Data processing: structural design – modeling – simulation – and em – Simulating nonelectrical device or system – Fluid
Reexamination Certificate
2000-06-13
2004-11-30
Teska, Kevin J. (Department: 2128)
Data processing: structural design, modeling, simulation, and em
Simulating nonelectrical device or system
Fluid
C703S009000, C703S006000, C702S006000, C702S012000, C702S009000, C367S072000, C166S335000
Reexamination Certificate
active
06826520
ABSTRACT:
FIELD OF THE INVENTION
This invention relates generally to simulating fluid flow in a porous medium and, more specifically, to a flow-based method of scaling-up permeability associated with a fine-grid system representative of the porous medium to permeability associated with a coarse-grid system also representative of the porous medium.
BACKGROUND OF THE INVENTION
Numerical simulation is widely used in industrial fields as a method of simulating a physical system by using a computer. In most cases, there is a desire to model the transport processes occurring in the physical systems. What is being transported is typically mass, energy, momentum, or some combination thereof. By using numerical simulation, it is possible to reproduce and observe a physical phenomenon and to determine design parameters without actual laboratory experiments or field tests. It can be expected therefore that design time and cost can be reduced considerably.
One type of simulation of great interest is a process of inferring the behavior of a real hydrocarbon-bearing reservoir from the performance of a numerical model of that reservoir. The objective of reservoir simulation is to understand the complex chemical, physical, and fluid flow processes occurring in the reservoir sufficiently well to predict future behavior of the reservoir to maximize hydrocarbon recovery. Reservoir simulation often refers to the hydrodynamics of flow within a reservoir, but in a larger sense reservoir simulation can also refer to the total petroleum system which includes the reservoir, injection wells, production wells, surface flowlines, and surface processing facilities.
The principle of numerical simulation is to numerically solve equations describing a physical phenomenon by a computer. Such equations are generally ordinary differential equations and partial differential equations. These equations are typically solved using numerical methods such as the finite difference method, the finite element method, and the finite volume method among others. In each of these methods, the physical system to be modeled is divided into smaller cells (a set of which is called a grid or mesh), and the state variables continuously changing in each cell are represented by sets of values for each cell. An original differential equation is replaced by a set of algebraic equations to express the fundamental principles of conservation of mass, energy, and/or momentum within each smaller unit or cells and of mass, energy, and/or momentum transfer between cells. These equations can number in the millions. Such replacement of continuously changing values by a finite number of values for each cell is called “discretization”. In order to analyze a phenomenon changing in time, it is necessary to calculate physical quantities at discrete intervals of time called timesteps, irrespective of the continuously changing conditions as a function of time. Time-dependent modeling of the transport processes proceeds in a sequence of timesteps.
In a typical simulation of a reservoir, solution of the primary unknowns, typically pressure and phase saturation or composition, are sought at specific points in the domain of interest. Such points are called “gridnodes” or more commonly “nodes.” Cells are constructed around such nodes, and a grid is defined as a group of such cells. The properties such as porosity and permeability are assumed to be constant inside a cell. Other variables such as pressure and phase saturation are specified at the nodes. A link between two nodes is called a “connection.” Fluid flow between two nodes is typically modeled as flow along the connection between them.
In conventional reservoir simulation, most grid systems are structured. That is, the cells have similar shape and the same number of sides or faces. Most commonly used structured grids are Cartesian or radial in which each cell has four sides in two dimensions or six faces in three dimensions. While structured grids are easy to use, they lack flexibility in adapting to changes in reservoir and well geometry and often can not effectively handle the spatial variation of physical properties of rock and fluids in the reservoir. Flexible grids have been proposed for use in such situations where structured grids are not as effective. A grid is called flexible or unstructured when it is made up of polygons (polyhedra in three dimensions) having shapes, sizes, and number of sides or faces that can vary from place to place. Unstructured grids can conform to complex reservoir features more easily than structured grids and for this reason unstructured grids have been proposed for use in reservoir modeling.
One type of flexible grid that can be used in reservoir modeling is the Voronoi grid. A Voronoi cell is defined as the region of space that is closer to its node than to any other node, and a Voronoi grid is made of such cells. Each cell is associated with a node and a series of neighboring cells. The Voronoi grid is locally orthogonal in a geometrical sense; that is, the cell boundaries are normal to lines joining the nodes on the two sides of each boundary. For this reason, Voronoi grids are also called perpendicular bisection (PEBI) grids. A rectangular grid block (Cartesian grid) is a special case of the Voronoi grid. The PEBI grid has the flexibility to represent widely varying reservoir geometry, because the location of nodes can be chosen freely. PEBI grids are generated by assigning node locations in a given domain and then generating cell boundaries in a way such that each cell contains all the points that are closer to its node location than to any other node location. Since the inter-node connections in a PEBI grid are perpendicularly bisected by the cell boundaries, this simplifies the solution of flow equations significantly. For a more detailed description of PEBI grid generation, see Palagi, C. L. and Aziz, K.: “Use of Voronoi Grid in Reservoir Simulation,” paper SPE 22889 presented at the 66th Annual Technical Conference and Exhibition, Dallas, Tex. (Oct. 6-9, 1991).
The mesh formed by connecting adjacent nodes of PEBI cells is commonly called a Delaunay mesh if formed by triangles only. In a two-dimensional Delaunay mesh, the reservoir is divided into triangles with the gridnodes at the vertices of the triangles such that the triangles fill the reservoir. Such triangulation is Delaunay when a circle passing through the vertices of a triangle (the circumcenter) does not contain any other node inside it. In three-dimensions, the reservoir region is decomposed into tetrahedra such that the reservoir volume is completely filled. Such a triangulation is a Delaunay mesh when a sphere passing through the vertices of the tetrahedron (the circumsphere) does not contain any other node. Delaunay triangulation techniques are well known; see for example U.S. Pat. No. 5,886,702 to Migdal et al.
Through advanced reservoir characterization techniques, it is common to model the geologic structure and stratigraphy of a reservoir with millions of grid cells, each populated with a reservoir property that includes, but is not limited to, rock type, porosity, permeability, initial interstitial fluid saturation, and relative permeability and capillary pressure functions. However, reservoir simulations are typically performed with far fewer grid cells. The direct use of fine-grid models for reservoir simulation is not generally feasible because their fine level of detail places prohibitive demands on computational resources. Therefore, a method is needed to transform or to scale up the fine-grid geologic reservoir model to a coarse-grid simulation model while preserving, as much as possible, the fluid flow characteristics of the fine-grid model.
One key fluid flow property for reservoir simulation is permeability. Permeability is the ability of a rock to transmit fluids through interconnected pores in the rock. It can vary substantially within a hydrocarbon-bearing reservoir. Typically, permeabilities are generated for fine-scale models (geologic models) using data from well core samples. Fo
Dawson Aaron G.
Khan Sameer A.
ExxonMobil Upstream Research Company
Ferris Fred
Teska Kevin J.
LandOfFree
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