Discretization methods are proposed for control-volume formulations on polygonal and triangular grid cells in two space dimensions. The methods are applicable for any system of conservation laws where the flow density is defined by a gradient law, like Darcy's law for porous-media flow. A strong feature of the methods is the ability to handle media inhomogeneities in combination with full-tensor anisotropy. This paper gives a derivation of the methods, and the relation to previously published methods is also discussed. A further discussion of the methods, including numerical examples, is given in the companion paper, Part II [SIAM J. Sci. Comput., pp. 1717--1736].

Discretization on Unstructured Grids for Inhomogeneous, Anisotropic Media. Part I: Derivation of the Methods

Introduction to Reservoir Management RESERVOIR ENGINEERING PRIMER: Basic Reservoir Analysis Multiphase Flow Concepts Derivation of the Flow Equations Fluid Displacement Frontal Stability Pattern Floods Recovery of Subsurface Resources Economics and the Environment RESERVOIR SIMULATION: Overview of the Modeling Process Conceptual Reservoir Scales Reservoir Structure Fluid Properties Rock-Fluid Interaction Fundamentals of Reservoir Simulation Modeling Reservoir Architecture Data Preparation for a Typical Study History Matching Predictions CASE STUDY: Study Objectives and Data Gathering Model Initialization History Matching and Predictions WINB4D USER'S MANUAL: Introduction to WINB4D Initializing Data Recurrent Data Program Output Evaluation TECHNICAL SUPPLEMENTS: Simulator Formation Rock and Fluid Models Initialization Well Models Well Flow Index (PID) The IMPES Formulation References Index

Principles of applied reservoir simulation

Discretization on Non-Orthogonal, Quadrilateral Grids for Inhomogeneous, Anisotropic Media

A Petragrid method and apparatus generates grid cell property information that is adapted for use by a computer simulation apparatus. An interpretation workstation includes at least two software programs stored therein: a first program called "Petragrid" and a second simulation program for generating a set of simulation results for display. The first Petragrid software program will: receive well log and seismic data which indicates each layer of a formation, grid each layer of the formation where the grid is comprised of a plurality of cells, and generate more accurate data associated with each grid cell, such as the transmissibility. The more accurate data for each cell will be transmitted to the second simulation program which will respond by generating a set of more accurate simulation results for each cell of the grid, and overlaying the more accurate simulation result for each cell onto each of the corresponding cells of the grid being displayed on the workstation display by the Petragrid software. The workstation will display each layer of the formation where each layer is gridded, and each grid cell has its own color corresponding in numerical value to a more accurate simulation result (e.g., pressure or saturation) that corresponds to that cell.

Method and apparatus for generating more accurate earth formation grid cell property information for use by a simulator to display more accurate simulation results of the formation near a wellbore

Control-Volume Discretization Methods for 3D Quadrilateral Grids in Inhomogeneous, Anisotropic Reservoirs

Distorted grid or ''corner point geometry'' have received increased attention as a means of enhancing the modelling flexibility of finite difference type reservoir simulators. Non-rectangular grids permit better alignment with reservoir boundaries and faults and may lead to fewer grid blocks and therefore less computational efforts in simulation of complex reservoirs. This paper shows that caution should be used as regards the transmissibility calculations for distorted grids. Specifically, it is demonstrated by simulation experiments that methods which try to maintain (for 2-D problems) the five-point connectivity of standard finite differences may lead to serious errors. A generalized nine-point scheme is constructed and shown to be more appropriate for distorted grids. For instance, the scheme seems to preserve the accuracy of a square nine-point scheme if the distortion is kept within certain limits. Although based on finite element techniques, the scheme is given a finite difference type form, and can therefore easily be implemented in more general-purpose finite difference type reservoir simulators.

Generalized Transmissibilities for Distorted Grids in Reservoir Simulation

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Generalized Transmissibilities for Distorted Grids in Reservoir Simulation