A Trickle bed Process for Hydration of Isobutene to Tert Butyl Alcohol

Prévia do material em texto

The Chemical Engineering Journal, 37 (1988) 43 - 52 43 
A Trickle-bed Process for Hydration of Isobutene to Tert-Butyl Alcohol: 
a Study of Reactor Performance 
E. CkERES, L. PUIGJANER and F. RECASENS 
Dept. of Chemical Engineering, Universitat Politknica de Catalunya, Diagonal 647, 08028 Barcelona (Spain) 
(Received June 30, 1986; in final form June 29,1987) 
ABSTRACT 
In this work a new process for hydrating 
isobutene-rich feeds to tert-butyl alcohol 
(TBA) is presented. The study aims at finding 
the best operating conditions for a trickle- 
bed reactor employing one pass of gas and 
liquid recycle for a specified production of 
100,000 t TBA per year. We use Amberlyst- 
15 ion-exchange resin as a catalyst, for which 
intraparticle effects as well as mass tmnsfer 
coefficients in trickle-bed operation are avail- 
able. The best recycle rates and temperatures 
are found by making a compromise between 
enhanced isobutene solubility caused by high 
alcohol concentration and a decrease in rate 
owing to the reverse reaction. 
1. INTRODUCTION 
In this paper we present a new tert-butyl 
alcohol (TBA) process using direct hydration 
of isobutene-rich feedstocks in a cocurrent 
downflow trickle-bed reactor. This type of 
reactor would be an alternative to processing 
in liquid-liquid reactors with catalyst recycle 
[l] or to single liquid-phase packed-bed 
reactors with [2,3] or without cosolvent 
141. 
Traditionally, selective removal of iso- 
butene (IB) from butenes has been carried 
out by absorption into H,SO, [5, 61. How- 
ever, processes using heterogeneous catalysts, 
such as acidic ion-exchange resins, seem 
more practical as they avoid corrosion prob- 
lems. Yet trickle-bed processes are known 
to be in commercial operation for propylene 
hydration to isopropyl alcohol [7, 81 under 
conditions that favour higher thermodynamic 
conversion and reaction rate. 
0300-9467/88/$3.50 
A trickle-bed process for direct hydration 
of IB would be interesting in that high water/ 
hydrocarbon ratios shift the equilibrium fa- 
vourably at relatively high temperatures, 
hence increasing the reaction rate. Also, since 
the formation of di-isobutene as a by-product 
is expected to be a competitive second-order 
reaction, its rate would be retarded because 
of the lower dissolved concentrations of IB 
and because of the low operating tempera- 
tures. This should result in higher selectivities 
toward the desired product, TBA. 
The resin Amberlyst-15 (Rohm & Haas) 
was chosen as the most appropriate catalyst 
for the process. This is a macroporous sul- 
phonic-type ion-exchange resin for which 
intrinsic kinetic data are available [ 91. 
Further work on intrinsic kinetics [lo] 
indicates that the presence of TBA inhibits 
the rate more than one would expect from 
the values of the chemical equilibrium con- 
stant available in the literature [ll - 131. 
Over the range of operating alcohol concen- 
trations, the direct reaction is pseudo-first- 
order in dissolved IB and the reverse reaction 
is linear in alcohol concentration. The ratio 
of the rate constants for the forward and 
reverse reactions compares well with the mea- 
sured equilibrium constant only at tem- 
peratures above 333 K [lo]. In summary, 
by using an intrinsic kinetic expression linear 
in both IB and TBA, standard methods can 
be applied to calculate the effectiveness 
factor for a reversible reaction [ 141. 
In order to predict the performance of a 
trickle-bed reactor, solubility data are neces- 
sary for the limiting gas reactant in the liquid 
mixture. In earlier work, Leung et al. [15] 
correlated the solubilities of IB with both 
temperature and alcohol concentrations for 
the ranges of interest. 
@ Elsevier Sequoia/Printed in The Netherlands 
44 
The purpose of the present study was to 
explore the best operating conditions for an 
adiabatic-type, trickle-bed reactor for the 
direct hydration of C, olefin with water. 
Various opposite effects are present owing 
to the kinetic and solubility behaviour of the 
system. On one hand, high alcohol concen- 
trations in the liquid would favour higher 
dissolved IB leading to a high direct rate of 
reaction because of a concentration effect. 
