Fractal measurements of sandstones, shales, and carbonates

Krohn, Christine E.

doi:10.1029/jb093ib04p03297

Cited by 247 publications

(131 citation statements)

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“…Thus, the surface area of a fractal interface increases faster with L than if it were Euclidean (D=2), but slower than if it were a volume filling object (D=3). Fractal dimensions of pore surfaces in sedimentary rocks are observed to range mostly between 2.6 and 2.8, with D increasing with diagenetic alteration [39,38,85].…”

Section: Introductionmentioning

confidence: 99%

“…A growing body of measurements [5,30,94,84,21,38,39,83] suggest that in most sandstones and shales these poregrain interfaces are fractal for length scales ranging over 4 orders of magnitude, from approximately 10-2 to 10 2 J.Lm. The measured surface area, S, of a fractal interface has a power-law dependence on the lateral extent L of the interface: i.e., S(L) ex: LD, where 2 < D < 3 is the interface fractal dimension (91].…”

Section: Introductionmentioning

confidence: 99%

“…This generic physical process may be responsible for the observed fractal structures on the pore scale of sedimentary rocks (38,85,1], for formation of channels in the mantle (3], or caves in calcite rocks (16]. It may influence rates of lava flow, and in turn rates of sea-floor accretion or eruption of volcanos, and determine where dikes will initiate in the mantle (Chapter IV).…”

Section: Introductionmentioning

confidence: 99%

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Solid-fluid interactions in porous media : processes that form rocks

Aharonov¹

1996

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Solid-fluid interactions in porous media : processes that form rocks

Aharonov¹

1996

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“…The surface fractal dimension has been determined for various sandstones by SEM (Scanning Electron Microscopy and BET (nitrogen adsorption) measurements, and the values range from 2.5 to 2.87 (Katz and Thompson. 1985;Krohn, 1988;Aharonov, Rothman and Thompson, 1997). From an empirical study on sandstones, Richardson (1961) Other investigators have also developed permeability models based on fractal studies Thompson.…”

Section: K=g (6)mentioning

confidence: 99%

3-D spectral IP imaging: Non-invasive characterization of contaminant plumes. Annual progress report, September 15, 1996--September 14, 1997

Frye¹,

Lesmes²,

Morgan³

et al. 1997

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The objective of this project is to develop the scientific basis for characterizing contaminant plumes in the earth's subsurface using field measurements of induced polarization (IP) effects. Our first-year accomplishments are (1) laboratory experiments on fluid-saturated sandstones quantifying the dependence of spectral IP responses on solution chemistry and rock micro-geometry; (2) library research on the current understanding of electromagnetic coupling effects on IP data acquired in the field: and (3) development of prototype forward modeling and inversion algorithms for interpreting IP data in terms of 3-D models of complex resistivity.ii . . . TABLE OF CONTENTSABSTRACT 111 OBJECTIVESThe overall objective of this project is to develop the scientific basis for characterizing contaminant plumes in the earth's subsurface using field measurements of induced polarization (IP) effects. Three specific objectives towards this end are 1. 2.3.Understanding IP at the laboratory level through measurements of complex resistivity as a function of frequency in rock and soil samples with varying pore geometries,. pore fluid conductivities and saturations, and contaminant chemistries and concentrations.Developing effective data acquisition techniques for measuring the critical IP responses (time domain or frequency domain) in the field.Developing modeling and inversion algorithms that permit the interpretation of field IP data in terms of subsurface geology and contaminant plume properties. ACCOMPLISHMENTS Laboratory StudiesOur laboratory experiments to date are described in Appendices A and B, which consist of two papers submitted to the annual SAGEEP conference (Frye et al., 1997; Sturrock et al., 1997). Our experiments involved measurements of complex resistivity vs. frequency on a suite of brine saturated sandstone samples. In one set of experiments. the fluid chemistry (pH, ionic strength, and cation type) was varied. In a second set of experiments, the microgeometry of the rock matrix was varied. The experiments showed that spectral IP responses are sensitive to subtle variations in both the solution chemistry and rock microgeometry. The results demonstrate that spectral IP responses have the potential of being sensitive indicators of in situ chemistry and microgeometry, the latter of which may be related to the hydraulic properties. Data AcquisitionWe have been looking in some detail at the effects of electromagnetic coupling and how to practically deal with it. Currently, we do not have conclusive results. 1 Modeling and InversionOur progress in the development of modeling and inversion algorithms for IP is described in Appendix C, a paper submitted to the annual SAGEEP conference (Shi et al., 1997).We have developed algorithms for forward modeling and inversion of spectral IP data in 3-D media. The algorithms accommodate. a general earth model with a complex electrical conductivity as a function of frequency and 3-D spatial position. Using regularization and optimization techniques. the inversion algorithm...

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“…The reservoir formation consists mainly of alternate layers of sandstone and shale. As we know that sandstones and shales are porous fractal media (Katz and Thomson, 1985;Krohn and Thompson, 1986;Krohn, 1988b;Sahimi, 2011), we performed Monte Carlo simulations based on the fractal nature of pore size distribution in porous media of the reservoir. We assumed the reservoir as a mono-dispersed porous medium to study the effect of macro-porosity on permeability.…”

Section: Introductionmentioning

confidence: 99%

Estimation of permeability of a sandstone reservoir by a fractal and Monte Carlo simulation approach: a case study

Vadapalli

Srivastava

Vedanti

et al. 2014

Nonlin. Processes Geophys.

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Abstract. Permeability of a hydrocarbon reservoir is usually estimated from core samples in the laboratory or from well test data provided by the industry. However, such data is very sparse and as such it takes longer to generate that. Thus, estimation of permeability directly from available porosity logs could be an alternative and far easier approach. In this paper, a method of permeability estimation is proposed for a sandstone reservoir, which considers fractal behavior of pore size distribution and tortuosity of capillary pathways to perform Monte Carlo simulations. In this method, we consider a reservoir to be a mono-dispersed medium to avoid effects of micro-porosity. The method is applied to porosity logs obtained from Ankleshwar oil field, situated in the Cambay basin, India, to calculate permeability distribution in a well.Computed permeability values are in good agreement with the observed permeability obtained from well test data. We also studied variation of permeability with different parameters such as tortuosity fractal dimension (D t ), grain size (r) and minimum particle size (d 0 ), and found that permeability is highly dependent upon the grain size. This method will be extremely useful for permeability estimation, if the average grain size of the reservoir rock is known.

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Fractal measurements of sandstones, shales, and carbonates

Cited by 247 publications

References 6 publications

Solid-fluid interactions in porous media : processes that form rocks

Solid-fluid interactions in porous media : processes that form rocks

3-D spectral IP imaging: Non-invasive characterization of contaminant plumes. Annual progress report, September 15, 1996--September 14, 1997

Estimation of permeability of a sandstone reservoir by a fractal and Monte Carlo simulation approach: a case study

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