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Simulation and resistivity modeling of a geothermal reservoir with waters of different salinity
Geothermics, Vol. 12, No. 4, pp. 291 -306, 1983. Printed in Great Britain.
0375- 6505/83 $3.00 + 0.00 Pergamon Press Ltd. © 1983 CNR.
SIMULATION A N D RESISTIVITY MODELING OF A GEOTHERMAL RESERVOIR WITH WATERS OF DIFFERENT SALINITY K. P R U E S S , M. W I L T , G. S. B O D V A R S S O N a n d N. E. G O L D S T E I N Lawrence Berkeley Laboratory, University of California, Berkeley, CA 94720, U.S.A. (Received November 1982, accepted for publication April 1983) Abstract--Apparent resistivities measured by means of repetitive dipole - dipole surveys show significant changes within the Cerro Prieto reservoir. The changes are attributed to production and natural recharge. To understand better the observed geophysical phenomena, we performed a simple reservoir simulation study combined with the appropriate DC resistivity calculations to determine the expected magnitude of apparent resistivity change. We consider production from a liquid dominated reservoir with dimensions and parameters of the Cerro Prieto 'A' reservoir and assume lateral and vertical recharge of colder and less saline waters. Based on rather schematic one- and two-dimensional reservoir simulations, we calculate changes in formation resistivity which we then transform into changes in apparent resistivity that would be observed at the surface. Simulated changes in apparent resistivities over the production zone show increases of 10 to 20% over a 3 year period at the current rate of fluid extraction. Changes of this magnitude are not only within our ability to discern using proper field techniques, but are consistent in magnitude with some of the observed effects. However, the patterns of apparent resistivity changes in the simulated dipole - dipole pseudosection only partially resemble the observed field data. This is explained by the fact that the actual fluid recharge into the 'A' reservoir is more complicated than assumed in our simple, schematic recharge models. DC resistivity monitoring appears capable of providing indirect information on fluid flow processes in a producing geothermal reservoir. Such information is extremely valuable for the development of quantitative predictions of future reservoir performance. INTRODUCTION S u r f a c e resistivity m e a s u r e m e n t s have o f t e n been successfully e m p l o y e d in g e o t h e r m a l e x p l o r a t i o n b e c a u s e g e o t h e r m a l reservoirs u s u a l l y have a n a s s o c i a t e d resistivity a n o m a l y which, w h e n i n t e r p r e t e d in c o n j u n c t i o n with t h e r m a l a n d g e o c h e m i c a l d a t a , p e r m i t s a p p r o x i m a t e i d e n t i f i c a t i o n o f field b o u n d a r i e s . Resistivity d a t a are o f t e n relied u p o n for initial resource e v a l u a t i o n a n d for t a r g e t i n g o f e x p l o r a t o r y wells. F o r several years resistivity s o u n d i n g a n d m o d e l i n g have b e e n c a r r i e d o u t at C e r r o P r i e t o b y the L a w r e n c e Berkeley L a b o r a t o r y (LBL) a n d the C o m i s i 6 n F e d e r a l de E l e c t r i c i d a d ( C F E ) . This w o r k has i d e n t i f i e d s u b s u r f a c e structures which c o r r e l a t e well with p r o d u c t i v e h o r i z o n s a n d g e o l o g i c a l m o d e l s o f C e r r o P r i e t o b a s e d on i n d e p e n d e n t d a t a . Repetitive resistivity m e a s u r e m e n t s m a d e since 1979 b y L B L have achieved a p r e c i s i o n a n d r e p r o d u c i b i l i t y which has m a d e it p o s s i b l e to clearly i d e n t i f y t e m p o r a l changes which can be a t t r i b u t e d to the large-scale e x p l o i t a t i o n o f the reservoir ( W i l t a n d G o l d s t e i n , 1981). It is o f interest to note that recent field tests in U t a h a n d K a n s a s have also shown significant changes in a p p a r e n t f o r m a t i o n resistivity as a c o n s e q u e n c e o f t e r t i a r y oil r e c o v e r y processes (Bartel a n d W a y l a n d , 1981). W i l t a n d G o l d s t e i n (1981) discuss p o s s i b l e m e c h a n i s m s which c o u l d cause the o b s e r v e d resistivity c h a n g e s at C e r r o P r i e t o . These include (i) r e c h a r g e o f fluids with d i f f e r e n t salinity, (ii) f o r m a t i o n o f t w o - p h a s e zones n e a r the wells a n d (iii) changes in reservoir t e m p e r a t u r e . T h e p r e s e n t p a p e r e x a m i n e s in m o r e detail the feasibility o f a p p l y i n g resistivity m e a s u r e m e n t s for m o n i t o r i n g reservoir processes caused b y e x p l o i t a t i o n . W e a p p l y n u m e r i c a l m o d e l i n g techniques to s t u d y m i g r a t i o n o f waters o f d i f f e r e n t t e m p e r a t u r e a n d salinity in r e s p o n s e to p r o d u c t i o n , a n d we use s i m u l a t e d changes o f t e m p e r a t u r e a n d salinity to p r e d i c t changes in a p p a r e n t resistivity at the surface. T h e analysis p r e s e n t e d here deals with the shallow, o r ' A ' 29!
292
K. Pruess, M. Wilt, G. S. Bodvarsson and N. E. Goldstein
reservoir, in which all wells drilled prior to 1979 in the Cerro Prieto I area were completed (Prian, 1981; Castafieda et al., 1982). Our studies employ rather schematic and simplified reservoir models in order to demonstrate how reservoir engineering and geophysical techniques can be combined for monitoring reservoir processes caused by exploitation. The conceptual model and reservoir parameters are similar to those employed in other recent schematic studies of the Cerro Prieto ' A ' reservoir (Grant and O'Sullivan, 1982, Castafieda et al., 1982). We believe that our simplified model is adequate and sufficient to permit a realistic assessment of the proposed methodology. H a l f m a n et al. (1982) have recently presented a detailed geological model of the Cerro Prieto field, which can serve as a starting point in future numerical modeling studies. A first effort in this direction was made by Lippmann and Bodvarsson (1983), who developed a twodimensional vertical model of the Cerro Prieto field which incorporates major geological features. The results obtained by Lippmann and Bodvarsson are encouraging, but it appears that a fully three-dimensional model is needed to adequately represent the complex flow patterns during exploitation.
S I M U L A T I O N OF A R E S E R V O I R W I T H T W O W A T E R S OF D I F F E R E N T S A L I N I T Y We consider production of liquid water f r o m a porous reservoir with an initial temperature of T = 300°C. Initial reservoir pressure is taken to b e p = 120 bars at 1000 m depth, which is approximately 20°70 larger than the estimated pre-exploitation pressure at this depth (Bermejo et al., 1979). The reason for adopting a somewhat larger pressure is that this suppresses possible boiling near production points, which facilitates the numerical analysis. No serious error is committed by this approximation, as it is known from field observations that boiling has remained confined to the immediate vicinity of wells (Grant et al., in press), The reservoir communicates with recharge waters of T = 100°C above a n d / o r at the margins. The mass fraction of recharge water is denoted by x; initially x -- 0 in the reservoir. The recharge waters are assumed to have different (lower) salinity than the water initially in place in the reservoir. For purposes of numerical modeling, however, we ignore all differences in thermophysical properties arising f r o m different salinity, such as differences in viscosity, density, boiling curve, etc. We write separate mass balances for 'water 1' (x = 0) and 'water 2' (x = 1) which makes it possible to keep track of the individual waters as they start flowing and mixing in response to production. A similar approach was presented by Geshelin et al. (1981) for tracing fluid migration during steam-assisted oil recovery. All reservoir models considered in this paper are assumed to be symmetric about a vertical n o r t h w e s t - southeast trending plane, so that calculations need to be made only for one-half of the systems. The reservoir simulations reported below were carried out with the LBL compositional simulator M U L K O M (Pruess, in press) which is similar to the geothermal reservoir simulator S H A F T 79 (Pruess and Schroeder, 1980) except that two water components are included. To demonstrate the mixing effects, we present results for two one-dimensional models. We consider a 1 m thick vertical slice of 700 m length and 400 m height, which roughly corresponds to a vertical section from the center of Cerro Prieto ' A ' (or upper) reservoir to the eastern margin of the present well field (see Fig. 1). The section shown in Fig. 1 is produced uniformly at a volumetric rate equal to the actual average rate over the last several years. Assuming reservoir parameters of thickness H = 400 m, radius R = 700 m for the presently exploited portion of Cerro Prieto field, the average production rate of 600 kg/s (-- 2160 tonnes/h; Goyal et al., 1981) corresponds to a volumetric rate of 9.74 × 10 -7 kg/s m 3. The total production rate from the 400 x 700 × 1 m 3 section is then 0.273 kg/s. Other model parameters were chosen to represent best estimates for Cerro Prieto reservoir (see Table 1).
