Large-Scale Physical Modeling of Water Injection into Geothermal

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Large-Scale Physical Modeling of Water Injection into Geothermal Reservoirs and Correlation to Self Potential Measurements Modelación Física a Gran Escala de Inyecciones de Agua en Depósitos Geotérmicos y Correlación con Medidas de Potencial Natural Jeffrey R. Moore, Steven D. Glaser, H.

Frank Morrison University of California, Berkeley Abstract Laboratory measurements of electric self potentials resulting from water injection through a known flow path in a 260 mm cube of Nugget sandstone are used to calibrate a new large-scale testing device that simulates the in-situ conditions at an injection point in a geothermal reservoir. Modeled in-situ temperatures were 20 ? C and 150 ?

C, while injection pressures were varied from 1 to 1200 kPa. The observed self potential response showed an accurate spatial correlation to the known flow path, with potential differences on the order of 100 mV. A surface contour map of potentials was generated for the sample cube, and the temporal variation of potentials with injection pressure shows good correlation.

Results suggest that at higher temperatures, and in the presence of steam, opposing electrokinetic and thermoelectric self potentials, combined two-phase effects, may counteract to lower the observed potential on the sample surface. A second testing program on Berea sandstone cores at ... more. less.

room temperature reinforces these results. This four-part program isolated the effects of intact rock, an empty flow pipe, a sand 3filled flow pipe, and quartz sand alone. Electrokinetic coupling coefficients for each test were observed to be approximately constant over a large pressure difference range (up to 1.2 MPa), and are 42 mV/atm, -10 mV/atm, 42 mV/atm, and 50 mV/atm respectively. This testing showed excellent correlation between applied pressure drop and observed streaming potential, and indicates the ability of streaming potentials to identify changes in sample conditions. Resumen Mediciones de laboratorio de los potenciales naturales que resultan de la inyección de agua a través de una trayectoria de flujo conocida dentro de un cubo de 260 milímetros de arenisca de Nugget se utilizan para calibrar un nuevo dispositivo de prueba a gran escala que simula las condiciones in-situ en un punto de la inyección en un depósito geotérmico. Las temperaturas in-situ fueron variadas entre 20° C y 150° C, mientras que las presiones de la inyección fueron variadas entre 1 kPa y 1200 kPa. La respuesta observada del potencial natural muestra una correlación espacial precisa con la trayectoria del flujo conocida, con diferencias potenciales del orden de 150 mV. Un mapa superficial de contornos de potencial fue generado para el cubo ensayado, la variación temporal de potenciales con la presión de la inyección muestran una buena correlación. Los resultados demuestran que en temperaturas más altas, y con la presencia de vapor, la oposición de potenciales naturales electrocinéticos y termoeléctricos pueden contrarrestarse para bajar el potencial observado en la superficie de la muestra. Estos resultados preceden pruebas de laboratorio futuras para determinar la mecánica del daño que resulta de la inyección de agua fresca en una muestra de masa de roca representativa del depósito en las condiciones in situ. 1 INTRODUCTION Self-potential, in this case streaming or electrokinetic potential, is a widely recognized method for identifying flow paths through rock and rock/soil matrices (Bogoslovsky and Ogilvy, 1970; Corwin and Hoover, 1979; Wurmstich and Morgan, 1994). This method is based on the existence of an electric double layer at the liquid- matrix interface where a diffuse mobile layer of ions can be effectively dragged away from their adsorbed immobile counterparts under a pore pressure gradient, creating a charge imbalance (Jouniax et al, 1999). Since many minerals have negatively charged surfaces, a diffuse layer of positive ions from the local pore solution weakly bonds to the surface, and can be carried away from the mineral surface yielding a negative anomaly. Areas where water collects (for the above case) would be then characterized by a collection of positive charges, and a positive anomaly (Vichabian and Morgan, 2002). The Helmholtz-Smoluchowski equation describes the relationship between streaming potentials and the pressure gradient under which they move. ? V = ( ?? / ?? ) ? P (1) Where ? is the dielectric constant of the fluid, ? is the zeta potential, ? is the conductivity of the fluid, and ? is the fluid viscosity (Overbeek, 1952). The quantity ( ?? / ?? ) is known as the streaming potential coupling coefficient, Cc. Precise quantitative interpretation of streaming potential data can sometimes be difficult, as the