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14 - Grid Coarsening
from Part IV - Reservoir Engineering Workflows
Knut-Andreas Lie
Book:

An Introduction to Reservoir Simulation Using MATLAB/GNU Octave

Published online:

22 July 2019

Print publication:

08 August 2019, pp 518-557
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Summary

Generating a coarser volumetric description of the reservoir rock is a common task in reservoir engineering. This chapter discusses how to partition a fine grid model into a smaller set of coarse blocks. After the partition, the coarse blocks will each consist of a finite collection of cells from the underlying fine model. Through a series of examples, we demonstrate a variety of different partition methods. Whereas the simplest methods only utilize the geometry or topology of the grid, the more advanced methods can compute partitions that adapt to petrophysical properties, fluid contacts, flow fields, near-well regions, or underlying geological properties like depositional environments, flow units, rock types, etc.

A central limit theorem for iterated random functions
Part of
- Classical measure theory
- Limit theorems
Wei Biao Wu, Michael Woodroofe
Journal:

Journal of Applied Probability / Volume 37 / Issue 3 / September 2000

Published online by Cambridge University Press:

14 July 2016, pp. 748-755

Print publication:

September 2000
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A central limit theorem is established for additive functions of a Markov chain that can be constructed as an iterated random function. The result goes beyond earlier work by relaxing the continuity conditions imposed on the additive function, and by relaxing moment conditions related to the random function. It is illustrated by an application to a Markov chain related to fractals.

A refinement of multivariate Bonferroni-type inequalities
Part of
- Distribution theory - Probability
Tuhao Chen, E. Seneta
Journal:

Journal of Applied Probability / Volume 37 / Issue 1 / March 2000

Published online by Cambridge University Press:

14 July 2016, pp. 276-282

Print publication:

March 2000
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Technology developed in a predecessor paper (Chen and Seneta (1996)) is applied to provide, in a unified manner, a sharpening of bivariate Bonferroni-type bounds on P(v1≥r, v2≥u) obtained by Galambos and Lee (1992; upper bound) and Chen and Seneta (1986; lower bound).

Multivariate Bonferroni-type lower bounds
Part of
- Distribution theory - Probability
Tuhao Chen, E. Seneta
Journal:

Journal of Applied Probability / Volume 33 / Issue 3 / September 1996

Published online by Cambridge University Press:

14 July 2016, pp. 729-740

Print publication:

September 1996
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We derive multivariate Sobel–Uppuluri–Galambos-type lower bounds for the probability that at least a1 and at least a2, and for the probability that exactly a1 and a2, out of n and N events, occur. The lower bound presented here reduces to a sharper bound than that of Galambos and Lee (1992). Our approach is by way of indicator functions and bivariate binomial moments. A new concept, marginal Bonferroni summation, is introduced in this paper.

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