Simulation of Mixing and Heat Transfer in Stirred
Tanks with VisiMix®
Solutia Inc.
Ke Liu
Indian Orchard Technical Center
730 Worcester Street
Springfield, MA 01151
ke.liu@solutia.com
(413) 730-3371
Kenneth Neeld (speaker)
Delaware River Site
Route 130 South
Bridgeport, NJ 08014
kkneel@solutia.com
(856) 467-8342
Abstract
VisiMix® is an engineering modeling tool which simulates mixing and heat transfer in
stirred tanks. Solutia has been using VisiMix® in product and process development to
assess the mixing and heat transfer capability of a pilot reactor for a new resin product,
to design pilot plant agitation configuration for a new process, to scale up a lab reactor
to a pilot vessel to match the particle size distribution of the final product and to scale
down from plant to pilot plant for design of pilot plant tests. The authors will share
examples of their experience using VisiMix® in process development, scale-up and
scale-down activities.
AIChE 1999 Annual Meeting
Topical Conference on Process Development from Research to Manufacturing
Industrial Mixing and Scale-up
November 3, 1999
For chemists and engineers working in a laboratory or pilot plant environment, mixing is
still pretty much a black art. Process engineering design groups can rely on vendor
expertise and experimentation, especially when it comes to sizing and specifying
equipment for specific applications. Dimensional analysis is commonly used and highly
regarded in computing agitator power requirements, mixing intensity, and other
parameters:
Po = f [ Re, Fr, T/D, W/D, H/D,…]
Po = Power Number = P / (  N3 D5 )
Re = Reynolds Number = (  N D2 ) / 
Fr = Froude Number = ( N2 D ) / g
but these tools are usually applied only when a project has reached the design phase.
In addition, dimensional analysis is dependent upon geometrical similarity, which is
difficult to achieve in scaling up and down from pilot plant to production scale and almost
impossible to or from lab scale.
Lab and pilot plant scale up, when it comes to mixing and agitation, are often based on
a combination of experience and trial and error. Time and effort spent in process scale
up can be extended significantly trying to “tweak” product properties or process
performance with mixing parameters. Too often the properties or performance sought
are dependent on microscale mixing characteristics which are not easily addressed by
dimensional analysis.
Liquid mixing involves three interdependent processes: bulk flow, turbulence, and
molecular diffusion. Turbulence plays a key role in many mixing applications, but the
measurement of turbulence is difficult and requires specialized equipment not typically
available to industrial labs and pilot plants. Consequently, it is often either overlooked or
simplified to a readily grasped concept, such as agitator tip speed.
Turbulence consists of eddies which vary in size from a maximum, Lmax, depending on
the scale of the equipment down to a minimum, L0 , which depends primarily upon the
power input per unit mass and the kinematic viscosity.
L0 = [ ( 3 V ) / ( P 2) ]0.25
This is called the Kolmogorov length. Turbulent shear stress, , is related to the “mixing
length” of these eddies, as is shear rate, .
L0 = (  )0.5 / 
 =  [ ( P L0) / (  V) ]2/3 = 
 = (  e )0.25 / L0 = ( e /  )0.25 = [ P / (  V ) ]0.25
where  is kinematic viscosity and e is the turbulent energy dissipation rate, or power
per unit mass. We will return to the issue of shear rate later in this paper.
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Understanding the impact of turbulent mixing on processes and being able to use it
easily in scale up could result in significant savings to industry, both in process
development cost and in time to market for new products.
In late 1996 we became aware of a new engineering software tool called VisiMix®
developed and marketed by a group of former Russian scientists and engineers now
working in Jerusalem, Israel. We obtained a copy of this software and have used it
frequently to address mixing applications within Solutia. We, and other users, have
found it to be useful in scale up and scale down of new and existing products and
processes.
As the name implies, VisiMix® is a highly interactive tool with graphical and visual
complements. It is also extremely easy to use. Although developed for mixing in
vertical stirred tanks, and self-contained and complete in this area, the principles can be
extended to other geometries and situations, such as horizontal tanks and pumparounds, with assistance from the VisiMix® staff.
The use of CFD (computational fluid dynamics) is expanding in industry, and mixing and
agitation applications have been a prime target for this software by most vendors. While
VisiMix® does not employ the same level of mathematical sophistication as CFD, it does
not require the same level of expertise to formulate a problem. CFD is useful in
evaluating flow patterns in complicated geometry or where complex multiphase mass
and/or heat transfer are occurring and the phenomena have adequate mathematical
description. For most problems involving stirred vessels, VisiMix® can provide useful
information, often sufficient to make decisions in a matter of minutes or a few hours.
Problem setup in VisiMix® consists of defining:
Vessel (and jacket) type and geometry
Agitator type, dimensions and speed
Baffle placement and geometry
Media physical properties such as density and dynamic viscosity
Menus with pictures of commonly employed commercial tanks, jackets, baffles, and
agitators are used to simplify the setup. Shaft design and rating are also possible with
input of shaft dimensions and metallurgy.
