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Modeling the thermal evolution of an active geothermal system
JOURNAL OF GEODYNAMICS4, 149- 163 (1985)
M O D E L I N G THE THERMAL GEOTHERMAL SYSTEM
149
EVOLUTION
OF
AN
ACTIVE
Y. ECKSTEIN, G. MAURATH and R. A. FERRY
Department (~f Geology, Kent State Uni~ersity, Kent, Ohio 44242, ~,.S.A. (Accepted July 4, 1984)
ABSTRACT Eckstein, Y., Maurath, G. and Ferry, R. A., 1985. Modeling the thermal evolution of an active geothermal system. In: L. Rybach (editorl, Heat Flow and Geothermal Processes. Journal 0/' Geo&,namics, 4: 149 163. Temperature inversions at shallow to moderate depths have been observed commonly in boreholes drilled in geothermal areas. The inversions result from thermal disequilibria generated by steam and, or hydrothermal fluids invading shallow horizontal, or sub-horizontal fractures, or permeable horizons, from a deep vertical, or sub-vertical feeder-fracture. Subsurface distribution of temperatures in Momotombo geothermal area of Nicaragua, Central America, indicates that the anomaly is generated by steam and water, convecting in a narrow feederfracture-zone located at the western edge of the field. The north-trending zone of the feeder-fracture is bound on the west by the area of massive, impermeable andesitic rocks, and is capped by an impermeable, approximately 300 m. thick silica-cap, which seals if from the ground surface. The thermal fluids penetrate a systcm of horizontal, or sub-horizontal fractures, extending east of the feeder-fracture beneath the silica cap. The flow of thermal fluids eastward through the system of the horizontal, or subhorizontal fractures is generating a plume-like geothermal anomaly, which is expressed by the temperature inversion zone pervasive in the boreholes to the east of the feeder-fracture. A time-dependant model for a semi-infinite half-space ( z > 0 ) in contact with a hot, well stirred, isotropic fluid flowing through an aquifer overlain by a finite space of constant thickness is solved for the data collected from the Momotombo geothermal boreholes. Curve fitting between the simulated and observed temperature/depth profiles suggests that the thermo-tectonic events which caused the presentday Momotombo hydrothermal system occurred approximately 5,500 years ago, following development of vertical, or subvertical fractures along a N5 E trending faultline. Hot fluids emerging from these fractures move eastward through a system of horizontal, or sub-horizontal fractures, with a velocity of 1 I to 20 myr.
|NTRODUCTION
Numerous mathematical models of active geothermal systems have been developed during the past two decades. The majority of such models are 0264-3"/07,85/$3.00
1985 Geophysical Press Ltd.
150
ECKSTEIN, MAURATH AND FERRY
based upon various general solutions to problems of heat conduction in solids under steady state or transient conditions (Carslaw and Jaeger, 1959). Non-linear temperature/depth profiles occur predominantly as a result of either cyclic variations of the temperature at the ground surface boundary, or subsurface convective heat transfer by ground water, magma, or hydrothermal fluids. Assuming certainf simplifications such profiles may be approximated by mathematical models. This paper describes the application of a time-dependant model for a semi-infinite half-space (z > 0) in contact with a hot, well stirred, isotropic fluid flowing through an aquifer overlain by a finite space of constant thickness (Fig. 1). The general solution for a temperature field generated by a heat source bound by an infinite half-space of finite thermal conductivity, normal to the direction of heat flow, was given by Carslaw and Jaeger (p. 395, 1959). This approach to fluid flow within a discrete horizontal aquifer bound by an infinite half-space was initially applied by Bodvarsson (1969, 1973). The model was modified by Ziagos and Blackwell (1981), and further refined by Ziagos and Blackwell (1983), to explain observed geothermal gradients in boreholes penetrating discrete horizontal aquifers. Modifications included introduction of the ground surface as a steady-state boundary condition, and removal of a boundary condition below the 0
~round ~urCace
Ts
X
aqutCer
Za
) T (de 9 C)
Za
t~p I.
¢p
toO
Z
Z
Fig. 1. Space parameters for the model and temperature/depth profile for a time (t) after the initiation of the flow through the system (to) and before the time of thermal equilibration (4u); modified after Bodvarsson, 1973 and Ziagos and Blackwell, 1983.
THE THERMAL EVOLUTION
151
aquifer introduced by Bodvarsson (1973). Thus the layer below the aquifer is assumed to be a semi-infinite half-space. Ziagos and Blackwell's (1983) version of the model is solved for the field data from a number of boreholes drilled in Momotombo geothermal area of Nicaragua, Central America, to evaluate the age of the hydrothermal system, and flow velocity of the hydrothermal fluids. Solution of the simplified version of the model (Ziagos and Blackwell, 1981) for the same set of data was presented by Eckstein and Cik (1982).
MATHEMATICAL MODEL
The model developed by Ziagos and Blackwell (1983) emulates the transient temperature field around a hydro-thermal system consisting of a thin horizontal aquifer recharged continuously from a vertical or sub-vertical feeder fracture (Fig. 1). Thermal effects around the feeder fracture are not considered. The aquifer is confined between aquicludes, which have thermal properties similar to the aquifer. The upper aquiclude is at least ten times the thickness of the aquifer. The ground surface is considered as a constanttemperature boundary condition. It is assumed that no convection occurs within the aquifer, and heat transfer through the aquicludes is by conduction only. Assuming that the tectonic event which led to the generation of the hydrothermal system occurred at least 500 years ago, the solution for this model, as formulated by Ziagos and Blackwell (1983) is as follows: Tu(x, z, t) = 0 ~
[erfc(/~, ) - erfc(/~2)]
(1)
n~O
T~(x, z, t) = 0 erfc(~x/7)
(2)
Tl(x, z, t) = 0 erfc[(~x + z - z,)/7]
(3)
where:
0 = To exp(-0tX/Za) e=K/pChV
~, = [ ( 2 n + 1) z , - z + ~ x ) ] / 7 /~2 = [(2n + 1 ) z~ + z + ~x)]/7 t' : t - ( x / V ) - (~xz,)/(3k )
K - thermal conductivity k - thermal diffusivity p - fluid density
152
ECKSTEIN, MAURATH AND FERRY
C - f l u i d heat capacity V - f l u i d flow velocity h - thickness of the aquifer t - t i m e since initiation of the flow through the system z - v e r t i c a l distance below the ground-surface x - l a t e r a l distance from the feeder fracture z , - d e p t h to the aquifer T o - temperature of the fluid in the feeder fracture T u ( x , z, t) - temperature field in the upper half-space (above the aquifer) T~,(x, z, t) - temperature field within the aquifer T / ( x , z, t) - temperature field in the lower half-space
(below the aquifer) The solution for T ( z , t), with x held constant (Fig. 2) defines the evolution of the temperature field through the time at the distance x from the feeder fracture. The net departure of the theoretical temperature profile from a "background" profile characteristic of a purely conductive heat
TFMPERRTURE 0
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Fig. 2. 1983).
