Chapter 20
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Description
of Reservoir Properties
Using FractalsM. Kelkar
S. Shibli
The University of Tulsa
Tulsa, Oklahoma, U.S.A.
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ABSTRACT
This work investigates the
utility of applying fractal geometry for describing the spatial correlation
structure of rock properties. It also provides a proper framework within
which to apply a stochastic conditional simulation technique to generate
equiprobable distributions of rock property.
A normalization technique is developed
to remove the seasonal effects found in the well-bore data. Where the seasonal
effects are unusually strong, as in the case of one carbonate reservoir,
removal of the local means will result in a narrower distribution of the
Hurst (H) exponent values. Theoreti-cal and analytical variogram
plots of the results of these estimations indicate that the box-counting
method gives slightly improved estimates over rescaled range (R/S) analysis.
Conditional simulation runs using simulated
annealing are performed for three fields. The results indicate that a combination
of the greedy algorithm and a bilinear interpolation technique to generate
the initial pattern decreases computer usage by as much as 85%. More important,
the simulations also indicate that an fGn (fractional Gaussian noise)
horizontal correlation structure gives better predictions of interwell
distributions in a carbonate environment. In contrast, in a sandstone field,
the use of an fBm (fractional Brownian motion) horizontal correlation
structure gives more reliable results. |