chapter 7 cfd characterization of multiphase flow in bench...
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154
Chapter 7
CFD Characterization of Multiphase
Flow in Bench-Scale Packed Beds 7.1 Introduction
Packed-bed reactors with multiphase flow have been used in a large number of
processes in refinery, fine chemicals and biochemical operations. Effective scale up of
bench-scale packed-bed reactors in the development of new processes and scale down of
the commercial units in the improvement of existing processes have become predominant
tasks in the research and development divisions of many companies (Sie and Krishna,
1998). The general paradigms of scaling up packed-beds reactors from bench-scale to
pilot scale and to commercial units have been explored in the literature (Le Nobel and
Choufour, 1959; Gieman, 1988; De Wind, 1988; Sie and Krishna, 1998) and reviewed
recently by Krishna and Sie (1994), Sie and Krishna (1998), Dudukovic et al (1999). The
scaling down of multiphase packed beds is, in fact, even tougher since many issues such
as liquid back-mixing and liquid maldistribution become more apparent when the reactor
scale is reduced (Mears, 1971; Tasmatsoulis and Papayannakos, 1994).
The first critical question is how to effectively produce reliable bench-scale data.
To answer this question, and to come up with a new strategy for scaling down packed-
beds, studies of the following issues are required: (1) Understanding multiphase flow
maldistribution in bench-scale packed beds. (2) Assessing the effect of flow
maldistribution on reactor performance in terms of conversion and selectivity; developing
155 a method to correct the bench-scale experimental data for non-ideal flow behavior and (3)
preventing flow maldistribution from happening in experimental units (e.g. using fines,
van Klinken and van Dongen, 1980; Al-Dahhan and Dudukovic, 1996). In this Chapter,
we mainly focus on the first aspect, which is to understand how multiphase flow is
distributed spatially and temporally in bench-scale packed-bed and how this flow
distribution affects the laboratory-scale experimental data.
The experimental studies of the flow pattern in packed beds have been conducted
mostly for the system with saturated single phase flow (e.g., gas flow or liquid upflow)
using exit velocity measurements (Lerou and Froment, 1976) and few non-invasive
measurements (Stephenson and Stewart, 1986; Sederman et al., 1997). Multiphase flow
measurements in bench-scale packed beds have not been reported in the open literature
although the recent high-resolution tomography techniques provide hope in that direction
(Lutran et al., 1991; Gladen, 1994; Chaouki et al., 1997; Reinecke et al., 1998).
Therefore, in this Chapter we intent to offer an improved understanding of such
multiphase flows through a series of CFD k-fluid model simulation of bench scale packed
beds.
The second critical question is how to utilize these bench-scale data for the design
of commercial scale units. In other words, how to scale up the packed beds based on the
information obtained from the bench-scale units. Since the precise description of the
steady-state hydrodynamics in packed-beds requires not only the information on global
mean quantities (i.e., overall holdup and pressure drop), which can be calculated
primarily by empirical or phenomenological models (Saez and Carbonell, 1985; Holub et
al. 1992, 1993), but also the information on the distribution of these quantities. Both
experimental studies (Lutran et al., 1991; Ravindra et al 1997) and numerical simulation
presented in Chapter 4 led to qualitative conclusions that fluid flow distribution under
steady-state condition is a function of bed structure (i.e., porosity distribution), external
particle wetting and the inlet superficial velocities of the two phases. However, there is
no quantitative relationship available in the literature, particularly, for the relationship of
bed porosity distribution and flow holdup distribution etc. To develop such correlations,
one needs to first understand the nature of the system. Fortunately, recent experiments
156 revealed that the fluid velocity distribution (Sederman et al., 1997, Volkov et al., 1986),
liquid holdup distribution (Toye et al., 1997) and porosity distribution (Chen, et al., 2000)
in packed beds are pseudo-random in nature. This means that the local hydrodynamic
quantities (such as holdups and velocities as well as particle external wetting efficiency)
and local porosity can be considered as random variables. The global hydrodynamics
then can be described by the local hydrodynamic parameters through a proper probability
density function (Crine et al., 1992). Therefore, the goal of this part of study is to search
for such a probability function and to describe its parameters in terms of measurable
quantities such as bed dimensions, particle size and shape, operating conditions, etc.
The logical way to pursue this goal is to conduct extensive measurements of the
bed-scale hydrodynamics and of the local-scale hydrodynamic parameters,
simultaneously. This requires the determination of bed structure characteristics, such as
porosity distribution, with the same spatial resolution as achieved in flow measurements.
Although the non-invasive tomography techniques are available for such high-cost
experiments (Toye et al., 1997; Sederman et al., 1997; Reinecke et al., 1998), the
numerical flow simulation provides also a rational way, with good cost-effectiveness, to
obtaining useful preliminary results needed to guide the future experimental validation
study.
In this Chapter we present two case studies using the CFD k-fluid model
developed in Chapter 5. The first case study focuses on two-phase flow modeling in
bench-scale cylindrical and rectangular packed beds. The results are presented for
operations at steady and unsteady state (e.g., periodic liquid feed), which have been
previously examined in the studies of catalyst screening and reactor-performance
enhancements (Khadilkar et al., 1999). To explore the fluid dynamic mechanism for
performance enhancement under periodic inflow mode, a comparison of flow distribution
under steady state liquid feed and periodic liquid input in packed beds is given. The
second case study focuses on modeling macro-scale flow distribution in trickle beds by
implementing the statistical description of the porosity structure and the consideration of
different particle external wetting efficiencies. By analyzing a series of bed structures and
157 flow simulation results, we develop the preliminary statistical correlations for the
structure-flow relationship in trickle-bed reactors.
7.2 Model Bench-Scale Packed Beds The difficulties in modeling flow in catalytic packed beds are mainly due to the
complex nature of the flow domain that is formed by passages around randomly packed
particles. The structure of this interstitial space inside the bench-scale packed bed is
mainly determined by particle size (dp), particle shape (φ), ratio of column diameter and
particle diameter (Dr/dp), and the packing method. Experimental measurement and
computer simulation of porosity distribution in packed beds have been the subjects of
many investigations for a considerable period of time (Benenati and Brosilow, 1962;
Jodrey and Tory, 1981). Although the detailed 3D porosity information can be achieved
through computer simulation of random packing (Jodrey and Tory, 1981), an
axisymmetric description of 2D porosity distribution, ε (r, z), can be considered a good
approximation in a certain sense. The longitudinally averaged radial porosity profile, ε (r)
was experimentally found to oscillate for a distance of 3 ~ 4 particle diameters from the
wall, whereas the cross-sectional averaged porosity along the length of the bed, ε (z), is
distributed randomly (Borkink et al., 1992). For flow simulation purpose, in
axisymmetric cylindrical coordinates (r-z) one can generate a 2D pseudo-random porosity
distribution constrained by the mean porosity and radial porosity profile (i.e., ε (r)).
Figure 7-1 shows such generated porosity distribution by displaying the porosity profiles
ε (r) and ε (z). The dimension of the bench-scale reactor in Figure 7-1 is 22.5 cm in
length and 2.4 cm in diameter. The spherical particles used are 1.5 mm in diameter. It is
well known that for a given reactor, the radial porosity profile, ε (r) is changed with the
change in particle diameter, and the axial profile, (ε (z) varies with repacking (Benenati
and Brosilow, 1962), but the mean porosity retains the same value.
158
(a)
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(b) (c)
Figure 7-1. Bench-scale cylindrical packed-bed and its porosity description (a) computer
generated 2D axisymmetric solid volume fraction distribution; (b) radial porosity profile,
ε (r); (c) axial porosity profile, ε (z).
We also generated a 2D porosity distribution in x-y coordinates for a bench-scale
rectangular bed packed with 3 mm particles as used in our discrete cell model approach
in Chapters 3 and 4. The inflow gas is distributed uniformly with given superficial
velocity whereas inflow liquid is treated as either in steady flow or in periodic flow mode
with uniform or non-uniform distributors.
7.3 Modeling Results of Bench-Scale Packed Beds To demonstrate the capability of CFD k-fluid model, we examined both the
spatial distribution and the temporal phenomena associated with liquid flow at steady
state and under periodic inflow conditions. Figure 7-2 shows the spatial distributions of
the phase volume fractions, interstitial velocity and pressure at steady state inflow
condition (Ug0 = 6 cm/s and Ul0 = 0.3 cm/s). The gas and liquid physical properties are
those typical of a hydrotreating reaction. The following values are selected for densities,
ρL = 0.652 g/cm3, ρG = 0.00187 g/cm3, and for kinematic viscosities for liquid: 0.0014
cm2/s, and for gas: 0.0809 cm2/s. Higher liquid holdup (THE2) occurs in higher porosity
zones (1.0-THE1) such as in the wall regions. Since the local porosity value is changed
0.380.390.400.410.420.430.44
0.0 0.3 0.6 0.9 1.2r (cm)
poro
sity
0.36
0.38
0.40
0.42
0.44
0 3 6 9 12 15 18 21z (cm)
poro
sityε (r)
ε (z)
160 by repacking the column even when using the same particles and procedure, it is clear
that the point measurement of liquid-solid mass transfer coefficient (ka)ls using a
conductivity method in repacked beds may result in a large scatter in data, which may
lead to erroneous conclusions based on single point experiments. (Highfill, 1998). Local
measurement with a fixed structural matrix may give some meaningful data by a
statistically generated set of large number of experimental conditions (Latifi et al., 1989),
which may be very time-consuming. Since the radial component of velocity is relatively
much smaller than the axial component and also normally distributed around the zero
value, only the axial velocity component (Vz) is shown in Figure 7-2 for the liquid (V2)
and the gas (V3). Inspection of these figures indicate that the lower the porosity, the
lower the liquid holdup, and the lower the liquid interstitial velocity. We do find some
backflow of gas in Figure 7-2(e), which is similar to the experimental findings for liquid
upflow inside packed beds reported by Sederman et al. (1997). The negative local gas
velocity leading to local counter-current flow of gas and liquid may explain why in the
high interaction regime the slit model of Holub et al. (1992) needed to be modified by Al-
Dahhan et al., (1998) to include a 'negative' slip between gas and liquid at the gas-liquid
interface. More back mixing can be expected for gas flow in high-pressure trickle-bed
reactors due to the negligible gravity effect at elevated pressure. In general, pressure
decreases along the bed axis (see Fig 7-2(f)), however, relatively lower pressure values
occur at the wall region at each cross-section of the column due to higher porosity in the
proximity of the wall. This may cause errors in pressure measurement if one detects
pressure just at the wall. Inserting multiple pressure sensors at different radial position is
a way to avoid such errors, however, special care does need to be taken for the
disturbance that the sensors can cause in the local flow distribution.
The capability of the CFD k-fluid model in predicting maldistribution is further
illustrated in Figures 7-3a and b, which display the simulated longitudinal-averaged
velocity profiles of the axial and horizontal velocity components, (Vz and Vx) for the gas
and liquid at relatively low gas and liquid superficial velocities (UL0 = 0.05 cm/s, UG0 =
6.0 cm/s). Figures 7-4a and b display the corresponding results at relatively high gas and
liquid velocities (UL0 = 1.0 cm/s, UG0 = 12.0 cm/s). Figure 7-5 shows the frequency plots
161 of each sectional relative interstitial velocity (V/V0) at both low and high flow conditions.
More uniform two-phase flow distribution is observed at high flow rate condition and at
such high flows more nonuniform gas flow is found when the liquid superficial velocity
is low (VL0 = 0.05 cm/s). Particle partial wetting causes more nonuniform interstitial
space left for gas flow.
(a) (b) (c)
Solid holdup Liquid holdup gas holdup
0
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162
(d) (e) (f)
Figure 7-2 Contours of packed bed structure and corresponding hydrodynamic
parameters: (a) solid holdup-THE1; (b) liquid holdup-THE2; (c) gas holdup-THE3; (d)
axial liquid interstitial velocity-V2; (e) axial gas interstitial velocity-V3; (f) pressure at
Ug0 = 6 cm/s and Ul0 = 0.3 m/s at steady state operation.
0
5
10
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20 V340.694430.644820.595210.54560.495983
-9.55362-19.6032-29.6528-39.7024-49.752-59.8016-69.8512-79.9008-89.9504-100
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163
0.2
0.4
0.6
0.8
1.0
0 0.2 0.4 0.6 0.8 1 1.2
r, cm
0.04
0.06
0.08
0.10
liqui
d ho
ldup
Vzl/Vl0 Vzg/Vg0 porositygas holdup liquid holdup
Figure 7-3a. Relative interstitial velocity profiles of the gas and liquid phase (left axis),
volume fraction profiles for porosity (left axis), gas (left axis) and liquid (right axis) in
the radial direction at low flow rates (Ul0 = 0.05 cm/s; Ug0 = 6.0 cm/s).
0.2
0.4
0.6
0.8
1.0
0 0.2 0.4 0.6 0.8 1 1.2
r, cm
0.16
0.17
0.18
liqui
d ho
ldup
Vzl/Vl0 Vzg/Vg0 porositygas holdup liquid holdup
Figure 7-3b. Relative interstitial velocity profiles of the gas and liquid phase (left axis),
volume fraction profiles for porosity (left axis), gas (left axis) and liquid (right axis) in
the radial direction at low flow rates (Ul0 = 1.0 cm/s; Ug0 = 12.0 cm/s).
