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160 Constant pressure/ Initial Conditions temperature boundary Temperature,C 100 200 300 400 \\ \ \T(40 C/km) P(S atic) \ \ v 500 1000 C O2 Pressure, bars Controlled flux boundary 3.17 x 1 0 ~3kg/s CO2 (plus 85 mW/m2) FIGURE 1 1.1 Schematic diagram of the one-dimensional model used to simulate CO2 movement through the crust. Graph shows initial temperature and pressure profiles. The CO2 flux at the lower boundary is derived by assuming that the global flux of CO2 (about 3 x 10~2 moles per year) is distributed over 1 percent of the Earth's surface area (1.3 x 106 imp. The heat flow is typical of tectonically active areas. heat by solving the appropriate set of coupled partial dif- ferential equations. It was originally developed to simu- late geothermal reservoirs (Bodvarsson, 1982~; we modi- fied it to describe the properties of CO2 rather than H2O. In our particular case we assumed one-dimensional flow vertically upward through a prism of crust, and we specify at the bottom of the prism what we believe to be a reason- able flux of CO2 and heat. We then adjusted the permea- bility in the course of a set of numerical experiments. A schematic diagram of the model is shown in Figure 11.1. For the purposes of calculation we assumed that the pore fluid is pure CO2. The fluid properties of CO2 were ob- tained from Kennedy and Holser (1966), Jacobs and Ker- rick (1981), Vargaftik (1975), and Atkins (1978~. The published density and viscosity data had to be extrapolated to higher pressures. Over the pressure and temperature ranges considered, CO2 appears to have transport proper- ties that are quite similar to water (Figure 11.2~. We assumed as the lower boundary condition a con- stant influx of CO2 and heat. One can hypothesize other conditions at this lower boundary; however, for an initial calculation, constant flux provides insight. We have taken the flux as 3 x 10~2 moles of CO2 per year, which seems well within the estimates given in Table 11.2. This flux is distributed over the tectonically active area, which we have taken as 1 percent of the Earth's surface; it is then something of an average and may be substantially higher or lower locally. JOHN D. BREDEHOEFT AND STEVEN E. INGEBRITSEN Given this set of simple assumptions, we made a series of calculations to determine how low permeability would have to be in order to cause pore pressures approaching lithostatic conditions by simple permeation (i.e., without invoking enhanced transport or focusing effects). The results are summarized in Table 11.3. Since the model is run in a transient mode, the results are presented in terms of the time to reach lithostatic fluid pressure at 10 km depth, the lowermost cell of our simulated column of crust. At a permeability of 10-7 darcies, pore pressures do not ap- proach lithostatic at steady state (infinite time). Given our assumed flux, the permeability must be on the order of 10-8 darcies or lower to generate pore pressures near lithostatic. Figure 11.3 shows pressure profiles at venous times as the pressure builds to lithostatic for a case in which pe~meability is 10-9 darcies. In Figures 11.3 through 11.6, k is permeability, Cr is rock compressibility, and o is porosity. Typical ranges of rock permeability are given by Brace (1980) and are discussed below (see Figures 11.7 and 11.8~. -- CO ___ H2O r Density (g/cm3) 1 1 1 1 Viscosity (poise x 10-3 1 1 2500 L-- 0200 400 Temperature, C FIGURE 11.2 Density and viscosity of CO2 and H2O as func- tions of pressure and temperature. CO2 properties (bold con- tours) are dashed where extrapolated from published data. H2O properties are from 13urnham et al. (1969), Keenan et al. (1969), and Haar et al. (1984). The pressure-temperature range of our experiment is shown by shading.

