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Geothermal Resources Council Transactions, Vol 22, September 20-23, 1 998

M o d ~ l i n ~ Post-Abandonm~nt Electrical Capacity Recovery for a Two-Phase Geothermal Reservoir

John W. Pritchett Maxwell Technologies San Diego, California

ABSTRACT A theoretical study has been carried out, using the STAR

geothermal reservoir simulator, of the behavior of an hypothetical geothermal reservoir which has been produced for electrical power for fifty years and then abandoned. These calculations indicate that, after a long period of shut-in, the electrical generating capacity of the field will recover. The degree of recovery increases with shut-in time. The shut-in time required for substantial recovery is much less than the time necessary for the reservoir to attain "natural-state" conditio^ starting fkorn cold starting c o n ~ t i o ~ ( 5 0 , ~ O years), but is also significantly greater than the the 50-year duration of the initial exploitation period. If the system is shut in for 150 years and then exploited again for 50 years, about 42 percent of the lost electrical capacity will be recovered. Complete recovery requires more than IO00 years.

Background Electricity generated using natural hot geothermal fluids

has traditionally been regarded as a "renewable" source of power, and has therefore been grouped with other so-called "renewable" energy sources such as hydroelectric, solar, and wind. It is generally recognized, however, that while geothennal resources are renewable in principle, realistic economic constraints require that most prospects be exploited at rates s i ~ ~ c a n t l y in excess of the rate of natural recharge. Consequently, it is usually acknowledged that most geothermal reservoirs will e v e n ~ l l y be depleted, in much the same way that an oilfield, natural gas field, coal seam, or uranium oxide deposit will be depleted.

On the other hand, it is important to realize that geothermal resources are relatively short-lived by comparison with traditional fossil energy sources. Oil, coal, and gas reserves which are presentl being exploited typically range in age between lo8 and 10 years. Most known geothermal reservoirs, by contrast, are between lo4 and lo6 years old. Accor~gly , time-scales for natural renewal of g e o t h ~ l reserves are expected to be several orders of magnitude shorter than for fossil firels.

3:

Generally speaking, conventional hydrothermal geothermal reservoirs will eventually become depleted due to one of the following three mechanisms: 1. Pressure depletion: excessive fluid production of

geothermal fields characterized by limited permeability may result in premature failure of geothermal power projects due to excessive downhole pressure drawdown.

2. Fracture short-circuiting: if just a few individual high- conductivity fkactures are present in the system which connect the production wellfield with either the injection wellfield or the shallow cold groundwater system, cold fluid may travel rapidly through these fkactures resulting in premature failure of the production wellfield. Essentially, the problem is inefficient heat-sweep; instead of cooling the entire reservoir, heat is only removed fkom the rock ~ e ~ a t e l y adjacent to these large fractures.

3. Thermal depletion: here, efficient heat sweep has been accomplished; a large volume of the reservoir has been cooled by injected waste fluids and has grown to encompass part or all of the production wellfield, resulting in field abandonment.

Usually, geothermal power projects which cease to operate owing to causes (1) or (2) above are deemed "failures" and must be abandoned or remediated within just a few years. If abandoned, it is expected that reservoir recovery (particularly for type (1) situations) will also take place within just a few years or at most a few decades. Case (3), by contrast, represents "successes"; large quantities of heat have been successfully extracted from the reservoir and the project has therefore presumably produced electrical power for a long period of tirne prior to abandonment. It is expected, as a result, that natural p o s t - a b a n d o ~ ~ t reservoir recovery will take a long time in these cases.

In the present study, attention is focussed on "successfW (Type 3) geothermal projects which produce economically significant amounts of electrical power for long periods of

52 1

Pritchett

time and then must be abandoned because of large-scale reservoir cooling. m e general approach is to develop a numerical model of the reservoir, and then to interrogate the model using a numerical reservoir simulator to examine the long-term behavior of the system after its productive life is over.

