Dynamic Behavior of an Adiabatic Fixed-Bed Methanator - Advances

37 Dynamic Behavior of an Adiabatic Fixed-Bed Methanator H. VAN DOESBURG and W. A. DE JONG

Downloaded by CORNELL UNIV on May 18, 2017 | http://pubs.acs.org Publication Date: June 1, 1975 | doi: 10.1021/ba-1974-0133.ch037

Laboratory of Chemical Technology, Delft University of Technology, Julianalaan 136, Delft, The Netherlands

The hydrogenation of small amounts of CO and CO to methane —a purification step in hydrogen synthesis—is used as the test reaction to study the transient behavior of an adiabatic fixed-bed reactor containing Ni/Al O catalyst. The response of a 0.5-liter methanator to step changes in inlet conditions was measured in the parameter space: 0.6-2.5 vol % CO or CO in hydrogen, 180°-250°C inlet temperature, and space velocity 5.000-32.000 hr . A quasi-homogeneous plug flow model was selected to compare the experimental results with calculations, integrating the partial differential equations with a finite difference approximation containing the Crank-Nicholson algorithm. The results show that the model gives a good description of the measurements. 2

2

3

2

-1

K

nowledge of the non-stationary behavior of chemical reactors is important to predict responses to changes in feed conditions, for control purposes, and so forth. Much progress has been made in this field during the last decade, particularly with catalytic fixed-bed reactors; detailed mathematical models have been developed and solved by computers. However, the results of such calculations are often not checked with experimental data, and it is not always clear whether the complex models developed by some authors are really required in practical applications (1,2, 3). In the present work we have tried to use as simple a model as possible by: (a) Defining the problem by choosing a test reaction, limiting ourselves to heterogeneous solid/gas catalytic reactions. (b) Writing down the requisite model equations. (c) Performing experiments and calculations to establish which of the theoretically possible terms of the equations are significant. (d) Performing experiments in a pilot reactor to compare the results of our calculations with actual data. Selection of Model Reaction The model reaction should preferably have the following properties: ( 1 ) The equation describing its chemical kinetics should apply to a wide temperature range. 489

Hulburt; Chemical Reaction Engineering—II Advances in Chemistry; American Chemical Society: Washington, DC, 1974.

CHEMICAL

490

REACTION ENGINEERING

II

(2) A commercial catalyst with high activity and stability should be available. (3) Reactants should be gases of high purity and low price. (4) Consecutive or side reactions should not occur. (5) The heat of reaction must be large. Furthermore, the test reaction should be industrially important; the same should apply, if possible, to the dynamic behavior of the reactor. The above requirements are met by the methanation of carbon oxides, a step in the process for manufacturing hydrogen and ammonia synthesis gas by steam reforming or partial oxidation of hydrocarbons. The stoichiometric equations involved are: CO + 3H -» C H + H 0 Downloaded by CORNELL UNIV on May 18, 2017 | http://pubs.acs.org Publication Date: June 1, 1975 | doi: 10.1021/ba-1974-0133.ch037

2

4

2

2

4

= - 49.3 kcal/mole CO

άΗ°

= - 39.4 kcal/mole C 0

Τ

C 0 + 4H -> C H + 2H 0 2

ΔΗ° 2

τ

2

The dynamic behavior of a methanator can be important when, for ex ample, the inlet concentration of C 0 increases suddenly because of misoperation or failure of the C 0 absorber, a previous process step. When the con centration of carbon dioxide in hydrogen increases by 1% (here concentration in % refers to vol % ) the adiabatic temperature rise increases by as much as 5 6 ° C in seconds when the feed temperature exceeds 2 5 0 ° C . It is thus impor tant to obtain a better knowledge of the response to such sudden changes in feed conditions. 2

2

Model Development Method. The mathematical model for an adiabatic methanator was de veloped according to the level scheme of Figure 1. This scheme is similar to those set up by Slin'ko (4), Matros et al. (5), and Beskov et al. (6). It can be used for stationary and dynamic reactor models. Each level is treated separately below. Level I

Separate stages of chemical change adsorption/reaction/desorption

Level II

Transfer processes inside catalyst pellet

Level III

Heat 1 Mass Transfer processes in a film layer

Level IV

Heat 1 Mass Transfer processes in a layer of catalyst Heat 1 Mass Interaction with the environment adiabatic | non-adiabatic

Level V Figure 1.

