Gas-Solid-Liquid Mixing Systems

GBH Enterprises, Ltd.

Process Engineering Guide:
GBHE-PEG-MIX-706

Gas-Solid-Liquid Mixing Systems

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Process Engineering Guide:

Gas-Solid-Liquid Mixing
Systems

CONTENTS

SECTION

0

INTRODUCTION/PURPOSE

3

1

SCOPE

3

2

FIELD OF APPLICATION

3

3

DEFINITIONS

3

4

SELECTION OF EQUIPMENT

3

5

THREE-PHASE MASS TRANSFER WITH CHEMICAL
REACTION

3

6

STIRRED VESSEL DESIGN

4

6.1
6.2
6.3
6.4

Agitator Design
Design for Solids Suspension
Vessel Design
Gas-Liquid Mass Transfer Coefficient and Surface Area

4
4
5
5


7

THREE-PHASE FLUIDIZED BEDS

6

7.1
7.2
7.3
7.4
7.5
7.6

Gas and Liquid Hold-Up
Calculation Procedure
Bubble Size
Mass Transfer
Heat Transfer
Elutriation

7
8
9
9
11
12

8

SLURRY REACTORS

12

8.1
8.2

Gas Rate
Mass Transfer

12
12

9

NOMENCLATURE

12

10

BIBLIOGRAPHY

14


FIGURES
1

MASS TRANSFER COEFFICIENT vs % v/v SOLIDS
CONCENTRATION

6

2

THREE-PHASE FLUIDISED BED

7

3

PLOT OF EXPERIMENTAL DRIFT FLUX DATA vs GAS
HOLD-UP System : Air-Water Particle sizes : 1 - 6 mm

8

RANGES OF BUBBLE SIZES IN WATER-FLUIDIZED
BEDS OF GLASS BEADS 0.5 m FROM THE
DISTRIBUTOR

9

DEPENDENCE OF SHERWOOD NUMBER ON PECLET
NUMBER

10

VOLUMETRIC ABSORPTION COEFFICIENTS IN GASLIQUID FLUIDIZED BEDS OF 1 mm PARTICLES

11

4

5

6

DOCUMENTS REFERRED TO IN THIS PROCESS
ENGINEERING GUIDE

16


0

INTRODUCTION/PURPOSE

This Guide is one in a series of Mixing Guides and has been produced for GBH
Enterprises.

1

SCOPE

This Guide covers the selection and design of equipment suitable for the mixing
of three phase (gas-solid-liquid) systems. It does not deal with systems where
the solid phase is stationary and not itself mixed; thus packed towers and fixed
beds are excluded. The main devices covered are agitated vessels, slurry
reactors (also known as particle - bubble columns) and fluidized beds.

2

FIELD OF APPLICATION

This Guide applies to Process Engineers in GBH Enterprises worldwide.

3

DEFINITIONS

No specific definitions apply to this Guide.
With the exception of terms used as proper nouns or titles, those terms with initial
capital letters which appear in this document and are not defined above are
defined in the Glossary of Engineering Terms.

4

SELECTION OF EQUIPMENT

The choice of equipment depends primarily on the nature of the system: particle
size, shape and density are important parameters as is the requirement to keep
solids in suspension in the absence of gas and/or liquid flows. An agitator may
also be required in a system which could be run as a slurry reactor if there is a
demand to keep the solids suspended when the gas feed is shut off. In fluidized
beds the particles are kept in suspension by the liquid flow and this permits
particle sizes in a range from approximately 0.5 to 6 mm.
Both the gas and liquid phases are back-mixed to some extent in an agitated
vessel. In slurry reactors and fluidized beds there is little axial dispersion of the
gas although there is generally back-mixing of the liquid. A slurry reactor can be
run in either co-current or counter-current flow.

Other types of three-phase contactors include the 'irrigated fluidized bed' and the
three-phase spouted bed, investigated by Vukovic et al 1973, 1974 [Ref. 2].

