DOI: 10.1063/1.448420. Bounds on fluid permeability for viscous flow through porous media

Bounds on fluid permeability for viscous flow through porous media

10.1063/1.448420

Crossref journal-article

AIP Publishing

The Journal of Chemical Physics (317)

Abstract

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.

Bibliography

Berryman, J. G. (1985). Bounds on fluid permeability for viscous flow through porous media. The Journal of Chemical Physics, 82(3), 1459â1467.

Authors 1

James G. Berryman (first)

References 22 Referenced 19

{'key': '2024021001503206300_r1'}
{'key': '2024021001503206300_r2', 'first-page': '214', 'volume': '4', 'year': '1966', 'journal-title': 'Isr. J. Technol.'} / Isr. J. Technol. (1966)
10.1007/BF01376989 / Acta Mech. (1977)
{'key': '2024021001503206300_r2b'}
10.1063/1.1706246 / Phys. Fluids (1961)
10.1063/1.1706534 / Phys. Fluids (1962)
10.1063/1.1692887 / Phys. Fluids (1970)
10.1143/JPSJ.40.567 / J. Phys. Soc. Jpn. (1976)
{'key': '2024021001503206300_r7'}
10.1016/0021-9991(83)90021-9 / J. Comput. Phys. (1983)
{'key': '2024021001503206300_r9'}
10.1063/1.1742339 / J. Chem. Phys. (1955)
{'key': '2024021001503206300_r11'}
10.1063/1.444011 / J. Chem. Phys. (1982)
10.1063/1.1677576 / J. Chem. Phys. (1972)
10.1017/S0022112074002503 / J. Fluid Mech. (1974)
10.1017/S0022112077001414 / J. Fluid Mech. (1977)
{'key': '2024021001503206300_r16'}
10.1016/0021-9991(78)90004-9 / J. Comput. Phys. (1978)
10.1063/1.445941 / J. Chem. Phys. (1983)
10.1063/1.1729783 / J. Appl. Phys. (1963)
10.1080/00268976300101411 / Mol. Phys. (1964)

Dates

Type	When
Created	23 years, 1 month ago (July 26, 2002, 9 a.m.)
Deposited	1 year, 6 months ago (Feb. 9, 2024, 10:05 p.m.)
Indexed	1 year, 6 months ago (Feb. 10, 2024, 8:11 a.m.)
Issued	40 years, 7 months ago (Feb. 1, 1985)
Published	40 years, 7 months ago (Feb. 1, 1985)
Published Print	40 years, 7 months ago (Feb. 1, 1985)

Funders 0

None

BibTeX

@article{Berryman_1985, title={Bounds on fluid permeability for viscous flow through porous media}, volume={82}, ISSN={1089-7690}, url={http://dx.doi.org/10.1063/1.448420}, DOI={10.1063/1.448420}, number={3}, journal={The Journal of Chemical Physics}, publisher={AIP Publishing}, author={Berryman, James G.}, year={1985}, month=feb, pages={1459–1467} }

