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HUNGARIAN JOURNAL 
OF INDUSTRIAL CHEMISTRY 

VESZPRÉM 
Vol. 36(1-2) pp. 65-69 (2008) 

MODELLING OF MULTI-STEP MICROFILTRATION PROCESS FOR 
SOLVENT EXCHANGE 

Z. KOVACS1 , M. DISCACCIATI2 

1Johannes Kepler University Linz, Institute of Process Engineering, Welser St 42 A-4060 Leonding, AUSTRIA 
E-mail: zoltan.kovacs@jku.at 

2Ecole Polytechinque Fédérale de Lausanne, IACS - Chair of Modeling and Scientific Computing (CMCS) 
CH-1015, Lausanne, SWITZERLAND 

 

Industrial-scale microfiltration (MF) separation is applied to process a dispersed ternary system containing an organic 
solvent, water and fine particles. The objective of the separation is to exchange the organic solvent with water and 
concentrate the water-particle dispersion. The MF separation is carried out in a multi-step batch operation including pre-
concentration, dilution mode, and post-concentration process steps. In this study, we present a practical computational 
algorithm which can be used as a basis for process simulations of both concentration and dilution modes. The numerical 
method is based on mass balance processing and on empirical relations of the rejection and the permeate flux to the feed 
composition. These empirical relations are obtained from the experimental data of a single test-run with the process 
liquid. We discuss the input data of the code and the respective experimental design with the necessary sampling. Finally, 
we provide optimum-search techniques considering economical aspects and technological demands. 

Keywords: microfiltration, modelling, solvent exchange, diafiltration, optimization 

Introduction 

One of the major solvent consuming processes in the 
chemical and the pharmaceutical manufacturing is 
solvent exchange. Organic solvents are widely used as 
reaction media for chemical synthesis, raw materials, 
and as cleaning agents [1].  

Membrane technology has a great potential to 
improve the performance of many liquid phase synthesis 
reactions by reducing the need for complex solvent 
handling operations. Membrane separation can provide a 
cheaper solution over the conventional solvent exchange 
via distillation, when the solvent to be removed has a 
lower boiling point than the replacing solvent [2].  

In batch membrane system design, a common 
separation strategy for selective removal of components 
with low retentions is to employ a multi-step membrane 
process. A multi-step batch process is a chain of 
operations of a defined number and order that are carried 
out consecutively using the same membrane module. 
There are two basic operation modes: the concentration 
and the dilution mode. In a general case, a multi-step 
process consists of three steps (e.g. operations): pre-
concentration, dilution mode and post-concentration 
steps. This concept is one of the conventional process 
techniques to achieve high purification of macro-solutes 
with an economically acceptable flux [3]. 

Batch membrane separation has been presented in a 
number of different forms in the past, which is, and 
continues to be an active area of interest both academically 

and industrially. The classical mathematical modelling 
[4,5] uses the concentration factor as a basis for the 
calculations, while numerical techniques [6,7] handle 
the permeate flux and the component rejections as 
(time-dependent) state functions of the feed composition. 

In this study, we present a practical computational 
algorithm which can be used for the simulation of batch 
operations. The numerical method is based on mass 
balance processing and on empirical relations of the 
rejection and the permeate flux to the feed composition. 
These empirical relations are obtained from experimental 
data that were obtained from a test-run with the process 
liquid. We discuss the input data of the computational 
algorithm and the respective experimental design with 
the necessary sampling. Finally, we provide optimum-
search techniques considering economical aspects and 
technological demands. 

Although real-life experimental data are used in this 
study, the latter strictly focuses on the mathematical 
programming approach, and it does not aim to give a 
detailed insight into the properties of the applied 
colloidal system and the confidential technological 
specifications of the industrial settings. 

Problem statement 

Industrial-scale MF separation is applied to process a 
ternary dispersed system containing an organic solvent, 
water and fine particles. The objective of the separation 



 

 

66

is to exchange the organic solvent with water, and 
concentrate the water-particle dispersion. The schematic 
configuration of the industrial membrane filtration plant 
is shown in Fig. 1. 

