Application of Solution Strategies for Numerical Estimation of Thermodynamic Equilibrium Parameters for an Acetone–Butanol Mixture

The development of reliable numerical estimation of thermodynamic parameters is a crucial aspect in the ongoing research about process engineering and design. The consideration of these concepts lets to design more precise processing units and separations stages based on the predicted nature of substances. Therefore, this study presents an application of different solution methods for the estimation of thermodynamic equilibrium parameters of an acetone–butanol mixture. This dissolution is a non-ideal system, so, the non-ideal Raoult’s Law and Wilson’s equation were used to model the liquid–vapor equilibrium. Otherwise, the solution of this system required the application of nonlinear least squares (NLS) for determination of adjustable parameters. As the above step transformed Wilson’s equation into a system of nonlinear equations, solution algorithms such as; Newton–Raphson method (NRM), Broyden’s method (BM) and Levenberg–Marquardt method (LMM) were applied. All algorithms converged towards the same solution ( Λ 12 = 0.689 and Λ 21 = 0.798 ), but Newton’s and Broyden’s methods employed fewer computational time and number of iterations compared to performance showed by the Levenberg–Marquardt algorithm.