=Paper=
{{Paper
|id=None
|storemode=property
|title=Advanced Prediction of Pulsed Extraction Column Performance using LLECMOD
|pdfUrl=https://ceur-ws.org/Vol-750/yrs03.pdf
|volume=Vol-750
}}
==Advanced Prediction of Pulsed Extraction Column Performance using LLECMOD==
https://ceur-ws.org/Vol-750/yrs03.pdf
Advanced Prediction of Pulsed Extraction Column
Performance using LLECMOD
Moutasem JARADAT1,2, Menwer ATTARAKIH1,3, and Hans-Jörg BART1,2
1
Chair of Separation Science and Technology, TU Kaiserslautern, POB 3049, 67653 Kaiserslautern, Germany
2
Centre of Mathematical and Computational Modelling, TU Kaiserslautern, Germany
jaradat@mv.uni-kl.de, bart@mv.uni-kl.de
3
Faculty of Eng. Tech., Chem. Eng. Dept., Al-Balqa Applied University, POB 15008, 11134 Amman, Jordan
attarakih@yahoo.com
Abstract— A bivariate population balance model (the base of the column have to be considered in order to describe
LLECMOD program) for the dynamic simulation of liquid conveniently the behaviour of the column. The dispersed
extraction columns is extended to simulate pulsed and sieve phase in the case of liquid-liquid extraction undergoes
extraction columns. The model is programmed using visual changes and loses its identity continuously as the drops break
digital FORTRAN and then integrated into the LLECMOD
and coalesce. Accordingly, detailed modelling on a discrete
program. In addition pulsed and sieve tray columns, LLECMOD
simulates stirred two types of agitated columns (RDC & Kühni). level is needed using the population balance equation as a
As a case study, LLECMOD is used to simulate the steady state mathematical framework. The multivariate non-equilibrium
performance of a pulsed extraction column. Two chemical test population balance models have emerged as an effective tool
systems recommended by the EFCE are used in the simulation. for the study of the complex coupled hydrodynamics and mass
Model predictions are successfully validated against steady state transfer in liquid-liquid extraction columns.
and dynamic experimental data, where good agreements with the The simulation of modern industrial chemical processes is
experimental data are achieved. becoming extremely important as an economical tool in the
integration of steady state and dynamic design as well as the
I. INTRODUCTION
simulation of the existing plants. The development of
Liquid-liquid extraction is an important separation computational tools to model industrial processes has
processes encountered in many chemical process industries increased in the last decades. However; to the best of the
[2]. Different types of liquid-liquid columns are in use authors’ knowledge, there are no comprehensive non-
nowadays, which can be classified into two main categories: equilibrium population balance models to describe in
agitated (RDC & Kühni) and pulsed (packed & sieve plate) sufficient detail the behaviour of extraction columns. One of
columns. The latter are frequently used in liquid–liquid the recent approaches in modelling liquid-liquid extraction
extraction operations due to their high throughput, high columns is by adequately describing the complex behaviour of
separation efficiency and insensitivity towards contamination the dispersed phase using the population balances equations
of the interface. These columns have found wide applications (PBE). However, even the numerical solution of the resulting
in nuclear fuel reprocessing and chemical industry. They have system of PBEs is still not efficiently developed particularly
a clear advantage over other mechanical contactors when when coupled hydrodynamics and mass transfer take place
processing corrosive or radioactive solutions. The absence of simultaneously.
moving mechanical parts in such columns obviates the need The main objective of this work is to develop a model that
for frequent repair and servicing. The internals (packing, sieve is capable of describing the dynamic and steady state
plates) reduces axial mixing; increases drop coalescence and behaviour of pulsed (packed & sieve plate) extraction columns.
breakage rates resulting in increased mass transfer rates, and The models of both columns are integrated into the existing
affect the mean residence time of the dispersed phase. The program: LLECMOD [1], which can also simulate agitated
performance of these columns is markedly dependent on the extraction columns (RDC & Kühni). LLECMOD can simulate
mechanical pulsation of the continuous phase. This is a result the steady state and dynamic behaviour of extraction columns
of an increase in shear forces and consequent reduction in size taking into account the effect of dispersed phase inlet (light or
of dispersed droplets so that the interfacial area, and hence the heavy phase is dispersed) and the direction of mass transfer
mass transfer rate, is increased [3]. (from continuous to dispersed phase and vice versa). So,
To shed more light on the extraction behaviour in pulsed scale-up and simulation of agitated and pulsed extraction
(packed & sieve plate) columns, the hydrodynamics and mass columns based on population balance modelling can now be
transfer characteristics must be well understood. Our present carried out successfully [1, 5].