Reservoir Description The geothermal system considered for this study consists

of an 81 km2 square region (9 km east-west and 9 km north- south) which extends to three kilometers depth. This area is illustrated in Figure 1, which also shows the locations of the production and injection wemelds and other pertinent features. For computational purposes, the region is subdivided into 8000 (20 x 20 x 20) gridblocks; the horizontal grid block spacing is 300 meters in the central part of the study area and increases to 900 meters adjacent to the outer boundary. East-west vertical cross-section "A-B" (identical to north-south section T-D") i s depicted in Figure. 2. Three geological -layers are present: the Taprock" (uppermost 500 meters), the "Aquifer" which extends to 2000 meters depth, and the "Basement" (the deepest 1000 meters of the section considered).

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The computational grid block spacing in the vertical direction is 125 meters in the Taprock" and "Aquifer" layers and 250 meters in the "Basement". Overall porosities are 30 percent, 20 percent and 5 percent for the "Caprock", "Aq~fer" and "Basement" respectively; horizontal permeabilities likewise depend only on depth (1 , 10 and 0.1 mi l l i~c i e s respectively for the three f o ~ t i o ~ ) . The "Caprock" vertical permeability is also uniform at one millidarcy, but both the "Aquifer" and '*Basement" layers are subdivided into inner and outer regions which differ in

vertical permeability. In the "Aquifer" layer, the vertical permeability in the inner region (-1.5 lun x c +1.5 km, -1.5 km y c +1.5 km) is ten millidarcies, but outside that region is smaller (one millidarcy - same as in the "Caprock"); similarly, for -0.3 km x +0.3 km, -0.3 km y 4-0.3 km the vertical permeability in the "Basement" is ten millidarcies (as in the overlying "Aquifer" layer), but is only 0.1 millidarcy elsewhere.

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Figure 2. V ~ ~ i ~ ~ ~ ~ i n ~ s t ~ ~ i ~ ~ p h y , distributions of porosity and permeability, and boundary conditions.

Other rock formation propefties (thermal conductivity, 3 W/m/OC; grain heat capacity, 1 J/gPC; grain mass density, 2.5 g/cm3; dispersivity scale, 50 meters) are uniform throughout the system. The dispersivity scale is the quantity which, when multiplied by local fluid velocity, yields kinematic dispersivity; hydraulic dispersion has the effect of " s m e ~ g f t both chemical and thermal fronts due to small- scale heterogeneities in the pore/fkacture network. Capillary pressure effects are ignored. Relative permeability effects are treated using "straight-line" functions with residual water and steam saturations equal to 0.3 and 0.05 respectively for all three rock formations (Figure 3).

Instead of simple porous media, all rock formations are treated as composites consisting of a small-vol~e but high- permeability "fracture zone" together with intervening relatively large blocks of impermeable country rock (the "matrix region") using the "MINC" technique originally developed by Pruess and Narasimhan (1985) as modified by Pritchett (1997), indicated schematically in Figure 4. In this

522

Pritchett

treatment, all fluid flow occurs within the "fiacture zone"; heat conduction takes place within the pore-fiee "matxix region". The mathematical treatment regards a typical element of the system as having spherical symmetry (instead of the cubical shape suggested by Figure 4), with the "fracture zone" lying outside the "matrix region". For the present calculations, the representative matrix region was subdivided into nine concentric ''shells", each of equal volumee. The diameter of the entire " ~ p r e s ~ ~ t i v e element" assembly including the "fracture zone" is 100 meters for all formations. The "ihcture zone" itself is treated as a porous medium with 80 percent porosity; the "matrix region" has zero porosity, and the partition of volume between "matrix region" and "fracture zone" is adjusted for each rock fonnation to provide the desired overall porosity value (30 percent, 20 percent or 5 percent for "Caprock", " A q ~ e r " or "Basement"). The permeability of the "fiacture zone" in isolation is relatively higk the average overall f o ~ t i o n permeabilities shown in Figure 2 are the result of volumetric weighting.

STEAM SATURATION Figure 3. Relative ~ ~ e a ~ i l i ~ functions employed in simulations.