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Evolution of the depth/temperature field at x
const. (modified after Ziagos and Blackwelk
THE THERMAL EVOLUTION
153
transfer regime, presumed to be valid prior to fracturing and inception of the flow, is gradually amplified with time lapse. Similarly, solution for T(x, z), with t held constant (Fig. 3) defines the temperature field of the system at time t after the initiation of the flow. It may be seen that the net departure of the temperature profile from the linear "background" profile characteristic of a purely conductive heat transfer regime is attenuated with increasing distance from the feeder fracture. Thus, for short time intervals, or very large distances from the feeder fracture, no thermal disturbance would be observed. Steady-state conditions are obtained for either very small distances from the feeder fracture, or for very long periods of time. Between these two extremes the model may be used to simulate the thermal evolution of a geothermal field conforming with the postulated geometry (Fig. 1) and assumptions. Shape of the simulated temperature/depth curves is - - except for being dependant on either the time that elapsed since initiation of the flow through the system, or the lateral distance from the feeder fracture - - particularly sensitive to such parameters as fluid flow velocity, thickness of the aquifer, thermal properties of the fluid, thermal properties of the rocks, and the temperature of the fluid in the feeder fracture. Since the model is composed of three simultaneous equations it may be used for approximation of at least three variables for a given geothermal system, by matching the TEMPERATURE 0
0
100 ,
[
I
1
( d e g r e e 8 C)
200 ,
I
;
I
I
300 I
I
'
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I
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I
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BOO
yr~
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.,,,y,
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-
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\ \
\
\
\
\
m
2000~ Fig. 3.
Depth/temperature field at t=const. (modified after Ziagos and Blackwefi, 1983).
154
ECKSTEIN, MAURATH AND FERRY
simulated temperature/depth curves with the temperature/depth profiles observed in boreholes, drilled into such geothermal system. It should be remenbered, however, that any attempt to compare simulated and observed temperature/depth profiles must be predicated upon conformity of the modeled system with the postulated geometry (Fig. 1) and all the assumptions inherent with the model. CASE STUDY
Location
Momotombo geothermal field is located in Nicaragua on the southern slope of Mt. Momotombo, one of the volcanoes of the principal belt of Quaternary volcanic activity in Central America (Fig. 4). The lower flanks of Momotombo have an approximate slope of 15%, which gradually increases over a distance of 3.5 km., to over 65% near the summit, at an ,'o*
H0NDURAS . / , . / ~
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o,
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7"
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COSTA
l
eeo
RICA
i
as°
j
eso
Fig. 4. Location of Momotombo geothermal anomaly in relation to the Volcanic Chain of Central America (triangles).
THE THERMAL E V O L U T I O N
155
N Q6
• ,t
2
\. ::.:',
Fig. 5.
0
KM
*0 ~1• • 022•19
9
! 29
•1
_1,2 ,7,,25 2o
5
Index map to Momotombo geothermal field. Broken lines delimit the bert of"feeder fractures".
elevation of 1,258 m. above the sea level (Fig. 5). The perfectly symmetrical cone is the dominant feature of the area. Lake Managua borders the southern, and part of the eastern slopes of the volcano. The Lake has an average depth ranging from 4 to 6 meters, with the surface at an average elevation of 39 m. above the sea level.
Regional and Local Geology The principal belt of Quaternary volcanoes of Central America is associated with the Benioff Zone of the descending Cocos plate at the Middle America Trench (Fig. 4). This volcanic chain outlines in Nicaragua the southwestern rim of the Nicaraguan Depression. The northeastern side of the Depression is delineated by a series of normal step faults. The Depression is filled mainly by Quaternary primary, or reworked pyroclastic and lava flows. The associated fault network consists of three major sets. The dominant set, by frequency as well as by cumulative lenght, outlines the Nicaraguan Depression, trending roughly in N50°W direction, parallel with the Middle America Trench, located 100kin. offshore. The second set of faults (in order of frequency and cummulative lenght), is perpendicular to the Nicaraguan Depression, and occurs predominantly as swarms of leftlateral strike-slip faults. These faults are responsible for the majority of the destructive shallow earthquakes in this region (Brown et al., 1973). The third set of faults trends approximately north, and is parallel to the compressional component of the Middle America Trench. The Momotombo geothermal field, located on the southern flanks of the volcano is on the southwestern rim of the Nicaraguan Depression. The
156
ECKSTEIN, MAURATH AND FERRY
volcano straddles an intersection between the Cordillera de los Marrabios, a segment of the Central American volcanic chain (Fig. 4), and a north trending right-lateral strike-slip faultline (Eckstein, 1980). Momotombo has a long record of Strombolian activity, including both, explosive and lava eruptions (McBirney, 1964). The most recent lava flows (1905) have left conspicuous gutters on the northern and northwestern slopes. They are composed of olivine-bearing basaltic to andestic aa lava flows, which are less than 20 m. thick. Lava flows on the southern flanks of the volcano, in the area of the Momotombo geothermal field are older, and composed of olivine-augite basalts, which have been extensively altered to kaolin, chalcedony and opal. LITHOLOGY AND SUBSURFACE TEMPERATURE DISTRIBUTION
Structural features of the temperature field in the subsurface of the Momotombo geothermal anomaly were defined on the basis of data from over 30 boreholes, drilled prior to 1979 to the maximum depth of 2,251 m. The boreholes penetrated a sequence of andesitic-basaltic pyroclastics and ignimbrites intercalated with variety of basaltic to andesitic lava flows. Zones of lost circulations encountered during drilling operations were assumed to correspond with fractures. This interpretation was further supported by core sample analysis and in some cases by reinjection tests (Moore, Osbun and Storm, 1981, 1982). Borehole temperature/depth profiles were constructed on the basis of multiple downhole temperature surveys conducted in each well following a shut-in period of several months to over a year (Moore, Osbun and Storm, 1981, 1982). Observed borehole temperature/depth profiles may be divided into the following three general categories: a. profiles showing consistent increase (althouth at varying rates) in temperature with depth (Fig. 6); b. profiles showing zero, or nearly zero temperature/depth gradient (Fig. 7); c. profiles showing temperature inversion (negative temperature gradient) at certain depths (Fig. 8). Boreholes with the temperature/depth profiles falling into the first category (MT-16, MT-10, MT-I1 and MT-4) are all located in the westernmost portion of the geothermal anomaly (Fig. 5). Consistently positive temperature gradients suggest that heat transfer in this area is exclusively by conduction. This presumption was further corroborated by the fact that the four boreholes produced negligible amounts of fluids. In
THE THERMAL EVOLUTION
157 (deg
TEMPERRTURE
0
4~
L
2~
'"l""l''"l
4~
....
I
~00
4~_,,,,~
0
..... I ....
4~
i'"'l
ZOO
400
0
-40C
C)
'T'l''''l''''l
400
....
0
I
0
400
ZOO
' ' ' 1 . . . . I ....
400
I ....
