A new time function has been defined which considers variations of gas viscosity and compressibility as a function of pressure, which in turn is a function of time. This function appears to be similar to the real gas pseudo-pressure, m(p) of Al-Hussainy et al., which takes into account the variations of gas viscosity and z-factor as a function of pressure. However, this is an approximate function as opposed to m(p). This time function will be referred to in this paper as the real gas pseudo-time, t a(p). This function has aided in pseudo-time, t a(p). This function has aided in post-treatment-pressure buildup analysis of post-treatment-pressure buildup analysis of fractured (including MHF) gas wells by type curve analysis. Results of computer simulated pressure buildup analysis indicate that the use of t a(p) provides satisfactory values of computed fracture provides satisfactory values of computed fracture lengths in fractured gas wells.
In this paper the real gas pseudo-time is described and its application is demonstrated by means of example problems. Although the discussion in this paper is limited to pressure buildup analysis of vertically fractured gas wells, the utility of this function is not meant to be restricted to such wells only.
In recent years, type curve analysis methods' have become well known in the petroleum industry for analyzing both pressure drawdown and buildup data in oil and gas wells. These methods are meant to be used in conjunction with the conventional methods whenever possible. Exceptions appear to be MHF gas wells with finite flow capacity fractures where conventional methods are not readily applicable and, at least to date, only type curve methods appear practical to determine fracture length and fracture flow practical to determine fracture length and fracture flow capacity. Although the majority of published type curves, including those for MHF wells, are based on the pressure drawdown solutions for liquid systems, they can be used in an approximate fashion to analyze pressure data from real gas wells. The first requirement is that the dimensionless pressure and time variables are appropriately defined for gas wells. For example, to use the liquid system type curves for an MET gas well, dimensionless variables are defined as follows:
(In SI units, the numerical constant is 128 × 10(-3))
Dimensionless pressure, for a gas well, may also be expressed in terms of Delta (p) or Delta p.
(In SI units, the numerical constant is 3.6 × 10(-9))
The definition of dimensionless fracture capacity remains the same.
Note that in Eq. (1), the real gas pseudo-pressure, m(p) of Al-Hussainy et al. has been used to take into account the variations of gas viscosity and z-factor as a function of pressure. In Eq. (2), viscosity-compressibility (mu c t)i is shown to be evaluated at the initial reservoir pressure. pressure.