The document discusses the design of a Karr reciprocating-plate extractor (T-102) for a liquid-liquid extraction process in a biodiesel production plant. Key details include: - Methanol will be used as the key component for the extractor design due to its solubility in both the feed and solvent streams. - Design calculations are provided for the methanol recovery, distribution coefficient, continuous phase flux, and mass fraction of methanol in the raffinate stream. - The operating feed to minimum solvent flow rate ratio is calculated as 2.2 based on the methanol distribution coefficient and mass fractions. This ratio is used to determine the minimum solvent flow rate of 2775.08 kg/h for

1. i
CONTENTS
LIST OF TABLES..................................................................................................ii
LIST OF FIGURES...............................................................................................iii
LIST OF ABBREVIATION ....................................................................................iv
CHAPTER 3 LIQUID LIQUID EXTRACTION COLUMN.....................................3-6
3.1 Liquid Liquid Extraction Column, T-102 ...................................................3-6
3.2 Extraction Unit Selection..........................................................................3-6
3.3 Chemical Design of Karr Reciprocating-Plate Extractor, T-102................3-8
3.3.1 Karr Reciprocating-Plate Extractor Designing Method ....................3-8
3.3.2 Summary of Flow Rate and Composition each Stream ...................3-9
3.3.3 Selection of Key Component......................................................... 3-10
3.3.4 Sizing of a Karr Reciprocating-Plate Extractor .............................. 3-10

2. ii
LIST OF TABLES
Table 3.1: Feed Stream Flow Rate and Composition........................................3-9
Table 3.2: Extract Stream Flow Rate and Composition.....................................3-9
Table 3.3: Raffinate Stream Flow Rate and Composition................................ 3-10
Table 3.4: Solvent Stream Flow Rate and Composition .................................. 3-10
Table 3.5: Minimum HETS and Volumetric Efficiency for the Karr, Reciprocating-
Plate Extractor............................................................................................................ 3-16

3. iii
LIST OF FIGURES
Figure 3.1: Decision guide for extractor selection .............................................3-7
Figure 3.2: The Karr Reciprocating-Plate Extractor...........................................3-8

4. iv
LIST OF ABBREVIATION
WCO Waste cooking oil
FAME Fatty acid methyl ester
TG Triglycerol
FFA Free fatty acid
MeOH Methanol

5. v

6. 3-6
CHAPTER 3
LIQUID LIQUID EXTRACTION COLUMN
3.1 Liquid Liquid Extraction Column, T-102
Liquid liquid extraction is one of the common method used in industries. Basically,
liquid liquid extraction is the separation of the components of a liquid mixture by treatment
which one or more of the desired components is preferentially soluble. In this process, it
is essential that the liquid-mixture feed and solvent are at least partially if not completely
immiscible. Fundamentally, three stages are involved. First is to bring the feed mixture and
the solvent into intimate contact resulting the separation of the two phases. Then the
solvent from each phase will be removed and recovered (R.K Sinnot).
Liquid-liquid extraction is an important unit operation and finds applications in
industries such as refinery, pharmaceutical industries, metallurgical industries and other
industries. In biofuel industry, the purity level of biodiesel has strong effect on fuel
properties, engine performance and engine life. Therefore, a purification step is necessary.
In biodiesel production plant, water washing method is used in order to purify biodiesel.
The main purpose of water washing is to separate FAME from the glycerol, methanol and
catalyst. This process also can remove other contaminant in the system that might interfere
with the next step of producing high purity level of biodiesel [1].
3.2 Extraction Unit Selection
The selection of extractor type depends upon many factors including the required
number of theoretical stages or transfer units, required production rate, tolerance to
fouling, ease of cleaning, availability of the required materials of construction, as well as
the ability to handle high or low interfacial tension, high or low density difference, and high
or low viscosities. Figure 3.1 below shows simplified guidance flowchart for selection of
extractor.

7. 3-7
Figure 3.1: Decision guide for extractor selection
Hence, from the guidance flowchart above, reciprocating plate column type of
extractor has been chosen for the water washing process. Since the water washing in
biodiesel production is a process that will cause the formation of emulsion, Karr
Reciprocating Plate Extractor which is a descendent of reciprocating plate column will be
used. This is because Karr Reciprocating Plate Extractor is an extractor that is well suited
with mixtures with emulsifying tendency [2]. Emulsion formation is caused by the reaction
of unreacted waste cooking oil and soap with water. Figure 3.2 below shows the Karr
Reciprocating Plate Column with its main components.