Also, low temperatures would enhance both 
solubility and catalyst effectiveness factors. 
Therefore a high liquid recycle rate would 
be recommended. On the other hand, how- 
ever, as the recycle rate is increased the 
reverse reaction will also be favoured. The 
precise effects of liquid recycle on the ob- 
served rate will depend on the relative im- 
portance of kinetics on the global rate of 
reaction. For instance, previous work indi- 
cates that liquid-to-particle mass-transfer 
resistance is relatively unimportant as it 
accounts only for about 20% of the observed 
resistance in a differential trickle-bed reac- 
tor [9]. 
The interest of this study is to see which 
parameters require a more careful examina- 
tion for setting up a trickle-bed reactor 
model. Particular emphasis is given to the 
effects of liquid recycle and operating tem- 
peratures. 
2. TRICKLE-BED REACTOR SIMULATION 
The scope of the design conditions is sum- 
marized in Table 1 where catalyst data and 
reactor operating conditions are given. For 
the integral trickle-bed reactor, it will be 
assumed that both liquid and gas travel in 
plug flow. While the axial dispersion of the 
gas is probably negligible in a trickle-bed 
reactor [ 161, the axial dispersion of the liq- 
uid is not so. However, Goto and Smith 
showed [17] that the uncertainties in inter- 
phase mass transfer coefficients are far more 
important in reactor performance than the 
effect of liquid dispersion. 
We will also assume liquid-filled catalyst 
pores and that the external surface of the 
catalyst is fully wetted by the liquid flow. 
This is a critical assumption whose effect on 
the overall rate depends on a number of 
factors. Thus, Herskowitz et al. [ 181 showed 
TABLE 1 
Scope of design conditions for 100 000 t year-’ TBA 
General 
Feedstock Ca cut from steam cracking 
IB content 45% 
Isobutene conversion 98% 
Molecular weight of gas 56 kg kmol-’ 
Liquid density lo3 kg me3 
Catalyst data 
Name Amberlyst-15 wet 
Average particle size d, = 0.7 mm 
(wet) 
Bulk density pn = 370 kg mm3 reactor 
Bed porosity eg = 0.35 
Particle density pp = 930 kg mW3 particle 
Trickle-bed reactor 
One pass of gas, liquid recycle allowed, adiabatic type 
Maximum h’/L 0.5 bar m-r 
Liquid/hydrocarbon 15 mol mol-’ 
ratio 
Superficial velocities UL~ = 2.7 X lop3 m s-l 
(at inlet conditions) use = 2.76 x lo-* m s-l 
that if the intrinsic rate was faster than the 
interphase mass transfer rates, the effect of 
partial wetting was to increase the observed 
reaction rate in the range of low liquid vel- 
ocities where partial wetting occurs. How- 
ever, if the reaction is intrinsically slower, 
mass-transfer resistances at the gas-liquid 
and liquid-solid interphases are not signifi- 
cant. In such cases, partial wetting does not 
affect the rate appreciably. Furthermore, 
the effect of partial wetting is implicitly 
accounted for provided that proper mass 
transfer coefficients, i.e. those determined 
under the same wetting conditions and fluid 
velocities, are used in the calculations. 
In order to choose the operating super- 
ficial velocities given in Table 1, we used the 
generalized Charpentier-Favier plot [ 191. 
This allowed us to locate the ranges of mass 
flow rates for the trickling-flow regime. When 
setting up a liquid-to-hydrocarbon ratio of 
15 (mole basis) as reported in other hydra- 
tion processes [ 1 - 31, the plot requires that 
G = 0.5 kg rnw2 s-’ and L = 2.67 kg mm2 SK’ 
or ugo = 2.76 X 1O-2 m s-l and uL= 2.7 X 
10e3 m s-l. 
2.1. Conservation equations 
The isothermal isobaric plug-flow case 
will be considered first. Let the conversion 
of IB at a bed length 2 be defined as 
x 
B 
= (%3oGJgo- %dh) 
~go%go 
(1) 
The gas velocity will change according to 
us = usO(l + EXB)(2) 
where E = -0.45 for a steam cracking feed. 