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SOURCE OF HIGH PORE PRESSURES IN THE CRUST TABLE 11.2 Global Carbon Reservoir (from 5 Sundquist, 1985) Reservoir Carbon (10~5 tonnes) 6 Atmosphere 0.036 6.4 7.3 Oceans Continents Carbonate rocks Oceans Continents Metamorphic rocks 10 28 54 Total 106 TABLE 11.3. Time to Reach Lithostatic Pressure at a Depth of 10 km Permeability (darcy) 10-8 Porosity 10-9 0.01 0.02 0.01 0.02 HYDRAULIC FRACTURING Time (106 yr) 0.15 0.30 1.5 3.0 If the boundary condition at the base of a rock column of low permeability has a constant influx of CO2, it is possible to calculate arbitrarily high pore pressures. At some point increased fluid pressure will generate either a hydraulic fracture or a shear failure, which would increase the local permeability. The nature of the failure depends ~ . 9 _ Initial pressure k = 10-9 darcy C,= 10~5bar .. ~ = 0.01 - -... .. Li~ostatic ~ pressure it\\ to\\ \ Time, ~ ~1 coo s years - . _ 10 ~1 lo TO ~60 100_~134-_= 0 500 1 000 1500 Pressure, bars 2000 2500 FIGURE 11.3 Pressure-depth profiles for venous times after initiating flux of CO2 into bottom of column (see Figure 11.4~. 161 9 _ ~-. k= 10~9darcy _ \ . C, = 10-5 bar lo\ .. ~ = 0.01 t ~1000's Years . Initial ~ pressure | 1 ~' ---- ~ ~ ~ ', . 2000 2500 10, ' 500 1000 1500 Pressure, bars FIGURE 11.4 Pressure-depth profiles for venous times. Once lithostatic pressure is reached, permeability is increased 1000 times, simulating the effect of fracturing. on the local state of stress. In the case of a hydraulic fracture, a true tensional opening, the fracture will occur normal to the least principal stress. The fracture will occur when the pore pressure exceeds the sum of the least prin- cipal stress and the tensile stress of the rick. If the least principal stress is horizontal, the hydraulic fracture will tend to be a vertical opening. A variety of fracture orien- tations are possible depending on whether they represent shear or tensional openings and the local state of stress. When the vertical permeability is increased locally, pres- sure effects are distributed upward very quickly. The lithospheric load is a convenient upper bound for failure. We have attempted to simulate a system in which hy- draulic fractures are created. It seems that two possible processes can occur following fracturing. Once the pres- sure falls following the break, the fissure can (1) remain open, thereby increasing the local permeability or (2) seal itself, and return to something approaching its initial per- meability. We have attempted to simulate both occur- rences. Figure 11.4 illustrates the pressure history in the lower portion of the column in the case where the fracture per- meability remains high following a break. In this case permeability is increased 1000 times once the pressure within the simulated rock block reaches lithostatic. Note that lithostatic pore pressure migrates upward with time and that once breaks occur in the lower rock units they do not reach lithostatic pressures again. Figures 11.5 and 11.6 show what happens when the breaks are resealed, that is, permeability is returned to its original value following a break. The pressure once again builds to a lithostatic level at the bottom of the column, a second break occurs, and this sequence continues to repeat itself. As in the case