Level scheme for model development

Level I. We began this investigation by studying the kinetics of C O and C 0 hydrogénation at atmospheric pressure; the results are published elsewhere (7). Care was taken to exclude transport resistances in the kinetic measurements. The following equations describe the reaction rates with good precision in the concentration ranges 0.1-2.5% C O or C 0 in H and at 1 7 0 ° 2 1 0 ° C and 2 0 0 ° - 2 3 0 ° C for C O and C 0 , respectively: 2

2

2

2


37.

VAN DOESBURG AND DE JONG

2.09 X 10 exp ( - 1 0 . 1 / β Γ ) P . . ( l + 4 . 5 6 X 1 0 - * e x p (12A/RT) P )> ^les /hr/gram 5

r c o

=

c o


C02

co

co

1.36 X 10 exp (-25.S/RT) P (i i270 P ) 12

r

491

Fixed-Bed Methanator

-

+

C02

CO2

„ , moles/hr/gram

m

(1) , * (2)

1

0

The equations were tested at temperatures up to 2 8 0 ° C and described the rates at those temperatures quite satisfactorily. Therefore, they were ap plied throughout this work. Level II. Table I contains data on the supported nickel catalyst used which were required to establish whether heat and mass transport resistances occur inside the catalyst particles. These data allow the calculation of effec tiveness factors under methanation conditions; we found that the effectiveness factor is invariably higher than 0.9 at reaction temperatures below 3 2 0 ° C . Thus, pore diffusion does not influence the overall rate. Furthermore, it was established using Anderson's criterion (8) that the particles are isothermal up to that temperature. Table I.

Properties of Catalyst

Girdler G-65 Catalyst composition : 25 wt % Ni on y — A1 0 crushed particles: d = 0.42 — 0.60 mm particle density : 2750 kg/m particle porosity : 0.46 bed density : 1175 kg/m bed porosity : 0.57 Sbet : 42.4 mVgram S i : 6.6 m /gram average pore diameter: 25 A 2

3

p

3

3

2

N

Level III. The formulas of Chu et al. (9) and Petrovic and Thodos (10) for mass transfer resistance and the graph of N u vs. R e given by Kunii and Smith (II) for heat transfer were applied to show that concentrations and temperatures in the two phases (gas and catalyst particles) do not differ sig nificantly. The result for heat transfer was confirmed experimentally by placing a 0.5-mm thermocouple in a 5 X 5 mm catalyst pellet and another in the sur rounding gas phase. A temperature difference could not be detected even at conditions known to give 100% carbon oxide conversion. This also confirms that the catalyst pellet is isothermal, as was concluded at Level II. Therefore, a quasi-homogeneous reactor model can be used to describe the methanator. Level IV. The questions to be answered at this level are (1) whether dispersion contributes to mass transport in the catalyst bed, and (2) whether conduction, radiation, and dispersion should be taken into account when considering heat transport in the reactor. In general, axial dispersion of mass and heat can be neglected whenever the bed is longer than 50 particle diameters (12); alternatively, the criterion of Marek and Hlavacek (13) can be applied: p

Pei ^

> 100

dp Since L/d = 600 and D/d = 92 for the pilot reactor used in this work and because P e = 0.5-2.0 (14, 15, 16) in the range of R e values encoun tered here (1.5-10), a plug flow description for mass transport applies. Furp

p

1 ( m a s g )

p


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CHEMICAL REACTION ENGINEERING