Simulation and Resistivity Modeling o f a Geothermal Reservoir
293
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Table 1. Parameters for production simulation Rock density Porosity Horizontal permeability Vertical permeability Heat conductivity Rock specific heat Vertical extent of reservoir Volumetric rate of production Initial reservoir temperature Average initial reservoir pressure
2600 kg/m 3 15% 100 x 10-~ m s 10 × 10-~ m 2 2.1 W / m °C 900 J/kg °C 400 m 9.74 x 10-7 kg/s m 3 300°C 12 MPa (120 bars)
In case (a) we study lateral recharge. The top and b o t t o m boundaries are assumed ' n o flow' whereas conditions of T = 100°C, p = 120 bars, x = 1 are maintained at the right boundary. The left boundary corresponds to the center of the reservoir and is always ' n o flow' due to symmetry. Thus, the system starts out with a step change in temperature and water composition at the right boundary. For the numerical simulation the reservoir is subdivided into 20 volume elements of 35 m length each. Five sinks with a strength of 0.0546 kg/s each were placed into elements 1, 5, 9, 13 and 17 to approximate a uniform depletion (Fig. 1). In response to production, water with T = 100°C, x = 1 starts to invade the reservoir from the margins. The temperature and composition profiles after t = 3 years are shown in Fig. 2. The thermal front advances at approximately one fourth the speed of the compositional front, due to heat transfer f r o m the rocks to the cold recharge waters. For the conditions assumed in our modeling study, no two-phase zones f o r m in the reservoir. It should be stressed that the smearing of compositional and thermal fronts is entirely due to numerical dispersion, as our model does not include actual physical dispersion due to multiple flow paths and other mechanisms. To illustrate the numerical dispersion effects, a calculation with a four times finer grid, using 80 grid blocks for the 700 m length is also shown in Fig. 2. A much steeper, less dispersed profile is then obtained for the fronts.
K. Pruess, M. Wilt, G. S. Bodvarsson and N. E. Goldstem
294
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Case (c) is the most realistic of the models considered here. The model is two-dimensiona and includes both vertical and lateral recharge and gradational changes in temperature an salinity, as suggested by the work o f Truesdell et al. (1979) and Grant et aL (in press). Th vertical recharge zone begins 600 m below ground surface and extends to the reservoir top 800 m depth (see Fig. 3). The reservoir height is again H = 400 m, but the lateral dimension slightly increased to 1600 m, as compared to 1400 m in the one-dimensional models. Laterall}
Simulation and Resistivity M o d e l i n g o f a G e o t h e r m a l Reservoir
295
the reservoir is connected to a recharge zone of 1000 m length with boundary conditions of T = 100°C, x -- 1 on the outer boundary. The initial variations in temperature and fluid composition between reservoir and vertical and lateral recharge boundaries are assumed to be smooth. Temperature and salinity are assumed to correlate linearly in the pre-exploitation state, based on field data which suggest mixing between hot saline brine and Colorado river waters (Truesdell et al., 1979). The following parameterization was used: (i) composition: 0 in reservoir, xn =
f(l) between reservoir i and recharge boundary,
] 1 at recharge boundary, (ii) temperature 300°C in reservoir, × (300 - 100)°C between reservoic and recharge boundary,
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L is the vertical or lateral distance between reservoir and recharge boundaries (Lver,ca~ = 200 m; L~te~ j = 1000 m). The computational mesh employs 100 m horizontal and 50 m vertical spacing, for a total of (18 × 8) + (8 × 4) = 176 elements, plus elements for representing the boundaries. The grid spacing is rather coarse, so that numerical dispersion will he somewhat stronger than in the onedimensional models. The actual broadening of chemical and thermal fronts will be much weaker, however, because here we employ smooth initial conditions, rather than sharp spatial variations. The natural state of the Cerro Prieto reservoir is non-static, due to the hydraulic connection between waters of different temperatures and densities. The natural flows are believed to be considerably smaller than those induced by large-scale exploitation. Lippmann and Bodvarsson (1983) estimate that production induced flows exceed natural flows by a factor of approximately 10. Our model is too simplistic to properly account for the natural flows. Instead, the simulation is initialized with approximate gravitational equilibrium relative to a reference pressure of p = 120 bars at 1000 m depth. The same volumetric production rate as was used in the one-dimensional models is employed. Production is divided among four sources, placed in elements D1, E3, D5 and E7 (see Fig. 3).