The Natural State First, a numerical calculation was carried out using the

STAR geothermal reservoir simulator (Pritchett, 1995) representing a long period of time in order to provide a nearly-steady stating condition for the subsequen~ calculations of reservoir exploitation. The initial conditions for this calculation of the "natural state" were a simple h e a r temperature distribution with depth ranging fiom 20°C at the ground surface to 2OOOC at the grid base (3 lctn depth), and a corresponding hydrostatic ~ s ~ b u t i o n of fluid pressure (equal to one bar at the ground surface).

The boundary conditions (indicated in Figure 2) include (1) impermeable insulated conditions on the vertical grid faces at large lateral distances (x or y = f 4.5 km), (2)

imposition of P = 1 bar, T = 20°C at the ground surface, (3) an upward co~ductive heat flux uniformly ~ s ~ b u t e d along the bottom surface at 3 lun depth (0.18 watts per square meter; corresponds to the initial t ~ p e r a ~ e gradient imposed multiplied by the system thermal conductivity), and (4) an impermeable condition on the lower surface except for a central region measuring 600 m x 600 m (corresponding to the high-permeability portion of the overlying "Basement" layer) through which a frxed-rate inflow (100 kg/s) of water at 350°C is maintained throughout.

0: f ''nL P1ERMEmE . 1'' 1

d 1 a( Figure 4. Schematic diagram of MlNC ("double-porosity")

f ~ ~ u ~ m a t r i x ~ p ~ e n t a t i o n .

The "natural state" calculation was carried forward in time for 50,000 years (see Figure 5, which represents either east- west cross-section "A-€3" or north-south section "C-I)" of Figure l), by which time an essentially steady condition was attained. Despite the fact that the starting conditions (Figure 5a) are too cold for the presence of underground steam, boiling began after only about 400 years. The shaded region in Figure 5b indicates the natural-state region of two-phase flow, in the upper part of the "Aquifer" layer and the lower part of the "Caprock". The natural-state is largely ond duct ion- dominated within the "Capro.ck" layer and the outer part of "Basement", but a large natural convection system is present within the permeable "Aquifer" layer, resulting in pronounced temperature inversion features.

Generation of Electric Power For all subsequent calculations of field exploitation, the

boundary conditions are maintained the same as for the calculation of the natural state (Figure 2), and the initial conditions correspond to the final (50,000 year) situation at the end of the natural-state computation (Figure 5b). In all cases, we consider fluid production &om twelve production wells with waste fluid reinjection taking place into six injection wells, as indicated in Figure 1. A shut-in "monitor" well is also present, lyhg between the production and injection wellfields, as shown. Note that both wellfields are located to the north of the center of the thermal anomaly.

523

Pritchett

Temperature (Celsius)

I I

Productivity or lnjectivity Index

1 50.

100.

I I i

0 -

1 -

2 -

t

collected in a condenser which operates at 39°C; 50 percent of the resulting liquid condensate is used by the evaporative cooling system, and the remaining 50 percent is reinjected. The liquid geothermal brine emerging from the separator (at 5.0 bars and 152°C) is expanded to one bar pressure (100°C) in an atmospheric flash tank (which evaporates about 10 percent of the brine), and then mixed with the excess steam condensate (at 39°C) and reinjected.

I f 1 I I I I I f -d -a -2 -I o +I +z +a +A

7 OR MpBp[

Figure 5. initial (a) and final (b) conditions in "A-B" and "C-D" vertical cross-sections in S~,OOO-year "natural-state" calculation. Isotherm

spacing: 1 O O C . Shaded area: two-phase (waterkteam) region.