From (1) and (2), IB concentration at 2 is 
c 
Bg 
= CBgo(1 -XB) 
(1 +EXB) 
(3) 
The mass conservation equations for IB in 
the gas and liquid phases are, respectively 
(=B 
- $b&Bg)= UgOCBgO z 
= #L"L)B 
1 
cBgO(l -XB) 
HB(1 + EXB) 
-cBL (4) 
cBgO(l-xB) _c 
H,(l + EXB) BL 
- (b&(Cm - CBS) (5) 
In eqns. (3) and (4) it is assumed that gas 
and liquid IB concentrations are related by 
a Henry’s law constant Ha and that the mass 
transfer rate is liquid-side controlled. For 
the desorption of TBA into the gas stream 
it is assumed that most of the resistance is 
in the gas-side film. Hence, TBA conservation 
in the liquid phase requires that 
dC.a 
uL dz - = (k&,)A(CAs--AL) 
-(kgaL),(CAL&--Ag) (6) 
where HA is the Henry’s law constant for 
TBA vapour. The conservation of TBA in 
the gas phase will be 
-& (ugcAg)= (kgag)A(CALHA--Ag) 
Performing the above differentiation 
ug given by eqn. (2), eqn. (7) becomes 
d&g 
ug dZ - = (kg'Jg)A(CALHA--CAg) 
(=B 
-cAgEUgO - 
dz 
(7) 
with 
(3) 
where dX,/dZ is substituted from eqn. (4). 
Mass transfer rates of IB and TBA at the 
liquid-solid interphase should balance in- 
45 
trinsic rates. Thus, for linear reversible ki- 
netics 
(k,%)A(CAs- CAL) = Psrl(k1%s--k2CAs) (9) 
(ks%)B(CBL --c,) = ,wdk1Gis-WJAs) (10) 
where 7 is the isothermal effectiveness factor 
of a sphere for a reversible reaction. r) takes 
the usual form [14] 
coth 34 - ?_ 
34 
with the Thiele modulus defined as 
(11) 
(12) 
where it is assumed that (De)A = (De)B. 
Integration of eqns. (4) - (8) will provide 
the profiles CAL, CAg, CaL and Xa (or C,) 
US. 2. The solution of the algebraic system 
of eqns. (9) and (10) at each integration step 
provides the point values of C,, and CBS. The 
initial conditions for the above system, for 
Z=O,are 
xg=o CAL= CAL0 C 
CBPJ 
BL= - 
HB 
CA, = CALOH, (13) 
These assume that the gas and liquid feeds 
are in equilibrium with respect to both IB 
and TBA. As discussed later, the effect of 
liquid recycle is to change CALa and CsLo 
at the entrance to the bed. 
A fourth-order Runge-Kutta algorithm is 
used to obtain the concentration profiles. 
Precision of integration is ensured by a short 
step size and checked by an overall mass 
balance on IB converted us. TBA formed at 
every bed length. For the non-isothermal 
case, T US. 2 is checked analogously by an 
overall heat balance. 
2.2. Allowance for adiabatic operation and 
pressure drop 
For simplicity of construction, an adiabatic 
reactor will be recommended. This mode of 
operation will affect the reactor model as 
follows. Neglecting interphase temperature 
gradients in view of the rather small catalyst 
particles and the slow reaction rate, a differ- 
ential heat balance at 2 over a unit super- 
ficial area, gives 
46 
dT/dZ = 
PI?rl(~lCBs - wJ*&- w 
WMPL + %&&, 
(14) 
with T = TO for 2 = 0. Now, the system of 
eqns. (4) - (13) will be augmented with eqn. 
(14) for integration. It is anticipated how- 
ever that because of the high L/G ratio the 
adiabatic temperature rise will be only about 
16 K. Even though this is not large, the sol- 
ubilities of IB as well as the direct and reverse 
kinetic constants are strongly sensitive to 
temperature variations. For the rest of the 
parameters that are not particularly sensi- 
tive, mean values can be taken. 
Because the catalyst size is small, the pres- 
sure drop along the reactor length can be 
large. To account for pressure changes along 
the bed only frictional losses will be con- 
sidered, disregarding the static head loss. 
