E. Simeonov,
J. Nedialcova
Journal of the University of Chemical
Technology
and Metallurgy, 41, 4, 2006, 445-448
PROCESS CONTROL AND ESTIMATION OF MULTISTAGE EXTRACTION
USING CHARACTERISTIC FUNCTION APPROACH
E. Simeonov, J. Nedialcova
University of Chemical Technology and Metallurgy
8 Kl. Ohridski, 1756 Sofia, Bulgaria
E-mail: [email protected]
Received 05 September 2006
Accepted 12 November 2006
ABSTRACT
Kinetic experiments have been carried out, under three-stage led process of extraction according to the scheme
crossed current, for the system tobacco leaves (Nicotiana tabacum L.) – water.
The solid phase is triple extracted and a fresh solvent is used for each stage. The experiments are obtained in a
batch extractor with a propeller.
The characteristic function for the experimental system is obtained from the kinetic curves. By using this function
the basic design size (length) of solid – liquid extractor is calculated. The new working speed (II and III stages) of solid
stage transition in the extractor is also obtained, which is done by screw’s rpm and constant design sizes calculated from
the kinetic curves for the Ist stage of the extraction. The obtained revolutions correspond to the necessary equilibrium
time of extraction, which is the time of reaching the reference extraction degree of the extracted component.
Keywords: solid–liquid extraction, kinetics, characteristic function, multistage extraction.
INTRODUCTION
The efficiency of extraction installations is usually estimated by technological criteria the degree of
extraction. According to the need of quality refining of
raw materials and reaching high extraction degree, the
solid phase refining is usually multistage and the number of stages is defined for each particular case.
It is well known that each experimental kinetic
curve holds in hidden way all the factors that have an
impact on the process of non-stationary diffusion extraction [1-4].
Kinetics by the characteristic function gives the
opportunity in the common case for polydisperse anisotropic solid phase, the characteristic in the structure of
solid particles and the value of the external diffusion
resistance to be integrally found [3,6].
The use of the characteristic function gives possibility not only to calculate but also to control the process [7] when the raw material is changed, the technological parameters of the multistage extraction.
EXPERIMENTAL
Kinetic experiments have been carried out, under three-stage led process of extraction according to
the scheme crossed current for the tobacco leaves –
water system.
The solid phase has been extracted three times
and fresh solvent has been used for each stage. The experimental data have been obtained in a batch vessel
extractor with a propeller under the following conditions: hydromodule î=0,02 m3/kg, temperature t=200C
and stirring revolutions n=7 s-1, for which have been
445
Journal of the University of Chemical Technology and Metallurgy, 41, 4, 2006
proved that the external diffusion resistance has been
eliminated.
The concentration trend of the extracted substances in the liquid phase versus time was recorded
during the experiments.
Weighting was used for measuring the concentrations with up to 10-3 g accuracy, after drying the
samples at 700C. The initial concentrations are defined
by experiments, too. The initial concentrations of the
solid phase is C0=607.97 kg/m3 and the saturation concentration is C*=801.04 kg/m3.
RESULTS AND DISCUSSION
Fig.1. Experimental kinetics curves in a stirred batch apparatus.
The experimentally obtained results for the investigated solid-liquid system are shown in Fig. 1 and
can be described with acceptable accuracy with equation (1). From the presented results can be seen that a
peak in the concentration curves for the second and
third stage of extraction is observed. The reason for
this is the more rapid obtaining of the equilibrium concentrations with the increasing the number of the extraction stages.
When designing the extraction apparatuses the
kinetic curve section, where the velocity is the biggest
i.e. to ensure certain stay of the material at a given extraction stage, is of any interest. The bigger velocity of
the process is due to the quickly increasing internal
porosity of the solid phase.
C1=A-Bexp(-Hô)
(1)
where A, B, H are numerically defined on the basis of
the experimental results.
The following equations are obtained from (1)
for each of the stages (I, II and III)
C1 = 22,20 − 22,10.å −2, 60.10
C1 = 2,47 − 1,29.å −9,81.10
−3
.τ
(2)
−3
.τ
(3)
−3
.τ
(4)
C1 = 8,47 − 7,56.å −9, 79.10
maximum of concentration for stage II and stage III –
shown as Fig. 1.
Equations (3) and (4) describe the experimental
results only up to the time necessary for reaching the
The standard function [8] for each stage is defined in equations (5), (6), and (7).