II

thermore, results of Vortmeyer and Jahnel (17, 18) indicate that much higher reactor temperatures would be required for radiation to contribute significantly to heat flow in the catalyst bed. Radial heat transport can be neglected because the methanator is adiabatic. To confirm the above calculations the axial heat conductivity was also determined experimentally because data for systems containing relatively good heat conductors like the N i / A l 0 methanation catalyst and hydrogen could not be found in the literature. We applied the method of Yagi et al. (19), which was also used in recent work by Votruba et ah; the results show that axial heat conduction can be described quite well by Votrubas equation (-20) for P e and that it is not important in our methanator. Level V . In the heat balance of a non-stationary adiabatic reactor it is necessary to take into account the heat capacity of the reactor wall as well as that of the catalyst bed. The two contributions to the time-dependent heat capacity term in the enthalpy balance of our pilot reactor are of the same order of magnitude. If the heat losses to the surroundings and heat conduction along the reactor wall are small and heat transfer from the catalyst bed to the wall is fast compared with the temperature changes in the reactor, the temperature profile along the reactor wall is invariably almost the same as the axial profile in the bed. Under such conditions the wall can be considered as part of the quasi-homogeneous catalyst medium relative to the temperature. The experiments were designed to comply with the above requirements, generating temperature profiles in catalyst bed and reactor wall which change synchronously. Final Model Equations. Based on the above, the mass balance of a small volume element of the reactor can be written as: 2

3


H

uS ^ dl dl

eS^- dl dt

=

pbed

Srdl

This balance was applied to C O as well as C 0 ; the concentration of all the other components of the reaction mixture can be calculated directly from the carbon oxide concentrations and the reaction stoichiometry. The heat balance reads as follows: 2

uctotCp^S ~ dl + ectotC S ^ dl + pbedC S ^ dl Pg

PcRt

+ izdl

(# out — 2

R in) 2

dT pwallC

P w a l l

—

=

—

ç dSrAH° dl he

T

It can be modified to WCtotCpg ^

+

C

pm

^

=

-

PbedAFV

(6)

where C stands for the heat capacity of the quasi-homogeneous system comprising gas phase, catalyst bed, and reactor wall: P

Cp

m

— SCtotCpg +

PbedC

Pcat

H

~ PwallCp

wall

(7)

The equations are handled best in the dimensionless form—i.e., by substituting:


37.



493

The final result is:

( 8 )

_ exp A JT>) {

co

*

(1 +

C

ÏC

^ 3

C

O


*

XC

c

X exp (A JT)

3 e o

X C )>

p b c d < :

U

=

re

= iT.C,,,

A,

Al

< > 13

(14)

re

—

(ID (12)

L

°

;

co

t

Ai = ~

A

V

CO!

exp (AtJT') (1 + A

COi

X C )

!

(15)

~ PbedfeooAff° Ci L r

n

WCtotCp Tin g

B

Table II.

* »

17

Data Used to Calculate Reactor Response Εa co ôo

1.039 X 10 10.1 6.76 X 10 25.3 - 49.3 - 39.4 28.5 10.2 X 10" 12.4 0.3 2.3 10" 2.7 10~ 1175 0.57 2900 0.19 7 ΙΟ" 44.7 0.211

3

^ o o CO

c02

Ea

C02

= = =

Κ co K

2

œco

L

= = =

9

6

2

•Rout Pbed

2

=

6

Pwall

= =

Ctot ^Pcat

3

m /kg/sec kcal/mole m /kg/sec kcal/mole kcal/mole kcal/mole m /mole m /mole kcal/mole m m m kg/m 3