5

THREE-PHASE MASS TRANSFER WITH CHEMICAL REACTION

The problem of gas absorption into a slurry with reaction has been treated
theoretically (Uchida and Wen, 1977 [Ref. 3]) by looking at reaction in the liquid
phase preceded by dissolution of the gas and solid and with the added
simplification that only fast, irreversible reactions and no gas-side resistance to
mass transfer were considered. Six different cases could be identified
depending on the concentration profiles of the dissolved gas and solid. One
particular case has been verified experimentally (Sada et al, 1977 [Ref. 4]) by
performing experiments with carbon dioxide and sulfur dioxide in a calcium
hydroxide slurry.

6

STIRRED VESSEL DESIGN

In spite of the wide application of three-phase stirred vessels, there is little
information available on their performance. For reasonably dilute suspensions (<
10% solids) it is probably better to design for a gas-liquid system with a low
agitator clearance to favor solids suspension, i.e. by the use of a disc turbine with
Z = T/4 (see GBHE-PEG-MIX-705 Figure 11). If full suspension of solids is
important then the design should be checked to ensure that solids shall be
suspended. This can be done by determining the power requirement to just
suspend the solids, PJS, for the un-gassed conditions (see GBHE-PEG-MIX-703)
and using an actual P/V greater than PJS.
For floating solids, consult GBHE-PEG-MIX-703.
There is little relevant company experience in the design of agitators for threephase systems, although there is substantial experience in the operation of some
large (up to 100 m3) three-phase reactors (e.g. KA, Terephthalic Acid,
Synprolam and Aniline). These reactors are generally part of licensed processes
and they incorporate the contractor's know-how. However, they look quite
different from each other and no general conclusion can be drawn from their
design.


The two basic requirements are:
(a)

adequate dispersion of gas to achieve the required gas-liquid mass
transfer, and

(b)

complete suspension of solid to prevent accumulation, although
homogeneous dispersion of solid may not be required.

In general the presence of a gas phase increases the speed and power required
to achieve both solid suspension and gas dispersion.

6.1

Agitator Design

Chapman et al, 1983 [Ref. 4], however, show that a pitched blade turbine,
pumping upwards, appears to be the best way to achieve simultaneous gas
dispersion and solid suspension because its specific power input is almost
independent of the gas flow and is therefore very stable during operation.
The chosen agitator shall provide sufficient power, Pg, to perform the necessary
gas-liquid mass transfer duty (see 6.4 and GBHE-PEG-MIX-705) which may
favor the disc turbine with its higher Power number (Po u = 5.5 compared with
1.2 for the pitched blade turbine).
Downward pumping impellers should not be used when both solids and gas are
present because they tend to develop unstable behavior which results in solid
sedimentation.

6.2

Design for Solids Suspension

The power required to suspend solids in a liquid, PJS, has to be maintained when
a gas is added, and if on increasing gas flow, the gassed power, Pg becomes
smaller than PJS then the solids will settle. The agitator speed, N, and hence the
un-gassed and gassed power, Pu and Pg should be increased to a value such
that Pg > PJS to achieve solids suspension.
The agitator speed required for complete suspension of particles without gas,
NJS, has been determined by Zwietering, 1958 [Ref. 5] for various agitator
geometries (see GBHE-PEG-MIX-703).


In general more power (higher agitator speed) is required to re-suspend the solid
once the gas has been introduced. However, there is not enough information
from large scale vessels to predict scale-up conditions. Experimental work using
small vessels of exactly the same configuration and the real fluids and particles
(or models with the same density, viscosity and particle size and shape) is
recommended.

6.3

Vessel Design

The aspect ratio (H/T) is very important for three-phase systems because of the
tendency of the gas to disengage and the solids to sink.
A single turbine is recommended for a 1:1 aspect ratio. However, for an aspect
ratio greater than 1.5:1 a pitched blade turbine located near the bottom of the
tank to guarantee complete suspension of the solids and a disc turbine higher up
to redistribute the gas and lift the particles further are required.
Sometimes the gas is fed in below the upper impeller so that it does not affect
the solids suspension characteristics of the bottom impeller. However, the bottom
part of the vessel may then contain only a very small amount of gas and be
under-utilized for mass transfer.