Except for location and ~ c t i o n ~roduction, injection, or monitoring), all nineteen wells share common physical characteristics. The inside diameter is uniform (33 cm; about thirteen inches), and the orientation is vertical. The feedpoint depth in all cases is within computational layer number 15 (depth between 625 and 750 meters, in the upper part of the "Aquifer" layer). All production wells operate at a fixed flowing wellhead pressure of 5.5 bars. The downhole productivity and injectivity indices for all wells are taken to be given by:

V* I = - %

where V* is a c o ~ t a n t (10''' cubic meters) and qe is the effective kinematic viscosity of the fluid mixture adjacent to the'well's feedpoint (which depends mainly on temperature and steam s a ~ ~ o n ) . For single-ph~e-liquid feedpoint conditions, the well flow indices vary with fluid temperature as indicated in Table 1. If two-phase conditions prevail near the feedpoint, the productivity index will be s i ~ f i c a n ~ y lower. Wellhead discharge rates of water and steam are automatically computed at each instant of time by the STAR simulator for each production well. It is assumed that, at each instant of time, the six injection wells share the injected fluid supply equally.

The two-phase mixture produced (at 5.5 bars wellhead pressure) by the various production wells is separated at 5.0 bars; the separated steam is then supplied to a single-flash steam generating plant, of which the steam c o ~ ~ p t i o n is taken to be 10 metric tons of 5-bar steam per hour per net megawatt of electricity (We) generated. This value is typical of existing single-flash condensing geothemal steam plants operating at comparable pressures. The spent steam is

~ o n t i ~ u o ~ s Field Operation For the fast hypothetical field exploitation calculation, all

twelve production wells were simply opened at zero time and allowed to discharge; produced fluids were passed through the separator and the power station, and simultaneously ~jection was initiated in the six injection wells. The initial computed generating capacity is about 230 MW,, but rapidly declines - to 200 We in six weeks, to 150 M W , after five months, and to 118 W e after one year of operation. Once reservoir pressures begin to stabilize, the electrical capacity continues to decline, but at a slower rate. Gradually, the relatively cold brine I condensate mixture (< 100°C) from the injection wells begins to invade the production wellfield causing a decline in discharge enthalpies, particularly for the e ~ t e ~ o s t production wells. Ele&cal capacity continues to decline due to cold-water invasion. After 37 years, the production well closest to the "monitor" well ceases to discharge; the well can no longer sustain 5.5 bars wellhead pressure. The well immediately to the north likewise ceases discharge at about 40 years. By t = 50 years, the electrical capacity has dropped below 38 MW,; the average electrical capacity for the fxst 50 years of operation is about 60 MWe.

The calculation was carried onward despite this decline in capacity, however - it was not terminated until after 2000 years of field operation had been simulated. As illustrated in Figure 6, electrical capacity and average discharge enthalpy continue to decline for hundreds of years and, one by one, the various production wells cease to discharge (Table 2). After about 550 years of production, the number of operating production wells remaining has been reduced to three and the total electrical generating capacity has declined to only about 12.4 MW,. From this point forward to the end of the calculation (2000 years), however, no additional wells stop flowing. Instead, both the average wellhead discharge

524

Pritchett

enthalpy and the electrical capacity begin to stabilize (at around 850 J/g and 9 Nw, respectively). The system appears to be approaching a new state of equilibrium, in which the therxnal power being withdrawn by the wellfields is in balance with the power supplied (both conductively and convectively) from great depth to the wellfield area through the lower grid bo^^.

1 -1 100 tam L 1

Figure 6. Computed results from 200O-year continuous-operation case.

Table 2. Lifetime of P r ~ u ~ i o n Wells Under

Reservoir Recovery After Fifty Years of Operation

Although the calculation d e s m i d above illustrates that geothermal power production is probably sustainable +definitely so long as power generation rates are restricted to

. values c o ~ e ~ ~ t e with natural reservoir thermal recharge rates, economic co~iderations will ordinarily dernand much higher electrical capacities. Accordingly, in the next case considered, the system was fmt produced for fifty years, and then was shut in (all production and injection ceased). As noted above, during the first fifty years of operation the average electrical production rate is around 60 MW,. Thereafter, the calculation was carried forward with no m e r fluid production or injection, and the recovery of the reservoir was observed. The first f q years of this calculation are of come identical to the "con~uous production" case discussed above, but after t = 50 years results are very different.