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162 5 6 9 _ 10< ~ :. k = 10-9 darcy Immediately C r = 104bar before fracturing . ~ = 0.02 Immediately '.. after fracturing . Lithostatic ~ pressure Time, ~ OOO's years .. pressure ~ ~ 500 i 1000 1500 2000 2 00 Pressure, bars FIGURE 11.5 Pressure-depth profiles for venous times for a system in which fracturing occurs once pressure reaches lithostatic and fractures quickly reseal themselves. In the simulation the following sequence is followed: (1) once pressure reaches lithostatic, permeability is temporarily increased 1000 times; (2) pressure drops quickly; and (3) once pressure drops, penneabil- ity is set back to its initial value, and the cycle repeats itself. There are two sets of profiles: the solid profiles are immediately before the fracturing and the dashed profiles immediately after. ce Pressure increases consistently with time within each set. JOHN D. BREDEHOEFT AND STEVEN E. INGEBRITSEN ing are also suggested by studies of hydrothermal ore deposits (see Titley, Chapter 3, this volume). DISCUSSION The results of our analysis suggest that degassing of CO2 could be a source of high pore pressure, provided that the permeability of the rocks is sufficiently low. We must now consider whether such low permeabilities might rea- sonably be expected deep within the crust. Brace (1980) has compiled both laboratory and field- measured permeability values for crystalline and argil- laceous rocks. Figures 11.7 and 11.8 are adapted from Brace. Clearly, the values suggested by our simulation are in the lower range of what has been measured, both in the laboratory and in situ. If one examines only the in situ 4 2 o -2 4 -6 Laboratory Permeability t Sand I Sandstone Limestone Volcanics dolomite Meta | Siltstone Gran jte ~ orphics | Ihaie l l l where the fissure remains open, the breaking will migrate upward (Figure 11.6~. An interesting feature of this model is the pulsing nature of the pore pressure at a given depth (see Figures 11.5 and 11.6) Gold and Soter (1985) sug gested a similar mechanism in considering the migration of fluids through the crust. Repeated episodes of fractur- FIGURE 11.7 Range of laboratory permeabilities for different rock types (from Brace, 1980~. 2S0or l ~A. ~. ~I ! 2000 1 000 I . 500 t 1 / / V . Lithostatic / / .. ~pressure D / Depth, km ~ 1500 / 9 5 ~ /.. . ~ '. : 1 1 1 2 Time, 1 OO,OOO's years k = 10-9 darcy or = 10-4 bar =0.02 3 4 FIGURE 11.6 Pressure versus time for a system in which frac- tunng occurs once pressure reaches lithostatic and fractures quickly reseal themselves. -8 -10 -12 Gneiss values, they are very near the low end of what has been measured. However, most of the in situ values have been measured near the Earth's surface, usually at depths above 500 m. It is our judgment that rock permeabilities in the range of 10-8 to 10-9 darcies are low but within the realm of expectation deep within the crust. We have assumed in our calculations that the pore fluid is entirely CO2. There is likely to be some H2O present in the crust in the pressure-temperature range of the experi- ments. If significant amounts of both H2O and CO2 are present, the pore fluid would be a homogeneous single- phase mixture of H2O and CO2 at temperatures 2300C and a heterogenous two-phase mixture of H2O-rich liquid and CO2-rich vapor at lower temperatures. The presence of NaC1 or other electrolytes would extend the two-phase region to higher temperatures (Bowers and Helgeson, 1983~.

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SOURCE OF HIGH PORE PRESSURES lN THE CRUST 4 2 o -2 o -4 -6 -8 -10 -12 In Situ Permeability '1~' 1' l,... Gig ; Gig I I - I i S cCD to I I _ c ~ . 0 co a, _ cO cn or Crystalline JO Argillaceous FIGURE 11.8 Range of in situ permeability measurements for crystalline and argillaceous rocks from various sites around the world (from Brace, 1980~. The limited solubility of CO2 in H2O in the pressure- temperature range considered (Takenouchi and Kennedy, 1964; Gehrig, 1980) implies that the volumetric flow rate required to transport a given flux of CO2 in solution or in a two-phase mixture would generally be somewhat greater than the flow rate required to transport the same CO2 as a separate phase. Since the density and viscosity of H2O and CO2 are comparable (Figure 