Homogeneous Reactors

GBH Enterprises, Ltd.

Process Engineering Guide:
GBHE-PEG-RXT-809

Homogeneous Reactors

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CONTENTS

Page

0
1
2
3
4

INTRODUCTION / PURPOSE
SCOPE
FIELD OF APPLICATION
DEFINITIONS
DESIGN STEPS

2
2
2
2
2

4.1
4.2
4.3

3
4
6

Residence Time and Flow Pattern
Modeling of Ideal Reactor Types
Costing

5

EQUIPMENT SELECTION SUMMARY

6

6

EQUIPMENT EXAMPLES

8

6.1
6.2
6.3
6.4

8
9
10
12

7

Gas Reactors - Plug Flow
Gas Reactors - Backmixed or Batch
Liquid Reactors - Low Viscosity
Liquid Reactors - High Viscosity

13

7.1
7.2
8

MEASUREMENT OF HOMOGENEOUS REACTION KINETICS

14
14

Gas Phase Reactions
Liquid Phase Reactions

NOMENCLATURE

15


TABLES
1

EQUIPMENT SUMMARY

7

FIGURES
1

LOOP REACTOR

9

2

BACKMIXED GAS REACTOR

9

3

IN-LINE FLOW MIXERS

10

4

SPINNING CONE THIN-FILM REACTOR

10

5

STIRRED VESSEL REACTOR

11

6

JET-MIXED REACTOR VESSEL

11

7

EXTRUDER

12

8

SCRAPED-FILM REACTOR

12

9

Z-BLADE MIXER

13

10

CONTINUOUS FLOW

14

11

STOPPED FLOW

15

DOCUMENTS REFERRED TO IN THIS PROCESS
ENGINEERING GUIDE

16


0

INTRODUCTIONS / PURPOSE
This Guide is one of a series of Guides produced by GBH Enterprises,
C2PT Catalyst Process Technology Consultancy.

1

SCOPE
This Guide sets out the key steps in the design of gas or liquid phase
homogeneous reactors and suggests appropriate types of reactor
according to the required residence time, flow pattern and heat transfer
duty.
A liquid phase reactor with a vapor product is covered only if the vapor
removal rate does not affect the overall rate. If it does, consider thin-film
reactors.

2

FIELD OF APPLICATION
This Guide applies to the process engineering community in the GBH
Enterprises.

3

DEFINITIONS
For the purposes of this Guide, the following definition applies:
Homogeneous
Reactions

Reactions having only one phase (gas or liquid) in the
reactor or, if there is another phase, it has no effect
on the reaction, on the fluid flow or on the
temperature.

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

DESIGN STEPS
A logical progression of events for the design of a homogeneous
phase reactor are:
(a)

Identify the important reaction products and by-products, and
the reaction steps. Specify the downstream equipment for
separation and treatment of the product, and for effluent
disposal if any. Decide the relative yield required for
satisfactory economics.

(b)

Decide on solvents or diluents, temperature, concentrations
and pressure. Reiterate from (a) if necessary.

(c)

Measure the kinetics (rate constants and orders of reaction)
of these steps, see Clause 7 for measurement methods.
Note any reversible (equilibrium) steps).

(d)

If the reaction scheme is complex and the economics justify
it, a computer model may be required to describe the
interactions between reactions; see GBHE-PEG-RXT-800
Series Proprietary Tools for Reactor Modeling.

(e)

Measure the heat of reaction; see GBHE-PEG-RXT-804
Decide on the materials of construction.

(f)

Recycle from (b) if necessary.

(g)

Decide on batch or continuous operation; see GBHE-PEGRXT-800. Decide on residence time, and flow pattern
(residence time distribution) ideally required in the reactor,
see below and GBHE-PEG-RXT-802.

(h)

Make an initial selection of equipment from Table 1 (see
Clause 5). If this is not possible or impractical, consider the
sensitivity of the reaction operational yield and selectivity to
the factors in steps (b) and (g) and make a new compromise.