6.4

Gas-Liquid Mass Transfer Coefficient and Surface Area

If the reaction rate in a three-phase stirred system is limited by the rate of
dissolution of the gas due to liquid film resistance, then the effect of the solid
particles on the liquid film mass transfer coefficient, KL, and the specific surface
area, a, shall be taken into account.


FIGURE 1

MASS TRANSFER COEFFICIENT vs % v/v SOLIDS
CONCENTRATION

Generalizations from limited experimental data is unwise; however for solid
particles in the size range 50 - 250 µm the volumetric mass transfer coefficient,
KLa, is apparently hardly affected by the presence of solids as long as the solids
concentration does not exceed 20% (v/v), see Figure 1 (Joosten et al, 1977 [Ref.
6]).

7

THREE-PHASE FLUIDIZED BEDS

The term 'three-phase fluidized bed' is applied to a system in which gas is
passed continuously into the bottom of a liquid fluidized bed. The gas may be
introduced with the liquid or via a separate sparger as shown in Figure 2.
In such a device the liquid is well-mixed while the gas is almost in plug flow with
only a small amount of axial diffusion. The particle sizes used so far have been in
the range 0.5 - 6 mm diameter.

If it is necessary to use smaller particles, then a slurry or stirred vessel is
preferable. A major advantage of the fluidized bed is its high thermal conductivity,
reducing the likelihood of hot spots in exothermic reactions.
FIGURE 2

THREE-PHASE FLUIDIZED BED


7.1

Gas and Liquid Hold-Up

Regimes of behavior are identified from the drift flux. The drift flux of gas, W, can
be defined as the volumetric flux of gas relative to a surface moving at the
average velocity (see Wallis 1962 [Ref. 7]). It is then possible to derive a
relationship between drift flux and the superficial velocities, see Darton, 1975
[Ref.8].

The drift flux calculated from some experiments by Michelsen and Ostergaard,
1970 [Ref. 9] is plotted as a function of gas voidage in Figure 3.
The point of transition from one regime to the other depends on the physical
properties of the gas and liquid, the particle size and the fluid flow rates. These
are the factors which principally determine the onset of coalescence.

FIGURE 3

PLOT OF EXPERIMENTAL DRIFT FLUX DATA vs GAS HOLDUP System Air-Water Particle sizes : 1 - 6 mm


Superficial Gas Velocities : 0.042 - 0.2 m/s
7.2

Calculation Procedure

For a bed operating in the uniform bubbling regime, the following data are
required: vSG, vSL, v tf and n, where n is the fluidization expansion index, which
varies with particle properties between 2 and 5 (Richardson, 1954 [Ref. 10]). If no
measured value of n is available, n = 4.5 should be used.
The calculation procedure is as follows:


7.3

Bubble Size

General quantification of bubble size is currently impossible. Lee et al, 1973 [Ref.
11] show that bubbles are smaller in beds of large particles, see Figure 4 (a) and
4 (b).
FIGURE 4

RANGES OF BUBBLE SIZES IN WATER-FLUIDISED BEDS OF
GLASS BEADS 0.5!m FROM THE DISTRIBUTOR (Lee et al,
1973 [Ref. 11

These data have been obtained for air bubbles in water-fluidized beds. As the
mechanism of bubble break-up depends on the interfacial tension and surface
activity effects, prediction of bubble sizes for other systems is uncertain.


7.4

Mass Transfer

7.4.1 Gas Film Coefficient
A numerical solution of the diffusion equation, allowing for recirculation in the
bubble (see Zaritzky & Calvelo, 1979 [Ref.12]) gives the Sherwood number
(ShGL = kG db/DG) as a function of the Peclet number (P e = db v b/DG) as
shown in Figure 5.
Note: DG is the diffusivity in the gas phase.
FIGURE 5

DEPENDENCE OF SHERWOOD NUMBER ON PECLET
NUMBER

At low bubble Reynolds numbers (< 300) the circulation inside the bubble can be
disregarded and the result

7.4.2 Liquid-Particle Mass Transfer
The transfer rate to the particle surface may be estimated from:


Selection of a suitable velocity for use in this equation is difficult, the terminal
velocity could be used, selecting the minimum value from those calculated from
each of the Re ranges. An alternative correlation, based on data from liquid
fluidized beds, see Beek, 1971 [Ref. 13], may be easier to use. This is given in
equation (8).

