Effect of fracture spacing distribution on pressure transient response in naturally fractured reservoirs

This paper presents a new model for pressure transient and derivative analysis for multi-porosity reservoirs that have a distribution of matrix block sizes. To highlight the effect of varying fracture spacing, this model uses matrix domain storativity parameters instead of the fracture storativity parameter introduced by Warren and Root. Unlike existing multi-porosity models, it provides a simple expression for the pressure transient response in the time domain. The paper also presents a method for determining shape factors for the different matrix domains of multi-porosity reservoirs that is based on measured fracture spacing distributions. For an example reservoir studied, the pressure transient response for double-porosity reservoirs was found to be very similar to that of triple- or quadruple-porosity reservoirs, as long as the volume fractions of the matrix domains for each respective model were equal. Because of this, multi-porosity models may not provide significantly more information about the reservoir than the simpler double-porosity models. The transition period began somewhat earlier and ended later when more matrix domains were included in the model. When the volume fractions for the different matrix domains were significantly different, the calculated pressure transient response was impacted.