| Abstract |
The author demonstrates an approach for connecting wellbore and reservoir simulation models seamlessly. Coupled models of a wellbore and reservoir are necessary in simulating the production of geothermal fluids through wells under an appropriate condition such as constant wellhead pressure. Since numerical grids generally applied in reservoir simulations are too rough to simulate the drop of reservoir pressure in the vicinity of a wellbore, we need some techniques for determining the bottomhole pressure. One practical and successful approach is to assume a steady-state mass flow near the wellbore as adopted in the reservoir simulator TOUGH2 (Pruess et al., 1999). In this approach, the productivity index relates the mass flow rate to the pressure difference between the bottomhole and reservoir proportionally. The author has developed another approach using a highly refined local grid defined around the wellbore. This approach enables us to compare the observed and simulated bottomhole pressure at a flowing well without limitations from the assumption of steady-state flows. We consider the transient drop of reservoir pressure in the vicinity of a wellbore intercepting a fractured zone forming a planar reservoir. The ring-shaped local grid around the wellbore is defined using a polar coordinate system. The inner boundary is along the wellbore surface. The inner boundary condition describes mass balance on the wellbore surface. The pressure distribution along the outer boundary is determined dynamically referring to the global grid describing the whole reservoir conventionally. The global grid refers to the mass flow rate of the well determined by solving a coupling problem of mass flows in the well and local grid. Using this technique, the analytic solution of the so-called line-source problem (e.g., Dake, 1978) is successfully simulated with high accuracy. The technique can be extended to non-isothermal problems by applying to the scheme developed by Matsumoto (2015). References: Dake (1978) Fundamentals of reservoir engineering. Developments in petroleum science, 8, Elsevier, 443p. Matsumoto (2015) Application of the Constrained Interpolation Profile (CIP) scheme to two-dimensional single-phase hydrothermal reservoir simulations. Geothermics, 54, 10-22. Pruess et al. (1999) TOUGH2 user’s guide, version 2. Lawrence Berkeley National Laboratory Report, LBNL-43134, 197p. |