3

3

3

—

kg/m kcal/kg/oK kcal/mole/°K mole/m kcal/kg / K 3

3

cat

0


494


II


Since the boundary conditions depend on the type of disturbance at the reactor inlet and the initial profiles of temperature and concentrations in the reactor, they are discussed together with the results. Solution Method. Because the Equations 8 and 9 are non-linear, an analytical solution is not possible, and a finite difference approximation was applied containing the Crank-Nicholson algorithm. The calculation requires expansion of the reaction rate equations in a Taylor series. The resulting set of linear equations can be solved easily by inversion of the linear band matrix, similar to the method for partial parabolic differential equations described by Valstar (21). The values of the physical and chemical parameters used in the calculations are given in Table II. The kinetic parameters were obtained by non-linear regression analysis of data obtained in a microreactor using Equations 1 and 2. For further details we refer to our earlier paper (7). Experimental Equipment. The response of a 0.5-liter methanator to step changes in feed temperature and reactant concentration was studied with the equipment shown in Figure 3. Two gas dosage systems can be connected in turn to reactor 4 via valves 2. One of the feed gas streams enters the reactor by way of preheater 3 equipped with by-pass 7. The flow rate of the reactor product is measured with Rotameter 6, and the compositions of feed and product gases are analyzed by on-line gas chromatograph 9. The reactor (Figure 2) was insulated by a vacuum mantle and placed in a metal cylinder to protect it. At the outlet (bottom), glass and metal are connected by a Quick-Fit joint; at the top, glass and metal can expand independently. Twenty 0.5-mm thermocouples are inserted in the bed—viz., 16 in the center and four near the wall as a check on the occurrence of radial temperature profiles. Since the previous discussion on model reduction has shown that the temperature of the catalyst particles is the same as that of the gas phase, it is immaterial whether the thermocouples are in contact with the catalyst or not. The thermocouples are connected to a 20-channel data logging system which can register a complete axial temperature profile on a tape puncher at certain intervals; the shortest possible interval is 3 sec. Materials. A commercial nickel on alumina catalyst, G-65 from Girdler Siidchemie (Munich, West Germany) was used; Table I contains the relevant data on this catalyst. Measurements of stationary temperature profiles indicated that the catalyst sample had a lower activity than the material with which the kinetic study (7) was done; it was possible to account for this by lowering the frequency factor by 20%. The fact that the second batch of catalyst is less active that the previous one was confirmed by kinetic measurements in a microreactor. The feed gases were commercially available, chemically pure; they were dried separately over molecular sieves, 3A. Procedures. The reactor is brought to a stationary state with the feed of one of the two dosage systems; the flow of the product gases is first measured with Rotameter 6 and then diverted to "vent" by switching valves 5. Simultaneously, valve system 5 directs the flow from the second feed unit to the Rotameter via by-pass 8; this feed stream differs from the other in reactant concentration. By switching valve system 2, a step change in feed concentration can be obtained. A temperature disturbance is created by feeding gas to the reactor through the preheater as well as by-pass 7 to give a steady state with a known inlet temperature. The temperature disturbance is produced by closing the valve in the by-pass.




495


37.

Figure 2. Reactor Safety Precautions. Since the hydrogen consumption of the experimental unit is high by laboratory standards (viz., 3-16 nm /hr), the unit was built in the open air. Valves, heaters, etc. could be operated from a control panel in the laboratory; the registration and data logging equipment was also placed indoors to separate it from the reactor system. The usual safety measures, such as automatic shutdown in case of power failures, a central switch to shut down the unit in case of emergency, and other precautions were taken. 3

Results Table III lists the ranges of flow, temperature, and concentration in which the experiments with mixtures of C 0 or C O in hydrogen were done. For comparison, the conditions for industrial methanators are also given. 2



496


Figure 3.

II

Simplifiedflowsheet of equipment

Table III.

Experimental Conditions S.V. hr~

l

CO 2 hydrogénation CO hydrogénation Industrial methanator

5000-32000 5000-32000 4000- 5000

T ^ , °C

C , vol % i n

190-250 190-250 300-310

Pressure, aim

0.6-2.2 0.6-2.0 0.3-0.5

1 1 10-40

The temperature at the wall and at the same axial position in the center of the catalyst bed were equal within experimental error. Therefore, radial temperature profiles were not taken into account in experiments under the conditions listed in Table III. Three types of disturbances in a feed of C 0 and C O in hydrogen are considered separately: Type 1 : step increase in concentration in the feed to an isothermal reactor. Type 2: a similar concentration step in the feed to a reactor with a temperature profile. Type 3: a temperature disturbance. Hydrogénation of C 0 . TYPE 1. Computer simulation with the model shows that the concentration profile in the reactor changes appreciably within 1-2 residence times after a step increase in concentration. This phenomenon, the fast concentration response ( F C R ) , is followed by the formation of a temperature profile, which develops much more slowly than the F C R . We refer to this as the slow temperature response, STR, which is accompanied by an equally slow further change in the concentration profile. Typical results of such calculated profiles are shown in Figure 4. Hansen made a similar approach to this problem (22, 23, 24). An F C R calculation requires a very small time step whereas an STR can be computed using 1000-fold longer time step. To minimize the computing time required, the F C R calculation, which takes about 10 min on an IBM 360/65, can be replaced by a simple 4th-order Runge Kutta integration of the isothermal stationary mass balance which reouires 2

2


37.