 

 
Figure 1: Schematic representation of the batch 

configuration 
 

Two basic modes of batch operation are considered: 
the concentration and the dilution mode. In the 
concentration mode, the retentate stream is completely 
recycled into the feed tank, and the permeate stream is 
collected separately, that results in a continuous volume 
decrease in the feed tank. In the dilution mode, a diluant 
is added into the feed tank at a rate equal to the 
permeation rate. A level sensor is activated in the feed 
tank, which keeps the adjusted level of the feed volume 
constant by continuous addition of the wash water. The 
total weight of the particle in the feed tank remains 
constant due to the complete rejection, but the solvent 
passes through the membrane. Since the permeate 
stream is replaced with wash water, there is a continuous 
decrease of solvent concentration in the feed tank during 
the dilution mode. 

The colloidal dispersion is produced batch-wise via 
chemical synthesis. This ca. 250 kg dispersion is the 
initial feed for the MF process, and it contains ca.  
10 w/w% fine particles and ca. 30 w/w% solvent. The 
MF separation is carried out in a multi-step batch 
operation including pre-concentration, dilution mode, 
and post-concentration process steps. Due to technical 
requirements, the solvent concentration has to be 
reduced to 0.05 w/w%, and the dispersion concentrated to 
100 kg. As far as the membrane separation performance 
is concerned, the water and solvent permeation rates 
through the MF membrane are equal, and the dispersed 
particles are completely rejected by the membrane. The 
stability of the colloidal system can also affect the MF 
process performance. At certain feed composition range, 
the dispersion becomes unstable. This phenomenon can 
lead to sludge formation which can completely plug the 
membrane. Thus, extra care is needed in the process 
design. 

The objective of this study is to define the 
mathematical basis of the chemical engineering problem 
by building a model based on real-life experimental 
data. The problem is attacked with suitable mathematical 
programming techniques that gives quantitative prediction 
for the unit operation steps, and provides the optimum 

operational settings for the overall multi-step separation 
process. 

Modelling concept 

The multi-step process is carried out at constant pressure 
and temperature, and the same hydrodynamic conditions 
are maintained during the operation. Thus, at any time 
and at any step of the process, the permeate flux can be 
described solely as a non-linear function of the actual feed 
composition. The computational technique summarized 
in the scheme of Fig. 2 was developed in order to 
predict the changes of the feed tank volume and the feed 
composition during the membrane filtration process. 

 

 
Figure 2: UML activity diagram of the process simulation 

 
It is assumed that the initial feed concentration of 

both particle cFp and solvent c
F

s are known. For 
simulation purpose, we prior define a sufficiently small 
time interval Δt. If the relationship between permeate 
flux and feed composition is known, than the permeate 
flux can be calculated for the initial feed dispersion at 
the beginning of the process. Therefore, the small 
volume of the permeate ΔV, which passes through the 
membrane in the small time-interval, can be quantified. 
The relationship between flux and feed composition, 
e.g. J = J(cFp, c

F
s), can be obtained from theoretical 

membrane transport models. However, in this study, we 
use a practical approach based on experimental data. This 
approach ensures the derivation of a reliable relation 
from a limited number of experimental data without 
prior approximations. The function J = J(cFp, c

F
s) was 

empirically determined during a test-run with the 
process stream. Complete particle retention is proved 
with analytical measurements, and the water and solvent 
permeation rates through the membrane are found to be 
equal. Thus, the mass of each component in the very 
small permeated volume ΔV can be estimated. 



 

 

67

Thereafter, mass and component balances for both 
permeate and feed tank can be used to determine the 
new compositions and total masses. Then, the above 
described procedure can be repeated with the new 
values. Obviously, in dilution mode operation, we 
assume a wash-water volume inlet into the feed tank, 
which is equal to the ΔV permeated volume. The exit 
condition of the cycle is the prior defined volume, 
which is collected in the permeate tank, or alternatively, 
the solvent concentration in the feed tank. During the 
computational cycle, the feed composition is checked to 
determine whether the dispersion is stable and 
separation can be continued. 

This code can be run either in concentration or in 
dilution mode and multi-step process can be built up 
from individual blocks by defining the input arguments 
of a latter step as the output arguments of the previous 
step. The number and the order of the individual steps 
can be freely chosen by the user. This practical 
computational technique is not restricted to MF 
applications, and one can simulate diverse modes of 
operations. In a recent study [7], a similar numerical 
approach is presented for the simulation of the 
separation of inorganic salts from organic molecules 
with multi-step batch nanofiltration.  

