Finite Horizontal Well Crossing a Natural Fracture Normally

Abstract

Summary An analytic solution in terms of the Laplace transformation is presented to calculate the pressure distribution in multizone, composite reservoirs intercepted by a finite horizontal well that is oriented normal to the plane interfaces in an infinite field. A three-zone reservoir is analyzed for illustrative purposes, with the horizontal well traversing a thin high-permeability central zone confined between two parallel planes representing the natural fracture, and with the well completed in the adjacent zones. The method provides the transient pressure field for each of the three zones, allowing analyses of the flow fields both within the fracture and within the reservoir as a function of pertinent parameters. The computational scheme considered is both viable and robust. To our knowledge, this topic is yet to be analyzed in this fashion analytically. The numerical results presented are limited to a parametric study of (1) transient well pressures and their time derivative and (2) steady-state flux and flow-rate distributions at the fracture faces as a function of distance from the well. A steady-state correlation of the productivity index is also provided. We discovered that of the two generally accepted procedures for estimating the average well pressure, the one based on well rates proportional to the local permeability and well length gives results consistent with our model, whereas the one requiring equal average pressure at each well segment introduces significant disturbances to the flow field near the fracture-well intercepts, at least when small and large well lengths are present, as is the case in the problem under consideration. This subject needs additional investigation.