Parallel generalpurpose reservoir simulation with coupled. Using new unique multipoint flux approximation and full permeability tensor we compare two orientations of the fractures. Firstorder convergence of multipoint flux approximation on triangular grids and comparison with mixed finite element methods. A multipoint flux mixed finite element method siam journal. A method for history matching of an inhouse petroleum reservoir compositional simulator with multipoint flux approximation is presented. A novel flowbased geometrical upscaling method to represent. Introduction webster defines simulate as to assume the appearance of without reality. The twopoint flux approximation tpfa is used in commercial reservoir simulators due to its simplicity and the optimization of. Purchase mathematical models and finite elements for reservoir simulation, volume 17 1st edition. Accurate modelling of faults by multipoint, mimetic, and. A schematic diagram of this process is shown in figure 1. Introduction to reservoir simulation analytical and numerical.
Implementation and application of a hybrid multipoint flux approximation for reservoir simulation. Pdf finite volume methods with multipoint flux approximation. Siam journal on scientific computing siam society for. A cellcentered multipoint flux approximation method with. Numerical simulations show that our new schemes can be more accurate than the current fitted finite volume. The technique may be referred to as enriched multipoint flux approximation empfa and may be used to improve the consistency and accuracy in constructing pressure interpolations in cells for the purpose of determining flux equations used in predicting flow in a reservoir.
The numerical tests are conducted using the framework of the open source matlab reservoir simulation toolbox mrst. Carvalhoa cellcentered multipoint flux approximation method with a diamond stencil coupled with a higher order finite volume method for the simulation of oilwater displacements in heterogeneous and anisotropic petroleum reservoirs. An introduction to multipoint flux approximations for quadrilateral. All the descriptions and explanations are only for quadrilateral control volumes, with straightforward extension to unstructured grids. Empfa can be used for modeling general multiphase flows in 2dimensional or 3dimensional reservoir models, and the grid can be cartesian, voronoi, or even arbitrary. Only the omethod with surface midpoints as continuity points is discussed. Multipoint flux approximations via upscaling onepetro. The new feature of our fault modeling is the scalar fault transmissibility density tf. Finite volume methods with multipoint flux approximation.
An efficient numerical model for immiscible twophase flow in fractured karst reservoirs volume issue 2 zhaoqin huang, jun yao, yueying wang. The mpfa module implements one such method, the mpfao method. I the equations of reservoir simulation contain variables which have elliptic and hyperbolic character. Pebi, etc and discretization schemes based on twopoint flux approximations tpfa. Simulation results will demonstrate the differences among empfa, mpfa, and the original twopoint flux approximation tpfa. Global variable compact multipoint methods for accurate upscaling with fulltensor effects. Numerical simulation of natural gas flow in anisotropic. A dirichletneumann representation method dnr was recently proposed for upscaling and simulating flow in reservoirs. A method for automatic history matching of a compositional reservoir simulator with multipoint flux approximation. A dirichlet neumann representation method for simulating. New directions in pure, applied, and computational mathematics, 4559. Implementation of the multipoint flux approximation mpfao method for incompressible poissontype pressure equations.
Abstract multipoint flux approximations mpfas have been developed in recent years to improve the accuracy of the flux computation for reservoir simulation when the reservoir grids are not korthogonal. It is shown that the nonlinear twopoint flux approximation method is versatile and an equally good candidate compared to other established methods within reservoir simulation. The dnr method expresses coarse fluxes as linear functions of multiple. Routines supporting the mpfao method for the pressure equation. Controlvolume distributed multipoint flux approximation. Siam journal on scientific computing society for industrial. This paper addresses the key issue of calculating fluxes at the controlvolume interfaces when finitevolumes are employed for the solution of partial differential equations. Pdf a fitted multipoint flux approximation method for pricing. Interblock transmissibility calculation analysis for. Proceedings of the 8th international forum on reservoir simulation, iles borromees.
Ebfvm, unstructured meshes, compositional reservoir simulation, utcomp simulator 1. It works for general polygon meshes like the multipoint flux approximation. Applied mathematics reservoir simulation fluid dynamics. The standard mpfa is used as our first method and is coupled with a fitted finite volume in our second method to handle the degeneracy of the pde and the corresponding. The multipoint flux approximation mpfao scheme is developed to be consistent on grids that are not necessarily korthogonal.
A new multipoint flux approximation method with a quasilocal stencil mpfaql for the simulation of diffusion problems in anisotropic and heterogeneous media. In the last decade, multipoint flux approximations have been developed as a. Lukyanov and cornelis vuik abstract the reservoir simulation of the complex reservoirs with anisotropic permeability,which includes faults and nonorthogonalgrids, with a fully discontinuous permeability tensor in the discretization is a major challenge. I the simulations are performed on nonorthogonal rough grids.
