A Mathematical Model for Three-Dimensional Nonsteady-State Streamline Simulation of Horizontally Drilled Reservoirs

Abstract

Among the recent technological breakthroughs that have revolutionized the search for oil and its production are innova-tions realized in the field of horizontal drilling. Once dormant, this practice is fast becoming routine in the oil industry. Thanks to the very large contact area they provide with the permeable medium and their ability to intercept natural fractures, horizontal wells have revived aging oil reservoirs and yielded remarkable augmentations of productivity compared to what is normally at-tained via conventional vertical wells. These most impressive results have warranted and spurred research on virtually all fronts of the upstream sector of the oil industry. One of the areas with a great need for new advances is that of reservoir engineering. New theories and techniques must be developed to parlay the tremendous potential of horizontal drilling. It is in this spirit that this work was undertaken. This study probes deeply into the subject of nonsteady-state fluid flow around horizontal wells. In particular, pressure distribution in closed reservoirs is investigated in detail, and the assumptions of uniform flux and infinite conductivity are put under close scrutiny. Most importantly, a three-dimensional mathematical model that describes fluid flow around horizontal wells is derived as a preliminary step for the development of a full-fledged three-dimensional nonsteady-state streamtube simulator. A major por-tion of the computer code is written and tested.