On the Solution of the Tao-Mason Equation of State by a Nonlinear Ordinary Differential Equation

Based on the Tao-Mason equation of state we have proposed a nonlinear ordinary differential equation that asymptotically converges to the compressibility factor of a pure substance or a mixture of chemical species. We have used the Dormand-Prince pair algorithm to solve the aforementioned differential equation in a purely numerical manner. Our method is devoid of the adverse convergence issues that are usually associated with the Newton-type solvers. We have provided two case studies concerning two industrially common compounds namely ethane and carbon dioxide, for the sake of exposition. For 96 points of different temperatures and pressures, our method succeeded at calculating the compressibility factor of carbon dioxide with an average absolute error of 6.53×10-5 and a maximum absolute error of 4.79×10-4. Unlike the previous root finding algorithms, we only need to perform “formal” polynomial deflations in our method, which circumvents the computation-intensive synthetic divisions, to obtain all compressibility factors offered by the Tao-Mason EOS.