Therefore 
AD 
LU 
-_= 6 
dZ ‘= 
(15) 
where 6,, is the two-phase flow pressure 
drop evaluated from single-phase flow losses, 
6, and a,, using the Ergun equation for 
packed beds. These, together with the Lar- 
kins correlation for two-phase flow, allow 
calculation of 6,, [ 201. The aBL values may 
be as high as 0.5 bar m-‘, but for the short 
beds obtained with large liquid recycle, mean 
pressures calculated from eqn. (16) can be 
used without substantial error. 
2.3. Effects of liquid recycle 
Referring to Fig. 1 in which a fraction of 
the liquid stream leaving the bed is mixed 
(If-b+ 
a2 
C AL.2 
L I 
a, a, -1 
c AL a C AL 2 
Fig. 1. Trickle-bed reactor with liquid recycle. 
with the incoming fresh liquid, we will see 
first how to account for recycle in the cal- 
culations. Later, the effects of recycle on 
kinetics will be discussed. Let R be the re- 
cycle ratio defined as 
R= !i& QR z- 
Qf Q, 
(16) 
A simple mass balance for TBA at the 
mixing point M (see Fig. 1) gives 
(17) 
Let AC,, be the per pass enrichment of 
liquid in TBA. Since u,CA, is a small fraction 
of all the TBA produced, we can write 
Wt, = CAL, 2 - cAL. lx 
&OUt?OXB 
(18) 
UL 
With C,,, 1 given by eqn. (17), AC,, becomes 
C AL. 2 C AL, 1 AC,, = _ = - 
(l+R) R 
(19) 
Given a design value of uL, the required 
reactor cross-section will be 
s2?L &JR + 1) (20) 
UL UL 
Now, if a production of 10s kg TBA year-’ 
is needed, we will have 
Q~CAL. 2 = 5.36 X low2 kmol s-l (21) 
In summary, given a recycle ratio R, the 
outlet concentration C,,, 2 will be obtained 
by solving the trickle-bed reactor model de- 
scribed before. As this requires an initial 
condition of C,, = CAL0 (eqn. (13)), eqns. 
(18) and (19) are used to calculate CAL0 = 
C AL, 1 for this value of R. After C!,,, 2 is 
known, the exit liquid flow Q, will be ob- 
tained from eqn. (21) and the reactor cross- 
section S from eqn. (20). Finally, the reac- 
tor size will be 
V=hS (22) 
where h is the bed length necessary for a 
specified conversion of IB. 
As noted earlier, the effect of recycle is 
to change the initial conditions for C,, and 
C BL. The initial value of CBL increases also 
because Hz can be much smaller because of 
the enhancement in solubility of IB in an 
aqueous mixture of TBA. We determined 
the solubility of IB in such mixtures [15] 
finding an empirical expression from which 
Hs, as a function of C,, and Z’, can be ob- 
tained. This is 
XB* = exp B + s 
i i 
where Xr,* is the mole fraction of IB at a 
partial pressure of 1 bar. The parameters A 
and B are related to C!,, as follows [ 151: 
B = -16.9 + 2.1CAL + 0.26&n’ (23b) 
A = 2320 - 662&n (23~) 
The effect of higher CsL will be to increase 
CBsr the concentration close to the catalyst 
surface, thus increasing the direct term of 
the kinetic equation (see eqns. (9) and (10)). 
Note that while CBS increases exponentially 
with C,, the reverse rate tends to decrease 
the net rate only linearly. This effect will be 
more apparent at low temperatures where 
solubility is higher. Because the reaction is 
exothermic, the reverse reaction is relatively 
slower in the low temperature range. There- 
fore the enhancement due to higher CB 
will be more advantageous at these low tem- 
peratures. 
In summary, it has been shown qualita- 
tively that mild temperatures with proper 
product recycle will favour higher rates. 
Furthermore, catalyst effectiveness factors 
will be higher at these temperatures. For a 
specified production these conditions should 
result in the use of a smaller reactor. Never- 
theless, if temperatures are too low, equilib- 
rium will be favoured but hi may be too low. 
Appropriate combinations of inlet tempera- 
tures and liquid recycle ratios can be found 
by minimization of the reactor size using a 
standard sequential search routine. 