11.2), the limiting permea- bilities suggested here for anhydrous systems may be rea- sonably limiting values for hydrous systems as well. Chemical controls on the buildup of CO2 pressure may significantly constrain the applicability of our analyses. CO2 pressures in natural systems at temperatures of 200 to 400C will generally be limited by the reaction of Ca- Al-silicates, H2O, and CO2 to form calcite and mica and/or clay. At 300C, for example, the partial pressure of CO2 is likely to be on the order of tens of bars (Giggenbach, 1986~. Where the available feldspar is converted to calcite and mica and/or clay, or the supply of H2O is limited, the partial pressure of CO2 is not fixed and may increase to greater values. This might occur where the flux of CO2 is greatest (e.g., in fault zones and volcanic terranes). In general, CO2 flux may be lower and/or permeabilities higher than those required to create high pore pressures; other- wise, we would expect most Ca-Al-silicates in the upper crust to be altered to calcite. i63 The question of fluid movement and pore pressure within the deep crust is complex. The intent of this chapter was a simple bounding calculation; we hope that it will provoke further thought, debate, and analysis. On balance it seems possible that fluid CO2 migrating through the crust may yield high pore pressure where the rocks deep in the crust are sufficiently "tight" and the local geochemistry does not preclude high CO2 fluid pressures. ACKNOWLEDGMENTS We thank R. O. Fourier and H. R. Shaw for helpful reviews of this manuscnpt. Our brief discussion of chemi cal controls on CO2 pressure is based largely on Fournier's comments. REFERENCES Anderson, A. T. (1975~. Some basaltic and andesitic gases, Reviews of Geophysics and Space Physics 13, 37-55. Atkins, P. W. (1978~. Physical Chemistry, W. H. Freeman and Company, San Francisco. Baes, C. F., H. E. Goeller, J. S. Olsen, and R. M. Rotty (1976~. The global carbon dioxide problem, Oak Ridge National Labo- ratory Report ORNL-5194, 78 pp. Barnes, I., W. P. Irwin, and D. E. White (1978~. Global distribu- tion of carbon dioxide discharges and major zones of seismi- city, U.S. Geological Survey, Water Resources Investigations 78-39, 12 pp. Barnes, I., W. P. Irwin, and D. E. White (1984~. Global distribu- tion of carbon dioxide discharges and major zones of seismi- city, U.S. Geological Survey, Miscellaneous Investigations Map I-1528, 10 pp. Bodvarsson, G. S. (1982~. Mathematical modeling of geother- mal systems, Ph.D. thesis, University of California, Berkeley. Borchert, H. (1951~. Zur geochemie des kohlenstoffs, Geochim- ica et Cosmochimica Acta 2, 62-75. Bowers, T. S., and H. C. Helgeson (1983~. Calculation of the thermodynamic and geochemical consequences of nonideal mixing in the system H2O-CO2-NaC1 on phase relations in geologic systems: Equation of state for H2O-CO2-NaC1 fluids at high pressures and temperatures, Geochimica et Cosmo- chimica Acta 47, 1247-1275. Brace, W. F. (1980~. Permeability of crystalline and argillaceous rocks, International Journal of Rock Mechanics: Mineral Sci- ences and Geomechanics 17, 241-251. Buddemeier, R. W., and C. Puccetti (1974~. C-14 dilution esti- mates of volcanic CO2 emission rates (abstract), EOS 55, 488. Burnham, C. W., J. R. Holloway, and N. F. Davis (1969~. Thermo- dynamic Properties of Water to 1,000C arid 10,000 bars, Special Paper 132, Geological Society of America, Boulder, Colo., 96 pp. Des Marais, D. (1985~. Carbon exchange between the mantle and crust and its effect upon the atmosphere: Today compared to Archean time, in The Carbon Cycle and Atmospheric CO2:

