An Alternative Numerical Interpretation of the Equal Area Rule and its Implications for Calculating Equilibrium Conditions

Abstract Equal area constructions are basic graphical or iterative procedures that allow calculations of equilibrium conditions for a pure component, or equilibrium compositions for binary nonreactive mixtures or reactive mixtures that satisfy the condition of components minus reactions equal to two. Reactive mixtures can be multicomponent mixtures as long as they satisfy the previous condition. This paper first demonstrates that previously reported equal area algorithms for solving equilibrium conditions are numerically equivalent to a Newton-Raphson procedure. Then, given that result, the equal area algorithm for equilibrium calculations is modified to involve fewer function evaluations; moreover, this new algorithm is able to converge from various initial conditions, even for systems that other numerical procedures cannot accommodate.