The twopoint flux approximation tpfa is used in commercial reservoir simulators due to its simplicity and the optimization of. Using new unique multipoint flux approximation and full permeability tensor we compare two orientations of the fractures. An efficient numerical model for immiscible twophase flow in. G spatiallyvarying compact multipoint flux approximations for 3d adapted grids with guaranteed monotonicity. Presented at the spe reservoir characterisation and simulation conference and exhibition, abu dhabi, uae. The analysis of the multi point flux approximation mpfa method has so far relied on the possibility of seeing it as a mixed. Global variable compact multipoint methods for accurate upscaling with fulltensor effects. Lukyanov, meshless multipoint flux approximation of fluid flow in porous media, in spe reservoir simulation symposium 2011, spe 2011, 141617 pp. Advanced discretization methods for flow simulation using. 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. Enriched multipoint flux approximation for general. A multipoint flux approximation of the steadystate heat conduction. A compact multipoint flux approximation method with.
A dirichletneumann representation method dnr was recently proposed for upscaling and simulating flow in reservoirs. Our new approach combines the simplicity and efficiency of the method introduced in. Abstract the reservoir simulation of the complex reservoirs with anisotropic permeability. Recent studies, however, have shown that commonly used. Finite volume methods with multipoint flux approximation with unstructured grids for diffusion problems. Meshless multipoint flux approximation springerlink. 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.
This method is used for the estimation of unknown reservoir parameters, such as permeability and. Pdf finite volume methods with multipoint flux approximation. In reservoir simulation a lot of work goes into making geological models. Multipoint flux approximations via upscaling onepetro. 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. Recent studies, however, have shown that commonly used mpfa approaches could pose severe limitations. Faults can either act as conduits for fluid flow in subsurface reservoirs or create flow barriers. Journal of petroleum science and engineering vol 188. Two finite volume methods with the ability in dealing with. Modelling and quantification of structural uncertainties in. Smooth basis and a nonorthodox multipoint flux approximation for the simulation of twophase flows on truly unstructured grids. However, it is sensitive to full permeability tensors on complex grids, and thus, as is, ineffective for the purpose it is intended.
The results of the original formulation of the utcomp simulator using cartesian meshes are also presented. Grid orientation effect and multipoint flux approximation 3 in the above system, we denote by m the. Lukyanov, adaptive fully implicit multiscale meshless multipoint flux method for fluid flow in heterogeneous porous media, in ecmor xiii conference proceedings 2012. Introduction webster defines simulate as to assume the appearance of without reality. Siam journal on scientific computing volume 33, issue 2 10. This paper addresses the key issue of calculating fluxes at the controlvolume interfaces when finitevolumes are employed for the solution of partial differential equations. Hybriddimensional finite volume discretizations for. Jeannin, a multipoint flux approximation scheme for well modelling in reservoir simulations, in. Modelling and quantification of structural uncertainties in petroleum reservoirs assisted by a hybrid cartesian cut cellenriched multipoint flux approximation approach. 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 threedimensional symmetric positive definite spd cellcentred controlvolume distributed multipoint flux approximation cvdmpfa is presented for porous media flow simulation on tetrahedral grids. A novel cellcentred controlvolume distributed multipoint flux approximation cvdmpfa finitevolume formulation is presented for discrete fracturematrix simulations in threedimensions. I the simulations are performed on nonorthogonal rough grids.
Simulation of petroleum reservoir performance refers to the construction and operation of a model whose behavior assumes the appearance of actual reservoir behavior. A multipoint flux mixed finite element method siam. Introduction to reservoir simulation analytical and numerical. The new feature of our fault modeling is the scalar fault transmissibility density tf. The dnr method expresses coarse fluxes as linear functions of multiple. Numerical simulation of natural gas flow in anisotropic. Simulation results will demonstrate the differences among empfa, mpfa, and the original twopoint flux approximation tpfa. Enriched multipoint flux approximation cheng, qianyong.
New methods for accurate upscaling with fulltensor effects. In the last decade, multipoint flux approximations have been developed as a. Implementation of the multipoint flux approximation mpfao method for incompressible poissontype pressure equations. Pdf a fitted multipoint flux approximation method for pricing. I the equations of reservoir simulation contain variables which have elliptic and hyperbolic character. Motivated by the multipoint flux approximation method where subedge fluxes are introduced, we consider the lowest order brezzidouglasmarini bdm mixed finite element method. This paper gives an introduction to these methods for quadrilateral grids in two and three dimensions. Grid orientation effect and multipoint flux approximation.
The limitedmemory broydenfletchergoldfarbshanno method is employed for minimization of. The mpfa module implements one such method, the mpfao method. The grid is aligned with the fractures and barriers which. Modelling and quantification of structural uncertainties. A compact multipoint flux approximation method with improved robustness. A compact multipoint flux approximation method with improved. The multipoint flux approximation mpfao scheme is developed to be consistent on grids that are not necessarily korthogonal.
This calculation becomes even more significant when unstructured grids are used, since the flux approximation involving only two grid points is no longer correct. 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. A method for automatic history matching of a compositional reservoir simulator with multipoint flux approximation. A new multipoint flux approximation method with a quasi. Siam journal on scientific computing siam society for. The scheme is very accurate for smooth pressure fields. Opensource matlab implementation of consistent discretisations on complex 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. 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. 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. A multipoint flux approximation finite volume scheme for two. 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. A cellcentered multipoint flux approximation method with.
