Evaluation of Pressure-Transient Behavior of Unfractured Vertical, Vertically Fractured, and Horizontal Wells in a Composite Reservoir with an Active Aquifer and Moving Fluid Interfaces

Abstract

AbstractPressure-transient models are presented for evaluation of the behavior of vertical, vertically fractured, and horizontal wells in radial and linear (three-region) composite reservoirs with moving fluid fronts. The Laplace Transform Finite Difference (LTFD) numerical solution methodology combined with the well- known Buckley-Leverett (BL) frontal-advance equation have been used to develop solutions for the moving boundary problem. Hybrid semi-analytic and numerical solutions have been constructed for finite-conductivity vertical fractures and infinite-conductivity horizontal wellbores. Complete descriptions of the mathematical models are presented; the pressure-transient solutions, frontal position and velocity, and saturation distributions. Indications are that monitoring of the transient behavior permits detection of water encroachment to the producing well, prior to breakthrough. This enables modifications in the production operations to be taken proactively to delay breakthrough.The results of the pressure-transient models reported in this paper have been compared with the available moving boundary radial composite solutions in the literature and the results of the vertically fractured and horizontal well solutions have been validated using analytic and numerical reservoir simulation. Six well and reservoir model combinations have been considered in this investigation for which oilfield applications exist for each composite system considered. These include solutions of the pressure-transient behavior of an unfractured vertical well in a radial composite reservoir, a vertically fractured well in linear and radial composite systems, a horizontal well in radial and linear composite systems, and a vertical fracture intersected by a horizontal well in a linear composite system. Extension of the solution methodology used in this study for evaluating the pressure-transient behavior of a selectively completed horizontal wellbore in a cylindrical composite reservoir has also been considered in this study. Each of these solutions include moving fluid fronts, whose position and velocity are determined from the frontal advance model and fractional flow theory. General fractional flow solutions have been implemented that utilize conventional laboratory relative permeability measurements.