K. Pruess, M. Wilt, G. S. Bodvarsson and N. E. Goldstein
296
Horizontal permeability is taken to be 100 × 10 -'~ m-', corresponding to a k H = 40 ~ 10 ..... m 3. This agrees closely with the 'field value' 36 x 10 -~2 m 3, which can be derived from an average transmissivity k H / p = 0.4 × 10-' m3/Pa s (Liguori, 1979) and ~t (300°C) = 9.01 × 10 -~ Pa s, Vertical permeability was assumed one-tenth of horizontal permeability. For these permeabilities, the reservoir can easily sustain the applied production rate. The largest observed pressure decline after 5 years is approximately 1 MPa, so that pressures remain well above saturation pressure and no two-phase zones evolve. Simulation results predict that production induced flows are typically one to two orders of magnitude larger than the flows occurring in the pre-exploitation state from the thermal imbalance between reservoir and recharge waters. This is consistent with the results of Lippmann and Bodvarsson (1983) and it shows that accurate representation of natural flows is not essential for a producing-state model. Temperature profiles for layers C, E and G after 3 years of simulation are presented in Fig. 4. The initial temperature distribution (t = 0) is also plotted for comparison. The figure shows a significant migration (vertical and lateral) of colder waters into the production zone ( 0 - 800 m away f r o m the symmetry line) due to the massive exploitation. The migration of the colder recharge waters from above is evident from the lower temperatures in the G layer in comparison with the temperature profile in the C layer in the production region. Lateral migration of the recharge waters is also evident in Fig. 4 when the temperature profiles for layers C and G are compared to the initial temperature distribution (t = 0). The temperatures in layer G are everywhere higher than the temperatures in layers C and E in the outside region ( > 800 m away from the symmetry line) because of buoyancy effects. I
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The composition profiles for layers C, E and G after 3 years of simulation are shown in Fig. 5. Again the initial composition profile (t = 0) is included for reference. The effects of vertical and lateral recharge, as well as buoyancy effects, are clearly evident. The interior of the production region (left portion of Fig. 5) is dominated by vertical recharge, which is strongest for the topmost layer. Accordingly, the mass fraction of recharge water is greatest in layer G, and smallest in layer C near the b o t t o m of the reservoir. A different picture is observed at the reservoir margins at a distance of 800 m f r o m the symmetry line. There, lateral recharge is dominant, which, due to buoyancy effects tends to be stronger in the lower portions of the
Simulation and Resistivity Modeling o f a Geothermal Reservoir
297
reservoir, so that x (layer C) > x (layer E) > x (layer G). The buoyancy effects cause x (layer G) to decrease more rapidly away from the lateral recharge boundary (at 1800 m distance from the symmetry line) than is observed for layer E or C. The decrease in x (layer G) is reversed inside the reservoir due to vertical recharge, giving rise to a minimum in x (layer G) near the reservoir margin (800 m). A complex interplay of vertical and lateral recharge is also observed for layer E. i
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RESISTIVITY M O D E L I N G OF A RESERVOIR W I T H W A T E R MIXING A two-dimensional finite difference computer code was used in numerical calculations for resistivity models in this study. The code RESIS2D solves finite difference equations for the electric potentials in, or on, the surface of a two-dimensional half-space with an arbitrary conductivity distribution (Dey and Morrison, 1976; Dey, 1976). Computer simulation may be done for a wide variety of surface and downhole resistivity arrays. The accuracy of the code has been verified by comparing results to analytical solutions and analog models. The code utilizes a mesh of 113 × 16 nodes of which 58 x 13 can be used for abitrary resistivity distributions. This limited size mesh has posed problems for this study because it is unable to provide fine resolution in the region where the resistivity changes are large. Because of the limited mesh size, only 32 elements can be used to describe resistivity within the production zone, and thus resistivity variations due to temperature and salinity changes were averaged over fairly large cross-sectional areas. C A L C U L A T I O N OF RESISTIVITY VARIATIONS A study of the variations in resistivity due to changes in fluid properties in geothermal systems has recently been published (Ershagi et al., 1981). In the present paper we use those results to calculate resistivity as a function of salinity and temperature. Figure 6 indicates the effect of salinity and temperature on resistivity for 'typical' sediments in a geothermal environment. For our study we assume that recharge waters have 0.3°70 dissolved solids by weight and are at a temperature of 100°C. In the production zone the parameters are 1.5 070 and 300°C, respectively. These values are based on observed water chemistry at Cerro Prieto (Truesdell et al., 1979; Grant et al., in press). Figure 6 shows that resistivity variations due to salinity and temperature changes can be quite large. In the recharge
tk. Pruess, M. Hqlt, G. S. Bodvarsson and N. A. Goldgtem
298
zone, initial resistivity is 50% larger than in the production zone, due to and more than 300% larger due to salinity differences. 0,O6 [
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The initial subsurface resistivity distribution assumed in this study is shown in Fig. 7. The 5 o h m - m surface corresponds to a caprock. The 15.6 o h m - m background is sedimentary rock with 15070 porosity and saturated with 100°C water at 0.3 wt% NaCI. The 15.6 o h m - m resistivity value for the background was calculated from Archie's Law. The geothermal reservoir is represented by a 1600 x 400 m zone buried at a depth of 800 m. Within the reservoir region the resistivity is initially 2.15 ohm-m. This number was derived by adjusting the background o f 15.6 o h m - m for increased salinity and temperature in the reservoir region.
RESULTS OF S A M P L E C A L C U L A T I O N S Resistivity calculations for the three reservoir models presented above were done for the d i p o l e - d i p o l e resistivity array over the producing zone. The calculations assume a station spacing o f 800 m and 'n-spacings' of 1 to 8, i.e. the distance between transmitter and receiver is one to eight times the 800 m station spacing. This corresponds to a maximum s o u r c e - receiver separation of 7200 m. For the three cases studied (see above) we calculate resistivity pseudosections for d i p o l e - d i p o l e surveys before exploitation and then at times of 0.5, 1, 3 and
Simulation and Resistivity Modefing o f a Geothermal Reservoir
299
5 years after production began. The resistivity distribution is adjusted to account for subsurface temperature and salinity changes due to production. Apparent resistivity differences between the pre-production and subsequent 'surveys' are then calculated on a point-by-point basis and presented in pseudosection form. Case a - - lateral recharge
In Fig. 8, per cent difference pseudosection plots for 1, 3 and 5 years after production begins are given for the lateral recharge case. The plots show a recognizable pattern of change at 1 year
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K. Pruess, M. Wilt, G. S. Bodvarsson attd ,N. E. Goldstem
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which grows increasingly stronger with time. The patterns are similar at all times. The plots show a narrow arcuate band where the effect is largest, below which is a 'shadow zone' where little effect is observed. The band of m a x i m u m change is strongly influenced by current paths that travel through the reservoir region, whereas the 'shadow zone' represents paths that are only weakly influenced by the reservoir. For all plots, significant apparent resistivity differences are observed at n = 2 to n = 8 for points directly above the reservoir region. After 3 years even the central nodes in the production region are affected by the intrusion of colder and less saline water and resistivity in this region increases sharply. The per cent difference pseudosection plot reflects this change by showing a more pronounced apparent resistivity increase in the center of the arc and a reduction of the shadow zone beneath the arc. Assuming an average survey error of 1 - 2%, which is typical for the Cerro Prieto monitoring studies (Wilt and Goldstein, in press) it should be possible to detect changes after one year and to quantitatively model data after 2 or 3 years. Case b - - vertical recharge
For this case cold water recharge is constrained to flow vertically downward into the reservoir. Figure 9 shows per cent difference pseudosections for 1, 3 and 5 years after production begins. The difference pattern is quite similar to the lateral case, an arcuate or chevron pattern with a shadow zone beneath, but in this case the arc is narrower and thicker at the top. Resistivity changes for 1 year are larger than for the lateral case and appear shallower with some signficiant change even at n = 1. After 1 year the effect is greater than 70% for a number of points, which is well above the measurement error levels. After 5 years the pattern appears similar to the lateral case for the same period. Case c - - vertical a n d lateral recharge
This case assumes both vertical and lateral recharge, with gradational initial variations in temperature and salinity outside the production zone. In Fig. 10, per cent difference
Simulation and Resistivity Modefing of a Geothermal Reservoir
301
pseudosections are shown for 0.5, 1, 3 and 5 years after the onset of production. There is very little change after 6 months and after 1 year only moderate change is observed. The intermediate zone seems to act as a buffer, slowing the rate of apparent resistivity change compared to the previous cases with step changes in temperature and salinity. After 3 years much of the less saline water reaches the production region, resulting in rather large resistivity changes. The patterns also seem broader than either the lateral or vertical case with significantly
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larger magnitudes. After 5 years the maximum resistivity change approaches 25°70 and a change of more than 10070 occurs for the n -- 1 points overlying the reservoir. It appears that, due to the smooth spatial variations in temperature and salinity, early-time resistivity changes are smaller and late-time changes larger than predicted from the one-dimensional step change models (a) and (b). DISCUSSION Case (c), the most realistic of the cases studied, has significant implications for resistivity monitoring studies. Despite the large rate of production the apparent resistivity changes are small after 1 year of production and during such early times reservoir related changes could be totally obscured by seasonal variations in rainfall, runoff or irrigation (Wilt and Goldstein, in press). However, given sufficient production time, the recharge waters will affect the reservoir region so that the pattern of resistivity change may help determine the parameters of fluid circulation. It is interesting to compare our calculated resistivity results to the actual monitoring measurements in Cerro Prieto (Wilt and Goldstein, in press). Figure 11 shows the per cent changes in apparent resistivity along a line over the production region (line E - E ' ) at times of 1, 1.5 and 2.5 years after the 1979 baseline measurements. Additional details concerning the monitoring work are given in Wilt and Goldstein (in press). The field data show a far more complex pattern of change than the relatively simple models used in the present study, but there are some striking similarities in pattern and magnitude of resistivity change, particularly in the production zone which is located between 9 and 13 km. This area has shown a continuous and steady resistivity increase very similar in character to the arc-like patterns of generic model (c) but with only half of the arc present. The other half is replaced with a zone of decreasing resistivity. The pattern seems to suggest that resistivity in the western part of the reservoir may be changing in accordance with our model, but in the eastern portion of the reservoir more complex processes are taking place. According to a fluid flow model, based on a lithofacies analysis and temperature profiles (Halfman et al., 1982) recharge to the 'A' reservoir is in part
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Fig. 11. Resistivity pseudosections as measured in Cerro Prieto (per cent changes from 1979 baseline). hot water ascending from below and from the east along permeable paths provided by a combination of faults and sandstone units. This circulation system might explain the differences between the actual resistivity changes and those simulated. The obvious next step is to attempt verification of the proposed fluid flow model by means of a more rigorous simulation study. CONCLUSIONS A methodolgy has been presented for indirect study of a geothermal reservoir which combines numerical reservoir simulation with modeling of apparent resistivities as measured with the d i p o l e - d i p o l e technique. For the Cerro Prieto reservoir, temporal changes in apparent resistivity due to production and recharge of colder and less saline waters are both calculated and are observed to be substantial over time intervals of several years. It therefore appears feasible to use resistivity surveys as a means for monitoring reservoir processes. While our schematic models predict resistivity changes which are roughly consistent with field observations, more detailed reservoir models are required to adequately represent the field data.