]
0
-400
-4~
-400
-I~
-12OC
-IZOC
-1200
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-16~
-160C
3 ~
MT-~000
MT-4
_
MT-IO
-200C
MT-II
-ZOO0
-~OOC
Fig. 6. Depth/temperature profiles observed in boreholes at the western edge of the Momotombo geothermal field.
addition downhole tests indicate that these boreholes penetrate an impermeable formation. Boreholes with the temperature/depth profiles falling into the second category (MT-26, MT-13, MT-23, MT-2 and MT-27) are all located in a narrow, north-trending belt (Fig. 5). High temperatures with zero, or near zero temperature gradient, as observed in these boreholes are characteristic of vertical, or subvertical systems of fractures with convecting hot fluids. This interpretation is supported by the fact that boreholes drilled in this belt are the most productive among all the boreholes drilled in Momotombo TEMPERRTURE 200 400
200
400
""1'"'1
400
.... t'""l
(de 9 C) 0
200
r"l'"'l'"'l'"'r
400
200
400
'"l'"'l'"'I'"'l
0 L m
-400
"
g -800
t
-I
w
-1200
d m -1600
MT-2B
MT-13
MT-23
MT-2
-EO00
Fig. 7. Depth/temperature profiles observed in boreholes located in the belt of "feeder fractures" of the Momotombo geothermal field.
158
ECKSTEIN, MAURATH AND FERRY TEMPERATURE 200
400
,ooi,,,,l,,,,l,,,,l,,,~I ~
200
_'"'1
....
r ....
400
(deg
C) 200
400
200
400
Ir'"l
-4oo
~ -~°°-
/
J -1200
-1800
MT-5
MT-7
MT-18
1
MT-I
Fig. 8. Depth/temperature profiles observed in boreholes located east of the "'feeder fractures" of the Momotombo geothermal field.
geothermal field. Goldsmith (1980) postulated that this belt is associated with a left-lateral strike-slip faultline, trending N5°E. Boreholes with the temperature/depth profiles falling into the third category are all located to the east of the non-productive zone, and the zone of convective belt, defined by the temperature/depth profiles of the first and second category, respectively (Fig. 5).
Conceptual Model o/ the Field A conceptual model of the Momotombo geothermal anomaly, based on data presented in an unpublished technical report by the drilling and development contractor to the Government of Nicaragua (California Energy Company, Inc., 1978), was developed by Lopez et al. (1980). According to this model the geothermal anomaly of Momotombo is generated by convective flow of steam and/or superheated water, rising along a system of vertical, or sub-vertical fractures, located within the narrow zone delimited by boreholes with zero, or near zero temperature gradient. The north-trending zone of the "feeder fractures" is bound on the west by the area of massive, impermeable "hot-dry rock", and is capped by an impermeable, approximately 300 m. thick silica-cap, which seals it from the ground surface. The thermal fluids penetrate a system of horizontal, or sub-horizontal fractures, extending east of the "feeder fractures" beneath the silica cap. The flow of thermal fluids eastward through the system of the horizontal, or sub-horizontal fractures is generating a plume-like geother-
THE THERMAL EVOLUTION
159
mal anomaly, which is expressed by the temperature inversion zone pervasive in the boreholes to the east of the "feeder fractures". Data Base ./'or the Model Evolution of the temperature field for 500 to 100,000 years was simulated for a number of boreholes, for which actual temperature/depth measurements were available. The parameters involved in the simulation were either approximated from the data base, available for each borehole, or assumed and tested by curve-fitting of the model to the respective temperature/depth profiles. Mean annual temperature of the region was taken as the constant ground surface temperature. Lopez (1982) estimated the temperature of the hydrothermal fluids within the "feeder fracture" (To), based upon hydrogeochemical considerations to be approximately 325°C. This temperature is very close to the maximum temperature measured in MT~4 (Fig. 6). Fluid density and heat capacity were based upon values for water at that temperature. Values for thermal conducivity (6 mcal/cm/sec/CC) and diffusivity (0.01 cm2/sec) were approximated by taking values typical for the rocks reported in the lithologic logs of the boreholes. Variation of each of these four variables by 20% affected the modeled results by less than 1%. Depth to the aquifer was assumed to correspond with the depth of the observed temperature inversion in each borehole. Lateral distance of each borehole from the "feeder fracture" was measured in perpendicular to the belt of boreholes with isothermal temperature/depth profiles (Fig. 5). The "background" temperature/depth gradient in the area for the time preceeding superposition of the hydrothermal flow system was assumed to be 0.1125°C/m, basing on the deeper part of the temperature/depth profile observed in MT-16, in the westernmost and least affected by the hydrothermal flow system borehole. The empirical best fit of the model to the observed data for each borehole was determined through trail and error by varying the flow velocity, aquifer thickness and age of the flow system. The tests were run at 500 years time increments, 2 m/year velocity increments and 5 m increments for the aquifer thickness. The best fit was obtained for flow velocities ranging between 6 and 20m/year, with a mode of approximately 17m/year. Aquifer thicknesses between 5 and 100 m were tested, with the best fit obtained, in most cases, for h = 12 + 5 m. All boreholes were then remodeled using a velocity of 17 m/year and a mean aquifer thickness of 12 + 5 m, leaving the time to be the one single variable.
160
ECKSTEIN, MAURATH A N D FERRY TEMPERRTURE
I00
0
C)
(degrees
200
300
' ~ ' ' ' I
0
400
~''' MT-]5
400 L -lJ E
BOO
I G. hi
odeled
1200
t ~500 yrs v - 15 m / y r
ISO0
h -
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931
~\ ~\
m
\\
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k
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Fig. 9.
,
,
,
I
,
,
,
,
1
,
,
J
i
I
i
i
,
j
Theoretical and observed temperature/depth profiles for M T 15.
Simulated and Observed Temperature/Depth Profiles The empirical "best fit" of the observed profiles was obtained years. Relatively good fits were and MT-5 (Fig. 10). The nature TEMPERATURE IOO
(degree3 ZOO
simulated temperature/depth profile to the for MT-15 (Fig. 9) using t = 5 , 5 0 0 _ 5 0 0 obtained using the same value for MT-8 of the deviations of the observed, from the
C)
TEMPERRTURE
300
400 0 0
I00
(d~grees
200
_ M T_- 8 400
eO0
BOO
b~ilyyrr~?
b~ckground
°b3erved made I e d
observed i~00 modmled
t
5500
v-
I I
h-
Fig. 10.
yrs
m/yr
lOre
300 NTIS
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background
C)
ISOO
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v
-
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m/yr
h
-
11
m
Theoretical and observed temperature/depth profiles for MT-8 and MT 5.
400
THE T H E R M A L E V O L U T I O N TEMPERRTURE
161
(degree=
]OO
TEMPERRTURE
C)
ZOO
300
.Ioo
Ioo
o
(degrees
~oo
C) 400
300
o p
MT-I~
MT-E 400
eoo
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~
400 L
~a b s e r v m d
eoo L
blckground
--
background
modeled
lZ00L
mode I e d
1~oo
observed
m
1600
t-
5 5 0 0 y~s
v
-
17
m/yr
h
-
II
m
t - 5500 yr~ v - 20 m / y r
i~oo
h
2000
-
13
m
aooo
Fig. I 1. Theoretical and observed temperature/depth profiles for MT-6 and MT 18.
simulated profiles in MT-6, MT-18 (Fig. 11) and MT-30, MT-7 (Fig. 12) may be explained by departure of the field conditions from rather stringent assumptions of the model. While comparing the simulated and observed temperature/depth profiles, it should be remenbered that very seldom a natural system ideally conforms with boundary conditions and simplistic assumptions inherent with mathematical models. The most commonly violated such condition of this model is the assumption that heat above, and paricularly below the aquifer is taking place solely by conduction. At Momotombo a silica cap forms the upper boundary of the aquifer. Over most of the area this cap extends to the ground surface, preventing convection of hydrothermal fluids above the aquifer. The only notable exception were hot springs and fumaroles, reported once to emerge beyond the eastern edge of the field at the shore of Lake Managua (Frobei, 1859). TEMPERRTURE I00
(de,tree3
ZOO
C)
TEMPERNTURE
SOO
400
0
Jo0
C) 300
(degrees
~00
400
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i xi:o:: .
