Computer Calculations Of Compressibility Of Natural Gas

Abstract

Abstract An alternative method for the calculation of pseudo reduced compressibility of natural gas is presented. The method applies the definition of reduced compressibility (Equation Available In Full Paper), where both Pr and (Equation Available In Full Paper) are variables available as DR and DP in both the Dranchuk et al. and Dranchuk and Abou-Kassem Z-Jactor subroutines. This method is incorporated into these routines by adding a single FORTRAN statement CR = O.270/(DR*DP}before the RETURN statement. This method is suitable for computer and hand-held calculator applications. It produces the same reduced compressibility as other available methods but is computationally superior. Methodology The methods of calculating compressibility of natural gas are derived from the following relationship between C and Z: Equation (Available In Full Paper) Trube(1) presented a graphical correlation of cr as a function of Pr and Tr based on equation (2) using the Brown et al. (2) Z-factor chart. While this correlation is useful for hand calculation, it is not suited to computer usage. Mattar et al. (3) used the following expression for cr that was based on the manipulation of equation (2) Equation (Available In Full Paper) Although the last two methods are suited to computer usage; they require the Dranchuk et al.(4) Z-factor subroutine that calculates Z which in turn would be used to calculate Pro Both Z and P, are used in equations (2), (4), (5), (7) and (8). Close examination of the Dranchuk et al.(4) Z-factor routine reveals that this routine solves for Pr for a given Tr and Pr using the Newton-Raphson iteration. The form of the equation used is Equation (Available In Full Paper) The suggested approach is applicable to all equation-of-state based romines for calculating Z-factor (e.g. Hall and Yarborough(6), Dranchuk and Abou-Kassem(7). Because of the similarity between the Dranchuk et al. (4) equation and the Dranchuk and Abou-Kassem(7) equation (based on BWR EOS), and the wide-spread use of these two routines for predicting Z-factor, the following is an account of why and where to incorporate necessary modifications to calculate cr in both routines using the suggested approach. These two equations can be expressed in a general form as: Equation (Available In Full Paper) Finally, the numerator in the right-hand-side of equation (13) is represented by DP in these routines. Therefore, A statement for Cr that is based on equation (11), may be incorporated in both routines by inserting the following FORTRAN Statement before the RETURN statement: Equation (Available In Full Paper) The modified versions or both the Dranchuk el al. (4) and Dranchuk and Abou-Kassern(7) routines, which were tested and verified to reproduce the Mattar et al.(3) graphical correlation for er are presented in Appendix I and Appendix 2 respectively. The results of the various method considered in this paper are compared in Table 2 for T, = 1.05, l.5, 2.5 and 3.