(j)

Calculate an approximate size for the reactor.
Assess how closely the flow is likely to approach the ideal
required. It may not be very close (especially if the reactor is
large), in which case, if the costs are sensitive to it, it will
be necessary to computer model the reaction within the flow
pattern (see 4.1). If a semitech or pilot scale plant is being
designed, its flow pattern should be made to copy that of
the proposed plant.

(k)

(l)

4.1

Obtain the flowsheet and approximate sizing of downstream
equipment.
Obtain an approximate costing of the system. Annualize the
capital cost and add raw materials and operating costs. If the
cost is unacceptable, reconsider the decisions of steps (b),
(d), (g) and (h) to find a new compromise. Examine how
sensitive the costs are to reactor flow pattern and revisit (j) if
necessary.

Residence Time and Flow Pattern
GBHE-PEG-RXT-802 gives the basic effects of residence time
distribution on reaction rate and conversion, see also
GBHE-PEG-RXT-802. This implies that, for simple reactions of the
order > 0, a backmixed reactor will be larger than the plug flow
reactor for the same conversion (e.g. by a factor of 3.9 for 90%
conversion, or 21.5 for 99% conversion with a first order reaction).
For multiple reactions, the reaction selectivity will also be affected,
for example, with the reaction:
A B C
high selectivity to B can only be obtained with plug flow whereas
backmixed flow favors conversion to C; or for:
A+B R
R+B S
high production of R requires plug flow, (and sufficiently rapid
mixing of A and B). Whereas formation of S is favored by
backmixing.


Sometimes reactions of widely differing rate have to be accommodated
together and a combination of reactor types is used. This can also be
done for temperature effects, for example a backmixed zone with an
exothermic reaction can be placed before a plug flow reactor in order to
bring reactants up to temperature quickly [Ref. 1].
The models used to simulate the performance of the basic ideal reactor
types are described in 4.2. Non-ideal and more complicated cases are
dealt with in many textbooks, for example [Ref. 2], [3] and [4].
Residence time distribution in continuous reactors refers to mixedness in
the main flow direction. In plug flow, for any but first order reactions, the
degree of cross or radial mixedness is important: the extremes are often
referred to as premixed or segregated feeds; see GBHE-PEG-RXT-802.
Sometimes rapid radial mixers (e.g. turbulent jets) are used at the entry to
tubular plug flow reactors.
Obviously the theory can only be used for real reactors if the fluid
dynamics provide a reasonably close approach to one of the ideal
residence time distribution. Often this is not so, and more complex RTD
models are used, either:
(a)

Using networks of interlinked ideal reactors of appropriate size to
model a measured RTD (this descriptive method is touched on in
GBHE-PEG-RXT-802.

Or
(b)

Computing the flow patterns and reaction progress using
computational fluid dynamics (CFD) programs, which are basically
predictive since they use fine-detail fundamental calculations
without specific empirical input? GBHE-PEG-RXT-800 Series
Proprietary Tools for Reactor Modeling.


4.2

Modeling of Ideal Reactor Types
This section illustrates the sort of equations which arise in describing the
ideal reactor types. They may be useful for initial design and approximate
reactor sizing.
Chemistry: Consider for example the general reaction scheme:

Where A, B, D, and E are chemical species, and R1, R2 and R3 are the
reaction rates (in moles/volume, time).
The rates are functions of concentration, temperature and sometimes
pressure and are defined by:

where C is a concentration in moles/volume, and t is time.
Each reaction has an associated heat of reaction ∆H1, ∆H2 and ∆H3 in
energy/mole, (negative for exotherms).


4.2.1 Ideal Batch Model
The above differential equations must be solved, often with R nonlinear in C, and certainly non-linear if temperature varies, in which
case a heat balance equation is required:

4.2.2 Ideal Plug Flow Reactor Model
Again a set of differential equations arises; the first of these is

These equations can be solved by writing a program using a standard
routine (e.g. from NAG Library) to do the integration from x=0 to x=reactor
length, see GBHE-PEG-RXT-800 Series Proprietary Tools for Reactor
Modeling.