8. 3-8
Figure 3.2: The Karr Reciprocating-Plate Extractor
3.3 Chemical Design of Karr Reciprocating-Plate Extractor, T-102
3.3.1 Karr Reciprocating-Plate Extractor Designing Method
1) Determination of mass fraction of key component
2) Calculate the maximum slope of operating line of the system.
3) Determination of the feed mass flow rate to the solvent mass flow rate, sf mm ,
and the operating solvent flow rate, sm .
4) Calculate the mass fraction of key component in the entering light phase, ky1 , in
the light phase.
5) Determine the extraction factor, EA .
6) Calculate the number of equilibrium stages, eN by using the Kremser-Souders-
Brown theoretical stage equation.
7) Calculate the cross sectional area, A , by dividing by the total volumetric flow rate
(the sum of the volumetric flow rates for both phases) by the total volumetric flow

9. 3-9
rate per unit of extractor cross-sectional area, obtained from the Minimum NETS
and Volumetric Efficiency for the Karr, Reciprocating-Plate Extractor table.
8) Hence, the diameter, D , can be calculated.
9) Find height equivalent tower stages (HETS), at 1D by obtaining required data from
the Effect of Interfacial Tension on HETS for RDC and RPC Extractors table.
10) Calculate the extractor height, Z .
3.3.2 Summary of Flow Rate and Composition each Stream
The data of mass flow rate is obtained from Aspen simulation, hence the molar flow
rate, mole fraction and mass fraction of each stream is calculated and tabulated in tables
below.
Table 3.1: Feed Stream Flow Rate and Composition
Component Flow rate
( hkg / )
Molar flow rate
( hkmol / )
Mole fraction Mass Fraction
Methanol 529.968 16.54081 0.60 0.15
FAME 2292.05 7.730494 0.28 0.66
Glycerol 237.31 2.576831 0.09 0.069
Sulphuric Acid 29.006 0.295746 0.01 0.008
Triacylglycerol 374.69 0.423169 0.015 0.11
Table 3.2: Extract Stream Flow Rate and Composition
Component Flow rate
( hkg / )
Molar flow rate
( hkmol / )
Mole fraction Mass Fraction
Methanol 529.968 16.54081 0.16 0.56
FAME - - - -
Glycerol 237.31 2.576831 0.01 0.25
Sulphuric Acid 29.006 0.295746 0.002 0.03
Water 153.3645 153.3645 0.89 0.16

10. 3-10
Table 3.3: Raffinate Stream Flow Rate and Composition
Component Flow rate
( hkg / )
Molar flow rate
( hkmol / )
Mole fraction Mass Fraction
Methanol - - - -
FAME 2292.05 7.730493 0.88 0.856
Glycerol - - - -
Triacylglycerol 374.687 0.42317 0.05 0.14
Water 12.178 0.675997 0.07 0.004
Solvent Stream
Table 3.4: Solvent Stream Flow Rate and Composition
Component Flow rate
( hkg / )
Molar flow rate
( hkmol / )
Mole fraction Mass Fraction
Water 2775.08 154.0404 1 1
3.3.3 Selection of Key Component
In biodiesel water washing liquid liquid extraction system, to design the Karr
Reciprocating Plate Extractor, methanol will be selected as the key component. This is
due to its solubility of methanol in both feed and solvent stream. Methanol (solute) also
has higher affinity towards the solvent which is water. Hence, making it easier to separate
methanol from FAME. Even though, glycerol is also soluble and miscible with both water
and FAME, glycerol is not selected as the key component as the amount is too small
compared to methanol.
3.3.4 Sizing of a Karr Reciprocating-Plate Extractor
To size the reactor, method or procedure above will be followed. Because FAME
is lighter than the solvent, water, it is introduced at the bottom and water at the top of the
extractor. Data such as flow rate and mass fraction of each stream are obtained from the
mass fraction and mole fraction.

11. 3-11
Feed Composition Data:
Methanol : 529.968 kg/h (0.15 mass fraction)
FAME : 2292.05 kg/h (0.66 mass fraction)
Glycerol : 237.31 kg/h (0.069 mass fraction)
Sulphuric Acid : 20.006 kg/h (0.008 mass fraction)
Triacylglycerol : 374.69 kg/h (0.11mass fraction)
Total flow rate : 3454.024 kg/h
3.3.4.1 Methanol Recovery
 = 99%
Based on the data obtained by Aspen simulation, the methanol recovery,  , should
be 100%, but it is impossible to have 100% of methanol recovery, hence, 99% of methanol
recovery value will be used in the calculation.
3.3.4.2 Methanol Distribution Coefficient
K = 2.0
Distribution coefficient is a the ratio of concentrations of a compound in a mixture
of two immiscible phases at equilibrium. The value of methanol distribution is estimated by
Drew et. Al [3].
3.3.4.3 Continuous Phase Flux
C = 0.5 gal/min-ft2
Karr Reciprocating Plate Extractor is one type of pulsed-column extractor, where
for pulsed-column extractor, a continuous-phase flux coefficient value of 0.5 is used [4].
3.3.4.4 Mass Fraction of Key Component (Methanol) in the Raffinate
In order to determine the calculated value of methanol in the raffinate, the mass
balance equation will be used

