Temperature and Concentration Gradients In a Catalytic Packed Bed

34 Temperature and Concentration Gradients In a Catalytic Packed Bed Reactor

Chemical Reaction Engineering—II Downloaded from pubs.acs.org by CORNELL UNIV on 05/18/17. For personal use only.

N. G. KARANTH and R. HUGHES Department of Chemical Engineering, University of Salford, England

Temperatures and concentrations were measured during the exothermic catalytic reaction between hydrogen and toluene in an experimental packed bed reactor. A nickel catalyst was used as cylindrical pellets 6 mm in diameter. Transient and steady-state measurements were made of both intraparticle and bed temperatures. The intraparticle temperature measurements showed that the assumption of an isothermal pellet was valid for most of the experimental range investigated but that large interphase temperature rises could occur. Attempts were made to model the system using standard procedures, but these predicted higher temperatures than were observed experimentally. Good agreement with the experimental results was obtained when the limiting non-key component effect was incorporated into the model.

P

acked bed catalytic reactors are used extensively in the chemical and process industries, and prediction of their behavior has resulted in many modeling studies. Because of the complicated interaction between diffusion, heat transport, and chemical reaction, coupled with the system hydrodynamics, the models must be complex if realistic predictions are to be obtained. It is also important to have experimental verification of theoretical models. Although studies on heterogeneous catalysis in packed bed reactors have been reported (1, 2, 3, 4), they have been few and have not generally kept up with theoretical developments. Therefore, there seemed to be a real need for experimental measurements of temperature and concentration in packed bed reactors. In the present work temperature measurements were made both within the catalyst particles and in the external field of the bed for the nickel-catalyzed hydrogénation of toluene; bed concentration profiles were also determined. Models for a Packed Bed Reactor The transient behavior of the packed bed reactor was modeled in two ways. In the first, pseudo-first order kinetics were assumed for the reaction, no account being taken of the low fractional order in toluene found experimentally (5). The second method used the limiting non-key component concept. This has been described in detail for single particles, and with certain simplifying assumptions it can be extended to packed beds. 449

450

CHEMICAL REACTION ENGINEERING

II

The complete set of equations for a non-adiabatic reactor with pseudofirst-order kinetics can be written in dimensionless form as: For the single particle exp [

V'Cp* -

(l

7

V ? V + φ*£ C * exp [


2

p

where

(l

7

^

-

-

iVi = 4 ^ D ,L A

)

(1)

] = ΛΓ,

-L;)]

=

(2)

N

2

iY = 4 K L 2

e

e

with the boundary conditions θΤ *| - 0 dy \y=0 ρ

y=0

a?/

,=i

ay

=

N

*[

u

T

*L=i- *] T

p

-ac * p

and for the external field 1 d d C* Pe L as

aC*

-

α' (τ*

2

p

(3)

2

M

Pe

H

L dx

2

dx

-

)

ίΓρ*|

+ TFF(T *-T*) W

=

a**

(4)

where α

a hL

2KL

v

=

#te2ttp Cg g

with the boundary conditions dC*

dT* = 0 dx I 2 = 1

dX x = l

* = 0,

-ac* ^!=Pe ^(c*| M

dx

-dT* - Pe dx

B

x = 0

_

( *|x=oT

The limiting non-key component effect is described in detail elsewhere (6, 7); only the salient features are presented below. Consider the reaction A + nB — > Products s

If component Β is much less than the stoichiometric ratio and its diffusivity is also less than that for A, this limiting component would be expected to be exhausted before reaching the center of the catalyst pellet. Such a situation occurs in many hydrogénation reactions including the work described here. Using this concept, the dimensionless material and energy balances for a single

34.

