T. Brikowski1 and D. Norton2
1Geosciences Department, University of Texas at Dallas
2School of Thought, Stanley, ID
Preliminary models of the natural state of The Geysers geothermal system reveal several important features. The models were made on a two-dimensional SW-NE cross-section through core hole SB-15D, and are constrained by petrologic geothermometers. Permeability zonation is based on present-day observations. Results indicate a maximum lifetime of 500,000 years for hydrothermal circulation after felsite intrusion, and early development of isothermal conditions in the location of the current steam reservoir. Preliminary flow system constraints based on observed whole rock oxygen isotope alteration demonstrate that the hydrothermal model is consistent with observed alteration.
The Geysers offers a unique opportunity to study an active hydrothermal system where the plutonic heat source is accessible. Natural state modeling of this system uses system-wide fluid mass and heat balances in space and time to derive a general view of system characteristics and lifetime. The benefits of such an approach at The Geysers are synthesis and advancement of our understanding of the nature and development of this important geothermal resource based on fundamental physical principles. This paper describes results of preliminary fluid and heat flow models for the pre-boiling state of The Geysers, including quantitative constraints on the hydrothermal system derived from vein-mineral geothermometry and observations of rock isotopic alteration. Our analysis begins from a geologically known condition, the initial appearance of the heat source (magma intrusion). From this starting condition, the dissipation of the original thermal and chemical energy of the intrusion into its host rocks can be calculated by the models. The models compute the temperature, pressure, fluid flow and chemical (d18O) composition fields for The Geysers geothermal/hydrothermal system from the time of its inception (magma intrusion) to a time immediately prior to boiling. These models are also constrained (calibrated) using the current state of the system, including the temperature and pressure fields, distribution of chemical and isotopic alteration, and distribution of fractures and permeability.
The driving force for the system is heat from the granodioritic "felsite" intrusive, which is found as shallow as 1.5 km depth in the southeastern Geysers. The geometry of the felsite top is relatively well-characterized, and has been summarized in a variety of publications (Hulen et al.,1994; Hulen and Nielson,1996). The present-day distribution of the steam reservoir is used as an initial estimate of the distribution of caprock and permeable zones above the felsite. Petrologic constraints on paleotemperatures are available from drilled core and cuttings (Hulen and Neilson, 1995; Moore et al.,1989). Moore and Gunderson (1995) have outlined the distribution of d 18O alteration at The Geysers, finding an 8 ‰ decrease in rock d 18O along the felsite-greywacke contact. Similar observations have been made for the Northwest Geysers (Walters et al.,1996). Modern fluid isotopic and non-condensible gas compositions have been cited as evidence of compartmentalization (i.e. faults form internal barriers) between the Northwestern and main Geysers steam reservoirs (Walters et al., 1996; Truesdell et al., 1995).
In order to investigate the basic time and length scales for hydrothermal circulation at The Geysers using system-wide mass and heat balances, preliminary finite difference models of heat and fluid flow were made (Norton and Hulen,1999). Modeling was carried out over a two-dimensional cross-sectional grid oriented SW-NE passing through Geysers Coring Project well SB-15D, and extending 10.8 km horizontally and 5.4 km vertically. Permeability zones were based on current distributions of steam reservoir and felsite (Fig. 1); a single instantaneous intrusion of granodiorite was assumed for the heat source. Caprock thickness was increased 30% over present values to account for erosion. Consequently, boiling conditions were not present in the reservoir and felsite in this model.
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Figure 1:
Distribution of modeled rock permeability zones (values in millidarcies). Well SB-15D TD located approximately at highest portion of steam reservoir-lithocap contact. Numbers 1-3 show locations of temperature vs. time plots (Fig. 2a).Model results demonstrate a number of fundamental features of The Geysers hydrothermal system. Perhaps of greatest significance are constraints on system lifetime. Purely conductive models of the geometry in Figure 1 indicate a maximum lifetime of 0.5 Ma, convective models using the indicated permeabilities reduce this lifetime to 0.35-0.5 Ma. The youngest dates available for the felsite are 1-1.5 Ma (Dalrymple, 1992; Hulen et al., 1997). This discrepancy indicates that The Geysers natural state system has had a considerably more complicated intrusive and hydrothermal history than is generally suspected. Of equal significance is the development of near-isothermal conditions throughout much of the permeable reservoir, and for much of the thermal lifetime of the system (Fig. 2b). This isothermal zone results from primarily horizontal fluid movement along the felsite-greywacke contact (Fig. 3), and enhanced heat transport at near-critical conditions for the fluid (see temperature inflection at -2 km, Fig.2b). In both the liquid and vapor-dominated systems near-isothermal conditions are present as a result of enhanced convective heat transport. To an unknown degree, the present-day isothermal conditions may have been inherited from the earlier liquid-dominated system.
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Figure 2:
Temperature solution summary: a) T vs. time at 3 representative points, point locations shown in Figure 1. b) Vertical profile of temperature (at 55Ka) and permeability along line of points shown in Figure 1.
Figure 3:
Streamfunction contours at 55Ka, showing fluid flow streamlines. Positive streamfunction values imply counterclockwise flow.Perhaps the most ubiquitous evidence left by magma-hydrothermal systems is zones of depleted d 18O associated with circulation of meteorically-recharged hydrothermal fluids at high temperatures. Several workers have analyzed such occurrences to quantify hydrothermal history (Brikowski, 1995; Norton and Taylor, 1979; Cook and Bowman, 1994), using tools ranging from analytic solutions of the non-dimensional 18O transport equation to finely discretized finite-difference and finite-element modeling. Although idealized, analytic solutions generally provide invaluable constraints on the system under study, as well as providing a basis for validating the more realistic discretized models. Analytic solutions are utilized below to constrain the time and length scales of d 18O alteration at The Geysers, based on the preliminary heat-fluid flow models described above.
