A Robust and Efficient Algorithm for Computing Reactive Equilibria in Single and Multiphase Systems

Abstract

Prediction of liquid–liquid phase equilibria in reacting systems is important in many applications such as reactive extraction. This problem poses several numerical challenges. These systems are governed by highly nonlinear algebraic equations and are plagued by the issue of nonconvergence of iterative algorithms. They exhibit strong sensitivity to the choice of the initial values or starting guesses for the variables. The nonconvergence stems primarily from the wide range of concentrations of various species at equilibrium. In this work, a new methodology for predicting thermodynamic equilibria of multiphase reacting systems is proposed. The mathematical formulation and solution are based on the use of the logarithms of the concentrations as the dependent variables. The proposed algorithm shows rapid convergence even when the initial guesses are far from equilibrium. The efficiency of the method is demonstrated by predicting the equilibrium concentrations of species in three systems of varying degrees of complexity.

Proteomic indicators of oxidation and hydration state in colorectal cancer

“…The implications of choosing different sets of components, called the “basis” ( Bethke , 2008 ), have received relatively little discussion in biochemistry, although Alberty ( 2004 ) in a similar context highlighted the observation made by Callen ( 1985 ) that “[t]he choice of variables in terms of which a given system is formulated, while seemingly an innocuous step, is often the most crucial step in the solution”. Models built with different choices of components nevertheless yield equivalent results when consistently parameterized ( Morel & Hering , 1993 ; Ravi Kanth et al , 2014 ). Accordingly, components are a type of chemical accounting for reactions in a system ( Morel & Hering , 1993 ), and do not necessarily constitute mechanistic models for those reactions.…”

Development of a Thermodynamic Model Using a Speciation Framework: Illustration on the HNO3–H2O System

“…A methodology for computing equilibrium concentrations of various species present in single and multiphase systems was developed recently based on a speciation framework . This requires the thermodynamic parameters as inputs.…”

“…In order to achieve this objective, the equilibrium concentrations of ionic species are required to be modeled. Recently we have discussed a rigorous speciation framework to predict equilibrium concentrations of a system when the thermodynamic parameters (equilibrium constant and activity coefficient models) are available . In the present work, we extend that approach and discuss the estimation of the thermodynamic parameters from experimental data in the same framework.…”

Unified Framework for Modeling Reactive Extraction of Metals: Illustration on Plutonium(IV) Extraction with Tri-n-butyl Phosphate

“…In order to determine the equilibrium compositions of all the phases in any subsystem, the robust and efficient speciation calculation algorithm developed by Ravi Kanth et al is used. This algorithm provides feasible solutions for systems containing species whose concentrations span a wide range.…”

“…Hence, the application of these algorithms for modeling liquid–liquid extraction systems is less effective. Recently, Ravi Kanth et al proposed a method for chemical speciation calculation which overcomes these limitations and also demonstrated its utility in computing the equilibrium compositions for the aqueous nitric acid system . This algorithm is used as a key component in our proposed framework both for computing the equilibrium compositions and to estimate unknown parameters of the model from experimental data.…”