15 1 0 05 x 2 20 x 3 250 tR 4 1000 "CR 5 stationary profile R

R

10

\ -\


Vl

V

5\ \ \4_ 0.5

1.0

05

10

1.15

1-1

-

105

10

Figure 4.

300

Sample response to a type 1 disturbance (calculated)

ο 43 S · 260 S • 108 S Δ 303 S χ 195 S

C

j n

= 0-8°/o CO2

SV = 17000 hr-1

280

260

240

Figure 5. Axial temperature profile at various times after a type 1 disturbance (lines: calculated; points: measured)


497

498


II

only a few seconds. The result is then used as the boundary condition for the STR calculation. About 20 experiments were done within the range of conditions in Table III, concerning a type 1 disturbance. In all cases examined the agreement between measured and calculated temperatures and their changes in time is quite satisfactory; a representative example is shown in Figure 5.


350 -

Figure 6. Axial temperature profile at various times after a type 2 disturbance (lines: calculated; points: measured) TYPE 2. Here the F C R develops in a different manner because the reactor is not isothermal but contains an axial temperature profile at the time of the step change in concentration. It appeared that, here too, the concentration profile after the F C R could be found by Runge-Kutta integration of the mass balance, but by substituting after each axial step the temperature at the corresponding position in the reactor obtained from the initial stationary temperature profile. Agreement between measured and calculated temperature profiles was very good for all experiments in which a feed concentration step was applied to a reactor containing an axial temperature profile; an example is shown in Figure 6. TYPE 3. With type 3 disturbances a distinction between F C R and STR cannot be made. Initial concentration and temperature profiles are first calculated from stationary mass and heat balances by Runge-Kutta integration, and a temperature disturbance is then imposed on the reactor inlet conditions. A sharp step increase or decrease of the feed temperature was impossible with the equipment used because of the large heat capacity of the piping between the cold and hot gas mixer and the reactor inlet. The resulting smooth inlet temperature/time curve could, however, be described adequately by two or three straight lines. A typical result of a type 3 disturbance is shown in Figure 7. Interestingly, the temperature in the second part of the bed decreases when the entrance temperature is raised; conversely, the temperature in the


37.


325

-

^

—

Û

û

B

— Δ

JJ

/ *

r /

300

1

—*—

/

ΓΙ 275

Α


//

/ / *

χ

x

a

&

x, r> ο

0 U

~ * — *

Ψ

/ ο

/

/

/

Γ

/

Χ

250

â—ù

/ο

U

//

JJ

"^""«««^

/

/

// Γ/

-

/ /

v

/

1

/ l

ο

499


Χ

ο 0 ψ 360 x 600 Δ 800

Â

Â

c

in=

C

S S S S Û2

SV = 2 5 0 0 0 h H

y *

S

T

i n

= 226

244 °C

• 1

.

:

500

Figure 7.

,

250 t (sec) -

220

I

I

10

0-5

C — · — λ

Inlet temperature and axial temperature profile for a type 3 disturbance (lines: cahufated; points: measured)

second part of the bed increases with decreasing feed temperature. This can be explained by considering that less C 0 is converted in the first part of the bed when the entrance temperature is lowered. Thus, more C 0 reaches the second part. This condition persists until the second part is cooled enough so that the exponential influence of the decrease in temperature overshadows the competitive effect of the increased concentration on the reaction rate. A 2

2

0-010 -

0010

0020

P c o (atm) Figure 8. Initial rate of CO hydrogénation (lines calculated from Equation 1; points: measured) similar explanation applies to an increased feed temperature. Similar conclusions were drawn for a packed tubular reactor by Crider and Foss (26) on the basis of calculations; the effects were determined experimentally by Hoiberg


