On the Production Analysis of a Multi-Fractured Horizontal Well

Abstract

This paper investigates the post fracture transient analysis of multi-fractured horizontal wells under the assumption of infinitely large fracture conductivity. Most of the existing studies of multi-fractured wells have considered finite fracture conductivity, when the dynamic fluid pressure drop in the flow within fractures is a part of the solution. This led to computationally intensive solution methods, particularly when a reasonably large number of fractures representative of current field applications is considered. In this work, we limit our consideration to low-permeability, tight (e.g., shale) reservoirs, when pressure losses in propped fractures can be neglected. This assumption allows to develop a rigorous, accurate, and computationally efficient solution method based on the fundamental problem of a unit step pressure decline in an array of identically sized and equally spaced fractures. The study of this fundamental problem is analogous to the well testing analysis of a fractured well produced at constant bottom-hole pressure conditions. The solution for a unit step pressure decline is used within the Green’s function framework to formulate and solve for the transient pressure response of a multi-fracture array produced at a constant volumetric flow rate. We also explore two simplified approaches to the production analysis of multi-fractured wells based on (1) the infinite fracture array approximation for finite arrays, and (2) an extension of the ad hoc method of Gringarten et al. (Soc Pet En J 14(04):347–360), respectively. We show that both methods lead to very good approximations of the rigorous solution for a finite fracture array problem, thus allowing to further simplify the transient analysis of multi-fracture wells.