A cellcentered multipoint flux approximation method with a diamond stencil coupled with a higher order finite volume method for the simulation of oilwater displacements in heterogeneous and. A new mixed finite element and its related finite volume. Global variable compact multipoint methods for accurate. Grid orientation effect and multipoint flux approximation. Opensource matlab implementation of consistent discretisations on complex grids. This paper gives an introduction to these methods for quadrilateral grids in two and three dimensions. G spatiallyvarying compact multipoint flux approximations for 3d adapted grids with guaranteed monotonicity. This method is used for the estimation of unknown reservoir parameters, such as permeability and. Lukyanov, adaptive fully implicit multiscale meshless multipoint flux method for fluid flow in heterogeneous porous media, in ecmor xiii conference proceedings 2012. Multipoint flux approximations mpfas have been developed in recent years to improve the accuracy of the flux computation for reservoir simulation when the reservoir grids are not korthogonal.
Presented at the spe reservoir simulation symposium, houston, texas. A new multipoint flux approximation for reservoir simulation. Fundamentals of numerical reservoir simulation, volume 6. Enriched multipoint flux approximation for general. The limitedmemory broydenfletchergoldfarbshanno method is employed for minimization of. Simulation results are presented and compared with results from other twopoint and multipoint flux approximations. However, it is sensitive to full permeability tensors on complex grids, and thus, as is, ineffective for the purpose it is intended. Meshless multipoint flux approximation springerlink. Abstract the reservoir simulation of the complex reservoirs with anisotropic permeability. Smooth basis and a nonorthodox multipoint flux approximation for the simulation of twophase flows on truly unstructured grids. Motivated by the multipoint flux approximation method where subedge fluxes are introduced, we consider the lowest order brezzidouglasmarini bdm mixed finite element method. A new multipoint flux approximation method with a quasi. Modelling and quantification of structural uncertainties in.
A compact multipoint flux approximation method with improved robustness. Upscaling for compositional reservoir simulation onepetro. The module implements the mpfao scheme, which is an example of a multipoint flux approximation scheme that employs more degrees of freedom when constructing the discrete fluxes across cell interfaces. A novel cellcentred controlvolume distributed multipoint flux approximation cvdmpfa finitevolume formulation is presented for discrete fracturematrix simulations in threedimensions. Introduction when solving problems on a geological structure, one of the challenges that confronts numerical methods is grid deformation. The upscaling of discrete fracture models for faster, coarsescale simulations of ior and eor. A threedimensional symmetric positive definite spd cellcentred controlvolume distributed multipoint flux approximation cvdmpfa is presented for porous media flow simulation on tetrahedral grids. A compact multipoint flux approximation method with improved. A fitted multipoint flux approximation method for pricing. Mohammad ahmadi, mike christie, margot gerritsen and hamid bazargan, new hybrid cartesian cut cellenriched multipoint flux approximation approach for modelling and quantification of structural uncertainties in petroleum reservoirs, international journal for numerical methods in fluids, 80, 3, 181228, 2015. The analysis of the multi point flux approximation mpfa method has so far relied on the possibility of seeing it as a mixed. A threedimensional symmetric positive definite control. Our new approach combines the simplicity and efficiency of the method introduced in.
In this paper, we develop novel numerical methods based on the multipoint flux approximation mpfa method to solve the degenerated partial differential equation pde arising from pricing twoassets options. Jul 25, 2006 siam journal on scientific computing 37. Grid orientation effect and multipoint flux approximation 3 in the above system, we denote by m the. A multipoint flux approximation finite volume scheme for two. Mathematical model computer codes numerical model physical model figure 1. Nov 12, 2009 the technique may be referred to as enriched multipoint flux approximation empfa and may be used to improve the consistency and accuracy in constructing pressure interpolations in cells for the purpose of determining flux equations used in predicting flow in a reservoir. The analysis of the multi point flux approximation mpfa. Modelling and quantification of structural uncertainties. The new technique has also practical advantage over other highaccuracy methods like. A multipoint flux approximation of the steadystate heat conduction. The results of the original formulation of the utcomp simulator using cartesian meshes are also presented. Mar 28, 2019 presented at the spe reservoir simulation symposium, houston, texas.
Siam journal on scientific computing volume 33, issue 2 10. Recent studies, however, have shown that commonly used mpfa approaches could pose severe limitations. Polygonal and polyhedral mesh, convergence, multipoint. The mpfa version discussed here is the socalled omethod on. Abstract pdf 8908 kb 2014 signpreserving of principal eigenfunctions in p1 finite element approximation of eigenvalue problems of secondorder elliptic operators.