2.4. Kinetics 
In order to evaluate the above-mentioned 
effects, two kinetic expressions will be con- 
sidered. For the hydration stoichiometry 
H@(l) + IB(aq) e TBA(aq) 
the intrinsic rate is 
rs = k&&B - k2CA (24) 
In view of the excess water k , = kCw . From 
our previous study with low TBA and excess 
water [9] 
47 
8460 
k1 = exp 17.81- - 
T 
m3 kg-’ s-l (25) 
D, = exp 
3660 
- m2 s-l 
T 
(26) 
The value of k2 can be determined from 
literature values of the equilibrium constant 
K,, defined as 
and then making 
k2= ; 
e(27) 
(28) 
Alternatively, experimentally determined 
values of k 1 and k2 can be used. In a recent 
study, Velo et al. [lo] determined k1 and 
k2 simultaneously by adjusting kinetic data 
with the complete equation, eqn. (24) for 
a suitable range of alcohol concentrations. 
Their results show that while k, is essentially 
the same as that given by eqn. (25), the value 
of k, is given by [lo] 
12313 
k2 = exp 23.029 - ___ 
T 
m3 kg-’ s-l (29) 
This value of k2 is larger than kl/K, giving 
in fact faster reverse rates and hence lower 
apparent equilibrium conversions. These two 
kinetic alternatives have been employed in 
the reactor calculations to see the effect of 
the uncertainty in k2 on reactor perfor- 
mance . 
When product recycle is used, the con- 
centrations of TBA may be as high as 4 kmol 
mp3. In such cases, the water concentration 
Cw will be reduced to about 34 kmol mp3, 
lower than the theoretical value for pure 
water, 55.5 kmol m-3. Therefore the pseudo- 
first-order kinetic constant k,, which in- 
cludes Cw, should be corrected accordingly. 
This is done by using an empirical factor, 
f= Cw/55.5, based on the density of liquid 
water-TBA mixtures given by Perry and 
Chilton [ 211. 
3. RESULTS AND DISCUSSION 
3.1. Isothermal reactor calculations 
Integrating eqns. (4) - (13) with the ki- 
netic expression just described, provides the 
48 
TABLE 2 
Sources of physical, transport and kinetic data 
Mass transfer coefficients Solubility and vapour pressure data 
(kLaL)B Goto-Smith correlation [ 231 or 
eqn. (31) 
(kse,)A,B eqn. (30) 
(k&e )A Onda correlation [ 211 
HB eqns. (23a) - (23~) 
H, L/V equilibrium data for water-TBA system at 
infinite dilution 
Kinetic and chemical reaction data Diffusivities 
kI Leung et al. [9], eqn. (25) 
k2 Velo et al. [lo], eqn. (29) or eqn. (28) 
K, Taft and Riesz [ 111 
AH Taft and Riesz [ 111 
DA from DB applying Wilke-Chang type of dependence 
1211 
DB Gehlawat-Sharma [ 5 ] 
D, eqn. (26) 
concentration profiles along the reactor 
length. In Table 2 the physical and mass 
transport properties used in the calculations 
are summarized. Since the performance of 
an integral reactor may depend on the values 
of mass transfer coefficients, the sensitivity 
of the profiles to some of them will be stu- 
died for the isothermal case at a fixed recycle 
ratio, R. Of the transport coefficients, we 
are particularly interested in the gas-to-liquid 
mass transfer coefficient (kne&. Also, we 
wish to study the effect of the reverse reac- 
tion coefficient k, on the calculated profiles. 
The effect of the liquid-to-particle mass 
transfer coefficient (iz&)a will not be studied, 
since an experimentally determined correla- 
tion is available. This is [ 221 
@,a,), = l.4!i?9uL”-382 s-l 
(dp = 0.45 mm, 50 “C) 
(30) 
The results of the reactor simulation are 
summarized in Fig. 2, where the various con- 
centrations us. a standard maximum length 
of 20 m, are plotted. The calculations are 
made for the operating conditions using the 
values of the parameters given in Table 3. 