coupling coefficient must be previously determined for each specific scenario. Many users of the streaming potential method have relied on a qualitative interpretation of data in which fluid flow paths are identified by contouring data collected on a dense grid of electrodes. Such methodology has been successfully applied to many field problems, most notably the detection of flow paths through earth dams (Ogilvy et al, 1969; Johansson, et al, 2000), and more relevantly, flow detection resulting from hydraulic stimulation of hot dry rock (or enhanced geothermal systems) reservoirs (Kawakami and Takasugi, 1994; Marquis et al, 2002). The results presented have been obtained as calibration experiments for large-scale physical testing to investigate damage mechanisms at injection points in geothermal reservoirs. Calibration of the streaming potential response for a known flow path will aid in the interpretation of data for an unknown, possibly chaotic and temporally variable, natural flow path. 2 EXPERIMENTAL LAYOUT Testing is subdivided into 2 programs. The first testing program involves large-scale tests on a 260 mm cube of Nugget sandstone. Streaming potential tests were performed for 2 different sample conditions: 1) water-filled, room temperature sample, and 2) steam-saturated, 150 ? C sample. The next testing program was designed to isolate certain mechanisms observed in the large-scale testing, and involves the use of a 127 mm long, 25 mm diameter core of Berea sandstone. This testing program has 4 subdivisions: a) intact core, b) core with 5 mm diameter empty hole along cylinder axis, c) core with hole filled with coarse quartz sand, and d) quartz sand only. Each of these tests reveals information that will aid in the interpretation of data from the large-scale test. 2.1 Large-Scale Triaxial Testing The testing device (Figure 1) is a true-triaxial cell containing a 260 mm cubic sample of Nugget Sandstone (American Stone, Salt Lake City, Utah). It is capable of 3 independent confining pressures up to 14 MPa, while being flooded by up to 250° C steam. The sample is surrounded by non-conductive PEEK plastic plates, which have a dense grid of machined grooves to allow for unimpeded movement of steam and condensate around the sample. Fifty non-polarizing copper electrodes are attached to these plates, distributed on all sides of the sample at 70 mm spacing. Four 2000 Watt heater coils are embedded in aluminum plates outside the PEEK plates, which can be used simultaneously with the steam to apply superheat, or independently, as in modeling a hot dry rock (or EGS) system. Steam (57 kg/hr) is produced in a Lattner 480 V, 2 MPa electric boiler fed by pre- heated water. The injection pump was created by coupling a hydraulic cylinder to a variable speed actuator. Injection rates up to 50 cc/sec are possible at pressures up 14 MPa. Injection rate is controlled either manually by a speed potentiometer, or by control loop feedback from the position sensor attached to the hydraulic actuator. Figure 1: Triaxial testing device including (from left to right) data acquisition digitizer, injection pump, true-triaxial cell, and air/hydraulic intensifiers. Boiler is in background. The calibration model was created by drilling two intersecting holes in the sample interior. One hole was 9.5 mm diameter and extended from the center of the top face of the sample to a depth of one half the sample height. This hole housed the injector. The other hole was 5 mm diameter and extended radial from the base of the main hole out to the center of one side face forming an 8L 9 (Figure 2). This hole was packed with coarse quartz sand (masonry sand). Water injected at the center of the sample traveled through the intersecting sand-filled hole horizontally towards the block edge. The surrounding PEEK plastic plate at the sample face was machined to allow this injectate to escape around the block perimeter. Confining stress was held at a constant 1 MPa in all three principle directions to minimize the contact resistance of the electrodes. The reference electrode for all testing was located at the center of the sample (Figure 2). The sampling rate was 200 samples per second for 80 second sweeps. Figure 2: Schematic of artificial flow path This testing configuration has been specifically designed to model the realistic condition of piped flow in a conducting rock matrix. Many previous laboratory measurements have neglected conducting boundaries, opting in the interest of simplicity for samples contained within a glass or plastic tube. The effect of conducting walls of the pipe will be to allow a portion of the induced current to flow through the rock matrix, while a portion flows in the pipe. We believe that this testing set-up provides a more realistic, and therefore useful, set of results for application to real-world problems. 