Presented at the spe reservoir characterisation and simulation conference and exhibition, abu dhabi, uae. Recent studies, however, have shown that commonly used. Controlvolume discretizations using multipoint flux approximations mpfa were developed in the last decade. Pdf this paper addresses the key issue of calculating fluxes at the. Journal of petroleum science and engineering vol 188. The new space is compatible with a piecewise constant pressure discretization and yields a convergent discretization.
Finite volume methods with multipoint flux approximation with unstructured grids for diffusion problems. Simulation of petroleum reservoir performance refers to the construction and operation of a model whose behavior assumes the appearance of actual reservoir behavior. Presented at the spe reservoir characterisation and simulation conference and exhibition, abu dhabi, uae, 1618 september. The introduction is kept on a basic level, and a brief summary to more advanced results is given. Proceedings of the spe reservoir simulation conference, society. For cartesian grids, this is in fact the classical mpfa omethod. This article presents a convergence analysis of the multipoint flux approximation control volume method, mpfa, in two space dimensions.
Enriched multipoint flux approximation for general grids. The scheme is very accurate for smooth pressure fields. Discretizations using conservative approximation techniques applicable to reservoir simulation are well known. The use of numerical reservoir simulation with highspeed electronic computers has gained wide acceptance throughout the petroleum industry for making engineering studies of a wide variety of oil and gas reservoirs throughout the world. Jeannin, a multipoint flux approximation scheme for well modelling in reservoir simulations, in. We study a two phase porous media ow model where dynamic e ects are included in the capillary pressure. This example demonstrates the basic use of the mpfao pressure solver by applying it to a singlephase flow problem posed on a square 0,30x0,30 m2 with homogeneous and isotropic permeability. This calculation becomes even more significant when unstructured grids are used, since the flux approximation involving only two grid points is no longer correct. To get a consistent discretization for anisotropic permeablities and general polyhedral grids, multipoint flux approximation method use, as the name says, more than two points to approximate the flux across each intercell face.
Finite volume methods with multipoint flux approximation with unstructured grids for diffusion problems j. New methods for accurate upscaling with fulltensor effects. An efficient numerical model for immiscible twophase flow in. Spe reservoir simulation symposium 2007 february 2628, 2007 houston, texas, usa printed from emedia with permission by.
Two finite volume methods with the ability in dealing with unstructured grids, the ebfvmelementbased finite volume method and the mpfamultipoint flux approximation are presented, pointing out the way the fluxes are numerically evaluated. Numerical experiments for discontinuous permeability. A new multipoint flux approximation method with a quasilocal stencil mpfaql for the simulation of diffusion problems in anisotropic and heterogeneous media article feb 2019. A multipoint flux mixed finite element method siam. Enriched multipoint flux approximation cheng, qianyong. We present a nite volume method for the simulation of the solution. An efficient multipoint flux approximation method for discrete fracturematrix simulations. This method is used for the estimation of unknown reservoir parameters, such as permeability and porosity, based on production data and inverted seismic data. Two finite volume methods with the ability in dealing with. The method requires a global finescale compositional simulation, from which we compute the required upscaled parameters and functions associated with each coarsescale interface or well block.
A special quadrature rule is employed that allows for local velocity elimination and leads to a symmetric and positive definite cell. In this section, we present a new multipoint flux approximation, called enriched multipoint flux approximation. Mathematical models and finite elements for reservoir. The grid is aligned with the fractures and barriers which. In this paper we develop an accurate and robust upscaling procedure for compositional flow simulation. Multipoint flux approximation solvers for pressure. In reservoir simulation a lot of work goes into making geological models. The scheme performs well for grids with a high aspect ratios, such as are commonly used in reservoir simulators. If the pressure field is not smooth, improved accuracy can be achieved by local grid refinement. Reservoir simulation process reservoir simulation is briefly. Lukyanov, meshless multipoint flux approximation of fluid flow in porous media, in spe reservoir simulation symposium 2011, spe 2011, 141617 pp. A new multipoint flux approximation method with a quasilocal. Introduction one of the key issues in petroleum reservoir simulation is the correct representation of the irregular reservoir shape. Modelling and quantification of structural uncertainties in petroleum reservoirs assisted by a hybrid cartesian cut cellenriched multipoint flux approximation approach.
Spe reservoir simulation symposium 2007 proceedings. A compact multipoint flux approximation method with. Advanced discretization methods for flow simulation using. The application of a vertexbased quadrature rule reduces the new mixed finite element method to a multipoint flux control volume method. This work also presents a complete extension of the family of controlvolume dis tributed cvd multipoint flux approximation mpfa flux continuous schemes for general three dimensional grids. Meshless multipoint flux approximation alexander a. I aavatsmark, gt eigestad, bt mallison, jm nordbotten.
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