Two classes of algebraic solution have been developed for application to alteration/metasomatism in geologic settings: exact analytic solutions to the simplified chemical-transport equation, and approximate Taylor's-series-based solutions. The former are useful in estimating ratios of reaction to advection (e.g. Peclet and Damkohler numbers; Cook and Bowman, 1994), provided that flow system geometry is relatively well understood. The Taylor's series approximations are useful in constraining fluid pathlines and system scale in space and time, but require independent estimates of advection rates. 
Norton (1988) developed a Taylor's series expression for fluid velocity given observations of metasomatism. The expression was derived from the differential form of the chemical transport equation including rock reaction, utilizing first order finite differences, or to be more accurate, truncated Taylor's series approximations to each term in the derivative. A generalized form for transport of the intensive property g i I in hydrothermal systems can be written as:
® ¶ (f g)f + S ¶ (f g)r + v.Ñ f = 0 (1) ¶ t r ¶ t 1 2 3 1 2 3 1 2 3 Fluid Reactants Advection
where reactants are minerals participating in equilibrium chemical exchange with the mobile fluid phase, f f is the volume fraction of fluid (porosity), f r is the volume fraction of reactant mineral r, v is the fluid pore velocity. As in Norton (1988) finite-difference approximations are applied to each term in (1). Implicitly integrating over the entire path from unaltered to fully-reacted fluid compositions (i.e. the downward portion of a ``typical'' fluid pathline) for the system, the following relation between the system time and space scales can be obtained:
D l å rf r(g t1 - g t0)r + f f(g t1 -g to)f D t = —{¾ ¾ ¾ ¾ ¾ ¾ ¾ ¾ ¾ ¾ ¾ ¾ ¾ ¾ ¾ — } v (g x1 - g x0 )f (2) where D l, D t are space and time increments along a pathline. For the case of 18O transport with water-rock exchange, can be expressed as (Brikowski, 1995):
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g r = g (r u d 18O)r , g f = (r d 18O)f (3) |
where r is phase density (reactant mineral r or fluid f) and n is atomic fraction of exchangeable oxygen in the reactant mineral r. Solution of equation (2) requires calculation of fluid composition in equilibrium with reactant minerals at known temperature; this can be achieved using standard isotope fractionation factor formulations (Faure, 1986).
Equation (2) can be solved for system constraints given the following considerations:
Average groundmass mineralogy of The Geysers host rock metagreywacke is approximately 40% quartz, 30% plagioclase (Moore and Gunderson, 1995). Lambert and Epstein (1992) note limited reaction of quartz grains in the greywacke, suggesting the primary reactant mineral is plagioclase. For this case, reactant properties are: mineral density r r = 2.76 g/cm3 , atomic mass fraction exchangeable oxygen n r = 0.46, volume fraction of plagioclase in rock f r = 0.30, and volume fraction of mobile water in rock f f =10-3. Isotopic parameters are the water-plagioclase isotope fractionation factor A = 2.61x106 and B = -3.7 (Javoy and Bottinga, 1973), unaltered rock d 18Otor = 140/00 and maximum alteration d 18Ot1r = 60/00 (Moore and Gunderson, 1995).
From the flow models described above, temperature at the end of alteration at the point of interest (point "2", Fig. 1) Tt1 = 300 0C initial temperature at that point Txo = 150oC, and temperature at the nearest upstream point of unaltered rock (D D x = 2.5x106cm) Txo = 50oC. Time required for the observed alteration to develop D t » 200,000 yr. From those inputs the minimum pore velocity implied by the observed alteration is v = 4.14 cm/yr.
More general system space and time constraints can be obtained based on the cross sectional model described above by plotting the value of D t (lifetime of active hydrothermal alteration) required for various choices of system scale (D x or recharging path length). Given an average velocity of 1x10-8 cm/sec computed by the model at the point of interest, the results of equation (2) indicate that the relatively sluggish, strongly horizontal flow predicted in the finite difference models is consistent with the observed distribution and and magnitude of d 18O alteration at The Geysers (Fig. 4). Note the approach taken above implicitly assumes a linear gradient in temperature and 18O composition along the recharge pathline passing through point 2 in Figure 1. As such it overestimates the amount of alteration present, and therefore a more realistic constraint on hydrothermal system scale lies somewhere between the maximum alteration D 18O = 8‰ and D 18O = 4‰ lines in Figure 4.
Figure 4: Length-time scales consistent with indicated depletion in rock 18O (computed using eqn. 2) compared to scales computed using finite difference hydrothermal model ("Validity Region").
Preliminary results of natural-state models at The Geysers reveal the following fundamental features of the system:
The first feature suggests that the intrusive history of the felsite heat source at The Geysers is much more complex than indicated by available radiometric dates. The latter two features are a consequence of the second: factors limiting fluid circulation at The Geysers are responsible for the unusual thermal and alteration structure above the intrusive. Consideration of system-wide heat, fluid and 18O mass balances at The Geysers allows a fundamental understanding of these features, and provides new insights regarding The Geysers as well as a firm basis for more focused reservoir engineering models.
This research supported by U. S. Dept. of Energy grant DE-FG07-98ID13677. Geologic and geochemical input by Jeff Hulen of EGI was instrumental in generating the models.
