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Experimental Study and Fractal Analysis of Heterogeneity in Naturally Fractured Rocks

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Abstract

Capillary pressure curves of six low porosity and low permeability core samples from The Geysers geothermal field were measured using the mercury-intrusion approach to characterize the heterogeneity of rock. One high permeability Berea sandstone core sample was analyzed similarly, for comparison. The maximum pressure of mercury intruded into the rock was about 200 MPa to reach the extremely small pores. Experimental data showed that the capillary pressure curves of The Geysers rock are very different from that of the Berea sandstone. It was found that the frequently used capillary pressure models could not be used to represent the data from The Geysers rock samples. This might be because of the fractures in the rock. To this end, a fractal technique was proposed to model the features of the capillary pressure curves and to characterize the difference in heterogeneity between The Geysers rock and Berea sandstone. The results demonstrated that the rock from The Geysers geothermal field was fractal over a scaling range of about five orders of magnitude. The values of the fractal dimension of all the core samples (six from The Geysers and one Berea sandstone) calculated using the proposed approach were in the range from 2 to 3. The results showed that The Geysers rock with a high density of fractures had a greater fractal dimension than Berea sandstone which is almost without fractures. This shows that The Geysers rock has greater heterogeneity, as expected.

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Abbreviations

D :

Euclidean dimension

D f :

Fractal dimension

l :

Length of a capillary tube

N(r):

Number of the unit needed to fill the fractal object

P c :

Capillary pressure

p e :

Entry capillary pressure

r :

Radius of the unit

S Hg :

Mercury saturation

S w :

Wetting-phase saturation

\({S_{\rm w}^\ast}\) :

Normalized wetting-phase saturation

S wr :

Residual saturation of the wetting-phase

V Hg :

Cumulative volume of mercury intruded into rock

V p :

Pore volume

θ :

Contact angle

σ :

Interfacial tension

λ:

Pore size distribution index

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Authors and Affiliations

  1. Department of Energy and Resources Engineering, College of Engineering, Peking University, Bei**g, 100871, China

    Kewen Li

  2. Department of Energy Resources Engineering, Stanford University, Stanford, CA, 94043, USA

    Kewen Li & Roland N. Horne

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  1. Kewen Li
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  2. Roland N. Horne
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Correspondence to Kewen Li.

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Li, K., Horne, R.N. Experimental Study and Fractal Analysis of Heterogeneity in Naturally Fractured Rocks. Transp Porous Med 78, 217–231 (2009). https://doi.org/10.1007/s11242-008-9295-8

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