Gas - Liquid Reactors

GBH Enterprises, Ltd.

Process Engineering Guide:
GBHE-PEG-RXT-810

Gas - Liquid Reactors

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Process Engineering Guide:

Gas - Liquid Reactors

CONTENTS

SECTION

0

INTRODUCTION/PURPOSE

3

1

SCOPE

3

2

FIELD OF APPLICATION

3

3

DEFINITIONS

3

4

PRELIMINARY CONSIDERATIONS

3

4.1
4.2
4.3

Preliminary Equipment Selection
Equipment for Low Viscosity Liquids
Equipment for High Viscosity Liquids

4
4
7

5

REACTOR DESIGN

8

6

ESSENTIAL THEORY

8

6.1
6.2
6.3
6.4

Rate and Yield Determining Steps
Chemical and Physical Rates
Modification for Exothermic and Complex Reactions
Preliminary Selection of Reactor Type

8
9
13
14


7

EXPERIMENTAL DETERMINATION OF REGIME

15

7.1
7.2

Direct Measurement of Reaction Kinetics
Laboratory Gas-Liquid Reactor Experiments

16
17

8

EQUILIBRIUM AND DIFFUSIVITY DATA SOURCES

19

9

OVERALL EFFECTS

20

9.1
9.2
9.3
9.4
9.5
9.6
9.7

Liquid Flow Patterns
Scale of Mixing
Gas Flow Pattern : Mean Driving Force for Mass Transfer
Gas-Liquid Reactor Modeling
Heat Transfer
Materials of Construction
Foaming

20
21
21
22
23
24
24

10

11

11.1
11.2
11.3
11.4
11.5
11.6
11.7
11.8
11.9
11.10
11.11
11.12
11.13

FINAL CHOICE OF REACTOR TYPE

24

SCALE-UP AND SPECIFICATION OF GAS-LIQUID
REACTORS

26

Bubble Columns
Packed Columns
Trickle Beds
Plate or Tray Columns
Spray Columns
Wiped Film
Spinning Film Reactors
Stirred Vessels
Plunging Jet
Surface Aerator
Static Mixers
Ejectors, Venturis and Orifice Plates
3-Phase Fluidized Bed

26
26
26
26
27
27
27
27
27
27
27
28
28


12

BIBLIOGRAPHY

28

TABLES

1

REGIMES OF GAS-LIQUID MASS TRANSFER WITH
ISOTHERMAL CHEMICAL REACTION

12

2

REGIMES OF GAS-LIQUID MASS TRANSFER IGNORING
LARGE EXOTHERMS OR OTHER COMPLICATIONS
15

3

COMPARATIVE MASS TRANSFER PERFORMANCE OF
CONTACTING DEVICES

18

4

COMPARATIVE MASS TRANSFER DATA

24

5

CHOICE OF GAS-LIQUID REACTOR TYPE

25

FIGURES

1

RATE AND YIELD DETERMINING STEPS

8

2

ENHANCEMENT FACTOR vs HATTA NUMBER

11

3

ENHANCEMENT FACTOR vs HATTA NUMBER : EFFECT
OF THERMAL & OTHER FACTORS
14

4

REACTORS FOR LIQUID-PHASE KINETICS
MEASUREMENT

17

EXPERIMENTS TO DETERMINE THE OPERATING
REGIME

19

5

6

EXPERIMENTS DETERMINE THE OPERATING REGIME
WHERE A SOLID CATALYST IS INVOLVED
20

7

THE MIXED ZONES IN LOOPS' MODEL FOR STIRRED
REACTORS

23


DOCUMENTS REFERRED TO IN THIS PROCESS
ENGINEERING GUIDE

30


0

INTRODUCTION/PURPOSE

This Guide is one in a series on Reactor Technology produced by GBH
Enterprises. Absorption of gases into liquids, followed by reaction in the liquid
phase, forms an important category of reactions of relevance to GBHE. Among
these are oxidation, hydrogenation, sulfonation, halogenation and carbonylation.
Sometimes the reactions are assisted by a catalyst, either dissolved or
suspended in the liquid phase.

1 SCOPE
This Guide provides a basic introduction to the theory of gas-liquid reactions. It
deals with the microscopic scale phenomena of absorption, mass transfer and
chemical reaction and indicates how these are integrated with fluid flow and heat
transfer to provide predictions of reactor performance. Some attention is given to
the experimental determination of the relevant physicochemical parameters.
Finally, guidance is offered on the selection of appropriate gas-liquid reactors for
a given system.

2

FIELD OF APPLICATION

This Guide applies to process engineers in GBH Enterprises worldwide.

3

DEFINITIONS

For the purposes of this Guide, no specific definitions apply.
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

PRELIMINARY CONSIDERATIONS

Reactions between gases and liquids are common in the chemical industry.
Typical examples are:
(a) Oxidation, hydrogenation, sulfonation, halogenation, carbonation, etc.,
(b) Fermentation, effluent aeration,
(c) Polymerization, polycondensation,
(d) Gas absorption (CO2, H2S, SO2, Cl2, NOX, etc.).
In all these cases the reactant gas is first absorbed into the liquid and the
reaction then occurs in the liquid phase.

4.1

Preliminary Equipment Selection

The most commonly used equipment is either:
(a) A liquid phase reactor (a vessel) into which the gas is introduced, or
(b) A gas absorber in which the reaction occurs.
These devices are not always successful or optimal. See Clause 10 for the
appropriate design methods. Newer devices, e.g. gas-liquid static mixers, are
expanding the range of operating regimes.
The reactor type is dictated by the following:
(1)

Viscosity
Turbulent mixing, which is used whenever possible, demands different
equipment from laminar mixing. The selection is thus divided into
equipment for low and high viscosity fluids.