Process simulation 

The permeate flux was experimentally determined for 
different feed compositions during one test-run of the 
industrial-scale membrane plant on place at the chemical 
company. The initial ca. 250 kg feed was concentrated 
to ca. 160 kg, and thereafter, 90 kg water was added into 
the feed tank. Then this procedure was repeated several 
times. Although membrane cleaning was not performed 
in between the concentration mode operations during 
the test-run, an increased permeate flux was always 
observed after each concentration step. This may indicate 
that fouling has minor importance during the process. 
During this test-run, the permeate flux was measured 
periodically, and at the same time, samples were taken 
from the permeate stream for solvent concentration 
analysis. The solvent/water ratio in the permeate stream 
was always equal to the actual solvent/water ratio of the 
feed tank. The total particle mass in the feed tank was 
28 kg, and it remained constant during the operation due 
to complete rejection. The particle concentration in the 
feed tank was determined by monitoring the total feed 
volume at the time of sampling. The experimental data 
of the permeate flux as function of particle and solvent 
feed concentrations are shown in Fig. 3. Both particle 
and solvent feed concentrations have significant 
contributions to the observed permeate flux.  

The unstable composition regime, that is where no 
permeate flux can be measured, is well visible in Fig. 3. 
Based on the experimental data, this regime is empirically 
defined by the set of feed concentrations which satisfy 

0.142 ≤ cFp ≤ 0.17 and 0.018 ≤ c
F

s ≤ 0.092, 

where cFp and c
F

s are the particle and the solvent 
concentration in the feed tank, respectively.  

 

 
Figure 3: Experimental data of permeate flux 

(illustrated with x) in the function of particle and 
solvent concentration (Lines are to guide eyes.) 

 
It is important to understand that the pronounced 

flux decline in the above defined region is provoked by 
the physical-chemical changes in the colloidal system, 
and the membrane permeation decline is a response to 
these radical dispersion-based changes. The experimental 
values of permeate flux follow a uniform trend which is 
broken only in the unstable regime. Thus, it seems 
reasonable to determine the overall trend for the 
permeate flux, and to handle the instable regime 
separately. The permeate flux can be expressed in terms 
of cFp and c

F
s by fitting the non-zero experimental 

results using an equation like: 

( ) ( ) ( )FsFsFs cxFpcxFpcx excexcexJ 642 5321 −−− ++= , 
where xi, i = 1, 2, … 6 are the fitting parameters. 

The estimated empirical plane and the set of 
coefficients are shown in Fig. 4. 

 

 
Figure 4: Estimated (solid lines) and experimental data (*) 
of permeate flux in the function of solvent and particle 

concentration 
(Curve-fitting is based on non-zero flux data.) 

 



 

 

68

The changes in the permeate flux and in the 
concentrations in feed tank are calculated through the 
computational procedure using the actual (time-
dependent) feed concentrations. This dynamic method 
differs from the conventional calculation procedures 
that are based on volume concentration factors. 

The currently applied process has three operational 
steps. First, the initial feed is pre-concentrated. This step 
is characterized with the pre-concentration grade mpre, 
which is defined as the total mass of the dispersion in 
the feed tank when the second step, the dilution mode, 
starts. Thus, for example a pre-concentration grade 
mpre=200 kg means that the initial 250 kg dispersion is 
concentrated to 200 kg before the dilution mode starts. 

Fig. 5 shows the complete simulation of a 3-step 
process. The feed was first concentrated to 200 kg, then 
dilution mode operation was carried out by applying 
1100 L wash-water, and finally the dispersion was 
concentrated to 100 kg. The permeate flux and the 
solvent concentration in the feed tank can be predicted 
over the operation time as shown in Fig. 5. 

 

 
Figure 5: Simulation example for a three-step process 

including pre-concentration, dilution mode,  
and post-concentration steps 

 
During the pre-concentration step, the increasing 

feed concentration causes a decreasing flux. It is a 
conventional wisdom that the amount of wash-water is 
minimized if it is added where the feed concentration is 
high [8]. However, as shown in Fig. 4, high feed 
concentrations lead to lower solvent fluxes through the 
membrane. Thus, an optimum pre-concentration grade 
exists for performing the dilution mode. 

