Study On Efficient Numerical Simulation Algorithm For Heterogeneous Reservoir

Strong heterogeneity in reservoir not only has a significant effect on reservoir development,but also causes great difficulties in numerical simulation.At first,the algorithm of calculating the cross-interface flow in multidimensional problems has a great influence on the accuracy of the numerical scheme.Traditional algorithms have large errors due to the strong heterogeneity,so how to establish a high accuracy discrete scheme is particularly important.Secondly,millions or even tens of millions grids are usually used to describe the heterogeneous reservoirs.Multi-grid method,such as adaptive mesh refinement method,is commonly used in numerical simulation to reduce the number of grids and improve the computational efficiency.For specially distributed permeability field of the reservoir,the proper grid refinement criterion need to be found in order to meet the demand of calculation accuracy and computational efficiency.In reservoirs with large number of frequency-switching wells,the physical quantities in the simulated area change drastically.Correspondingly,the computational efficiency will decrease and the required memory will increase also dramatically.Improving the relative numerical schemes to make them suitable for stand-alone computer with limited storage,has great value of practical application in engineering.To study these problems,the following three aspects are included in the dissertation:1.Finite analytic method has been established for 3D single-phase steady flow with permeability in tensor form.It is found that the 3D flow characters quasi-two-dimensional behavior in the vicinity of the common edge of the adjacent grids.That is,the pressure gradient in a plane normal to the edge joining different permeability regions will tend to infinite as approaching the edge according to a typical power-law solution and the tangential derivate of the pressure along the edge must be of limited value due to the pressure continuity.Then a quasi-2D assumption is proposed,and based on this,an approximate local analytical solution can be obtained.Furthermore,the finite analytic method has been established by using control volume method.Numerical examples show that the proposed numerical scheme can provide rather accurate solutions only with few subdivisions of the original meshes.More important,the convergent speed is independent of the permeability anisotropy,rotation of coordinate axis and the strength of heterogeneity.On the contrary,the traditional algorithm usually needs very refined subdivisions to get accurate solution and the convergent speed is very slow for strong heterogeneous porous medium.2.Adaptive mesh refinement method(AMR)for reservoirs with argillaceous interlayer or rhythm is studied.For reservoirs with argillaceous interlayer,considering the complexity of their spatial distribution,a method for calculating grid permeability is established for the two most basic type of grids including argillaceous interlayer.After this handling,it can be seemed as a normal heterogeneous reservoir so that the traditional AMR method can be applied.A number of examples show that compared with the results of full-fine meshes,AMR method has high accuracy in this case,and the computational efficiency has been greatly improved,which is about 6-7 times higher than using the full-fine meshes.For rhythm reservoirs,by defining the average permeability of the corner-point grids in the layer,a new mesh coarsening criterion considering the permeability distribution is introduced.And the new criterion can compensate for the loss of geological information caused by by the criterion only consideringto the physical quantity of the fluid.Numerical examples show that the AMR method with the new proposed criterion has higher calculation accuracy.3.An improved numerical solver has been proposed in this dissertation which is suitablefor two-phase oil-water flow with ten million girds on stand-alone computer.The sequential solution method is used to decouple the two-phase mass conservation equations into the corresponding pressure equation and saturation equation,which can be both solved alone.For the pressure equation,in order to reduce the amount of data storage in the solving process,it is decomposed into three parts according to the different directions using an alternating direction implicit method(ADI).The iterative parameters are analyzed and modified to suit the heterogeneous reservoir in practical case.The OpenMP parallel algorithm is used to improve the computational efficiency.For the saturation equation,a topological sorting method is used which realizes a direct solving from upstream to downstream along the flow direction.The examples show that the modified numerical solver achieves a simulation of 10 million grids regardless in regular area or in irregular area.Compared with the traditional algorithm,the maximum number of the meshes that a stand-alone computer can afford has been greatly improved,and it also has a high calculation efficiency.In summary,this dissertation has studied several key problems in the numerical simulation in heterogeneous reservoirs,and the corresponding new schemes have been proposed.The use of these algorithms improves greatly the calculation accuracy,efficiency and the maximum number of the meshes.They have important significance in the study of heterogeneous reservoirs.