500


II

et al. (25) for a fixed-bed catalytic reactor. According to Eigenberger (27) it occurs even in a homogeneous tubular reactor when the influence of the reactor wall is taken into account. Hydrogénation of C O . Figure 8 shows a maximum in the rate of C O hydrogénation as a function of C O content in the feed. Thus, the response of the reactor to a step change in C O concentration should differ from the response to a step change in the C 0 content of the feed; an increase of C O concentration causes the rate of hydrogénation to decrease when the partial pressure of C O is above p . The maximum in the C O hydrogénation rate found by Van Herwijnen et al. (7) is confirmed by the pilot plant experiments, as follows from the stationary temperature profiles in Figure 9 at various inlet 2

m a x


350 SV = 15750 hr~ T = 201 C C =o 0-66 % CO

/*

1

e

/

jn

/

in

An.Qft«»/

χ Δ

/

e

/j / /

1 -38% „ 1 -97 % „

C

X

>

ο

200,

1

0

0-5

10

Figure 9. Stationary axial temperature profiles for CO hydrogénation (lines: calcuhted; points: measured)

300

-

η

η

η

η

β /

250 Aw

ο

C * 1-21 — • 0·64·/β CO SV* 16000 hr~ T = 210«C ο OS 7 30S χ 78S Δ 350 S i n

Àûyo

1

ln

200

I

0

05

10

~ λ Figure 10. Axial temperature profile after a type 3 disturbance (CO hydrogénation; lines: calculated; points: measured) Hulburt; Chemical Reaction Engineering—II Advances in Chemistry; American Chemical Society: Washington, DC, 1974.

37.

VAN DOESBURG AND DE JONG 300

-


501

C = 0-59% CO SV = 16000 hr-1 Tjn = 2 2 8 - * 199 °C


i n

400

200 t (sec)

10

Figure 11. Inlet temperature and axial temperature profile for CO hydrogénation observed after a type 3 disturbance (lines: calculated; points: measured) concentrations of C O . The typical behavior of the rate of C O methanation is also reflected in the response to a type 2 disturbance. When the C O concentration in the feed is lowered from 1.21 to 0.65%, the temperature in the front end of the catalyst bed increases because the reaction rate increases (Figure 10). Note also that the temperature in the second part of the bed then becomes lower. The agreement between theory and experiment is also satisfactory for type 1 disturbances. For type 3 disturbances, it is difficult to predict reactor behavior because the exit temperature change is a composite of, e.g., decreasing inlet temperature, increasing concentration, and decreasing rate of hydrogénation. A typical example is shown in Figure 11. Discussion The good agreement between calculated and measured temperature profiles shows that non-linear effects other than the dependence of concentration and temperature on the methanation rate need not be taken into account in the parameter space investigated. The question can now be answered as to how soon after a sudden increase of the C 0 concentration in the feed the temperature of an industrial methanator reaches a maximum. The experiments and calculations for methanation at atmospheric pressure show that the new stationary state of the reactor is reached within a few seconds when the reactor inlet temperature exceeds 2 5 0 ° C . In practical applications, however, the pressure is usually much higher than atmospheric (cf., Table II). The effect of pressure on the rate of C 0 hydrogénation can be estimated from laboratory experiments which show that the reaction rate of 1% C 0 in H at 2 0 8 ° C increases by a factor of 1.7 when the pressure is raised from 1 to 10 atm. Thus, response times of 1-2 sec must be expected in industrial methanators. 2