JSON

{
  "indexed": {
    "date-parts": [
      [
        2024,
        2,
        10
      ]
    ],
    "date-time": "2024-02-10T13:11:01Z",
    "timestamp": 1707570661529
  },
  "reference-count": 22,
  "publisher": "AIP Publishing",
  "issue": "3",
  "content-domain": {
    "domain": [
      "pubs.aip.org"
    ],
    "crossmark-restriction": true
  },
  "published-print": {
    "date-parts": [
      [
        1985,
        2,
        1
      ]
    ]
  },
  "abstract": "<jats:p>General properties of variational bounds on Darcy\u2019s 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\u2019s 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\u2019s 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\u2013Carman empirical relation for porous materials.</jats:p>",
  "DOI": "10.1063/1.448420",
  "type": "journal-article",
  "created": {
    "date-parts": [
      [
        2002,
        7,
        26
      ]
    ],
    "date-time": "2002-07-26T13:00:36Z",
    "timestamp": 1027688436000
  },
  "page": "1459-1467",
  "update-policy": "http://dx.doi.org/10.1063/aip-crossmark-policy-page",
  "source": "Crossref",
  "is-referenced-by-count": 19,
  "title": "Bounds on fluid permeability for viscous flow through porous media",
  "prefix": "10.1063",
  "volume": "82",
  "author": [
    {
      "given": "James G.",
      "family": "Berryman",
      "sequence": "first",
      "affiliation": [
        {
          "name": "Lawrence Livermore National Laboratory, L-200 Livermore, California 94550"
        }
      ]
    }
  ],
  "member": "317",
  "reference": [
    {
      "key": "2024021001503206300_r1"
    },
    {
      "key": "2024021001503206300_r2",
      "first-page": "214",
      "volume": "4",
      "year": "1966",
      "journal-title": "Isr. J. Technol."
    },
    {
      "key": "2024021001503206300_r2a",
      "doi-asserted-by": "crossref",
      "first-page": "153",
      "DOI": "10.1007/BF01376989",
      "volume": "25",
      "year": "1977",
      "journal-title": "Acta Mech."
    },
    {
      "key": "2024021001503206300_r2b"
    },
    {
      "key": "2024021001503206300_r3",
      "doi-asserted-by": "crossref",
      "first-page": "1477",
      "DOI": "10.1063/1.1706246",
      "volume": "4",
      "year": "1961",
      "journal-title": "Phys. Fluids"
    },
    {
      "key": "2024021001503206300_r4",
      "doi-asserted-by": "crossref",
      "first-page": "1390",
      "DOI": "10.1063/1.1706534",
      "volume": "5",
      "year": "1962",
      "journal-title": "Phys. Fluids"
    },
    {
      "key": "2024021001503206300_r5",
      "doi-asserted-by": "crossref",
      "first-page": "2958",
      "DOI": "10.1063/1.1692887",
      "volume": "13",
      "year": "1970",
      "journal-title": "Phys. Fluids"
    },
    {
      "key": "2024021001503206300_r6",
      "doi-asserted-by": "crossref",
      "first-page": "567",
      "DOI": "10.1143/JPSJ.40.567",
      "volume": "40",
      "year": "1976",
      "journal-title": "J. Phys. Soc. Jpn."
    },
    {
      "key": "2024021001503206300_r7"
    },
    {
      "key": "2024021001503206300_r8",
      "doi-asserted-by": "crossref",
      "first-page": "142",
      "DOI": "10.1016/0021-9991(83)90021-9",
      "volume": "52",
      "year": "1983",
      "journal-title": "J. Comput. Phys."
    },
    {
      "key": "2024021001503206300_r9"
    },
    {
      "key": "2024021001503206300_r10",
      "doi-asserted-by": "crossref",
      "first-page": "1514",
      "DOI": "10.1063/1.1742339",
      "volume": "23",
      "year": "1955",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024021001503206300_r11"
    },
    {
      "key": "2024021001503206300_r12",
      "doi-asserted-by": "crossref",
      "first-page": "2071",
      "DOI": "10.1063/1.444011",
      "volume": "77",
      "year": "1982",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024021001503206300_r13",
      "doi-asserted-by": "crossref",
      "first-page": "2527",
      "DOI": "10.1063/1.1677576",
      "volume": "56",
      "year": "1972",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024021001503206300_r14",
      "doi-asserted-by": "crossref",
      "first-page": "449",
      "DOI": "10.1017/S0022112074002503",
      "volume": "64",
      "year": "1974",
      "journal-title": "J. Fluid Mech."
    },
    {
      "key": "2024021001503206300_r15",
      "doi-asserted-by": "crossref",
      "first-page": "695",
      "DOI": "10.1017/S0022112077001414",
      "volume": "83",
      "year": "1977",
      "journal-title": "J. Fluid Mech."
    },
    {
      "key": "2024021001503206300_r16"
    },
    {
      "key": "2024021001503206300_r17",
      "doi-asserted-by": "crossref",
      "first-page": "192",
      "DOI": "10.1016/0021-9991(78)90004-9",
      "volume": "27",
      "year": "1978",
      "journal-title": "J. Comput. Phys."
    },
    {
      "key": "2024021001503206300_r18",
      "doi-asserted-by": "crossref",
      "first-page": "1505",
      "DOI": "10.1063/1.445941",
      "volume": "79",
      "year": "1983",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024021001503206300_r19",
      "doi-asserted-by": "crossref",
      "first-page": "2636",
      "DOI": "10.1063/1.1729783",
      "volume": "34",
      "year": "1963",
      "journal-title": "J. Appl. Phys."
    },
    {
      "key": "2024021001503206300_r20",
      "doi-asserted-by": "crossref",
      "first-page": "591",
      "DOI": "10.1080/00268976300101411",
      "volume": "7",
      "year": "1964",
      "journal-title": "Mol. Phys."
    }
  ],
  "container-title": "The Journal of Chemical Physics",
  "original-title": [],
  "language": "en",
  "link": [
    {
      "URL": "https://pubs.aip.org/aip/jcp/article-pdf/82/3/1459/18952243/1459_1_online.pdf",
      "content-type": "application/pdf",
      "content-version": "vor",
      "intended-application": "syndication"
    },
    {
      "URL": "https://pubs.aip.org/aip/jcp/article-pdf/82/3/1459/18952243/1459_1_online.pdf",
      "content-type": "unspecified",
      "content-version": "vor",
      "intended-application": "similarity-checking"
    }
  ],
  "deposited": {
    "date-parts": [
      [
        2024,
        2,
        10
      ]
    ],
    "date-time": "2024-02-10T03:05:03Z",
    "timestamp": 1707534303000
  },
  "score": 1,
  "resource": {
    "primary": {
      "URL": "https://pubs.aip.org/jcp/article/82/3/1459/219388/Bounds-on-fluid-permeability-for-viscous-flow"
    }
  },
  "subtitle": [],
  "short-title": [],
  "issued": {
    "date-parts": [
      [
        1985,
        2,
        1
      ]
    ]
  },
  "references-count": 22,
  "journal-issue": {
    "issue": "3",
    "published-print": {
      "date-parts": [
        [
          1985,
          2,
          1
        ]
      ]
    }
  },
  "URL": "http://dx.doi.org/10.1063/1.448420",
  "relation": {},
  "ISSN": [
    "0021-9606",
    "1089-7690"
  ],
  "subject": [],
  "published-other": {
    "date-parts": [
      [
        1985,
        2,
        1
      ]
    ]
  },
  "published": {
    "date-parts": [
      [
        1985,
        2,
        1
      ]
    ]
  }
}