12. 3-12
kk xx 12 )1( 
Where
kx2 = Mass fraction of methanol in raffinate
 = Methanol recovery
kx1 = Mass fraction of methanol in feed
15.0)99.01(2 kx
0015.02 kx
3.3.4.5 Operating Feed to Minimum Solvent Flow Rate Ratio
kk
kkk
SM
f
xx
yxK
m
m
21
21



Where
fm = Operating feed flow rate, hkg /
SMm = Minimum solvent flow rate, hkg /
K = Methanol distribution coefficient
ky2 = Mass fraction of methanol at solvent stream
0015.015.0
0)15.0(0.2



SM
f
m
m
02.2
SM
f
m
m
3.3.4.6 Minimum Solvent Flow Rate, kg/h
The minimum solvent flow rate can be calculated by using the operating feed flow
rate to minimum solvent flow rate ratio.
02.2
SM
f
m
m

13. 3-13
fm = total operating feed flow rate = 3454.024 kg/h
Hence,
02.2
f
SM
m
m 
02.2
/024.3454 hkg
mSM 
hkgmSM /913.1709
The minimum amount of water flow rate at the solvent stream is 1709.913 kg/h
3.3.4.7 Operating Solvent Flow Rate, kg/h
SM
f
S
f
m
m
C
m
m

)02.2(5.0
/024.3454

Sm
hkg
hkgmS /826.3419
3.3.4.8 Mass Fraction of Methanol at the Extract Stream, ky1
To obtain the mass fraction of methanol at extract, substitute 0015.02 kx , which
is the mass fraction of methanol in the raffinate stream, and 01.1/ Sf mm into the
equation below:
)( 2121 kk
s
f
kk xx
m
m
yy 
)0015.015.0(01.101 ky
15.01 ky

14. 3-14
3.3.4.9 Extraction Factor, AE
Extraction factor is a measure of the ability of the system to separate between two
or more components in a liquid mixture. Extraction factor can be calculated by using the
equation below:
k
S
f
E
K
m
m
A







Where
AE = Extraction factor
fm = Operating feed flow rate, hkg /
sm = Operating solvent flow rate, hkg /
K = Methanol distribution coefficient
2
01.1
EA
505.0EA
3.3.4.10 Number of Equilibrium Stages, NE
It is assumed that, in the system, the solutions are dilute so that the operating and
equilibrium curves are linear. Thus, the Kremser-Souders-Brown Equilibrium Stage
Equation, can be used to calculate the number of equilibrium stages [2].
















E
EE
kk
kk
E
A
AA
Kyx
Kyx
N
1
log
)1(
)/(
)/(
log
22
21
Where,
NE = Number of equilibrium stages
kx2 = Mass fraction of methanol in raffinate
kx1 = Mass fraction of methanol in feed
K = Methanol distribution coefficient

15. 3-15
AE = Extraction factor
















505.0
1
log
505.0)505.01(
00015.0
015.0
log
EN
73.5EN Equilibrium stages 6 equilibrium stages
3.3.4.11 Determination of Height Equivalent Tower Stage, HETS
HETS is co-related with the interfacial tension of components in a mixture. The
common method to determine HETS is by using the Effect of Interfacial Tension on HETS
for the RDC and RPC Extractors table. However, the interfacial tension data of the
components in this process does not appear to be available.
To solve this problem, Karr et. al, comes out with an alternative method to find
HETS where the HETS for an extractor can be estimated by using scaling rule developed
by them and the experimental values of HETS was summarized in the Minimum HETS
and Volumetric Efficiency for the Karr Reciprocating-Plate Extractor table [5]. Before that,
we must determine whether the extraction system is low interfacial tension system (MIBK,
acetic acid, water system) or high interfacial tension system (o-xylene, acetic acid, water
system).
According to Binks et. al, the extraction system of biodiesel purification (water washing)
process is a low interfacial tension system. This can be proved by the formation of
emulsion in the system [6]. Emulsification is one of the indication that the extraction system
is low interfacial tension system.