KARANTH AND HUGHES

451

Catalytic Packed Bed Reactor

particle many be combined, utilizing the modified Prater relation which includes finite film effects (8) to give: dT* dy* 2

p

2 dT

(

Y

Sh*J

(J \

(5)

with the boundary conditions dT *\


P

dy Now,

=

0

dT *

= Nu*(l - T *)

p

t

I y=\

(6)

8

dy y = i

redefining a radial coordinate

where λ is the radius of the unreacted core. Equations 5 and 6 are transformed as 1 dT* (1 - λ ) d? 2

2 1 (λ + (1 - λ)ξ) (1 - λ) άζ

p

2

Nu*

j

d

-?f|

=0 = ' 0

S

|

ξ =

1

TeV

NU*\

=Νπ*(1-λ)(1-Γ *) 8

Τ»*)

(9)

The limiting non-key component effect is accounted for by the parameter φ where CAO Π*

7)eA

Thus, as C (the limiting component) increases, the value of ψ decreases and approaches zero as C approaches C n D /D . The temperature at the junction of the reactive outer shell and the inert inner core is then given by the dimensionless form of the modified Prater relation B o

B o

ξ = ο, Τ* = ( β +

Ao

8

eA

+ (l -

eB

T V - βΨ

(10)

The limiting non-key effect as described above applies only to single particles. Effectiveness factor values are reduced almost 20 times when ψ = 0.81. The most obvious way to take this factor into account is to apply a suit able correction factor in the reaction rate term in the mass and energy balance equations of the packed bed reactor. This factor is based on the limiting non-key component effect on the first particles at the entrance with an average reactor temperature and is equal to the factor of reduction of the effectiveness factor at this point. This uniform average correction factor is assumed to apply throughout the length of the bed. Both models were solved using the orthogonal collocation method as described by Villadsen and Stewart (9). Experimental Kinetics. Kinetic data were obtained in a small differential reactor using powdered catalyst material (coprecipitated nickel (55%) on silica), diluted

452


II

with an equal part of inert silica carrier. The results are reported in detail elsewhere (7); briefly they conformed to the following expressions Below 170°C R* = 0.1815 e~ ^ l

RT

Above 170°C R* = 6.49 X 10"° e ^


l

pn ρ τ

RT

0 2 4

pn ρ · τ

0

24

Packed Bed Reactor. The reactor was a preheater section packed with stainless steel turnings and raschig rings mounted above a catalyst bed. The latter was 300 mm long, 41 mm diameter and was packed with 4.8 mm equant cylindrical silica-supported nickel catalyst pellets. Two instrumented pellets containing embedded thermocouples were positioned at dimensionless bed depths of 0.17 and 0.31 respectively. These pellets were as dense as normal ones but were slightly larger (6 mm X 6 mm). Unfortunately, during reactor packing the small diameter thermocouple wires (0.025 mm) in the pellet at the lower position (x = 0.31) were broken so that intraparticle temperature measurements were available only for the upper position. A movable capillary sampling probe was situated on the axis of the reactor, and gas samples were analyzed using an MS 10 mass spectrometer. Bed thermocouples were located

T, * t63 5 *C

0/

01

03 Axt'ol

Figure 1.

04

OS

06

07

~oë

2&

distance , x

Transient axial bed temperature profiles. High reactivity—effect of toluene introduction.

34.

KARANTH AND HUGHES


453

Ζ -32'C F, *t 34*10* m'/sec


0

0

Figure 2.

3

0

4

O

S

Αχ/αί distance,*

Transient axial bed temperature profiles. Lower reactivity—effect of toluene introduction.

at five positions close to the central axis including the entrance, and radial tem peratures were measured at the two planes χ = 0.17 and χ = 0.31, with three thermocouples in each plane. The estimated maximum error of the chromelalumel bed thermocouples was 1 ° C . That of the intraparticle thermocouples was also within this range since conduction losses were minimized by the use of 0.025-mm wire. Originally the reactor was intended to be operated adiabatically so that heating was placed around the preheater only, the bed section having lagging only. Initial experiments showed that this ideal was not achieved, and small radial heat losses were occurring. This accounts for the gradual drop in axial temperature obtained in the bed under non-reactive conditions. ±

Results Transient Bed Temperature Profiles. HIGH REACTIVITY, HIGH INLET TEMPERATURE. Figure 1 shows the transient temperature profiles in the axial direction in the external field when the vaporized toluene is introduced into


454

II

the entering hydrogen stream at a time t = 0 min. In the first two minutes the profile moved relatively slowly, but then the temperature buildup at all points in the reactor was swift. Initially (t < 8 min) the temperature at the reactor entrance (shown by the thermocouple at χ = 0.17) attained a high value first, and the section further down the bed responded more slowly. However, at a later time (t > 8 min) the temperatures in the region closer to the exit responded much faster, and those in the entrance section climbed only ?9 r" ^ 7


— -π

RADIAL DISTANCE, r *

Figure 3. Transient radial bed temperature profiles at χ = 0.17 and x = 0.31 (corresponding to axial profiles of Figure 2)

34.

