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Subsurface Fluid Flow: The Hydrology of Geothermal Systems 65

depth intervals that occur in boreholes 66-29 and the lower portion of M-1 must be maintained by
vertical fluid flow in a fracture dominated system in which convective fluid movement is driven by
a heat source at depth. Temperature reversals in these sections are likely due to interaction with a
small volume of infiltrating meteoric water.

synopsIs
Flow of water in the subsurface depends upon the characteristics of the pores in the rock (i.e., the
porous medium) and the properties of fractures (i.e., the fractured medium). In both of these pos-
sible flow pathways, the permeability controls the volumetric rate of fluid flow that can be accom-
modated by the rock. This in turn, directly controls the rate at which energy can be transferred
to the surface for geothermal uses. The variables that control flow in the porous medium are the
tortuosity and surface area affecting flow. For fractures, the primary variables are the aperture and
number of fractures per rock volume. In both instances, the pressure gradient is an additional influ-
ence that affects flow rate. Both porosity and permeability are affected by the lithostatic load on the
rock, and thus are also a function of depth. The sophistication of hydrologic modeling efforts has
greatly improved over the last two decades, to the point where quantitative analysis allowing predic-
tive capabilities is now possible. However, the accuracy of modeling results is directly dependent on
the availability of high quality analytical data for in situ rock properties.

Problems
4.1 What would be the exposed surface area in 1 cubic meter of rock that was cut by planar
fractures with an aperture of 10 microns and that had a total fracture porosity of 10%?
4.2 What would be the fracture permeability of this rock?
4.3 What would be the fracture transmissivity of that same rock?
4.4 What would be the total volume of water that would move through a conducting fracture
over an hour if the aperture were 1 cm and the pressure gradient was 1 kPa per meter?
4.5 What would be the permeability of a sandstone with a cross-sectional area of 0.1 m if
2
0.01 m /s of fluid with a dynamic viscosity of 0.001 Pascal-seconds flowed through it
3
under a pressure gradient of 1 MPa per meter?
4.6 In Figure 4.9 the maximum and minimum fracture permeability differ by more than
three orders of magnitude, at a porosity of 3%. Using Figure 4.6, determine the range
of respective fracture aperture and spacing for these conditions.
4.7 Develop two hypotheses for the temperature distribution shown in Figure 4.11 for well
M-1. What would be the most likely?

reFerences
Bailey, R. A. 1989. Geologic map of Long Valley Caldera, Mono Inyo volcanic chain and vicinity, Eastern
California. U.S. Geological Survey Misc. Invest. Ser. Map I-1933.
Bear, J. 1993. “Modeling Flow and Contaminant Transport in Fractured Rocks.” In Flow and Contaminant
Trans port in Fractured Rock, eds. J. Bear, C.-F. Tsang, and G. de Marsily, 1–27. New York: Academic
Press, Inc.
Björnsson, G., and G. Bodvarsson. 1990. “A Survey of Geothermal Reservoir Properties.” Geothermics
19:17–27.
Carman, P. C. 1937. “Fluid Flow Through a Granular Bed.” Transactions of the Institute of Chemical Engineering
London 15:150–156.
Carman, P. C. 1956. Flow of Gases Through Porous Media. London: Butterworths.
Evans, J. P., and K. K. Bradbury. 2004. “Faulting and Fracturing of Non-Welded Bishop Tuff, Eastern
California.” Vadose Zone Journal 3:602–23.
Farrar, C. D., M. L. Sorey, W. C. Evans, J. F. Howle, B. D. Kerr, B. M. Kennedy, C.-Y. King, and J. R. Southon.
1995. “Forest-Killing Diffuse CO2 Emission at Mammoth Mountain as a Sign of Magmatic Unrest.”
Nature 376:675–78.