Computational%20Study%20of%20Liquid-Liquid%20Dispersion%20in%20a%20Rotating%20Disc%20Contactor

1
Computational Study of Liquid-Liquid Dispersion
in a Rotating Disc Contactor
A. Vikhansky and M. Kraft Department of Chemical
Engineering, University of Cambridge, UK M.
Simon, S. Schmidt, H.-J. Bart Department of
Mechanical and Process Engineering, Technical
University of Kaiserslautern, Germany
2
Rotating disc contactor Department of Mechanical
and Process Engineering, Technical University of
Kaiserslautern, Kaiserslautern, Germany
3
Flow patterns
4
The approach Compartment model Weighted
particles Monte Carlo method for population
balance equations Monte Carlo method for
sensitivity analysis of the Smoluchowskis
equations Parameters fitting
5
Compartment model Breakage, coalescence,
transport
Population balance equation
6
Smoluchowski's equation
7
Identification procedure
1. Formulate a model.
2. Assume a set of the models parameters.
3. Solve population balance equations.
4. Calculate the parametric derivatives of the
solution.
5. Compare the solution with the experimental
data and update the models parameters.
8
A Monte Carlo method for sensitivity analysis of
population balance equations
n
n
x
x
Stochastic particle system
9
A Monte Carlo method for sensitivity analysis of
population balance equations
n
n
x
x
Stochastic particle system
10
A Monte Carlo method for sensitivity analysis of
population balance equations

Stochastic particle system

11
Acceptance-rejection method

1. generate an exponentially distributed time
   increment with parameter

2. choose a pair to collide according to the
distribution
3. the coagulation is accepted with the
probability
4. or reject the coagulation and perform a
fictitious jump that does not change the size of
the colliding particles with the probability
12
Calculation of parametric derivatives of the
solution of the coagulation equation
A disturbed system
13
Evolution of the disturbed system is the same as
the undisturbed one, while
have to be recalculated as
the factors
if the coagulation is accepted, or as
if the coagulation is rejected
14
The model Breakage of the droplets
15
The model Collision and coalescence
16
The model Transport
17
Operational conditions
18
Identified parameters and residuals
19
Experimental vs. numerical results
fitted
unfitted
20
Coefficients of sensitivity
Volume fraction
Mass-mean diameter
Sauter mean diameter
21
Conclusions A Monte Carlo method was applied
to a population balance of droplets in two-phase
liquid-liquid flow. The unknown empirical
parameters of the model have been extracted from
the experimental data. The coefficients
identified on the basis of one set of
experimental data can be used to predict the
behaviour of the system under another set of
operating conditions. The proposed method
provides information about the sensitivity of the
solution to the parameters of the model.