The Study And Application Of MPFA Algorithm Based On Unstructured Hexahedral Grid System

The numerical simulation of fractured reservoir based on the unstructured hexahedral grid system is a great challenge and research hotpot in the area of reservoir numerical simulation. This topic and the main research contents of this thesis is one of the scientific issues in the National Natural Science Foundation of China-"Numerical simulation research in fractured reservoir based on unstructured hexahedron grid model and parallel calculation"Generally unstructured grids can represent the complexity of real geological formations more accurately and efficiently compared with structured grids. The great potential of unstructured grids comes with many challenges including (1) the discretizing of the fractured porous media; (2) Improvement of numerical calculation efficiency based on the grid system; and (3) the more efficient discretization of governing equations as to the full property tensor and unstructured grid system. The purpose of this thesis is to establish a set of numerical simulation theory and approach aiming at the fractured porous media hybrid grid model. The discretizing approach of the fractured reservoir and discretization method of the governing equations based on the unstructured grid system and MPFA algorithm are particularly analyzed. The main research contents and findings of this thesis is as follows:1. The unstructured quadrilateral grid system is established using front advanced Paving method, then connecting the neighboring layers the unstructured hexahedral grid model can be established. However there is difference of the grid size between the fracture grid size (mm or cm) and the matrix grid size (Dozens or even hundreds of meters) with several orders of magnitude, which make the large amount of extremely small grids generated in the transition section when expanded from fracture grids to matrix grids, the line fracture concept is used to decrease the extremely small grids generated when grids expanding from the fracture to matrix, while the fracture parameters are assigned in the line. This approach can solve the convergence problem when solving the large linear matrix equations on the premise of representing all the fracture parameters. Moreover this approach has obtained the authorized patent "a method to numerically measure the flow conditions of reservoir using line fracture concept"2. As to the TPFA method-Two Point Flux Approximation is unsuitable for the equation discretization based on the unstructured grid system and cannot handle the full permeability tensor, the MPFA algorithm-Multi-Point Flux Approximation is presented to discrete the flow equations. Due to the transmissibility calculation for contact faces involves six grids in two dimension and 27 grids in three dimension, it can solve the problems for TPFA method above, while improves the accuracy in numerical calculation. Take governing equations model for water-oil two phases, the standard control volume MPFA method is used for Matrix-Matrix flow, and the revised MPFA method to calculate the transmissibility for Fracture-Matrix and Fracture-Fracture flow through establishing the Matrix-Fracture hybrid virtual interactive grids, this ensure the calculation accuracy for Fracture-Matrix and Fracture-Fracture flow.3. The oil-water two phase flow mathematical model for the Matrix, Fracture and Matrix-Fracture cross flow is established separately firstly, then the control volume for MPFA method is partitioned on the unstructured quadrilateral grid system meshed by Paving method, and for every control volume integrate the flow mathematical model to establish the numerical calculation model of Control Volume-MPFA method. So the fractured reservoir oil-water two phase flow using fractured porous media hybrid grid model based on the unstructured hexahedral grid system can be realized finally.4. The correctness and high computational efficiency of discrete fracture model based on Control Volume-MPFA method flow simulation theory is verified through examples. The results show that numerical calculation results of fractured hybrid model based on control volume method shows a good agreement with single porosity media model, but the discrete fracture network has higher computational efficiency. The comparison and analysis of series flow models shows the MPFA has better accuracy and efficiency compared with conventional TPFA method when describing the Heterogeneous anisotropic reservoir due to the calculation evolves more neighboring grids. Combined with the research subject-Futai block in Shengli oilfield of National 12th Five-Year major project-"the numerical simulation research of complex well in Shengli oilfield", the theory and approach based on the fractured porous media hybrid grid modle is applied to simulate its flow, which further verifies the practicability of this set of theory.