1971
DOI: 10.1137/0120047
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On Diffusion in a Fractured Medium

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Cited by 63 publications
(38 citation statements)
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“…However, the problem (3.8) with the factor deleted from the two terms can be used as a fracture model with highly anisotropic permeability. We include this case to show what assumptions are required to arrive at the narrow fracture model described in [2].…”
Section: The Concentrated Capacity Modelmentioning
confidence: 99%
See 1 more Smart Citation
“…However, the problem (3.8) with the factor deleted from the two terms can be used as a fracture model with highly anisotropic permeability. We include this case to show what assumptions are required to arrive at the narrow fracture model described in [2].…”
Section: The Concentrated Capacity Modelmentioning
confidence: 99%
“…from hydraulic fracturing in which narrow channels of high permeability are created in the vicinity of a well to enhance the flow rate and consequently the production. The narrow fracture approximation leads to a model like the one above for thin channel flow, and by taking advantage of the symmetry about the center surface defining the fracture, one can reduce such a problem to one of the type considered here with the high-permeability region located on the boundary [2,6]. Analogous models of heat conduction arise from regions of high conductivity, and these may also include a concentrated capacity.…”
Section: Introductionmentioning
confidence: 96%
“…Let A 1 , A 3 and A 5 be the vertices of a regular triangle with unit side length, ie, |A 1 − A 3 | = |A 1 − A 5 | = |A 3 − A 5 | = 1. We define a family Ψ 1 of four suitable contractions (1) 1 , … , (1) 4 , with respect to the same ratio 1 3 (see Freiberg and Lancia 23 ). Let V (1)…”
Section: Preliminariesmentioning
confidence: 99%
“…We consider a divergence-type nonlinear evolution conductivity with a highly conductive outer film or shell. Problems of this nature also arise in modeling fluid flow in fractured media, See [3], [7], [8], [12], [15], [16].…”
Section: Introductionmentioning
confidence: 99%