164
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0 0.2 0.4 0.6 0.8 1 1.2
r, cm
V/V0
0.3
0.5
0.7
0.9
poro
sity
Vxl/Vl0 Vxg/Vg0 porosity
Figure 7-4a. Relative interstitial velocity profiles of the gas and liquid phase, porosity
profiles in the radial direction at low flow rates (Ul0 = 0.05 cm/s; Ug0 = 6.0 cm/s).
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0 0.2 0.4 0.6 0.8 1 1.2
r, cm
V/V0
0.3
0.5
0.7
0.9
poro
sity
Vxl/Vl0 Vxg/Vg0 porosity
Figure 7-4b. Relative interstitial velocity profiles of the gas and liquid phase, porosity
profile in the radial direction at low flow rates (Ul0 = 1.0 cm/s; Ug0 = 12.0 cm/s).
165
-50
0
50
100
150
200
250
300
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
n/nt
Vzl/Vl0(1)Vzl/Vl0(2)Vzg/Vg0(1)Vzg/Vg0(2)
Figure 7-5. Histogram of the relative interstitial velocities of gas and liquid phase at low
flow rates (1: Ul0 = 0.05 cm/s; Ug0 = 6.0 cm/s) and high flow rates (2: Ul0 = 1.0 cm/s;
Ug0 = 12.0 cm/s).
166 The temporal phenomena of liquid flow are shown in Figure 7-6 in a 1-inch
cylindrical tube with uniform gas inflow but with a periodic liquid inflow (60s cycle time
= 15s turn-on + 45s turn-off as used in reaction studies of Lange et al., 1994; Castellari &
Haure, 1995; Khadilkar et al., 1999). Since the axisymmetric assumption is used in the
simulation, there is no way to catch all the real time scales of the flow, but we are able to
look at the time scale in the axial direction due to the dominant velocity component (Vz).
It is clear that the simulated liquid flow readily reaches the steady state values because
the fluid cannot flow azimuthally. Once the front of the liquid stream reaches the bottom
of the packed bed, the flow field is developed as shown in Figure 7-6. The liquid draining
from the bed takes time and certain amount of liquid still stays in the bed even after
another 15 seconds.
A test case with a possibility of significant liquid maldistribution was chosen for
investigating the effects of induced liquid flow modulation. A 2D rectangular model bed
of dimensions 29.7 cm × 7.2 cm was considered with pre-assigned porosity values to
different cells (33 in the vertical (Y) direction and 8 in the horizontal (X) direction as
shown in Fig 7-7a). Liquid flow was introduced at the two central cells at the top of the
bed at mean superficial velocity of 0.1 cm/s, while gas flow was introduced at the top in
all the cells at a superficial velocity of 10.0 cm/s in simulations of both steady and
unsteady state operation. Steady state simulations show evidence of significant liquid
maldistribution, particularly at the top and bottom of the reactor. Complete absence of
liquid is seen in zones near the bottom of the reactor (Figure 7-7b).
The liquid flow distribution observed in the steady state case was compared with
transient simulations carried out with a liquid flow ON time of 15 seconds and a total
cycle time of 60 seconds (45 seconds liquid OFF).
167
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CFDLIB97.2
T=7.000E+00
N=304102
CFDLIB97.2
T=9.000E+00
N=386541
CFDLIB97.2
T=1.100E+01
N=469257
CFDLIB97.2
T=1.100E+01
N=469257
CFDLIB97.2
T=1.300E+01
N=552404
CFDLIB97.2
T=1.500E+01
N=635047
CFDLIB97.2
T=1.700E+01
N=715394
CFDLIB97.2
T=1.700E+01
N=715394
CFDLIB97.2
T=1.900E+01
N=778732
CFDLIB97.2
T=2.100E+01
N=811894
CFDLIB97.2
T=2.300E+01
N=845457
CFDLIB97.2
T=2.500E+01
N=879825
CFDLIB97.2
T=2.500E+01
N=879825
CFDLIB97.2
T=2.700E+01
N=915431
CFDLIB97.2
T=2.900E+01
N=950779
CFDLIB97.2
T=1.000E+00
N=43405
CFDLIB97.2
T=3.000E+00
N=132551
CFDLIB97.2
T=5.000E+00
N=219907
CFDLIB97.2
T=3.000E+00
N=132551
CFDLIB97.2
T=7.000E+00
N=304102
CFDLIB97.2
T=9.000E+00
N=386541
CFDLIB97.2
T=1.100E+01
N=469257
CFDLIB97.2
T=1.100E+01
N=469257
CFDLIB97.2
T=1.300E+01
N=552404
CFDLIB97.2
T=1.500E+01
N=635047
CFDLIB97.2
T=1.700E+01
N=715394
CFDLIB97.2
T=1.700E+01
N=715394
CFDLIB97.2
T=1.900E+01
N=778732
CFDLIB97.2
T=2.100E+01
N=811894
CFDLIB97.2
T=2.300E+01
N=845457
CFDLIB97.2
T=2.500E+01
N=879825
CFDLIB97.2
T=2.500E+01
N=879825
CFDLIB97.2
T=2.700E+01
N=915431
CFDLIB97.2
T=2.900E+01
N=950779
CFDLIB97.2
T=3.100E+01
N=985604
0
5
10
15
20
THE20.120.1121430.1042860.09642860.08857140.08071430.07285710.0650.05714290.04928570.04142860.03357140.02571430.01785710.01
CFDLI B97.2
T=2.300E+01
N=845457
CFDLI B97.2
T=2.500E+01
N=879825
CFDLI B97.2
T=2.300E+01
N=845457
CFDLI B97.2
T=3.000E+01
N=956120 Figure 7-6 Liquid holdup distribution in a periodic liquid inflow mode (15s-on and 45s-
off) (left) and steady state mode (right) in 1-inch cylindrical packed bed at Ug0 =6 cm/s
and Ul0 =0.3 cm/s.
Snapshots of liquid flow distribution were taken at several time intervals (t = 15,
25, 40, 55 seconds from beginning of liquid ON time) (Figures 7-7c, 7-7d, 7-7e, 7-7f) to
compare them with the steady state liquid holdup data (Figure 7-7b). Liquid holdup
variation over the reactor cross section is depicted at several axial locations at different
times in a typical flow modulation cycle (Figures 7-8a-d). These figures clearly
demonstrate that unsteady state operation ensures better uniformity in liquid distribution
at all locations compared to that observed in steady state operation. This improved
distribution, though not perfect, does ensure enhanced liquid supply to all locations not
previously possible during steady state (in particular, the bottom zone shown in Figure 7-
8a). This clearly shows that induced flow modulation results in better liquid spreading
and even distribution of liquid over the entire cross section at each axial location at some
point in time in the cycle. This also indicates that although the average liquid holdup at
2 6 10 14 18 22 26
Steady
168 each location may not exceed the steady state holdup, the reactor performance may still
be enhanced due to higher than steady state holdup for a sub-interval of the entire cycle.
This time interval of enhanced liquid supply can allow exchange of liquid reactants and
products with the stagnant liquid and with the catalyst pellets present in any particular
zone. Another observation that can be made from Figure 7-7d is that for some time
interval, all zones in the reactor become almost completely devoid of liquid, and can
allow enhanced access of the gaseous reactant to externally dry catalyst during this time
interval. Temperature rise and internal drying of catalyst and faster gas phase reaction
may also occur in this interval, which can be quenched by the liquid in the next cycle.
The above simulation demonstrates the possibility of controlled rate enhancement
due to induced flow modulation. It also facilitates our understanding and visualization of
the phenomena occurring in the reactor. It confirms the reasons behind improved
unsteady state performance observed experimentally and simulated in the reaction
transport models (Khadilkar, 1998; Khadilkar et al., 1999; Lange et al., 1994; Castellari
and Haure, 1995; Silveston, 1990). It seems that upon scale-up large reactors operated
with flow modulation should perform with the same enhancement over steady state
operation as seen in the scaled-down version.
0 2 4 60
5
10
15
20
25
30THE1
0.610.6057140.6014290.5971430.5928570.5885710.5842860.580.5757140.5714290.5671430.5628570.5585710.5542860.55
CFDLIB97.2
T=1.950E+02
N=196037
CFDLIB97.2
T=2.050E+02
N=207428
CFDLIB97.2
T=2.150E+02
N=218598
CFDLIB97.2
T=2.200E+02
N=224118
CFDLIB97.2
T=2.000E+02
N=201760
CFDLIB97.2
T=3.200E+02
N=353282
0 2 4 60
5
10
15
20
25
30THE2
0.220.2061940.1923880.1785820.1647760.1509710.1371650.1233590.1095530.0957470.08194110.06813520.05432930.04052340.0267175
CFDLIB97.2
T=1.950E+02
N=196037
CFDLIB97.2
T=2.050E+02
N=207428
CFDLIB97.2
T=2.150E+02
N=218598
CFDLIB97.2
T=2.200E+02
N=224118
CFDLIB97.2
T=2.000E+02
N=201760
CFDLIB97.2
T=3.200E+02
N=353282 (a) (b)
169
0 2 4 60
5
10
15
20
25
30CFDLIB97.2
T=1.950E+02
N=196037
0 2 4 60
5
10
15
20
25
30CFDLIB97.2
T=1.950E+02
N=196037
CFDLIB97.2
T=2.050E+02
N=207428 (c) (d)
0 2 4 60
5
10
15
20
25
30CFDLIB97.2
T=1.950E+02
N=196037
CFDLIB97.2
T=2.050E+02
N=207428
CFDLIB97.2
T=2.150E+02
N=218598
CFDLIB97.2
T=2.200E+02
N=224118
0 2 4 60
5
10
15
20
25
30CFDLIB97.2
T=1.950E+02
N=196037
CFDLIB97.2
T=2.050E+02
N=207428
CFDLIB97.2
T=2.150E+02
N=218598
CFDLIB97.2
T=2.200E+02
N=224118
CFDLIB97.2
T=2.000E+02
N=201760
CFDLIB97.2
T=2.100E+02
N=213040
CFDLIB97.2
T=2.250E+02
N=229697
CFDLIB97.2
T=2.300E+02
N=235461
CFDLIB97.2
T=2.350E+02
N=241297
CFDLIB97.2
T=2.400E+02
N=247142
CFDLIB97.2
T=2.450E+02
N=252965
CFDLIB97.2
T=2.350E+02
N=241297 (e) (f)
Figure 7-7 (a) Solid volume-fraction (THE1 = 1.0 - Bed Porosity) distribution in the
model 2D rectangular bed; (b) liquid holdup (THE2) contour at steady state liquid feed;
snapshot of liquid holdup (THE2) contours at (c) t =15s; (d) t = 25s; (e) t = 40s;
(f) t = 55s from start of the liquid ON cycle (left) in comparison with steady state holdup
contours (right).
170
0.000
0.020
0.040
0.060
0.080
0.100
0.120
0.0 1.8 3.6 5.4 7.2X, cm
Liqu
id h
pZ=1.8 cm
0.000
0.020
0.040
0.060
0.080
0.100
0.120
0.0 1.8 3.6 5.4 7.2X,cm
Liqu
id h
p
Z=18.9 cm from bottom
(a) (b)
0.000
0.020
0.040
0.060
0.080
0.100
0.120
0.0 1.8 3.6 5.4 7.2X, cm
Liqu
id h
p
Z=26.1 cm
0.000
0.020
0.040
0.060
0.080
0.100
0.120
0.0 1.8 3.6 5.4 7.2X, cm
Liqu
id H
oldu
p
Z=28.8 cm
(c) (d)
Figure 7-8 Comparison of cross sectional liquid holdup profiles at different axial
locations under steady (! filled squares) and unsteady state operation ((a) Z= 1.8 cm;
(b) Z=18.9 cm; (c) Z = 26.1 cm; (d) Z = 28.8 cm) (!-15s; ∆-25s; ×-40s; "-55s)
171
7.4 Statistical Nature of Bed Structure and Flow
7.4.1 Bed Structure The porosity and its distribution in a packed bed are the key parameters in
determining the flow distribution. The effective implementation of the porosity
distribution in the flow simulation model is the critical point, which affects the capability
and applicability of the developed flow model. To achieve a quantitative understanding
of the porosity distribution in packed beds, numerous research efforts have been made
during the past several decades. For instance, measurements of the longitudinally
averaged radial porosity profiles (Benenati and Brosilow, 1962), correlations of radial
porosity distribution (Mueller, 1991; Bey and Eigenberger, 1997) and computer
simulation of a 3-D porosity structure for a packing of spheres (Jodrey and Tory, 1981)
have been reported. It was found that the mean porosity and porosity distribution are
determined largely by particle size, shape, and particle surface properties (i.e. roughness
and hardness) as well as the method of packing the bed.
The recent advances in computer tomography (CT) and magnetic resonance
imaging (MRI) techniques can provide the 3-D structure in packed beds in a non-invasive
way (Reinecke et al., 1998; Baldwin et al., 1996). Depending on the spatial resolution of
the techniques used, different types of porosity distributions were found. For instance, the
porosity data obtained from γ-ray CT scan of a cylindrical column packed with 3-mm
monosize spheres has definitely exhibited a Gaussian distribution of the pixel porosity
values at a pixel size (i.e., spatial resolution) of 4 mm (Chen et al., 2000). However, it has
been found by MRI that there are two peaks in the distribution of voxel porosity values of
the bed with 3mm particles if the voxel size is reduced to 180 µm (Sederman, 2000): one
with low value due to voxels filled with solid and one high value due to voxels filled with
pore space. This implies that the type of porosity distribution depends on the size of voxel
(or pixel size) chosen in the measurements. In general, the porosity distribution is
certainly Gaussian if the voxel size is larger than the particle diameter. In this study we
focus on the modeling of macroscale flow texture, which is on the scale of a cluster of
particles.