Note:
The addition of a solvent can reduce the viscosity.
(2)

Relative Rates of Reaction and Gas-Liquid Mass Transfer
From a knowledge of the rate of reaction and the mass transfer rate, it is
possible to determine which family of devices will be appropriate.

(3)

Flow Pattern Requirements
The overall flow pattern requirements (i.e. plug flow or back mixed) narrow
down the choice within a family.

(4)

Residence Time Requirements
The residence time requirements are based on the previously determined
rate-controlling step and also influence the selection.

(5)

Other Constraints
The presence of solid particles, the need for heat transfer and the
materials of construction will impose constraints on the selection process.

4.2

Equipment for Low Viscosity Liquids
For low liquid viscosities (say less than about 200 cP [0.2 Ns/m2]),
turbulence can be used to obtain good mixing, high interfacial area and
high heat and mass transfer coefficients.
Degassing can be done by gravity. Suitable devices include:
(a) Simple Bubble Columns
The gas is sparged into the liquid at the
bottom of the contactor.
Well established in plants and much
design information available.


(b) Plate Columns
The gas is redispersed and disengaged
at each plate up the column.

(c) Packed Column & Trickle Bed
Gas and liquid film flow can be either
co-current or counter-current.

(d) Mechanically Agitated Vessels
An impeller rotates in a tank (usually
baffled) to give enhanced rates of mass
transfer and heat transfer.

(e) Recirculating Bubble Columns
Gas is sparged into a 'riser' and
disengaged at the surface. The liquid
recirculation is driven by the voidage
difference.
Established on plants, but only scant

(f) Surface Aerators
Agitators at the liquid surface entrain
gas from the head space into the liquid.
Established on plants, but only scant

(g) In-line Static Mixers
Mixing energy is derived from the flow
itself.
Newer devices; few plant installations,
but fair small-scale information available.

(h) Jet Ejectors
The gas is sucked into the liquid flow in
a tube and dispersed by intense
turbulence.

(j) Plunging Jets
Gas is entrained into the liquid surface
by a liquid jet.


(k) Three Phase Fluidized Beds
The presence of the solid phase helps
to promote good contact between the
gas and liquid phases.

(l) Spinning Cone
The "turbulent" film is generated
centrifugally and gives high mass and
heat fluxes.

4.3

Equipment for High Viscosity Liquids

For high viscosity liquids, turbulence cannot be achieved practically and hence a
laminar mechanism (cutting and folding) has to be used to incorporate the gas.
Highly viscous systems are reluctant to degas under gravity, so degassing is best
done in a thin-film device. Suitable devices include:
(a) Dough Mixers
Dough mixers (or dough beaters)
incorporate the bubbles into the liquid
surface.
Widely used, but only scant design
information is available.


(b) In-line Dynamic Mixers
These are capable of generating high
shear rates suitable for producing a high
gas content.

(c) Scraped-film Devices
A thin film of liquid is generated by a
blade moving near a surface.

(d) Centrifugal Devices
In these, e.g. a rotating disc contactor, a
thin film is generated on the disc by
centrifugal force.

(e) Mechanically Agitated Vessel
The bubbles are incorporated from the
surface or dispersed by a separate high
shear device in the base of the vessel.


The reaction conditions required will set the priorities for design. For example, in
effluent aeration or many fermentations, the systems are dilute and the reactions
are slow; so large vessels are used and energy efficiency is important but the
mass transfer intensity requirements are modest. In chlorination’s and
sulfonation’s, the reactions are generally fast and the gases quite soluble so high
intensity mass and heat transfer are essential but contact times may be
slow. With many oxidations and hydrogenations the gases are less soluble and
longer contact time or gas recycling is needed; often the mixing pattern and solid
suspension are also important. For food batters and creams the rheological
limitations overrule, and control of the local shear rate and temperature is all
important.

5

REACTOR DESIGN

Ideally the reactor design involves a quantitative idea of both the chemical
kinetics and the mixing and mass transfer. Analysis of the chemistry can be
difficult or impossible and mass transfer prediction is uncertain because of the
effects of bubble coalescence and flow pattern. Design from first principles is
therefore not normally possible.
Small scale experiments should be carried out to determine the relevant rates
and other necessary reaction characteristics such as the heat of reaction, the
degree of foaming and bubble coalescence, which are then scaled-up to the final
plant design. If time and techniques permit, this experimentation also guides the
choice of reactor type and indicates whether mathematical modeling should be
carried out and if so, to what complexity.
Generally, the combination of the difficulties associated with the analysis of the
chemistry and the uncertainties in the gas-liquid fluid dynamics renders the
scale-up of gas-liquid reactors a thorny procedure. Experiments should be
carried out at the final plant conditions (pressure, temperature, catalyst
concentration). Because of the difficulty and cost of experiments,
allowances for the uncertainly be should made in scaling-up.
Methods of calculation for both traditional and newer devices are presented in
Clauses 6 to 9. They also give further guidance on the selection, experimentation
and scale-up for gas-liquid reactions.


6

ESSENTIAL THEORY

6.1

Rate and Yield Determining Steps

Most industrial reactions are multi-step reactions and therefore their description
is generally simplified by focusing on the rate determining step. For parallel
reactions, the yield is the outcome of competition between two or more
simultaneous rates.
The example shown in Figure 1, based on the oxidation of cyclohexane,
illustrates the rate and yield determining steps:

FIGURE 1

RATE AND YIELD DETERMINING STEPS

C is the desired product; reaction steps (1), (2) and (3) are first order in dissolved
gas (oxygen), steps (4) and (5) are second order. The overall Rate is determined
by step (1).