306
K. Pruess, M.
Wilt, G. S. B o d v a r s s o n a n d N. E. G o l d s t e r n
F o r m o s t g e o t h e r m a l r e s e r v o i r s , the p a t t e r n s o f f l u i d f l o w a n d r e s i s t i v i t y c h a n g e will be t htecd i m e n s i o n a l . T h e r e f o r e , a c c u r a t e r e s i s t i v i t y m o n i t o r i n g r e q u i r e s m e a s u r e n t e n t s a l o n g :,cvetal intersecting profiles. The proposed
methodology
s h o u l d also be a p p l i c a b l e for m o n i t o r i n g
the migration of
reinjected fluids. Acknowledgements--We thank Drs M. Lippmann and C. F'. Tsang for a critical review of the manuscript. This work was supported by the Assistant Secretary for Conservation and Renewable Energy, Office of Renewable Technology, Division of Geothermal and Hydropower Technologies of the U.S. Department of Energy under Contract No. DE-AC03-76SF00098. REFERENCES Bartel, L. C. and Wayland, J. R. (1981) Results from using the CSAMT geophysical technique to map oil recovery processes. Paper SPE 10230, presented at the 56th Annual Fall Technical Conference and Exhibition of the SPE, San Antonio, Texas, 5 - 7 October, 1981. Bermejo M., F. J., Navarro O., F. X,, Castillo B., F., Esquer P., C. A. and Cortez A., C. (1979) Variation de presion en el yacimiento de Cerro Prieto durante su explotacion. Proceedings Second Symposium on the Cerro Prielo Geothermal Field, Mexicali, Mexico, October 1979, pp. 473- 493. Castafieda, M., Abril, A., Arellano, V. and Marques, R. (1982) Reservoir simulation studies on the Cerro Prieto geothermal field: preliminary results. Paper presented at Eighth Workshop on Geothermal Reservoir Engineering, Stanford University, Stanford, California. Dey, A. (1976) Resistivity modelling for arbitrarily shaped two-dimensional structures part 11. Guide to the FORTRAN algorithm RESIS2D. Lawrence Berkeley Laboratory Report LBL-5283, Berkeley, California. Dey, A. and Morrison, H. F. (1976) Resistivity modelling for arbitrarily shaped two-dimensional structures part 1. Theoretical formulation. Lawrence Berkeley Laboratory Report LBL-5233, Berkeley, California. Ershagi, I., Dougherty, E. E. and Hardy L. (1981) Formation evaluation in liquid dominated geothermal reservoirs. Report for Department of Energy No. DOE/ET/28384-TI, U.S.A. Geshelin, B. M., Grabowski, J, W. and Pease, E. C. (1981) Numerical study of transport of injected and reservoir water in fractured reservoirs during steam stimulation. Paper SPE 10322, presented at 56th Annual Fall Technical Conference and Exhibition of the SPE, San Antonio, Texas, 5 - 7 October, 1981. Goyal, K. P., Miller, C. W., Lippmann, M. J. and Vonder Haar, S. P. (1981) Analysis of Cerro Prieto production data. Proceedings Third Symposium on the Cerro Prieto Geothermal FieM, San Francisco, California. pp. 496 - 500. Grant, M. A., Truesdell, A. H. and A. Ma66n M. Production induced boiling and cold water entry in the Cerro Prieto geothermal reservoir indicated by chemical and physical measurements. Presented at Third Symposium on the Cerro Prieto Geothermal Field, San Francisco, March 1981. Geothermics, in press. Grant, M. A. and O'Sullivan, M. J. 0982) The Old Field at Cerro Prieto considered as a leaky aquifer. Proceedings Fourth Symposium on the Cerro Prieto Geothermal Field, Guadalajara, Mexico, August 1982. Halfman, S. E., Lippmann, M. J., Zelwer, R. and Howard, J. H. (1982) Fluid flow model of the Cerro Prieto geothermal field based on well log interpretation, t.awrence Berkeley Laboratory, LBL-14898 and Proceedings, Fourth Symposium on the Cerro Prieto Geothermal Field, Guadalajara, Mexico, August 1982. Liguori, P. E. (1979) Simulation of the Cerro Prieto geothermal field using a mathematical model. Proceedings Second Symposium on the Cerro Prieto Geothermal Field, Mexicali, Mexico, October 1979, pp. 521 - 524. Lippmann, M. J. and Bodvarsson, G. S. (1983) Modeling studies on Cerro Prieto. Paper presented at Fourth Symposium on the Cerro Prieto Geothermal Field, Guadalajara, Mexico. Water Resour. Res. 19, 753 - 767. Prian C., R. (1981) Velocidad de perforacion de la secuencia estratigrafica del area de Cerro Prieto. Proceedings Third Symposium on the Cerro Prieto Geothermal Field, San Francisco, California, March 1981, pp. 77 o 84. Pruess, K. Development of the general purpose simulator MULKOM. Annual Report 1982, Earth Sciences Division, Lawrence Berkeley Laboratory, Berkeley, California, in press. Pruess, K. and Schroeder, R. C. (19801 SHAFT79 user's manual. Lawrence Berkeley Laboratory Report LBk-10861, Berkeley, California, March 1980. Truesdell, A. H., Thompson, J. M., Coplen, T. B., Nehring, N. L. and Janik, C. J. (1979) The origin of the Cerro Prieto geothermal brine. Presented at Second Symposium on the Cerro Primo Geothermal Field, Mexicali, Mexico, October 1979. Geothermies 10, (3/4), 225- 238. Wilt, M. J. and Goldstein, N. E. (1981) Results from two years of resistivity monitoring at Cerro Prieto. Proceedings Third Symposium on the Cerro Prieto Geothermal Field, San Francisco, March 19gl, Lawrence Berkeley Laboratory Report LBL-11967, Berkeley, California, pp. 372-379. Wilt, M. J. and Goldstein, N. E. Interpretation of dipole - dipole resistivity monitoring data at Cerro Primo. Presented at Fourth Symposium on the Cerro Prieto Geothermal Field, Guadalajara, Mexico, August 1982. Geothermics. in press.