Fig. 12.
.
.
.
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-
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l
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-
m/yr
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I
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,
Theoretical and observed temperature/depth profiles for MT-7 and MT-30.
,
,
I
~
162
ECKSTEIN, MAURATH AND FERRY
Flow of the springs and fumarolic activity ceased reportedly during the drilling operations of 1974-78. Therefore the assumption that conduction is the predominant, if not the only, mode of heat transfer within the upper half-space above the aquifer of Momotombo is justified, and relatively good curve fit between the simulated and observed temperature/depth profiles of the Momotombo boreholes was achieved for the upper half-space above the temperature inversion (Fig's 9-12). The fit is less apparent within the half-space below the aquifer of the Momotombo geothermal system, because of circulation of colder water through a deeper system of fractures, not connected with the "feeder fracture" in the western portion of the field. The disturbance is particularly evident along the eastern portion of the anomaly, growing in amplitude to the east-southeast (Fig's 10-12). CONCLUSIONS
The case study presented in this paper illustrates problems associated with modeling of active geothermal systems. Computers may facilitate solution of relatively complex mathematical models of systems with intricate geometry and boundary conditions. Because of their restrictive assumptions, such models are generally more site-specific and limited in validity and application. Models assuming a generalized, relatively simple geometry, such as the one developed by Ziagos and Blackwell (1983), may be effectively applied to simulate the evolution of relatively complex geothermal systems. Curve fitting between simulated and observed temperature/depth profiles may be used to approximate the age of the modeled hydrothermal system, as well as to estimate the flow velocity of the geothermal fluids moving through the system. The thermo-tectonic events which caused the present-day Momotombo hydrothermal system occurred approximately 5,500 years ago, following development of verical, or subvertical fractures along a N5°E trending faultline. Hot fluids emerging from these fractures move eastward through a system of horizontal, or subhorizontal fractures, with a velocity of l l to 20 m/yr. ACKNOWLEDGEMENTS
Two of the authors were supported while working on this paper by stipends from the Department of Geology, Kent State University. The authors benefited from extensive discussions with John Ziagos (of Sohio
THE THERMAL EVOLUTION
163
Exploration, Inc. in San Francisco) and Dave Blackwell (of Southern Methodists University in Dallas), who also offered many critical comments on the manuscript. Critical review of the manuscript by L. Rybach (of Swiss Federal Polytechnical Institute in Zurich) is gratefully acknowledged. REFERENCES Brown, R, D., Ward, P. L. and Plafker, G., 1973. Geologic and Seismologic Aspects of the Managua, Nicaragua, Earthquakes of Dec. 23 1972; U. S. Geol. Survey, Prof. Paper 838, 34 pp. Bodvarsson, Gunnar, 1969. On the Temperature of Water Flowing Through Fractures; .l. Geoph. Res., Vol. 74, No. 8, p. 1987-1992. Bodvarsson, Gunnar, 1973. Temperature Inversions in Geothermal Systems; Geoexploration, Vol. 11, p. 141-149. California Energy Company, Inc., 1978. Feasibility Report; Momotombo Geothermal Field Expansion to 105 Megawatts; unpubliched technical report to the Government of Nicaragua. Carslaw H. S. and Jaeger, J. C., 1959. Conduction of Heat in Solids; 2-nd edit., Clarendon, Oxford, 510 pp. Eckstein, Y., 1980. Tectonic Control of the Geothermal Resources in Nicaragua, Central America: 26-th Int. Geol. Congr,, Paris, Abstr. Vol. 1, p. 335. Eckstein, Y. and Cik, R., 1982. Use of Temperature Inversion Data for Determining the Age of Fracturing in a Geothermal Area; EOS, Vol. 63, No. 45, p. 1091. Frobel, J., 1859. Seven Years Travel in Central America, Northern Mexico, and the Far West of the United States: R. Bentley, London, 587 p.; cited in Waring, G. A., 1965. Thermal Springs of the United States and Other Countries of the World, A Summary: U.S. Geol. Surv. Prof. Paper 492, p. 65. Goldsmith, L. H., 1980. Regional and Local Geologic Structure of the Momotombo Field, Nicaragua: Geoth. Res. Counc., Trans. Vol. 4, p. 125-128. Lopez, C. A. V., 1982. Thermal Structure and Hydrogeochemistry of the Momotombo Geothermal Field, Nicaragua, C, A.; M. S. thesis, Kent State Univ., Dept. of Geology, Kent, 174 pp. Lopez, C. A. V., Hoyt B. R. and Eckstein Yoram, 1980. Subsurface Temperature Distribution and Structure of the Geothermal Reservoir at Momotombo, Nicaragua; Geoth. Res. Counc., Trans. Vol. 4, p. 459~462. McBirney, A. R., 1964. Notas sobre los Centros Volcanicos Cuaternarios al Este de la Depresion Nicaraguense; Serv. Geol. Nac. de Nicaragua, Bol. 8, p. 91-96. Moore, J. L., Osbun, Erik and Storm, P. V., 1981. Geology and Temperature Distributionf of Momotombo Geothermal Field, Nicaragua; in Halbouty, M. T. (ed.), Energy Resources of the Pacific Region; Tulsa, AAPG Studies in Geology No. 12, p. 33-54. Moore, J. L., Osbun, Erik and Storm, P. V., 1982. Geology and Temperature Distribution of M omotombo Geothermal Field, Nicaragua; Geoth. Res. Counc. Special Report No. 12, p. 13(~ 151. Ziagos, J. P. and Blackwell, D. D., 1981. A Model for the Effect of Horizontal Flow in a Thin Aquifer on Temperature-Depth Profiles; Geoth. Res. Counc., Trans. Vol. 5, p. 221 223. Ziagos, J. P. and Blackwell, D. D., 1983. A Model for the Transient Temperature Effect of Horizontal Fluid Flow in Geothermal Systems; unpubl, manuscr. Contribution No. 265 Department of Geology Kent State University Kent, Ohio 44242, U.S.A.