Mar 28, 2019 presented at the spe reservoir simulation symposium, houston, texas. 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. Interblock transmissibility calculation analysis for. Numerical experiments for discontinuous permeability. Firstorder convergence of multipoint flux approximation on triangular grids and comparison with mixed finite element methods. Jul 25, 2006 siam journal on scientific computing 37. We present a nite volume method for the simulation of the solution. Pebi, etc and discretization schemes based on twopoint flux approximations tpfa. Introduction one of the key issues in petroleum reservoir simulation is the correct representation of the irregular reservoir shape. Fundamentals of numerical reservoir simulation, volume 6. The analysis of the multi point flux approximation mpfa. The mpfa version discussed here is the socalled omethod on. A multipoint flux mixed finite element method siam journal.
Mathematical model computer codes numerical model physical model figure 1. Polygonal and polyhedral mesh, convergence, multipoint. Finite volume methods with multipoint flux approximation. Introduction when solving problems on a geological structure, one of the challenges that confronts numerical methods is grid deformation. Presented at the spe reservoir simulation symposium, houston, texas.
Abstract pdf 8908 kb 2014 signpreserving of principal eigenfunctions in p1 finite element approximation of eigenvalue problems of secondorder elliptic operators. An efficient multipoint flux approximation method for discrete fracturematrix simulations. Purchase mathematical models and finite elements for reservoir simulation, volume 17 1st edition. In this section, we present a new multipoint flux approximation, called enriched multipoint flux approximation. An introduction to multipoint flux approximations for quadrilateral. A threedimensional symmetric positive definite control. Simulation results are presented and compared with results from other twopoint and multipoint flux approximations. 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. If the pressure field is not smooth, improved accuracy can be achieved by local grid refinement.
Proceedings of the spe reservoir simulation conference, society. A new mixed finite element and its related finite volume. Discretizations using conservative approximation techniques applicable to reservoir simulation are well known. This method is used for the estimation of unknown reservoir parameters, such as permeability and porosity, based on production data and inverted seismic data. Applied mathematics reservoir simulation fluid dynamics. A new multipoint flux approximation for reservoir simulation. The upscaling of discrete fracture models for faster, coarsescale simulations of ior and eor. Implementation and application of a hybrid multipoint flux approximation for reservoir simulation. Mathematical models and finite elements for reservoir.
Abstract multipoint flux approximations mpfas have been developed in recent. 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. Reservoir simulation process reservoir simulation is briefly. In this paper we develop an accurate and robust upscaling procedure for compositional flow simulation. 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. The scheme performs well for grids with a high aspect ratios, such as are commonly used in reservoir simulators. 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.
Routines supporting the mpfao method for the pressure equation. Spe reservoir simulation symposium 2007 proceedings. Presented at the spe reservoir characterisation and simulation conference and exhibition, abu dhabi, uae, 1618 september. A new multipoint flux approximation method with a quasilocal. Global variable compact multipoint methods for accurate. 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. For cartesian grids, this is in fact the classical mpfa omethod. 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. The application of a vertexbased quadrature rule reduces the new mixed finite element method to a multipoint flux control volume method. Pdf this paper addresses the key issue of calculating fluxes at the.
Only the omethod with surface midpoints as continuity points is discussed. Numerical simulations show that our new schemes can be more accurate than the current fitted finite volume. An efficient numerical model for immiscible twophase flow in fractured karst reservoirs volume issue 2 zhaoqin huang, jun yao, yueying wang. 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. A novel flowbased geometrical upscaling method to represent. 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. It works for general polygon meshes like the multipoint flux approximation. Controlvolume discretizations using multipoint flux approximations mpfa were developed in the last decade. Spe reservoir simulation symposium 2007 february 2628, 2007 houston, texas, usa printed from emedia with permission by. 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. A schematic diagram of this process is shown in figure 1. A new multipoint flux approximation method with a quasilocal stencil mpfaql for the simulation of diffusion problems in anisotropic and heterogeneous media.
A method for history matching of an inhouse petroleum reservoir compositional simulator with multipoint flux approximation is presented. The new space is compatible with a piecewise constant pressure discretization and yields a convergent discretization. The numerical tests are conducted using the framework of the open source matlab reservoir simulation toolbox mrst. New directions in pure, applied, and computational mathematics, 4559. Siam journal on scientific computing society for industrial. Enriched multipoint flux approximation for general grids. 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.
Multipoint flux approximation solvers for pressure. We study a two phase porous media ow model where dynamic e ects are included in the capillary pressure. Ebfvm, unstructured meshes, compositional reservoir simulation, utcomp simulator 1. Proceedings of the 8th international forum on reservoir simulation, iles borromees. Controlvolume distributed multipoint flux approximation. A special quadrature rule is employed that allows for local velocity elimination and leads to a symmetric and positive definite cell. This article presents a convergence analysis of the multipoint flux approximation control volume method, mpfa, in two space dimensions. A fitted multipoint flux approximation method for pricing. The new technique has also practical advantage over other highaccuracy methods like. Parallel generalpurpose reservoir simulation with coupled. A dirichlet neumann representation method for simulating.
682 334 167 1412 243 570 1032 266 684 1444 1190 517 1049 1143 350 66 1399 249 500 577 623 726 96 1048 433 78 505 776 675 800 1060 364 730 1298