0375- 6505/83 $3.00 + 0.00 Pergamon Press Ltd. © 1983 CNR.
SIMULATION A N D RESISTIVITY MODELING OF A GEOTHERMAL RESERVOIR WITH WATERS OF DIFFERENT SALINITY K. P R U E S S , M. W I L T , G. S. B O D V A R S S O N a n d N. E. G O L D S T E I N Lawrence Berkeley Laboratory, University of California, Berkeley, CA 94720, U.S.A. (Received November 1982, accepted for publication April 1983) Abstract--Apparent resistivities measured by means of repetitive dipole - dipole surveys show significant changes within the Cerro Prieto reservoir. The changes are attributed to production and natural recharge. To understand better the observed geophysical phenomena, we performed a simple reservoir simulation study combined with the appropriate DC resistivity calculations to determine the expected magnitude of apparent resistivity change. We consider production from a liquid dominated reservoir with dimensions and parameters of the Cerro Prieto 'A' reservoir and assume lateral and vertical recharge of colder and less saline waters. Based on rather schematic one- and two-dimensional reservoir simulations, we calculate changes in formation resistivity which we then transform into changes in apparent resistivity that would be observed at the surface. Simulated changes in apparent resistivities over the production zone show increases of 10 to 20% over a 3 year period at the current rate of fluid extraction. Changes of this magnitude are not only within our ability to discern using proper field techniques, but are consistent in magnitude with some of the observed effects. However, the patterns of apparent resistivity changes in the simulated dipole - dipole pseudosection only partially resemble the observed field data. This is explained by the fact that the actual fluid recharge into the 'A' reservoir is more complicated than assumed in our simple, schematic recharge models. DC resistivity monitoring appears capable of providing indirect information on fluid flow processes in a producing geothermal reservoir. Such information is extremely valuable for the development of quantitative predictions of future reservoir performance. INTRODUCTION S u r f a c e resistivity m e a s u r e m e n t s have o f t e n been successfully e m p l o y e d in g e o t h e r m a l e x p l o r a t i o n b e c a u s e g e o t h e r m a l reservoirs u s u a l l y have a n a s s o c i a t e d resistivity a n o m a l y which, w h e n i n t e r p r e t e d in c o n j u n c t i o n with t h e r m a l a n d g e o c h e m i c a l d a t a , p e r m i t s a p p r o x i m a t e i d e n t i f i c a t i o n o f field b o u n d a r i e s . Resistivity d a t a are o f t e n relied u p o n for initial resource e v a l u a t i o n a n d for t a r g e t i n g o f e x p l o r a t o r y wells. F o r several years resistivity s o u n d i n g a n d m o d e l i n g have b e e n c a r r i e d o u t at C e r r o P r i e t o b y the L a w r e n c e Berkeley L a b o r a t o r y (LBL) a n d the C o m i s i 6 n F e d e r a l de E l e c t r i c i d a d ( C F E ) . This w o r k has i d e n t i f i e d s u b s u r f a c e structures which c o r r e l a t e well with p r o d u c t i v e h o r i z o n s a n d g e o l o g i c a l m o d e l s o f C e r r o P r i e t o b a s e d on i n d e p e n d e n t d a t a . Repetitive resistivity m e a s u r e m e n t s m a d e since 1979 b y L B L have achieved a p r e c i s i o n a n d r e p r o d u c i b i l i t y which has m a d e it p o s s i b l e to clearly i d e n t i f y t e m p o r a l changes which can be a t t r i b u t e d to the large-scale e x p l o i t a t i o n o f the reservoir ( W i l t a n d G o l d s t e i n , 1981). It is o f interest to note that recent field tests in U t a h a n d K a n s a s have also shown significant changes in a p p a r e n t f o r m a t i o n resistivity as a c o n s e q u e n c e o f t e r t i a r y oil r e c o v e r y processes (Bartel a n d W a y l a n d , 1981). W i l t a n d G o l d s t e i n (1981) discuss p o s s i b l e m e c h a n i s m s which c o u l d cause the o b s e r v e d resistivity c h a n g e s at C e r r o P r i e t o . These include (i) r e c h a r g e o f fluids with d i f f e r e n t salinity, (ii) f o r m a t i o n o f t w o - p h a s e zones n e a r the wells a n d (iii) changes in reservoir t e m p e r a t u r e . T h e p r e s e n t p a p e r e x a m i n e s in m o r e detail the feasibility o f a p p l y i n g resistivity m e a s u r e m e n t s for m o n i t o r i n g reservoir processes caused b y e x p l o i t a t i o n . W e a p p l y n u m e r i c a l m o d e l i n g techniques to s t u d y m i g r a t i o n o f waters o f d i f f e r e n t t e m p e r a t u r e a n d salinity in r e s p o n s e to p r o d u c t i o n , a n d we use s i m u l a t e d changes o f t e m p e r a t u r e a n d salinity to p r e d i c t changes in a p p a r e n t resistivity at the surface. T h e analysis p r e s e n t e d here deals with the shallow, o r ' A ' 29!
292
K. Pruess, M. Wilt, G. S. Bodvarsson and N. E. Goldstein
reservoir, in which all wells drilled prior to 1979 in the Cerro Prieto I area were completed (Prian, 1981; Castafieda et al., 1982). Our studies employ rather schematic and simplified reservoir models in order to demonstrate how reservoir engineering and geophysical techniques can be combined for monitoring reservoir processes caused by exploitation. The conceptual model and reservoir parameters are similar to those employed in other recent schematic studies of the Cerro Prieto ' A ' reservoir (Grant and O'Sullivan, 1982, Castafieda et al., 1982). We believe that our simplified model is adequate and sufficient to permit a realistic assessment of the proposed methodology. H a l f m a n et al. (1982) have recently presented a detailed geological model of the Cerro Prieto field, which can serve as a starting point in future numerical modeling studies. A first effort in this direction was made by Lippmann and Bodvarsson (1983), who developed a twodimensional vertical model of the Cerro Prieto field which incorporates major geological features. The results obtained by Lippmann and Bodvarsson are encouraging, but it appears that a fully three-dimensional model is needed to adequately represent the complex flow patterns during exploitation.
S I M U L A T I O N OF A R E S E R V O I R W I T H T W O W A T E R S OF D I F F E R E N T S A L I N I T Y We consider production of liquid water f r o m a porous reservoir with an initial temperature of T = 300°C. Initial reservoir pressure is taken to b e p = 120 bars at 1000 m depth, which is approximately 20°70 larger than the estimated pre-exploitation pressure at this depth (Bermejo et al., 1979). The reason for adopting a somewhat larger pressure is that this suppresses possible boiling near production points, which facilitates the numerical analysis. No serious error is committed by this approximation, as it is known from field observations that boiling has remained confined to the immediate vicinity of wells (Grant et al., in press), The reservoir communicates with recharge waters of T = 100°C above a n d / o r at the margins. The mass fraction of recharge water is denoted by x; initially x -- 0 in the reservoir. The recharge waters are assumed to have different (lower) salinity than the water initially in place in the reservoir. For purposes of numerical modeling, however, we ignore all differences in thermophysical properties arising f r o m different salinity, such as differences in viscosity, density, boiling curve, etc. We write separate mass balances for 'water 1' (x = 0) and 'water 2' (x = 1) which makes it possible to keep track of the individual waters as they start flowing and mixing in response to production. A similar approach was presented by Geshelin et al. (1981) for tracing fluid migration during steam-assisted oil recovery. All reservoir models considered in this paper are assumed to be symmetric about a vertical n o r t h w e s t - southeast trending plane, so that calculations need to be made only for one-half of the systems. The reservoir simulations reported below were carried out with the LBL compositional simulator M U L K O M (Pruess, in press) which is similar to the geothermal reservoir simulator S H A F T 79 (Pruess and Schroeder, 1980) except that two water components are included. To demonstrate the mixing effects, we present results for two one-dimensional models. We consider a 1 m thick vertical slice of 700 m length and 400 m height, which roughly corresponds to a vertical section from the center of Cerro Prieto ' A ' (or upper) reservoir to the eastern margin of the present well field (see Fig. 1). The section shown in Fig. 1 is produced uniformly at a volumetric rate equal to the actual average rate over the last several years. Assuming reservoir parameters of thickness H = 400 m, radius R = 700 m for the presently exploited portion of Cerro Prieto field, the average production rate of 600 kg/s (-- 2160 tonnes/h; Goyal et al., 1981) corresponds to a volumetric rate of 9.74 × 10 -7 kg/s m 3. The total production rate from the 400 x 700 × 1 m 3 section is then 0.273 kg/s. Other model parameters were chosen to represent best estimates for Cerro Prieto reservoir (see Table 1).
