Adomian Decomposition Method (ADM) Versus Nonlinear Solution of Natural Gas Compressibility Factor Correlations

Many mathematical correlations were proposed for the calculation of the natural gas compressibility or z factor. Those correlations are implicit in z which means that they are iteratively solved using nonlinear solvers. In some normal cases, however, nonlinear solvers may diverge from the solution. This behavior has led some researchers to think about simpler and explicit methods for solving the z factor correlations. In a recent paper by Fatoorehchi et al. (J Petrol Sci Eng. doi:10.1016/j.petrol.2014.03.004, 2004), the authors have implemented the Adomian Decomposition Method (ADM) which was introduced by George Adomian in the 1980's. They used the ADM method to tackle the nonlinearity of natural gas z-factor of the Hankinson-Thomas-Phillips correlation. The authors presented examples of gas gravities in the range 0.6-0.8 and pressure ranges no more than 6,000 psi. The contribution of this paper, however, is that it presents the discretization and solution method of the widely accepted natural gas z-factor correlations using the ADM method. It extensively covers the procedure and methodology of evaluating the Adomian polynomials along with a listing of the first ten polynomials and nonlinearities in a very compact form. In addition, it compares the nonlinear and ADM solutions via extensive examples for gas gravities 0.6-1.5 and for pressures 100-9,000 psi.