Solid-Liquid Extraction (Leaching)

SOLID-LIQUID EXTRACTION (LEACHING) • • • •

Overview Types of system Simple multiple extraction Countercurrent multistage operation  Kremser equation – constant underflow  Graphical solution – variable underflow  Ponchon-Savarit method I  Ponchon-Savarit method II

Overview Solid-liquid extraction or leaching generally refers to the removal of a component from a solid using a solvent liquid. The desired component, solute (A), is washed by the solvent (C) leaving the inert or insolu insoluble ble solid solid (B) undisso undissolve lved. d. Two phases phases result, result, the overflow overflow,, V, which which is a clear clear solution of the solute and solvent and the underflow, L, which which is the undissolved solid solid with some solution adhering to it. At equilibrium, the solution adhering in the underflow has the same composition as the overflow. Types of system Systems in leaching may be divided into two: constant underflow (Type I) and variable underf underflow low (Type (Type II). II). The The soluti solution on being being retain retained ed in the undisso undissolve lved d solid solid may vary at different concentrations. C

C

B

A

Type I

B

A

Type II

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Simple multiple extraction The number of theoretical equilibrium stages may be determined graphically by contacting the resultant underflow with fresh solvent in each stage. V

V

0

L L

1

0

V

V

0

L

1

2

V

1

0

2

3

V 2

L

3

3

The procedure is to determine the resultant mixture, Σ , in each stage after which the composition of the overflow and underflow is located using the underflow locus provided for each system. Equilibrium is achieved when no mass transfer exist between the underflow (inert (inert + soluti solution on adhering adhering to the inert) inert) and the overfl overflow ow (clear solutio solution). n). The The result resulting ing composition in the underflow is then mixed with another batch of fresh fr esh solvent. yN+1 yA3 yA2

t n e v l o s n o i t c a r f s s a m c y ,

yA1

Σ3

Σ2

xA3

xA2

C

X

Σ1

xA1 xA0

XA,yA mass fraction solute

Countercurrent multistage extraction V L

V

V

2

1

1

2

N+1

N L

0

L

N

1

∆

Kremser equation – constant underflow If the solvent or solution adhering to the undissolved solid is constant then the number of theoretical equilibrium stages may be determined by the Kremser equation. This equation was derived from the operating line equation. When the solution retained by the inerts is constant, both the underflow Ln and overflow V n are constant and the equation of the



log N − 1 = log

y AN

1 −

+

x AN

y A 2 − x A1 y AN 1 − y A 2 +

x AN

−

x A1

where where y = mass mass frac fraction tion in the the overflo overflow w x = mass fraction in the underflow The first or letter subscript denotes component and second or number subscript denotes equilibrium stage. Note Note that that this this equa equatio tion n cann cannot ot be used used for for the the entir entire e casc cascad ade e if L0 differs differs from from the succeeding underflows. Therefore the compositions of streams entering and leaving the first stage are separately calculated by material balance. Kremser equation is then applied to the remaining stages. In the material balance, the inert is excluded from the calculation. Also, remember that the overflow is the same concentration as the solution leaving with the underflow; i.e. y A1 x A1 . =

Graphical solution – variable underflow For variable underflows, the number of theoretical equilibrium stages may be determined graphi graphica cally lly using using the Ponch Ponchonon-Sav Savarit arit Method Method.. This This metho method d can also also be adapte adapted d for systems exhibiting constant underflow. Ponchon-Savarit method Just like in the liquid-liquid extraction, the method makes use of the delta, streams passing in opposite direction.

∆

, to relate the

Total mass balance: L0 + Vn+1 = Σ = V1 + Ln = L0 – V1 = Ln - Vn+1 ∆ Theoretical stages are calculated after locating delta. Starting at V1, the underflow L1 is located by drawing a line to the right angle. V 2 is then located using the delta. The procedure is continued until the last composition in the underflow is reached. yN+1

t n e v l o s n o i t c a r f s s a m c y , C

X

yA3

yA2 yA1

xN

Σ

xA3 xA2

xA1

xA0



A modification of the Ponchon-Savarit method can also be used. The modifications are (1) consider each stream a mixture of solid and solution and (2) use the ratio of solid to solution in place of enthalpy. The underflow, X, and overflow, Y, is redefined as X = mass of solute per mass of solution; A/(A + C) Y = mass of inert per mass of solution; B/(A + C) Stages are computed after the delta is located from the four end streams. The procedure in “stepping off’ is the same as the previous method but the tie lines are vertical in this case. XA2

XN

XA1

B + A s s a m / C s s a m Y

XA0

YA3 YA2

YN+1

YA1

X mass A/ mass A + B

∆

References Das, D.K. and R.K. Prabhudesai. 1999. Chemical Engineering License Review. 2 nd edition. Engineering Press. Austin, Texas. Crokett, William E. 1986. Chemical Engineering. A Review for the P.E. Exam. John Wiley & Sons, Inc. New York. Foust, Alan S., L.A. Wenzel, C.W. Clamp, L. Maus, and L.B. Andersen. 1980. Principles of Unit Operations. 2nd ed. John Wiley & Sons, New York. Perry, Robert H. and D.W. Green. 2001. Perry’s Chemical Engineers’ Handbook. 7th edition. McGraw-Hill. Singapore.

Solid-Liquid Extraction (Leaching)

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