II
M O D E L I N G THE THERMAL GEOTHERMAL SYSTEM
149
EVOLUTION
OF
AN
ACTIVE
Y. ECKSTEIN, G. MAURATH and R. A. FERRY
Department (~f Geology, Kent State Uni~ersity, Kent, Ohio 44242, ~,.S.A. (Accepted July 4, 1984)
ABSTRACT Eckstein, Y., Maurath, G. and Ferry, R. A., 1985. Modeling the thermal evolution of an active geothermal system. In: L. Rybach (editorl, Heat Flow and Geothermal Processes. Journal 0/' Geo&,namics, 4: 149 163. Temperature inversions at shallow to moderate depths have been observed commonly in boreholes drilled in geothermal areas. The inversions result from thermal disequilibria generated by steam and, or hydrothermal fluids invading shallow horizontal, or sub-horizontal fractures, or permeable horizons, from a deep vertical, or sub-vertical feeder-fracture. Subsurface distribution of temperatures in Momotombo geothermal area of Nicaragua, Central America, indicates that the anomaly is generated by steam and water, convecting in a narrow feederfracture-zone located at the western edge of the field. The north-trending zone of the feeder-fracture is bound on the west by the area of massive, impermeable andesitic rocks, and is capped by an impermeable, approximately 300 m. thick silica-cap, which seals if from the ground surface. The thermal fluids penetrate a systcm of horizontal, or sub-horizontal fractures, extending east of the feeder-fracture beneath the silica cap. The flow of thermal fluids eastward through the system of the horizontal, or subhorizontal fractures is generating a plume-like geothermal anomaly, which is expressed by the temperature inversion zone pervasive in the boreholes to the east of the feeder-fracture. A time-dependant model for a semi-infinite half-space ( z > 0 ) in contact with a hot, well stirred, isotropic fluid flowing through an aquifer overlain by a finite space of constant thickness is solved for the data collected from the Momotombo geothermal boreholes. Curve fitting between the simulated and observed temperature/depth profiles suggests that the thermo-tectonic events which caused the presentday Momotombo hydrothermal system occurred approximately 5,500 years ago, following development of vertical, or subvertical fractures along a N5 E trending faultline. Hot fluids emerging from these fractures move eastward through a system of horizontal, or sub-horizontal fractures, with a velocity of 1 I to 20 myr.
|NTRODUCTION
Numerous mathematical models of active geothermal systems have been developed during the past two decades. The majority of such models are 0264-3"/07,85/$3.00
1985 Geophysical Press Ltd.
150
ECKSTEIN, MAURATH AND FERRY
based upon various general solutions to problems of heat conduction in solids under steady state or transient conditions (Carslaw and Jaeger, 1959). Non-linear temperature/depth profiles occur predominantly as a result of either cyclic variations of the temperature at the ground surface boundary, or subsurface convective heat transfer by ground water, magma, or hydrothermal fluids. Assuming certainf simplifications such profiles may be approximated by mathematical models. This paper describes the application of a time-dependant model for a semi-infinite half-space (z > 0) in contact with a hot, well stirred, isotropic fluid flowing through an aquifer overlain by a finite space of constant thickness (Fig. 1). The general solution for a temperature field generated by a heat source bound by an infinite half-space of finite thermal conductivity, normal to the direction of heat flow, was given by Carslaw and Jaeger (p. 395, 1959). This approach to fluid flow within a discrete horizontal aquifer bound by an infinite half-space was initially applied by Bodvarsson (1969, 1973). The model was modified by Ziagos and Blackwell (1981), and further refined by Ziagos and Blackwell (1983), to explain observed geothermal gradients in boreholes penetrating discrete horizontal aquifers. Modifications included introduction of the ground surface as a steady-state boundary condition, and removal of a boundary condition below the 0
~round ~urCace
Ts
X
aqutCer
Za
) T (de 9 C)
Za
t~p I.
¢p
to
Z
Z
Fig. 1. Space parameters for the model and temperature/depth profile for a time (t) after the initiation of the flow through the system (to) and before the time of thermal equilibration (4u); modified after Bodvarsson, 1973 and Ziagos and Blackwell, 1983.
THE THERMAL EVOLUTION
151
aquifer introduced by Bodvarsson (1973). Thus the layer below the aquifer is assumed to be a semi-infinite half-space. Ziagos and Blackwell's (1983) version of the model is solved for the field data from a number of boreholes drilled in Momotombo geothermal area of Nicaragua, Central America, to evaluate the age of the hydrothermal system, and flow velocity of the hydrothermal fluids. Solution of the simplified version of the model (Ziagos and Blackwell, 1981) for the same set of data was presented by Eckstein and Cik (1982).
MATHEMATICAL MODEL
The model developed by Ziagos and Blackwell (1983) emulates the transient temperature field around a hydro-thermal system consisting of a thin horizontal aquifer recharged continuously from a vertical or sub-vertical feeder fracture (Fig. 1). Thermal effects around the feeder fracture are not considered. The aquifer is confined between aquicludes, which have thermal properties similar to the aquifer. The upper aquiclude is at least ten times the thickness of the aquifer. The ground surface is considered as a constanttemperature boundary condition. It is assumed that no convection occurs within the aquifer, and heat transfer through the aquicludes is by conduction only. Assuming that the tectonic event which led to the generation of the hydrothermal system occurred at least 500 years ago, the solution for this model, as formulated by Ziagos and Blackwell (1983) is as follows: Tu(x, z, t) = 0 ~
[erfc(/~, ) - erfc(/~2)]
(1)
n~O
T~(x, z, t) = 0 erfc(~x/7)
(2)
Tl(x, z, t) = 0 erfc[(~x + z - z,)/7]
(3)
where:
0 = To exp(-0tX/Za) e=K/pChV
~, = [ ( 2 n + 1) z , - z + ~ x ) ] / 7 /~2 = [(2n + 1 ) z~ + z + ~x)]/7 t' : t - ( x / V ) - (~xz,)/(3k )
K - thermal conductivity k - thermal diffusivity p - fluid density
152
ECKSTEIN, MAURATH AND FERRY
C - f l u i d heat capacity V - f l u i d flow velocity h - thickness of the aquifer t - t i m e since initiation of the flow through the system z - v e r t i c a l distance below the ground-surface x - l a t e r a l distance from the feeder fracture z , - d e p t h to the aquifer T o - temperature of the fluid in the feeder fracture T u ( x , z, t) - temperature field in the upper half-space (above the aquifer) T~,(x, z, t) - temperature field within the aquifer T / ( x , z, t) - temperature field in the lower half-space
(below the aquifer) The solution for T ( z , t), with x held constant (Fig. 2) defines the evolution of the temperature field through the time at the distance x from the feeder fracture. The net departure of the theoretical temperature profile from a "background" profile characteristic of a purely conductive heat
TFMPERRTURE 0
I O0
(degrees
ZOO
C) SO0
400
0
,oop
\ " ~ - " ~ _-Z--~ _~
~ ~
,ooo.\
\,ooo./~ooo./,oo.
