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3 - Grids in Subsurface Modeling
from Part I - Geological Models and Grids
Knut-Andreas Lie
Book:

An Introduction to Reservoir Simulation Using MATLAB/GNU Octave

Published online:

22 July 2019

Print publication:

08 August 2019, pp 55-110
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Summary

The chapter explains how you can generate grid models to represent subsurface reservoirs. We outline a number of elementary grid types: structured/rectilinear grids, fictitious domains, Delaunay triangulations, and Voronoi grids. We then explain stratigraphic grids that are commonly used to model real subsurface formations, including in particular corner-point and perpendicular bisector (PEBI) grids. We explain how such grids are represented in MRST using a data structure for general unstructured grids, and we discuss how to compute geometric properties like volumes, face areas, face normals, etc. We end the chapter by presenting an overview of alternative gridding techniques, including composite grids, multiblock grids, and control-point and boundary conformal grids.

Gamma-type results and other related properties of Poisson processes
Part of
- Inference from stochastic processes
- Geometric probability and stochastic geometry
Jesper Møller, Sergei Zuyev
Journal:

Advances in Applied Probability / Volume 28 / Issue 3 / September 1996

Published online by Cambridge University Press:

01 July 2016, pp. 662-673

Print publication:

September 1996
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Families of Poisson processes defined on general state spaces and with the intensity measure scaled by a positive parameter are investigated. In particular, mean value relations with respect to the scale parameter are established and used to derive various Gamma-type results for certain geometric characteristics determined by finite subprocesses. In particular, we deduce Miles' complementary theorem. Applications of the results within stochastic geometry and particularly for random tessellations are discussed.

On the volume distribution of the typical Poisson–Delaunay cell
Part of
- Discrete geometry
- Stochastic processes
P. N. Rathie
Journal:

Journal of Applied Probability / Volume 29 / Issue 3 / September 1992

Published online by Cambridge University Press:

14 July 2016, pp. 740-744

Print publication:

September 1992
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A method of obtaining the distribution of the volume of the typical cell of a Delaunay tessellation generated by a Poisson process in is developed and used to derive the density when d = 1, 2, 3.