2.2 Small-Scale Core Testing This testing device was constructed to hold a 127 mm long core of 25 mm diameter Berea sandstone (Lang Stone, Columbus, Ohio). The device (Figure 3) was made using clear PVC pipe and 2 end flanges, to which were attached 100 mm square Plexiglas end plates. The sample was coated with silicon adhesive prior to being inserted into the pipe to ensure that there was no flow allowed at the sample/pipe interface. A copper screw at each end was used as an electrode. Figure 3: Core sample testing device with Berea sandstone. Water was applied to the sample by each of two methods. First, a static head method was employed where a large container of water was placed at different elevations above the sample, and the head difference measured. The maximum attainable pressure drop using this method was 30 kPa. Second, the injection pump applied water to the sample at pressures up to 1300. All injectate was 200 Ohm-m tap water. 3 RESULTS AND DISCUSSION 3.1 Large-Scale Triaxial Testing Testing for this sample configuration was done at both low and high temperatures. The low- temperature sample was 20 ? C. For high- temperature samples, the rock was flooded with steam produced in a boiler to bring it to 150 ? C. Streaming potentials were generated by applying injectate via the injection pump, and this applied pressure measured. The spatial variation in observed potentials, as well as the temporal variations of potentials and injection pressure was noted. Streaming potential coupling coefficients were not determined in this testing program because the pressure at the outlet of the sand-filled flow pipe was unknown. 3.1.1 Low Temperature 3 Water Filled Large-scale injection testing was first investigated at room temperature, or about 20 ? C. Testing included injections at various pressures and flow rates. Streaming potential measurements were made spatially on each of the 4 sides of the block perimeter (neglecting the top and bottom Reference Electrode Injectate Inlet faces). Spatial variations in streaming potentials resulting from a 275 kPa injection are shown contoured in Figure 4. These results are typical of the near 100 injections performed. Recall that the flow direction is towards the east face. The location of the outlet pipe is marked with an X on the east face, and the observed streaming potentials accurately define the spatial orientation of this outlet. For the other side faces, observed potentials showed a ~25 mV drop with only slight spatial variation. This variation, however, weakly defined the flow orientation within the sand-filled pipe, which is denoted by the arrows on the contour plot. Figure 4: Spatial variation of potentials over the sample surface for large-scale sample at 20 ? C. Flow is towards the east face and the outlet of the flow pipe is indicated by an X. Values taken at 40 seconds time. Figure 5: Injection pressure and streaming potential temporal response for large-scale sample at 20 ? C for electrode nearest the flow pipe outlet. Figure 5 illustrates the temporal variation of streaming potentials with injection pressure for the electrode nearest the flow pipe outlet. The observed potentials and the applied pressure showed good correlation. For all testing, streaming potentials responded well to increasing head, mimicking the pressure increase, while for decreasing head experiments, potentials were observed to decay slowly following the decreasing in pressure. 3.1.2 High Temperature 3 Steam Saturated The sample was brought to 150 ? C at 400 kPa pore pressure by applying steam produced in a boiler. The steam-saturated sample was then subjected to the same testing program as the low- temperature sample. Spatial variations in streaming potentials resulting from a 500 kPa injection are illustrated in Figure 6. Again, the variations in potentials accurately define the spatial orientation of the sand-filled flow pipe. For the other side faces, observed potentials showed a ~230 mV drop with only slight spatial variation. The large magnitude of this drop as compared to the cool sample indicates that there may be additional mechanisms contributing the observed potentials. A hypothesis to this end will follow. For the high-temperature sample, observed peak potentials were actually lower in magnitude for the high-temperature sample than the low- temperature sample. This result is in contradiction to Morgan et al (1989) and others who predicted that two-phase flow may enhance streaming potentials by up to 4 times. We will discuss a hypothesis that competing effects may interact to produce lower potentials. The temporal variation of streaming potential and applied pressure showed a relationship different than that for the cold sample. While the streaming potential response reacted well to the beginning of injection, it began to decline shortly thereafter and continued to decline then rise as injection progressed (Figure 7). It is clear from this complicated response that there are many mechanisms contributing to observed potentials. To investigate these mechanisms, the second testing program was employed. 