Adaptive Mesh Refinement (AMR) Technique For Steam Thermal Recovery In Complex Reservoirs

Steam injection is commonly used to recover heavy oils from petroleum reservoirs. Numerical simulation is a very difficult task, since high nonlinearity in the problem formulation may lead to very sharp thermal and saturation fronts. Because of these rapid variations of the physical quantities across the fronts, numerical grids must be fine enough to achieve reasonable accuracy. As a result, huge CPU time and memory are needed if applying a uniform fine grid to the whole calculation area. In addition, due to the complexity of the reservoir, unstructured meshes are widely used, which is bound to increase the complexity of the numerical discrete. If we use structured grids, the scale should be fine enough to satisfy the simulation accuracy of the complex region. Therefore, improving the calculation efficiency for such problems has great theoretical and practical interest, and the adaptive mesh refinement(AMR) technique is a class of strategies that address this problem.In this paper, we present an application of the AMR technique to the numerical simulation of steam thermal recovery processes in complex petroleum reservoirs. And several problems relevant to the AMR numerical simulations are carefully studied.For homogeneous reservoirs, we suggest using structured program design to write the AMR programs. We can easily check the flow-up studies and the preparation time of the numerical procedure can be substantially reduced. The numerical examples for2D and3D SAGD process shows that, the AMR technique results are fast compared with the solutions under referenced uniformly fine grids, and can give good accuracy. AMR grid structure shows that the number of fine grids of the reservoir is significantly reduced.For heterogeneous reservoirs, effective permeability of the coarse grids must be calculated while we apply the AMR techniques, and the renormalization method is adopted. To reduce the grid orientation effect, a nine-point, finite-difference reservoir simulator is applied to calculate the steam drive processes, and the AMR technique is also contained in the simulator.2D simulations of SAGD process and steam drive good accuracy, and the speed of the calculation is highly faster than the fine grid solutions.Before applying the AMR algorithm to the complex faulted reservoirs, we should divide structured grids first. Faults in reservoir are treated as porous media with ultra-low absolute permeability rather than internal boundary, and we could treat the faulted reservoirs as heterogeneous reservoirs. A simple method is given to calculate the permeability of the fine grids crossed by faults, and the permeability is calculated by the fluid flow channel rather than set very low values directly. When both grids are crossed by the same fault, we must consider the continuity of the fault while calculating the flow between the two grids. In the refinement criteria for deciding if the regridding is necessary, the local spatial variations of temperature and phase saturations are used as control values. As a result, coarse grids are applied around faults in the simulations until the steam front arrived, and the renormalization method is adopted to calculate the equivalent permeability of coarse grids in the AMR multi-level grid system.2D SAGD and steam drive examples show that treatment methods of the faults won’t destroy the physical properties of the faults, and the AMR technique can still have a highly fast speed. Coarse girds used in faulted regions do not reduce the accuracy, and they are a very important part of reasons of the high calculating speed.When the AMR technique is applied to the numerical simulation of the steam injection process in complex boundary reservoir, there is a difficulty to divide structured grid system. A large rectangular area is used to cover the entire reservoir, and we provide structured grids to this area. The grids outside the boundary will not be involved in the calculation, so this method do not need extra memory. The permeability of grid interface is involved in the calculation instead of the grid permeability to consider the impact of the border comprehensively. Before implementing the AMR algorithm, the parameters on the fine cells on the reservoir boundary are pre-calculated, and a simple and effective pretreatment method is proposed for the grids across the impermeable layer and the porous media. Single-phase flow examples show that the computing solution of the equivalent permeability is very close to the converged solution according to the pretreatment method even the grid size is large. In the refinement criteria for deciding if the regridding is necessary, the local spatial variations of temperature and phase saturations are used as control values. As a result, the boundary area adopts the coarse grids automatically before the temperature and saturations fronts reach. The same pretreatment method is utilized to calculate the equivalent permeability of the coarse cells of different levels of AMR grids on the reservoir boundary.2D steam drive process with horizontal wells and SAGD process simulation show that the proposed AMR technique is fast with good accuracy. Adoption of the coarse grids rather than the fine grids in the boundary area, according to the AMR refinement criteria, does not reduce the accuracy of the simulations. The same method is applied to the3D simulation of groundwater heat pump system, and the AMR technique is still very successful.In summary, the object of this paper is to apply the AMR algorithm to the numerical simulation of steam thermal recovery process in complex petroleum reservoirs, and problems relevant to the AMR simulation are studied. The numerical results demonstrate that the AMR technique has a huge advantage in the calculation efficiency, and the accuracy is good compared with the fine grid solutions. We expect the AMR technique to have a practical help to the complex petroleum reservoir simulations in the future.