Features of this calculation are illustrated in Figure 7, which shows, for both the fifty-year pr~uct ion period (shaded) and the fmt 250 years of the recovery period, (a) the feedpoint pressure history in the shut-in "monitor well" located between the injection and production weltfields (see Figure l), (b) the c o ~ e s p o n ~ g monitor well feedpoint temperature history, and (c) the total volume of the reservoir

occupied by steam (as opposed to liquid water or solid rock). Since the monitor well is located midway between the production and injection wellfields, the monitor well pressure responds to both fields during the fifty-year period of field operation. At field shutdown, however, local pressure gradients associated with the various flowing wells dissipate rapidly and the monitor well pressure quickly attains a minimum value of 56.1 bars (as compared to the natural-state value of 70.5 bars) d e r about nine months of field shutin. Then, the pressure begins to recover; as Figure 7a shows, after 100 years of shutin, the monitor well pressure has reached 68.8 bars (-88 percent recovery) and continues to approach the natural-state value asymptotically thereafter. Pressure recovery for the present reservoir system is much slower than would be expected for an all-liquid geothermal reservoir owing to the extremely high effective compressibility of the two-phase (waterhtearn) zone.

eo 754

30

6s

60

Eis

I OF S M I N Figure 7, Computed changes in monitor-weil feedpoint pressure (a) and

temperature (b) and in total volume of steam present in reservoir (c) during SO-year production interval and subsequent reservoir recovery.

Reiovery of reservoir t e ~ e ~ ~ e is even slower, as illustrated in Figure 7b. The initial ("natural-state") monitor- well feedpoint temperature i s 285.3"C. By the end of the 50- year production interval, this temperature has declined to 106.7"C. After 100 years of field shutin, the monitor well t e m p e ~ ~ e has only recovered to 144.2"C (21 percent recovery: compare to 88 percent pressure recovery at the same time) and even after 250 years of shutin the monitor well temperature has risen to only 243.7"C ('77 percent recovery).

Figure 7c shows that the recovery of in-situ steam volume is slower yet. The initial volume of steam present is 0.1 1 16

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Pritchett

cubic kilometers. During the production phase, the steam volume increases with time at an ever-decreasing rate and fmally reaches a maximum of 0.2705 cubic kilometers after 43.9 years of field operation. Thereafter, the volume declines slightly, to 0.2689 cubic kilometers at field shutin (SO years). This variation during the production phase arises fiom the competing effects of reservoir pressure reduction (which promotes boiling) and cold water injection (which promotes condensation). After the field is abandoned, the steam volume starts to decrease at a much higher rate, due to reservoir pressure recovery. A minimum value of 0.0204 cubic kilometers is reached after 73 years of shutin, after which the steam volume begins to gradually recover. After 250 years of field shutin, total steam volume has increased to 0.0709 cubic kilometers (55 percent recovery).

This calculation was actually carried out much farther in time, to a total shutin time of 1000 years. A series of successive plots of conditions in the "E-F" east-west vertical cross-section which passes through the centers of the wellfields (see Figure 1) is illustrated in Figure 8. The region considered is four kilometers long and extends to 2 km depth (the bottom of the "Aquifer" layer). In Figure 8, the shaded area denotes the two-phase (waterfsteam) region, and the contour lines represent fluid temperature (the contour level spacing is 10OC). The horizontal dotted line indicates the interface between the Taprock" and "Aquifer" layers. Figure 8a illustrates the undisturbed natural-state which prevails prior to startup, and Figure 8b depicts the situation at the moment of shutin after 50 years of operation. The remaining fiames (Figures 8c-8h) show the cross-section during recovery.

Clearly, major changes are induced by power production (compare Figures 8a and 8b). Cold-water injection creates a large low-temperature volume centered around the injection wells which has begun to invade the production area after 50 years of operation. The two-phase region has expanded to the west of the production area ovhg to reservoir pressure decline, but has been condensed to the east by cold injectate. Note that, owing to the relatively rapid pressure recovery which takes place after shutin, the two-phase region has condensed away altogether (in this cross-section) by 50 years after shutin (Figure 8c). Two-phase conditions do not reappear until Figure 8f (500 years of shutin). As recovery proceeds, the large injected cold-water zone heats up due to both heat conduction and hydraulic dispersion, and also sinks downward due to its greater density compared to the surrounding hot water. The final state (Figure 8h, after 1000 years of shutin) bears a strong resemblance to the original pre-production situation (Figure 8a). After 1000 years of shutin, reservoir recovery appears to be nearly complete.