600 400 200 0 Pressure (kPa) 60 40 20 0 Time (sec) 200 150 100 50 0 Streaming Potential (mV) Pressure (kPa) SP (mV) Figure 6: Spatial variation of potentials over the sample surface for large-scale, steam-saturated sample at 150 ? C. Flow is towards the east face and the outlet of the flow pipe is indicated by an X. Readings taken at 42 seconds time. Figure 7: Injection pressure and streaming potential temporal response for large-scale steam- saturated sample at 150 ? C. Electrode location is that nearest the flow pipe outlet. 3.2 Small-Scale Core Testing This testing in this program had 4 stages designed to isolate the mechanisms contributing to the streaming potential response observed in the large-scale testing. Stage #1 included streaming potential investigations for an intact core of Berea sandstone. For stage #2, a 5 mm diameter hole was drilled down the axis of the core. In stage #3, this hole was filled with coarse quartz sand. Stage #4 investigated streaming potentials generated in a sample of the coarse sand only. Central to this investigation was determining the streaming potential coupling coefficient (Cc) for each stage. 3.2.1 Coupling Coefficient For the intact core of Berea sandstone, the streaming potential coupling coefficient was determined to be about 45 mV/atm. This value was constant over a pressure drop range of 1 to 600 kPa. Figures 8 and 9 illustrate both static head experiments at low pressures, and higher- pressure experiments using the injection pump. These figures illustrate that the coupling coefficient is constant over the large pressure range tested. For the core sample of Berea sandstone with a 5 mm diameter hole drilled down its axis, static head experiments revealed that the coupling coefficient was 310 mV/atm. Accordingly, potential differences generated were quite low. Figure 10 illustrates this result. For this setup, trials using the injection pump were inconclusive because it was difficult to generate a significant head loss over the sample. The next test performed was a sample of coarse quartz sand only, the same that filled the pipe in the large-scale test sample. For this sand-only sample, the coupling coefficient was observed to vary inversely with the pressure drop across the sample. This variation is described by equation (2) for injection pressures above 75 kPa, and is illustrated in Figures 11 and 12. Cc = -8 ln ( ? P) + 80 (2) At pressures less than 75 kPa the coupling coefficient was constant at 50 mV/atm. Coupling coefficient values at higher pressures (300 kPa) were smaller than those at low pressures by nearly half. These results are consistent with observations reported by Morgan et al (1989) that at high pressures the coupling coefficient decreases in magnitude by 2-4 times. The fourth and final testing configuration was the Berea sandstone core with a 5 mm diameter axial drill hole filled with the coarse quartz sand. This configuration mimics that of the large-scale triaxial testing. For this configuration a coupling coefficient of 42 mV/atm was observed to be approximately constant over a large pressure difference range. Figure 13 shows the results of low-pressure static head testing for this sample, while Figure 14 shows the high-pressure injection pump testing results. The pressure range of testing was from 1-1125 kPa, and the streaming potential coupling coefficient was observed to be constant over this range. 1200 1000 800 600 400 200 0 Pressure (kPa) 80 60 40 20 0 Time (sec) 100 50 0 -50 Streaming Potential (mV) Pressure (kPa) SP (mV) Valve Open Injection Begins 14 12 10 8 6 4 2 0 Streaming Potential (mV) 25 20 15 10 5 Pressure Drop (kPa) Intact Core - Static Head Cc = 50 mV/atm Figure 8: Streaming potentials generated by various pressure drops for the intact core test using the static head method. 700 600 500 400 300 200 100 0 Pressure Drop (kPa) 160 120 80 40 0 Time (sec) 250 200 150 100 50 0 Streaming Potential (mV) Pressure (kPa) SP (mV) Cc = 42 mV/atm Intact Core - Pump Figure 9: Streaming potential and pressure temporal response for the intact core. Coupling coefficient is determined by overlaying curves. Figure 10: Streaming potentials generated by various pressure drops for the core with empty hole test using the static head method. Figure 11: Streaming potentials generated by various pressure drops for the quartz sand test using the static head method. Figure 12: Streaming potential and pressure temporal response for the quartz sand test. Coupling coefficient decreases with increasing pressure drop across the sample. Figure 13: Streaming potentials generated by various pressure drops for the sand-filled pipe test using the static head method. 