Solid-Liquid Extraction
Engr. Elisa G. Eleazar
CHE135-1P: SEPARATION PROCESSES
1
Outline
Mechanism
1.
2.
3.
Representation of
Equilibrium Data
Equilibrium Stage
Model for Leaching
Learning Objectives
Explain the mechanism of Solid-Liquid Extraction
Perform equilibrium and material balance calculations for Liquid-Liquid
Extraction
Perform solid-liquid extraction calculations
CHE135-1P: SEPARATION PROCESSES
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Mechanism
Solid-Liquid Extraction (Leaching)
involves the removal of a soluble fraction (solute or leachant) of a
solid material by a liquid solvent
Overflow
solvent + most
of the solute
Underflow
solids wet with
almost pure solvent
CHE135-1P: SEPARATION PROCESSES
Wash Stages
used to reduce the
concentration of solute in the
liquid portion of the underflow
The solute diffuses
from inside the solid
into the surrounding
solvent.
Applications:
• Removal of copper
from ore using
sulfuric acid
• Extraction of sugar
beets using hot
water
• Recovery of proteins
and other natural
products from
bacterial cells
3
Representation of Equilibrium Data
Ponchon-Savarit Diagram
Right Triangle Diagram
6
1
0,9
kg inert/kg soln
5
0,8
0,7
4
0,6
Xsolvent
3
0,5
0,4
2
0,3
0,2
1
0,1
0
0
0,1
0,2
0,3
0,4
0,5
kg solute / kg soln
CHE135-1P: SEPARATION PROCESSES
0,6
0,7
0,8
0
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1
Xsolute
4
Representation of Equilibrium Data
The experimental data on the retention of oil by livers are given below. Construct (a) right triangular
diagram; (b) Ponchon-Savarit diagram for the system.
kg liver oil in 1 kg solution
kg solution in 1 kg oil-free liver
CHE135-1P: SEPARATION PROCESSES
0
0.10
0.20
0.30
0.40
0.50
0.60
0.65
0.70
0.72
0.205
0.242
0.286
0.339
0.405
0.489
0.600
0.672
0.765
0.81
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Equilibrium Stage Model for Leaching
Assumptions:
• The solid feed consists of a solute that is completely
soluble in the solvent and an inert substance that is not.
• Leaching is rapid such that it is completed in a single
leaching stage.
• All overflow streams are assumed to be free of solids.
CHE135-1P: SEPARATION PROCESSES
S
Mass flow rate of inert solids
V
Mass flow rate of entering
solvent or overflow liquid
L
Mass flow rate of underflow
liquid
y
Mass fraction of solute in the
overflow
x
Mass fraction of solute in the
underflow
If conditions of equilibrium are met, the
concentration of the solution leaving a stage is
the same as the concentration of the solution
adhering to the inerts. The equilibrium
relationship is, therefore, xe = ye.
6
Equilibrium Stage Model for Leaching
An ideal leaching or washing stage is one where:
Any entering solid solute is completely dissolved into the liquid in the
stage (assuming that the liquid contains sufficient solvent).
The composition of the liquid in the stage is uniform throughout,
including any liquid within pores of the inert solid.
Solute is not adsorbed on the surfaces of the inert solid.
The inert solids leaving in the underflow from each stage are wet with
liquid, such that the mass ratio of solvent in that liquid (or the total
liquid) to inert solids is constant from stage to stage.
Because the composition of the liquid in the stage is uniform
throughout, the concentration of solute in the overflow is equal to
that in the liquid portion of the underflow (equilibrium assumption).
Overflows contain no solids.
Solvent is not vaporized, adsorbed or crystallized in a stage.
CHE135-1P: SEPARATION PROCESSES
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Equilibrium Stage Model for Leaching
A finely divided solids feed, F, of 150 kg/h, containing 1/3 water-soluble Na2CO3 and 2/3 insoluble ash
is to be leached and washed at 30C in a two-stage, countercurrent system with 400 kg/h of water.
The leaching stage consists of an agitated vessel that discharges the slurry into a thickener. The
washing stage consists of a second thickener. Experiments show that the sludge underflow from each
thickener will contain 2 kg of liquid (water and carbonate) per kg of insoluble ash. Assume ideal
stages.
a. Calculate the percent recovery of carbonate in the final extract.
b. If a third stage is added, calculate the amount of additional carbonate that will be
recovered.
CHE135-1P: SEPARATION PROCESSES
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Equilibrium Stage Model for Leaching
In the previous example (part b), leaching was assumed to be completed in one stage, with two
additional stages provided for washing. The recovery of the solute in the extract was 89.8%.
Recalculate this example, assuming that ½ of the carbonate is leached in the first stage and the
remaining ½ on the second stage, leaving only the last stage as a true washing stage.
