Summary
Significant mass transfer between the steam and water phases makes it difficult to measure steam/water capillary pressure using routine methods. Because of the difficulties, few experimental data are available. A formula was derived on the basis of the Kelvin equation to calculate steam/water capillary pressure. The water-phase temperatures and pressures measured with a steady-state flow method were used to perform the calculations. The preliminary results of both drainage and imbibition steam/water capillary pressure were obtained. It was confirmed that the lowering of vapor pressure was small, but the capillary pressure was significant for the system studied. This experimental observation is consistent with thermodynamic analysis.
Introduction
It has often been assumed in steam numerical simulators that steam/water flow in porous media can be represented as gas (air or nitrogen)/water flow. In recent years, attention has been paid to the measurements of steam/water relative permeability.1–6 Horne et al.2 found that there were significant differences between nitrogen/water and steam/water relative permeabilities. Accordingly, there may also be significant differences between nitrogen/water and steam/water capillary pressures. To compare the two, reliable experimental data for steam/water capillary pressure are required. However, there have been few direct measurements of steam/water capillary pressure from steam/water flow experiments. Less attention has been paid to the measurements of steam/water capillary pressure, even though capillary pressure is of equal significance to relative permeability and plays an important role in controlling fluid distributions and recoveries in petroleum and geothermal reservoirs.
Tsypkin and Calore7 developed a mathematical model of steam/water phase transition. They found that steam/water capillary pressure could play a stabilizing role for the vaporization front, causing a sharp zone to develop. Urmeneta et al.8 also studied the role of capillary forces in fractured reservoirs and found that capillary pressure tended to keep the vapor phase in the fracture and the liquid phase in the matrix.
Using the adsorption data of Horne et al.9 for rock samples from The Geysers geothermal field, Sta. Maria and Pingol10 inferred the values of steam/water capillary pressure. They found that the steam/water capillary pressure ranged from 0 to 86,000 psi. Persoff and Hulen11 also inferred the capillary pressure from adsorption data of The Geysers rock samples and found that the steam/water capillary pressure ranged from 0 to approximately 28,000 psi. The graywacke core samples used by Persoff and Hulen11 were similar to those used by Sta. Maria and Pingol.10 The porosity was approximately 2%, and the permeability was in the nanodarcy (nd) range.
The adsorption/desorption tests that have been used to infer steam/water capillary pressure are static processes in which there is no steam/water flow. In actual petroleum and geothermal reservoirs, however, capillary pressure plays an important role while steam and water flow simultaneously through the rocks. Hence, the process governing an adsorption test may not represent the mechanisms under actual fluid-flow conditions in those reservoirs. The steam/water capillary pressures from adsorption data may or may not be the same as those measured with a dynamic method in which steam and water are flowing.
Very strict sealing requirements must be achieved for long periods of time during the adsorption tests, which is very difficult, especially at high temperatures. These disadvantages may be overcome by using a steady-state flow method.
The main purpose of this paper was to develop a method to calculate steam/water capillary pressure using data from the experiments of steady-state steam/water flow. An X-ray computerized tomography (CT) technique was used to measure the water saturation and its distribution in the core sample. The effect of temperature on CT values used to calculate the water saturations was studied experimentally.
Method
Capillary Pressure.
Using the Kelvin equation, steam/water capillary pressure can be calculated from the experimental data of liquid-phase pressure, temperature, and related parameters. The procedure is described in this section.
The relative pressure (pv/p0) is used to characterize the capillary condensation on curved surfaces. Kelvin established the relationship between the relative pressure and the curvature of the interface, along with other properties of the fluid and the substrate. In a circular capillary tube with a radius of r, the relative pressure can be calculated using the Kelvin equation as follows:Equation 1
where p0=the vapor pressure when the vapor/liquid interface is flat; pv=the vapor pressure in a capillary tube of radius r when the vapor/liquid interface is curved; s=the interfacial tension and ?=the contact angle measured through the liquid phase; R=the gas constant; T=the absolute temperature; Mw=the molecular weight of liquid; and ?w=the density of liquid.
The Kelvin equation assumes that (1) all adsorption is caused only by capillary condensation, (2) adsorbate density is equal to bulk liquid density, and (3) the validity is unimpaired at low values of r.
The capillary pressure, Pc, in a circular capillary tube is also determined by the interface curvature and fluid and substrate properties and can be calculated asEquation 2
Combining Eqs. 1 and 2,Equation 3
Capillary pressure is defined as the pressure difference between the nonwetting and the wetting phases and is expressed as follows:Equation 4
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