20 15 10 5 0 Streaming Potential (mV) 25 20 15 10 5 Pressure Drop (kPa) Sand Only - Static Head Cc = 52 mV/atm 350 300 250 200 150 100 50 0 Pressure Drop (kPa) 60 50 40 30 20 10 0 Time (sec) 100 80 60 40 20 0 Streaming Potential (mV) Pressure (kPa) SP (mV) Sand Only - Pump Cc = 32 mV/atm Cc = 35 mV/atm Cc = 45 mV/atm Cc = 52 mV/atm Cc = 60 mV/atm 15 10 5 0 -5 Streaming Potential (mV) 25 20 15 10 5 Pressure Drop (kPa) Cc = 42 mV/atm Core w/ Sand Hole - Static Head -6 -4 -2 0 2 4 6 Streaming Potential (mV) 25 20 15 10 5 Pressure Drop (kPa) Core With Hole - Static Head Cc = -10 mV/atm Fig ure 14: Str ea mi ng pot enti al and pre ssu re temporal response for the sand-filled pipe test. Increasing pressure levels shows no change in coupling coefficient with pressure drop. Table 1: Summary of the coupling coefficient results from the Berea sandstone streaming potential testing. Stage Cc Range Cc Average 1 42 3 50 mV/atm 45 mV/atm 2 -10 mV/atm -10 mV/atm 3 40 3 42 mV/atm 41 mV/atm 4 32 3 60 mV/atm 50 mV/atm 4 DISCUSSION 4.1 Large-Scale Triaxial Testing 4.1.1 Low Temperature 3 Water Filled In general, streaming potentials responded well to increasing head, mimicking changes in pressure gradient. For decreasing head, however, potentials were observed to decay slowly following the decrease in pressure (Figure 5). This observation is attributed to delayed release of injectate stored within the rock matrix. Under high injection pressure, some portion of the injectate enters the rock matrix via high permeability layers. As injection pressure is quickly reduced to zero, the rock mass releases this stored portion of injectate, creating the exponential decay in potentials following the end of injection. Potentials were observed to require many minutes to achieve the background level observed prior to the injection event. 4.1.2 High Temperature 3 Steam Saturated It is clear that the temporal streaming potential response for this test (Figure 7) is influenced by many mechanisms. At the simplest level, qualitative interpretation reveals that time variations in streaming potentials are a good indicator of changes in sample conditions, more specifically, injection, flow, and pore pressure conditions. For a quantitative interpretation of the data we have attempted to retrieve coupling coefficient information from the increasing pressure and potential area following the start of injection. Relating the pressure and observed potential reveals a coupling coefficient of about 10 mV/atm. This information, however, cannot completely describe the observed response, and it is clear that future testing must be performed to investigate the other mechanisms contributing the streaming potential response. Such mechanisms may include the effect of injectate flashing to steam, the movement of 2 phase fluid/gas through a sand and rock matrix, thermoelectric self potentials, and sample resistivity changes at high temperature. For this test we observed large potential drops for all sample faces other than that to which water was flowing towards. That is, water flowing towards the east face was mimicked in the streaming potential response by an increase in potential, where as all other side faces showed a potential drop of around 225 mV. We attribute this observation to a combination of factors. First, we propose that current induced in the sand-filled flow pipe is entering the rock via the conducting rock walls of the flow pipe. Therefore, the potential observed on these side faces of the block may be an indicator of that portion of current that is entering the rock matrix. Furthermore, the sample at high temperature will have a lower resistivity, and thus, more current may enter the rock matrix than at low temperatures. Additionally, we note that a thermoelectric self potential may cause a potential difference on non- flow side faces. This type of self-potential is created by the temperature gradient from the center of the sample radial outwards, and in this experiment could be significant resulting from a large temperature gradient (Corwin and Hoover, 1979). 