F8. Solvent Extraction Formulas

Crosscurrent Extraction:

Locate feed point F having a composition x_F of solute A.

Draw a tie-line RE through the point M having composition of x_M. Two phases are in equilibrium. Extract rich phase is represented by E having composition x_E, whereas raffinate rich phase is represented by R having composition x_R.

The overall balance can be represented by Equation 8.1 given below.

Composition of the solvent-free raffinate can be represented by R' on line AC. The point R' can be located by extending the line BR. The point R' has a composition of x_R' and is free of solvent.

Composition of the raffinate-free extract can be represented by E' on line AB. The point E' can be located by extending the line CE. The point E' has a composition of x_E' and is free of raffinate.

Mixing operation of feed with solvent results in a mixture M having composition x_M that lies on line FB.

F + B₁ = E₁ + R₁ = M₁

R₁ + B₂ = E₂ + R₂ = M₂

R₂ + B₃ = E₃ + R₃ = M₃

R_n-1 +B_n = E_n + R_n = M_n

Similar calculations can be repeated for additional stages, till we reach a desired concentration in the raffinate phase R.

Immiscible Solvents: If solvents A, and B are immiscible at all concentrations, solution technique is bit different.

Determine x_F' = x_F /(1 - x_F)

Calculate ratio A/B

Locate point F representing the corresponding feed composition.

Draw a line FD from point F with a slope -A/B such that it intersects equilibrium curve

Read the coordinates of point D (x₁', y₁')

Solute removed = A(x_F - x₁')

Use appropriate A/B for the following stages.

Draw a perpendicular line from point D till it meets the base at F₁.

Draw a line F₁E from point F₁ with a slope -A/B such that it intersects equilibrium curve.

Read the coordinates of point E(x₂', y₂').

Repeat this procedure till raffinate concentration reaches the desired value, x_n'.

Countercurrent Extraction:

Locate feed point F having a composition x_F of solute A.

Draw a line BF representing mixing operation, thus forming a hypothetical mixture M having composition x_M such that x_M = x_FF/(F+B)

Locate the point R_n representing the concentration in the final raffinate x_n.

Draw a line R_nM and extend it to E₁. The point E₁ represents the solvent rich phase with a composition of x_E1.

Draw line E₁F and extend it to Δ such that another line BR_n when extended also passes through Δ (difference stream). This fact is represented by Equation 8.6 given as below.

Δ = E₁ - F = B - R_n

Draw a tie line E₁R₁ from E₁. The point R₁ represents composition of raffinate from 1st stage.

Draw a line ΔR₁ and extend to E₂ on extract rich phase. The point E₂ represents composition of extract from 2nd stage.

Repeat last two steps till composition of raffinate is equal or less than on represented by point R_n.

Minimum amount of solvent B_min can be found as follows.

Draw a tie line E_1minR_1min such that when extended passes through F.

Draw a line E_1minR_n.

Draw another line BF.

Locate point M_min at the intersection of lines E_1minR_n and BF.

Calculate M_min from the mass balance = x_FF/ x_Mmin or any other graphical technique.