The Yield of C is determined by two ratios, namely:
Rate (2)
Rate (4)

i.e. the dissolved oxygen ratio, and

Rate (3) + Rate (5)
Rate (2)


For single phase reactions, consult GBHE-PEG-RXT-809. In gas-liquid reactions
in which one or more reactants have to transfer from the gas phase to the liquid,
the rate of this transfer has to be taken into account since it often modifies or
controls the overall rate of a chemical step and possibly the rate or yield
determining step. The theory and the implications are covered in 6.2
and 6.3; thus often mass transfer limitations are minimized to give high rates, but
they can be useful to manipulate yields in complex reactions.

6.2

Chemical and Physical Rates

For simple reactions the theory is well covered in several works (e.g. see Ref. [2],
Ref. [14] and Ref.[15]) and is summarized below using the film theory.
Note:
Other theories can be used, but they result in almost identical predictions.
The diffusion of a reactant through the gas to the interface and thence through
the liquid film into the bulk liquid with simultaneous reaction is covered. Additional
complications such as:
(a)
(b)
(c)
(d)

Multi-component diffusion;
Escape of volatile products;
Heats of reaction;
Concurrent reactions.

Require the solution of more complex basic equations.
The treatment centers around the relative rates of gas-liquid mass transfer and
reaction. The reaction rate controls the overall rate if it is very slow; often,
however, it is fast, so that the overall rate is mass transfer controlled. Very fast
reactions can influence the diffusion process, causing enhancement of mass
transfer above the purely physical rate. This enhancement is a function of the
reaction rate. In extreme cases (so-called "instantaneous" reactions) mass
transfer again controls the overall rate of the process.
Consider a reaction between n moles of a dissolving gas A and m moles of a
liquid phase reactant B. Assume negligible diffusion resistance in the gas phase.


nA + mB

Products

Let q = m/n
Let CA and CB represent the molar concentrations of A and B respectively in the
liquid. The rate of reaction of A is then described by:

Where:

n and m are the orders of reaction in A and B, and
e is the liquid hold-up fraction.

Taking A as the limiting reactant, "reaction time” tR is defined by:

The mass transfer of A into the liquid is described by:

Where:

k L= mass transfer coefficient
a = interfacial area per unit reactor volume
C*A = interface concentration of A


A mass transfer "diffusion time" tD may be defined as:

Where:

DLA = diffusivity of A in the liquid.

If a fast reaction occurs near the interface (within the "diffusion film") it will
enhance the mass transfer rate and equation (2) becomes:

Where:

Note:
k*L depends on the reaction rate, not the hydrodynamics which affects k L, and
0 for these fast reactions since the gas reacts as soon as it is transferred.
CA
The ratio of the diffusion to reaction times in the neighborhood of the gas liquid
interface is conveniently expressed as (tD/tR) which is also known as the Hatta
Number (Ha). Its value determines the extent to which diffusion controls the liquid
phase reaction. Several regimes are identified by the range of (tD/tR) values and
each regime has different requirements for reactor design (see Table 1).
Resistance to diffusion in the gas phase has to be accounted for in many cases.
The rate of transfer through the gas phase alone is given by:


Where:

kG = gas film mass transfer coefficient
PA = partial pressure of A in the gas phase
p*A = partial pressure of A at the interface.

Generally more than one resistance is important, so they have to be combined
into an overall coefficient KL, e.g.:

Where:

He

=
=

gas-liquid equilibrium constant
Henry's Law coefficient, i.e.:

The regimes can be seen, for example for n = 1 and m = 1, on a graph of the
enhancement factor k*L/kL against the Hatta Number, given in Figure 2.


FIGURE 2

ENHANCEMENT FACTOR vs HATTA NUMBER
(for Case m = 1, n = 1)

Note:
The group

is the ratio of the liquid bulk to film volumes.

Table 1 lists the Regimes (marked I to V in Figure 2), together with the
conditions, important variables, diagrams of the concentration profiles and
the local rate equations.


TABLE 1

REGIMES OF GAS-LIQUID MASS TRANSFER
WITH ISOTHERMAL CHEMICAL REACTION


6.3

Modification for Exothermic and Complex Reactions

Exothermic reactions occurring in the film or interface can dramatically influence
the enhancement factor. The rise of temperature near the interface affects the
gas solubility (decreasing the reaction rate), but also in general increases the
reaction rate (Arrhenius effect). The juxtaposition of these effects can lead to
multiplicity of steady states. This is illustrated in Figure 3 (from Ref. [23] and Ref.
[1]) for SO3 reacting with dodecylbenzene.


The following list covers complexities of reactions which have been covered in
the literature:
(a)

Simultaneous Absorption of two Reacting Gases
An example is the absorption of H2S and CO2 in ethanolamines.
See Cornelissen (Ref. [13]), summarized in Charpentier (Ref. [11]),
demonstrating resolution of the film model equations and the possibility of
apparently negative kG. Also see Ref. [12].

(b)

Reactive Particles within the Liquid Film

(c)

Autocatalytic Reactions in the Film (see Ref. [37])

(d)

Reaction Forming Volatile Products

These can occur if the liquid diffusivity of the product is less than that of
the reactant. See Ref. [11] and Ref. [36].

(e)

Reversible Reactions
See Ref. [13], Ref. [11], Ref. [16] and Ref. [10].

(f)

Free Radical Multiplying Chain Reactions
See Ref. [18].