knowledge of the design and performance of extraction
columns is still far from satisfactory. The reason is mainly due II. MATHEMATICAL MODELLING
to the complex interactions of the hydrodynamics and mass The modelling of extraction columns still demands
transfer [4]. It is obvious that the changes in the characteristics improvement. Simulating liquid-liquid extraction columns is a
(holdup, Sauter diameter, etc.) of the drop population along
challenging task due to the discrete character of the dispersed A. multivariate non-equilibrium population balance model
phase. This results from random breakage and coalescence of The general spatially distributed population balance
droplets, which are highly coupled to the mass transport of (SDPBE) for describing the coupled hydrodynamics and mass
solutes between the two existing phases. Modelling of such transfer in liquid extraction columns in a one spatial domain
extremely important and complex transport phenomena is can be written as:
resolved by using a multivariate population balance equation.
∂fd ,c (ψ ) ∂[uy fd ,c (ψ )] i d ,cy (ψ )]
2 ∂[ζɺ f
The population of droplets is modelled by a multivariate y
+ y
+∑ =
number concentration function, which takes into account ∂t ∂z i =1 ∂ζi
droplet size and solute concentrations. Understanding of ∂fd ,c (ψ ) Q in f in
∂ + y y (d, c ; t )δ(z − z ) + ϒ ψ
dynamic behaviour of liquid-liquid extraction columns can be Dy
y
y y { }
notably used in the design of process control strategy or the ∂z ∂z Ac vin
.. (1)
start-up and shutdown procedures [6-9]. The attempts to
model this dynamic behaviour are not well established In this equation the components of the vector ψ= [d cy z t]
because of the discrete nature of the dispersed phase. This is are those for the droplet internal coordinates (diameter and
due to the complex nature of the macroscopic dispersed phase solute concentration), the external coordinate (column height),
interactions as well as the microscopic interphase mass z, and the time, t, where the velocity along the concentration
transfer occurring in the continuously turbulent flow field. coordinate (cy) is cɺy . The source term Υ.߲ζ represents the net
These macroscopic interactions such as droplet breakage and number of droplets produced by breakage and coalescence per
coalescence coupled to the interphase mass transfer result in a unit volume and unit time in the coordinates range [ζ, ζ+߲ζ].
distributed population of droplets. This population is The left hand side is the continuity operator in both the
distributed not only in the spatial domain of the contacting external and internal coordinates, while the first part on the
equipment, but also randomly distributed with respect to the
right hand side is the droplets axial dispersion characterized
droplet state (properties) such as size, concentration and age.
by the dispersion coefficient, Dy, which might be dependent
Several attempts have been done to propose the proper on the energy dissipation and the droplet rising velocity [24].
mathematical model for liquid-liquid extraction columns [10]. The second term on the right hand side is the rate at which the
An empirical model for predicting the hydrodynamics in a droplets entering the LLEC with volumetric flow rate, Qy,in,
pulsed sieve plate column was proposed by Kumar and
that is perpendicular to the column cross-sectional area, Ac, at
Hartland [11]. A stagewise model for the transient behaviour
of a sieve-plate extraction column taking into account the a location zy with an inlet number density, fyin , and is treated
back flow and assuming constant hold-up, was developed by as a point source in space. The dispersed phase velocity, uy,
Blass and Zimmerman [10]. Reference [6] evaluated a relative to the walls of the column is determined in terms of
differential model in a Kühni column. Hufnagl et al. [12] the relative (slip) velocity with respect to the continuous phase
modelled a packed column using differential contact model and the continuous phase velocity, ux, with respect to the walls
without axial mixing. Flow models such as the dispersion or of the column [22, 23].