Simulation and Resistivity Modeling o f a Geothermal Reservoir
293
(a) Lateral Recharge i,/
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T = 500°C x=O
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(b) Vertical Recharge Recharge boundary T= IO0°C x=l~
j
T =3000C x=O Production zone
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Table 1. Parameters for production simulation Rock density Porosity Horizontal permeability Vertical permeability Heat conductivity Rock specific heat Vertical extent of reservoir Volumetric rate of production Initial reservoir temperature Average initial reservoir pressure
2600 kg/m 3 15% 100 x 10-~ m s 10 × 10-~ m 2 2.1 W / m °C 900 J/kg °C 400 m 9.74 x 10-7 kg/s m 3 300°C 12 MPa (120 bars)
In case (a) we study lateral recharge. The top and b o t t o m boundaries are assumed ' n o flow' whereas conditions of T = 100°C, p = 120 bars, x = 1 are maintained at the right boundary. The left boundary corresponds to the center of the reservoir and is always ' n o flow' due to symmetry. Thus, the system starts out with a step change in temperature and water composition at the right boundary. For the numerical simulation the reservoir is subdivided into 20 volume elements of 35 m length each. Five sinks with a strength of 0.0546 kg/s each were placed into elements 1, 5, 9, 13 and 17 to approximate a uniform depletion (Fig. 1). In response to production, water with T = 100°C, x = 1 starts to invade the reservoir from the margins. The temperature and composition profiles after t = 3 years are shown in Fig. 2. The thermal front advances at approximately one fourth the speed of the compositional front, due to heat transfer f r o m the rocks to the cold recharge waters. For the conditions assumed in our modeling study, no two-phase zones f o r m in the reservoir. It should be stressed that the smearing of compositional and thermal fronts is entirely due to numerical dispersion, as our model does not include actual physical dispersion due to multiple flow paths and other mechanisms. To illustrate the numerical dispersion effects, a calculation with a four times finer grid, using 80 grid blocks for the 700 m length is also shown in Fig. 2. A much steeper, less dispersed profile is then obtained for the fronts.
K. Pruess, M. Wilt, G. S. Bodvarsson and N. E. Goldstem
294
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Simulation and Resistivity M o d e l i n g o f a G e o t h e r m a l Reservoir
295
the reservoir is connected to a recharge zone of 1000 m length with boundary conditions of T = 100°C, x -- 1 on the outer boundary. The initial variations in temperature and fluid composition between reservoir and vertical and lateral recharge boundaries are assumed to be smooth. Temperature and salinity are assumed to correlate linearly in the pre-exploitation state, based on field data which suggest mixing between hot saline brine and Colorado river waters (Truesdell et al., 1979). The following parameterization was used: (i) composition: 0 in reservoir, xn =
f(l) between reservoir i and recharge boundary,
] 1 at recharge boundary, (ii) temperature 300°C in reservoir, × (300 - 100)°C between reservoic and recharge boundary,
300 - f ( l )
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f(l) =
2 -× l2 f o r l < ~ L / 2 L2 2 1 - --(l1_,)2 f o r l >>. L / 2 L~
L is the vertical or lateral distance between reservoir and recharge boundaries (Lver,ca~ = 200 m; L~te~ j = 1000 m). The computational mesh employs 100 m horizontal and 50 m vertical spacing, for a total of (18 × 8) + (8 × 4) = 176 elements, plus elements for representing the boundaries. The grid spacing is rather coarse, so that numerical dispersion will he somewhat stronger than in the onedimensional models. The actual broadening of chemical and thermal fronts will be much weaker, however, because here we employ smooth initial conditions, rather than sharp spatial variations. The natural state of the Cerro Prieto reservoir is non-static, due to the hydraulic connection between waters of different temperatures and densities. The natural flows are believed to be considerably smaller than those induced by large-scale exploitation. Lippmann and Bodvarsson (1983) estimate that production induced flows exceed natural flows by a factor of approximately 10. Our model is too simplistic to properly account for the natural flows. Instead, the simulation is initialized with approximate gravitational equilibrium relative to a reference pressure of p = 120 bars at 1000 m depth. The same volumetric production rate as was used in the one-dimensional models is employed. Production is divided among four sources, placed in elements D1, E3, D5 and E7 (see Fig. 3).
