Adaptive Mesh Refinement For Numerical Simulation In Reservoirs Comprised Of Different Rock Types

Heavy oil plays an important role in the field of hydrocarbon energy due to the abundant reserves. Thermal methods such as steam injection are common technologies used for heavy oil recovery. Steam injection is a multiphase flow with phase change in porous media. There are sharp and narrow temperature and saturation fronts existing in the flow field. Because of the rapid variations of temperature and saturation around the fronts, very fine gridblocks are required. If a uniformly fine grid is applied to the whole domain, huge memories and CPU times are required. Therefore, the objective of our research focuses on the adaptive mesh refinement method, which can track the fronts existing in the flow field with fine meshes.Reservoir characterization is performed on a geocellular model, while scale gaps exist between geocellular models and simulation models. Therefore, geological models usually need upscaling to generate the effective absolute permeabilities in the coarse scale, which are tensors in a strict point view. For the permeability tensor, the solution of the interface flux is a difficult problem. To deal with it on the adaptive meshes, we introduce the flux solution through the flux conservation and the assumption of linear pressure distribution in each gridblock. In addition, the solution is combined with the adaptive mesh refinement in two dimensional reservoirs. Because of the different spatial scales of neighboring gridblocks, the coupling of flux solutions between different-level gridblocks is presented. The sub-blocks of each coarse grid block are introduced to couple the different level gridblocks, and they also provide flux conservation to each neighboring gridblocks in the same level. The accuracy and efficiency of the proposed adaptive mesh refinement method were verified by numerical simulation examples with two-dimensional steam drive and steam assisted gravity drainage.Generally, there are different rock types in the reservoirs. Due to the different relative permeability functions, capillary pressure functions, residual saturations and initial saturations, the saturations are discontinuous across the rock interface. These discontinuities bring more difficulties to the regridding and refining operations. For simulations with different rock types, the cases whether considering gravity are studied, respectively. While the gravity is ignored, we deduce that the ratios between different phase relative permeability in the same coarse block are always continuous in all regions. With the aid of these continuous variables, we successfully implement the regridding and refining operations within the adaptive mesh refinement method. The two-dimensional steam drive numerical example verified the correctness of the proposed continuous variables, and also showed the accuracy and efficiency of adaptive mesh refinement method. While the gravity is important in the flow field, we find out that the oil-gas capillary pressure is always continuous in three-phase regions. And in the same coarse block, the ratio between oil relative permeability and water relative permeability is also continuous in the oil-water regions. Using these continuous ratio and capillary pressure, we solve the problems of adaptive mesh refinement in steam injection process considering gravity. The two-dimensional steam assisted gravity drainage numerical example verified the advantage of the adaptive mesh refinement method in terms of computing speed.In the above steam injection problem, it is assumed that there is no obvious difference for the capillary pressure of different rock types and the effect of the capillary pressure gradient is neglected. However, for some special cases, such as those in fractured reservoirs, the capillary pressure gradient may be very large at the fracture-matrix interface. It is because that there are significant gaps in capillary pressure between the two kinds of media. For simplicity, this work mainly focuses on the porous media with two rock types. One rock has positive capillary pressure and the other has zero capillary pressure. Considering the heterogeneity of the capillary pressure, interface conditions between two rock types are given. Based on our study, we found out that either the saturation gradient may be divergent when approaching to the interface or the capillary pressure may be discontinuous when crossing the interface. We give the mathematical proofs based on the governing equations. An analytic solution around the rock interface is proposed to construct the numerical method. The numerical examples showed that while the rock with positive capillary pressure is on the upstream, the wet saturation will approach to unity closed to interface. Meanwhile, when the rock with zero capillary pressure is on the upstream, the capillary pressure may be discontinuous.In summary, this dissertation presents an adaptive mesh refinement method to solve the non-isothermal multi-phase flows in heterogeneous porous media comprised of different rock types with tensor permeability. Problems coming from different rock types within the adaptive mesh refinement are studied. The accuracy and efficiency of the proposed adaptive mesh refinement algorithm are supported by the numerical examples of steam drive and steam assisted gravity drainage. In addition, the one dimensional incompressible immiscible two-phase flow with heterogeneous capillary pressure is studied. The interface conditions and numerical method are given in this dissertation. The flow characteristic at the interface is revealed by the numerical examples.