Recovery of Electrical Generating Capacity The fmal series of numerical exploitation calculations

explores the quanti~tive recovery of electrical generating capacity as a Mction of shutin t h e . As before, the field is fast produced for 50 years (the "production duration time": tp) at constant wellhead pressure (5.5 bars). Next, the field is

shut in after 50 years of operation and pennitted to recover for a period of time (denoted by "shutin duration" 4). Finally, the field is restarted, and permitted to operate for another 50 years (t,,). The total electrical energy generated ,during the second fifty-year production interval (denoted by E2) may then be compared with that for the fust interval (El). Calculations of this type were carried out for a variety of values for t, (the shut-in time separating the two fifty-year production intervals). It is assumed that the same wells (or equivalent wells) are employed for both production and injection in the second phase of power generation as in the first, and that all other properties of the power generation system (wellhead and separator pressures, condenser temperature, turbine efficiency, etc.) are the same for both phases.

It j/ It ji

I -E -1 0 1

recovery in east-west vertical cross-section 'E+" (see Figure 1) through wellfields. Shaded area: two-phase flow. Contours: fluid temperature.

An example of one of these c ~ c u l a ~ o ~ is illustrated in Figure 9, for shutin time t, equal to 100 years. The shaded areas represent the two fifty-year intervals of power production; the area enclosed by the dashed curve represents the second-phase power production in the absence of any shutin period. During the flirst fifty years of production, the total electrical energy produced amounts to 26.23 Twh, ( t ~ a w a ~ - h o ~ s of electrical energy); the average rate of power production is -60 MW,. If the system is not shut in but simply c o n ~ u e s to operate for another 50 years (dashed line), the total energy production for the second 50 years is only about half that of the fust (13.25 m; average of -30 We). If the reservoir is allowed to recover for 100 years

526

Pritchett

(Years)

0 10 25 50 75

after the first 50 years of production, however, the energy obtainable during the second 50-year production phase increases somewhat, to 17.41 lV& (average of -40 MW,).

Energy Et Energy EZ Recovery Cfwhef CTwhS (%I

26.23 13.25 0.0 26.23 14.08 6.4 26.23 14.69 11.1 26.23 15.66 18.6 26.23 16.58 25.6

0 so 100 130 ZOO Tcw

Figure 9. Electrical energy production history for (50 year production - 100 year shutin - 50 year p ~ u ~ i o n } case.

Calculations of this type were carried out for values of the shutin time t, ranging from 10 years to 1000 years. Results are summarized in Table 3 and in Figure 10. Note that, for very large values of the shutin time, the electrical energy obtainable fiom the second phase of production (E2) should approach that for the fmt phase (El) since the original natural state should re-establish itself during the shutin period. It appears that, for this and sirnilar systems, the time required for substantial recovery of the electrical generating capacity after the reservoir has been depleted is likely to be a fairly large multiple of the production time interval.

Table 3. Calculated Electrical Capacity Recovery as a Function of Field Shutin Time.

1 ~hutinTimeT~ I First Phase I Second Phase I Relative 1

l~plications and ~onclusions

These results indicate that, for g e o ~ ~ a l systems which become depleted due to large-scale reservoir cooling (as contrasted to excessive pressure decline or " s h o ~ - c ~ c ~ ~ g ' ' through large individual fractures), the resource is still "renewable", but long periods of time (centuries) are likely to be required for substantial recovery. Accordingly, it seem

