A New Bilinear Flow Model for Naturally Fractured Reservoirs with Transient Interporosity Transfer

Abstract

This paper presents the results of the pressure behavior research of a well intersected by a dominant fracture into a Naturally Fractured Reservoirs (NFR), which presents two simultaneous linear flows: a linear flow from a fractured bulk (which considers matrix, vugs, micro and meso fractures) to a dominant fracture, and another from the dominant fracture to the wellbore. This new bilinear flow model considers Transient Interporosity Transfer (TIT) between two porous media, which was modeled by a convolution (de Swaan, 1975) and an Interporosity Skin was possible to quantify.
The characteristic curve of the pressure response developed for this model, shows at early times a dominating flow into dominant fracture, at intermediate times, a restricted interaction between fractured bulk and dominant fracture can be seen, and at late times a bilinear flow occurs. We also developed another new model considering Pseudosteady-state Interporosity Transfer (PSSIT) between two porous medias (see Appendix B). Such model was based on the Warren & Root (1963) theory and was necessary to extend the parameters for dominant fracture and fractured bulk.
The development of the PSSIT model was to use it as a framework, in order to make a comparison between TIT and PSSIT models. It was found that increasing Interporosity Skin factor in the TIT model reaches the Pseudosteady-state behavior. The advantages of using TIT models were discussed. As a result of this study, we found that the time at which the bilinear flow appears, is directly related to the damage in the interface of the two porous media. We found a relation between Interporosity Skin value and the new parameters of the PSSIT model.
A new methodology for well test interpretation is presented; useful when the solution can be expressed as a convolution. The results of this methodology were compared with the actual solution.