This paper presents a new method of estimating drainage area size and shape from production data (bottomhole pressures and flowrates) for gas wells. This method is rigorously based on theory presented earlier for the slightly compressible liquid case and requires a computer program to iterate on gas-in-place until the gas flow and material balance equations are satisfied.
The component equations and analysis technique are strictly applicable only after the initial pressure transient has reached the outer boundary. The gas f low equation that we present is an approximation for variable-rate, post-transient flow, but it has provided excellent results for all of the cases investigated. These results imply, as was also noted for the liquid case, that as long as the changes in flowrate do not dominate the influence of the outer boundary, this method should give acceptable results. Currently, this method is only derived for single-phase gas flow and does not consider the effects of geopressured gas reservoirs or non-darcy flow.
The purpose of this paper is to present a rigorous method of estimating reservoir size and shape using variable-rate production data from a gas well. This method was initially developed for the slightly compressible liquid case. I The new gas flow equation that we present here is similar to the liquid equation in form due to the linearization of the gas flow diffusivity equation. This linearization is accomplished by the use of "adjusted" time and pressure functions which account for the pressure dependent changes in gas properties.
The calculation of the adjusted time function for this case is complicated because the gas properties must be evaluated at the average reservoir pressure, p, as explained by Fraim and Wattenbarger. However, it is not likely that p as a function of time will be known. If values of p were known ahead of time the calculation of adjusted time would be straightforward and the new method could be done by hand. We have developed a strategy to determine the gas-in-place, G, and the average reservoir pressure function simultaneously by iteration of the new gas flow equation and the gas material balance equation. This method is only applicable to post transient or boundary-dominated flow, although the results of the verification cases suggest that the calculated relation may also be valid for transient flow.
In the "Development of the New Method" section, we present the new gas flow equation and discuss the iteration scheme used to obtain the Gas material balance required to apply this method. This new method is verified using data from reservoir simulators for homogeneous reservoirs and for wells containing a vertical fracture. Three field examples are included to compare our method to the results obtained using other analysis techniques. Finally, a step-by-step development of the new method and programmable algorithms for the application of this method are included in the Appendices of this paper.