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Departments & Programs


Laboratory Measurements of Properties for Steam/Water Flow in Geothermal Rock (2002-2003)

Figure 3: Examples of gas-water flow channels.


PI: Roland N. Horne
Email address:
Funding Level: $120,000

Steam/water relative permeability and capillary pressure are important properties for geothermal reservoir engineering, in that they have a major influence on the performance of geothermal reservoirs under development. All numerical simulations of geothermal reservoir performance require the input of relative permeability and capillary pressure values, yet actual data on these parameters has not been available. The Stanford Geothermal Program (SGP) has succeeded in making fundamental measurements of steam/water flow in porous media and thereby made significant contribution to the industry by providing both understanding of the phenomena as well as actual parameter value measurements. Two of the important problems left to undertake is the measurement of steam/water relative permeability and capillary pressure in geothermal rock (most of the previous study was conducted in high permeability sandstone as well-controlled test material), as well as the understanding of how steam-water boiling mixtures flow in fractures.

Project Objective
The main objective is to improve the ability of engineers and scientists to forecast the future performance of geothermal reservoirs. By understanding the production characteristics, development decisions can be made sooner and with greater certainty. This will result in more efficient utilization of the geothermal energy resource. Another objective is to provide engineers and scientists direct methods to estimate the energy production rate of geothermal reservoirs and practical models of steam-water flow properties, including steam-water relative permeability and capillary pressure models.

The Stanford Geothermal Program uses both theoretical and experimental approaches to conduct the research. We use numerical simulation for modeling work and we use an X-ray CT scanner as one of our main experimental tools to measure in-situ water saturation and its distribution. We also design and construct purpose-built apparatus to conduct the experiments needed.

(a) Capillary Pressure and Relative Permeability Task

Various capillary pressure approaches were used to calculate steam-water relative permeabilities using the measured data of steam-water capillary pressure in both drainage and imbibition processes. The calculated results were compared to the experimental data of steam-water relative permeability measured in sandstone core samples. The steam-water relative permeability and capillary pressure were measured simultaneously. The differences between the Purcell model and the measured values were almost negligible for water phase relative permeability in both drainage and imbibition but not for the steam phase. The lack of significance of the effect of tortuosity on the wetting phase was revealed. A physical model was developed to explain the insignificance of the tortuosity. Steam phase relative permeabilities calculated by other models were very close to the experimental values for drainage but very different for imbibition as expected. The same calculation was made for nitrogen-water flow to confirm the observation in steam-water flow. The results showed that it would be possible and useful to calculate steam-water relative permeability using the capillary pressure method, especially for the drainage case. One of the comparisons between calculated and measured steam-water relative permeabilities is shown in Fig. 1.


Figure 1: Calculated steam-water relative permeability and the comparison to the experimental data in the drainage case.

The general conclusion based on this study was that the Purcell model can be used to calculate the water phase relative permeability and the Corey model can be used to calculate the steam phase relative permeability.

(b) Water Injection Task
Water injection has proven to be a successful engineering technique to maintain reservoir pressure in geothermal reservoirs and to sustain well productivity. However, many questions related to water injection into geothermal reservoirs still remain unclear. For example, how the in-situ water saturation changes with reservoir pressure and temperature, and the reservoir pressure influences well productivity. To answer these questions, we studied the effects of temperature and pressure on the in-situ water saturation in a core sample using an apparatus developed for the purpose. The in-situ water saturation decreases very sharply near the saturation pressure but not to the residual water saturation. When the mean pressure in the core sample decreases further, the in-situ water saturation decreases sharply again to the residual water saturation at a pressure much less than the saturation pressure. This demonstrated the significant effects of steam-water capillary pressure and physical adsorption on the in-situ water saturation.

Also investigated were the effects of pressure on the well productivity index (see Fig. 2 as an example). The well productivity increased with an increase of mean reservoir pressure within a certain range and then decreased. The well productivity reached the maximum value at a pressure close to the saturation pressure. The results of this study should be useful to evaluate projects such as the waste water injection scheme at The Geysers.

Figure 2: Effect of reservoir pressure on the productivity index.