4.2.3 Ideal Backmixed Reactor Model
This model gives a series of algebraic equations, e.g.:

The heat balance equation if the reactor is non-isothermal is:

4.3

Costing
The item cost of the reactor may be obtained from in-house engineers if it
is a vessel, tube, heat exchanger, etc., or from manufacturers if it is
proprietary device (such as a Sulzer mixer, Buss Loop Reactor, or high
viscosity mixer). This must be multiplied by factors (consult GBH
Enterprises, Engineering) for instrumentation, installation and design
charges to give the installed cost. Downstream equipment could be
specified approximately from short-cut design methods (see [Ref. 5], and
costed as above. Its cost may be substantially greater than that of the
reactor.

5

EQUIPMENT SELECTION SUMMARY
Table 1 lists a wide selection of designs, classified by Gas, Low Viscosity
Liquid, or High Viscosity Liquid, then according to flow pattern and heat
exchange system. Low Viscosity refers to liquids which can be practically
processed in turbulent flow; say Reynolds Number,
Re = ρDU / µ > 1000 or viscosity µ > 1 Pas (1000 cp).


6

EQUIPMENT EXAMPLES

6.1

Gas Reactors - Plug Flow
Thermal crackers are typical examples; generally multiple tubular reactors
in furnaces. High process side heat transfer coefficients and close
approach to plug flow require turbulence, hence high velocities and short
residence times. Pressure drop consideration may require a compromise
on the tube velocity. Multiple tubes in parallel are often used to increase
heat transfer area.
For a given process, throughput Q and mean residence time t are
specified i.e.:

An empty tube is cheap and easy to clean, but has a longer mixing length
(95% mixed in about 100 diameters, if turbulent) than a jet mixer or static
mixer (95% mixed in about seven diameters). An empty tube in laminar
flow provides no mixing. With a static mixer, flow is more pluggish and
process side heat transfer coefficient is about four times that in an empty
tube.
Adding a swirl component to the jet flow in a coaxial jet mixer improves the
mixing substantially (common in combustor technology).


GBH Enterprises examples are:
(a) Naphtha cracking;
(b) Arcton cracking;
(c) EDC cracking.
Stirred tube reactors were used on the polythene process to get near the
plug flow without having to use turbulent flow (the gas had a density of
about 1000 kg/m3) at the cost of mechanical complexity.
Inert-solids fluidized beds can be used for heat transfer to gas reactions,
with heat input via jacket, induction heating, internal heaters (preferably
short vertical plate heaters), or submerged combustion. Gas superficial
velocity would be around 1 m/s.
Gas turbines can be used for very rapid reactions with positive volume
change, to provide mechanical work.
6.2

Gas Reactors - Backmixed or Batch
Any of the above plug flow reactors can be used within a loop to provide a
batch reactor, or a good approach to a continuous backmixed reactor (if
the recirculation rate > 10 x throughflow rate). A blower or compressor will
be required to drive the recirculation flow (Fig. 1), unless there is sufficient
feed pressure to re-induce it by means of an eductor.
Where the kinetics are appropriate a backmixed reactor can also act as
the preheater for exothermic reactions.
FIGURE 1

LOOP REACTOR


For short residence times an approximately backmixed vessel can be
used, with jet mixing provided by the input stream (or a recycle stream)
(Fig. 2). Typically a draught tube is used to organize the flow pattern.
FIGURE 2

BACKMIXED GAS REACTOR

Early work by Bush and Shires attempts to model the degree of
recirculation: now it is preferable to use CFD methods.
Examples are: Chloromethanes reactors; HCl generators.
Internal combustion engines are a special case for very rapid reactions
with large volume increase (e.g. combustion) where shaft work is to be
extracted.
6.3

Liquid Reactors - Low Viscosity

6.3.1 Plug Flow
The above remarks for gas tubular and stirred tube reactors apply here
also. Coaxial or side entry jet mixers in turbulent flow provide very rapid
mixing between streams, as do turbulent static mixers, which also give
near-plug flow (Fig. 3).
If velocities or tube lengths preclude these, the oscillating-flow baffled tube
(M Mackley et al, Cambridge University) could be considered: a pilot scale
example is used in the CANDID project.
Examples are: Burn Hall plant scale jet mixer; reaction injection moulding;
nitroglycerine reactor; CANDID reactor.

