Modeling the Performance of Fractured Wells in Pattern Floods Using Orthogonal, Curvilinear Grids

Abstract

ABSTRACT Previous investigators have used orthogonal, curvilinear grids to simulate oil recovery processes in repeated well patterns. These grids are radial in the vicinity of the wells, allowing accurate resolution of the near well region. This paper extends the applicability of curvilinear grids to include patterns with vertically fractured wells, where elliptical coordinates provide better representation of fluid flow near the fracture. Appropriate curvilinear coordinate systems are obtained from an analytic solution for steady, unit mobility displacements. This solution encompasses a variety of pattern geometries, including fractured five and nine spots, line drives, staggered line drives and single wells. The analytic potential for unfractured wells in these patterns is available in the literature, while the extension to fractured wells is developed in this work. Unit mobility flow rates and areal sweep out in fractured well patterns can be easily obtained from the analytic solution. Examples are given for line drives and staggered line drives, for different fracture lengths and pattern aspect ratios. Pore volumes and transmissibilities are calculated from the analytic potential, and are incorporated into a thermal reservoir simulator. Excellent agreement is demonstrated in comparing the curvilinear formulation with Cartesian grids for a miscible displacement at a mobility ratio of 40 in a five spot pattern, and a steamflood in an inverted nine spot pattern. The fracture formulation is verified against published numerical solutions for the performance of finite conductivity, vertically fractured wells in single-layer reservoirs. Fewer grid blocks are required by the curvilinear grid to obtain the same accuracy as a Cartesian grid. The main advantage of using a curvilinear model lies in the ability to accurately describe flow around the well, while simultaneously modeling the flow at a distance. Several applications have been chosen to demonstrate this capability. An adverse mobility, miscible line drive between fractured wells demonstrates that the large fluid flux near the injection well fracture tip has a strong influence on areal sweep. This is also shown in a steamflood between horizontal wells, where curvilinear and Cartesian grids predict significantly different recoveries. Finally, a waterflood in an inverted nine spot pattern, shows the importance of accurately modeling fractured injection wells.