FINITE ELEMENT SIMULATIONS FOR COMPRESSIBLE MISCIBLE DISPLACEMENT WITH MOLECULAR DISPERSION IN POROUS MEDIA

We consider a nonlinear parabolic system describing compressible miscibledisplacement in a porous medium [5]. Continuous time and discrete time Galerkinmethods are introduced to approximate the solution and optimal H^1 error estimatesare obtained. One contribution of this paper is a demonstration of how moleculardispersion can be handled.

A MIXED FINITE ELEMENT AND CHARACTERISTIC MIXED FINITE ELEMENT FOR INCOMPRESSIBLE MISCIBLE DARCY-FORCHHEIMER DISPLACEMENT AND NUMERICAL ANALYSIS

In this paper a mixed finite element-characteristic mixed finite element method is discussed to simulate an incompressible miscible Darcy-Forchheimer problem.The flow equation is solved by a mixed finite element and the approximation accuracy of Darch-Forchheimer velocity is improved one order.The concentration equation is solved by the method of mixed finite element,where the convection is discretized along the characteristic direction and the diffusion is discretized by the zero-order mixed finite element method.The characteristics can confirm strong stability at sharp fronts and avoids numerical dispersion and nonphysical oscillation.In actual computations the characteristics adopts a large time step without any loss of accuracy.The scalar unknowns and its adjoint vector function are obtained simultaneously and the law of mass conservation holds in every element by the zero-order mixed finite element discretization of diffusion flux.In order to derive the optimal 3/2-order error estimate in L^(2) norm,a post-processing technique is included in the approximation to the scalar unknowns.Numerical experiments are illustrated finally to validate theoretical analysis and efficiency.This method can be used to solve such an important problem.

FINITE ELEMENT METHOD FOR INCOMPRESSIBLE MISCIBLE DISPLACEMENT IN POROUS MEDIA

Under the assumptions of nonlinear finite element and △t=o(h),Ewing and Wheeler discussed a Galerkin method for the single phase incompressible miscible displacement of one fluid by another in porous media.In the present paper we give a finite element scheme which weakens the △t=o(h)-restriction to △t=o(h~ε),0<ε≤1/2.Furthermore,this scheme is suitable for both linear element and nonlinear element.We also derive the optimal approximation estimates for concentration c,its gradient ▽c and the gradient ▽p of the pressure p.

A CHARACTERISTIC MIXED FINITE ELEMENT TWO-GRID METHOD FOR COMPRESSIBLE MISCIBLE DISPLACEMENT PROBLEM

A nonlinear parabolic system is derived to describe compressible miscible displacement in a porous medium.The concentration equation is treated by a mixed finite element method with characteristics(CMFEM)and the pressure equation is treated by a parabolic mixed finite element method(PMFEM).Two-grid algorithm is considered to linearize nonlinear coupled system of two parabolic partial differential equations.Moreover,the L q error estimates are conducted for the pressure,Darcy velocity and concentration variables in the two-grid solutions.Both theoretical analysis and numerical experiments are presented to show that the two-grid algorithm is very effective.

ON THE APPROXIMATION OF INCOMPRESSIBLE MISCIBLE DISPLACEMENT PROBLEMS IN POROUS MEDIA BY MIXED AND STANDARD FINITE VOLUME ELEMENT METHODS

The incompressible miscible displacement problem in porous media is modeled by a coupled system of two nonlinear partial differential equations,the pressure–velocity equation and the concentration equation.In this paper,we present a mixed finite volume element method(FVEM)for the approximation of the pressure–velocity equation and a standard FVEM for the concentration equation.A priori error estimates in L^(∞)(L^(2))are derived for velocity,pressure and concentration.Numerical results are presented to substantiate the validity of the theoretical results.

A Posteriori Error Estimates of a Combined Mixed Finite Element and Discontinuous Galerkin Method for a Kind of Compressible Miscible Displacement Problems

Akind of compressiblemiscible displacement problemswhich includemolecular diffusion and dispersion in porous media are investigated.The mixed finite element method is applied to the flow equation,and the transport one is solved by the symmetric interior penalty discontinuous Galerkin method.Based on a duality argument,employing projection estimates and approximation properties,a posteriori residual-type hp error estimates for the coupled system are presented,which is often used for guiding adaptivity.Comparing with the error analysis carried out by Yang(Int.J.Numer.Meth.Fluids,65(7)(2011),pp.781-797),the current work is more complicated and challenging.

CO_(2)storage with enhanced gas recovery(CSEGR):A review of experimental and numerical studies

CO_(2)emission mitigation is one of the most critical research frontiers.As a promising option of carbon capture,utilization and storage(CCUS),CO_(2)storage with enhanced gas recovery(CSEGR)can reduce CO_(2)emission by sequestrating it into gas reservoirs and simultaneously enhance natural gas production.Over the past decades,the displacement behaviour of CO_(2)—natural gas has been extensively studied and demonstrated to play a key role on both CO_(2)geologic storage and gas recovery performance.This work thoroughly and critically reviews the experimental and numerical simulation studies of CO_(2)displacing natural gas,along with both CSEGR research and demonstration projects at various scales.The physical property difference between CO_(2)and natural gas,especially density and viscosity,lays the foundation of CSEGR.Previous experiments on displacement behaviour and dispersion characteristics of CO_(2)/natural gas revealed the fundamental mixing characteristics in porous media,which is one key factor of gas recovery efficiency and warrants further study.Preliminary numerical simulations demonstrated that it is technically and economically feasible to apply CSEGR in depleted gas reservoirs.However,CO_(2)preferential flow pathways are easy to form(due to reservoir heterogeneity)and thus adversely compromise CSEGR performance.This preferential flow can be slowed down by connate or injected water.Additionally,the optimization of CO_(2)injection strategies is essential for improving gas recovery and CO_(2)storage,which needs further study.The successful K12—B pilot project provides insightful field-scale knowledge and experience,which paves a good foundation for commercial application.More experiments,simulations,research and demonstration projects are needed to facilitate the maturation of the CSEGR technology.