backmixing model; describe the non-ideal flow, where one The solute concentration in the continuous phase, cx, is
parameter accounts for all deviations from the ideal plug flow predicted using a component solute balance on the continuous
behaviour [13]. These models are too simple to describe the phase [22, 23]:
real hydrodynamics, where one of the liquid phases is
∂(φx cx ) ∂ ∂(φx cx )
normally dispersed as droplets in the second continuous phase − ux φx cx + Dx =
[14]. Therefore, the influences of droplet movement, droplet ∂t ∂z ∂z
interaction (breakage and coalescence), energy input (2)
Qxincxin ∞ cy ,max
(agitation, pulsation) and mass transfer cannot be described δ(z − z y ) − ∫ ∫0 cɺy v(d )fd ,c (ψ)∂d ∂cy
satisfactorily. Weinstein et al. [7] evaluated the differential Ac 0 y
model for a Kühni column. An improved dynamic combined
Note that the volume fraction of the continuous phase, Φx,
model considering the influence of drop size distribution was
satisfies the physical constraint: Φx + Φy =1, where y denotes
developed by Xiaojin et al. [9]. Several population balance
the droplet phase. The left hand side of Eq.(2) as well as the
models have been proposed by various authors. Garg and Pratt
first term on the right hand side have the same interpretations
[15] developed a population balance model for a pulsed sieve-
as those given in Eq.(1); however, with respect the continuous
plate extraction taking into account experimentally determined
phase. The last term appearing in Eq.(2) is the total rate of
values for drop breakage and coalescence. Casamatta and
solute transferred from the continuous to the dispersed phase,
Vogelpohl [16] proposed a population balance model for
where the liquid droplets are treated as point sources. Note
which a good review is found in [17]. Al Khani et al. [18]
that Eq.(1) is coupled to the solute balance in the continuous
have applied this model for dynamic and steady-state
phase given by Eq.(2) through the convective and the source
simulations of a pulsed sieve-plate extraction column.
terms.
Recently much works have been done in the population
balance modelling for extraction columns [1, 17, 19-23].
B. Model parameters E. The terminal droplet velocity
The SDPBE is general for any type of extraction column. The terminal droplet velocity used in the simulation is
However, what makes the equation specific is the internal given by [27]:
geometry of the column as reflected by the required vos,de vsph
correlations for hydrodynamics and mass transfer. vt = (8)
a a16 1/a16
Experimental correlations are used for the estimation of the (vos15,de + vsph )
turbulent energy dissipation and the slip velocities of the In this velocity model, ai the adjustable parameters can be
moving droplets along with interaction frequencies of fitted to the experimental data. vsph is the spherical droplet
breakage and coalescence [1, 22, 23]. velocity, vos,de is a smooth transition from oscillating to
C. Breakage probability and daughter droplet distribution deformed droplets [27].
For the description of the drop motion in the structured
For pulsed packed extraction column the daughter droplet packing, the correlation for the slowing factor developed by
distribution is assumed to follow the beta distribution β, which Garthe [26] is applied:
is given by Bahmanyar and Slater [25]. In Eq.(3) below ν is
kv = 0.077 πH0.138 πa−0.566 πd−0.769 πσ0.184 ( 1 + πaf )
0.08
the average number of daughter drops per breakage event. (9)
Pk Pk
ν = 2 + 0.34 ( (d´/dstab ) − 1 )
1.96
(3) where πHpk, πapk, πd, πσ, πaf are dimensionless numbers [26].
( )
ν −2 F. Mass –transfer
βn (d | d ') = 3 ν ( ν − 1 ) 1 − ( d / d´) (d 5 / d´6 )
3
(4)
The mass transfer fluxes in the LLECMOD program are
Here, dstab is the stable droplet diameter, where droplets calculated based on the two-film theory, where the individual
having diameter less than dstab are not expected to break. The mass transfer coefficients are defined separately for the
data for the stable drop diameters for pulsed packed and sieve continuous (kx) and the dispersed (ky) phases. The mass
trays columns under different operating conditions for the two transfer model used here in this simulation is taken from the
standard EFCE test systems (water-acetone-toluene and water- work of Henschke [27].
acetone-butyl acetate) are given in [26]. The droplet breakage G. Numerical solution
frequency and the daughter droplet distribution are correlated
based on single droplet experiments. The droplet breakage The mathematical model, which consists of integro-partial
frequency used in the simulation is given by [26]: differential and algebraic equations is solved using an
optimized and efficient numerical algorithms developed in
( d − dstab ) / ( d100 − dstab ) C 3
PB ( d )
C
= C 1πaf2 (5)
[20-22]. These are utilized successfully for the simulation of
coupled hydrodynamics and mass transfer for general liquid-
C 4 + (d − dstab ) / ( d100 − dstab ) 3
C
liquid extraction columns.
