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  • 1
    Electronic Resource
    Electronic Resource
    Use of digital image analysis to estimate fluid permeability of porous materials: Application of two-point correlation functions (1986)
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 60 (1986), S. 1930-1938 
    Details
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Scanning electron microscope images of cross sections of several porous specimens have been digitized and analyzed using image processing techniques. The porosity and specific surface area may be estimated directly from measured two-point spatial correlation functions. The measured values of porosity and image specific surface were combined with known values of electrical formation factors to estimate fluid permeability using one version of the Kozeny-Carman empirical relation. For glass bead samples with measured permeability values in the range of a few darcies, our estimates agree well (±10–20%) with the measurements. For samples of Ironton-Galesville sandstone with a permeability in the range of hundreds of millidarcies, our best results agree with the laboratory measurements again within about 20%. For Berea sandstone with still lower permeability (tens of millidarcies), our predictions from the images agree within 10–30%. Best results for the sandstones were obtained by using the porosities obtained at magnifications of about 100× (since less resolution and better statistics are required) and the image specific surface obtained at magnifications of about 500× (since greater resolution is required).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.337245
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  • 2
    Electronic Resource
    Electronic Resource
    Normalization constraint for variational bounds on fluid permeability (1985)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 83 (1985), S. 754-760 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A careful reexamination of the formulation of Prager's original variational principle for viscous flow through porous media has uncovered a subtle error in the normalization constraint on the trial functions. Although a certain surface integral of the true pressure field over the internal surface area always vanishes for isotropic materials, the corresponding surface integral for a given trial pressure field does not necessarily vanish but has nevertheless been previously neglected in the normalization. When this error is corrected, the form of the variational estimate is actually simpler than before and furthermore the resulting bounds have been shown to improve when the constant trial functions are used in either the two-point or three-point bounds.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.449489
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  • 3
    Electronic Resource
    Electronic Resource
    Bounds on fluid permeability for viscous flow through porous media (1985)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 82 (1985), S. 1459-1467 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: General properties of variational bounds on Darcy's constant for slow viscous flow through porous media are studied. The bounds are also evaluated numerically for the penetrable sphere model. The bound of Doi depending on two-point correlations and the analytical bound of Weissberg and Prager give comparable results in the low density limit but the analytical bound is superior for higher densities. Prager's bound depending on three-point correlation functions is worse than the analytical bound at low densities but better (although comparable to it) at high densities. A procedure for methodically improving Prager's three point bound is presented. By introducing a Gaussian trial function, the three-point bound is improved by an order of magnitude for moderate values of porosity. The new bounds are comparable in magnitude to the Kozeny–Carman empirical relation for porous materials.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.448420
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  • 4
    Electronic Resource
    Electronic Resource
    Scattering by a spherical inhomogeneity in a fluid-saturated porous medium (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 1408-1419 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A fast compressional wave incident on an inhomogeneity in a fluid-saturated porous medium will produce three scattered elastic waves: a fast compressional wave, a slow compressional wave, and a shear wave. This problem is formulated as a multipole expansion using Biot's equations of poroelasticity. The solution for the first term (n=0) in the multipole series involves a 4×4 system which is solved analytically in the long-wavelength limit. All higher-order terms (n≥1) require the solution of a 6×6 system. A procedure for solving these equations by splitting the problem into a 4×4 system and a 2×2 system and then iterating is introduced. The first iterate is just the solution of the elastic wave scattering problem in the absence of fluid effects. Higher iterates include the successive perturbation effects of fluid/solid interaction.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.526955
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  • 5
    Electronic Resource
    Electronic Resource
    Exponential convergence for nonlinear diffusion problems with positive lateral boundary conditions (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 660-663 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is established that the solution u of ut=Δ(um)〉0, with positive initial data, positive lateral boundary data, and positive exponent m, converges exponentially to the solution v of the corresponding stationary equation Δ(vm)=0. The analysis also provides the form of the leading contribution to the difference (u−v).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.526603
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  • 6
    Electronic Resource
    Electronic Resource
    Relationship between specific surface area and spatial correlation functions for anisotropic porous media (1987)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 28 (1987), S. 244-245 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A result of Debye, Anderson, and Brumberger [P. Debye, H. R. Anderson, Jr., and H. Brumberger, J. Appl. Phys. 28, 679 (1957)] for isotropic porous media states that the derivative of the two-point spatial correlation at the origin is equal to minus one-quarter of the specific surface area. This result is generalized for nonisotropic media by noting that the angular average of the anisotropic two-point spatial correlation function has the same relationship to the specific surface area.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.527804
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  • 7
    Electronic Resource
    Electronic Resource