4.2 Small-Scale Core Testing We were able to retrieve coupling coefficients from the injection pump tests at varying pressures by overlaying the pressure drop and streaming potential curves. In this way we effectively average hundreds of potential / pressure combinations to determine the average coupling coefficient. This testing program revealed close temporal correlation between the induced pressure drop across the sample and the observed streaming 1400 1200 1000 800 600 400 200 0 Pressure Drop (kPa) 60 50 40 30 20 10 0 Time (sec) 500 400 300 200 100 0 Streaming Potential (mV) Pressure (kPa) SP (mV) Core w/ Sand Hole - Pump Cc = 40 mV/atm potential. In general, streaming potentials responded well to both increasing and decreasing head. For the streaming potential test of only coarse quartz sand, the coupling coefficient was observed to decrease with increasing pressure drop in a logarithmic fashion, as described by equation 2. This effect has been explained as resulting from flow that is not cfully established d (Reichardt, 1935). That is, for fully established flow the coupling coefficient is constant, as observed in the static head experiments at low pressures. As pressure increases, however, as in the applied pressure experiments, the coupling coefficient decreases. For the intact core test, the core with hole, and the core with sand-filled hole tests, however, the streaming potential coupling coefficient was found to be constant over a wide range of pressure differences (up to 1.2 MPa). This is in contradiction to experiments by Morgan et al. (1989) and other investigators who observed that the coupling coefficient decreased with increasing pressure drop. We propose that for the empty and sand-filled flow pipe scenario, flow may always be fully established, as the hole diameter is small with respect to the mineral grain diameter. The coupling coefficient determined for the experiment with a sand-filled hole in the Berea core is the same as that determined for the intact core of Berea sandstone. Furthermore, we observe that the intact core of Berea sandstone and the coarse quartz sand had similar coupling coefficients at low pressures. These coincidental outcomes make it difficult to distinguish the relative effects of each material on the final streaming potential response. 5 CONCLUSION Streaming potential experiments on both large- scale 260 mm cubic sandstone samples, and small-scale 25 mm diameter cores show that streaming potentials are a good indicator of flow through a porous medium. Large-scale experiments for steam-saturated samples indicate that at high-temperatures the streaming potential response is complex. Future testing will identify the mechanisms contributing to this response. Small-scale testing on Berea sandstone cores investigated streaming potential coupling coefficients for different samples including those with conducting boundaries. Coupling coefficients for all testing on Berea sandstone cores were found to be approximately constant over a large range of pressure drop (up to 1.2 MPa), while the coupling coefficient for the coarse quartz sand sample decreased with increasing head. Streaming potentials will be used in future testing to investigate two-phase fluid/gas flow through a rock matrix resulting from the injection of cool water into a steam- saturated sample. These results will aide in investigation of the precise mechanisms controlling rock mass damage at injection points in geothermal reservoirs. REFERENCES Bogoslovsky, V., and Ogilvy, A. (1970) cApplication of Geophysical Methods for Studying the Technical Status of Earth Dams d Geophysical Prospecting, Vol. 18, pp 758-773. Corwin, R., and Hoover, D. (1979) cThe Self-Potential Method in Geothermal Exploration d Geophysics, Vol. 44, pp 226-245. Johansson, S., Dahlin, T., and Friborg, J. (2000) cSeepage Monitoring by Continuous Measurements of Resistivity and Streaming Potential in Hallby and Sadva Embankment Dams, Sweden d Proc., Commission Internationale des Grand Barrages, Vingtieme Congres des Grands Barrages, Beijing, pp 1099-1123. Jouniaux, L., Bernard, M., Pozzi, J., and Zamora, M. (2000) cElectrokinetic in Rocks: Laboratory Measurements in Sandstone and Volcanic Samples d Phys. Chem. Earth (A), Vol. 25, No. 4, pp 329-332. Kawakami, N., et Takasugi, S. (1994) cSP Monitoring During the Hydraulic Fracturing Using the TG-2 Well, Extended Abstracts of Papers d EAGE-56 th Meeting & Technical Exhibition, Florence, Italy, I004. Marquis, G., Darnet, M., and Sailhac, P. (2002) cMonitoring the Electric Potential During the 2000 Hydraulic Stimulation: Results and Perspectives d Document Soultz, IPG Strasbourg, UMR 7516, March. Morgan, F., Williams, E., and Madden, T. (1989) cStreaming Potential Properties of Westerly Granite with Applications d Journ. Geophys. Res., Vol. 94, No. B9, pp 12,449-12,461. Ogilvy, A., Ayed, M., and Bogoslovsky, V. (1969) cGeophysical Studies of Water Leakages From Reservoirs d Geophys. Prospect., Vol. 17, pp 36-62. Overbeek, J. Th. (1952) Colloid Science vol. I, Irreversible Systems, Elsevier, New York. Reichardt, H. (1935) cElektrisches Stroemungspotential bei turbulenter stroeming d Phys. Chem. Ser. A, 174, pp 15. Vichabian, Y., and Morgan, F. (2002) cSelf Potentials in Cave Detection d The Leading Edge, September, pp 866-871. Wurmstich, B., and Morgan, F. (1994) cModeling of Streaming Potential Responses Caused by Oil Well Pumping d Geophysics, Vol. 59, pp. 46-56.

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