Process optimization 

The aim of the optimization is to find the set of 
operation parameters that result in the most economical 
process, and satisfy the given technological demands of 
the final product. Thus, the total processing cost is the 
objective function that has to be minimized; the 
operational parameters of pre-concentration grade mpre 
and xdiluant volume VD are the decision variables, and 
the given technological requirements are the constraints 

of the optimization. We define a product quality and a 
product mass constraint, e.g. the final solvent 
concentration has to be reduced under a limit value of 
climit=0.05 w/w% and the final product mass m

final of  
100 kg has to be obtained.  

The objective function can be defined as the total 
cost per unit of product produced. The total cost is a 
sum of two terms, which are the operational cost of the 
pump and the cost of the utilized dilution water. 

The mathematical problem can be described as 
follows: 

Minimize f(mpre,VD) = k1t + k2VD 
subject to the constraints 

mfinal =100 kg and cs
final ≤ climit 

where f(mpre,VD) is the objective function, t is the total 
operation time, VD is the dilution water consumption, 
while k1 and k2 are constants. The constant k1 is a 
product of the power consumption of the pump and the 
electricity price, and k2 is the unit price of the utilized 
dilution water.  

Computer simulation of 3-step processes was 
performed for sets of mpre and VD input parameters. 
Thus, in the first process step, the dispersion was 
concentrated to a pre-concentration grade mpre, then the 
diluant volume of VD was applied to wash out the 
solvent, and finally the dispersion was concentrated to 
100 kg in the last step. During these 3-step processes, 
membrane plugging caused by sludge formation can 
occur when the composition in the feed tank becomes 
instable. Fig. 6 shows the instable area for the applied 
operational parameters.  
 

 
Figure 6: Instable dispersion area illustrated for the 

applied operational parameters 
 
A flux decline can also occur due to high feed 

concentration as shown in Fig. 4. With other words, the 
dispersion can not be concentrated to a too high extend, 
because in that case no permeate flux can be gained. 
Obviously, the location of the optimum is affected, not 
only by the pre-concentrated grade, but also by the 
extent to which the solvent concentration is reduced in 
the dilution mode step. The applied diluant volume VD 
has to be sufficiently big in order to exchange the 



 

 

69

solvent in the feed tank. If VD is too low, the final 
solvent concentration can not be reduced to the desired 
limit value. These issues all contribute to a reduced 
feasible region in the (mpre,VD) matrix. Fig. 6 shows the 
calculated objective function values in the feasible 
range. 

 

 
Figure 7: Objective function in the feasible range as 

function of pre-concentration grade and diluant volume 
 

As shown in Fig. 6, for each pre-concentration grade 
mpre can be found a diluant volume VD, where the quality 
demand for the final solvent content is satisfied. The 
optimum operational parameters (mpre,VD) are given by 
the minimum value of the half-plane of the calculated 
objective function in the feasible range, and it can be 
directly read from the graph. It should be noted that the 
outcome of the optimization is not generally valid. A 
change in the constants k1 and k2 of the objective 
function, or the utilization of an other type of membrane 
would result in a different set of optimum operational 
parameters. 

Summary 

A numerical technique is presented to simulate and 
optimize multi-step batch membrane processes for solvent 
exchange. This technique can be also used to simulate 
membrane filtration processes where not only the flux, 
but also the rejections of the components are dependent 
on the feed composition. The approach followed in this 
work did not use the volume concentration factor as a 
basis for the calculations, but rather the flux as a state 
function of the feed concentrations.  
 

REFERENCES 

1. HELLWEG S., FISCHER U., SCHERINGER M., 
HUNGERBUHLER K.: Green Chem. 6 (2004) 418 

2. LIN J. C., LIVINGSTON A. G.: Chem. Eng. Sci. 62 
(2007) 2728-2736 

3. BLATT W., ROBINSON S.: Anal. Biochem. 26 (1968) 
151-173 

4. BAKER: Membrane Technology and Applications, 
Wiley, West Sussex, (2004) 

5. MULDER M.: Basic Principles of Membrane 
Technology, Kluwer Academic Publishers, Dordrecht, 
(2000) 

6. DISCROLL K.: Development of a Process Simulator 
for the Ultrafiltration/Diafiltration Process. Ph.D. 
Thesis, University of Arkansas, Fayetteville, US 
(2004) 

7. KOVACS Z., DISCACCIATI M., SAMHABER W.:  
J. Memb. Sci. 324 (2008) 50-58 

8. MORISON K. R., SHE X.: J. Memb. Sci. 211 (2003) 
59-70