Single-Well Pressure Testing Solutions for Naturally Fractured Reservoirs With Arbitrary Fracture Connectivity

Abstract

ABSTRACT Traditional pressure testing models for naturally fractured reservoirs assume that the rock formation is heavily fractured to an extent that the matrix blocks are completely surrounded by fracture surfaces. Thus, the matrix blocks are unconnected and fluid transport over macroscopic distances can take place only in the fracture network. The model presented here overcomes this deficiency by allowing for matrix and fracture network permeabilities over macroscopic distances; it is thus able to represent moderately fractured formations as well as the limiting cases of unfractured and heavily fractured formations. Also, a new unsteady interporosity fluid flow formulation, which accounts for independent variation of the matrix and fracture system pressures is employed in this model. This feature has not been included in previous interporosity flow formulations. Analytical solutions and type curves for single-well pressure tests in one, two and three dimensional fluid flow configurations in unbounded domains are presented. Interporosity fluid transfer is modelled using the standard unsteady flow models and the new unsteady interporosity flow formulation. The effects of well bore storage and of the matrix and fracture system skin factors on constant rate drawdown well tests are illustrated through numerical examples. The significance of the special features of this model, namely, that of modelling the macroscopic permeability of the matrix system in addition to that of the fracture system and of using the new unsteady interporosity flow model is demonstrated. The numerical results show that, for moderately fractured formations, significant errors are incurred in the predicted formation properties when matrix block connectivity and the resulting direct fluid transport between matrix blocks are neglected. Also, the results show that the dependence of interporosity flow on the independently varying matrix and fracture system pressures must be accounted for in the interporosity flow model.