/
,oo
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2000
Fig. 2. 1983).
t
-
10000
~-2o..,y~
I
y,-,
I
\\\
\\\
\
\
,,,
Evolution of the depth/temperature field at x
const. (modified after Ziagos and Blackwelk
THE THERMAL EVOLUTION
153
transfer regime, presumed to be valid prior to fracturing and inception of the flow, is gradually amplified with time lapse. Similarly, solution for T(x, z), with t held constant (Fig. 3) defines the temperature field of the system at time t after the initiation of the flow. It may be seen that the net departure of the temperature profile from the linear "background" profile characteristic of a purely conductive heat transfer regime is attenuated with increasing distance from the feeder fracture. Thus, for short time intervals, or very large distances from the feeder fracture, no thermal disturbance would be observed. Steady-state conditions are obtained for either very small distances from the feeder fracture, or for very long periods of time. Between these two extremes the model may be used to simulate the thermal evolution of a geothermal field conforming with the postulated geometry (Fig. 1) and assumptions. Shape of the simulated temperature/depth curves is - - except for being dependant on either the time that elapsed since initiation of the flow through the system, or the lateral distance from the feeder fracture - - particularly sensitive to such parameters as fluid flow velocity, thickness of the aquifer, thermal properties of the fluid, thermal properties of the rocks, and the temperature of the fluid in the feeder fracture. Since the model is composed of three simultaneous equations it may be used for approximation of at least three variables for a given geothermal system, by matching the TEMPERATURE 0
0
100 ,
[
I
1
( d e g r e e 8 C)
200 ,
I
;
I
I
300 I
I
'
[
I
400 I
I
I
I
0 yr
BOO
yr~
p
16oo F_
~-
15
.,,,y,
.-looo. h
-
I0
\ \
\
\
\
\
m
2000~ Fig. 3.
Depth/temperature field at t=const. (modified after Ziagos and Blackwefi, 1983).
154
ECKSTEIN, MAURATH AND FERRY
simulated temperature/depth curves with the temperature/depth profiles observed in boreholes, drilled into such geothermal system. It should be remenbered, however, that any attempt to compare simulated and observed temperature/depth profiles must be predicated upon conformity of the modeled system with the postulated geometry (Fig. 1) and all the assumptions inherent with the model. CASE STUDY
Location
Momotombo geothermal field is located in Nicaragua on the southern slope of Mt. Momotombo, one of the volcanoes of the principal belt of Quaternary volcanic activity in Central America (Fig. 4). The lower flanks of Momotombo have an approximate slope of 15%, which gradually increases over a distance of 3.5 km., to over 65% near the summit, at an ,'o*
H0NDURAS . / , . / ~
~,o--
(
:
.'o
~IBBEAN '*~'.c-~ "~.~. ~
~io"
%,,
,
,z*
PLATE
ZONE ||
elo°
o~,A
- -
'
o
.',
~i
CARIBBEAN
•
~ '"
_
,~o
A &•
i
ip.
- -
_ _ , , o
o,
!
7"
~,.
COSTA
l
eeo
RICA
i
as°
j
eso
Fig. 4. Location of Momotombo geothermal anomaly in relation to the Volcanic Chain of Central America (triangles).
THE THERMAL E V O L U T I O N
155
N Q6
• ,t
2
\. ::.:',
Fig. 5.
0
KM
*0 ~1• • 022•19
9
! 29
•1
_1,2 ,7,,25 2o
5
Index map to Momotombo geothermal field. Broken lines delimit the bert of"feeder fractures".
elevation of 1,258 m. above the sea level (Fig. 5). The perfectly symmetrical cone is the dominant feature of the area. Lake Managua borders the southern, and part of the eastern slopes of the volcano. The Lake has an average depth ranging from 4 to 6 meters, with the surface at an average elevation of 39 m. above the sea level.
Regional and Local Geology The principal belt of Quaternary volcanoes of Central America is associated with the Benioff Zone of the descending Cocos plate at the Middle America Trench (Fig. 4). This volcanic chain outlines in Nicaragua the southwestern rim of the Nicaraguan Depression. The northeastern side of the Depression is delineated by a series of normal step faults. The Depression is filled mainly by Quaternary primary, or reworked pyroclastic and lava flows. The associated fault network consists of three major sets. The dominant set, by frequency as well as by cumulative lenght, outlines the Nicaraguan Depression, trending roughly in N50°W direction, parallel with the Middle America Trench, located 100kin. offshore. The second set of faults (in order of frequency and cummulative lenght), is perpendicular to the Nicaraguan Depression, and occurs predominantly as swarms of leftlateral strike-slip faults. These faults are responsible for the majority of the destructive shallow earthquakes in this region (Brown et al., 1973). The third set of faults trends approximately north, and is parallel to the compressional component of the Middle America Trench. The Momotombo geothermal field, located on the southern flanks of the volcano is on the southwestern rim of the Nicaraguan Depression. The
156
ECKSTEIN, MAURATH AND FERRY
volcano straddles an intersection between the Cordillera de los Marrabios, a segment of the Central American volcanic chain (Fig. 4), and a north trending right-lateral strike-slip faultline (Eckstein, 1980). Momotombo has a long record of Strombolian activity, including both, explosive and lava eruptions (McBirney, 1964). The most recent lava flows (1905) have left conspicuous gutters on the northern and northwestern slopes. They are composed of olivine-bearing basaltic to andestic aa lava flows, which are less than 20 m. thick. Lava flows on the southern flanks of the volcano, in the area of the Momotombo geothermal field are older, and composed of olivine-augite basalts, which have been extensively altered to kaolin, chalcedony and opal. LITHOLOGY AND SUBSURFACE TEMPERATURE DISTRIBUTION
Structural features of the temperature field in the subsurface of the Momotombo geothermal anomaly were defined on the basis of data from over 30 boreholes, drilled prior to 1979 to the maximum depth of 2,251 m. The boreholes penetrated a sequence of andesitic-basaltic pyroclastics and ignimbrites intercalated with variety of basaltic to andesitic lava flows. Zones of lost circulations encountered during drilling operations were assumed to correspond with fractures. This interpretation was further supported by core sample analysis and in some cases by reinjection tests (Moore, Osbun and Storm, 1981, 1982). Borehole temperature/depth profiles were constructed on the basis of multiple downhole temperature surveys conducted in each well following a shut-in period of several months to over a year (Moore, Osbun and Storm, 1981, 1982). Observed borehole temperature/depth profiles may be divided into the following three general categories: a. profiles showing consistent increase (althouth at varying rates) in temperature with depth (Fig. 6); b. profiles showing zero, or nearly zero temperature/depth gradient (Fig. 7); c. profiles showing temperature inversion (negative temperature gradient) at certain depths (Fig. 8). Boreholes with the temperature/depth profiles falling into the first category (MT-16, MT-10, MT-I1 and MT-4) are all located in the westernmost portion of the geothermal anomaly (Fig. 5). Consistently positive temperature gradients suggest that heat transfer in this area is exclusively by conduction. This presumption was further corroborated by the fact that the four boreholes produced negligible amounts of fluids. In
THE THERMAL EVOLUTION
157 (deg
TEMPERRTURE
0
4~
L
2~
'"l""l''"l
4~
....
I
~00
4~_,,,,~
0
..... I ....
4~
i'"'l
ZOO
400
0
-40C
C)
'T'l''''l''''l
400
....
0
I
0
400
ZOO
' ' ' 1 . . . . I ....
400
I ....