(c) Relative Permeability in Fractures Task
The mechanism of two-phase flow through fractures exerts an important influence on the behavior of geothermal reservoirs. Currently, two-phase flow through fractures is still poorly understood. In this study, nitrogen-water experiments were conducted in both smooth- and rough-walled fractures to determine the governing flow mechanisms. The experiments were done using a glass plate to allow visualization of flow. Digital video recording allowed instantaneous measurement of pressure, flow rate and saturation. Saturation was computed using image analysis techniques. The experiments showed that the gas and liquid phases flow through fractures in nonuniform separate channels (see Fig. 3).

Figure 3: Examples of gas-water flow channels.

The data from the experiments were analyzed using Darcy's law and using the concept of friction factor and equivalent Reynold's number for two-phase flow. For both smooth- and rough-walled fractures a clear relationship between relative permeability and saturation was seen. The calculated relative permeability curves follow Corey-type behavior, as shown in Fig. 4. The sum of the relative permeabilities of the two phases is not equal to one, indicating phase interference. The equivalent homogenous single-phase approach did not give satisfactory representation of flow through fractures. The graphs of experimentally derived friction factor with the modified Reynold's number do not reveal a distinctive linear relationship.

Figure 4: Drainage relative permeability curves in a rough-walled fracture.

FY 2002 Milestones
1. Scaling of experimental data of spontaneous water imbibition.

2. Measurement of steam-water relative permeability through fractures.

3. Development of apparatus and techniques to measure relative permeability in extremely low permeable geothermal rocks.

Major Reports Published
1. Diomampo, G.P.: "Relative Permeability Through Fractures," June 2001.

2. O'Connor, P.A.: "Constant-Pressure Measurement of Steam-Water Relative Permeability Through Fractures," June 2001.

3. Habana, M.D.: "Relative Permeability of Fractured Rock", June 2002.

Major Articles Published
1. Belen, R.P., Jr.. and Horne, R.N.: "Inferring In-Situ and Immobile Water Saturations from Field Measurements", Geothermal Resources Council Transactions 24 (2000).

2. Chen, C.Y., Diomampo, G.P., Li, K., and Horne, R.N.: "Steam-Water Relative Permeability in Fractures", Geothermal Resources Council Transactions 26 (2002).

3. Li, K., Nassori, H., and Horne, R.N.: “Experimental Study of Water Injection into Geothermal Reservoirs,” proceedings of the GRC 2001 annual meeting, August 26-29, 2001, San Diego, USA; Geothermal Resources Council Transactions 25 (2001).

4.Li, K. and Horne, R.N.: “An Experimental Method of Measuring Steam-Water and Air-Water Capillary Pressures,” proceedings of the Petroleum Society’s Canadian International Petroleum Conference 2001, Calgary, Alberta, Canada, June 12 – 14, 2001.

5. Li, K. and Horne, R.N.: “Steam-Water Relative Permeability by the Capillary Pressure Method,” proceedings of the International Symposium of the Society of Core Analysts, Edinburgh, UK, September 17-19, 2001.

6. Li, K. and Horne, R.N.: “Differences between Steam-Water and Air-Water Capillary Pressures,” presented at the 26th Stanford Workshop on Geothermal Reservoir Engineering, Stanford University, Stanford, CA 94043, USA, January 29-31, 2001.

7. Li, K. and Horne, R.N.: “Gas Slippage in Two-Phase Flow and the Effect of Temperature,” SPE 68778, presented at the 2001 SPE Western Region Meeting, Bakersfield, CA, USA, March 26-30, 2001.

8. Li, K. and Horne, R.N.: “Wettability Determination of Geothermal Systems,” presented at the 27th Stanford Workshop on Geothermal Reservoir Engineering, Stanford University, Stanford, CA 94043, USA, January 28-30, 2002.

9. Li, K., and Horne, R.N.: "A Capillary Pressure Model for Geothermal Reservoirs", Geothermal Resources Council Transactions 26 (2002).

10. Li, K. and Horne, R.N.: “An Experimental and Theoretical Study of Steam-Water Capillary Pressure,” SPEREE (December 2001), 477-482.

11. Li, K. and Horne, R.N.: “Characterization of Spontaneous Water Imbibition into Gas-Saturated Rocks,” SPEJ (December 2001), 375-384.

12. Sullera, M.M., and Horne, R.N.: "Inferring Injection
Returns form Chloride Monitoring Data", Geothermics, 30, (2001),

13.Wang, C., and Horne, R.N.: "Boiling Flow in a Horizontal Fracture", Geothermics, 29, 2000, 759-772.