Since only a very rough estimate of mass transfer rates can be obtained, they
should always be confirmed by experimental data on the system of interest.

7.4.3 Gas-Liquid Mass Transfer
An approximate value of the liquid film coefficient for transfer from the liquid-gas
interface can be obtained by using the correlations recommended for bubble
columns (see GBHE-PEG-MIX-705).
Work by Ostergaard et al, 1972 [Ref. 14] using oxygen, water and ballotini shows
the variation of KLa with distance from the distributor for two different particle
sizes in a bubble column; see Figure 6.


FIGURE 6

VOLUMETRIC ABSORPTION COEFFICIENTS IN
GAS-LIQUID FLUIDISED BEDS OF 1 mm PARTICLES


7.5

Heat Transfer

Experimental studies have been confined to measurements of heat transfer from
a surface to a water-air-glass beads system. Work to date is adequately
reviewed by Baker et al, 1978 [Ref.15] who also present their own data. Heat
transfer coefficients increase rapidly when gas is injected into a liquid-fluidized
bed but the rate of increase tails off at high gas rates. The heat transfer
coefficients also increase with increasing particle size and liquid velocity. For the
water air- glass system all the data could be adequately correlated by the
expression:

This gives some idea of the effect of those parameters which have been
investigated.

7.6

Elutriation

A height of liquid is required above the bed to reduce particle entrainment;
particles will not be carried far out of the bed if the upward velocity of liquid in the
bubble wake is less than the terminal velocity of the particles.
If elutriation is likely to be a problem, a wire mesh baffle in the freeboard can be
used to reduce it by splitting bubbles and encouraging wake shedding. Although
a mesh can significantly reduce the amount of elutriation it does not affect the
maximum height above the bed that particles reach.
A comprehensive review of three-phase fluidized beds has been published by
Wild et al, 1984 [Ref. 16]. Their main conclusions are that further research is
required using organic systems
as well as columns heights and diameters close to industrial scale.


8

SLURRY REACTORS

Slurry reactors have much in common with bubble columns containing no solid
particles. Considerably more data are available on bubble column design (see
GBHE-PEG-MIX-705) and that Guide should be consulted in conjunction with
this Clause.
8.1

Gas Rate

The solid particles in a slurry reactor are suspended by momentum transfer from
the gas phase via the liquid medium and thus the relationship between solids
hold-up and the gas flowrate is of importance. The range of operating gas
velocities decreases with increasing solids concentration; the lower limit
increases because of an increasing tendency towards sedimentation and the
upper limit decreases because of bubble coalescence and a corresponding
increase in bubble size.
The gas rate also affects the solids distribution in the reactor: an increase in gas
velocity leads to a more uniform solids distribution. Quantitative information is
sparse: Kölbel et al, 1964 (Ref.17) observed large deviations from the average
solids concentration when operating at Vsg = 0.035 m/s, using 5% by weight
sand particles of 0.1 - 0.125 mm diameter. Kato, 1963 [Ref.18] and Roy et al,
1964 [Ref. 19] have made some measurements on the amount of solids that can
be suspended at a given gas velocity.

8.2

Mass Transfer

The usual practice is for a solid (e.g. a catalyst) to be in a finely divided form to
produce a large surface area. The calculation of mass transfer coefficients for the
transfer from the gas phase to the liquid is described in GBHE-PEG-MIX-705.
Transfer from the liquid to the particle can be calculated from:

where Re is the particle Reynolds number:


DOCUMENTS REFERRED TO IN THIS PROCESS ENGINEERING GUIDE
This Process Engineering Guide makes reference to the following documents:

GBHE ENGINEERING GUIDES

GBH Enterprises

Glossary of Engineering Terms
(referred to in Clause 3)

GBHE-PEG-MIX-703

Mixing of Solid-Liquid Systems
(referred to in Clause 6 and 6.2)

GBHE-PEG-MIX-705

Mixing of Gas Liquid Systems
(referred to in Clause 6, 6.1, 7.4.3, 8 and 8.2).


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