FIGURE 3

IN-LINE FLOW MIXERS

Centrifugal thin-film reactors have been developed to semi-tech scale by
the GBH Enterprises Process Technology Group. The preferred type is
the spinning cone in which a thin, turbulent liquid film flows up the inside of
a rotating cone and is collected for recirculation at the top (Fig. 4). Heat
transfer (by evaporation or rotating jacket) is intense.
FIGURE 4

SPINNING CONE THIN-FILM REACTOR

6.3.2 Backmixed or Batch
The most common near-backmixed reactor for liquids is the stirred vessel
(Fig. 5); it is versatile and flexible (mixing varied independently of
throughput). Heat transfer via jacket must often be supplemented by
internal coils or recirculation through external heat exchangers; boiling and
reflux must be resorted to for highly exothermic processes, though this is
limited by liquid entrainment by the exit vapor (maximum vapor superficial
velocity 1.5 m/s).
Recommended agitators are axial flow hydrofoil types for overall blending
or disk turbines for high local (micro-) mixing. Liquid mixing is often
promoted by wall baffles (though mixing per unit power input is claimed to
be higher without). It is difficult to predict (varied correlations
from unreliable data);

CFD could help here. 95% mixing times are around 5 sec for a lab vessel
to 100 sec for a large plant vessel, so an ideal mixing assumption cannot
be made with rapid reactions. If the reaction is sensitive to mixing CFD
(MIXFLOW) modeling is required. Local shear stress is highly nonuniform.
FIGURE 5

STIRRED VESSEL REACTOR

Thermal instabilities (multiple steady states) can occur by interaction
between reaction thermodynamics and heat transfer rate.
Capital cost depends on vessel size and drive torque but is often an
insignificant fraction of plant cost (beware of agitator manufacturers
excessively paring down shaft sizes). Operating cost depends on drive
power.
Jet-mixed vessels (Fig. 6) are a somewhat less vigorous and flexible
alternative, useful mainly when a feed or recirculating stream of sufficient
momentum is to hand. They are also useful where a rotating stirrer shaft
seal would be a problem (but not the pump seal!), and where exotic
materials of construction are necessary.
FIGURE 6

JET-MIXED REACTOR VESSEL


6.4

Liquid Reactors - High Viscosity

6.4.1 Plug Flow
Static mixers may be used up to very high viscosities; limited only by
practicalities of pumping. Again flow is much more pluggish that an empty
tube (N.B. laminar flow). Heat transfer area per unit reaction volume is
high.
Extruders are common for very high viscosity transport and heat transfer.
Mixing of streams is poor in a conventional single-screw extruder (Fig. 7),
but is good when mixing zone (e.g. Cavity Transfer Mixer) is added, or if a
twin-screw extruder is used (expensive!).
FIGURE 7

EXTRUDER

Scraped-surface thin film machines (Fig. 8) offer very high heat transfer
per unit liquid volume (via either jacket or evaporation), with near-plug
flow, so are suitable for temperature-sensitive reactions or materials.
FIGURE 8

SCRAPED-FILM REACTOR


6.4.2 Backmixed or Batch
For the moderate viscosity range (up to say 104Pa.s) stirred vessels with
helical ribbon, helical screw (both for shear-thinning or yield-stress fluids),
anchor, or bent-anchor stirrers are recommended. The standard anchor
provides only poor mixing, but good heat transfer to the wall. The bentanchor was devised to improve the axial turnover and mixing.
With higher viscosities mechanical stresses and power intensities are
high, and the specialized stirred chamber mixers are used. These have
rotating blades (of various types) which cover the entire volume of the
enclosed chamber. Common blade shapes include twin concentrate
helices, Z-blades (Fig. 9), double naben blades, and intermeshing cams.
Twin-screw extruders also come into this category. Some theory is
available (see the GBHE Mixing and Agitation Manual) but design is
limited to trials with the manufacturers' specific machines.
EQUIPMENT SUPPLIERS: APV-Baker-Perkins Ltd. (D Todd,USA).
Werner-Pfleiderer GmbH.
Banbury Mixers Ltd.
FIGURE 9

