Productivity simulation of hydraulically fractured wells based on hybrid local grid refinement and embedded discrete fracture model

Using current Embedded Discrete Fracture Models(EDFM) to predict the productivity of fractured wells has some drawbacks, such as not supporting corner grid, low precision in the near wellbore zone, and disregarding the heterogeneity of conductivity brought by non-uniform sand concentration. An EDFM is developed based on the corner grid, which enables high efficient calculation of the transmissibility between the embedded fractures and matrix grids, and calculation of the permeability of each polygon in the embedded fractures by the lattice data of the artificial fracture aperture. On this basis, a coupling method of local grid refinement(LGR) and embedded discrete fracture model is designed, which is verified by comparing the calculation results with the Discrete Fracture Network(DFN) method and fitting the actual production data of the first hydraulically fractured well in Iraq. By using this method and orthogonal experimental design, the optimization of the parameters of the first multi-stage fractured horizontal well in the same block is completed. The results show the proposed method has theoretical and practical significance for improving the adaptability of EDFM and the accuracy of productivity prediction of fractured wells, and enables the coupling of fracture modeling and numerical productivity simulation at reservoir scale.

Local grid refinement in multigrid method for point contact problems of polycrystalline anisotropic material under dry and lubricated conditions

Predicting rolling bearing fatigue life requires knowledge of the three-dimensional(3D)stress fields in the roller and raceway near the lubricated contact.Owing to the increasingly severe operating conditions,the effect of localized features such as surface roughness,subsurface inclusions,and even the crystallographic structure of the material becomes important.Achieving such detail requires(locally)extremely dense gridding in simulations,which in 3D is a major challenge.Multigrid techniques have been demonstrated to be capable of solving such problems.In this study,multigrid techniques are shown to further increase the efficiency of the solution by exploiting local grid refinement while maintaining the simplicity of a uniform discretization.This is achieved by employing increasingly finer grids only locally,where the highest resolution is required.Results are presented for dry contact and elastohydrodynamically lubricated contact cases,circular as well as elliptic,with varying crystallographic structure,and with surface roughness.The results show that the developed algorithm is very well suited for detailed analysis,with also excellent prospects for computational diagnostics involving actual material crystallographic structure from electron backscatter diffraction measurements.

Zonal Embedded Grids for LES of Self-Sustaining Structures of Wall Turbulence

In this study,a zonal grid refinement method based on the solution of weakly compressible flow equations with large eddy simulation in the finite volume method（FVM） and dynamic subgrid-scale model framework was used to simulate the turbulence structures of a plane-wall flow with Reynolds number Re=U0δ /ν =10 000.Comparison and analysis were conducted on the distributions of time-averaged velocity and velocity fluctuations,as well as on the actual near-wall structures,to verify the accuracy of the turbulence features that were simulated using the zonal grid refinement method.The results show that the zonal embedded grid is a very efficient way to illustrate the turbulence structures of the near-wall region.The present method is easy to implement and extend to small Mach number flow modeling on a collocated irregular FVM mesh system.

Stability Analysis of a Fully Coupled Implicit Scheme for Inviscid Chemical Non-Equilibrium Flows

Von Neumann stability theory is applied to analyze the stability of a fully coupled implicit(FCI)scheme based on the lower-upper symmetric Gauss-Seidel(LUSGS)method for inviscid chemical non-equilibrium flows.The FCI scheme shows excellent stability except the case of the flows involving strong recombination reactions,and can weaken or even eliminate the instability resulting from the stiffness problem,which occurs in the subsonic high-temperature region of the hypersonic flow field.In addition,when the full Jacobian of chemical source term is diagonalized,the stability of the FCI scheme relies heavily on the flow conditions.Especially in the case of high temperature and subsonic state,the CFL number satisfying the stability is very small.Moreover,we also consider the effect of the space step,and demonstrate that the stability of the FCI scheme with the diagonalized Jacobian can be improved by reducing the space step.Therefore,we propose an improved method on the grid distribution according to the flow conditions.Numerical tests validate sufficiently the foregoing analyses.Based on the improved grid,the CFL number can be quickly ramped up to large values for convergence acceleration.

Numerical Entropy andAdaptivity for FiniteVolume Schemes

We propose an a-posteriori error/smoothness indicator for standard semidiscrete finite volume schemes for systems of conservation laws,based on the numerical production of entropy.This idea extends previous work by the first author limited to central finite volume schemes on staggered grids.We prove that the indicator converges to zero with the same rate of the error of the underlying numerical scheme on smooth flows under grid refinement.We construct and test an adaptive scheme for systems of equations in which the mesh is driven by the entropy indicator.The adaptive scheme uses a single nonuniform grid with a variable timestep.We show how to implement a second order scheme on such a space-time non uniform grid,preserving accuracy and conservation properties.We also give an example of a p-adaptive strategy.