(g)

Consecutive Reactions in the Film
See Ref. [8].


FIGURE 3

ENHANCEMENT FACTOR vs HATTA NUMBER :
EFFECT OF THERMAL & OTHER FACTORS


6.4

Preliminary Selection of Reactor Type

Table 1 shows how the various factors dominate reactor behavior according to
the regime. A preliminary choice of the reactor type can therefore be made to
give designs (e.g. film or bulk liquid, high or low kL, etc.) appropriate to the
regime expected, having regard for practically achievable kG, kL, a and eL values.
Table 2 presents suggestions for cases without large exotherms or other
complications.
Before a final choice can be made other considerations intervene, e.g.:
(a)

The overall (macro) flow pattern;

(b)

Heat transfer requirements;

(c)

Materials of construction;

(d)

Foaming properties.

These are dealt with in Clause 9. Table 3 provides a summary of comparative
mass transfer performance estimates.


TABLE 2

REGIMES OF GAS-LIQUID MASS TRANSFER IGNORING
LARGE EXOTHERMS OR OTHER COMPLICATIONS


7

EXPERIMENTAL DETERMINATION OF REGIME

There are two basic methods to determine the mass transfer/reaction regime and
thence select and design or scale-up the reactor. One method consists of
measuring the true liquid phase reaction kinetics (without mass transfer
interference) directly and then using this information with typical values of the
mass transfer coefficient (e.g. from Table 3) for the candidate reactors
selected from Table 1. When this is not possible, the other method is to run the
reaction in a laboratory-scale gas-liquid reactor and follow its responses to
certain changes of conditions.
7.1

Direct Measurement of Reaction Kinetics

The direct measurement of the reaction kinetics is difficult for fast reactions since
it is necessary to remove all mass transfer influences, i.e. to work in Regime I.
With slow reactions a bubble column or stirred vessel will operate in Regime I.
With somewhat faster reactions a more intense contactor (i.e. high kL) might be
used. Examples are the turbulent static mixer (see 11.11) and the spinning film
reactor (see 11.7).
In either case, experiments should preferably be carried out under steady state
conditions and as nearly at the intended plant operating temperature, pressure
and concentrations as possible with the rate measured by mass balance
between the inlet and outlet streams. The residence time of the liquid phase
should be measured either by tracer tests or by measuring the liquid
throughput and the liquid holdup volume in the reactor. Prior to carrying out the
kinetic measurements the absence of any effect due to changing gas rate or
stirrer speed on the measured rate of reaction per unit liquid volume should be
confirmed.
If laboratory-scale intense contactors still show a mass transfer influence, the
reactions are fast and mass transfer will influence the performance of the plantscale gas-liquid reactor (Regimes II - V). It may be possible to predissolve the
gas in the reaction solvent (probably at different conditions from the plant
operating conditions), in which case mass transfer effects are eliminated
(assuming no gas desorbs) and one of the following liquid phase techniques may
be used (Figure 4 illustrates the first two):


(a)

Stopped Flow Technique
This technique is currently limited to < 70°C, atmospheric pressure and
low viscosities in glass, followed by spectrometric analysis. Ninety-nine
percent completion of the reaction should occur in not more than 5
milliseconds (see Ref. [7]).

(b)

Continuous Flow T-jet mixed Reactor
This technique is suitable for higher pressures and temperatures, can be
made from various materials of construction, but is limited to low viscosity
liquids and reaction times tR >> 10 milliseconds. Analysis may be by
temperature rise (should only be a few degrees), by spectrophotometer
(using windows) or from samples (rapid quenching is required). See Ref.
[33].

(c)

Temperature Jump
The reactants are mixed at a low temperature (such that the reaction rate
is negligible) and the temperature is instantly raised to the desired reaction
condition and progress of the batch is monitored (see Ref. [3]).

(d)

Pressure Jump
This technique is similar to the temperature jump but is intended for gasliquid reactions (i.e. without predissolving).


FIGURE 4

REACTORS FOR LIQUID-PHASE KINETICS MEASUREMENT

7.2

Laboratory Gas-Liquid Reactor Experiments

7.2.1

Special Laboratory Devices
A number of specialized devices have been developed and used for
determining which regime applies. The idea is that they provide a known
interfacial area and mass transfer coefficients kL and kG which are the
same as or can be related to those at a point in a plant scale reactor.
These devices have been reviewed by Charpentier (Ref. [11]). Table 3
summarizes the devices and their characteristics.


The spinning cone reactor could be added to the list with a time of contact
between 0.01 and 0.15 seconds, kL of about 0.5 cm/s and an interfacial
area of 50 to 300 cm2. Comparison with Table 4 will indicate which
devices are most likely to represent a given plant contactor. The
experiments should cover the range of concentrations and partial
pressures expected in the plant reactor.