K. Pruess, M. Wilt, G. S. Bodvarsson and N. E. Goldstein
296
Horizontal permeability is taken to be 100 × 10 -'~ m-', corresponding to a k H = 40 ~ 10 ..... m 3. This agrees closely with the 'field value' 36 x 10 -~2 m 3, which can be derived from an average transmissivity k H / p = 0.4 × 10-' m3/Pa s (Liguori, 1979) and ~t (300°C) = 9.01 × 10 -~ Pa s, Vertical permeability was assumed one-tenth of horizontal permeability. For these permeabilities, the reservoir can easily sustain the applied production rate. The largest observed pressure decline after 5 years is approximately 1 MPa, so that pressures remain well above saturation pressure and no two-phase zones evolve. Simulation results predict that production induced flows are typically one to two orders of magnitude larger than the flows occurring in the pre-exploitation state from the thermal imbalance between reservoir and recharge waters. This is consistent with the results of Lippmann and Bodvarsson (1983) and it shows that accurate representation of natural flows is not essential for a producing-state model. Temperature profiles for layers C, E and G after 3 years of simulation are presented in Fig. 4. The initial temperature distribution (t = 0) is also plotted for comparison. The figure shows a significant migration (vertical and lateral) of colder waters into the production zone ( 0 - 800 m away f r o m the symmetry line) due to the massive exploitation. The migration of the colder recharge waters from above is evident from the lower temperatures in the G layer in comparison with the temperature profile in the C layer in the production region. Lateral migration of the recharge waters is also evident in Fig. 4 when the temperature profiles for layers C and G are compared to the initial temperature distribution (t = 0). The temperatures in layer G are everywhere higher than the temperatures in layers C and E in the outside region ( > 800 m away from the symmetry line) because of buoyancy effects. I
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The composition profiles for layers C, E and G after 3 years of simulation are shown in Fig. 5. Again the initial composition profile (t = 0) is included for reference. The effects of vertical and lateral recharge, as well as buoyancy effects, are clearly evident. The interior of the production region (left portion of Fig. 5) is dominated by vertical recharge, which is strongest for the topmost layer. Accordingly, the mass fraction of recharge water is greatest in layer G, and smallest in layer C near the b o t t o m of the reservoir. A different picture is observed at the reservoir margins at a distance of 800 m f r o m the symmetry line. There, lateral recharge is dominant, which, due to buoyancy effects tends to be stronger in the lower portions of the
Simulation and Resistivity Modeling o f a Geothermal Reservoir
297
reservoir, so that x (layer C) > x (layer E) > x (layer G). The buoyancy effects cause x (layer G) to decrease more rapidly away from the lateral recharge boundary (at 1800 m distance from the symmetry line) than is observed for layer E or C. The decrease in x (layer G) is reversed inside the reservoir due to vertical recharge, giving rise to a minimum in x (layer G) near the reservoir margin (800 m). A complex interplay of vertical and lateral recharge is also observed for layer E. i
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,000'
,200'
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RESISTIVITY M O D E L I N G OF A RESERVOIR W I T H W A T E R MIXING A two-dimensional finite difference computer code was used in numerical calculations for resistivity models in this study. The code RESIS2D solves finite difference equations for the electric potentials in, or on, the surface of a two-dimensional half-space with an arbitrary conductivity distribution (Dey and Morrison, 1976; Dey, 1976). Computer simulation may be done for a wide variety of surface and downhole resistivity arrays. The accuracy of the code has been verified by comparing results to analytical solutions and analog models. The code utilizes a mesh of 113 × 16 nodes of which 58 x 13 can be used for abitrary resistivity distributions. This limited size mesh has posed problems for this study because it is unable to provide fine resolution in the region where the resistivity changes are large. Because of the limited mesh size, only 32 elements can be used to describe resistivity within the production zone, and thus resistivity variations due to temperature and salinity changes were averaged over fairly large cross-sectional areas. C A L C U L A T I O N OF RESISTIVITY VARIATIONS A study of the variations in resistivity due to changes in fluid properties in geothermal systems has recently been published (Ershagi et al., 1981). In the present paper we use those results to calculate resistivity as a function of salinity and temperature. Figure 6 indicates the effect of salinity and temperature on resistivity for 'typical' sediments in a geothermal environment. For our study we assume that recharge waters have 0.3°70 dissolved solids by weight and are at a temperature of 100°C. In the production zone the parameters are 1.5 070 and 300°C, respectively. These values are based on observed water chemistry at Cerro Prieto (Truesdell et al., 1979; Grant et al., in press). Figure 6 shows that resistivity variations due to salinity and temperature changes can be quite large. In the recharge
tk. Pruess, M. Hqlt, G. S. Bodvarsson and N. A. Goldgtem
298
zone, initial resistivity is 50% larger than in the production zone, due to and more than 300% larger due to salinity differences. 0,O6 [
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The initial subsurface resistivity distribution assumed in this study is shown in Fig. 7. The 5 o h m - m surface corresponds to a caprock. The 15.6 o h m - m background is sedimentary rock with 15070 porosity and saturated with 100°C water at 0.3 wt% NaCI. The 15.6 o h m - m resistivity value for the background was calculated from Archie's Law. The geothermal reservoir is represented by a 1600 x 400 m zone buried at a depth of 800 m. Within the reservoir region the resistivity is initially 2.15 ohm-m. This number was derived by adjusting the background o f 15.6 o h m - m for increased salinity and temperature in the reservoir region.
RESULTS OF S A M P L E C A L C U L A T I O N S Resistivity calculations for the three reservoir models presented above were done for the d i p o l e - d i p o l e resistivity array over the producing zone. The calculations assume a station spacing o f 800 m and 'n-spacings' of 1 to 8, i.e. the distance between transmitter and receiver is one to eight times the 800 m station spacing. This corresponds to a maximum s o u r c e - receiver separation of 7200 m. For the three cases studied (see above) we calculate resistivity pseudosections for d i p o l e - d i p o l e surveys before exploitation and then at times of 0.5, 1, 3 and
Simulation and Resistivity Modefing o f a Geothermal Reservoir
299
5 years after production began. The resistivity distribution is adjusted to account for subsurface temperature and salinity changes due to production. Apparent resistivity differences between the pre-production and subsequent 'surveys' are then calculated on a point-by-point basis and presented in pseudosection form. Case a - - lateral recharge
In Fig. 8, per cent difference pseudosection plots for 1, 3 and 5 years after production begins are given for the lateral recharge case. The plots show a recognizable pattern of change at 1 year
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which grows increasingly stronger with time. The patterns are similar at all times. The plots show a narrow arcuate band where the effect is largest, below which is a 'shadow zone' where little effect is observed. The band of m a x i m u m change is strongly influenced by current paths that travel through the reservoir region, whereas the 'shadow zone' represents paths that are only weakly influenced by the reservoir. For all plots, significant apparent resistivity differences are observed at n = 2 to n = 8 for points directly above the reservoir region. After 3 years even the central nodes in the production region are affected by the intrusion of colder and less saline water and resistivity in this region increases sharply. The per cent difference pseudosection plot reflects this change by showing a more pronounced apparent resistivity increase in the center of the arc and a reduction of the shadow zone beneath the arc. Assuming an average survey error of 1 - 2%, which is typical for the Cerro Prieto monitoring studies (Wilt and Goldstein, in press) it should be possible to detect changes after one year and to quantitatively model data after 2 or 3 years. Case b - - vertical recharge
For this case cold water recharge is constrained to flow vertically downward into the reservoir. Figure 9 shows per cent difference pseudosections for 1, 3 and 5 years after production begins. The difference pattern is quite similar to the lateral case, an arcuate or chevron pattern with a shadow zone beneath, but in this case the arc is narrower and thicker at the top. Resistivity changes for 1 year are larger than for the lateral case and appear shallower with some signficiant change even at n = 1. After 1 year the effect is greater than 70% for a number of points, which is well above the measurement error levels. After 5 years the pattern appears similar to the lateral case for the same period. Case c - - vertical a n d lateral recharge
This case assumes both vertical and lateral recharge, with gradational initial variations in temperature and salinity outside the production zone. In Fig. 10, per cent difference
Simulation and Resistivity Modefing of a Geothermal Reservoir
301
pseudosections are shown for 0.5, 1, 3 and 5 years after the onset of production. There is very little change after 6 months and after 1 year only moderate change is observed. The intermediate zone seems to act as a buffer, slowing the rate of apparent resistivity change compared to the previous cases with step changes in temperature and salinity. After 3 years much of the less saline water reaches the production region, resulting in rather large resistivity changes. The patterns also seem broader than either the lateral or vertical case with significantly
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larger magnitudes. After 5 years the maximum resistivity change approaches 25°70 and a change of more than 10070 occurs for the n -- 1 points overlying the reservoir. It appears that, due to the smooth spatial variations in temperature and salinity, early-time resistivity changes are smaller and late-time changes larger than predicted from the one-dimensional step change models (a) and (b). DISCUSSION Case (c), the most realistic of the cases studied, has significant implications for resistivity monitoring studies. Despite the large rate of production the apparent resistivity changes are small after 1 year of production and during such early times reservoir related changes could be totally obscured by seasonal variations in rainfall, runoff or irrigation (Wilt and Goldstein, in press). However, given sufficient production time, the recharge waters will affect the reservoir region so that the pattern of resistivity change may help determine the parameters of fluid circulation. It is interesting to compare our calculated resistivity results to the actual monitoring measurements in Cerro Prieto (Wilt and Goldstein, in press). Figure 11 shows the per cent changes in apparent resistivity along a line over the production region (line E - E ' ) at times of 1, 1.5 and 2.5 years after the 1979 baseline measurements. Additional details concerning the monitoring work are given in Wilt and Goldstein (in press). The field data show a far more complex pattern of change than the relatively simple models used in the present study, but there are some striking similarities in pattern and magnitude of resistivity change, particularly in the production zone which is located between 9 and 13 km. This area has shown a continuous and steady resistivity increase very similar in character to the arc-like patterns of generic model (c) but with only half of the arc present. The other half is replaced with a zone of decreasing resistivity. The pattern seems to suggest that resistivity in the western part of the reservoir may be changing in accordance with our model, but in the eastern portion of the reservoir more complex processes are taking place. According to a fluid flow model, based on a lithofacies analysis and temperature profiles (Halfman et al., 1982) recharge to the 'A' reservoir is in part
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305
Simulation and Resistivity Modeling of a Geothermal Reservoir kilometers 0
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Fig. 11. Resistivity pseudosections as measured in Cerro Prieto (per cent changes from 1979 baseline). hot water ascending from below and from the east along permeable paths provided by a combination of faults and sandstone units. This circulation system might explain the differences between the actual resistivity changes and those simulated. The obvious next step is to attempt verification of the proposed fluid flow model by means of a more rigorous simulation study. CONCLUSIONS A methodolgy has been presented for indirect study of a geothermal reservoir which combines numerical reservoir simulation with modeling of apparent resistivities as measured with the d i p o l e - d i p o l e technique. For the Cerro Prieto reservoir, temporal changes in apparent resistivity due to production and recharge of colder and less saline waters are both calculated and are observed to be substantial over time intervals of several years. It therefore appears feasible to use resistivity surveys as a means for monitoring reservoir processes. While our schematic models predict resistivity changes which are roughly consistent with field observations, more detailed reservoir models are required to adequately represent the field data.