7

Z-BLADE MIXER

MEASUREMENT OF HOMOGENEOUS REACTION KINETICS
Elucidation of reaction pathways and measurement of kinetics in sufficient
detail is the key to the design of efficient and predictable reactors. The
measurements are often hampered by the limitations of quantitative
analysis of intermediates or products, so the analysis methods should
be established before any kinetics measurements are contemplated. If
unsteady-state (batch) measurements are to be made, the response of the
measurement instrument or sampling and quench system must be much
more rapid than the characteristic time of the reactions under study.


Wherever possible all reactants and products should be measured so that a
mass balance can be established. This is a valuable check on the accuracy of
the concentration measurements.
Generally isothermal conditions are required for ease of interpretation, except
where the rate of temperature rise in an adiabatic system is being used to
measure overall reaction rate.
The kinetics measuring reactor should preferable operate without mixing effects
influencing the reaction progress, or at least mixing influences must be
comparatively minor and modellable.
The reactor can be either used in batch or continuous steady-state mode.
Steady-state measurements are easier to interpret but batch experiments are
often more convenient, especially for slower reactions. If a continuous reactor is
used it should approximate well to either an ideal plug-flow or backmixed reactor
for ease of interpreting the results. Plug flow reactors can be operated in
differential (low conversion) or integral (high conversion) mode; see
GBHE-PEG-RXT-805 for a discussion of these.
The kinetics of most homogeneous reaction steps are represented by one of the
following rate equations (CA and CB are reactant concentrations for liquids or
facilities for gases):

Sometimes it is not possible to elucidate a step in full detail, and rates must be
modeled using non-integral apparent orders.


Complex interactions of species can be modeled with GBHE-PEG-RXT800 Series Proprietary Tools for Reactor Modeling.
Fitting of parameters to models is covered in GBHE-PEG-RXT-800 Series
Proprietary Tools for Reactor Modeling.

7.1

Gas Phase Reactions
Steady-state measurements are made using a small-diameter (<10 mm)
tubular reactor (a microreactor) installed in an appropriate constant
temperature environment. Integral or differential experiments can be
carried out according to ease of concentration measurement and
temperature control. as described in GBHE-PEG-RXT-805. Reactor
diameters of less than about 10mm are recommended to minimize the
effects of mass and heat transfer on the kinetic results. [Ref. 6] (Section
1.6) gives some guidance for handling complex reactions.
Batch methods available include temperature jump and pressure jump
methods, in which the well-mixed reactants are placed in a closed vessel
at non-reacting conditions, which are suddenly adjusted to the desired
reaction conditions. A suitable transient (pressure, temperature,
concentration) is measured and analyzed by fitting rate expressions to it.
Very rapid reactions can be studied in this way. See [Ref. 7].

7.2

Liquid Phase Reactions
Removal of diffusion limitations and mixing effects is more difficult than
with gas reactions.
For steady-state isothermal work a tubular microreactor can be used but it
must be of very small diameter (Goddard and Deans recommend 0.2 - 0.5
mm [Ref. 13]) or run at high velocity to achieve adequate radial mixedness
to match a fully turbulent plant reactor. Radial mixing through the reactor,
and approach to plug flow, can be improved by using Static mixer (if a
sufficiently small one can be found). Initial mixing is often achieved using a
turbulent jet mixer of coaxial or T-jet design (Fig. 10) which for low
viscosity systems enable reaction times down to 10 msec to be studied.
See Reports [Refs 8], [9], [10] and [11]. Experiments should be repeated
at different velocities to check for absence of mixing effects.


