Decoupled Overlapping Grids for Numerical Modelling of Transient Wellbore Pressure

Accurate modelling of transient wellbore pressure is important in well test analysis, where measured pressure responses are interpreted by comparing them to model results. Traditionally analytical models are used, but these models are limited to homogeneous reservoirs of regular shapes. Alternatively the wellbore pressure can be computed from a numerical simulation, allowing for more complex reservoir geometry and permeability heterogeneity to be included. The conventional point source or line source well approximation implemented in most commercial reservoir simulators does not provide good information about transient behaviour at the well. Another approach is to implement the well as an internal boundary with local refinement in the well vicinity. However this would significantly increase the computational cost of the iterative parameter fitting process in well testing, especially for field-scale models with large number of wells. This paper explores a new method for accurately computing wellbore and near-wellbore pressure. The method addresses the problem in two stages solved on different grids that overlap. In the first stage a global problem is solved in the entire domain with the conventional point/line source well approximation, and in the second stage a local problem is solved in a smaller near-well region with the well implemented as an internal boundary. The two solutions are linked via the external boundary condition for the local problem which is interpolated from the global solution. This method has the advantage of capturing both global reservoir properties, which can be accurately modelled using existing reservoir simulators, and the details of pressure transient phenomena associated with near-well refinement. The proposed method is validated against exact analytic solutions for a homogeneous 2D case study, and numerical results for some heterogeneous case studies are presented.