Mbedded Discrete Fracture Model For Numerical Simulation In Low Permeability Reservoir

Artificial fracturing technology is one of the important approaches to increase oil production, and it has been widely used in oil recovery from low permeability reservoir. In order to accurately estimate the effects of fractures and to optimize the oil production, a fracture model is necessary in the reservoir simulators. Currently, discrete fracture model (DFM) and embedded discrete fracture model (EFM) are the primary models for reservoir simulations with fracture. In the DFM, considering aperture is much smaller than the scale of matrix, fractures are described as (N-1) dimensional elements in an N-dimensional system. The exchange flux between the fracture and the two sides of a matrix, can be calculated conveniently using Darcy’s law by coupling the matrix and fracture equations. To simplify the grid structure, the EFM applies structured grids for matrix with fractures overlaying on the matrix grid blocks. Analogous to the Peaceman’s well model, the concept of wellbore productive index was applied to derive a transport index to describe the coupling between fracture and matrix blocks. For single-phase flow, the difference between the two models is related to the ratio of the grid size and the reservoir. Since the computing grids are much smaller than the reservoir, the two models have good agreement with each other. However, for the multiphase flow in the fractured reservoir, the EFM ignores the discontinuity of saturation caused by the distinction between fracture and matrix, and hence its accuracy is lower than the DFM.Combining the advantages of DFM, a modified algorithm for the embedded discrete fracture model is proposed. In this algorithm, structured grids are applied to the whole reservoir, which are independent with the distribution of fracture. For the reservoir with complex fracture, it can greatly reduce the complexity in meshing, and improve the efficiency of simulation. The exchange rate between fracture and matrix on two sides of the interface are calculated separately, and can accurately describe the discontinuity of saturation. To deal with the problem for defining the physical variables on the matrix grid blocks overlaid by the fracture, these matrix grid blocks do not participate in the practical computations and only provide the Neumann boundary conditions during the calculations of other matrix grid blocks.For applying to the actual fractured reservoir, the proposed algorithm is extended to cross fractures and fracture network, and the multiphase flows are corrected in fracture and matrix respectively near the cross nodes. Inside the fracture, the equivalent conductivities calculated by the analogy with the electric current are used to directly define the flows between fracture grids nearby, so as to avoid the simulation of fracture cross nodes and increase the computational time step. For the matrix grid overlaid multi-fractures, the pressure in the matrix is calculated from the interpolation of the fracture independently. And the saturations are calculated from the simultaneous mass conservations in the matrix area near fracture.The matrix has a strong capillary force, while the capillary in fracture is very weak. Therefore, as the fluid passes through the matrix-fracture interface, the difference of capillary force in the two media would have different effects upon the water and oil. The matrix capillary force would make oil difficult to flow out of the fracture, and reduce the transport of components nearby. The numerical examples show that the simulation results of the proposed algorithm agree very well with the DFM, while in low capillary reservoir the EFM have some differences compared with the other two methods. Meanwhile, with the increase of capillary force, the difference would gradually decreases. The grid resolution has a subtle influence upon the accuracy of numerical simulations, which is also effected from the capillary force. The matrix capillary pressure will make the matrix saturation gradients diverge at the matrix-fracture interface. It causes that the matrix grids should be refined enough in the neighborhood of the matrix-fracture interface to achieve high numerical accuracy. When ignoring the matrix capillary pressures, the matrix grid resolution needs less refined in the neighborhood of the matrix-fracture interface because the physical quantities in matrix medium are unilaterally continuous on each side of the matrix-fracture interface.In summary, this dissertation presents the study of conductive fracture model for low permeability reservoir, in which a modified algorithm is proposed and promoted to the fracture network. Since the grid meshing is independent with the distribution of fracture, it has high efficiency for the simulation of complex fractures. Also, with the respective definition of exchange rate on each side of matrix, the proposed algorithm has the same accuracy of the DFM. Therefore, this algorithm can be applied in the simulation of artificial fracturing reservoir. In addition, the effect of capillary force in fracture simulation is studied. With the analysis of the flow field at the fracture-matrix interface, it is found that with the capillary force in matrix, the saturation gradients diverge would be infinite close to the interface, and need refined grids to be accurately described.