2

2

2


502


350

Cin

300

SV = 15500 hr~

c o

=0.2lo

II

/ o

T = 211 »C in

1

υ 250


/ 200

10

0-5

Figure 12. Measured stationary axial temperature profile for the hydrogénation of a mixture of carbon oxides in hydrogen There are, however, two important differences between our experiments and industrial methanation. First, the effect of the heat capacity of the reactor wall is much smaller industrially than with our pilot methanator. In the latter case the thermal capacity of the reactor wall is almost equal to the capacity of the catalyst bed; this means that the small reactor responds more slowly than an industrial reactor. Secondly, feeds to industrial reactors used in making ammonia synthesis gas or hydrogen invariably contain both C O and C 0 . Since previous work has shown (7) that C O inhibits the hydrogénation of C 0 until the C O concentration has decreased to about 200 ppm, the response to an increase in C 0 concentration is noticeable only in the second part of the reactor—i.e., after C O has been hydrogenated. This causes the response time to step change in C 0 concentration to be much shorter when the feed also contains C O . The reactor behaves as if the first part of the bed in which C O is hydrogenated does not contribute to the changes; in other words, the response of the second part is similar to that of a reactor with an inlet temperature equal to the temperature of a C 0 / H feed plus the adiabatic temperature rise caused by the conversion of C O . An example of a measured stationary profile is given in Figure 12. At the time of writing only a few experimental results with feed consisting of C O , C 0 , and H were available. These data confirm that with C O present the response of C 0 is faster than in the absence of C O . Further work with mixed feeds is in progress. 2

2

2

2

2

2

2

2

2

Nomenclature

A A ,A ,A iy

2

B , B* c C c C x

tot

o g

3

é

dimensionless constants dimensionless constants concentration, moles/m dimensionless concentration total concentration, moles/m specific heat of gas, kcal/mole/°Κ 3

3


37.


c

Fixed-Bed

503

Methanator

specific heat of catalyst, k c a l / k g / ° K specific heat of wall, kcal/kg/°K specific heat pseudo-homogeneous medium, k c a l / m / ° K cat

Ôcat ^flwall

3

d

Pe,

particle diameter, m activation energy, kcal/mole frequency factor, m /kg /sec adsorption equilibrium constant, m /mole heat of adsorption, kcal/mole heat of reaction, kcal/mole running variable in reactor length, m reactor length, m axial Péclet number

Pe

axial Péclet number for heat transport =

r

gas constant, kcal/mole/° Κ inner tube diameter, m outer tube diameter, m reaction rate, moles/kg /sec Reynolds particle number cross-sectional area of cylindrical reactor, m temperature, °K or ° C inlet temperature, °K or ° C dimensionless temperature time, seconds superficial gas velocity, m /m /sec

2

O

Ea

Κ

3

κ»

3

AH°

r

I


L

uc C d tot

H

R #in ôut r

Re

cat

D

S

Τ T Τ

in

t u

pe

O

cat

3

2

Greek Symbols viscosity of gas, kg/m/sec V ε porosity of catalyst bed density of catalyst bed, k g / m Pbed density of wall material, kg/m Pwall Τ dimensionless time variable λ dimensionless reactor length c a t

3

3

Literature Cited 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.

Beek, W. J., Symp. Chem. React. Eng., 5th, Amsterdam 1972, review section 4. Froment, G. F., Symp. Chem. React. Eng., 5th, Amsterdam 1972, review section 5. Ray, W. H., Symp. Chem. React. Eng., 5th, Amsterdam 1972, review section 8. Slin'ko, M. G., Brit. Chem. Eng. (1971) 16 (4/5) 363. Matros, Yu. Sh., Kirillow, V. Α., Slinko, M. G., Proc. IFAC Symp. DISCOP, Gyor, Hungary, Sept. 1971, paper M3. Beskov, V. S., Vyatkin, Yu. L., Proc. IFAC Symp. DISCOP, Gyor, Hungary, Sept. 1971, paper B6. Van Herwijnen, T., Van Doesburg, H., De Jong, W. Α., J. Cat. (1973) 28, 391402. Anderson, J. B., Chem. Eng. Sci. (1963) 18, 147. Chu, C. J., Kalil, J., Wetteroth, W. Α., Chem. Ens. Progr. (1953) 49, 141. Petrovic, L. J., Thodos,G.,Ind. Eng. Chem., Fundamentals (1968 ) 7, 274. Kunii, D., Smith, J. M., A.I.Ch.E. J. (1961) 7 (1) 29. Carberry, J.C.,Wendel, M. M., A.I.Ch.E.J.(1963) 9 (1) 129.


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CHEMICAL REACTION ENGINEERING II


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