]
0
-400
-4~
-400
-I~
-12OC
-IZOC
-1200
-1GO0
-IGO¢
-16~
-160C
3 ~
MT-~000
MT-4
_
MT-IO
-200C
MT-II
-ZOO0
-~OOC
Fig. 6. Depth/temperature profiles observed in boreholes at the western edge of the Momotombo geothermal field.
addition downhole tests indicate that these boreholes penetrate an impermeable formation. Boreholes with the temperature/depth profiles falling into the second category (MT-26, MT-13, MT-23, MT-2 and MT-27) are all located in a narrow, north-trending belt (Fig. 5). High temperatures with zero, or near zero temperature gradient, as observed in these boreholes are characteristic of vertical, or subvertical systems of fractures with convecting hot fluids. This interpretation is supported by the fact that boreholes drilled in this belt are the most productive among all the boreholes drilled in Momotombo TEMPERRTURE 200 400
200
400
""1'"'1
400
.... t'""l
(de 9 C) 0
200
r"l'"'l'"'l'"'r
400
200
400
'"l'"'l'"'I'"'l
0 L m
-400
"
g -800
t
-I
w
-1200
d m -1600
MT-2B
MT-13
MT-23
MT-2
-EO00
Fig. 7. Depth/temperature profiles observed in boreholes located in the belt of "feeder fractures" of the Momotombo geothermal field.
158
ECKSTEIN, MAURATH AND FERRY TEMPERATURE 200
400
,ooi,,,,l,,,,l,,,,l,,,~I ~
200
_'"'1
....
r ....
400
(deg
C) 200
400
200
400
Ir'"l
-4oo
~ -~°°-
/
J -1200
-1800
MT-5
MT-7
MT-18
1
MT-I
Fig. 8. Depth/temperature profiles observed in boreholes located east of the "'feeder fractures" of the Momotombo geothermal field.
geothermal field. Goldsmith (1980) postulated that this belt is associated with a left-lateral strike-slip faultline, trending N5°E. Boreholes with the temperature/depth profiles falling into the third category are all located to the east of the non-productive zone, and the zone of convective belt, defined by the temperature/depth profiles of the first and second category, respectively (Fig. 5).
Conceptual Model o/ the Field A conceptual model of the Momotombo geothermal anomaly, based on data presented in an unpublished technical report by the drilling and development contractor to the Government of Nicaragua (California Energy Company, Inc., 1978), was developed by Lopez et al. (1980). According to this model the geothermal anomaly of Momotombo is generated by convective flow of steam and/or superheated water, rising along a system of vertical, or sub-vertical fractures, located within the narrow zone delimited by boreholes with zero, or near zero temperature gradient. The north-trending zone of the "feeder fractures" is bound on the west by the area of massive, impermeable "hot-dry rock", and is capped by an impermeable, approximately 300 m. thick silica-cap, which seals it from the ground surface. The thermal fluids penetrate a system of horizontal, or sub-horizontal fractures, extending east of the "feeder fractures" beneath the silica cap. The flow of thermal fluids eastward through the system of the horizontal, or sub-horizontal fractures is generating a plume-like geother-
THE THERMAL EVOLUTION
159
mal anomaly, which is expressed by the temperature inversion zone pervasive in the boreholes to the east of the "feeder fractures". Data Base ./'or the Model Evolution of the temperature field for 500 to 100,000 years was simulated for a number of boreholes, for which actual temperature/depth measurements were available. The parameters involved in the simulation were either approximated from the data base, available for each borehole, or assumed and tested by curve-fitting of the model to the respective temperature/depth profiles. Mean annual temperature of the region was taken as the constant ground surface temperature. Lopez (1982) estimated the temperature of the hydrothermal fluids within the "feeder fracture" (To), based upon hydrogeochemical considerations to be approximately 325°C. This temperature is very close to the maximum temperature measured in MT~4 (Fig. 6). Fluid density and heat capacity were based upon values for water at that temperature. Values for thermal conducivity (6 mcal/cm/sec/CC) and diffusivity (0.01 cm2/sec) were approximated by taking values typical for the rocks reported in the lithologic logs of the boreholes. Variation of each of these four variables by 20% affected the modeled results by less than 1%. Depth to the aquifer was assumed to correspond with the depth of the observed temperature inversion in each borehole. Lateral distance of each borehole from the "feeder fracture" was measured in perpendicular to the belt of boreholes with isothermal temperature/depth profiles (Fig. 5). The "background" temperature/depth gradient in the area for the time preceeding superposition of the hydrothermal flow system was assumed to be 0.1125°C/m, basing on the deeper part of the temperature/depth profile observed in MT-16, in the westernmost and least affected by the hydrothermal flow system borehole. The empirical best fit of the model to the observed data for each borehole was determined through trail and error by varying the flow velocity, aquifer thickness and age of the flow system. The tests were run at 500 years time increments, 2 m/year velocity increments and 5 m increments for the aquifer thickness. The best fit was obtained for flow velocities ranging between 6 and 20m/year, with a mode of approximately 17m/year. Aquifer thicknesses between 5 and 100 m were tested, with the best fit obtained, in most cases, for h = 12 + 5 m. All boreholes were then remodeled using a velocity of 17 m/year and a mean aquifer thickness of 12 + 5 m, leaving the time to be the one single variable.
160
ECKSTEIN, MAURATH A N D FERRY TEMPERRTURE
I00
0
C)
(degrees
200
300
' ~ ' ' ' I
0
400
~''' MT-]5
400 L -lJ E
BOO
I G. hi
odeled
1200
t ~500 yrs v - 15 m / y r
ISO0
h -
1o
x -
931
~\ ~\
m
\\
m
k
\ ,
200C
Fig. 9.
,
,
,
I
,
,
,
,
1
,
,
J
i
I
i
i
,
j
Theoretical and observed temperature/depth profiles for M T 15.
Simulated and Observed Temperature/Depth Profiles The empirical "best fit" of the observed profiles was obtained years. Relatively good fits were and MT-5 (Fig. 10). The nature TEMPERATURE IOO
(degree3 ZOO
simulated temperature/depth profile to the for MT-15 (Fig. 9) using t = 5 , 5 0 0 _ 5 0 0 obtained using the same value for MT-8 of the deviations of the observed, from the
C)
TEMPERRTURE
300
400 0 0
I00
(d~grees
200
_ M T_- 8 400
eO0
BOO
b~ilyyrr~?
b~ckground
°b3erved made I e d
observed i~00 modmled
t
5500
v-
I I
h-
Fig. 10.
yrs
m/yr
lOre
300 NTIS
4oo
background
C)
ISOO
t -
550O y r s
v
-
17
m/yr
h
-
11
m
Theoretical and observed temperature/depth profiles for MT-8 and MT 5.