Where πaf is a dimensionless number taking into account
the influence of the pulsation intensity on the breakage III. LLECMOD PROGRAM
probability and is given by [26]: The complete mathematical model described above is
πaf = a .f . ( ρc2 / µc .∆ρ.g )
1/ 3 programmed using Visual Digital FORTRAN. To facilitate
(6)
the data input and output, a graphical user interface is
This breakage frequency describes the breakage in a packed designed. The graphical interface of the LLECMOD program
and sieve tray compartment with only one set of constant contains the main input window and sub-windows for
parameters for a liquid/liquid-system. The constants Ci parameters and correlations input. The basic feature of this
appearing in Eq.(5) for pulsed (packed & sieve plate) columns program [1] is to provide an easy tool for the simulation of
are listed in [26]. To predict the breakage probability in pulsed coupled hydrodynamics and mass transfer in liquid-liquid
columns with Eq.(5), the characteristic drop diameters d100 & extraction columns based on the population balance approach
dstab have to be experimentally determined for each pulsation for both transient and steady states conditions through an
intensity. Data of the characteristic drop diameter for pulsed interactive windows input dialog. Note that LLECMOD is not
columns investigated here are listed in [26]. restricted to a certain type of liquid-liquid extraction column
since it is built in the most general form that allows the user to
D. Droplet coalescence probability input the various droplet interaction functions. These
In this work droplet coalescence probability for a pulsed functions include droplet terminal velocity (taking into
extraction column is given by [27]: account the swarm effect) and the slowing factor due to
( ∆ρg ) column geometry, the breakage frequency and daughter
1/6 1/2
ε H cd ∆t σ1/3
PC ( d ) = (7) droplet distribution, the coalescence frequency and the axial
ξ8 µc d 1/3 dispersion coefficients. Using LLECMOD simulations can
The parameter ξ8 was fitted to experimental data for two now be carried out successfully for different types of
standard EFCE test systems, for t-a-w ξ8 is 2500, and for b-a- extraction columns including agitated (RDC & Kühni) and
w ξ8 is 1500 [27], Hamaker constant Hcd values used in the pulsed (sieve plate & packed) columns. The design of
simulation are listed in table I & II. LLECMOD is flexible in such a way that allows the user to
define droplet terminal velocity, energy dissipation, axial between the simulation and experiment is excellent for both
dispersion, breakage and coalescence frequencies and the test systems.
other internal geometrical details of the column. The
correlation parameters that are obtained based on single
2
droplet and droplet swarm experiments, are considered in a
modularized structure for the simulation program.
1.5
A. Coalescence parameter optimization package
d32 (mm)
As a new feature of LLECMOD, the program is reinforced
1
by a parameter estimation package for the droplet coalescence
models, which enables the user to fit the column
hydrodynamics (droplet size distribution, holdup and mean 0.5 Exp. d32
droplet diameter) to the available experimental data. Sim. d32
Prediction of the mass transfer profiles is then performed 0
based on correlations obtained only from single droplet 0 1 2 3 4 5
Column Height (m)
experiments. Simulation results are compared with data from
pilot plant columns, such as agitated and pulsed/ un-pulsed 2.5
columns. Different case studies showing columns’
performance are presented using only optimized coalescence 2
parameters. Additional results will be published in separate
publications.
1.5
d32 (mm)
IV. RESULTS AND DISCUSSION
In this section a sample problem is considered to illustrate 1
the basic features of the LLECMOD and the coalescence
parameters estimation package. For this purpose, a pilot plant 0.5 Exp. d32
laboratory scale pulsed (packed & sieve plate) columns are Sim. d32
considered whose dimensions are: column height H =4.4 m, 0
inlet of the dispersed phase zy = 0.85 m, inlet of the 0 1 2 3 4 5
Column Height (m)
continuous phase zx = 3.8 m, column diameter d = 0.08 m. The
two EFCE test systems toluene-acetone-water (t-a-w) and Fig. 1 Simulated mean droplet diameter along the column height compared to
butyl acetate-acetone-water (b-a-w) are used whose physical the experimental data [26]. Upper panel the test system is (b–a-w) and the
lower panel is (t-a-w) in packed column.
properties are available online (http//dechema.de/extraktion).