reasonable to conclude that geothermal systems which have been thermally depleted in this way will not recover after abandonment on time-scales comparable to lifetimes of typical electrical power development projects. They will, however, recover on time-scales typical of lifetimes of civilizations - millions of years of geological time are not required, as is the case for fossil he1 reserves. Furthermore, even though complete recovery appears to take of order 1000 years or more, partial recovery can occur on time-scales of several decades. This suggests that the sustainability of geothermal power projects could be enhanced by techniques such as periodically moving production wellfields from one part of a regional thermal anomaly to another, so that each local site is revisited only occasionally (and exploited for time periods which are small compared to the time-interval between successive episodes of e ~ ~ o i ~ t i o n ) . Also, a l ~ o u ~ the fifty-year production pqiod considered herein is short compared to the "reservoir recovery time", it is s u b s ~ t i a l in terms of the time-scales required for the development of new geothermal technology. Research and development is now underway around the world to develop better and cheaper ways to drill geothermal wells to greater depths and to " s ~ ~ a t e " geothermal reservoirs by various techniques to create new formation permeability and to open hitherto inaccessible hot rock masses to energy extraction. E c o n o ~ c conditions in energy markets are also not expected to remain static for periods of fifty years.

I Shutln tiam tr. uemr 1 Figure IO. Effect of shutin time on electrical

generating capacity recovery.

The present hypothetical model of a geothermal system and of the fiftyyear exploitation operation represent what would normally be considered a very "successfbl" operation characterized by high reservoir electrical capacity, long economic lifetime, and efficient heat sweep. Experience has shown that many actual geothermal power projects have not been so successfbl, because of less promising subsurface conditions andlor inefficient development and exploitation technique. Because of the success of the operation (and the consequent creation of a very large subterranean volume which has been cooled by the injection wells), a very long period of time is required for reservoir recovery. Had the initial 50-year operation been less successkl, the d i s ~ b ~ c e induced in the reservoir prior to abandonment would have

527

Pritchett

been less extreme and recovery would therefore have been quicker.

It is very important to recognize that the geothermal fields of the world exhibit a remarkable degree of variation in physical characteristics. Power has been produced from fields with maximum temperatures less than 160°C, but downhole maximum temperatures in other operating fields have exceeded the critical point. In-situ fluid states range from all- liquid to all-steam. Production depths range from very shallow systems like Wairakei in New Zealand (300 meters) to systems requiring drilling to several kilometers. Electrical capacities range from over 1000 M W , (the Geysers in California) to single-well projects of only a megawatt or two. Fluid chemistry ranges from benign virtually pure-water systems to heavy corrosive brines with over 300,000 ppm dissolved solids (the Salton Sea field). Reservoir permeabilities are also highly variable, from nearly Smite (Wairakei; the O g y i field in Japan; Steamboat Hills in Nevada) to. very tight systems with high pressure drawdown and poor productivity indices. Consequently, caution must be exercised in using the results reported herein. Indiscriminate application of these conclusions to systems which are significantly different from the present "hypothetical reservoir" may prove misleading.

To further characterize the natural recovery of geothermal systems after economic abandonment, more mathematical studies along these same general lines may prove usefbl. Different systems should be examined, with a broad variety of reservoir physical characteristics (and power extraction strategies) included. Although additional "hypothetical" systems such as that examined here can be usefbl for this purpose, it would appear preferable to employ well- established and validated mathematical models of actual operating geothermal systems. The objective would be to determine how the "recovery time" depends on the physical characteristics of the geothermal reservoir and upon the techniques employed to harvest its energy.

References Pritchett, J. W. (1993, "STAR A Geothermal Reservoir Simulation

System," Proceedings of the World Geothermal Congress, Florence, Italy, May, pp. 2959.

Pritchett, J. W. (1 997), "Eficient Numerical Simulation of Nonequilibrium Mass and Heat Transfer in Fractured Geothermal Reservoirs," Proceedings Twenty-Second Workshop on Geothermal ReservoirEngineering, Stan ford University, January, pp. 2 87.

Pruess, K. and T. N. Narasimhan (1 989, "A Practical Method for Modeling Heat and Fluid Flow in Fractured Porous Media," SOC. Petrol. Eng. J., 25, pp. 14.

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