KARANTH AND HUGHES


455

slowly. After 40 minutes the profile was virtually equal to the steady-state values, and the maximum temperature was stationary at the reactor entrance whereas the exit temperature slowly approached the entrance temperature level. At the steady state, the total temperature drop from entrance to exit was only about 5 ° C .


The radial temperature profiles corresponding to the axial profile of Figure 1 were determined at dimensionless bed depths of 0.17 and 0.31 at radial positions r* of 0.12, 0.59, and 0.86. At steady state the central two thermocouples recorded identical temperatures while the junction at r* = 0.86 was only 6 ° C lower, thus justifying the lumped wall heat transfer assumption. Low INLET TEMPERATURE. Figure 2 shows the transient response of the system when toluene is admitted, the entrance temperature now being lower than earlier ( 9 2 ° C ) . In this case the temperature maximum was developed at a point inside the reactor and moved towards the exit. Initially (t ^ 2 min) the temperatures started rising more slowly compared with the high entrance temperature case, the largest increases being registered in the entrance section. At t = 2 min, the temperature continuously decreased from the entrance to the exit. However, at t = 4 min, a temperature maximum had developed at about χ = 0.4. This maximum moved gradually towards the reactor exit. The temperatures at all reactor positions increased continuously with time except for the final steady state) but with different speeds. In the initial period the rate of temperature rise at χ = 0.7 was the highest. This zone of highest rate of increase gradually moves towards the exit with time. After t = 30 min, the temperatures in the entrance regions started declining slowly, probably because of the decrease in the inlet temperature. At the steady state the temperature profile increased steeply from entrance to exit. The radial temperature transients corresponding to the above case (Figure 3) show that the temperature rise at χ = 0.17 is quite small and occurs in the initial period whereas at χ = 0.31 the temperature rise is larger and spread over a longer time interval. At both positions the character of the radial tem perature profiles remained unchanged through the transients. Intraparticle Temperature Measurements. The pellet in which 0.025 mm Pt-13% Rh-Pt thermocouples were embedded was positioned at the same axial distance as the first set of external thermocouples (x = 0.17). The cylin drical pellet was placed upright, and the center of the pellet was approximately 8 mm from the center of the bed. The thermocouples in the pellet were situated at dimensionless radial distances (r/R) of 0.25, 0.73, and 0.98. The last ther mocouple was situated so close to the surface of the pellet that readings there can be regarded as surface temperatures. For the high inlet temperature corresponding to the axial profiles of Figure 1 there was virtually no temperature gradient within the particle, all three thermocouples recording the same temperature. This was achieved rap idly (in about 8 minutes). The interphase gradient was appreciable however, reaching a peak of 41 °C before decreasing slightly at the steady state. The intraparticle temperature profiles at a lower entrance temperature of the reactor are shown in Figure 4. The toluene composition was the same as in the last case. In this case temperature gradients developed within the particle. Within one minute the temperature close to the center had risen by about 14.5°C and that close to the surface by about 1 1 ° C , establishing intra particle gradients. This gradient increased slightly in the later stages, and the

456


II

β. ΊB4 *t0 m'/sec 4


150-

90 -

80-

70 -

Ο

02

Ol Radiai

Figure 4.