TABLE 3

COMPARATIVE MASS TRANSFER PERFORMANCE OF
CONTACTING DEVICES


7.2.2

Laboratory Stirred Reactors

Laboratory stirred reactors are more commonly available than the specialized
devices and tend to serve as both "kinetic machines" and "semi-tech reactors". If
designed according to the standard configuration given in GBHE-PEG-MIX-705,
the values of kLa and gas hold-up determined in the laboratory can be scaled up.
Laboratory stirred reactors can therefore give useful design information for all
regimes so long as the same regime operates throughout the vessel (beware
that many laboratory autoclaves have a non-standard configuration and use
surface entrainment of the gas, which affects the mechanism, and hence model,
since the gas feed rate depends on the agitator speed).
The partial backmixing of the gas phase may however lead to uncertainties in
relating gas concentration profiles. A thorough study of the film reactions is best
carried out in one of the film reactors described in 7.2.1 and Table 3. The stirred
reactor should be set up to operate at conditions as near as possible to those
intended for the full-scale plant when producing the desired products and yields.
No materials should be omitted if they are to be present in the final process. The
rig should be so designed that agitator speed, temperature, pressure and
gas concentration can be varied. Continuous steady-state experiments are
recommended.
Figure 5 proposes a sequence of experiments to establish which regime is
operative and hence guide in the selection of an appropriate reactor type. Each
change of condition should be approached from both directions to confirm that
regime "boundaries" have not been crossed in the process.
Note:
Processes during which solvent or product boils off may not respond in the ways
inferred by Figure 5 because changes in reaction rate alter the gas hold-up (and
hence the volume of liquid in the reactor if it is level-controlled) and the gas
phase reactant concentration.
Figure 6 is an extension of Figure 5 to incorporate cases in which a solid catalyst
in suspension participates in the reaction.


8

EQUILIBRIUM AND DIFFUSIVITY DATA SOURCES

The use of laboratory stirred reactor experiments and the scale-up methods
described in Clause! 9 eliminate the need for data on gas-liquid equilibria
(Henry's Law coefficient, He) and diffusivity (DLA) in the design. These will,
however, be required if the design uses the basic reaction rate constants and the
previously determined mass transfer coefficients.
Some data will be found in Perry's "Chemical Engineer's Handbook" and in
International Critical Tables. Data on gas solubility can also be obtained from
standard collections such as Ref. [38], Ref. [35], Ref. [26] and Ref. [4]. For simple
molecules the solubility can be estimated from the surface tension, molecular
dimensions and interaction energy (see Ref. [39]). Chemical Abstracts could also
be consulted.

FIGURE 5

EXPERIMENTS TO DETERMINE THE OPERATING REGIME


FIGURE 6

9

EXPERIMENTS TO DETERMINE THE OPERATING
REGIME WHERE A SOLID CATALYST IS INVOLVED

OVERALL EFFECTS
So far only the "local" effects on the reactions have been described. It is
important to consider how local conditions change throughout the reactor
and what effects the reaction has on the design of the reactor as a whole.

9.1

Liquid Flow Patterns
A reaction in Regime I 'sees' the flow patterns in the liquid phase, and may
be influenced by the resulting liquid phase concentration changes through
the reactor, as outlined below. Each reactor type gives a different flow
pattern: see Clause 10.

Three types of ”axial mixing” (mixing in the general flow direction or ”residence
time distribution”) are distinguishable for ”ideal” reactors:


(a)

Batch:

All reactant is in the reactor for the same period.
Mean concentration = log mean of initial and final.

(b)

Plug flow:

As in 9.1(a) but continuous. Tubular reactors in
turbulent flow, or several stirred vessels in series,
approximate to this.

(c)

Backmixed: Reactant has a wide distribution of residence times in
the reactor; mean concentration = outlet concentration.
Continuous stirred vessels, or plug flow reactors with large
recycle loop, aim to approximate to this.

These types should not be confused with ”radial” or ”cross” mixing, which is
uniformly across the general flow direction and is required for all reactors.
For reactions of the order n 1, the required reactor volume will evidently be
greater for a Backmixed reactor than for plug flow of liquid (e.g. by a factor of
3.91 for 90% conversion,  21.5 for 99% conversion, etc. for first order reaction).
This is also true for gas-liquid mass transfer controlled systems, where it is the
gas phase axial mixing which affects the driving force and hence reactor size for
a given throughput.
For certain more complicated reactions, the yield of the reaction is also
influenced by the mode of mixing. Full discussion of this is outside the scope of
this Guide (see Ref. [14] for an introduction), but, briefly, for consecutive
reactions:
ABC
high yield of B (compared with C) is favored by plug flow, but if C is the desired
product, a backmixed reactor should be chosen. For parallel reactions:
A B (product) (of order p in A)
A  C (of order q in A)
if p > q, high yield of B requires high CA, hence plug flow is required, conversely if
p < q, high CA has to be avoided, so a backmixed reactor is preferred. If p = q,
the yield is unaffected by the mixing mode.


9.2

Scale of Mixing

To see the above effects, obviously the timescale of mixing has to compare with
the reaction time. The backmixing found in stirred vessels etc. may be described
by a seconds  minutes timescale (often called ”macromixing”). If, however, the
reaction is mixing sensitive and is substantially complete within milliseconds, any
yield effects will arise from mixing on the microsecond  millisecond timescale
(”micromixing”).
In such cases local effects round the reactant feedpoint (or round the bubbles if a
gas reactant is involved) are controlling, and overall residence time distribution is
irrelevant to the reaction selectivity. High intensity mixers (e.g. turbulent static
mixers) should be considered here. Bourne (Ref. [6]) discussed modelling of
micromixing.
9.3

Gas Flow Pattern: Mean Driving Force for Mass Transfer

In regimes other than I, the overall axial mixing (residence time distribution) of
the gas is important, as it affects the mean concentration difference which drives
the gas-liquid mass transfer. Gas flow patterns depend upon the type of reactor
(see Clause 4) and sometimes its geometry and gas velocity. In using equation
(2) over the whole reactor,

the appropriate mean value of the ‘driving force'
used.

has to be

Since CA y 0, for batch gas (rare) or ideal plug flow of gas, this mean value


and for fully backmixed gas, the mean value

Hence backmixing gives lower mean driving force (implying larger reactor
volume), but lower peak gas concentration (which may influence the reaction
selectivity) than plug flow or batch gas.
In real reactors the ideal flow patterns are not achieved, but may be approached.
More detailed flow modeling is required if deviations from the ideals are
substantial, in other words where selectivity is governed by reactions of timescale
similar or faster than the mixing timescale.