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164 Natural Variations Archean to Present, Geophysical Mono- graph 32, American Geophysical Union, Washington, D.C., pp. 602-611. Gehrig, M. (1980~. Phasenglichgewichte und PVT-daten ter- narer mischungen aus wasser, kohlendioxid und natriumchlo- rid his 3 kbar und 550C, Ph.D. thesis, University of Karlsruhe, Freiburg, Germany. Gerlach, T. M. (1986~. Carbon and sulphur isotopic composition of Kilauea parental magma, Nature 319, 480-483. Gerlach, T. M. (1988~. Plutonic degassing of carbon dioxide at transitional and mid-oceanic spreading centers, Earth and Planetary Science Letters. Giggenbach, W. T. (1986~. Graphical techniques for the evalu- ation of water/rock equilibrium conditions by use of Na, K, Mg, and Ca-contents of discharge waters, in Proceedings of the Eighth New Zealand Geothermal Workshop, Aukland, pp. 37-43. Gold, T., and S. Soter (1980~. The deep-Earth-gas hypothesis, Scientific American 242, 154- 161. Gold, T., and S. Soter (1985~. Fluid ascent through the solid lithosphere and its relation to earthquakes, PAGEOPH 122, 492-530. Haar, L., J. S. Gallagher, and G. S. Kell (1984~. NBSINRC Steam Tables, Hemisphere Publishing Corp., New York. Hanshaw, B. B., and E. Zen (1965~. Osmotic equilibrium and overthrust faulting, Geological Society of America Bulletin 76, 1379-1386. Harris, D. M. (1981~. The concentration of CO2 in tholeiitic basalts, Journal of Geology 89, 689-701. Hubbert, M. K., and W. W. Rubey (1959~. Role of fluid pressure in mechanics of overthrust faulting, Geological Society of America Bulletin 70, 115-206. Irwin, W. P., and I. Barnes (1975~. Effect of geologic structure and metamorphic fluids on seismic behavior of San Andreas fault system in central and northern California, Geology 3, 713-716. Jacobs, G. K., and D. M. Kerr~ck (1981~. APL and Fortran programs for a new equation of state for H2O, CO2, and their mixtures at super-critical conditions, Computers in Geoscience 7, 131-143. Javoy, M., F. Pineau, and C. J. Allegre (1982~. Carbon geody- namic cycle, Nature 300, 171 -173. Keenan, J. H., F. G. Keyes, P. G. Hill, and J. G. Moore (1969~. Steam Tables, John Wiley & Sons, New York. Kennedy, G. C., and W. T. Holser (1966~. Pressure-volume JOHN D. BREDEHOEFT AND STEVEN E. INGEBRITSEN temperature and phase relations of water and carbon dioxide, in Handbook of Physical Constants, Revised Edition, Memoir 97, Geological Society of America, Boulder, Colo., pp. 371- 383. Leavitt, S. W. (1982~. Annual volcanic carbon dioxide emission: An estimate from eruption chronologies, Environmental Geol- ogy 4, 15-21. Li, Y-H. (1972~. Geochemical mass balance among lithosphere, hydrosphere, and atmosphere, American Journal of Science 272, 119-137. Libby, L. M., and W. F. Libby (1972~. Vulcanism and radiocar- bon dates, in Proceedings of the 8th International Conference on Radiocarbon Dating, Wellington, New Zealand, pp. A72- A75. Marty, B., and A. Jambon (1987~. C/3He in volatile fluxes from the solid Earth: Implications for carbon geodynamics, Earth and Planetary Science Letters 83, 17-26. Moore, J. G., J. N. Bachelder, and C. G. Cunningham (1977~. CO2-filled vesicles in mid-ocean basalt, Journal of Volcanol- ogy and Geothermal Research 2, 309-327. Pineau, P., M. Javoy, and Y. Bottinga (1976~. ~3C/~2C ratios of rocks and inclusions in popping rocks in Mid-Atlantic Ridge and their bearing on the problem of isotopic composition of deep seated carbon, Earth and Planetary Science Letters 29, 413-421. Plass, G. N. (1956~. The carbon dioxide theory of climate change, Tellus 8, 140-154. Rubey, W. W. (1951~. Geologic history of the sea, Geological Society of America Bulletin 61, 1111-1148. Rubey, W. W., and M. K. Hubbert (19594. Role of fluid pressure in mechanics of overthrust faulting: (II) Overthrust belt in geosynclinal area of western Wyoming in light of fluid-pres- sure hypothesis, Geological Society of America Bulletin 70, 167-206. Sundquist, E. T. (1985~. Geological perspectives on carbon dioxide and the carbon cycle, in The Carbon Cycle and Atmo- spheric CO2: Natural Variations Archean to Present, Geo- physical Monograph 32, American Geophysical Union, Wash- ington, D.C., pp. 5-59. Takenouchi, S., and G. C. Kennedy (1964~. The binary system H2O-CO2 at high temperatures and pressures, American Jour- nal of Science 262, 1055-1074. Vargaftik, N. B. (1975~. Tables on the Thermophysical Proper- ties of Liquids and Gases in Normal and Disassociated States, John Wiley & Sons, New York.