In addition to those data, the other necessary 
parameters are in Table 2. Four alternative 
cases are studied (Table 3). In cases I and 
II, experimental values of @r&a correlated 
with uL are used [ 221. The experimentally 
obtained correlation is 
(&,(I& = 5.124~~ 0.401 s-1 
(d, = 0.45 mm, 50 “C) 
(31) 
This was determined assuming that the 
Amberlyst-15 particles were fully wetted 
and is based on rate measurements in a dif- 
ferential trickle-bed. Therefore the profiles 
obtained for cases I and II (Fig. 2) show the 
effect of intrinsic kinetics on the bed length 
needed for 95% IB conversion. Cases III and 
IV use (&a& values obtained from the 
Goto-Smith correlation [ 231. These results 
show once more the kinetic effect. The two 
sets of alternative kinetics described before 
TABLE 3 
Operating conditions for the isothermal trickle-bed reactor (Fig. 2) 
Parameter Value Alternative cases (kLaL)B Kinetics 
Temperature 323 K Case I Experimental values, eqn. (31) Velo et al. [lo] 
Mean absolute pressure I bar II 
Mass flow rates L 2.67’kg m-2s-1 
Experimental values, eqn. (31) eqns. (25) - (28) 
III Goto-Smith [ 231 correlation 
G 0.5 kg rnw2 s-r 
Velo et al. [lo] 
IV GotoSmith [ 231 correlation eqns. (25) - (28) 
Recycle ratio, R 1.5 
cAL, 1 1.75 kmol mP3 
CBgc 0.123 kmol rnw3 
Conversion of IB 95% 
49 
L I I 
2 .4 .6 .8 1. 
0 
Fig. 2. Effects of kinetics and gas-to-liquid mass 
transfer coefficients on concentration profiles. See 
Table 3 for the operating conditions and alternative 
cases I to IV (concentrations in kmol mw3). 
were employed. In cases I and II, the com- 
plete equation proposed by Velo et al. [ 101, 
is used (eqns. (25) and (29)). In cases III 
and IV, the simple value of k 2 = hi/K,, with 
K, from Taft and Riesz [ 111 and k1 from 
Leung et al. [9], were taken. 
At the temperature of the study (323 K), 
the kinetic effect for constant gas-to-liquid 
mass transport coefficients, is not large. This 
is best seen by comparing the C, profiles 
for cases I and II or III and IV. The required 
bed lengths differ by about 20% with 
&,(I& taken either from Goto-Smith 
[23] or from the experimental correlation 
obtained by Zorrilla [ 221. 
The effect of (kr,a&, for constant kinet- 
ics, is more dramatic. This is seen when C, 
profiles of cases I and III (or II and IV) are 
compared. For instance, with the kinetics 
of Velo et al. [lo] (cases I and III), the ef- 
fect of (kLar,)n almost doubles the bed length 
needed. This is not surprising since our val- 
ues for (&a& were found to be as many 
as 40 times higher than those predicted by 
the Goto-Smith correlation. A possible ex- 
planation is that this correlation was based 
on measurements of O2 absorption in a non- 
reacting trickle-bed, while those determined 
by Zorrilla [22] were based on measured 
reaction rates, thus including the effects 
caused by a partial wetting of the catalyst. 
In any case, it seems more appropriate to 
use the experimentally determined mass 
transfer coefficients developed for the same 
system in predicting the reactor perfor- 
mance. 
3.2. Effects of product recycle and inlet 
tempemtures 
As seen in Fig. 2 the beds needed for 95% 
conversion are rather long. For case I, the 
length required for a recycle rate of 1.5 and 
constant temperature of 323 K is about 8 
to 10 m. Such a long bed would involve a 
large pressure drop, and hence high operating 
costs associated with compressor and pump- 
ing power inputs. Bed length can be reduced 
by choosing larger recycle rates, increasing 
the inlet pressure and temperature and 
operating the reactor adiabatically. Although 
the cross-section of the bed is directly pro- 
portional to R (eqn. (20)), the bed height 
needed for a given gas conversion will de- 
crease exponentially with R. This is so in 
view of the autocatalytic effect of the alcohol 
when it is present in the liquid feed. This is 
best seen in the initial condition for CBL, 
eqn. (13), in which HB decreases exponen- 
tially with alcohol concentration, see eqn. 
(23). 
To see the effect of recycle and inlet 
temperatures, the bed volumes for 98% con- 
version of IB were calculated us. inlet tem- 
perature and constant recycle ratio. The cor- 
responding reactors were operated adiabat- 
ically. Thus, bed sizes were calculated by 
solving the non-isothermal, plug-flow model. 