9.4

Gas-Liquid Reactor Modeling

More complicated approaches are required when the reaction yield is sensitive to
the mode of mixing, and is carried out in a reactor which is neither in ideal plug
flow, nor perfectly mixed, but somewhere between. The mixing is then described
by a model of the flow pattern, whose equations have to be solved together with
those describing the reaction kinetics. Since backmixing implies some degree of
recirculation, the solution of the equations has to be iterative and generally
requires a substantial computer program.
There are three types of mixing model for continuous reactors, based on:
(a)

Arbitrary zones of mixedness and segregation (or dispersion and
recoalescence) of elements of fluid;

(b)

Measured flow patterns;

(c)

Calculated flow patterns.

Much effort has been put into developing type (a) models, (see Ref. [31]) but they
remain unsuitable for scale-up use because they require fitted parameters which
are not available. In other words they can describe mixing but not predict it. They
have not been applied to gas-liquid systems.


Type (b) models are at present the most useful, though still requiring more basic
data. Mann (Ref. [23]) describes a successful example, with models of the liquid
and gas circulations in a stirred vessels as loops of x connected mixed zones
(see Figure 7) with feed and offtake where appropriate. The zones can have
different kLa and gas hold-up if these are determined experimentally. The mean
circulation flow and relevant number of zones, x, have to be supplied
from experiment, so the model is again not in itself predictive, also the
parameters have physical meaning, so are more amenable to scale-up.
Middleton (Ref. [27]) describes a measurement technique and some scale-up
correlations (applicable to zero or low gas holdups, with the standard vessel
configuration) for mean circulation time

and circulation time distribution, which can be converted to the number of zones,
x, in a loop.

A more detailed modelling technique using the same information is proposed in
Ref. [25].Patterson (Ref. [29]) describes a reactor model which uses actual local
fluid velocity and turbulence measurements throughout a vessel to describe the
flow pattern (simplified to a rectangular grid of 'cells'). This is getting even nearer
the true hydrodynamics, but does not yet have sufficient velocity data behind it
for reliable application to large vessels or gas-liquidsystems.
The ultimate model is type (c) which involves a complete solution of the 'Navier
Stokes' equations (with a turbulence model), together with the reaction
equations, using 'Computational Fluid Dynamics' (CFD). Middleton (Ref. [28])
gives an example of this for competing reactions in turbulent stirred reactors. A
wide variety of configurations and conditions can be modelled in detail. GBHEPEG-RXT-800 should be consulted for guidance to experts.


FIGURE 7

THE MIXED ZONES IN LOOPS' MODEL FOR
STIRRED REACTORS

9.5

Heat Transfer

Obviously the reactor has to be capable of transferring (supplying or removing)
heat at the appropriate rate, which is a question of supplying sufficient boil-off or
condensation rate, or if sensible heat is being transferred, sufficient temperature
difference, heat transfer area, and liquid velocities over the transfer surfaces.
Design correlations for liquids are widely available, but less so for gas-liquid
systems. Correlations are available (see GBHE-PEG-MIX-705) for stirred vessels
and bubble columns, which are frequently used where heat transfer is a problem.
For low gas volume fractions (at least in stirred vessels), say 15%, Edney and
Edwards (Ref. [17]) show that the gas does not significantly affect the heat
transfer to the liquid. With typical boiling systems the extra bubbles

affect the hydrodynamics, increasing backmixing in bubble columns, and adding
to gas 'flooding' of agitators (for safe design use the maximum, i.e. exit, gas rate
in hydrodynamic calculations). Gas absorption 'driving force' is also reduced by
the dilution of the gas phase by vapour. High boil-off vapour velocities (say >
0.05 m/sec) should be avoided to prevent carry-over of liquid mist into the vapour
off-take.

9.6

Materials of Construction

Selection of materials of construction for plant reactors is often not easy and
should be made at an early stage of experimentation to ensure that research
work is done under conditions, and in devices, that are practical at full scale
considering the materials to be used. Conditions in reactors are often corrosive to
common materials; in gas-liquid reactors erosion/cavitation phenomena add to
these problems, especially for spargers, agitator blades, baffles, and other
high-velocity zones. Specialist engineers should be consulted if problems are
anticipated. High intensity devices (tubular jet mixers, turbulent static mixers),
where applicable, provide small materials weight per unit performance and so
may allow more exotic materials to be used than with vessels (although erosion
problems may be worse).

9.7

Foaming

Foaming should be anticipated in all gas-liquid reaction cases unless known to
be absent, since it is not possible to predict whether a foaming problem will
occur. Surface active solutes, fine non-wetter solid particles, rapid gas-liquid
mass transfer and reactions near the gas-liquid interface can all lead to foaming
problems.
Methods of dealing with foaming are reviewed in GBHE-PEG-MIX-705 and in the
GBH Enterprises Mixing and Agitation Manual.

10

FINAL CHOICE OF REACTOR TYPE

Tables 4 and 5 summarize the typical properties of gas-liquid reactors from which
the selection may be made. The values given in Table 4 are comparative and
should not be used for design calculations. The design values will depend on the
physical properties of the fluids in the reactor.


TABLE 4

COMPARATIVE MASS TRANSFER DATA
(low viscosity systems, non-boiling)

Note:
These are orders of magnitude for comparison, not design figures.
They are based on air and water physical properties at 20 °C. Approximate
adjustment for other systems may be made by:

(Calderbank, Ref. [9]), though others find the index of DAL to be 1.
For further background see Ref. [32], Ref. [22] and Ref. [21].