172 7.4.2 Multiscales of Flow and Role of Various Forces
Due to the mixed definitions encountered in the literature, it is necessary to
clearly define each spatial scale referred to in this Chapter.
• Microscale level: the scale of interstitial space (< particle diameter), also called 'local
scale or particle scale
• Mesoscale level: The scale of a cluster of particles, also called section scale
• Macroscale level: the scale of an elementary volume large enough to be
representative of the bed (Crine et al., 1992), also called large scale or bed scale
The experimental observations in packed beds have also shown that the fluid flow
distribution is multiscale in nature, and flow distribution/maldistribution can be observed
from the macroscale to the microscale (Hoek et al., 1986; Melli et al., 1990; Wang et al.,
1998). From flow modeling point of view, it means that, to describe the different scales
of flow textures, one needs to implement the governing flow equations with the different
level of description of the basic-forces (i.e., inertial, viscous, capillary, and gravitational
force etc.). As we found in Chapter 3, the contribution of the Reynolds stress term to the
fluid momentum equations is not important for the macroscale flow modeling, but it
could be very important for the microscale flow simulation (Nijemeisland et al., 1998).
On the other hand, also depending on the scale of packing elements used in the packed
beds, which essentially determine the scale of flow passages, the contributions of each
basic-force on liquid flow distribution are of different magnitudes (Melli et al., 1990). In
packed beds of large packing elements (e.g., separation packing: 10 ~ 30 mm Pall rings
and Rasching rings etc.), the liquid distribution patterns were not sensitive to the
wettability of the packing surface (Bemer and Zuiderweg, 1978). For the trickle-bed
packing: typically, 0.5 ~ 3 mm spherical or cylindrical particles, however, the effect of
external particle wetting on liquid distribution is significant (Levec et al., 1986; Lutran et
al., 1991; Ravindra et al., 1997a; see also Chapter 2). This implies that even for the same
macroscale flow texture (e.g. macroscale flow distribution), the contribution of each
basic-force is of different magnitude depending on the different characteristic radius of
the flow passages.
173 7.4.3 Link of Macroscale and Cell-Scale Hydrodynamics
Because the multiscale spectrum of fluid flow textures exists in packed beds with
multiphase flow, two critical questions are raised accordingly: (i) 'what is the
fundamental mechanism that links those different scales of flow textures in packed beds?'
(ii) 'Is it realistic to develop a universal flow model which can capture the whole
spectrum of flow structures?'
The experimental evidence (Melli et al., 1990) and relevant theoretical study
(Melli et al., 1991) have shown that in a nearly 2-D network, the macroscale flow
regimes can be described in terms of different combination of microscale flow regimes.
That means that the microscale and meso-scale hydrodynamics in packed beds are the
roots of global hydrodynamics. Theoretically, one can link the macroscale and micro- or
meso-scale flow textures through certain rules. Crine et al (1992) introduced the concept
of statistical hydrodynamics, in which all the local hydrodynamic quantities were
considered as random variables, like the packing properties discussed in Section 7.2.1.
Then the link of the bed scale, section scale and local scale hydrodynamics is the
probability density function (pdf) of the random variables, through which the global
hydrodynamic quantities can be determined at the bed scale.
In this Chapter we start from the section scale (i.e., meso-scale) flow and structure
elements, and examine how the section scale flow hydrodynamics is affected by the
section scale bed structure and relevant basic-forces. We then seek the link which bridges
the bed scale (i.e., global) and section scale hydrodynamics in a statistical manner.
7.4.4 Statistical Quantities Since the section scale flow and porosity are random in nature in packed beds,
one can use statistical approach to characterize such randomness of the system. The
relevant quantities can be described by a probability density function (p.d.f.)
characterized by its moments such as mean (µ), variance (σ2), skewness (γ1) and kurtosis
(γ2). The definitions of these are readily available in the literature (Roussas, 1997). In this
work, we will use the mean, µ
174 ( )j
jj xpx∑=µ (7-1)
Where p(xj) is the probability density function of the random variable xj of system and the
variance, σ2
( ) ( )∑ −=j
jj xpx 22 µσ (7-2)
Which characterizes the spread around the mean. We examine the effect of skewness and
kurtosis on the results also, since these can indicate the changes caused by a non-
Gaussian probability density function.
7.5 Modeling Results and Correlation Development As discussed in Sections 7.4.1 and 7.4.2, the observed flow textures in trickle
beds result from a combination of interstitial structure (porosity distribution), interaction
of fluids with particles and interaction of the gas and liquid phase. In this study, we
examine each individual contribution to two phase flow distribution by performing a
series of numerical experiments. The following important issues are addressed: (i) how
does the capillary force affect the flow distribution for different factors? (ii) how is the
flow distribution affected by porosity distribution? (iii) what is the influence of
superficial velocities at the inlet?
7.5.1 Model Packed Beds Recall that the type of porosity distribution in packed beds is scale-dependent. A
pseudo-Gaussian distribution of porosity at a section scale (5-10 mm) can be considered
as a reasonable assumption for section-scale flow simulation in trickle beds.
A 2D rectangular model bed of dimensions 50 cm × 10 cm was considered with
pre-assigned porosity values to different sections (50 sections in the vertical (z) direction
and 10 sections in the horizontal (x) direction as shown in Fig 7-9).
175
Figure 7-9. Trickle bed and model bed with 500 cells
The generated pseudo-Gaussian porosity distributions have the same mean value
(µ ~ 0.40) but have different standard deviation (std), skewness (γ1) and kurtosis (γ2) as
listed in Table 7-1. The gas and liquid flow were introduced at the top of the bed at
certain constant superficial velocities. The physical properties used in the simulations are
for air and water, but any type of system such as hydrogen and hydrocarbons can be
simulated by changing the physical properties of the fluids. Atmospheric condition is
considered in this study but high-pressure condition can be handed by using different
physical properties and high-pressure formulations for the drag coefficients.
G
G
L 10 cells 50
cel
ls
176 Table 7.1 Statistical quantities of porosity distribution
Beds Mean
(µ)
Std
(σ)
Skewness
(γ1)
Kurtosis
(γ2)
I 0.399 0.0082 0.2736 0.1335
II 0.399 0.0118 -0.2093 0.6746
III 0.399 0.0217 0.0351 0.0203
IV 0.404 0.0439 -0.1128 -0.2972
7.5.2 Capillary Force Effect To examine the effect of capillary force on the two phase flow distribution in a
packed bed, a series of CFDLIB simulations have been performed by incorporating a
particle wetting factor (f) in k-fluid pressure calculation (see Eq.7-8) which is the same as
what we did in the extended Discrete Cell Model in Chapter 4. Two limiting wetting
conditions are defined, namely, 'complete prewetting' (f =1) and 'complete non-
prewetting’ (f = 0). The actual situation of particle wetting in trickle beds is somewhere
between these two limits. The 'complete prewetting' means that there is always a liquid
film covering all the particle surfaces, this results in the negligible effect of capillary
force on liquid flow. Correspondingly, capillary pressure is not accounted for in flow
computation by assigning a value of unity to f. Strictly speaking, this does not happen in
practice, even if one pre-wets the bed at high gas and liquid flow rates before starting to
operate the trickle bed. One often drains the liquid from the bed after terminating the
liquid and gas flow (Levec et al., 1988). On draining, the liquid films over the particles,
connecting the pendular rings, might rupture, leaving isolated pendular rings at the
contact points of the particles. It is argued by Ravindra et al (1997a) that the bed with
isolated pendular rings, especially with large diameter particles, could behave as the
nonprewetted bed. On the other hand, 'completely non-prewetted' bed means there is no
liquid film over the particles, then the capillary force fully contributes to the liquid flow
distribution. Correspondingly, capillary pressure is fully incorporated in CFDLIB
computation by assigning to f the value of zero. By changing the wetting factor (f) from
0.0 to 0.5 and 1.0, one can study the effect of capillary force on flow distribution in
177 completely nonprewetted, partially prewetted and completely prewetted beds,
respectively.
Figure 7-10 shows the simulated longitudinal profiles of porosity, liquid holdup
and liquid saturation at different wetting factors (f = 0, 0.5 and 1.0). Here the cell liquid
saturation is defined as the ratio of cell liquid holdup and cell porosity. In the completely
nonprewetted bed (f = 0.0), the liquid saturation profile and porosity profile in the
longitudinal direction (z) have similar trends. Lower liquid saturation occurs in lower
porosity regions (see Fig 7-11a). This can be explained by higher capillary force
occurring at smaller interstice when the particle surface is nonprewetted. Because the cell
liquid holdup is a product of the cell porosity and cell liquid saturation, the variation of
liquid holdup is more pronounced than the variation of porosity.
178
0.36
0.37
0.38
0.39
0.40
0.41
0.42
0.43
0.44
0 10 20 30 40 50
Por &
Sat
.0.150
0.152
0.154
0.156
0.158
0.160
hp
0.36
0.37
0.38
0.39
0.40
0.41
0.42
0.43
0.44
0 10 20 30 40 50
Por &
Sat
.
0.150
0.152
0.154
0.156
0.158
0.160
hp
0.360.370.380.390.400.410.420.430.44
0 10 20 30 40 50
Por
& Sa
t.
0 .150
0.152
0.154
0.156
0.158
0.160
hp
Figure 7-10. Transverse averaged profiles of porosity (hard line), liquid holdup (square)
and liquid saturation (least line) vs. longitudinal position (z) at different wetting states (a)
f = 0.0; (b) f = 0.5; (c) f = 1.0 at Ul = 0.3 cm/s, Ug = 6.0 cm/s.
(a)
(b)
(c)
179
Figure 7-11. Distribution of gas and liquid interstitial velocity components in non-prewetted bed (f = 0) (up-2 rows plots) and in prewetted bed (f = 1) (low-2 rows plots) at Ul = 0.3 cm/s, Ug = 6.0 cm/s (G-gas, L-liquid).
-1 -0.5 0 0.5 10
20
40
60
80
100
-4 -3 -2 -1 00
20
40
60
80
100
-40 -20 0 20 400
50
100
150
-40 -30 -20 -10 00
20
40
60
80
100
-1 -0.5 0 0.5 10
20
40
60
80
100
-4 -3 -2 -1 00
20
40
60
80
100
f = 0 Vx (L)
f = 0 Vz (L)
-40 -20 0 20 400
50
100
150
-40 -30 -20 -10 00
20
40
60
80
100
f = 0 Vx (G)
f = 0 Vz (G)
f = 1 Vx (L)
f = 1 Vz (L)
f = 1 Vx (G)
f = 1 Vz (G)
180 When the wetting factor, f, increases, the capillary force effect becomes less
significant. For the case of completely prewetted particles, liquid occupies the low
porosity regions with higher liquid saturation. The liquid saturation profile and the
porosity profile now have opposite trends as shown in Figure 7-10c. The variation of
liquid holdup in the longitudinal direction, then, becomes small. Similar results are
obtained for the lateral profiles of liquid saturation at different wetting factors indicating
that completely prewetted particles can diminish the effect of local porosity variation on
liquid distribution and improve liquid holdup distribution.
Histograms showing the distribution of the gas and liquid velocity components
are illustrated in Figure 7-11. The distribution in horizontal velocity components Vx (L)
and Vx (G) for both liquid and gas, respectively, in prewetted and non-prewetted (Figure
7-11) beds are, as expected, symmetric about zero velocity, but higher standard
deviations of Vx (L) and Vx (G) are found in the case of the nonprewetted bed. The
distribution for vertical velocity components, Vz (L) and Vz (G), are Gaussian in nature,
and almost symmetric about the mean value. The observed zero velocities of the vertical
velocity components Vz (L) and Vz (G) are due to the no-slip boundary condition used for
two reactor walls. As the Z-axis points upward the axial downward velocities are
negative. It is of interest to note that in the case of nonprewetted beds some positive axial
velocity component Vz (G) exist, indicating counter-current gas flow is observed locally
(see Figure 7-11). This may be explained by the high heterogeneity of liquid holdup
which occurs in the nonprewetted bed due to capillary force. This implies that the effect
of liquid maldistribution on gas flow distribution in trickle bed can be significant,
especially in nonprewetted beds. The negative local gas velocity leading to local counter-
current flow of gas and liquid may explain why in the high interaction regime the slit
model of Holub et al. (1992) needed to be modified by Al-Dahhan et al., (1998) to
include a 'negative' slip between gas and liquid at the gas-liquid interface.
7.5.3 Porosity Distribution Effect To examine the porosity distribution effect, the beds with the same mean porosity
but with different standard deviations (std) of the porosity distribution (see Table 7-1) are
181 used in k-fluid model simulation at given operating conditions (Ul = 0.3 cm/s; Ug = 6.0
cm/s) and wetting conditions. Figures 7-12 and 7-13 show contours of the solid volume
fraction distribution in the model beds (II, III, IV) and the corresponding liquid volume
fraction (i.e., holdup) distributions. It is clear that the effect of porosity distribution on
liquid holdup distribution is significant in the case of non-prewetted beds (f = 0). The
higher the std of porosity distribution, the higher the std of liquid holdup distribution.