To completely specify the model, the inlet feed is fitted to a Fig.(2) depicts the variation of the mean droplet diameter
normal distribution with mean equals to 3.2 mm and standard along the height of the pulsed sieve plate column and
deviation of 0.5 mm. The direction of mass transfer is from the compared to the experimental data for both chemical systems.
continuous to the dispersed phase. All the operating A fairly good agreement between the experimental and
conditions for the packed column are listed Table (I), and for simulated profiles is achieved for both systems.
sieve plate column in Table (II).
2.5
TABLE I
OPERATING CONDITIONS: PACKED COLUMN
2
Test Qc Qd Cy,in Cx,in af Hcd
System lit/h lit/h % % cm/sec Nm
1.5
d32 (mm)
t-a-w 61.3 74.5 0.6 5.89 2 10e-10
b-a-w 62.0 72.0 0.0 5.21 2 10e-10
1
TABLE III
OPERATING CONDITIONS: SIEVE PLATE COLUMN
0.5
Exp.
Test Qc Qd Cy,in Cx,in af Hcd Sim.
system lit/h lit/h % % cm/sec Nm 0
b-a-w 62.0 72.0 0.0 5.46 1 10e-10 0 1 2 3 4 5
Column Height (m)
t-a-w 61.3 74.5 0.15 5.52 1 10e-12
Fig.(1) shows the variation of the mean droplet diameter
along the height pulsed packed column and compared to the
experimental data for both chemical systems. The agreement
2.5 16
14
2
12
10
1.5
d32 (mm)
φ (%)
8
1 6
4
0.5 Exp.
Exp. 2
Sim.
Sim.
0 0
0 1 2 3 4 5 0 1 2 3 4 5
Column Height (m) Column Height (m)
Fig. 2 Simulated mean droplet diameter along the column height compared to 14
the experimental data [26]. Upper panel the test system is (b–a-w) and the
lower panel is (t-a-w) in sieve plate column. 12
A comparison between the simulated holdup profiles along 10
the height of the pulsed packed column and the experimental
data [26] is shown in Fig.(3). Again, an excellent agreement is 8
φ (%)
achieved for both test systems. 6
25
4
20 2 Exp.
Sim.
0
15 0 1 2 3 4 5
φ (%)
Column Height (m)
10 Fig. 4 Simulated holdup profiles along the column height compared to the
experimental data [26]. Upper panel the test system is (b–a-w) and the lower
panel is (t-a-w) in sieve plate column.
5 Exp. φ
Sim. φ
Fig.(5) shows the simulated and experimental solute
concentration profiles as function of column height in both
0
0 1 2 3 4 5 phases. The agreement between the simulation and experiment
Column Height (m)
is very good for both test systems.
16 As a conclusion, the very good agreement between the
simulated profiles and the experimental data appearing in
14
Figs.(1-5) for different columns and chemical systems shows
12 that LLECMOD capability of predicting the actual steady
10
state performance of pulsed (packed and sieve plate)
extraction columns.
φ (%)
8
6 6
4 5
2 Exp. φ
Concentration (%)
Sim. φ 4
0
0 1 2 3 4 5
Column Height (m) 3
Fig. 3 Simulated holdup profiles along the column height compared to the 2
experimental data [26]. Upper panel the test system is (t-a-w) and the lower Exp. Cx
panel is (t-a-w) in packed column. Exp. Cy
1 Sim. Cx
Fig.(4) depicts the variation of the holdup profiles along the Sim. Cy
height of pulsed sieve plate column compared to the 0
0 1 2 3 4 5
experimental data for both chemical systems. A fairly good Column Height (m)
agreement between the experimental and simulated profiles is
achieved for both systems.
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ACKNOWLEDGMENT conservative discretization approach, Chem. Eng. Sci., 59, 2547-2565.
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Forschungsgemeinschaft) financial support. Interacting Hydrodynamics and Mass Transfer in Liquid-Liquid
Extraction Columns, Chem. Eng. Sci., 61, 113-123.
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