TABLE 5

CHOICE OF GAS-LIQUID REACTOR TYPE


11

SCALE-UP AND SPECIFICATION OF GAS-LIQUID REACTORS

This Clause gives some sources of reference to correlations which can be used
in the design of gas-liquid reactors or in the scale-up from laboratory rigs or other
plants.
Depending on the regime, the design will require quantitative information on:
(a)
(b)
(c)
(d)
(e)

(f)
(g)
(h)

11.1

Practical range of reactor sizes.
Range of practical flowrates.
Gas hold-up (voidage fraction).
Interfacial area per unit volume.
Mass transfer coefficient (often together with (d) above):
(1)
KL for liquid-side diffusion control.
(2)
KG for gas-side diffusion control.
Liquid backmixing.
Gas backmixing.
Heat transfer.

Bubble Columns

Bubble columns are simple to build and maintain, have no rotating seal problems
and can be made in large sizes. However, they have a low mass transfer
intensity (especially for coalescing systems), an uncontrolled degree of liquid
backmixing and mediocre heat transfer performance. Low concentrations of
easily-suspended solids can be handled.
For scale-up correlations consult GBHE-PEG-MIX-705.

11.2

Packed Columns

These liquid film devices have the advantage of counter-current flow (where
applicable, i.e. for incomplete absorption from a multicomponent gas stream), low
pressure drop and a wide range of available materials of construction. They can
be designed for high or low gas/liquid ratios. The flowrates are limited by
hydraulics.
For design for mass transfer consult GBHE-PEG-MAS-612, manufacturers'
literature (e.g. Norton, ETA, Sulzer) and/or Ref. [32].


11.3

Trickle Beds

These are co-current downflow, low intensity variants of the packed column and
are often used where the packing is or supports a solid catalyst and where cocurrent flow has no disadvantage (e.g. irreversible simple reactions with
complete consumptions of adsorbed components or when the gas phase is a
single component). Pressure drop is less and hydraulic limits are wider than
those for countercurrent columns. Heat transfer is difficult and poor.
Design information can be found in:
(a)
(b)
(c)

11.4

Froment (1979), page 70 (Ref. [19]).
Herskowitz (1983) (Ref. [20]).
Satterfield (1975) (Ref. [34]).

Plate or Tray Columns

Plate or tray columns are similar to packed columns, but have a larger liquid
hold-up. The hydraulic operating range is wider and heat transfer is easier.
However blockages due to the presence of solids and problems due to foaming
may be more severe.
The mass transfer and hydraulic design is usually based on the methods
developed by Fractionation Research Inc. (e.g. their program FRISIEVE for
sieve-plate columns). GBHE-PEG-MAS-611and Ref. [32] should also be
consulted.

11.5

Spray Columns

Spray columns are rarely used because coalescence of droplets often results in
a mediocre interfacial area, and the entrainment of fine droplets into the gas
outflow can be a problem. They are, however, simple and easily cleanable
(therefore suitable for "dirty" gases) and have a low pressure drop on the gas
side.
Design information is sparse; see Froment (1979), page 725 (Ref. [19]).


11.6

Wiped Film

Wiped film devices are commonly sold as evaporators for heat sensitive or high
viscosity liquids. Mass transfer intensity is high, but such devices require a heavy
maintenance effort.
For design information consult the manufacturers (e.g. Luwa).

11.7

Spinning Film Reactors

These devices are still at the research stage as reactors, although centrifugal
thin-film evaporators are available commercially (e.g. from Alfa-Laval and Luwa).
With a 45° cone, gas-liquid mass transfer is enhanced by surface waves on the
film giving rise to very high values of KL for low viscosity liquids.
For more information, consult the experts listed in GBHE-PEG-RXT-800.

11.8

Stirred Vessels

Stirred vessels are widely used (in the higher KL regimes) as they provide
flexibility, good intensity of mass and heat transfer and some control of bubble
size and backmixing. The additional cost of the agitator system and possible
shaft sealing difficulties should, however, be considered compared with the
simplicity of a bubble column. Stirred vessels should be used where there are
solids suspension problems. Because of shaft mechanical limitations they are
not usually very tall.
Design correlations are given in GBHE-PEG-MIX-705.

11.9

Plunging Jet

The plunging jet is a low-cost low-intensity contactor which has recently come
into use for aerating effluent ponds and reservoirs. The energy efficiency is good.
There is little design information available, but see Ref. [5].


11.10

Surface Aerator

The surface aerator is the older, mechanical equivalent of the plunging jet. It is
less energy efficient and requires more maintenance. The degree of mixing is
difficult to quantify.
Design information can be obtained from manufacturers (e.g. SEM, Lightnin).

11.11

Static Mixers

When used with low viscosity liquids in the turbulent regime, static mixers give
very high intensities of gas-liquid mass transfer and approach plug flow
conditions. They offer good heat transfer as they can be used within shell-andtube heat exchangers. They can be operated at low gas/liquid ratios in bubble
flow for Regime II or at high gas/liquid ratios and gas velocities in
film flow (liquid film on all internal surfaces) for Regimes IV and V or under gasfilm controlled situations. Static mixers are new in the gas-liquid reaction area but
there are some plant applications. "Honeycomb" type static mixers can also be
useful for reactions between a gas and a high viscosity liquid.
Design data may be obtained from GBHE-PEG-MIX-705, from Section E4 of the
GBHE Mixing and Agitation Manual or from Ref. [30].