Menus allow you to choose which parameters you want to simulate, and these include:
Tangential velocity distribution
Heat transfer
Power
Shaft design
Axial circulation flow
Macro scale eddy diffusion
Micro scale turbulence
Single phase mixing and mixing time
Single phase reaction
Pick up of solids
Axial and radial solids distribution
Drop break up and coalescence
Mass transfer in solid-liquid and gas-liquid systems
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VisiMix® can be a valuable tool in agitation scale up or scale down, especially where the
process involves laboratory, pilot plant and production scale vessels.
Figure 1 illustrates this process. VisiMix® modeling can be employed at any stage of
scale down or scale up. In addition, it can be used from the onset of new product or
process introduction to troubleshooting and modifications at the same equipment scale.
A common question to engineers is how well a new product or process will perform in
existing production scale equipment, since such equipment is expensive and not easily
modified or replaced. VisiMix® can be used to identify critical mixing parameters and
predict performance in pilot plant and process equipment based on laboratory results.
We have used VisiMix® in this manner to reduce fouling on scale down to pilot plant
equipment and to scale up liquid suspension drop size to maintain product performance.
For liquid-liquid systems VisiMix® uses correlations based on integration of the following
equation over the tank volume:
dDm / dt = Dm [Integral ( Nc - Nbr ) dV ] / (3 Z)
VT
where Dm = mean drop size
Nc = mean frequency of coalescence
Nbr = mean frequency of drop breakup
Nc and Nbr depend on the frequency of turbulent pulsation of scale c and br and the
probability of drops being in an area of scale c and br.
Figure 2 is a typical VisiMix® graph of equilibrium drop size distribution in a liquid-liquid
agitation system. In addition to the density and viscosity of the continuous and disperse
phases, VisiMix® utilizes a user supplied interfacial surface tension and “index of
admixtures” in computing drop size. The latter influences drop coalescence and can be
used to define stability in surfactant emulsified systems, for example.
VisiMix® uses correlations in performing simulations to save calculating time. We do
not include these correlations here, but this information is contained in Reference 1 and
is available upon request or from VisiMix, Ltd. Correlations consist of rigorous
calculations verified against published and unpublished experimental results.
We have also used VisiMix® to select agitator design to minimize expensive catalyst
attrition and loss in a new reactor.
Axial transport of solids is based on a one-dimensional diffusion model:
X / t = ( vax - W s ) ( C / z ) + Dl (2X / z2 )
where vax is the average axial velocity, W s is the particle settling velocity and Dl is the
macro-scale eddy diffusivity.
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This model divides the tank into two zones, one for upward and one for downward flow,
with crossover regions at the top and bottom treated separately. We note this paper is
based on VisiMix® Version 3.02 which is for the turbulent flow regime only. A separate
software suite exists for laminar mixing.
Radial transport in solids suspension is based on:
d[ 2 r H ( W pr - Dradl dX / dr ) ] - 2 q r (Xavg - X ) dr = 0
where W pr = W s [ vtg / ( g r )0.5 ] is the settling velocity of particles resulting from the
separating effect of the tangential velocity component, vtg.
In the application involving catalyst attrition we were faced with three different existing
reactor sizes and agitator designs and two vendor proposals for a new larger reactor,
choosing instead a design created using VisiMix®.
Figure 2 illustrates the different types of agitation used in this application for the same
process! The figure does not indicate that the reactors are also of different volumes.
The vessel in the lower right corner is a VisiMix® model of a lab reactor used in catalyst
suspension studies.
VisiMix® calculates minimum agitation required for off-bottom solids suspension and
provides graphical output of axial and radial non-uniformity in solids suspension.
Off-bottom suspension requires that the rate of particle pick up off the bottom equal or
exceed the rate of settling particles:
dGup / dS >= dGdown / dS
which is satisfied when
n ( v’ >= vcr ) >= W s Xp / ( Xb dp )
where n is the mean frequency of pulsation of scale  and  is a velocity pulsation
probability that v’ >= vcr, the critical velocity for pickup.
And
vcr = [ 2 dp g ( p - l ) / l ]0.5
Figures 4 & 5 are examples of graphs generated by VisiMix® for axial and radial
distributions of the solid phase in a liquid-solid mixing application. Note that the curves
are plotted as ratios to average concentration so that differences are exaggerated. The
patterns are typical for dual axial flow turbines. The axial distribution highlights the
zones of mixing for each turbine, and the radial distribution highlights the zones of
upward and downward flow.
VisiMix® is sometimes valuable in simply demonstrating good and bad blending
practices. In one application, two batch blending in an existing storage could easily be
seen to be superior to single batch mixing using the animated general flow pattern
feature of VisiMix®.
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Figures 6 & 7 illustrate this. Blending of additives into a single batch is seen to be
qualitatively inferior to mixing into a two-batch blend. The second turbine does not show
in Figure 6 because it is above the liquid surface. Here is an example where the
simplest analysis is very revealing to the engineer who does not realize what is going on
inside the tank.