FIGURE 10

CONTINUOUS FLOW

In the Integral form, extra information can be gathered by on-line
measurement (e.g. spectrophotometry, NMR, or small temperature
changes) or sampling (with rapid quench) at intervals along the tube.
For slower reactions a continuous stirred vessel reactor could be useful if
the backmixing is near ideal. Stirrer speed should be varied to check for
mixing effects.
A batch method is available for rapid aqueous reactions (reaction time 5
milliseconds) at <70°C and 1atm. This is the stopped flow technique (Fig.
11). Reactants flow through a small jet-mixed glass mixing cell, the flow is
suddenly stopped and the concentrations followed versus time by
spectrophotometry, or some other rapid response technique. The
equipment is available commercially; see Report [Ref. 12].


FIGURE 11 STOPPED FLOW

For slower reactions (reaction times > 5 sec for low viscosities; slower for
higher viscosities) a batch stirred vessel is commonly used. Experiments
must be repeated at various stirrer speeds to confirm freedom from mixing
limitations. Guidance on design can be obtained from GBHE-PEG-MIX701; if the design is unconventional it may be modeled using the GBHEPEG-RXT-800 Series Proprietary Tools for Reactor Modeling,
computer program to calculate mixing time, etc. see GBHE-PEG-RXT800 Series Proprietary Tools for Reactor Modeling.
Temperature is kept constant by means of a jacket or immersed coil
(which must not interfere with the mixing), or by boiling and reflux, in which
case care must be taken to design for the minimum unmixed holdup in the
condenser.
8

NOMENCLATURE

D
U
Re
L
n
Q
ρ
µ
t
∆p

Characteristic length; tube diameter; agitator diameter.
Characteristic velocity; tube mean velocity.
Reynolds Number = uDU/o.
Tube length.
Number of tubes.
Volumetric throughput of reactor.
Mean fluid density.
Mean fluid viscosity.
Mean residence time in reactor.
Pressure drop over reactor tube.


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

GBHE-PEG-MIX-700

Experts on Mixing and Agitation
(referred to in 7.2)

GBHE-PEG-MIX-701

Mixing of Miscible Liquids
(referred to in Clause 5 and 7.2)

GBHE-PEG-MIX-702

Gas Mixing
(referred to in 5.1)

GBHE-PEG-RXT-800

How to use the Reactor Technology Guides

GBHE-PEG-RXT-802

Residence Time Distribution Data

GBHE-PEG-RXT-804

Physical Properties and Thermochemistry for
Reactor Technology
(referred to in Clause 4)

GBHE-PEG-RXT-805

Solid Catalyzed Reactions

GBHE-PEG-RXT-810

Gas-Liquid Reactors
(referred to in Clauses 0 and 1)

GBHE-PEG-RXT-800 Series Proprietary Tools for Reactor Modeling.
Reactor Dynamics Control and Safety
Tools for Reactor Modeling


REPORTS
Use of a Semi-Tech Rapidly Mixed Tubular Reactor for a Preliminary Study of
the Methacrylamide Reaction System (referred to in 7.2 and Clause 9)
A Rapidly Mixed Continuous Flow Tubular Reactor Rig for the Study of Fast
Liquid Phase Reactor Systems (referred to in 7.2 and Clause 9)
The Measurement of Fast Liquid Phase Reaction Rates by Kinetic Spectrometry
in a Stopped Flow Apparatus (referred to in 7.2 and Clause 9)
A Rapidly Mixed Continuous Flow Tubular Reactor Rig for the Study of Fast
Liquid Phase Reaction Systems at High Temperatures and Pressures
(referred to in 7.2 and Clause 9)
The Design of an Experimental Rig to Study the Nitration of Chlorobenzene in
Liquid Hydrogen Fluoride (referred to in 7.2 and Clause 9)
Integrated Reactor Systems Procedure (referred to in 4.3 and Clause 9)
Reactor Design (referred to in 4.1 and Clause 9).


Homogeneous Reactors

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