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Index A Actinolite, 82 Advection, 9, 29-30, 31, 32, 33, 47-48 Africa, 132, 145 Alaska, 81, 137, 148-155 Alberta, 136, 137 Alps, 10, 32, 69, 153 Aluminum andalusite, 98, 101, 109 chlorites, 77-78, 82, 83, 98, 99 mica, 97, 98, 99, 100, 106, 163 see also Feldspar Amphiboles, 82, 88, 97, 98-99, 101, 106, 109, 153 Anatexis, 108-111 Andalusite, 98, 101, 109 Appalachian Mountains, 12, 35, 132, 133, 134-135, 136, 138, 140-146, 153 Aquifers, see Groundwater tables Arizona, 38, 51, 52, 54, 55, 58, 130 Arrow Lake, 78 Asia, 145, 158 see also geographical subunits Atlantic Ocean, 150 B Barbados, 150, 153 Barium, 15 Basalts carbon dioxide solubility, 159 fluid-rock ratios, 65 magma, 84-90, 159 Basement complexes Hercynian orogeny, 98, 99, 100, 103, 106-110 seismic reflection, 128-138 Batholiths, 33, 54, 75-80, 81, 87-88, 115 Bentonite, 33 Biotites, 77, 82, 99, 101, 103, 104, 105 Boreholes, see Drilling Boundary conditions, 15, 16, 23 Breccias, 53, 80 Brines, 20, 125, 133-138 British Columbia, 73, 81 cordilleran batholiths, 75-78 British Institutions Reflection Profiling Syndicate, 128 Brittleness, 5, 54, 73, 90, 111, 116 C Calderas, 79-80, 81, 84-85, 89, 90 California, 21, 22, 81, 136 San Andreas Fault, 12-13, 35-36, 116 Canada, 135, 136, 137 see also geographic subunits Carbonates, 64-65, 68, 98-105' 106, 109, 158 Carbon dioxide, 5, 39, 64, 65-66, 96, 130, 141, 154, 159-163 Carboniferous period, 97, 98, 99, 105, 106, 109 Carbon isotopes, 96, 158-159 Cascade Mountains, 80 165 Caspian Basin, 14, 36, 37 Cenozoic era, 51, 76, 84 see also Quaternary period; Tertiary period Channelized flows, 9, 29, 45, 47-48, 69-70, 132 Chemical processes, 4, 5, 8, 9, 19 carbon dioxide, 5, 39, 64, 65-66, 96, 130, 141, 154, 159-163 diagenesis, 12, 13-15, 27, 36-37, 134, 149 equations, 4, 10, 31-32 fault zones, 153 free water, 5 global geochemical budget, 149 hydration/dehydration, 15-16, 37-38, 56-57, 68 metamorphism, 64-65 phase equilibria, 4, 64, 65, 66 quartz precipitation, 69-70 research recommendations, 21 salt and systems, 20, 59, 65, 133-135 transport, 3, 31-33, 48 volatiles, 39, 47, 67-6S, 69, 132, 158 see also Isotope geochemistry; Minerals and mineralogy Chlorites, 77-78, 82, 83, 98, 99 Clay, 11, 14, 37, 67, 82, 150 bentonite, 33 montmorillonite-illite transformation, 14, 17, 37'39, 134, 149 petite, 65, 68-70, 98-99, 100, 101, 102, 107, 108, 111 Coal, 133 Colorado, 22, 33, 81, 90

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166 Computer applications, 4, 22 fracture processes, 19, 20 heat/mass transport, 15 Conservation equations, 6-9, 28-32 Consortium for Continental Reflection Profiling, 128-138 Contamination, 10, 21, 27, 31-32 Continental margins, 64, 75-76, 132, 138 Convection, 6, 15-16, 27, 30, 33, 37, 38, 42, 50, 73, 77, 90, 110, 111 Cordilleran phenomena batholiths, British Columbia, 75-78 hydrocarbons, 136 Cores, see Drilling Coupling of processes, 3, 10, 14, 17, 22-23, 32, 38, 39, 48, 153, 160 Cretaceous period meteoric hydrothermal activity, 76, 81 shale, 8, 33, 96 Crystalline rock and crystallization, 8, 19, 38 basement complexes, 98-100, 103, 106, 107, 108, 109, 110, 128-138 batholiths, 33, 54, 75-80, 81, 87-88, 115 chlorites, 77-78, 82, 83, 98, 99 geometry, 84 granitic, 97 magmatic, 16, 38, 45, 46, 47, 53-54, 80, 83-84, 87, 9~91 paragenesis, 55-59 