Application of Two-phase Deviation Factor to Material Balance Calculations For Gas-condensate Reservoirs
Authors: Ambastha A.K. , Barman I. 
Published: March 2010

Abstract
Material balance calculations for gas-condensate reservoirs with reservoir pressures below the dew-point pressure require the use of two-phase deviation factor to account for the phase behaviour effects of a gas-condensate fluid. Recently, an empirical correlation for the two-phase deviation factor has also been presented in the literature.
In this study, a phase behaviour package based on the Redlich-Kwong equation of state as modified by Zudkevitch and Joffe has been used to investigate some of the issues in connection with the application of two-phase deviation factor to material balance calculations for gas-condensate reservoirs.
This study shows that the two-phase deviation factor does not necessarily increase in the two-phase region as the pressure increases, whereas the empirical correlation shows that the twophase deviation factor always increases with pressure. A study has also been carried out to quantify the errors in estimating the initial gas-in-place due to input data errors, fluid composition effects, computation methodology for deviation factor, and the use of improper deviation factor.

Introduction
For a normally-pressured, volumetric, dry gas reservoir, the relevant material balance equation is(1):
Equation 1 (available in full paper)
Equation (1) is also suitable for material balance analysis of pressure-cumulative production data with all data collected at reservoir pressures above dew-point pressure for a volumetric, gas-condensate reservoir. However, material balance analysis for pressure-production data below dew-point pressure can be carried out in combination with the pressure-production data above dewpoint pressure, if two-phase deviation factor (z2ph) replaces gas deviation factor (zv) in Equation (1) for all data below dew-point pressure(2,3). The variable, z2ph, is expressed by the following equation:
Equation 2 (available in full paper)
As stated in References (2) and (3), two-phase deviation factor can be computed using constant-composition expansion (CCE) calculations for typical reservoir engineering applications. Obviously, z2ph = zv for pressures above dew-point pressure because liquid phase does not exist (i.e., L = 0) above dew-point pressure. References (2) and (3), among others(4), have suggested that the Redlich-Kwong equation of state as modified by Zudkevitch and Joffe(5,6) (referred to as ZJRK EOS in this paper) is adequate for computations of phase behaviour aspects of typical gas-condensate reservoirs. Details of the ZJRK EOS used in this study appear in Reference (7).
Recently, Rayes et al.(8), have presented an empirical correlation for the two-phase deviation factor for gas-condensate fluids. The correlation expresses two-phase deviation factor as a function of pseudo-reduced pressure and pseudo-reduced temperature. They developed their correlation based on 67 constant volume depletion studies with C7+ &gt;4%. They concluded that their correlation yields an average error of 3.66% in predicting two-phase deviation factor. Rayes et al.,(8) also recommended that for C7+&lt; 4% and for a well stream specific gravity &lt; 0.911, the singlephase gas deviation factor can be used for the material balance calculations. In this study, the results from the Rayes et al.(8), correlation are compared with the results from the ZJRK EOS.
Ambastha and van Kruysdijk(9) studied the effects of input data error on material balance analysis for volumetric, gas and gascondensate reservoirs.