400
THE T H E R M A L E V O L U T I O N TEMPERRTURE
161
(degree=
]OO
TEMPERRTURE
C)
ZOO
300
.Ioo
Ioo
o
(degrees
~oo
C) 400
300
o p
MT-I~
MT-E 400
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- b
~
400 L
~a b s e r v m d
eoo L
blckground
--
background
modeled
lZ00L
mode I e d
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observed
m
1600
t-
5 5 0 0 y~s
v
-
17
m/yr
h
-
II
m
t - 5500 yr~ v - 20 m / y r
i~oo
h
2000
-
13
m
aooo
Fig. I 1. Theoretical and observed temperature/depth profiles for MT-6 and MT 18.
simulated profiles in MT-6, MT-18 (Fig. 11) and MT-30, MT-7 (Fig. 12) may be explained by departure of the field conditions from rather stringent assumptions of the model. While comparing the simulated and observed temperature/depth profiles, it should be remenbered that very seldom a natural system ideally conforms with boundary conditions and simplistic assumptions inherent with mathematical models. The most commonly violated such condition of this model is the assumption that heat above, and paricularly below the aquifer is taking place solely by conduction. At Momotombo a silica cap forms the upper boundary of the aquifer. Over most of the area this cap extends to the ground surface, preventing convection of hydrothermal fluids above the aquifer. The only notable exception were hot springs and fumaroles, reported once to emerge beyond the eastern edge of the field at the shore of Lake Managua (Frobei, 1859). TEMPERRTURE I00
(de,tree3
ZOO
C)
TEMPERNTURE
SOO
400
0
Jo0
C) 300
(degrees
~00
400
4oo
eoo
l~oc
12OO
i xi:o:: .
Fig. 12.
.
.
.
I~_,
"i.:'::L !
1800
-
,
l
I
J
,
L
~
[
,
L
,
,
......... \)\ v
-
m/yr
18
h - lore 1570 m
2 o o o ~ , ,
~
,
I
J
,
Theoretical and observed temperature/depth profiles for MT-7 and MT-30.
,
,
I
~
162
ECKSTEIN, MAURATH AND FERRY
Flow of the springs and fumarolic activity ceased reportedly during the drilling operations of 1974-78. Therefore the assumption that conduction is the predominant, if not the only, mode of heat transfer within the upper half-space above the aquifer of Momotombo is justified, and relatively good curve fit between the simulated and observed temperature/depth profiles of the Momotombo boreholes was achieved for the upper half-space above the temperature inversion (Fig's 9-12). The fit is less apparent within the half-space below the aquifer of the Momotombo geothermal system, because of circulation of colder water through a deeper system of fractures, not connected with the "feeder fracture" in the western portion of the field. The disturbance is particularly evident along the eastern portion of the anomaly, growing in amplitude to the east-southeast (Fig's 10-12). CONCLUSIONS
The case study presented in this paper illustrates problems associated with modeling of active geothermal systems. Computers may facilitate solution of relatively complex mathematical models of systems with intricate geometry and boundary conditions. Because of their restrictive assumptions, such models are generally more site-specific and limited in validity and application. Models assuming a generalized, relatively simple geometry, such as the one developed by Ziagos and Blackwell (1983), may be effectively applied to simulate the evolution of relatively complex geothermal systems. Curve fitting between simulated and observed temperature/depth profiles may be used to approximate the age of the modeled hydrothermal system, as well as to estimate the flow velocity of the geothermal fluids moving through the system. The thermo-tectonic events which caused the present-day Momotombo hydrothermal system occurred approximately 5,500 years ago, following development of verical, or subvertical fractures along a N5°E trending faultline. Hot fluids emerging from these fractures move eastward through a system of horizontal, or subhorizontal fractures, with a velocity of l l to 20 m/yr. ACKNOWLEDGEMENTS
Two of the authors were supported while working on this paper by stipends from the Department of Geology, Kent State University. The authors benefited from extensive discussions with John Ziagos (of Sohio
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Exploration, Inc. in San Francisco) and Dave Blackwell (of Southern Methodists University in Dallas), who also offered many critical comments on the manuscript. Critical review of the manuscript by L. Rybach (of Swiss Federal Polytechnical Institute in Zurich) is gratefully acknowledged. REFERENCES Brown, R, D., Ward, P. L. and Plafker, G., 1973. Geologic and Seismologic Aspects of the Managua, Nicaragua, Earthquakes of Dec. 23 1972; U. S. Geol. Survey, Prof. Paper 838, 34 pp. Bodvarsson, Gunnar, 1969. On the Temperature of Water Flowing Through Fractures; .l. Geoph. Res., Vol. 74, No. 8, p. 1987-1992. Bodvarsson, Gunnar, 1973. Temperature Inversions in Geothermal Systems; Geoexploration, Vol. 11, p. 141-149. California Energy Company, Inc., 1978. Feasibility Report; Momotombo Geothermal Field Expansion to 105 Megawatts; unpubliched technical report to the Government of Nicaragua. Carslaw H. S. and Jaeger, J. C., 1959. Conduction of Heat in Solids; 2-nd edit., Clarendon, Oxford, 510 pp. Eckstein, Y., 1980. Tectonic Control of the Geothermal Resources in Nicaragua, Central America: 26-th Int. Geol. Congr,, Paris, Abstr. Vol. 1, p. 335. Eckstein, Y. and Cik, R., 1982. Use of Temperature Inversion Data for Determining the Age of Fracturing in a Geothermal Area; EOS, Vol. 63, No. 45, p. 1091. Frobel, J., 1859. Seven Years Travel in Central America, Northern Mexico, and the Far West of the United States: R. Bentley, London, 587 p.; cited in Waring, G. A., 1965. Thermal Springs of the United States and Other Countries of the World, A Summary: U.S. Geol. Surv. Prof. Paper 492, p. 65. Goldsmith, L. H., 1980. Regional and Local Geologic Structure of the Momotombo Field, Nicaragua: Geoth. Res. Counc., Trans. Vol. 4, p. 125-128. Lopez, C. A. V., 1982. Thermal Structure and Hydrogeochemistry of the Momotombo Geothermal Field, Nicaragua, C, A.; M. S. thesis, Kent State Univ., Dept. of Geology, Kent, 174 pp. Lopez, C. A. V., Hoyt B. R. and Eckstein Yoram, 1980. Subsurface Temperature Distribution and Structure of the Geothermal Reservoir at Momotombo, Nicaragua; Geoth. Res. Counc., Trans. Vol. 4, p. 459~462. McBirney, A. R., 1964. Notas sobre los Centros Volcanicos Cuaternarios al Este de la Depresion Nicaraguense; Serv. Geol. Nac. de Nicaragua, Bol. 8, p. 91-96. Moore, J. L., Osbun, Erik and Storm, P. V., 1981. Geology and Temperature Distributionf of Momotombo Geothermal Field, Nicaragua; in Halbouty, M. T. (ed.), Energy Resources of the Pacific Region; Tulsa, AAPG Studies in Geology No. 12, p. 33-54. Moore, J. L., Osbun, Erik and Storm, P. V., 1982. Geology and Temperature Distribution of M omotombo Geothermal Field, Nicaragua; Geoth. Res. Counc. Special Report No. 12, p. 13(~ 151. Ziagos, J. P. and Blackwell, D. D., 1981. A Model for the Effect of Horizontal Flow in a Thin Aquifer on Temperature-Depth Profiles; Geoth. Res. Counc., Trans. Vol. 5, p. 221 223. Ziagos, J. P. and Blackwell, D. D., 1983. A Model for the Transient Temperature Effect of Horizontal Fluid Flow in Geothermal Systems; unpubl, manuscr. Contribution No. 265 Department of Geology Kent State University Kent, Ohio 44242, U.S.A.
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