permeability/porosity, 8, 47, 83-84 pressure relations, 117 see also Quartz D Darcy's Law, 7, 10, 28-29, 30, 32, 34, 37, 150 F Deep crustal processes, 4, 5, 16-17, 38, 64, 96, 128-138 Density, 10, 15, 29, 32, 37-38 fracturing, 58, 59 pressure and, 38, 43, 68, 82 rock/mineral, 43, 68 Devonian period, 35, 97, 135, 141, 143-144 Diagenesis, 12, 13-15, 27, 36-37, 134, 149 Differential equations, see Equations Diffusion, 15, 29-31, 32, 117 see also Advection; Convection Dispersion processes, 29-30, 32 Drilling, 5, 58, 86, 90, 96, 111 Ductility, 5, 89, 90, 111 E INDEX Energy factors, 47 Energy resources coal, 133 hydrothermal, commercial use, 16, 38 natural gas, 21, 27 oil, 10, 21, 27, 135, 136 Energy transport, 3, 6-7, 27-32, 30 see also Heat transport; Momentum Eocene epoch, 78 magmatism, hydrothermal effects, 78-80 Epidote, 82, 83 Equations, 3 boundary conditions, 15, 16, 23 carbon dioxide flux, 159-160 conservation, 4, 6-9, 28-32 coupling of processes, 3, 10, 14, 17, 22-23, 32, 38, 39$ 48, 153, 160 Darcy's Law, 7, 10, 28-29, 30, 32, 34, 37, 150 density, 37-38, 68 dispersion-diffusion-advection, 29-30, 31, 32, 33, 48 geothermal reservoirs, 16, 38 hydration/dehydration, 38-39 magma-associated flow, 38, 42 permeability, 60, 120 pressure effects, 4, 10, 29, 32, 37, 42-48, 68-69, 120, 121, 122 research recommendations, 22-23 stress and strain, 31, 36-37 tectonic stress, 35, 121 time factors, 121-122 volume, failure, 46-47, 48, 122, 123 Europe, 106, 158 see also geographical subunits Earthquakes, 3, 5, 10, 21-22, 27, 33, 115, 124 Elasticity, 30, 45, 124 visco, 22, 32 see also Stress and strain Electrical conductivity/resistivity, 5, 11, 33, 115, 150 Electromagnetic techniques, 5, 115 Elkhorn Mountains, 81 Faults, 149, 150, 151-154 Appalachian Fold-Thrust Belt, 35, 140-146 joint/fracture systems, 54, 144-145, 146 magma conduits, 129 rift zones, 72, 86, 87, 89, 90, 91, 109, 110, 129-130 San Andreas, 12-13, 35-36, 116 strain rates, 121, 124 see also Earthquakes Feldspar, 73-75, 78, 81, 82, 83, 88, 99, 101, 104, 134, 163 plagioclase, 82, 83 sericite, 83, 98 see also Granite and granitoids Fick's Law, 29 Field studies, 17-19, 33 fluid inclusion, 150-155, 158 joint sets and systems, 51-61, 144-145, 146 Finger Lakes, 141 Flows artesian, 141 channelized flows, 9, 29, 45, 47-48, 69-70, 132 flow equations, 29 grain boundaries, 8, 65, 69 lithostatic fluid pressure, 5, 10, 14, 21, 33, 37,66,67-69,90,91, 110, 111, 117, 12~123, 141, 145, 146, 149-151, 158, 159 mid- to lower-crustal levels, 5, 16-17, 64, 66-68 velocity, 20, 28, 29, 68-69 viscosity, 10, 22, 37, 46, 47, 66, 68-69, 82, 120 see also Advection; Convection; Diffusion; Permeability and porosity Flux, 9, 30, 31, 6066, 68-69 carbon dioxide, 159, 160, 163 Darcy's Law, 7, 10, 28-29, 30, 32, 34, 37, 150 mass/energy, 6-7 thermal, 44 Fourier's Law, 30 Fracture processes brittleness, 5, 54, 73, 90, 111, 116 channelized flows, 9, 29, 45, 47-48, 69-70, 132 deep crustal, 5 diffusive, 29 failure criteria, 15, 27, 38, 44, 45-48, 50, 54, 122, 123, 124 gabbros, 84 healing/sealing, 118, 120-121, 122, 124, 151 hydraulic, 6, 8, 13~16, 27-28, 36' 38, 42, 45, 54, 68, 69, 117-120, 122, 123, 144, 150, 151-152, 161-162 hydrothermal, 5~61, 69 joint sets and systems, 50-61, 144 145, 146 magma, 44-48, 50-61 mineralization, 4, 15, 27-28, 47-48, 53, 55-59, 69-70, 81, 82, 118, 12~121, 122, 124, 153 ocean lithosphere, 123 permeability, 6, 20-21, 27, 5~61, 78, 84, 90 research recommendations, 17, 19 France, Pyrenees, 33, 65, 73, 89, 91, 96-111 G Gabbros, 73, 81-84 Geometry crystallization, 84 fractures, 19 joint/fracture systems, 51, 54-59 pores, 42, 45 Gold, 81 Gneisses, 97, 98-99, 101-110 (passim), 117 Gondwanaland, 137 Grain boundaries, 8, 65, 69, 118, 149 Granite and granitoids, 73, 76, 77, 98, 99, 100, 102, 105, 108 crystallization, 97 gabbros vs. 73, 83-84 gneisses, 101