Solid-liquid Extraction (leaching) 385e43

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 insoluble solid (B) undissolved. Two phases result, the overflow, V, which is a clear solution of the solute and solvent and the underflow, L, which is the undissolved 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 underflow (Type II). The solution being retained in the undissolved solid may vary at different concentrations. C

C

B

A Type I

B

A Type II

Simple multiple extraction The number of theoretical equilibrium stages may be determined graphically by ing the resultant underflow with fresh solvent in each stage. V0

L0

V0 L1

1

V0 L2

2

V1

3

L3

V3

V2

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 + solution adhering to the inert) and the overflow (clear solution). The resulting composition in the underflow is then mixed with another batch of fresh solvent. yN+1 yA3 XC,yc mass fraction solvent

yA2 yA1

Σ3 xA3

Σ2 xA2

Σ1

xA1 xA0 XA,yA mass fraction solute

Countercurrent multistage extraction V1 L0

V2 1

2 L1

N ∆

VN+1 LN

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 Vn are constant and the equation of the operating line is straight.

y AN +1 − x AN y A 2 − x A1 N −1 = y − yA2 log AN +1 x AN − x A1 log

where y = mass fraction in the overflow x = mass fraction in the underflow The first or letter subscript denotes component and second or number subscript denotes equilibrium stage. Note that this equation cannot be used for the entire cascade if L0 differs 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, 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 graphically using the Ponchon-Savarit Method. This method can also be adapted for systems exhibiting constant underflow. Ponchon-Savarit method Just like in the liquid-liquid extraction, the method makes use of the delta, ∆ , to relate the streams ing in opposite direction. 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. V2 is then located using the delta. The procedure is continued until the last composition in the underflow is reached.

XC,yc mass fraction solvent

yN+1

yA3

yA2 yA1

xN

xA3 xA2

Σ xA1

xA0

XA,yA mass fraction solute

∆

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

XA1

Y mass C/ mass A + B

XN

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. 2nd 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. 7 th edition. McGraw-Hill. Singapore.