In this work we consider coupled-parallel flow through a finite channel bounded below by a porous layer that is either finite or infinite in depth. The porous layer is one in which Darcy’s equation is valid under the...In this work we consider coupled-parallel flow through a finite channel bounded below by a porous layer that is either finite or infinite in depth. The porous layer is one in which Darcy’s equation is valid under the assumption of variable permeability. A suitable permeability stratification function is derived in this work and the resulting variable velocity profile is analyzed. It will be shown that when an infinite porous layer is implemented, Darcy’s equation must be used with a constant permeability.展开更多
Permeability is an important index in reservoir evaluation,oil and gas accumulation control,and production effi ciency.At present,permeability can be obtained through several methods.However,these methods are not suit...Permeability is an important index in reservoir evaluation,oil and gas accumulation control,and production effi ciency.At present,permeability can be obtained through several methods.However,these methods are not suitable for tight sandstone in general because the pore type in tight sandstone is mainly secondary pores and has the characteristics of low porosity and permeability,high capillary pressure,and high irreducible water saturation.Mud invasion depth is closely related to permeability during drilling.In general,the greater the permeability,the shallower the mud invasion depth,and the smaller the permeability,the deeper the mud invasion depth.Therefore,this paper builds a model to predict the permeability of tight sandstone using mud invasion depth.The model is based on the improvement of the Darcy flow equation to obtain permeability using mud invasion depth inversion of array induction logging.The influence of various permeability factors on the model is analyzed by numerical simulation.The model is used to predict the permeability of tight sandstone in the south of the Ordos Basin.The predicted permeability is highly consistent with the core analysis permeability,which verifi es the reliability of the method.展开更多
In this report,we give a viscosity splitting method for the Navier-Stokes/Darcy problem.In this method,the Navier-Stokes/Darcy equation is solved in three steps.In the first step,an explicit/implicit formulation is us...In this report,we give a viscosity splitting method for the Navier-Stokes/Darcy problem.In this method,the Navier-Stokes/Darcy equation is solved in three steps.In the first step,an explicit/implicit formulation is used to solve the nonlinear problem.We introduce an artificial diffusion term qDu in our scheme whose purpose is to enlarge the time stepping and enhance numerical stability,especially for small viscosity parameter n,by choosing suitable parameter q.In the second step,we solve the Stokes equation for velocity and pressure.In the third step,we solve the Darcy equation for the piezometric head in the porous media domain.We use the numerical solutions at last time level to give the interface condition to decouple the Navier-Stokes equation and the Darcy’s equation.The stability analysis,under some condition △t≤k0,k0>0,is given.The error estimates prove our method has an optimal convergence rates.Finally,some numerical results are presented to show the performance of our algorithm.展开更多
文摘In this work we consider coupled-parallel flow through a finite channel bounded below by a porous layer that is either finite or infinite in depth. The porous layer is one in which Darcy’s equation is valid under the assumption of variable permeability. A suitable permeability stratification function is derived in this work and the resulting variable velocity profile is analyzed. It will be shown that when an infinite porous layer is implemented, Darcy’s equation must be used with a constant permeability.
基金supported by the National Natural Science Foundation of China project(No.41504103 and No.41804097).
文摘Permeability is an important index in reservoir evaluation,oil and gas accumulation control,and production effi ciency.At present,permeability can be obtained through several methods.However,these methods are not suitable for tight sandstone in general because the pore type in tight sandstone is mainly secondary pores and has the characteristics of low porosity and permeability,high capillary pressure,and high irreducible water saturation.Mud invasion depth is closely related to permeability during drilling.In general,the greater the permeability,the shallower the mud invasion depth,and the smaller the permeability,the deeper the mud invasion depth.Therefore,this paper builds a model to predict the permeability of tight sandstone using mud invasion depth.The model is based on the improvement of the Darcy flow equation to obtain permeability using mud invasion depth inversion of array induction logging.The influence of various permeability factors on the model is analyzed by numerical simulation.The model is used to predict the permeability of tight sandstone in the south of the Ordos Basin.The predicted permeability is highly consistent with the core analysis permeability,which verifi es the reliability of the method.
文摘In this report,we give a viscosity splitting method for the Navier-Stokes/Darcy problem.In this method,the Navier-Stokes/Darcy equation is solved in three steps.In the first step,an explicit/implicit formulation is used to solve the nonlinear problem.We introduce an artificial diffusion term qDu in our scheme whose purpose is to enlarge the time stepping and enhance numerical stability,especially for small viscosity parameter n,by choosing suitable parameter q.In the second step,we solve the Stokes equation for velocity and pressure.In the third step,we solve the Darcy equation for the piezometric head in the porous media domain.We use the numerical solutions at last time level to give the interface condition to decouple the Navier-Stokes equation and the Darcy’s equation.The stability analysis,under some condition △t≤k0,k0>0,is given.The error estimates prove our method has an optimal convergence rates.Finally,some numerical results are presented to show the performance of our algorithm.