Even for the case of partial particle external wetting this effect still exists, which often
occurs deep in the trickling flow regime. However, further simulations indicate that such
porosity effect could be diminished partly if the packed-bed operates with completely
prewetted particles.
Figure 7.12 Contours of solid volume fraction (=1.0-porosity) distribution of model beds
(II, III, IV) for CFDLIB
7.5.4 Correlation Development Based on the presented k-fluid model simulation results, it can be concluded that
high heterogeneity of porosity distribution and high capillary force result in high
0 5 100
10
20
30
40
50 CFDLIB97.2
T=0.000E+00
N=0
CFDLIB97.2
T=8.000E+01
N=94249
CFDLIB97.2
T=1.300E+02
N=137075
0
10
20
30
40
50THE1
0.650.6428570.6357140.6285710.6214290.6142860.6071430.60.5928570.5857140.5785710.5714290.5642860.5571430.55
CFDLIB97.2
T=8.000E+01
N=94249
0
10
20
30
40
50CFDLIB97.2
T=2.100E+02
N=211803
182 heterogeneity of liquid holdup and two phase flow velocities. To quantify this
relationship of bed structure, particle wetting and resultant flow distribution, we correlate
these distribution results in terms of statistical parameters (e.g., standard deviation, std),
given in Equations (7-9) ~ (7-10c). Figure 7-14 shows the standard deviation comparison
of the k-fluid model computed value with the value calculated from the correlation below
Figure 7-13 Contours of CFDLIB simulated liquid volume fraction (holdup) distribution
in model beds (II, III, IV).
( ) ( ) ( )σ σ σ σl B B Ba f a f a= + +12
2 3 (7-9)
( )a B B1 01696 0 0002σ σ= − −. . (7-10a)
( )a B B2 0 2593 0 0012σ σ= − +. . (7-10b)
( )a B B1 05002 0 0019σ σ= +. . (7-10c)
In the above σl is the standard deviation (S.D.) of liquid holdup, f is the particle external
wetted fraction, σB is the standard deviation of cell porosity. With respect to its two limits
0
10
20
30
40
50THE2
0.20.1928570.1857140.1785710.1714290.1642860.1571430.150.1428570.1357140.1285710.1214290.1142860.1071430.1
CFDLIB97.2
T=8.000E+01
N=94249
0 5 100
10
20
30
40
50 CFDLIB97.2
T=0.000E+00
N=0
CFDLIB97.2
T=8.000E+01
N=94249
CFDLIB97.2
T=1.300E+02
N=137075
CFDLIB97.2
T=5.000E+01
N=52619
CFDLIB97.2
T=1.300E+02
N=137075
0
10
20
30
40
50CFDLIB97.2
T=2.100E+02
N=211803
CFDLIB97.2
T=1.300E+02
N=137075
CFDLIB97.2
T=5.000E+01
N=52619
183 of the prewetting states (i.e. f = 0.0 and f = 1.0), it is possible to establish Eqs (7-11a) and
(7-11b) which correspond to the nonprewetted case and the prewetted case, respectively.
0019.05002.0 += Bl σσ (f = 0.0) (7-11a)
σ σl B= +0 0713 0 0029. . (f = 1.0) (7-11b)
The ratio of the slopes of the two straight linear lines (Eqs 7-11a and 7-11b) is about
7.0 for the given operating condition as plotted in Figure 7-15. A higher degree of
particle wetting diminishes the effect of bed structure on two phase flow distribution.
0.000
0.004
0.008
0.012
0.016
0.020
0.024
0.0 0.2 0.4 0.6 0.8 1.0f-value
S.D
. of l
iqui
d ho
ldup
bed-II: CFD data bed-III: CFD data
bed-IV: CFD data bed-II by correlation
bed-III by correlation bed-IV by correlation
Ul = 0.3 cm/sUg = 6.0cm/s
Figure 7-14. Standard deviation (S.D.) of the liquid holdup distribution from CFD
simulations and from Eq (7-9) calculations vs. bed wetting factor (f) in model Bed-II, III,
IV.
184
0.000
0.005
0.010
0.015
0.020
0.025
0.030
0.035
0.040
0 0.02 0.04 0.06 0.08S.D. of porosity distribution
S.D
. of l
iqui
d hp
Figure 7-15. Standard deviation (S.D.) of the liquid holdup distribution vs. standard
deviation of the bed porosity at two wetting limits at Ul = 0.3 cm/s, and Ug = 6.0 cm/s.
The choice of f-value in the k-fluid model simulation is very important due to the
major effect of the f-value on flow distribution. Since the f-value can be described as the
percentage of particle external surface covered by a continuous liquid film (unbroken) in
whole packed beds, the particle external wetting efficiency developed in the trickle-bed
literature can be used as a good approximation of the f-value. One may use the correlation
of overall liquid holdup (e.g., Holub et al., 1992) to calculate the mean liquid holdup, and
use the correlation of particle external wetting efficiency (e.g., Al-Dahhan et al., 1995) to
evaluate the f-value, then use Equation (7-9) to calculate the std of holdup distribution if
the std of porosity is available for given inflow condition, and eventually establish the
Gaussian p.d.f. for liquid holdup distribution in trickle beds.
7.5.5 Superficial Velocities at the Inlet The above simulation results are given for certain inlet conditions (Ul = 0.3 cm/s;
Ug = 6.0 cm/s). Figure 7-16 shows the dependence of the global liquid holdup and
particle external wetting efficiency on liquid superficial velocity at gas superficial
Increased wetting
f = 0
f = 1
185 velocity of 3 cm/s. Particle partial-wetting occurs at the liquid superficial mass velocity
less than 6 kg/m2/s where both porosity distribution and partial wetting contribute to the
two phase flow distribution.
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0 2 4 6 8 10 12 14 16L (kg/m2/s)
Liqu
id h
oldu
p
0.00
0.20
0.40
0.60
0.80
1.00
1.20
Parti
cle
Wet
ting
Effic
ienc
y
partial wetting
Full wetting
Figure 7-16. Liquid holdup (filled squares) (Holub et al., 1992) and overall particle
external wetting efficiency from correlation (empty circles) (Al-Dahhan & Dudukovic,
1995).
186
0.05
0.08
0.11
0.14
0.17
0.20
0.23
0 2 4 6 8 10 12 14L (kg/m2/s)
Liqu
id h
oldu
p
CFDLIBHolub et al. 1992
Plus & minus bars: S.D. of hL
Figure 7-17. Liquid holdup values from CFDLIB simulations (mean +/- S.D.) and from
Holub’s correlation (1992): εB = 0.399; dp = 3 mm; Ug = 0.03 m/s (hL: liquid holdup).
Figure 7-17 shows CFDLIB simulated liquid holdup (mean +/- S.D.) at different
liquid superficial mass velocities. The holdup values calculated from the Holub’s et al
(1992) correlation are also plotted (filled squares). Clearly, the global holdup correlation
gives higher values than those from CFDLIB simulations particularly at high liquid flow
rate. One of the reasons could be the use of the global correlation for 3D beds on the 2D
bed which were simulated.
It is interesting to note that the higher S.D. values of liquid holdup are obtained at
low and high liquid superficial mass velocities, and a minimum S.D. value exists at L of
6 kg/m2/s where a complete particle external wetting is just reached. A similar
experimental observation was reported (Jensen, 1977). In the partial wetting regime, a
decrease in liquid superficial velocity causes lower f-values, and further enhances the
capillary force effect, and eventually results in more liquid nonuniformity (e.g. higher
187 standard deviation of liquid holdup). In the fully wetted regime, however, the flow
passage size decreases with increasing inlet liquid velocity and, it causes more significant
gas-liquid interactions which result in nonuniformities.
7.6 Conclusions and Remarks CFD flow modeling of bench-scale packed beds provides valuable information
for improving experimental protocol and data interpretation of scaled down reactors. The
combination of this work with developed mixing-cell network model allows one to
evaluate the performance of packed-bed reactor more realistically, even for the system of
complex reaction kinetics (See Chapter 8).
Because of the statistical nature of the cell-scale porosity distribution in packed-
beds, the cell-scale gas and liquid distributions in trickle-beds has been characterized by a
pseudo-Gaussian function in which the mean value is evaluated by the global correlation
(e.g. Holub et al., 1992), and the standard deviation (S.D.) is estimated based on the std-
correlation developed in this Chapter provide that the std of porosity is known. Capillary
pressure partially contributes to the liquid distribution if particles are partially wetted by
liquid flow. The effect of porosity nonuniformity on liquid distribution is diminished if
the particles are fully wetted. CFD is shown to be an efficient numerical tool for
developing quantitative relationships among bed structure, particle wetting and operating
conditions. Although the present numerical study was limited to a 2D rectangular bed, the
approach can be extended to 3D cylindrical packed-columns. The extensive experimental
validations of numerical results using MRI and high resolution CT technique are
proposed as recommended future work to establish the final structure-flow correlation.
188
Chapter 8
A Combined k-Fluid CFD Model and
the Mixing-Cell Network Model 8.1 Introduction
The bed-scale axial dispersion models (ADM) (El-Hisnawi et al., 1982) and the
pellet-scale diffusion-reaction models (Beaudry et al., 1987; Harold and Watson, 1993)
have been extensively used in predicting the performance of multiphase packed-bed
reactors by assuming simple ideal flow patterns and without attempts to solve the
momentum balance. To account for the non-ideal flow patterns in reactor modeling, the
efforts made in the literature include a two-region cell model (Sims et al., 1994), a cross-
flow model (Tsamatsoulis and Papaynnakos, 1995), and other models based on liquid
flow maldistribution (Funk et al., 1990), the stagnant liquid zones (Rajashekharam et al.,
1998), and one-dimensional variations of gas and liquid velocities along the reactor
(Khadilkar, 1998) etc. None of these models has a complete fundamental basis.
In principle, the performance of multiphase reactors can be predicted by solving
the conservation equations for mass, momentum and (thermal) energy in combination
with the constitutive equations for species transport, chemical reaction and phase
transition. However, because of the incomplete understanding of the physics, plus the
nature of the equations- highly coupled and nonlinear, it is difficult to obtain the
complete solutions unless one has reliable physical models, advanced numerical
algorithms and sufficient computational power. For most multiphase reactive flow, the
189 challenge exists in both numerical technique and physical understanding. The use of
direct numerical simulation (DNS) in single particle and single void scale micro-flow
modeling requires complete characterization of solids boundaries and voids
configuration, which is obviously undoable for a massive packed bed. To focus on the
macroscale flow distribution, a statistic method in implementing the porosity distribution
has recently shown its promise in multiphase flow modeling using ensemble-averaged k-
fluid CFD, model (see Chapters 5 and 6). The next attempt is to utilize the simulated flow
distribution results to assess the impact of the flow pattern on the reactor performance for
a given kinetics.
In the k-fluid CFD model, the finite volume method is used to discretize the
conservation equations of mass and momentum. The solutions for the continuous field
(e.g., velocities, phase holdup etc) are represented by a discrete data set at certain spatial
resolution. In other worlds, packed beds are treated as a network of interconnected
discrete cells as displayed in Figure 8-1a. In a two-dimensional case, for example, each
cell has four vertices and four faces. Each interface is common to two cells, and each
interior vertex is common to four cells. After performing the k-fluid CFD flow
simulation, one can directly obtain the phase volume-fractions and the fluid interstitial
velocities at each interior vertex of cells. Based on the mass balance for the fluid in each
cell, the data set can be further converted into the phase volume-fraction for each cell and
the fluid superficial velocity at each interface of the cells, as depicted in Figure 8-1b.
One should note that the cell network concept itself is not new. It was already
appeared in early 1960s, in which the effluent of each cell was assumed to split into two
streams, which were fed into the next row of cells (Deans and Lapidus, 1960). To let the
cell network be fed by the flow that modifies its values randomly, as in a stationary
Markov process, Krambeck et al (1967) suggested a general cell model, where are a
priori postulated network of channels connects the cells. In the two-dimensional array of
cells (well mixed tanks), alternate rows are offset half a stage to allow for radial mixing.
Jaffe (1974) applied this model to the heat release of a petroleum hydrogenation process,
and simulated the occurrence of steady state hot spots due to flow maldistribution. These
discrete cell models predict an infinite speed of signal propagation, which is not
190 fundamentally correct as pointed by Sundaresan et al. (1980). Schnitzlein and Hofmann
(1987) then developed an alternative cell network model in which the elementary unit
consists of an ideal mixer and a subsequent plug flow unit. The fluid streams are split or
merged in infinitesimally small adiabatic mixing cells (without reaction), located between
the different layers of the elementary units. The fluid streams are split according to the
rule of preserving a constant flux through all elementary units, and the additional model
parameter δ as a measure of the relative size of the two mini-units is needed. A better
prediction of the axial temperature profile for partial oxidation of methanol to
formaldehyde was achieved by this cell model than by the continuum dispersion model.
Later on, Kufner and Hofmann (1990) incorporated the radial porosity distribution into
the above cell model, which led to an even better agreement of the predicted temperature
profile with the experimental data. One should note that the above-mentioned cell models
were examined only for single-phase flow. Although they were claimed to be applicable
for multiphase flow in principle, the extensive needed algebra largely diminishes the
advantages of the model, particularly, when the complex bed-structure and the
complicated multiphase interactions need to be considered as that in the k-fluid CFD
model.
