An accurate explicit form of the Hankinson–Thomas–Phillips correlation for prediction of the natural gas compressibility factor

The use of the Hankinson–Thomas–Phillips correlation for prediction of the natural gas compressibility factor is a common practice in natural gas engineering calculations. However, this equation suffers a serious deficiency from a computational viewpoint; in that it is not explicit with respect to the z-factor and hence is subject to time-consuming trial and error procedures. In this paper, we propose an explicit series expansion equivalent to the Hankinson–Thomas–Phillips equation by the aid of a powerful mathematical technique known as the Adomian decomposition method. Furthermore, we have enhanced our formula by a applying nonlinear convergence accelerator algorithm, namely the Shanks transform. The proposed equation is simple, easy to use, and is shown to be extremely accurate in reproducing the experimental PVT data of natural gases. Moreover, in contrast to the previous numerical algorithms such as the Newton–Raphson algorithm, the explicit nature of our formula obviates the need for any initial guess as an input for calculation of the z-factor. Such independence permits our formula to always quickly converge to the correct z-factor.