0~6

OB

/

d/'shnce , y

Transient intraparticle temperature profiles

final temperature difference between the center and the surface was about 9 ° C . The character of the profile changed little with time. Interphase and Intraparticle Temperature Rises. The transient variations of the intraparticle and interphase temperature rises are plotted in the upper part of Figure 5 for the high reactivity case. There was a rapid interphase temperature rise in the beginning, which peaked and then slowly dropped. The intraparticle temperature rise, however, was slightly negative in the begin ning but quickly (within 20 min) settled down to a negligible value, showing the isothermal nature of the particle. Figure 5 also shows the transient response when the feed is at a lower temperature level and toluene is introduced into the feed stream. Here again, the interphase temperature rise increased rapidly in the beginning, reached a maximum, and then slowly decreased. The intra particle temperature rise on the other hand, rose more slowly and to a much lower maximum and then decreased slightly to settle at a lower level. On the whole, the steady-state temperature within the particle is attained much faster than the interphase steady state. The latter is more gradual but higher in magnitude.

34.

KARANTH AND HUGHES


457


AT. 169^5 »C

TIME, MIN

Figure 5. Interphase and intraparticle temperature rises corresponding to inlet temperatures of 169.5° and 92°C Steady-State Concentration Profiles. Concentration profiles were measured by moving the tip of the capillary sampling probe along the axis of the reactor. For convenience, the concentrations were measured at every 25-mm length. Only steady-state profiles were measured because of the lengthy operation in moving the capillary to different axial positions. Figure 6 shows the effect of a change in the toluene concentration of the feed from 6 to 10%. At 6% a large part of the reaction takes place in the early part of the bed and remains almost constant in the later sections. At the higher concentration, the reaction takes place at a greater distance from the entrance, indicating that the reaction zone has moved towards the exit. The conversion in the latter case is slightly more than in the first case. Discussion Figures 1 and 2 show the effect of bed reactivity on the axial temperature profiles. For the high inlet temperatures of Figure 1 the reaction was so fast

458


II


that the zone of highest temperature was located near the reactor entrance throughout the whole run. The temperature increases in the inlet region were very fast initially whereas those at the outlet responded more slowly. This is because of the finite time required to heat up the particles along the length of the bed so that for positions further down the bed a correspondingly larger time is required. The expected hot spot in the reactor appeared when the entrance tem perature of the feed was lowered to 9 2 ° C (Figure 2). The temperature rise was now faster in the entrance section and later in the section near the outlet.

77* 75 c* F *t37*/0*m /sec 3

fo

2 -

01

_k

_L_

I

Ax/al distance

Figure 6.

_ l _ t

gl_

_L

_L_

χ

Steady-state axial concentration profiles. Effect of feed composition.

This similarity to the profile shape in an adiabatic reactor is the result of the small amount of wall heat transfer present. The radial temperature profiles confirm these effects. For the high inlet temperature the particle temperature profiles were flat. Under these conditions the chemical reaction resistance is negligible; thus, the external transport resistances predominate, causing the pellet to be isothermal, even in the transient state. Intraparticle gradients appeared only at lower feed


34.

Ό

Of

02

03

04

AXÏQI distance,

Figure 7.

459


KARANTH AND HUGHES

OS

06

07

06

09

χ

Comparison of theoretical and experimental axial bed temperature profiles at steady state

temperatures, but these were much smaller than the interphase gradients. Figure 5 shows that although the interphase temperature rise was greater than the intraparticle, the latter occurred more quickly. This is probably caused by the higher thermal conductivity of the particle. Experimental vs. Simulated Results. Transient and steady-state tempera ture and concentration profiles were calculated for some experimental runs using the non-adiabatic model with pseudo-first-order kinetics and the approxi mate method based on the limiting non-key component concept. The parame ters required for the theoretical model were determined experimentally where possible (pore volume, pore size distribution, effective thermal conductivity, etc. ) ; otherwise they were estimated using standard formulas available in the literature. For the kinetic rate expression, a single activation energy and fre quency factor could not be used because an inversion temperature existed for the reaction. Therefore two different sets of frequency factors and activation energies for the two temperature ranges ( Γ ^ 170°C and Γ > 1 7 0 ° C ) were used.


460


0L δ

Figure 8.