In this Chapter, a novel application of the discrete cell network concept to
modeling of multiphase packed-bed reactors is developed in which the flow distribution
and the structure heterogeneity of the packed bed are implemented in a realistic way. For
example, the spatial distribution of fluid velocities is not obtained by the empirical flow-
splitting rule as in previous cell models, but is obtained from the solution of the k-fluid
CFD flow simulations. The detailed description and discussion of the k-fluid CFD model
for multiphase flow in packed beds are available in Chapters 5 and 6. The objective of
this Chapter is to illustrate how to utilize this combination of a CFD and cell-network
model for prediction of reactor performance.
191
Figure 8-1a. Two-dimensional interconnected cell network
Figure 8-1b. Fluid superficial velocities and concentrations of species i at interface of the
cell j, where C3 i,j = C4 i,j due to the well-mixing.
U4j, C4 i,j
U1j, C1 i,j
U3j, C3 i,j
U2j, C2 i,j
192
8.2 k-Fluid CFD Model for Flow Simulation A k-fluid CFD model has been recently developed for packed beds to obtain the
spatial distributions of flow velocity and phase volume-fraction at certain spatial
resolution provided that the porosity distribution at the same scale is known. To consider
the effect of particle wetting on liquid distribution, the capillary pressure and particle
fractional wetting of the external surface have been taken into account in the pressure
calculations.
As discussed in Chapter 5, macroscopic flow velocity and phase holdup
distributions can be obtained by the k-fluid CFD model provided that the following
information are available: (i) the mean porosity, (ii) the longitudinally-averaged radial
porosity, if using a cylindrical column, and (iii) the type of sectional porosity distribution
and its variance. Input information (i) and (ii) is available in the literature for most of the
random packing (see Benenati and Brosilow, 1962). Information (iii) is obtainable
through the magnetic resonance imaging (MRI) of packed-bed structures (see Sederman
et al., 1997). The momentum exchange coefficients, Xkl, are computed by Ergun type of
expressions developed by Holub et al (1992) and Attou et al (1999). The detail discussion
of these issues is provided in Chapter 5.
A generated porosity contour based on a pseudo-Gaussian distribution with a
mean porosity of 0.399 and a variance of 0.012 is shown in Figure 8-2a in Cartesian
coordinates. The spatial resolution (i.e., discrete size) for this case is 1 cm, which is about
three particle diameters (if dp = 0.3 cm). The total number of discrete sections is 500
(=10 in horizontal, 50 in vertical direction). Figure 8-2b gives the histogram of 500
sectional porosity values. The multiphase flow simulation using the k-fluid CFD model is
based on such a porosity distribution, which was used as initial porosity value for each
section in solving for ensemble-averaged three-phase mass and momentum equations.
The momentum equation for the solid phase is turned off while solving the rest of
equations. Therefore, the porosity structure can be retained during the simulation. Figures
8-3a and 8-3b display the computed liquid velocity components at the same resolution as
the porosity distribution. Since the mass transfer coefficient of liquid to particle, kls, a
function of liquid superficial velocity. From the liquid velocity distribution given in
193 Figures 8-3a and 8-3b, one can compute the kls value at each cell based on proper
correlation, and then come up with a contour plot of the kls value distribution as shown in
Figure 8-4. It is clear that high liquid velocity corresponds to high mass transfer
coefficients.
Figure 8-2a. Porosity distribution at spatial resolution of 1 cm (dp = 3 mm, L = 50 cm,
D = 10 cm).
194
0.3 0.35 0.4 0.45 0.50
10
20
30
40
Figure 8-2b. Histogram of porosity distribution (Gaussian distribution) used in the k-fluid
CFD model.
195
Figure 8-3a. Simulated liquid superficial velocity component (Ux, m/s): Ul0 = 0.003 m/s;
Ug0 = 0.06 m/s.
196
Figure 8-3b. Simulated liquid superficial velocity component (Uz, m/s): Ul0 = 0.003 m/s;
Ug0 = 0.06 m/s.
197
Figure 8-4. Computed cell scale mass transfer coefficient (kls, cm/s): Ul0 = 0.003 m/s;
Ug0 = 0.06 m/s.
8.3 Mixing-Cell Network Model To incorporate the gas-liquid mass transfer into the mixing-cell model at the cell
scale (i.e. a scale of group particles; centimeter scale in this study), one writes the mass
balance equations for the species in the gas and liquid bulk phase and at the catalyst
surface. By assuming that each cell behaves like a well-mixed unit, the mass balances are
essentially algebraic in nature.
198 For an irreversible solid catalyzed reaction between gas A and liquid reactant B of
the general form γA g B l P l( ) ( ) ( )+ → , the rate of reaction, per unit volume of the
catalyst, is given by nB
mArP CCkρ=Ω .
The concentrations of various components in the gas and liquid streams leaving
cell j are represented by CAg, out, CAl, out, CBl, out, and in the streams entering the jth cell by
CAg, k, CAl, k, CBl, k. The species mass balances for species A and B for the jth cell can then
be written as follows.
Species A, in the bulk gas phase
( )
−−−= ∑∑
−−outAl
A
outAgLLc
outkkkgoutAg
inkkAgkkg
outAgc C
HC
aKVauCCaudt
dCV ,
,,,,,
, (8-1)
Species A, in the bulk liquid phase
( )
( ) [ ]AsoutAlAssc
outAlA
outAgALLc
outkkkloutAl
inkkAlkkl
outAlc
CCakV
CH
CaKVauCCau
dtdC
V
−−
−+−= ∑∑
−−
,
,,
,,,,,
(8-2)
Species A, at the catalyst particle surface
( ) [ ] ( ) CEn
Bsm
AsjrPAsoutAlASSAs
c CCkCCakdt
dCV ηηεγρ −−−= 1, (8-3)
Species B, in the liquid phase
( ) [ ]BsoutBlBsscoutk
kkloutBlink
kBlkkloutBl
c CCakVauCCaudt
dCV −−−= ∑∑
−−,,,,,
, (8-4)
Species B, at the catalyst particle surface
( ) [ ] ( ) CEn
Bsm
BsjrPBsoutBlBssBs
c CCkCCakdt
dCV ηηερ −−−= 1, (8-5)
The appropriate dimensionless quantities are defined as follows:
0,AgAgg CCy = 0,AgAlAl CCHx = 0,AgAsAs CCHx = 0,BlBll CCx =
0,,'
, / gkgkg uuu = 0,,', / lklkl uuu = Assume kaa =0
199 ( )
00, aHuaKV
Ag
LLCA =α
( )00, au
akV
l
BssCB =α βA
g A
l
u Hu
= ,
,
0
0
( )( )ALL
AssA ak
ak=γ
( )( ) 0,
0,1
AlALL
AgmABss
B CaKCHak −
=γ ( )
( )nBl
m
A
Ag
Ass
jrP CH
Cak
kk 0,
10,* 1 −
−=
ερ (8-6)
By substituting the above dimensionless quantities into the mass balance equations (8-1)
~ (8-5), one gets the following dimensionless equations (8-7) ~ (8-11) at steady state
conditions.
[ ]outAloutAgAoutk
kgoutAgink
kAgkg xyuyyu ,,,'
,,,' −=− ∑∑
−−
α (8-7)
[ ] [ ]AsoutAlAAAoutAloutAgAAoutk
kloutAlink
kAlkl xxxyuxxu −+−−=− ∑∑−−
,,,,'
,,,' γβαβα (8-8)
( ) nBs
mAsCEAAsoutAl xxkxx ηηγγ *
, =− (8-9)
[ ]BsoutBlBoutk
kloutBlink
kBlkl xxuxxu −=− ∑∑−−
,,'
,,,' α (8-10)
( ) nBs
mAsCEBBsoutBl xxkxx ηηγ*
, =− (8-11)
Since we know the cell inflow and outflow velocities ( ,, ',
', inklinkg uu −−
',
', , outkloutkg uu −− ) and the cell inflow species concentration ( inkBlinkAlinkAg xxy −−− ,,, ,, ),
the variables to be solved are out-flow species concentrations and species concentrations
at the catalyst particle surface ( BsAsoutBloutAloutAg xxxxy ,,,, ,,, ). For each cell there are
five equations with five unknown. Note that the mass transfer coefficient values
( AAAAABA γβαβααα ,,, ) and the extent of particle wetting (ηCE) are affected by
the local two phase flow distribution, and these values are evaluated using empirical
correlations based on local fluid velocities which are calculated from the CFD model.
The computational scheme of the mixing-cell network model is direct and simple.
To obtain the species concentration for every cell-interface in the 2D reactor domain, one
needs to solve Equations (8-7) to (8-11) for all the cells. Basically, this can be
accomplished layer by layer starting from the top of the bed. For a layer of cells there are
normally four configurations of the inflow and outflow as shown in Figure 8-5. A set of
200 boundary conditions for flow velocities and species concentration are given at the first
layer of cells (input cells, input conditions) as well as the cell adjacent to the walls. By
solving such a set of algebraic equations layer by layer downward, one can get a whole
set of solutions for species concentrations at cell interface of the packed bed. The
physical properties of the fluids and the relevant kinetics parameters of the reaction are
given in the Nomenclature.
Figure 8-5. Cells with different inflow and outflow configurations
For demonstration purpose, Figure 8-6 illustrates the concentration distribution of
species B in the liquid bulk. Such a concentration mapping of species provides value in
analyzing the performance of the packed beds. This can reveal the structures and flow
heterogeneities encountered due to the changes in operating conditions or other
disturbances of process variations. Figure 8-7 shows the longitudinally averaged liquid
velocity and the corresponded species concentration profile in the horizontal X direction.
As expected, the high local liquid superficial velocity causes a lower residence time of
the liquid, and yields lower conversion (higher concentration) of species B. The existing
U4j, C3i,j
U1j, C1i,j
U3j, C3i,j
U2j, C3i,j
(type-1)
U4j, C3i,j
U1j, C1i,j
U3j, C3i,j
U2j, C2i,j
(type-2)
U4j, C4i,j
U1j, C1i,j
U3j, C3i,j
U2j, C3i,j
(type-3)
U4j, C4i,j
U1j, C1i,j
U3j, C3i,j
U2j, C2i,j
(type-4)
201 liquid superficial velocity profile suggests that the plug flow model will over-predict
conversion. This is indeed the case as shown in Figure 8-8. The axial dispersion model, in
which the dispersion coefficient, De is calculated from the correlation by Sater and
Levenspiel (1966), gives an under-prediction of conversion compared to the mixing-cell
network model. As displayed in Figure 8-8, by adjusting the De value, the ADM
predicted solution approaches the profile computed by the mixing-cell network model
based on the flow field from by the k-fluid CFD simulation.
Figure 8-6. Concentration contour of species B in the liquid phase (m = 0.0; n = 1.0;
r = 1.0) CBl, 0 = 5.4 kmol/m3, Ul0 = 0.003 m/s; Ug0 = 0.06 m/s.
202
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
0 2 4 6 8 10X
Con
cent
ratio
n of
B, k
mol
/M3
2.85E-03
2.90E-03
2.95E-03
3.00E-03
3.05E-03
3.10E-03
3.15E-03
Liqu
id s
uper
ficia
l vel
ocity
, m/s
Figure 8-7. Longitudinally averaged concentration profile of species B and liquid velocity
component (Uz) profiles in the X direction. (CBl - filled circle; Uz - blank square; CBl, 0 =
5.4 kmol/m3; Ul0 = 0.003 m/s; Ug0 = 0.06 m/s).
203
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
0 10 20 30 40 50Axial position from top (cm)
Spec
ies
B co
ncen
tratio
n, k
mol
/m3
iv- ADM (set De)iii- Mixing-cell Networkii- ADM (Sater and Levenspiel, 1966)i- Plug Flow
Figure 8-8. Calculated concentration profiles of species B at k = 1.E-04 m3/kg.s, n = 1.0,
m = 0.0 by (i) plug flow; (ii) ADM (De = 2.53E-04 m2/s calculated from Sater and
Levenspiel, 1966, Pe = 5.92); (iii) Mixing-cell network model; (iv) ADM (set De = 1.5E-
04 m2/s, Pe = 10). CBl, 0 = 5.4 kmol/m3; Ul0 = 0.003 m/s; Ug0 = 0.06 m/s
8.4 Concluding Remarks A k-fluid CFD model has been recently adopted for simulating multiphase flow in
packed beds as discussed in Chapters 5 and 6. To evaluate the impact of flow distribution
on the performance of packed-bed reactors for a given kinetics, a mixing-cell network
model has been proposed in which the k-fluid CFD model results are used as input
information regarding the multiphase flow field. The preliminary results of flow and
reaction modeling have shown promise that such a combination of models is capable of
providing the information on the distribution of species concentrations. While striving to
solve multiphase reaction and multiphase flow simultaneously, the sequential modeling
scheme for complex flow and reaction is suggested here as a plausible engineering
204 approach, particularly for isothermal systems in which the flow distribution is not
significantly affected by reaction(s).
