Analytical and semi‐analytical kinetics models for design and optimization of double‐resistance resin in pulp and carbon in pulp processes with both reversible and irreversible nature

Abstract

The current study was aimed at developing a package of “model + algorithm” for the design of resin in pulp (RIP) and carbon in pulp (CIP) processes of gold, uranium, and base metals. For this purpose, we first formulated a double‐resistance model for irreversible adsorption (accompanied by chemical reaction) in CSTRs, and modified the McKay et al. semi‐analytical model for reversible uptake in a similar system. We then devised two algorithms for the design and optimization of reversible and irreversible RIP and CIP cascades. The developed algorithms were applied on the extraction of copper, uranium, and gold. The packages are able to specify the optimum number of stages, reactor volume (V), resin flow rate (m.), and resin hold up (φs). This shows an evident advantage over the McCabe‐Thiele method, whose only result is the number of stages. The new methods have only two adjustable parameters of diffusivity (Deff) and liquid film coefficient (k), whose determination can be carried out through simple batch experiments. As an additional work, this study also presents a method for mathematical troubleshooting for the Mc Kay et al. model.

A novel analytical second‐order sensitivity calculation approach using the finite element method for chemical engineering problems

“…[3][4][5] Considerable work has been carried out to improve the productivity and stability of chemical processes, where numerous optimal control methods are widely utilized both analytically and numerically. [6][7][8] Generally speaking, it is difficult to find the analytical results of DOPs, and with the significant improvements in computer science and technology, numerical methods have become the preferred approaches for solving DOPs. [9,10] There are several numerical methods that use nonlinear programming techniques to compute the solutions of DOPs.…”

“…As a result, dynamic optimization problems (DOPs) arise naturally in the area of chemical engineering . Considerable work has been carried out to improve the productivity and stability of chemical processes, where numerous optimal control methods are widely utilized both analytically and numerically . Generally speaking, it is difficult to find the analytical results of DOPs, and with the significant improvements in computer science and technology, numerical methods have become the preferred approaches for solving DOPs …”