φ * (τ ) = 1,027 − 1,0244.å −2,5051.10
(5)
φ (τ ) = 1,1642 − 1,0522.å −9,654.10
*
(6)
φ (τ ) = 1,545 − 1,0461.å −9, 7698.10
*
.τ
−3
.τ
−3
.τ
(7)
The conditions that equations (5), (6), and (7)
are
derived
are:
C0 = 607,97, kg / m3 ,
C1 ð = 22,20êg / m3 and β = 0,0370 .
It is well known that the representations of the
experimental data using the standard function give the
ability to predict the kinetics when there is a change in
the phase ratio (î) and an internal diffusion regime.
The conditions and the sequence for defining the
characteristics function are discussed in detail in [5, 6].
Equation (2) gives kinetics information for the investigated material derived in batch vessel extractor with a
propeller and î=0,02 m3/kg.
Using the standard function (5) the data is recalculated for working hydromodule in continuous screw
extractor - î=2,604 m3/kg.
The predicted kinetic curves for all the three stages
are shown in Fig. 2.
γ
θ (γ ) = − ∫
1
446
−3
dγ
Ψ (γ )
(8)
E. Simeonov, J. Nedialcova
Fig. 2. Calculated kinetics curves in a continuous apparatus.
Fig. 4. Relationship between process kinetic and design.
Characteristics in a screw extractor for system I.
Fig. 3. Sequence for obtaining function è(ã).
where:
Ψ (γ ) = 1 m0 ∫ De ∂τ
∂n
F
dF
De, m2/s – coefficient of diffusion
θ (γ ) - Characteristic function
㠖 relative solid mass reduction
The sequence system shown in Fig. 3 is used to
obtain equation (8).
The following system of equations (9) is used to
calculate periodical and continuous processes:
dθ (τ )
= C ∗ − C1 (τ )
dτ
(9)
(1 − γ )ξ − 1 = C1 (τ ) − C m
It is also used to define the residence time of
substances in the extractor under the following conditions î=2,604 m3/kg, Cm=0,172 kg/m3, C1n=0.
θ
dθ
−1
0 C − C m − ξ [1 − γ (θ )]
τ =∫
∗
(10)
The equation is numerically solved by linear
point on Simpson’s method. The necessary extraction
time and the corresponding reference degree of leaching are also found. After the elimination of θ at co-
Fig. 5. Main design characteristics of the screw conveyer.
solving of θ (γ ) and τ (θ ) / time in the extractor/ is
derived the function γ (τ ) for counter-flow in continuous extractor Fig. 4.
The screw length (Fig. 4) of continuous screw
extractor is calculated on the following conditions: solid
phase productivity G=11,57.10-3kg/s, external porosity
of the solid phase in the space between screw grinds
åsc=0,91m3/m3, material density ñc=928 kg/m3.
At any time there is corresponding value of h:
h=w τ
(11)
Where w is the speed of the solid phase in the
extractor
w=
G
ρ c f sc (1 − ε sc )
(12)
as shown in Fig. 4 the necessary length of the
screw for the Ist stage of extraction is h=2,555 m.
447
Journal of the University of Chemical Technology and Metallurgy, 41, 4, 2006
Table 1. Main parameters in the screw extractor operation.
τ eq
d sc
w.10 3
s
N .10 2
z
h
s
m
m/ s
m
s −1
pcs.
m
I-st
900
0,249
2,839
0,112
2,535
23
2,555
II-nd
400
0,249
6,388
0,112
5,703
23
2,555
III-rd
300
0,249
8,517
0,112
7,604
23
2,555
Stage
It shows the abilities of the characteristic function for defining the new necessary speed of solid phase
for passing through the extractor (new screw revolu
h
tions N=
τ eq s ) and reaching the reference degree of
leaching.
In Table 1 are shown the derived values for more
important technological parameters for all three stages
of extraction. The calculations are made on main construction sizes base obtained from the Ist extraction stage.
Table 1. Main parameters in the screw extractor
operation.
CONCLUSIONS
Three-stage extraction kinetics is investigated in
the counter-flow scheme for tobacco leaves – water system.
Kinetics curves for each stage are obtained in a
batch stirred vessel extractor.
The standard and characteristic function for the
investigated system are calculated.
The ability of the characteristic function for process controlling is demonstrated for three stage extraction of the solid phase. When there are constant screw
dimensions, the necessary screw revolution is defined.
They guarantee that the real time of staying corresponds
to the reference degree of leaching.
Acknowledgement
The authors would like to thank the Science &
Research Programme of the University of Chemical
448
Technology and Metallurgy for the financial support
(Project 10266).
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