205
Chapter 9
Thesis Accomplishments and Future
Work 9.1 Summary of Thesis Accomplishments The accomplishments of each portion of the thesis are summarized as follows
9.1.1 Discrete Cell Model (DCM) For the flow distribution in packed beds, the numerical comparison of DCM
predictions and k-fluid CFD results over a range of Reynolds numbers (i.e. feed
superficial velocities) leads to the conclusion that the two models with different
numerical schemes yield results which are comparable within engineering accuracy
bound of 10%. These results are also comparable with the experimental data in the
literature. This work justified, for the first time, the main assumption used in the DCM
approach that flow in packed beds is governed by the minimum rate of total mechanical
energy dissipation.
For single-phase flow modeling, DCM was revisited by analyzing the
contributions of the individual terms in the equation for the rate of energy dissipation.
The inertial term in the energy dissipation rate per unit cell was found negligible
compared to the kinetic and viscous term except in the regions of structural obstacles in
the bed. The Reynolds stress term can be ignored due to the negligible contribution of
this term to cell-scale (i.e. particle diameter scale) fluid velocity distribution.
206 The extension of DCM for simulation of two phase flow in trickle-bed reactors
was carried by introducing the particle fractional wetting effect to distinguish between the
flow patterns in prewetted and non-prewetted beds. The effect of liquid distributor on
liquid flow distribution was found significant in the upper half of the bed.
9.1.2 k-Fluid CFD Model The Eulerian k-fluid CFD model has been adopted to model the macroscale
multiphase flow in packed beds in which the geometric complexity of bed structure is
resolved through statistical implementation of sectional porosities, and the complicated
multiphase interactions are evaluated using the Ergun type of expressions which were
developed based on bench-scale hydrodynamics experiments. The effect of particle
wetting on flow distribution is incorporated in the phase pressure computations. The drag
exchange coefficients for the solid particle and fluid, Xks, are obtained based on the
models of Holub et al. (1992) or Attou et al. (1999). The drag exchange coefficient for
gas and liquid is calculated by the model of Attou et al. (1999). Due to the relationship
between the section size and the variance of the sectional porosity, the selection of the
section-size has to follow a certain relation, which is expected to be available by
analyzing the full 3-D porosity distribution data by MRI at fine spatial resolution
(Sederman et al., 1997). The comparison of the k-fluid CFD simulation and the
experimental results has been performed for both liquid upflow and gas-liquid cocurrent
downflow in packed beds. The effects of feed flow distributions have been simulated for
bench-scale and pilot scale packed at steady state and unsteady state flow conditions.
The following conclusions are reached:
• The k-fluid CFD model can capture the longitudinally averaged radial profile of the
axial velocity and the statistical features of the 2-D sectional velocity distribution
provided that the following information on bed structure is available: (i) mean
porosity, (ii) longitudinally-averaged radial porosity and (iii) sectional porosity
distribution type and its variance.
207 • For two phase flow systems, the predictions of the k-fluid CFD model for the
overall liquid saturation and pressure gradient are comparable with experimental
data and prediction of other hydrodynamic correlations.
• Nonuniform gas and liquid feed distribution have an effect on flow distribution
downstream in the bed.
• The k-fluid model can simulate the dynamic macroscopic flow pattern at periodic
inflow condition, which ensures better uniformity of liquid distribution at all
locations over that observed in steady state operation.
The applications of the k-fluid CFD model in the scale-down and scale-up of
packed beds have been demonstrated in Chapter 7 in which the k-fluid CFD model was
found is capable of establishing the structure-flow relationship for bed scale-up, and for
simulating the multiphase flow in a bench reactor for the interpretation of experimental
data.
9.1.3 Mixing-Cell Network Model To evaluate the impact of the flow distribution on the performance of packed-bed
reactors for a given kinetics, a mixing-cell network model has been proposed as a
sequential model in which the k-fluid CFD model results are used as input information on
the multiphase flow field. The preliminary results of flow and reaction modeling have
shown some promise that such a combination is capable of providing the distribution
information on species concentration and selectivity. While striving to solve multiphase
reaction and multiphase flow simultaneously, such a combined modeling scheme is
suggested as an alternative engineering approach for complex flow and reaction system.
208
9.2 Recommendations for Future Research Several recommendations can be made for extending the work conducted in
different parts of this study as listed below:
9.2.1 Discrete Cell Model (DCM) DCM was applied to model single- and two-phase flow in packed beds. The
subroutine DN0ONF from the International Mathematical Statistics Library (IMSL) was
used to solve the nonlinear multivariable minimization problem with constraints. A more
efficient numerical algorithm is recommended for simulating the flow in large scale
packed beds. The capillary pressure term due to particle fractional wetting was
incorporated in the calculation of local liquid holdup. Further model development can
expand the work by directly considering the particle fractional wetting effect in terms of
the energy dissipation rate due to capillary force in the equation of the total energy
dissipation rate.
The potential application of the DCM is recommended to simulate the
macroscopic flow pattern in packed beds with structural packing in which the cell
pressure drop and the cell liquid holdup can be calculated by formulas other than the
Ergun equation.
9.2.2 k-Fluid CFD Model There are two major phases for future efforts in modeling of multiphase packed
beds using the k-fluid CFD model. The first is to validate the k-fluid simulation results in
packed beds, particularly for multiphase flow, and to fully verify the drag coefficients
used and to further confirm the porosity implementation method proposed in this study.
To date, there have been no comparisons between the k-fluid model simulations and
measured flow fields in a porous sample even for single-phase flow. Due to lack of
proper experimental data, most previous comparisons were limited to some assemble-
averaged quantities such as longitudinal averaged radial velocity profile (see Chapter 3),
and the statistical information for sectional flow velocity distribution as given in Chapter
6 for liquid upflow in packed beds. The advances in noninvasive flow measuring
209 techniques such as nuclear magnetic resonance (NMR), and radioactive computer
tomography (CT) have shown great promise in providing high quality data for the above
comparison purposes. Manz et al (2000) recently have performed NMR velocimetry and
magnetic resonance imaging (MRI) volume-measurements, and the lattice-Boltzmann
simulations of the flow field within the same porous structure to quantitatively assess the
simulation ability of the lattice-Boltzmann method. The structure for the simulation was
taken from a 3-D image of the pore space for which the flow measurements were
conducted. Good quantitative agreement between flow visualization and the results of the
lattice-Boltzmann simulation was reported. Following such a research path, one should
be able to fully validate the two-fluid simulations even for multiphase flow
quantitatively. Since the statistical distribution of the section porosities depends on the
chosen section size (ls), based on which the flow velocity data are obtained (Sederman,
2000), the comparison between fluid flow measurement and two-fluid simulation can be
conducted at different section sizes. Although the CT scanner cannot provide the
velocimetry data, it can give the distributions of the three-phase volume fraction at
certain spatial resolution (pixel size) in packed beds (Toye et al., 1997).
Since the MRI technique can provide full 3-D structural information of packed
beds, the second phase of this research should be to extend the 2-D flow simulation to the
3-D cylindrical coordinates (r, z, ϕ) in which the angular heterogeneities of porous
structure are taken into account. This is believed to be important for the dynamic two-
fluid modeling to be able to capture the time scale of fluid flow in packed beds
reasonably.
To further expand this work to gas-liquid cocurrent upflow and counter-current
flow systems, more efforts are needed to treat the boundary conditions of the inflow and
outflow, and to develop ways to evaluate the closures.
For a long term research plan, the extensions of the k-fluid CFD model should consider
non-isotherm systems and add the mass source terms due to the reaction and phase
transition.
210 9.2.3 Mixing-Cell Network Model
The novel mixing-cell network approach based on the flow field information
provided by the k-fluid CFD model was shown to be suitable for modeling multiphase
flow and reaction in packed beds. The results from such combined modeling scheme of
flow and reaction are valuable for the purpose of diagnostic analysis of the operating
commercial units. The experimental study of using a 2D rectangular bench-scale bed with
a well-defined reaction system is recommended for validating the model results by liquid
flow imaging and collection of species concentration distribution data. The case study in
Chapter 9 was presented only in 2-D coordinates for the isothermal case with simple
kinetics. Further model development can expand this work to (i) non-isothermal case
where the influence of temperature maldistribution can be incorporated, both in the k-
fluid CFD flow simulation and mixing-cell reaction modeling; (ii) complex reaction
system; (iii) 3D cylindrical coordinates.
211
Appendix
Comparison of Trickle Bed and
Packed Bubble Column Reactor
Performance for the Hydrogenation of
Biphenyl A.1 Introduction
Removal of sulfur and nitrogen from petroleum feedstocks, heavy oils, and
residua by catalytic hydrotreating, hydroprocessing, and hydrocracking, or saturation of
olefinic bonds in these feeds via catalytic hydrogenation, represent critical technologies
in petroleum refining for the production of fuels, lubricants, waxes, and lower
hydrocarbons (Speight, 1980, 1981). Commercial petroleum processes where the
feedstock can be processed without significant deactivation and plugging of a fixed
catalyst bed employ packed-bed reactors with either cocurrent downflow (trickle-bed
reactors) or cocurrent upflow (packed bubble-flow reactors) of the gas and liquid.
Heavier feedstocks, that result in appreciable rates of catalyst deactivation such that
fixed-bed operations are not economical, utilize three-phase fluidized beds (ebullated-bed
reactors) or entrained catalyst flow reactors. Design and scale-up of these various
multiphase reactor types for a new process, or rating of an existing commercial reactor
for a different feedstock or catalyst, is widely practiced in most petroleum refining
212 companies as a proprietary art and science. Only few recent studies (i.e. Toppinen, 1996;
Toppinen et al. 1996) consider reactor modeling and process optimization.
Performance comparison of laboratory scale packed-bed reactors operated in
downflow and upflow modes using the hydrogenation of α-methystyrene to cumene in
hexane solvent as a test reaction, has been reported (Wu et al., 1996; Khadilkar, et al.,
1996). In these studies, experimental performance (conversion) data over a range of
operating conditions have been compared to model predictions, and good agreement was
obtained. The advantage of using either an upflow or downflow mode depends on
whether liquid or gas reactant is rate limiting. Upflow mode is preferred for liquid
reactant limited case since it provides better accessibility of the rate limiting reactant to
the catalyst. Downflow is a preferred mode for gas limited reaction as transport to the
catalyst particles is faster through thinner liquid films or via partially wetted pellets. No
analogous study has been reported for a petroleum feedstock system whose intrinsic
reaction kinetics are more complex, and which depend upon the concentrations of both
the reactants and products. The choice of the operating mode, i.e., downflow or upflow, is
not always obvious in such a case.
The primary objective of this study is to compare the effect of gas-liquid
contacting pattern on the performance of packed-bed reactors for a reaction system whose
kinetics and other characteristics are typical of those encountered in the hydrogenation of
a petroleum feedstock. Biphenyl was chosen as the model petroleum compound for
several reasons: (1) it is a primary product of the hydrodesulfurization of
dibenzothiophene compounds in heavy feedstocks (Nag et al., 1979); (2) it is
representative of the least reactive aromatic hydrocarbons derived from coal; (3) the low
solubility of biphenyl in n-hexadecane solvent (ca. 1 mol %) results in a dilute biphenyl
solvent solution that mimics the concentration of active compounds in a typical
petroleum feed; (4) detailed biphenyl hydrogenation kinetics have been reported in the
literature over several different types of hydrogenation catalysts (Sapre and Gates, 1982;
Toppinen et al., 1996). Because the biphenyl-hydrocarbon solution is very dilute, the
resulting process requires huge volumetric processing capability in the range of 10,000 to
50,000 tons per year, which is analogous to petroleum processing.
213
A2 Reactor Models A2.1 Analysis of Kinetic Model
In the biphenyl hydrogenation network catalyzed by sulfided CoO-MoO3/γ-Al2O3,
literature reports indicate that the primary hydrogenation reaction produces
cyclohexylbenzene at a rate that is at least one order of magnitude faster than the other
reactions (Sapre and Gates, 1981). Thus, the modeling work of this study was based upon
this primary reversible hydrogenation that is described by a Langmuir-Hinshelwood
kinetic model in the range of 573-648 K and 70 - 200 atm (Sapre and Gates, 1982). The
effect of concentration of H2S, which was added to the system to stabilize the activity of
the catalyst, was also taken into account in the kinetics model. The final form of the rate
equation used for the reactor modeling studies is shown below, where A, B, C and D
correspond to hydrogen, biphenyl, cyclohexylbenzene and H2S, respectively.
( ) ( )25
243
23
1
11sec ADB
cABB CKCKCK
CkCCkgcat
gmolr+++
−=
−
(A-1)
K3, K4 and K5 are the adsorption equilibrium constants corresponding to components B, D
and A, respectively. k1, k2 are the forward and reverse reaction rate constants,
respectively. At the different reaction temperatures, the corresponding reaction rate
constants, ki and adsorption constants, Ki are reported as listed in Table A-1.
From a designer’s point of view, a primary analysis of the kinetic model should
help indicate the preferred reactor type. It is evident that the rate of the forward reaction
will decrease when increasing the concentration of product, C; and will increase when
increasing the concentration of A (increasing hydrogen pressure). The effective
dependence of the reaction rate on the concentration of reactant, B, however, is associated
with the magnitudes of K3CB. When the value of K3CB is much less than 1, the
approximately first order behavior with respect to B (biphenyl) will be encountered;
whereas the –1 order behavior with respect to B will occur when the K3CB is much larger
than 1.0. The values of K3CB vary from approximately 0.115 to approximately 0.575 at
the CB of 0.025 mol/L and conditions of this study (temperature from 573 K to 648 K).