11.12

Ejectors, Venturis and Orifice Plates

Ejectors, venturis and orifice plates can provide high intensity mass transfer if
correctly designed. Ejectors are used in the Buss loop reactor which has several
commercial applications (e.g. H-Acid plant, FCMO).
Ejectors and venturis are covered in GBHE-PEG-MIX-705. Orifices are a crude
alternative and are not generally recommended because of the separated flow
zones behind the orifice plates where coalescence and extended residence times
may occur.


11.13

3-Phase Fluidised Bed

The upward flow of gas and liquid supports a bed of particles which can enhance
break-up or coalescence of bubbles depending on the properties of the particles.
They are not widely used or understood.
Limited design information is given in GBHE-PEG-MIX-706 and Section F2 of the
GBH Enterprises Mixing and Agitation Manual.


12

BIBLIOGRAPHY

[1] Allan J C & Mann R (1979), Chem. Engineering Science, 34, 413.
[2] Astarita (1967), "Mass Transfer with Chemical Reaction", Elsevier.
[3] Bamford C H (1969) & Tipper C F H (eds), "Comprehensive Chemical
Kinetics", Vol. 1, p.134 (Elsevier).
[4] Battino (1966) & Clever, Chem. Rev., 66, 395.
[5] Bin A K (1982) & Smith J M, Chem. Engineering Commun. 15, 367.
[6] Bourne J R (1982), Chem. Engineering Commun, 16, 79.
[8] Brian P L T (1965) & Beaverstock M C, Chem. Engineering Science, 20, 47.
[9] Calderbank P H (1961) & Moo-Young M B, Chem. Engineering Science, 16,
39.
[10] Carmichael G R (1980) & Chang S C, Chem. Engineering Science, 35, 2459
and 2463.
[11] Charpentier J C (1982), Trans.IChemE., 60, 131.
[12] Chaudhari R V (1975) et al, Chem. Engineering Science, 30, 945.
[13] Cornelissen A E (1980), Trans.IChemE., 56, 242.
[14] Coulson J M (1971) & Richardson J F, "Chemical Engineering", Vol. 3,
Second edition, Pergamon Press.
[15] Danckwerts P V (1970), "Gas-Liquid Reactions", McGraw-Hill.
[16] deCoursey W J (1982), Chem. Engineering Science, 37, 1483.
[17] Edney H G (1976) & Edwards M F, Trans. IChemE, 54, 160.
[18] Flores-Fernandez G (1978) & Mann R, Chem. Engineering Science, 33,
1545.
[19] Froment G F (1979) & Bischoff K B, "Chemical Reactor Analysis and
Design", Wiley.

[20] Herskowitz M (1983) & Smith J M, AIChE J., 29, 1.
[21] Horak J (1978) & Pasek J, "Design of Industrial Chemical Reactors from
Laboratory Data", Heyden.
[22] Laurent A (1983) & Charpentier J C, Int. Chem. Engineering, 23, 265.
[23] Mann R (1977) & Moyes H, AIChE J. 23, 17.
[24] Mann R (1977a), Middleton J C & Parker I B, Proc. 2nd Eur. Conf. Mixing,
BHRA, Cambridge, paper F3.
[25] Mann R (1981), Manros P P & Middleton J C, Trans.IChemE, 59, 271.
[26] Markham A (1941) & Kobe K, Chem. Rev., 28, 519.
[27] Middleton J C (1979), Proc. 3rd Eur. Conf. Mixing, BHRA, York, paper A2.
[28] Middleton J C (1986), Pierce F & Lynch P M, ChERD, 64, 18.
[29] Patterson G K (1975), in Brodkey (ed) "Turbulence in Mixing Operations",
Academic Press.
[31] Rao D P (1973) & Edwards L L, Chem. Engineering Science, 28, 1179.
[32] Rase H F (1977), "Chemical Reactor Design for Process Plants", Wiley.
[34] Satterfield C N (1975), AIChE J., 21, 209.
[35] Seidell A (1965), rev. Linke W, "Solubilities", American
[36] Shah Y T (1974), Pangarkar V G & Sharma M M, Chem. Engineering
Science, 29, 1601.

[37] Sim M T (1975) & Mann R, Chem. Engineering Science, 30, 1215.
[38] Stephen H (1963) & Stephen T (eds), "Solubilities of Inorganic and Organic
Compounds", Pergamon.
[39] Uhlig H H (1937), J phys. Chem., 41, 1215.


DOCUMENTS REFERRED TO IN THIS PROCESS ENGINEERING GUIDE
This Process Engineering Guide makes reference to the following documents:
GBHE ENGINEERING GUIDES
Glossary of Engineering Terms (referred to in Clause 3)
GBHE-PEG-MAS-611 Design and Rating of Trayed Distillation Columns
(referred to in 11.4).
GBHE-PEG-MAS-612 Design and Rating of Packed Distillation Columns
(referred to in 11.2).
GBHE-PEG-MIX-705 Mixing of Gas Liquid Systems
(referred to in 7.2.2, 9.5, 9.7, 11.1, 11.8, 11.11 and 11.12).
GBHE-PEG-MIX-706 Gas-Solid-Liquid Mixing Systems (referred to in 11.13).
GBHE-PEG-RXT-800 Experts on Reactor Technology (referred to in 9.4 and
11.7).
GBHE-PEG-RXT-809 Homogeneous Reactors (referred to in 6.1).

OTHER GBHE DOCUMENT

GBHE Mixing and Agitation Manual (referred to in 9.7, 11.11 and 11.13).


Gas - Liquid Reactors

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