Fluid Flow Through a Large Vertical Crack in the Earth's Crust

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In this investigation, we are primarily concerned with modeling fluid flow through vertical cracks that were created for the purpose of extracting heat from hot, dry rock masses. The basic equation for the two-dimensional problem of fluid flow through a crack is presented and an approximate solution is found. The basic equation is a non-linear, Cauchy-singular integro-differential equation. Moderately simple formulae for the crack opening displacement and the effective pressure difference between the crack tips are derived. The results are valid for arbitrary vertical cracks, provided that the fluid injection and removal points are not placed too close to the ... continued below

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193-197

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Weertman, J. & Chang, S.P. December 1, 1976.

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Description

In this investigation, we are primarily concerned with modeling fluid flow through vertical cracks that were created for the purpose of extracting heat from hot, dry rock masses. The basic equation for the two-dimensional problem of fluid flow through a crack is presented and an approximate solution is found. The basic equation is a non-linear, Cauchy-singular integro-differential equation. Moderately simple formulae for the crack opening displacement and the effective pressure difference between the crack tips are derived. The results are valid for arbitrary vertical cracks, provided that the fluid injection and removal points are not placed too close to the crack tips. (A more complete treatment of this problem is given by us in a paper to appear in the Journal of Geophysical Research.) There are two corrections that can be made to our results. One of these is for the influence of the earth’s surface. Another correction takes into account the force in the vertical direction produced at the crack walls by the fluid pressure because the crack walls are not vertical when the crack is filled with fluid. It can be shown (Weertman and Chang, Ref. 6) that both of these corrections are negligibly small. We conclude from this analysis that the crack profile and stress intensity factors of any large vertical fluid-filled crack for heat extraction purposes will not be changed appreciably when fluid is forced to flow through the crack at physically practical velocities. 6 refs.

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193-197

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  • Proceedings Second Workshop Geothermal Reservoir Engineering, Stanford University, Stanford, Calif., December 1-3, 1976

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  • Report No.: SGP-TR-20-27
  • Grant Number: E043-326-PA-50
  • Office of Scientific & Technical Information Report Number: 887395
  • Archival Resource Key: ark:/67531/metadc885713

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Office of Scientific & Technical Information Technical Reports

Reports, articles and other documents harvested from the Office of Scientific and Technical Information.

Office of Scientific and Technical Information (OSTI) is the Department of Energy (DOE) office that collects, preserves, and disseminates DOE-sponsored research and development (R&D) results that are the outcomes of R&D projects or other funded activities at DOE labs and facilities nationwide and grantees at universities and other institutions.

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  • December 1, 1976

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  • Sept. 21, 2016, 2:29 a.m.

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  • Dec. 9, 2016, 4:25 p.m.

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Weertman, J. & Chang, S.P. Fluid Flow Through a Large Vertical Crack in the Earth's Crust, article, December 1, 1976; United States. (digital.library.unt.edu/ark:/67531/metadc885713/: accessed December 18, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.