306
K. Pruess, M.
Wilt, G. S. B o d v a r s s o n a n d N. E. G o l d s t e r n
F o r m o s t g e o t h e r m a l r e s e r v o i r s , the p a t t e r n s o f f l u i d f l o w a n d r e s i s t i v i t y c h a n g e will be t htecd i m e n s i o n a l . T h e r e f o r e , a c c u r a t e r e s i s t i v i t y m o n i t o r i n g r e q u i r e s m e a s u r e n t e n t s a l o n g :,cvetal intersecting profiles. The proposed
methodology
s h o u l d also be a p p l i c a b l e for m o n i t o r i n g
the migration of
reinjected fluids. Acknowledgements--We thank Drs M. Lippmann and C. F'. Tsang for a critical review of the manuscript. This work was supported by the Assistant Secretary for Conservation and Renewable Energy, Office of Renewable Technology, Division of Geothermal and Hydropower Technologies of the U.S. Department of Energy under Contract No. DE-AC03-76SF00098. REFERENCES Bartel, L. C. and Wayland, J. R. (1981) Results from using the CSAMT geophysical technique to map oil recovery processes. Paper SPE 10230, presented at the 56th Annual Fall Technical Conference and Exhibition of the SPE, San Antonio, Texas, 5 - 7 October, 1981. Bermejo M., F. J., Navarro O., F. X,, Castillo B., F., Esquer P., C. A. and Cortez A., C. (1979) Variation de presion en el yacimiento de Cerro Prieto durante su explotacion. Proceedings Second Symposium on the Cerro Prielo Geothermal Field, Mexicali, Mexico, October 1979, pp. 473- 493. Castafieda, M., Abril, A., Arellano, V. and Marques, R. (1982) Reservoir simulation studies on the Cerro Prieto geothermal field: preliminary results. Paper presented at Eighth Workshop on Geothermal Reservoir Engineering, Stanford University, Stanford, California. Dey, A. (1976) Resistivity modelling for arbitrarily shaped two-dimensional structures part 11. Guide to the FORTRAN algorithm RESIS2D. Lawrence Berkeley Laboratory Report LBL-5283, Berkeley, California. Dey, A. and Morrison, H. F. (1976) Resistivity modelling for arbitrarily shaped two-dimensional structures part 1. Theoretical formulation. Lawrence Berkeley Laboratory Report LBL-5233, Berkeley, California. Ershagi, I., Dougherty, E. E. and Hardy L. (1981) Formation evaluation in liquid dominated geothermal reservoirs. Report for Department of Energy No. DOE/ET/28384-TI, U.S.A. Geshelin, B. M., Grabowski, J, W. and Pease, E. C. (1981) Numerical study of transport of injected and reservoir water in fractured reservoirs during steam stimulation. Paper SPE 10322, presented at 56th Annual Fall Technical Conference and Exhibition of the SPE, San Antonio, Texas, 5 - 7 October, 1981. Goyal, K. P., Miller, C. W., Lippmann, M. J. and Vonder Haar, S. P. (1981) Analysis of Cerro Prieto production data. Proceedings Third Symposium on the Cerro Prieto Geothermal FieM, San Francisco, California. pp. 496 - 500. Grant, M. A., Truesdell, A. H. and A. Ma66n M. Production induced boiling and cold water entry in the Cerro Prieto geothermal reservoir indicated by chemical and physical measurements. Presented at Third Symposium on the Cerro Prieto Geothermal Field, San Francisco, March 1981. Geothermics, in press. Grant, M. A. and O'Sullivan, M. J. 0982) The Old Field at Cerro Prieto considered as a leaky aquifer. Proceedings Fourth Symposium on the Cerro Prieto Geothermal Field, Guadalajara, Mexico, August 1982. Halfman, S. E., Lippmann, M. J., Zelwer, R. and Howard, J. H. (1982) Fluid flow model of the Cerro Prieto geothermal field based on well log interpretation, t.awrence Berkeley Laboratory, LBL-14898 and Proceedings, Fourth Symposium on the Cerro Prieto Geothermal Field, Guadalajara, Mexico, August 1982. Liguori, P. E. (1979) Simulation of the Cerro Prieto geothermal field using a mathematical model. Proceedings Second Symposium on the Cerro Prieto Geothermal Field, Mexicali, Mexico, October 1979, pp. 521 - 524. Lippmann, M. J. and Bodvarsson, G. S. (1983) Modeling studies on Cerro Prieto. Paper presented at Fourth Symposium on the Cerro Prieto Geothermal Field, Guadalajara, Mexico. Water Resour. Res. 19, 753 - 767. Prian C., R. (1981) Velocidad de perforacion de la secuencia estratigrafica del area de Cerro Prieto. Proceedings Third Symposium on the Cerro Prieto Geothermal Field, San Francisco, California, March 1981, pp. 77 o 84. Pruess, K. Development of the general purpose simulator MULKOM. Annual Report 1982, Earth Sciences Division, Lawrence Berkeley Laboratory, Berkeley, California, in press. Pruess, K. and Schroeder, R. C. (19801 SHAFT79 user's manual. Lawrence Berkeley Laboratory Report LBk-10861, Berkeley, California, March 1980. Truesdell, A. H., Thompson, J. M., Coplen, T. B., Nehring, N. L. and Janik, C. J. (1979) The origin of the Cerro Prieto geothermal brine. Presented at Second Symposium on the Cerro Primo Geothermal Field, Mexicali, Mexico, October 1979. Geothermies 10, (3/4), 225- 238. Wilt, M. J. and Goldstein, N. E. (1981) Results from two years of resistivity monitoring at Cerro Prieto. Proceedings Third Symposium on the Cerro Prieto Geothermal Field, San Francisco, March 19gl, Lawrence Berkeley Laboratory Report LBL-11967, Berkeley, California, pp. 372-379. Wilt, M. J. and Goldstein, N. E. Interpretation of dipole - dipole resistivity monitoring data at Cerro Primo. Presented at Fourth Symposium on the Cerro Prieto Geothermal Field, Guadalajara, Mexico, August 1982. Geothermics. in press.