Study On The Transfer Flow Function In Dual-porosity Model For The Spontaneous Imbibition Flow And The Pressure Displacement Flow

Numerical reservoir simulation is an important technique in petroleum and natural gas industry.In the numerical reservoir simulation,suitable mathematical models are constructed and then solved numerically according to the different reservoir conditions and flow mechanisms,to study the physical phenomenon during the reservoir development.For naturally fractured reservoir,the connected fractures are the main flow channels due to their high permeabilities.However,the matrix,often of low permeability,provides most storage space for oil or gas.The dual porosity model has been widely used to describe naturally fractured reservoirs for several decades,in which the fracture and the matrix are idealized as two dynamically interacting continuous medium.At each point in space,two fluid pressures-fluid pressure in matrix and in fracture are defined respectively.In the dual porosity model,how to determine the transfer flow between matrix and fracture is crucial.This is obvious because the oil or gas stored in matrix first flow into the fractures,and then into wellbores through these high conductive fracture paths.The traditional matrix-fracture transfer flow function was proposed as proportional to the difference of the local matrix and fracture pressure,which was based on the assumption of slightly compressible flow and the description of the release of reservoir elastic energy.Different values of the proportional coefficient in the transfer flow function,which is called the shape factor,were proposed by many scholars according to different reservoir conditions.However,to the best of our knowledge,the existing transfer flow functions are not suitable for two cases.One case is for the incompressible flow in high permeability reservoirs,where the transfer flow is mainly dominated by the phase displacement.In this situation,the traditional transfer function predicts no transfer flow between matrix and fracture,and this is obviously incorrect.The other case is for the low permeability reservoirs with high capillary pressure in matrix.In this situation,the matrix-fracture transfer flow is dominated by spontaneous imbibition due to the strong capillary difference between matrix and fracture.The traditional transfer flow functions are tested for these two cases in this thesis,and numerical results show that it results in significant errors compared to the reference solution.In order to improve the simulation accuracy,new matrix-fracture transfer flow functions are proposed respectively for these two cases.For one dimensional spontaneous imbibition process,its solution can be described as two stages:the early stage self-similar analytical solution and the late stage approximate analytical solution.In this thesis,the approximate analytical solution of the spontaneous imbibition process under different boundary conditions is studied for two-dimensional rectangular matrix block.The two-dimensional imbibition problem is equivalent to one-dimensional with the help of the defined characteristic length,so that the matrix-fracture transfer flow function can be constructed according to the approximate one-dimensional analytic solution.A new mixed characteristic length is proposed,where the early stage characteristic length is given by the ratio of the area of rock block to the length of open boundary,and the late stage characteristic length is given by the interpolation of the early stage characteristic length and Ma’s characteristic length.The performance of the proposed mixed characteristic length is compared with other existing ones.Numerical tests show that the overall performance of the proposed mixed characteristic length is better than the other existing ones,and it is suitable for all the boundary conditions listed in this thesis.By this means,the matrix-fracture transfer flow function for the spontaneous imbibition process in two dimensional case is constructed.For the incompressible flow in high permeability reservoirs,the original matrix-fracture transfer flow function does not consider the displacement effect of the multiphase flow.To improve this,a modified transfer flow function is proposed,in which the displacement effect is considered and the phase transfer flow rate is related to the local pressure gradient.The shape factor of this modified transfer flow function is also derived.For the anisotropic case,the shape factor of displacement depends upon the filtration velocity direction.Several numerical tests on different simulation domains are performed including square and rectangular reservoirs and reservoirs with wells located in,and the accuracy and the efficiency of the proposed transfer flow function are indicated.In summary,two new matrix-fracture transfer flow functions for the dual porosity model are proposed in the thesis.One is for the case of the incompressible flow in high permeability reservoirs where the matrix-fracture transfer flow is dominated by the displacement under the local pressure gradient.The other is for the case of the two dimensional low permeability reservoirs with high capillary pressure in matrix,where the matrix-fracture transfer flow is dominated by spontaneous imbibition process.The accuracy and the efficiency of the proposed two transfer flow functions are indicated by numerical tests.