A statistical model of a porous medium with nonuniform pores

Haring, Robert E.; Greenkorn, Robert A.

doi:10.1002/aic.690160327

Cited by 113 publications

(32 citation statements)

References 14 publications

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“…This relation shows a length dependence without any asymptotic (large length) behavior. A similar treatment is given by Haring and Greenkorn (1970), except distributions in the pore radius and the pore length are allowed using a two-parameter prob ability distribution function. Saffman (1959aSaffman ( ,b, 1960 analyzed the dispersion in porous media as being analogous to the Brownian motion.…”

Section: (C) Dynamic and Geometric Treatmentsmentioning

confidence: 99%

Principles of Heat Transfer in Porous Media

Kaviany

1991

Mechanical Engineering Series

827

752

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except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use of general descriptive names, trade names, trademarks, etc., in this publication, even if the former are not especially identified, is not to be taken as a sign that such names, as understood by the Trade Marks and Merchandise Marks Act, may accordingly be used freely by anyone.Camera-ready copy prepared from the author's LaTeX file. 987654321 To my parents Farideh and Morad Series PrefaceMechanical engineering, an engineering discipline born of the needs of the industrial revolution, is once again asked to do its substantial share in the call for in dust rial renewal. The general call is urgent as we face profound issues of productivity and competitiveness that require engineering solutions, among others. The Mechanical Engineering Series is a new series, featuring graduate texts and research monographs, intended to address the need for information in contemporary areas of mechanical engineering.The series is conceived as a comprehensive one that will cover a broad range of concentrations important to mechanical engineering graduate education and research. We are fortunate to have a distinguished roster of consulting editors, each an expert in one of the areas of concentration. The names of the consulting editors are listed on the first page of the volume. PrefaceThis monograph aims at providing, through integration of available theoretical and empirical treatments, the differential conservation equations and the associated constitutive equations required for the analysis of transport in porous media. Although the empirical treatment of fluid flow and heat transfer in porous media is over a century old, only in the last three decades has the transport in these heterogeneous systems been addressed in sufficient detail. So far, single-phase flow and heat transfer in porous media have been treated or at least formulated satisfactorily. But the subject of two-phase flow and the related he at transfer in porous media is still in its infancy. This monograph identifies the pr in ci pIes of transport in porous media, reviews the available rigorous treatments, and whenever possible compares the available predictions, based on these theoretical treatments of various transport mechanisms, with the existing experimental results. The theoretical treatment is based on the local volume-averaging of the momentum and energy equations with the closure conditions necessary for obtaining solutions. While emphasizing abasie understanding of heat transfer in porous media, the monograph does not ignore the need for the predictive tools. Therefore, whenever a rigorous theoretical treatment of a phenomenon is not available, semiempirical and empirical treatments are given.The monograph is divided into two parts: part 1 deals with single-phase flows and part 2...

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Section: (C) Dynamic and Geometric Treatmentsmentioning

confidence: 99%

Principles of Heat Transfer in Porous Media

Kaviany

1991

Mechanical Engineering Series

827

752

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“…However, the negative values associated with the distribution do not have physical significance. Some authors have described the nonuniformity of circular capillaries by a parametric probability distribution function [15], the so-called beta function. Derjani-Bayeh and Rodgers [16] compared a two-parametric empirical model with conventional models such as the gamma distribution, which is named from the fact that it is an incomplete function arising from the sum of exponential processes.…”

Section: Introductionmentioning

confidence: 99%

Capillary Pressure Estimation Using Statistical Pore Size Functions

et al. 2007

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Capillary pressure curves, which have been employed for a long period of time by researchers interested in pore size distribution, are commonly obtained from experimental measurements. The dynamic capillary pressure that influences the flow is affected by many factors including the pore size characteristics and pore scale dynamics. Hence, it is important to investigate the variation of the estimated pore size distribution with capillary number. In this study, a glass type micromodel is considered as the porous media sample. A parametric probability density function is proposed to express the pore size distribution of the porous model, which is also measured using an image analysis technique. The capillary pressure saturation mathematical model is developed by integrating the pore size distribution function. Model parameters with a physical significance are estimated by fitting the model to the measured capillary pressure data at different capillary numbers. The results of capillary pressure obtained are well matched to the measured values. The results show that the trends of the extracted pore size distribution curves have similar trends, but they are not exactly the same. Therefore, the dynamic capillary pressure data alone are not sufficient for estimation of the pore size distribution. As a related development, the prediction of the capillary pressure curves based on measured pore size distributions is also presented. The proposed probability distribution function has the flexibility of representing a wide variety of pore size distributions.

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“…Statistical structural models (Scheidegger, 1954;de Josselin de Jong, 1958;Saffman, 1959;Haring and Greenkorn, 1970;Guin et al, 1971;Payatakes and Neira, 1977) are highly simplified idealizations of the local pore structure, in which pores are randomly oriented in space, but no pore interconnections are recognized. There is no allowance for the posaiblity that portiona of the displaced phaae may be bypassed and trapped, that there may be a nonzero irreducible saturation of wetting phaae at the conclusion of drainage, or that there may be a nonzero residual saturation of non-wetting p'naseat t'neconclusion of iiDkiibition.…”

Section: Knnlik~n~l~sseeermentioning

confidence: 99%

“…Statistical models of the pore space have also been used in describing steady-state flows (Scheidegger, 1954;de Joaselin de Jong, 1958;Saffman, 1959;Haring and Greenkorn, 1970;Guin et al, 1971;Payatakes and Nefra, 1977). These models do not rigorously recognize interconnections among the pores: they do not require equality of pore pressure and conservation of mass at interconnections.…”

Section: Structural Modelsmentioning

confidence: 99%