Thus, the reaction behavior is approximately first order in B only at higher temperature
214 (i.e. 648K) and/or lower concentration of B. At those conditions, it is assured that the
effect of CB on conversion is negligible. One should note, however, that the above
analysis rests on the case when the reaction is kinetically controlled. When the mass
transfer resistance is taken into account, the effect of species concentration on reactor
conversion only becomes clear a quantitative sense after performing the reactor modeling
study.
A2.2 Key Assumptions The axial-dispersion model (ADM) can be used to describe the deviations from
plug- flow (the discussion of these deviations will be given later).
1. Pure hydrogen in the gas phase is in excess such that concentration of hydrogen is
constant in the gas phase (non-volatile liquid phase at high pressure).
2. Catalyst internal wetting is complete due to capillary action.
3. Steady state and isothermal conditions prevail.
4. In the upflow mode, the catalyst external wetting is complete, but in the downflow
mode, the catalyst surface may be partially externally wetted by the flowing liquid
(The extent of wetting depends on the operating conditions).
5. Gas solubility in the liquid can be described by Henry’s law.
6. Intrinsic reaction rate is the same as that suggested by Sapre and Gates (1982).
7. Finite mass transfer resistances (Gas-to-liquid, Liquid-to-solid, etc.) and internal
particle diffusional resistances may be present.
A2.3 Cocurrent Trickle Bed and Packed Bubble Flow Bed Models The reactor model allows for the different concentration in the liquid and on the
surface of particles by considering liquid-solid mass transport with pertinent kinetics.
Subject to the above assumptions, the species mass balance for the reactor can be
written as follows for the liquid phase for all 3 components, A, B, C:
( ) [ ] [ ]Dd C
dzu
dCdz
ka C C k a C CEL AA L
SLA L
gL A e A L LS LS A L A LS,, ,
, , , ,
2
2 0− + − − − = (A-2)
215
[ ]Dd C
dzu
dCdz
k a C CEL BB L
SLB L
LS B LS B L B LS,, ,
, , ,
2
20− − − = (A-3)
[ ]Dd C
dzu
dCdz
k a C CEL CC L
SLC L
LS C LS C L C LS,, ,
, , ,
2
2 0+ − − = (A-4)
The species mass balance on the catalyst particles is:
[ ] ( )k a C C rLS m LS m L m LS B CE m, , ,− = −η ε η1 ; m A B C= , , (A-5)
Reactor boundary conditions are of the Danckwerts type:
[ ]− = −DdC
dzu C CEL m
m LL m i m L,
,, , m A B C= , , ; at z = 0 (A-6)
dCdz
m L, = 0 m A B C= , , ; at z = L (A-7)
The above equations can be written in dimensionless form by introducing the following
variables:
Let cCC
CC HA L
A L
A L i
A L
A G i A,
,
, ,*
,
, , /= = ; c
CCB L
B L
B L,
,
, ,
=0
; cCCC L
C L
B L,
,
, ,
=0
;
ξ = zL
; ( )α G L
gL
SL
ka L
u, = ; α L SLS A LS
SL
ka a Lu,
,( )= ;
β η1 = C
L A L i
wLu C , ,
*; β η
2 = C
L B L i
wLu C , ,
* ; Pe u LD
L
E L
=,
Substitution of the above dimensionless variables into the equations, and introduction of
dimensionless groups lead to 3 ordinary differential equations:
( ) ( )1 1 02
2Ped cd
dcd
c c cA L A LG L A L L S A L A L S
, ,, , , , , ,ξ ξ
α α− + − − − = (A-8)
( )1 02
2Ped c
ddc
dc cB L B L
L S B L B L S, ,
, , , ,ξ ξα− − − = (A-9)
( )1 02
2Ped cd
dcd
c cC L C LL S C L C L S
, ,, , , ,ξ ξ
α+ − − = (A-10)
There are 3 algebraic equations:
[ ]α βLS m L m S mc c r, ,− = 1 ; m A= , (A-11a)
[ ]α βLS m L m S mc c r, ,− = 2 ; m B C= , (A-11b)
216 Boundary conditions are:
ζ = 0 (reactor inlet), we have
[ ]1Pe
dcd
c cm Lm L m L i
,, , ,ξ
= − ; m A B C= , , (A-12)
ζ = 1.0 (reactor outlet),
dcd
m L,
ξ= 0 ; m A B C= , , (A-13)
This set of reactor model equations demands the numerical solution due to non-
linearity of the reaction rate equation. There are some algebraic equations involved in this
set of nonlinear coupled ODEs due to the consideration of mass transfer in the liquid film
around the surface of the catalyst particles. Hence, the numerical code COLDAE, which
is based on a spline collocation method, was used to solve the nonlinear coupled ODEs
with algebraic constrains.
In order to obtain the solution for the species concentration profiles, the model
requires an a-priori knowledge of the intrinsic rate constants and adsorption equilibrium
constants (Table A-1), the catalyst effectiveness factor for a totally wetted particle,
hydrogen solubility in the solvent, external liquid-solid contacting efficiency, mass
transfer coefficients (kalg and kals) and reactor bed characteristics. The summary of
various correlations used to calculate the model parameters and the properties of catalyst
are listed in Tables A-2 and A-3. The selection of operating conditions depends not only
on the processing requirement, but also on the contacting pattern. The details are given
later.
A3 Results and Discussion A3.1 Flow Characteristics and Flow Regimes
The knowledge of flow characteristics and flow regimes is essential in
understanding the hydrodynamics and mass transfer as well as reactor performance. The
nature of multiphase contacting in different flow configurations (cocurrent down-
flow/cocurrent up-flow) is very different as shown in Figure 1. Even at the same
operating conditions, the local scale hydrodynamics and mass transfer character are not
217 following the same rules. Thus, it is essential to make sure that one understands in which
flow regime the reactor will be operated based on the requirements of the process. Since a
high volumetric flow rate (industrial scale) is required for both gas and liquid in this
study, it may be desirable to operate it in a downflow ‘pan cake’ packed bed reactor
(large diameter) to achieve a trickle flow regime for the liquid, whereas we may operate it
in a up-flow packed bed reactor with bubble flow regime. For this purpose, the
Charpentier flow type regime map, proposed by Larachi et al. (1994), which accounts for
pressure effects, has been used to guide the selection of gas and liquid flow rates for the
down-flow mode. Five typical conditions (I to V) have been selected and are listed in
Table 4. All these conditions, as marked in Figure 2, were found to be on the border of
trickling and pulsing flow except at very high pressure (105 atm). Nevertheless, Gianetto
and Spechia (1992) reported that, at relatively low pressure (< 0.2 Mpa), the transition
between flow regimes is well defined, whereas at elevated pressure, the transition zone
shifts. The same consideration was made to determine the gas and liquid velocity for the
bubble flow packed bed where Fukushima and Kusaka’s (1979) flow map was used. The
operating conditions listed in Table A-4 are not only above the minimal gas velocity for
bubble flow predicted by Saada (1972), but also guarantee the bubble flow regime. The
reactor simulation results and discussions will be based on these ranges of operating
conditions for the corresponding operational modes.
A3.2 Trickle Bed Reactor Performance Figure A-3 shows the typical species concentration profiles along the trickle-bed
reactor at a given operating condition (II). Solution of the model equations reveals that
hydrogen concentration in the liquid phase is almost constant along the reactor except in
the entrance zone, whereas the concentrations of components B and C reach constant
levels after a certain reactor length. Although no significant effect of feed concentration
of B on conversion was found, the effect of hydrogen concentration on reactor conversion
was dominant. This conclusion can be drawn from Figure A-4. in which the effect of
operating pressure on the exit biphenyl conversion is shown. Increasing hydrogen feed
218 concentration by increasing operating pressure (Henry’s Law) effectively improves the
reactor conversion.
The effect of liquid flow rate on the exit conversion and global hydrogenation rate
are given in Figure A-5. Higher liquid flow rate leads to lower exit conversion and higher
global hydrogenation rate. This implies that liquid reactant limiting behavior is observed
for this reaction conducted in cocurrent downflow trickle-bed mode.
A3.3 Packed Bubble Flow Reactor Performance Similar simulations have been performed for the case of a single cocurrent upflow
packed-bed reactor where gas flows through the liquid in bubble flow (flooded packed
bed reactor with a diameter of 4 m). The same reactor model was applied except with
different model parameters corresponding to the upflow operation (i.e. different mass
transfer coefficients). The effect of biphenyl feed concentration on the exit conversion
was again not apparent, whereas the hydrogen concentration in the liquid phase plays an
important role in achieving high conversion. As shown in Figure A-6, the effect of liquid
superficial velocity on the biphenyl conversion profiles along the reactor axis is obvious.
When the liquid superficial velocity is 0.03 m/s, the biphenyl conversion reaches a
‘constant’ value (~80%) at the location 16 m from the entrance under given operating
conditions. If we double the liquid flow rate, one can obtain a ‘constant’ value of
conversion (~80%) at the location of 32 m from the inlet. This implies that at lower feed
flow-rates, a shorter length of the packed bed would be required to achieve the 'final
constant' conversion.
So far the performances of single packed beds in both down-flow and up-flow
reactor have been discussed. Since both different operating flow rate and different
configurations are used, the exact comparison between two modes can only be given at
the same gas and liquid flow rate as well as when the same catalyst volume is used. This
case is illustrated in Figure A-7. It was found that, per unit volume of catalyst, based on
the directly calculated mass transfer coefficients, the difference of the exit biphenyl
conversions in two modes is less than 2% (a little higher exit conversion was found in the
up-flow mode). It is noted, however, that this difference becomes large as shown in
219 Figure A-7, when we decrease the calculated values of mass transfer coefficients by a
factor of 10. Different hydrogen concentration profiles in the liquid phase were also
found while using the decreased mass transfer coefficients. The magnitude of mass
transfer coefficients in the up-flow model are almost 3 ~ 4 times larger than in the down-
flow mode. That causes lower hydrogen concentration in the liquid phase in the trickle
bed. As a consequence, the exit biphenyl conversion in the up-flow mode was found to be
10 % higher than that in the down-flow mode. As mentioned earlier, the hydrogenation
rate is higher in the entrance region, and causes the steep decrease of hydrogen
concentration in the liquid. After that, the hydrogen concentration will increase along the
reactor length while the hydrogenation rate decreases along the reactor length.
A3.4 Sensitivity to Model Parameters A number of correlations are used in modeling, and the reliability of correlations
for so parameter estimations, especially at elevated pressure, is uncertain (Al-Dahhan et
al., 1997). The values of mass transfer coefficients predicted from different correlations
sometimes may be dramatically different (Martínez, et al., 1998). Hence, it is important
to evaluate the sensitivity of model predictions to various parameters. In order to perform
the parameter sensitivity study, the gas-liquid and liquid-solid mass transfer coefficients
obtained from the correlations in the trickle-bed reactors as listed in Table 3, have been
increased and decreased several fold as additional information suggested (Toppinen et al.,
1996). It was found that an increase in (ka)gl by 10 times increases the exit conversion of
biphenyl only by 1~2 % (Fig 8a). However, when the (ka)gl value was decreased by 10
times, the conversion is reduced up to 12 % at liquid velocity larger than 0.003 m/s. This
is a clear indication that the gas-liquid mass transfer resistance is important now.
Similarly, the effect of liquid-solid mass transfer on the exit conversion is shown in
Figure 8b. The results indicate that the influence of liquid-solid mass transfer on the exit
conversion of biphenyl is also significant. When the (ka)ls value was decreased by 10
times the biphenyl conversion decreased by approximately 8 % at higher liquid
superficial velocity (0.015 m/s). However, an increase in the value of (ka)ls by 10 times
does not increase substantially the biphenyl conversion. The sensitivity of the axial
220 dispersion coefficient, in terms of Peclet number, Pe, on model prediction was found to
be neglected in trickle bed reactor modeling. Plug flow behavior for gas and liquid flow
can be considered in absence of gross flow maldistribution. The importance of mass
transfer resistance on the exit biphenyl conversion is gas-liquid mass transfer > liquid-
solid mass transfer. It is noted further that the current model is close to the limit of mass
transfer control, and close to reaction control. This is the reason that the exit conversion
does not increase much when we increase the mass transfer coefficients 10 times.
Similarly, the sensitivity of mass transfer in the upflow packed bed predictions was
performed. The model predictions are found not to be sensitive to mass transfer
coefficients [(ka)gl, (ka)ls]. This implies that reaction control behavior occurs in the
upflow mode. This is not surprising since the mass transfer coefficients in the upflow
mode are generally larger than those in the downflow mode (Shah, 1978). It is known
that petroleum hydrodesulfurization and certain types of petroleum hydrogenations are
liquid-limiting and proceed slowly enough that only intraparticle diffusion or combined
pore diffusion and liquid-to-solid resistance are controlling (Mills and Dudukovic, 1984;
Somers et al., 1979). The findings of this study are relevant to these situations.
A4 Conclusions Reactor performance both in cocurrent down-flow (trickle-bed) and in up-flow
(bubble packed-bed) have been modeled. For both types of flow patterns the biphenyl
feed concentration has little effect on reactant conversion. However, hydrogen pressure
plays an important role in biphenyl conversion due to its effect on the hydrogen
concentration in the liquid phase. For trickle-flow reactors, the gas-liquid mass transfer
resistance is important to the overall reactor performances. Whereas for the up-flow
packed bed, reaction control occurs and mass transfer effects are not significant due to
the nature of this intrinsic reaction (sufficiently slow). The single packed bubble column
process at elevated pressure was found more efficient from the economic point of view.
