperature. It will be seen in a later section, however, that this is not the case for an improperly designed reactor, as when the process demands an excessive conversion per unit length. HEAT
TRANSFER
COEFFICIENTS COIL
FOR TUBULAR
AND
GEOMETRCRS
The packed-bed heat transfer parameters, h, and k,, have been studied in tubular geometry by a number of investigators (Froment and Bischoff, 1979; Coberly and Marshall, 1951; Dixon, et seq.). In tubutar reactors, these parameters may be combined to give an overall heat transfer parameter: 1
1
R
U
h,
4k,
-=-+---. A comparison
_.
(6)
was made between the overall heat
transfer coefficients obtained from this study, using the coil reactor design in both reacting and nonreacting systems, and those predicted for tubular geometries (Froment and Bischoff, 1979; Coberly and Marshall, 1951; Dixon, et seq.) (Fig. 7). Shown in Fig. 7 are the measured overall coefficients, U, from this work and literature values for h, versus Reynolds Number. As eq. (6) illustrates the only way U and h, could be equivalent is the case when k, approaches infinity. Since this is not the case here we conclude that the values of U for our geometry are larger than values of U for tubular systems. (Heat fluxes during the experiments which generated the data of Fig. 7 are comparable. In the reacting system, the heat flux was 4.3 kW/m’. In the nonreacting experiments the heat flux ranged from 1.6 to 15 kW/m2. Typical tubular reaction heat Aux is 2-5 kW/m2.) We believe the overall heat transfer coefficient, U, for the coil reactor geometry is higher than that of a tubular reactor geometry, given the same Reynolds and Prandtl numbers. The exact reasons for this are not quantitatively understood. The higher values may be caused by enhanced convective heat transfer due to increased gas mixing which, in turn, is caused by the presence of the cooling coils. Heat transfer may be increased because of decreased boundary-layer thickness on the upstream side of the cooling surfaces. Also, the staggered nature of the cooling coils causes the disruption of peaks in the radial temperature profiles, preventing them from propagating axially downstream. Each of these factors may account for the enhanced heat transfer observed in the coil reactor design, compared to a conventional tubular design. COMMERCIAL
REACTOR
DESIGNS
The mathematical model of the coil reactor was used to predict the performance of several different
96.5
Fischer-Tropsch synthesis gas conversion reactor commercial coil reactor designs. The results for both a controllable and an uncontrollable designs are shown in Figs 8-11. This design was based upon a 4.57 m diameter reactor. Either 0.025 or 0.051 m diameter cooling coils were found to be sufficient to control the reactor temperature. However, the axial and radial spacing between coils was found to be the difference
210
c! 209
B :e ;
208
Axialposition Gas flow
*
Fig. 10. Axial temperature profile For commercial reactor.
240
,
,
,
I
I
Axial position 230 Gas flow w
Fig. 8. Axial temperature profile for commercial reactor.
210
220
210
200
q90
160 Horizontal spacing
Fig. 11. Cross-flow temperature profile for commercial reactor. ( x ) Initial temperature at first coil, (0) outlet temperature from first coil, (0) initial temperature at second coil, (1) outlet temperature from second coil, (A) initial temperature at third coil.
Horizontal spacing
Fig. 9. Cross-flow temperature profile for commercial re-
actor. ( x ) Initial temperature at first coil, (0) outlet temperature from first coil, (0) initial temperature at second coil, (0) outlet temperature from second coil, (A) initial temperature at third coil.
between the controllable and the uncontrollable designs. Although a commercial-scale version of the coil reactor design was never constructed, pilot-plant data and economic analyses suggest it is a cheaper alternative to conventional multitubular reactor designs. An analysis was done for a world-scale plant, processing 2.5 million standard cubic meters per day of
ROBERT F. BLANKS
966
natural gas. The result was that the ratio of the capital cost of a bank of conventional tubular reactors, capable of controlling the FT reaction at design conditions, to the capital cost of a bank of coil reactors was four. CONCLUSIONS
NOTATION
AH, h,
sK
effective J/msK
bed
radial
TW u uX X Y Greek Pb Pf
reaction parameter defined in eq. (5), kmol/kg h partial pressure, Pa reaction rate defined in eq (S), kmol/kg h characteristic length, m; or gas constant, 8.314 J/mol K temperature, K wall temperature, K overall heat transfer coefficient, J/m’ s K gas velocity in axial direction, m/s axial dimension, m radial dimension, m letters catalyst bulk density, kg/m’ fluid density, kg/m’ REFERENCES
Anderson, R. B., 1984, 7’he Fischer-Tropsch Synthesis, Academic Press, Orlando, FL. Coberly, C. A. and Marshall, W. P., 1951, Chem. Engng Prog. 47, 141. Dixon, A. G., 1978. Ifeat Transfm in Packed Beds, p. 238. Chemical Reaction Engineering, Houston. Dixon, A. G., 1986. Effective heat transfer parameters f&r transient packed bed models. A.I.Ch.E. J. 32, 1978, 809; Heat Trctnsjer in Packed Beds, p. 238. Chemical Reaction Engineering, Houston; 1979, Theoretical prediction of effective heat transfer parameters in packed beds. A.I.Ch.E. J. 25, 663; 1985, Thermal resistance models of packed bed effective heat transfer parameters. A.I.Ch.E. J., 31, 826; 1985, Wall to fluid coefficients for fixed bed heat and mass transfer. Int. J. Heat Mass Transfer 28, 879; 1985, Solid conduction in low d Jd beds of spheres, pellets, and rings. Int. J. Heat Mass Transfer 28, 383; 1984, Fluid phase radial transport in packed beds of low tube to particle diameter ratio. Int. J. Heat Mass Transfer 27,
1701.
reaction parameter defined in eq. (5), l/Pa fluid-phase heat capacity, J/kg/ K reaction parameter defined eq. (5), kJ/mol heat of reaction, J/km01 heat transfer bed-to-wall coefficient, J/m*
k,
P rA R T
A reactor design was developed to control the temperature of a highly exothermic gas-phase reaction. In this design, cooling coils are placed directly inside a fixed bed of catalyst pellets. The cooling coils are oriented perpendicular to the direction ofbulk gas flow and serve to remove the heat of reaction while maintaining a narrow distribution of temperatures within the reactor. The coil reactor design was examined both experimentally, via a pilot-plant reactor, and mathematically using a two-dimensional pseudo-homogeneous reaction model. The model was found to predict the performance of the pilot-plant reactor. Heat transfer coefficients for the coil reactor design were found to be greater than those for tubular reactor designs. The increased values of the heat transfer coefficients are probably due to enhanced fluid mixing, a reduction in the fluid boundary layer near the upstream surface of the cooling_coils, and improved placement of the cooling surfaces within the reactor. The enhanced heat transfer coefficients of the coil reactor design resulted in lower capital cost estimates for commercial-scale coil reactors, compared to conventional multitubular designs.
b c E,’
ko
thermal
conductivity,
Dixon, A. G., 1987, Private communication. Froment, G. F. and Bischoff, K. B., 1979, Chemical Reactor Analysis and Design. Wiley, New York. Kulkarni, B. D. and Doraiswamy, L. K., 1980, Estimation of effective transDort orooerties in oacked bed reactors. Cakal. Rev. Sci Engig &3), 431. Schiesser. W. E.. DSSM Manual. Lehiah Universitv. _, Bethlehem, PA. Starch, H. N., Golumbic, N. and Anderson, R. B., 1951, The Fischer-Tropsch and Related Syntheses. Wiley, New York.