    Measurement of spatial correlation functions using image processing techniques (1985)
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 57 (1985), S. 2374-2384 
    Details
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A procedure for using digital image processing techniques to measure the spatial correlation functions of composite heterogeneous materials is presented. Methods for eliminating undesirable biases and warping in digitized photographs are discussed. Fourier transform methods and array processor techniques for calculating the spatial correlation functions are treated. By introducing a minimal set of lattice-commensurate triangles, a method of sorting and storing the values of three-point correlation functions in a compact one-dimensional array is developed. Examples are presented at each stage of the analysis using synthetic photographs of cross sections of a model random material (the penetrable sphere model) for which the analytical form of the spatial correlations functions is known. Although results depend somewhat on magnification and on relative volume fraction, it is found that photographs digitized with 512×512 pixels generally have sufficiently good statistics for most practical purposes. To illustrate the use of the correlation functions, bounds on conductivity for the penetrable sphere model are calculated with a general numerical scheme developed for treating the singular three-dimensional integrals which must be evaluated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.334346
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  • 8
    Electronic Resource
    Electronic Resource
    Kozeny–Carman relations and image processing methods for estimating Darcy's constant (1987)
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 62 (1987), S. 2221-2228 
    Details
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A natural connection is demonstrated between Kozeny–Carman relations for porous media and the image processing techniques which have recently been applied to the problem of estimating the parameters in such relations. It is shown that the term in the Kozeny–Carman relation related to the specific surface area is best estimated from a smoothed version of the actual material surface. To measure this image specific surface, the magnification of a cross section of the porous material should be chosen so that a typical correlation length for the sample corresponds to a distance comparable to 100 discrete picture elements. Under these conditions, the assumptions typically made in the derivation of a Kozeny–Carman relation are entirely compatible with the resolution constraints imposed by digitizing the image. Thus, although the measured image specific surface may be considerably smaller in magnitude than the true specific surface area of the material (due to resolution constraints), this smaller value is nevertheless the required input to the Kozeny–Carman relation. The argument is based on a known comparison theorem relating the permeabilities of two porous materials which differ only by the addition (without rearrangement) of the solid to the more porous material.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.339497
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  • 9
    Electronic Resource
    Electronic Resource
    Effective medium approximation for elastic constants of porous solids with microscopic heterogeneity (1986)
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 59 (1986), S. 1136-1140 
    Details
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Formulas for the scattering from an inhomogeneous sphere in a fluid-saturated porous medium are used to construct a self-consistent effective medium approximation for the coefficients in Biot's equations of poroelasticity [J. Acoust. Soc. Am. 28, 168 (1956)] when the material constituting the porous solid frame is not homogeneous on the microscopic scale. The discussion is restricted to porous materials exhibiting both macroscopic and microscopic isotropy. Brown and Korringa [Geophysics 40, 608 (1975)] have previously found the general form of these coefficients. The present results give explicit estimates of all the coefficients in terms of the moduli of the solid constituents. The results are also shown to be completely consistent with the well-known results of Gassmann and of Biot and Willis, as well as those of Brown and Korringa.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.336550
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  • 10
    Electronic Resource
    Electronic Resource
    Planar spatial correlations, anisotropy, and specific surface area of stationary random porous media (1998)
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 83 (1998), S. 1685-1693 
    Details
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: An earlier result of the author showed that an anisotropic spatial correlation function of a random porous medium could be used to compute the specific surface area when it is stationary as well as anisotropic by first performing a three-dimensional radial average and then taking the first derivative with respect to lag at the origin. This result generalized the earlier result for isotropic porous media of Debye et al. [J. Appl. Phys. 28, 679 (1957)]. The present article provides more detailed information about the use of spatial correlation functions for anisotropic porous media and in particular shows that, for stationary anisotropic media, the specific surface area can be related to the derivative of the two-dimensional radial average of the correlation function measured from cross sections taken through the anisotropic medium. The main concept is first illustrated using a simple pedagogical example for an anisotropic distribution of spherical voids. Then, a general derivation of formulas relating the derivative of the planar correlation functions to surface integrals is presented. When the surface normal is uniformly distributed (as is the case for any distribution of spherical voids), our formulas can be used to relate a specific surface area to easily measurable quantities from any single cross section. When the surface normal is not distributed uniformly (as would be the case for an oriented distribution of ellipsoidal voids), our results show how to obtain valid estimates of specific surface area by averaging measurements on three orthogonal cross sections. One important general observation for porous media is that the surface area from nearly flat cracks may be underestimated from measurements on orthogonal cross sections if any of the cross sections happen to lie in the plane of the cracks. This result is illustrated by taking the very small aspect ratio (penny-shaped crack) limit of an oblate spheroid, but holds for other types of flat surfaces as well.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.366885
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