A tank material-balance equation for gas reservoirs has been written, taking into account the effective compressibility of matrix and fractures.
The method has direct application to stress-sensitive naturally fractured reservoirs (NFRs). Under some conditions, ignoring the effect of fracture compressibility (Cf) can lead to overestimating the volume of original gas in place with a crossplot of p/z vs. cumulative gas production (Gp). The equation presented in this paper has been developed to overcome that weakness. The use of the tank material balance is illustrated with an example.
It is concluded that fracture compressibility can play an important role in the calculation of gas in place in stress-sensitive NFRs.
The subject matter is significant because, historically, formation and water compressibilities have been neglected when carrying out material-balance calculations for conventional gas reservoirs. This assumes that these compressibilities are negligible compared to that of gas. The assumption implies that the reservoir strata are static. When water influx is ignored, the assumption leads to a straight line in a crossplot of p/z vs. Gp. However, this study shows that in those instances in which fracture compressibility is large, such assumptions can lead to significant error.
Forecasting the performance of NFRs is a major challenge. Various authors have tackled the problem throughout the years with material-balance calculations. To the best of my knowledge, the effect of fracture compressibility usually has been ignored in material-balance equations for gas reservoirs. The work presented in this paper is not meant to replace a detailed reservoir simulation, which, in my opinion, is the best way to try to solve the problem, provided that the reservoir characterization and the quality of the pressure and production data is good. The idea is to have a tool that can provide a quick idea with respect to potential gas in place and recovery from stress-sensitive NFRs.
The conventional material balance for gas reservoirs leads to a straight line in a Cartesian crossplot of p/z vs. Gp, provided that (1) water influx is equal to zero, (2) the reservoir strata are static, and (3) the water and formation compressibilities are negligible compared to gas compressibility. Although these assumptions are reasonable in many instances, there are cases in which the fractures are quite compressible. In these cases, the conventional approach can lead to significant errors in the estimation of original gas in place. Similar problems have been observed in the past in geopressured reservoirs (Roach 1981; Ramagost and Farshad 1981) and stress-sensitive naturally fractured oil reservoirs. Possible solutions have been proposed by Aguilera (2006, 2007).
This paper presents a material-balance equation that takes into account the effective compressibility of matrix and fractures. Stress-sensitive properties such as fracture porosity, fracture permeability, and the portions of gas stored in matrix and fractures are taken into account.