Numerical Methods
using toluene. Aqueous and organic phases will form after adding the organic solvent into the water phase. The extraction is carried out in a 10-stage countercurrent tower, shown in the following figure. The equilibrium relationship valid at each stage is, to a first approximation:
where:
Yi = (lb of aniline in the toluene phase)/(lb of toluene in the toluene phase)
Xi = (lb of aniline in the water phase)/(lb of water in the water phase)
(a) The solution to this problem is a set of 10 simultaneous equations. Derive these equations from material balances around each stage. Present these equations using compact notation. (15%)
(b) Solve the above set of equations to find the concentration in both the aqueous and organic phases leaving each stage of the system (Xi and Yi). (25%)
(c) If the slope of the equilibrium relationship is replaced by the expression m = 8 +20 Xi, the solution becomes a set of simultaneous nonlinear equations. Describe a procedure which would solve this problem. (15%)
(d) Solve the problem described in (c) above. (25%)
(e) Prepare a report to summarize the mathematical modeling and numerical solution procedures. Make sure to attach all MATLAB or excel codes used in this project. (20%)