16. 3-16
Table 3.5: Minimum HETS and Volumetric Efficiency for the Karr, Reciprocating-Plate Extractor
From the table above, extractor with 12 inches (0.305 m) diameter which is
estimated to be close to the calculated diameter is selected. Then, the solvent or
extractant of the extraction system must be determine in order to choose the right
combination of extractant and dispersed phase. In water washing extraction system, the
solvent (water) is dispersed at the top of the extractor, (take note that in MIBK-Acetic acid-
Water system, when water is selected as solvent, water will be dispersed at the top of the
extractor because the density is higher than MIBK). Hence, this will narrow down the
choice of extractor into only 3 which is in the blue box. Then, between these three, choose
the extractor that give the maximum volumetric efficiency (red box).
After deciding the extractor from the table, minimum HETS and the total volumetric
throughput can be determined.
Minimum HETS = 11.05 stages

17. 3-17
Total Volumetric Throughput = 1694 gal/(h)(ft2
) or 69.023 m3
/(m2
)(h)
3.3.4.12 Cross-sectional Area of Extractor’s Column
In order to calculate the column cross-sectional area, volumetric flow rate of both
inlet streams is required.
Feed stream volumetric flow rate =
f
fm

fm = Operating feed flow rate, hkg /
f = Density of component at feed stream
Sm = Operating feed flow rate, hkg /
S = Density of component at feed stream
Feed stream volumetric flow rate:
33333
/875
/69.374
/1840
/006.29
/1260
/31.237
/9.873
/05.2292
/792
/968.529
mkg
hkg
mkg
hkg
mkg
hkg
mkg
hkg
mkg
hkg

kgm /92.3 3

Solvent stream volumetric flow rate:
3
/1000
/826.3419
mkg
hkg

hm /42.3 3

Then, substitute the value of volumetric flow rate obtained into the equation below
to obtain the cross-sectional area of the extractor’s column
T
SSff
J
mm
A
)]/()/[(  

A = Cross-sectional area of extractors column
TJ = Total volumetric flow rate per unit area
hmm
hm
A 23
3
/023.69
]/)42.392.3[( 


18. 3-18
2
106.0 mA 
3.3.4.13 Extraction Column’s Diameter
Substitute the value of cross-sectional area of the extractor’s column into the
equation below to obtain the diameter of the column.
4
2
D
A


2/12
)106.0(4








m
D
mD 367.0 or inches45.14
3.3.4.14 Karr Reciprocating-Plate Extractor Scale Up
In order to maximize the production of biodiesel and also to increase the level of
purity of biodiesel, Karr Reciprocating-Plate Extractor must be scaled up from pilot to
commercial scale. Equation below is used for this step:
38.0












D
D
HETS
HETS CC
Where,
CHETS = Height equivalent tower stages at commercial scale
HETS = Height equivalent tower stages at pilot scale
Because D obtained is less than 30 inches or 0.762m, standard pipe size which is
the Schedule 10S pipe will be used. Schedule 10S pipe has an inside diameter of 10.42
inches and the most common used pipe for extraction unit system. Hence, the scaling up
calculation can be proceeded.
38.0
12
42.10
05.11 





CHETS
inchesHETSC 473.10 , m266.0
20% increment is done to prevent flooding at the extractor’s column. Therefore, the design
of HETSc after 20% increment is 12.567 inches [5].

19. 3-19
3.3.4.15 Extractor Height
After obtaining the HETSC, the height of the extractor can be calculated by using
equation below
DHETSNZ CEE  )(
45.14)567.12(6 EZ
inchesZE 85.89 or m28.2
3.3.4.16 Top and Bottom Settler Diameter and Height
Finally is to add top and bottom sections which will act as settlers to separate the
phases. The diameter of both settlers is 50% greater than the extractor diameter and the
height of each settler is equal to the settler diameter [7].
Diameter of both settlers is:
)42.10(5.1 inchesDS 
inchesDS 63.15 or m397.0
Therefore, the total height for both settlers is:
inchesZS 26.31)42.10)(5.1(2  or m794.0
3.3.4.17 Total Height of Karr Reciprocating-Plate Extractor Tower
SE ZZZ 
inchesZ )26.3185.89( 
inchesZ 11.121 or m076.3

20. 3-20
REFERENCES
[1] Shuchen B Thakore and Bharat I Bhatt, Introduction to Process Engineering and
Design, Second. New Delhi: Mc Graw Hill, 2015.
[2] John W. green & Robert H. Perry, Perry’s Chemical Engineers Handbook. 2008.
[3] J. . Drew, “Design for Solvent Recovery,” Chem. Eng. J., vol. 2, 1975.
[4] J. . Valle-Riesta, “Project Evaluation in The Chemical Process Industries,” Proj.
Eval. Chem. Process Ind., 1983.
[5] T. C. Karr, A., Lo, “Scale-up of Large Diameter Reciprocating-Plate Extraction
Column,” Chem. Eng. Progr., no. 72, p. 11, 1976.
[6] B. P. Binks, P. D. I. Fletcher, and D. N. Petsev, “Tension System,” no. 9, pp. 1025–
1034, 2000.
[7] H. Silla, Design and Economics. 2003.