221
Table A-1. Kinetic parameters for hydrogenation of biphenyl (Sapre and Gates, 1981)
Temperature, K k1,
Lit4/(mol3.gcat.s)
k2,
Lit/(gcat.s)
K3,
Lit/mol
K4,
Lit/mol
K5,
Lit/mol
573 1.498 × 10-2 3.3 × 10-6 23.0 25.6 32.2
598 1.796 × 10-2 4.5 × 10-6 10.8 14.6 29.8
623 2.441 × 10-2 5.0 × 10-6 4.6 12.0 27.2
648 2.054 × 10-2 12.0 × 10-6 6.6 4.6 19.0
Table A-2. Summary of various correlations used in this study
Model parameter Trickle bed
correlation
Bubble flow column
correlation
Gas-liquid mass transfer coefficient,
(ka)Lg
Goto and Smith
(1975)
Reiss (1967)
Liquid-solid mass transfer
coefficient, (ka)ls
Goto and Smith
(1975)
Mochizuki and Matssui
(1974)
Wetting efficiency, ηCE El-Hisnawi et al
(1982)
ηCE = 1
Péclet number, Pe Michell and Furzer
(1972)
Stiegel & Shah,
(1977)
Table A-3. Properties of the catalyst particles
Catalyst
Particle diameter
Particle density
Void fraction of the bed
Catalyst loading
2mm
2.7 g/cm3
0.40
1.62 g cat./cm3.bed
222 Table A-4. List of gas and liquid feed velocity
Trickle-bed Reactor Bubble-flow Reactor
G: 0.001 ~ 0.330 kg/m2.s
L: 1.94 ~ 5.81 kg/m2.s
G: 0.005 ~ 0.98 kg/m2.s
L: 23.2 ~ 69.7 kg/m2.s
Ug (m/s) Ul (m/s)
I. 0.06; 0.0025
II. 0.06 ; 0.0075
III. 0.06; 0.0150
IV. 0.03; 0.0075
V. 0.12; 0.0075
Ug (m/s) Ul (m/s)
I. 0.12; 0.03
II. 0.24 ; 0.03
III. 0.24; 0.06
IV. 0.24; 0.09
V. 0.36; 0.03
Note: Trickle-bed: pan cake packed bed with diameter of 11.3 m. Packed-bubble column: packed bed with diameter of 4 m. P: 20 ~100 atm.;
T: 573 ~ 648 K
PARTIAL WETTING COMPLETE WETTING
CATALYSTLIQUID
GAS
(Trickle Flow Regime) (Bubble Flow Regime)
Figure A-1. Contacting pattern in the trickle flow regime and bubble flow regime
223
0.1
1
10
100
1000
10000
0.001 0.01 0.1 1 10
G/
(L/G
)
1atm35 atm70 atm105 atmTransition
Pulsing flow
Trickle flow
λ
λψ
Figure A-2. Effect of pressure on the flow regime in downflow packed bed using the flow
chart of Larachi et al. (1993).
0.05
0.07
0.09
0.11
0.13
0.15
0 1 2 3 4 5 6Axial position, m
Hyd
roge
n co
ncen
tratio
n, m
ol/L
3
0.001
0.010
0.100
conc
entra
tion
of B
and
C
, mol
/L3
CalCblCcl
Figure A-3. Species concentration profiles along the reactor. D = 11.3 m; Ul = 0.0075
m/s; Ug = 0.06 m/s; P = 70 atm; T = 603K; CaL : hydrogen; CbL : biphenyl; CcL : product.
224
0
20
40
60
80
100
0 15 30 45 60 75 90 105Pressure, atm.
Bip
heny
l con
vers
ion,
%
Ug = 0.06 m/s Ul = 0.0025 m/s T = 603K
Figure A-4. Effect of operating pressure on the exit biphenyl conversion (H = 4 m;
D = 11.3 m)
0
20
40
60
80
100
0 0.005 0.01 0.015
Liquid surperficial velocity, m/s
Bip
heny
l con
vers
ion,
%
0
1
2
3
4
5
6
Rg,
(10^
-2 m
ol/m
3/s)
X%Rg
Figure A-5. Effect of liquid superficial velocity on the exit biphenyl conversion and
global hydrogenation rate (Rg). H = 4 m; D = 11.3 m
225
0.010.020.030.040.050.060.070.080.090.0
0 8 16 24 32
AXIAL POSITION, m
BIPH
ENYL
CO
NVE
RSI
ON
, %
Ul=0.03Ul=0.06Ul=0.09
Figure A-6. Effect of liquid superficial velocity on the exit biphenyl conversion in the
upflow packed bed. Ul = 0.03; 0.06; 0.09 m/s; D = diameter of bed; Ug = 0.12 m/s;
P = 70 atm; T = 605K.
226
01020304050607080
0 0.5 1 1.5 2 2.5 3 3.5 4
Axial position, m
Biph
enyl
con
vers
ion,
%
1.00E-01
1.05E-01
1.10E-01
1.15E-01
1.20E-01
1.25E-01
Hyd
roge
n co
ncen
tratio
n in
liq
uid,
mol
/L
XupXdow nC(up)C(dow n)
Figure A-7. Comparison of biphenyl conversion profile and hydrogen concentration
profile in liquid phase in the up-flow and down-flow packed beds. H = 4 m; D = 4 m; Ul
= 0.0075 m/s; Ug = 0.12 m/s; P = 70 atm; T = 648K; mass transfer coefficients used: for
the up-flow mode, 0.1× (ka)gl = 0.0144 s-1, 0.1× (ka)ls = 0.129 s-1; for the down-flow
mode, 0.1×(ka)gl = 0.00344 s-1, 0.1× (ka)ls = 0.0338 s-1. (For the directly calculated values
of mass transfer coefficients, the corresponding exit biphenyl conversion for up-flow is
72.35%, and for down-flow, 71.56%).
227
55606570758085
0.002 0.007 0.012
Liquid superficial velocity, m/s
Biph
enyl
con
vers
ion,
% (original)10kla0.1kla
(a)
55
65
75
85
0.002 0.007 0.012
Liquid superficial velocity, m/s
Biph
enyl
con
vers
ion,
%
(original)10ksa0.1ksa
(b)
Figure A-8 (a)-(b). Sensitivities of the model with respect to gas-liquid, liquid-solid mass
transfer coefficients in trickle-bed reactor at 605 K, 70 atm. with flow conditions:
Ug = 0.06 m/s; H=32 m; D=4 m.
228
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244
VITA Name Yi Jiang Degrees B.Sc. Petrochemical Engineering, June 1986
Jiangsu Institute of Petrochemical Technology, China. M.Sc. Chemical Engineering, May 1989 Nanjing University of Chemical Technology, China. D.Sc. Chemical Engineering, December 2000 Washington University, St. Louis, MO, USA.
Professional Experience Assistant Professor (1989.6 ~ 1995.12) Jiangsu Institute of Petrochemical Technology, Changzhou, China, (1989-1996) Research Associate at CREL (1996.1 ~ 1997.7) Washington University, St. Louis, MO, USA. Summer Intern (1999.7 ~ 1999.9) DuPont Company, Wilmington, DE, USA. Staff Engineer (2000.7 ~) Conoco Inc. Ponca City, OK, USA Professional Societies American Institute of Chemical Engineers (AIChE) Journal Publications 1. M. R. Khadilkar; Y. Jiang; M. H. Al-Dahhan and M. P. Dudukovic', S. K. Chou, G.
Ahmed, and R. Kahney, "Investigation of a Complex Reaction Network: I. Experiments in a High Pressure Trickle-Bed Reactor", A.I.Ch.E. Journal, 44, 912-920 (1998).
2. Y. Jiang; M. R. Khadilkar; M. H. Al-Dahhan and M. P. Dudukovic', S. K. Chou, G. Ahmed, and R. Kahney, "Investigation of a Complex Reaction Network: II. Kinetics, Mechanism and Parameter Estimation", A.I.Ch.E. Journal, 44, 921-926 (1998).
245 3. Y. Jiang; M. R. Khadilkar; M. H. Al-Dahhan and M. P. Dudukovic', "Single Phase
Flow Modeling in Packed Beds: Discrete Cell Approach Revisited", Chem. Engng Sci. 55, 1829-1844 (2000).
4. Y. Jiang; M. R. Khadilkar; M. H. Al-Dahhan and M. P. Dudukovic', " Two Phase Flow Distribution in 2D Trickle Bed Reactors ", Chem. Engng Sci. 54, 2409-2419 (1999).
5. Y. Jiang; M. H. Al-Dahhan and M. P. Dudukovic', “Statistical Characterization of Macroscale Multiphase Flow Textures in Trickle Beds”, Chem. Engng Sci., in press (2000).
6. Y. Jiang; M. R. Khadilkar; M. H. Al-Dahhan and M. P. Dudukovic', “CFD Modeling of Multiphase Flow Distribution in Catalytic Packed-bed Reactors: Scale Down Issues”, Catalysis Today, in press (2000)
Conference Presentations 1. Y. Jiang; M. H. Al-Dahhan and M. P. Dudukovic', “Statistical Characterization of
Macroscale Multiphase Flow Textures in Trickle Beds”, 16th International Symposium on Chemical Reaction Engineering (ISCRE-16), 281a, Cracow, Poland, September 10-13 (2000).
2. Y. Jiang; M. R. Khadilkar; M. H. Al-Dahhan and M. P. Dudukovic', “CFD Modeling of Fluid Flow Packed Beds”, Chemical Reaction Engineering VII: Computational Fluid Dynamics, Quebec, Canada, August 6-11 (2000).
3. Y. Jiang; M. R. Khadilkar; M. H. Al-Dahhan and M. P. Dudukovic', “CFD Modeling of Multiphase Flow Distribution in Catalytic Packed-bed Reactors: Scale Down Issues”, 3rd International Symposium in Catalysis in Multiphase Reactors, Naples, Italy, May 29-31 (2000).
4. Y. Jiang; M. H. Al-Dahhan and M. P. Dudukovic', Mixing-Cell Network Model for Design of Trickle-Bed Reactors, AIChE Annual Meeting, at 20012 Industrial Applications of Multiphase Reactors, Dallas, TX, Oct. 31 ~ Nov. 5 (1999).
5. Y. Jiang; M. H. Al-Dahhan and M. P. Dudukovic', Statistical Characterization of Two Phase Flow Distribution in Trickle Beds, AIChE Annual Meeting, at 20013 Computational Fluid Dynamics in Chemical Reaction Engineering, Dallas, TX, Oct. 31 ~ Nov. 5 (1999).
6. Y. Jiang; J. Mettes; M. R. Khadilkar; M. H. Al-Dahhan, Experimental Investigation of Liquid Flow Distribution in Trickle Beds: Steady State and Periodical Operation, AIChE Annual Meeting, Poster 181-1b, Miami Beach, FL, November 15 ~20 (1998), (2nd place at National Student Poster Session).
7. Y. Jiang; M. H. Al-Dahhan and M. P. Dudukovic', Liquid Flow Maldistribution and Reaction Performance in Trickle-bed Reactors, AIChE Annual Meeting, Paper 304e, Miami Beach, FL, November 15 ~20 (1998).
8. Y. Jiang; M. R. Khadilkar; M. H. Al-Dahhan and M. P. Dudukovic', Gas Flow Modeling in Packed Beds, AIChE Annual Meeting, Poster 318bi, Miami Beach, FL, November 15 ~20 (1998).
246 9. Y. Jiang; M. R. Khadilkar; M. H. Al-Dahhan and M. P. Dudukovic', Two Phase Flow
Distribution in 2D Trickle Bed Reactors, 15th International Symposium on Chemical Reaction Engineering (ISCRE-15), P-113, Newport Beach, California (1998).
10. Y. Jiang; P. L. Mills and M. P. Dudukovic', Comparison Between Trickle Bed and Packed Bubble Column Reactor Performance for the Hydrogenation of Biphenyl, 15th International Symposium on Chemical Reaction Engineering (ISCRE-15), P-17, Newport Beach, California. (1998).
11. Y. Jiang; M. R. Khadilkar; M. H. Al-Dahhan and M. P. Dudukovic', Prediction of Two Phase Flow Distribution in 2D Trickle Bed Reactors, AIChE Annual Meeting, (Poster 276a), Los Angeles, November (1997).
12. M. R. Khadilkar; Y. Jiang; M. H. Al-Dahhan and M. P. Dudukovic', S. K. Chou, G. Ahmed, and R. Kahney, Investigation of a Complex Reaction Network in a High Pressure Trickle-Bed Reactor, AIChE Annual Meeting, (Paper 252a), Los Angeles, CA (1997).
13. Y. Jiang; F. Zhang and G. Gao, Effect of Supersaturation on the Mass Transfer of the Solvent in the Vacuum Devolatilization of Polymer Solution, 1997, 2nd Joint AIChE/CSCE Chemical Engineering Conference, Paper D56, Beijing, China (1997).
14. Y. Jiang; F. Zhang and G. Gao, 1997, Fluidized Chlorination of the Grained Polyethlene, 2nd Joint AIChE/CSCE Chemical Engineering Conference, Poster Session A, Beijing, China (1997)
December, 2000
247
Short Title: Flow Distribution in Packed-Beds Jiang, D. Sc. 2000