The necessary kinetic constant and mass 
transfer coefficients are the same as in case 
I of Table 3. Kinetic constants and IB solu- 
bilities are allowed to change with T and 
C,, along the bed. In Fig. 3, the bed volumes 
for a conversion of 40% are compared, 
50 
I I I I I I 
50 60 70 80 
T;C 
Fig. 3. Effects of product recycle and inlet tempera- 
tures for an adiabatic trickle-bed reactor. IB conver- 
sion is 40% for all cases; ULO = 2.7 X lop3 m s-r; 
us0 = 2.76 X lo-* m se1 ; inlet pressure = 7.5 bar. 
although the integration of the model pro- 
ceeds toan outlet conversion of 98%. 
For a fixed recycle ratio, it is seen that 
the required bed volumes generally decrease 
with decreasing inlet temperature, reaching 
an optimum temperature at which bed vol- 
ume is at a minimum. Further decreasing 
the temperature results in a need for larger 
beds. This effect is more pronounced for 
low recycle ratios, R = 1 to 1.5. For R values 
above 1.75, the curve is very flat. For a 
fixed recycle ratio, this is due to the accel- 
eration of the forward reaction rate relative 
to the reverse rate at low temperatures. 
Increasing the temperature favours the re- 
verse reaction. The effect of the recycle ratio 
is much more important since doubling R 
from 1 to 2 reduces bed volumes almost lo- 
fold for given inlet temperatures within the 
range 333 - 353 K. This is because of the 
exponential increase in CaL with recycle 
ratio at a fixed temperature. 
The next step is to see if 98% IB conver- 
sion can be achieved in an adiabatic trickle- 
bed reactor. The conditions are such that for 
low recycle ratios (R = 1 to 1.3) and inter- 
mediate inlet temperatures, conversions of 
98% cannot possibly be reached owing to 
the chemical equilibrium limitations which 
are met when employing adiabatic operation. 
Therefore recycle ratios of 1.7 or above and 
I I I I 1 
50 60 70 80 
T;C 
J 
Fig. 4. Reactor size vs. inlet temperature at constant 
recycle rate: numbers on the curves represent IB con- 
version at reactor outlet; ULO = 2.7 X 10e3 m s-l; 
uze = 2.76 x lo-* m SK’; inlet pressure = 7.5 bar. 
TABLE 4 
Trickle-bed reactor sizes and operating conditions 
(100 000 t year-’ TBA)a 
Recycle Inlet Cross- Bed IB 
ratio temperature section length conversion 
(“C) (m*) (m) @b) 
2.0 50 16 4.6 96 
60 17 3.6 95 
70 18 3.4 91 
80 20 3.7 81 
2.25 50 16 2.5 98 
60 16 2.3 98 
70 17 2.1 96 
80 19 2.4 91 
aInlet pressure = 7.5 bar; L = 2.67 kg m-* s-l; G = 
0.5 kg me2 s-r. 
low inlet temperatures should be used. The 
corresponding minimization of reactor size 
is shown in Fig. 4 for R = 1.7, 2.0 and 2.25. 
Table 4 gives an idea of reactor cross-sec- 
tions, bed lengths required and conversions 
achieved with R = 2 and 2.25 for a specified 
production of 100 000 t year-’ of TBA. 
4. CONCLUSIONS 
The idea of creating a new TBA process 
arises in response to the problem of finding 
octane enhancers which would help elimi- 
nate lead additives following the present 
automotive fuel legislation in Western Eu- 
rope. Along this line of work, we have set 
up a mathematical model for a trickle-bed 
reactor based on experimentally evaluated 
data derived from intraparticle catalyst data, 
kinetic constants, diffusivities and mass trans- 
fer coefficients for trickle-bed operation. 
The model can predict the reactor per- 
formance under any given real initial condi- 
tions, such as temperature, pressure and 
concentration of alcohol in the feed-stream. 
Temperature and pressure effects are con- 
sidered in the reactor model which includes 
different kinds of operation modes such as 
isothermal, adiabatic, or even with product 
recycle to the inlet. 
As an addition to the solution derived for 
the integral reactor, an important variable 
(the recycle ratio) has been considered, 
allowing us to minimize the bed volume at 
a given inlet temperature. 
Obviously the performance of a multiphase 
reactor depends on many kinds of factors 
and this demands rigorous calculation. In 
other words, all the coefficients and constants 
have to be based on the most reliable sources. 
