Use of Water-Vapor Desorption Data in the Determination of Capillary Pressures at Low Water Saturations

Abstract

Summary. The equilibrium conditions applicable to a single liquid phase held by capillary forces within the pore space of a reservoir rock sample are reviewed. It is shown that if the conditions for both chemical and capillary equilibrium are satisfied, an extended form of the classic Kelvin equation is obtained. With available thermodynamic data, it is also shown that the classic form of the Kelvin equation can be used to compute air/brine capillary pressures for core-plug samples. Experimentally, it is only necessary to allow such samples to reach equilibrium in a constant-vapor-pressure environment. Thus the conventional methods for determining capillary pressures can be usefully supplemented by vapor-phase desorption experiments. Although such experiments require relatively tong equilibration time, they are simple to perform and are free from the difficulties common to other methods. A convenient way to establish a constant-vapor-pressure environment is to use saturated solutions of such salts as BaCl, KNO, and K SO . The available vapor-pressure data for these solutions are reviewed and tabulated. From these data, Kelvin capillary pressures are calculated for a range of NaCl brine compositions and temperatures. Some preliminary data obtained by this technique are reported for a pair of matched Berea core plugs of about 10 cm PV. Introduction It has long been known that a relationship exists between the curvature of a gas/liquid interface and the vapor pressure of the liquid phase. Because interface curvature is related directly to capillary pressure, it follows that a measurement of the reduction in vapor pressure over a concavely curved interface can be used to determine the capillary pressure applicable to that interface. A rigorous thermodynamic analysis of this approach to the measurement of capillar pressure is given elsewhere. Capillary pressures determined by vapor-pressure reduction are called Kelvin capillary pressures.n this paper, previous work on the measurement of Kelvin capillary pressures is briefly reviewed. It is then shown that the corrections to the classic form of the Kelvin equation are of negligible magnitude for values of the air/brine capillary pressure less than about 10 MPa [100 bar]. Next, a simple experimental method for controlling the water-vapor pressure for a partially desaturated core-plug sample is described. The corresponding Kelvin capillary pressures are presented in graphic form. Some preliminary data for a pair of Berea core-plug samples are given. The measured saturations for these samples ranged from 3.3 to 6.8 % PV. Previous Work Scientific studies on the retention of liquids in porous solids by capillary forces have been carried out for more than 250 years. However, the first to apply the Kelvin equation to the interpretation of such data appears to be Zsigmondy in 1911. The literature relating to this use of the Kelvin equation is now very extensive. The earlier work is reviewed by McBain and Brunauer. Some of the more recent work is cited in Ref. 3. Although the method was first applied to the study of core-plug samples by Calhoun et al. in 1949, it has seldom been used in this field. Recently, Hsieh and Ramey reported some high- temperature water-vapor adsorption/desorption data on Berea samples. Hsieh and Ramey suggest, however, that for these data, adsorption is dominant and the Kelvin equation is not applicable. On the other hand, the equivalent or Kelvin pore radii calculated from the Hsieh and Ramey data at the highest relative vapor pressure range from 1.9 to 3.1 nm [19 to 31 A]. Uncertainties in the liquid- phase specific volume and surface tension are such that these Kelvin radii may actually be too small by a significant amount. Consequently, it seems possible that the saturations may include at least a small contribution from capillary-held liquid. Other recent studies in which the Kelvin equation was used are those of Morrow et al. and Ward and Morrow. In these papers, room-temperature desorption isotherms were reported for water vapor in contact with a set of low-permeability gas-sand samples. Kelvin capillary pressures ranged from about 70 to 1.4 MPa [700 to 14 bar]. At pressures below about 5.5 MPa [55 bar], approximate agreement was found with independent high-speed centrifuge data. Thus, in the range of air/brine capillary pressures from about 5.5 to 1.4 MPa [ 55 to 14 bar] it appears clearly established that the Kelvin equation can be used to deter-mine valid capillary pressures. The experimental technique used by Morrow et al. and Ward and Morrow is extremely simple. Samples are equilibrated in a series of controlled humidity chambers. Saturation is then determined gravimetrically. This method is actually widely used in fields other than core analysis. Descriptions of the method are given by Bums, Martin, Porter et al., and in literature dealing with standard test methods. A variation of the method uses saturated solutions of various salts for humidity control. In Fig. 1 a schematic of a controlled humidity chamber is shown. In Refs. 9 and 10, equilibration times of up to 3 weeks were required. The solutions used to control the humidity were sulfuriacid solutions of various concentrations. A somewhat more complex version of the method is that described by Weatherwax. In this work, the vapor phase was circulated through the sample, while NaCl solutions of various concentrations were used to control the water-vapor Pressure. Equilibration never required more than 8 days, but runs were carried out for as long as 44 days. The highest relative pressure used corresponded to a Kelvin capillary pressure of only 40 kPa [0.4 bar]. In the present work, saturated solutions of BaCl, KNO, and K SO were used to control the water-vapor pressure to which the samples were exposed. Two advantages of this variation of the method should be mentioned. First, because an excess amount of the solid salt was always present, the water-vapor pressure depends on only the temperature. No independent determination of the amount of salt in solution is required. Second, any possible complication caused by adsorption of SO on the sample is avoided. Such complications have been reported by Some. Negative Pressures and the Kelvin Equation As indicated previously, the relationship between the curvature of a gas/liquid interface and the vapor pressure of the liquid can be subjected to an exact thermodynamic analysis. SPERE P. 913^