We recommend using VisiMix® to develop standard models of pilot plant and production
scale equipment, including vessel jackets, where frequent scale up is practiced in new
product development. We have done this at our Springfield, MA, pilot plant. In one
application we developed and verified heat transfer capabilities of pilot and plant
reactors and used these models to predict the ability to control polymerization reactions
within temperature limits.
Figures 8 & 9 show the results of simulations for heating and cooling of water in one
jacketed pilot plant vessel. The simulation results are plotted against experimental data,
and this is an easy way to build confidence in the extrapolation of the heat transfer
capabilities of VisiMix® to more complicated systems involving reactions, for example.
VisiMix® can provide insight into the relationship between mixing and chemical reaction.
Irreversible main and side reactions can be simulated in batch, semi-batch and
continuous reactors with time-dependent animated and graphical representation of
reactant and product composition.
The reactions are based on a one-dimensional diffusion model and calculated for the
different agitation zones as described above.
Ca / t = q ( Ca / z ) + Sl Dl ( 2Ca / z2 ) - kr Ca Cb for reactant “A”
Fast reactions will depend upon mixing to bring reactants close together through eddy
turbulence to a scale where molecular diffusion can take place. Relatively slow
reactions that exceed the macromixing time scale will be less dependent on turbulence
and more so on diffusion.
Mixing times may differ significantly in production scale equipment from the laboratory.
VisiMix® can assist in understanding the time-dependent distribution of additives to
tanks under agitation.
Figure 10 illuminates another one of the animated features of VisiMix®. This is a
snapshot 10 seconds after the introduction of a tracer at the solid dot into an agitated
tank. The solid dot corresponds to the entry point of a reactant. The relative darkness
of the contents of the tank relate to the concentration of tracer. The animation clearly
shows that the tracer travels up the outer zone along the tank wall, across the liquid
surface, and down the center into the agitator zone where the highest energy dissipation
occurs. If turbulence is important in this reaction, the relatively long duration of
“unmixed” reactant may create problems, such as promotion of undesirable side
reactions or reactant-wall interactions.
At the beginning of this paper we discussed the importance of turbulence in mixing.
One of the standard parameters for scale up is shear rate, and one of the simpler ways
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to calculate average shear rate is agitator tip speed over the distance between the tip
and the vessel wall:
avg = N D / ( T - D )
VisiMix®, however, defines shear rate as the ratio of turbulent fluctuation velocity, v0, to
the Kolmogorov turbulence scale, L0
 = v0 / L0
L0 has already been defined, and
v0 = (  e )0.25
The difference can be considerable as illustrated in Table I, which compares the two
calculations for vessels of lab, pilot plant, and production scale. VisiMix® values for
shear rate are higher, and the higher resultant shear stress may have a profound effect
on processes involving dispersion, coalescence, mass transfer and reaction. The
effects of non-Newtonian viscosity must also be kept in mind.
It is literally possible to make modifications to pilot plant agitation equipment in less than
a day based on experimental data and a good VisiMix® model. Troubleshooting mixing
problems is so easy that the process engineer can often provide better understanding
and even suggest a solution within hours of initial problem awareness.
For this reason, it is a goal of VisiMix® marketing to place this tool on the desk of every
process engineer. This may not be desirable for a number of reasons:
While verification against published literature for mixing systems invites a high
level of confidence in VisiMix® results, this is an ongoing process, and there are
still some significant gaps, for example in the area of mass transfer.
The tool is so easy to use that almost anyone can get results, and the simulation
output is extensive compared to the effort involved to set up a problem.
Interpretation of the results still requires someone with some background and
experience in agitation and mixing.
The price tag for VisiMix® is currently high enough to limit its availability to
engineers who have a real need and ability to use it.
Having said these things, we believe that wherever scale up and scale down in stirred
tanks are important, and this is probably the majority of industrial pilot plants, VisiMix® is
an engineering tool powerful enough to provide competitive advantage.
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NOTATION
Ca,b =
D=
Dradl =
dp =
G=
g=
H=
kr =
N=
P=
q=
r=
S=
T=
t=
V=
v’ =
W=
X=
Z, z =
=
l =
p =
=
concentration of reactant “A”, “B”
impeller diameter
radial diffusivity
solid particle diameter
mass flow rate
gravitational acceleration
liquid height
specific reaction rate
impeller shaft speed
impeller power
liquid circulation rate
Radius
cross sectional area
tank diameter
Time
Volume
random turbulent constituent of velocity
impeller width
transport flux
length, axial length
Density
liquid density
solid particle density
dynamic viscosity
REFERENCES
1. VisiMix, Ltd. “A Review of the Main Mathematical Models Used in the VisiMix®
Software.
2. Harnby, N.; Edwards, M. F. & Nienow, A. W. Mixing in the Process Industries, 2e.
Butterworth-Heinemann (Oxford, U. K.) 1992.
3. Oldshue, J. Y. Fluid Mixing Technology. McGraw-Hill. 1983
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