ι

ai

j

02

ι

j

ι

03 ai os Axial distance, *

i_

ol>

ι

ι

oï

oë

II

ι

09

Comparison of theoretical and experimental axial bed temperature profiles at t= 10 min

The computed steady-state axial temperature profiles, with and without the limiting non-key component effect, are compared with the experimental axial profiles for an inlet temperature of 92°C in Figure 7. The simulated profile based on the non-adiabatic model with pseudo-first-order kinetics gives a high temperature peak at χ = 0.3, which is not obtained experimentally. This peak is also about 2 0 0 ° C higher than the experimental value at this point. The temperature profile based on a limiting non-key component gives much better agreement with the experimental values. A similar result is also found when the transient profiles are compared for the same initial conditions (Figure 8). Thus a closer approach to the measured profiles can be obtained using this model. For the computations seven collocation points in the external field and three in the pellet (including the boundary points) were used. More collocation points would no doubt refine the calculations and possibly give less deviation between curves 2 and 3 in Figures 7 and 8. Nevertheless the marked disparity between the pseeudo-first-order kinetic model and the exprimental curve would

34.

KARANTH AND HUGHES


461

still exist. Closer agreement between the experimental and limiting non-key component model would probably be obtained if the latter effect was incorpo rated directly into the reactor equations instead of using the effect to modify the particle effectiveness factors as was done here. Nomenclature a c c C* ( C * ) v

g


s

p

surface area of catalyst per unit volume of bed average specific heat of gas specific heat of solid dimensionless concentration in bulk fluid, C / C ( particulate phase, 0

Cps/Co)

d D h h k K L Nj, Ν Nu* PH> ΡΎ Pe (Pe ) R* Sh* t* Τ* ( Γ * ) p

e

w m e

2

M

H

ρ

diameter of catalyst particle effective diffusivity of catalyst particle heat transfer coefficient, bulk phase to particle surface wall heat transfer coefficient mass transfer coefficient effective thermal conductivity of catalyst particle reactor length defined by Equation 2 modified Nusselt number, hR/K partial pressure of hydrogen, toluene longitudinal Peclet number for mass (heat) dispersion reaction rate modified Sherwood number, k R/D dimensionless time, tu/h dimensionless temperature in external field, T/T (particulate phase, T / T ) temperature at particle surface interstitial gas velocity dimensionless axial distance, z/L dimensionless radius in particle, r/R c

m

0

p

T u χ y

s

e

0

Greek Letters a, a β γ «i(e ) Pg(Ps) ξ λ 2

defined in Equation 4 thermicity factor, (-AH)D C /KJ activation energy parameter, Ε/R T void fraction of particle (bed) average gas (bulk-solid) density modified radial coordinate in the pellet, (y — λ ) / ( 1 — λ ) radius of unreacted core e

0

0

e

a

Subscripts A, Β ο ρ ps Τ

components A and Β in binary mixture (specifically Β = toluene) conditions in the bulk fluid for single particle; conditions at entrance for packed bed reactor particle particle surface toluene

Literature Cited 1. Maymo, J. Α., Smith, J. M., AIChE J. (1966) 12, 845. 2. Hawthorn, R. D., Ackerman, G. H., Nixon, A.C.,AIChE J. (1968) 14, 69.

462

CHEMICAL REACTION ENGINEERING II

3. Richarz, V. W., Lattmann, M. A. S., Symp. Chem. Reaction Eng., 4th, Brussels, 1968. 4. Yamazaki, T., Noguchi, Y., Akazuka, T., Iwamuru, T., Otani, S., Kagaka Kogaku (1970) 34, 402. 5. Karanth, N.G.,Koh, H-P., Hughes, R., Chem. Eng. Sci. (1974) 29, 451. 6. Gioia, F., Greco,G.,Gibilaro, L.G.,Chem. Eng. Sci. (1970) 25, 969. 7. Karanth, N.G.,Ph.D. thesis, Salford University (1973). 8. McGreavy, C., Cresswell, D. L., Can. J. Chem. Eng. (1969) 49, 583. 9. Villadsen, J. V., Stewart, J. M., Chem. Eng. Sci. (1967) 22, 1483.


RECEIVED January 2, 1974.

Temperature and Concentration Gradients In a Catalytic Packed Bed

Recommend Documents