This aspect is demonstrated when comparing 
@,a& calculations obtained following either 
Zorrilla [ 221 or the Goto-Smith [ 171 corre- 
lation. The only exception is for (k,a,), 
where the Onda correlation [21] has to be 
used. 
In conclusion, we have created a practical 
tool for predicting the performance of a 
trickle-bed reactor and for evaluating the 
best operating conditions for it and its useful- 
ness for real-plant operation in the TBA 
process. 
ACKNOWLEDGMENTS 
The discussions held with Mr. Enric Velo 
and with Professor J. M. Smith (University 
of California, Davis) are thankfully acknowl- 
edged. Financial support for this project was 
provided by CAICYT, Spain. 
REFERENCES 
1 F. Franz, K. Volkamer, G. Nestler and E. Schu- 
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2 
7 
8 
9 
10 
11 
12 
13 
14 
15 
16 
17 
18 
19 
20 
21 
22 
23 
51 
H. Matsuzawa, M. Ikeda, Y. Sugimoto and S. 
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706. 
APPENDIX A: NOMENCLATURE 
A, B parameters in eqn. (23) 
CA concentration of TBA, C& in the gas 
phase, CA, in the bulk liquid, C, in 
the external surface of the particle 
(kmol mp3) 
CB concentration of IB, C, in the gas 
phase, CBL in the bulk liquid, CBS in 
the external surface of the particle 
(kmol mw3) 
52 
G 
cw 
4 
0.Z 
G 
h 
HA 
HB 
k 
(kg ag) 
(kd 
(kLad 
k2 
K 
K, 
L 
Q 
rB 
R 
S 
T 
% 
heat capacity, C,, of the gas, C,, of 
the liquid (kJ kg-’ K-‘) 
concentration of water in the bulk 
liquid (kmo 1 mP3) 
particle diameter (m) 
intraparticle diffusivity (m2 s-i) 
mass flow rate of gas (kg me2 s-i) 
total bed length (m) 
Henry’s law constant for TBA, HA = 
(CA~,/CAL)~~ 
Henry’s law constant for IB, HB = 
(CB~/CBL~ 
enthalpy of the reaction (kJ kmol-‘) 
direct kinetic constant, k, = k X 55.5 
(m3 (kg cat.))‘s-l) 
liquid-to-gas mass transfer coefficient 
(s-i) 
liquid-to-particle mass transfer coeffi- 
cient (s-i) 
gas-to-liquid mass transfer coefficient 
(s-9 
direct kinetic constant (m6 (kg cat.)-’ 
kmol-’ s-l) 
reverse kinetic constant (m3 (kg 
cat.))’ s-l) 
equilibrium constant, K = (CA/C,),, 
equilibrium COnStaId, K, = (CA/ 
CBCw)eq =KlCw 
mass flow rate of liquid (kg m-2 s-l) 
volumetric flow rate (m3 s-l) 
reaction rate, eqn. (24) (kmol (kg 
cat.) -l s-l) 
recycle ratio, eqn. (16) 
empty section of the reactor (m2) 
temperature (K) 
superficial velocity of gas (m s-l) 
UL 
V 
xB 
xB* 
2 
Greek 
6 gL 
Pk? 
PL 
PP 
4 
superficial velocity of liquid (m s-l) 
bed volume (m3) 
molar fractional conversion of IB 
(mol mol-‘) 
mole fraction of dissolved IB at a 
partial pressure of 1 bar (mol mol-‘) 
bed length coordinate (m) 
symbols 
two-phase pressure drop, eqn. (15) 
(bar m-‘) 
single-phase pressure dropsfor gas and 
liquid (bar m-‘) 
Levenspiel expansion factor 
bed porosity 
particle porosity 
effectiveness factor, eqn. (11) 
dimensionless bed length, t? = Z/20 
mass of catalyst/unit volume bed (kg 
dry cat. rnd3) 
density of gas (kg rnA3) 
density of liquid (kg rnd3) 
mass of catalyst/unit volume particle 
(kg dry cat. rne3) 
Thiele modulus, eqn. (12) 
Subscripts 
A tert-butyl alcohol 
B isobutene 
: 
exit stream 
feed stream 
g gas phase 
L liquid phase 
R recycle stream 
b 
solid phase 
water