CHE135-1P: SEPARATION PROCESSES
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Equilibrium Stage Model for Leaching
Graphical Solution Using Ponchon-Savarit Diagram
XC,yc mass fraction solvent
yN+1
Difference Point:
yA3
𝐼𝑛𝑡𝑒𝑟𝑠𝑒𝑐𝑡𝑖𝑜𝑛: 𝐿0 𝑉𝐿 𝑎𝑛𝑑 𝐿𝑁 𝑉𝑁+1
yA2
yA1
𝑅1

xN
xA3
xA2
xA1
From VL, draw a vertical line to the underflow locus:
xA0
Connect R1 and 
𝐼𝑛𝑡𝑒𝑟𝑠𝑒𝑐𝑡𝑖𝑜𝑛 𝑤𝑖𝑡ℎ 𝑙𝑜𝑐𝑢𝑠: 𝑉2
XA,yA mass fraction solute

CHE135-1P: SEPARATION PROCESSES
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Equilibrium Stage Model for Leaching
Graphical Solution Using Ponchon-Savarit Diagram
Oil is to be extracted from halibut livers by means of ether. The solution retention data are given
below:
kg liver oil in 1 kg solution
kg solution in 1 kg oil-free liver
0
0.10
0.20
0.30
0.40
0.50
0.60
0.65
0.70
0.72
0.205
0.242
0.286
0.339
0.405
0.489
0.600
0.672
0.765
0.81
Halibut livers contain 0.257 mass fraction oil. If 95% of the oil is to be extracted and the strong
solution from the system is to contain 0.7 mass fraction oil, determine:
a. quantity and composition of discharged solids
b. kg of ether (oil-free) required to treat 1,000 kg of feed
c. number of ideal stages required
d. number of actual stages required if the stage efficiency is 70%
CHE135-1P: SEPARATION PROCESSES
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Equilibrium Stage Model for Leaching
McCabe-Smith Graphical Solution
CHE135-1P: SEPARATION PROCESSES
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Equilibrium Stage Model for Leaching
McCabe-Smith Graphical Solution
Two tons (4,000 lb) per day of waxed paper containing 25 wt% soluble wax and 75 wt% insoluble pulp
are to be dewaxed by leaching with kerosene in a continuous, countercurrent contacting system. The
wax will be completely dissolved by the kerosene in the leaching stage L. Subsequent washing stages
will be used to reduce the wax content in the liquid adhering to the pulp leaving the last stage N, to
0.2 lb wax/100 lb pulp. The kerosene entering the system is recycled from a solvent-recovery system
and contains 0.05 lb wax per 100 lb kerosene. The final extract is to contain 5 lb wax per 100 lb
kerosene. Experiments show that the underflow from each stage will contain 2 lb kerosene per lb
insoluble pulp. Determine the number of washing stages required.
CHE135-1P: SEPARATION PROCESSES
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Equilibrium Stage Model for Leaching
McCabe-Smith Algebraic Solution
When the solution retained by the inerts is constant:
𝑥𝑁 − 𝑦𝑁+1
log
𝑦𝐿 − 𝑦1
𝑁=
𝑦1 − 𝑦𝑁+1
log
𝑦𝐿 − 𝑥𝑁
use mass fractions and total liquid flow rates
CHE135-1P: SEPARATION PROCESSES
When the solvent retained by the inerts is constant:
𝑋𝑁 − 𝑌𝑁+1
log
𝑌𝐿 − 𝑌1
𝑁=
𝑌1 − 𝑌𝑁+1
log
𝑌𝐿 − 𝑋𝑁
use mass ratios and solute-free solvent flow rates
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Equilibrium Stage Model for Leaching
McCabe-Smith Algebraic Solution
Determine the number of ideal, continuous, countercurrent washing stages for the previous example
using McCabe-Smith Algebraic solution.
CHE135-1P: SEPARATION PROCESSES
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Equilibrium Stage Model for Leaching
McCabe-Smith Algebraic Solution
A countercurrent extraction system is to treat 100 kg/min of sliced sugar beets with fresh water as
solvent. Analysis of the beets is as follows:
water
48%
sugar
12%
pulp
40%
If 97% sugar is to be recovered and the extract phase leaving the system is to contain 15% sugar,
determine the number of cells required:
a. if each kg of dry pulp retains 3 kg of solution
b. if each kg of dry pulp retains 3 kg of water
CHE135-1P: SEPARATION PROCESSES
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Outline
Mechanism
1.
2.
3.
Representation of
Equilibrium Data
Equilibrium Stage
Model for Leaching
Learning Objectives
Explain the mechanism of Solid-Liquid Extraction
Perform equilibrium and material balance calculations for Liquid-Liquid
Extraction
Perform solid-liquid extraction calculations
CHE135-1P: SEPARATION PROCESSES
17
Solid-Liquid Extraction
Engr. Elisa G. Eleazar
CHE135-1P: SEPARATION PROCESSES
18