By Benoit B. Mandelbrot (auth.), Christopher C. Barton, Paul R. La Pointe (eds.)
ISBN-10: 1461357330
ISBN-13: 9781461357339
ISBN-10: 1461518156
ISBN-13: 9781461518150
In this specified quantity, popular specialists talk about the functions of fractals in petroleum research-offering a very good advent to the topic. Contributions disguise a extensive spectrum of purposes from petroleum exploration to creation. Papers additionally illustrate how fractal geometry can quantify the spatial heterogeneity of other points of geology and the way this knowledge can be utilized to enhance exploration and construction results.
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Extra resources for Fractals in Petroleum Geology and Earth Processes
Example text
2 Schuenmeyer and Drew, 1991 Fig. 6 Root and Attanasi, 1988 Fig. , 1990 Fig. 63 V. 1. " ~ ~ ~ ~ ~ ~ ~ o i ~ n ~ Root and Attanasi, 1988 Fig. 1 Root and Attanasi, 1988 Fig. 3 Carmalt and St. , 1982 Fig. 16 Oil, USA, Lower 48 States onshore (through 1984) Gas, USA lower 48 states onshore (through 1984) Giant Fields worldwide (equiv. , 1990 Source of comparison aCalculated values for Eq. 7 in text: C, constant of proportionality; n, slope of line fit to cumulative frequency versus size distributions; r2, coefficient to fit; D, fractal dimension.
To define a total volume that does not become arbitrarily large as Vmin goes to zero, the integral in Eq. 5 must be convergent, which means that the exponent (l-~»O (6) and therefore D < 3, where D is the fractal dimension. The distribution function (Eq. 2) can be written N(V) = C(V)-a where a = D/3. (7) 2. FRACTAL SIZE OF HYDROCARBON ACCUMULATIONS 19 Since this paper is concerned with volume distributions defined by Eq. 7, lines fitted to cumulative frequency versus size distributions on log-log plots should have slopes of -ex, and the convergence constraint is that the absolute value of ex must be less than 1.
Thus, the dashed line in Fig. 1 is the theoretical fractal population, the thin solid line is the true population, and the heavy solid line is the observed population. Since the time of Krige (1951), the size distribution of mineral deposits, including oil accumulations, has been thought to be lognormal (Arps and Roberts, 1958; Kaufman, 1962, 1983; McCrossan, 1968; Barouch and Kaufman, 1976; Lee and Wang, 1983a,b; Forman and Hinde, 1985; David and Chang, 1989; and Power, 1992). This distribution has a thinner right tail than the power-law, or fractal, distribution, but is truncated at the left end, and unlike the scale-independent power-law distribution, has a characteristic size (mode) at which the distribution peaks and rolls off.
Fractals in Petroleum Geology and Earth Processes by Benoit B. Mandelbrot (auth.), Christopher C. Barton, Paul R. La Pointe (eds.)
by Ronald
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