Computer simulation of a steady-state coutercurrent
multistage metal solvent extraction−stripping process (ESP) using cation-exchange reagents shows that there
is a value of extraction
equilibrium constant, K, yielding the maximum metal recovery
when the other operational
parameters are constant. Qualitatively, this is because the larger
K makes stripping more
difficult. Steady-state local linearization reveals the symbolic
relation behind the numerical
results. The coefficient of d(ln K) in the differential
equilibrium relation extended to the
countercurrent multistage process is the weighted average of the
partial derivative, in each
stage, of the equilibrium organic-metal molarity with respect to ln
K under constant equilibrium
aqueous-metal molarity, where the weight is related to the partial
derivative of the equilibrium
organic-metal molarity with respect to the equilibrium aqueous-metal
molarity under constant
K. The balance of these coefficient values for the
extraction and stripping sections of ESP
determines the trend of the recovery with varying K: at
the maximum recovery, these values
are equal to each other. The stagewise plot of the partial
derivative of the equilibrium organic-metal molarity with respect to ln K under constant
equilibrium aqueous-metal molarity versus
organic-metal loading ratio clarifies the relation between the trend of
the recovery with varying
K and the organic-metal loading.