Perpustakaan Digital ITB

This paper addresses the problem of reservoir modeling in the context of large scale developments, in which multiple wells with hundreds of fractures are placed in a formation. In particular, the goal is to develop an ability to compute the production rate for each well for the given bottomhole pressure variation and also to evaluate the associated change of stress in the reservoir, e.g. for the purpose of subsequent modeling of hydraulic fracturing in neighboring wells. In addition, it is desired to compute the solution rapidly, in which case this makes it possible to consider sensitivities of the solution to various parameters. In order to achieve the goal, i.e. having an ability to solve large scale problems quickly, it is necessary to consider a series of simplifications in the model. The primary assumptions are zero vertical permeability and single phase flow, which makes the flow equations linear and decoupled for each layer. In addition, the use of an analytical solution that captures linear flow for imposing the boundary condition at the fracture surface allows to avoid having fine discretization near the fracture surface. Finally, the use of a uniform grid together with employing Fast Fourier Transform algorithm and Graphics Processing Unit for calculations leads to the desired performance. The model has been benchmarked by comparing its predictions to reference numerical and analytical solutions. Computational performance of the algorithm is analyzed and it is shown that it is possible to simulate large scale problems within minutes. Finally, a field scale example with eight wells is presented, which illustrates a potential application of the algorithm and quantifies the characteristic variations of pressure and stress caused by injection of the fracturing fluid and production.