Saturated Pressure Data Research Articles

Prediction of relative and absolute permeabilities for gas and water from soil water retention curves using a pore‐scale network model

Functional relationships for unsaturated flow in soils, including those between capillary pressure, saturation, and relative permeabilities, are often described using analytical models based on the bundle‐of‐tubes concept. These models are often limited by, for example, inherent difficulties in prediction of absolute permeabilities, and in incorporation of a discontinuous nonwetting phase. To overcome these difficulties, an alternative approach may be formulated using pore‐scale network models. In this approach, the pore space of the network model is adjusted to match retention data, and absolute and relative permeabilities are then calculated. A new approach that allows more general assignments of pore sizes within the network model provides for greater flexibility to match measured data. This additional flexibility is especially important for simultaneous modeling of main imbibition and drainage branches. Through comparisons between the network model results, analytical model results, and measured data for a variety of both undisturbed and repacked soils, the network model is seen to match capillary pressure–saturation data nearly as well as the analytical model, to predict water phase relative permeabilities equally well, and to predict gas phase relative permeabilities significantly better than the analytical model. The network model also provides very good estimates for intrinsic permeability and thus for absolute permeabilities. Both the network model and the analytical model lost accuracy in predicting relative water permeabilities for soils characterized by a van Genuchten exponent n≲3. Overall, the computational results indicate that reliable predictions of both relative and absolute permeabilities are obtained with the network model when the model matches the capillary pressure–saturation data well. The results also indicate that measured imbibition data are crucial to good predictions of the complete hysteresis loop.

Direct estimation of air–oil and oil–water capillary pressure and permeability relations from multi-step outflow experiments

Vadose zone description of multi-fluid flow requires measurement techniques capable of determining the capillary pressure and permeability functions of multi-fluid soil systems. Multi-step outflow experiments are presented that use a modified Tempe cell for air–water, oil (Soltrol)–water, and air–oil fluid pairs in Columbia fine sandy loam and a Lincoln sandy loam. In addition to measurements of cumulative outflow and wetting fluid pressure in outflow experiments of air displacing water or oil, pressure changes of the oil (non-wetting fluid) were measured in oil–water experiments. Results from the multi-step measurements were successfully used to directly estimate capillary pressure–saturation and wetting fluid permeability functions. The capillary pressure saturation data for each fluid pair were scaled using their interfacial tension values relative to that of air–water, thereby yielding a combined capillary pressure–saturation curve for the three measured fluid pairs. The combined relative permeability data for both soils nearly coalesce to a single curve, indicating that the relative permeability is solely a function of the porous medium properties. Furthermore, the directly estimated permeability data agreed well with permeability functions obtained using a parameter estimation approach, by which parameters were optimized from comparison of observed and numerically-simulated values of capillary pressure and cumulative outflow.

Improved scaling technique for two-phase pressure—saturation relationships

Current methods of scaling imbibition and drainage pressure-saturation data scale the capillary pressure head using ratios of surface tension, constant intrinsic contact angle, fluid density difference and bubbling pressure. These methods are applicable to scaling either the main drainage or imbibition curve for different fluid pairs. However, for a given fluid pair, scaling of the drainage to the imbibition curve is generally unsatisfactory. For the drainage to imbibition case, the maximum error in computed saturations typically occurs at saturations representative of the funicular zone. It is proposed that an empirical functional relationship between advancing and receding apparent contact angles for a specific porous medium can be used to improve the scaling of imbibition to drainage pressure-saturation data for organic liquid-water systems. The Leverett J scaling function is modified by including the ratio of the apparent contact angles as a new scaling term. In the term cos (φ R ) cos(φ A ) p , the advancing apparent contact angle is first corrected for the combined effects of hysteresis and surface roughness by a constant exponent p. The exponent p is equal to the power of the fit of the advancing apparent contact angle, φ A, to the receding apparent contact angle, φ R. The magnitude of the correction appears to be a characteristic of the medium; however, more laboratory tests are needed for verification. The scaling procedure is tested for a limited series of fluid pairs in several porous media that are characterized by differing pore size distributions and granular compositions. The scaling technique is inadequate, however, for systems subjected to forced imbibition.

Effect of temperature and pore size on the hydraulic properties and flow of a hydrocarbon oil in the subsurface

Capillary pressure relationships in a porous medium determine the distribution of immiscible fluids under static conditions and can largely influence the movement of the fluids when the system is not at equilibrium. Theory predicts that for a given porous medium, the effect of different fluid properties or changes in temperature on capillary pressure are due to changes in interfacial tension and contact angle of the system. The capillary pressure-saturation curves measured here for hydrocarbon oil-water do not have a constant capillary pressure ratio with saturation when compared to the water-air system, and changes in ratio were found when comparing the water-air curves measured at different temperatures. Thus, the scaling theory based on interfacial tensions and contact angles does not adequately account for differences in capillary pressures due to different fluid pairs or temperatures. Also, the curves show the residual wetting and nonwetting phase saturations are greatly affected by temperature and sometimes by the fluid pair, which is not accounted for in the scaling theory and cannot be predicted. When the capillary pressure-saturation relationship is extended to the calculation of relative permeabilities and the prediction of fluid flow in the subsurface, the differences in measured and scaled capillary pressure curves lead to differences in the predicted flow rates and saturations of the immiscible fluids in the subsurface. Thus, care must be used when applying capillary pressure-saturation data from one fluid system to that of another, or when applying it to different conditions.

The influence of porous medium characteristics and measurement scale on pore-scale distributions of residual nonaqueous-phase liquids

A series of experiments was performed to characterize the morphologic distribution of nonaqueous-phase liquids (NAPL's) at residual saturation, as a function of porous medium size. Morphologic characterization of NAPL distributions was accomplished using a novel in situ polymerization technique. The porous medium consisted of glass beads. Blob length, volume and shape characteristics were determined for each experiment, and pore size distributions were determined through capillary pressure-saturation experiments. Both the blob lenght and pore size distributions were fitted to a van Genuchten function. Both blob lenght and pressure-saturation data could be scaled with the same averaged porous medium characteristics. The blob length distributions were found to be wider than the pore size distributions. Estimates of representative elementary volumes (REV's) were generated from statistical analysis using a van Genuchten cumulative frequency distribution function for blob lenght and an empirical function for blob volume as a function of blob length. Simulations were also performed using a Monte Carlo method. The size of the REV needed for a given level of prediction of the residual saturation level was found to increase as a function of mean particle volume for the similar used in this study. Extrapolation of the REV analysis suggests that the size of an REV will increase rapidly as uniformity of the medium decreases. If this extrapolation holds true, significant uncertainty would exist in most determination of residual saturation for poorly sorted media that have been reported to date.

Effects of Clay‐Solution Interactions on Water Retention

Capillary pressure-saturation data were measured on unconsolidated porous media containing 40% montmorillonite, as a function of total electrolyte concentration and sodium adsorption ratio (SAR) of the wetting fluid. Data were also obtained with a nonpolar wetting fluid. The Su-Brooks retension function was fit to the experimental data; the average R² for all treatments was 0.9967. The liquid retention curves were scaled to account for differences in properties of the wetting fluids. The change in scaled liquid retention curves due to changes in solution concentration and SAR followed a pattern reported by earlier investigators, except at high solution concentrations. There were significant clay-solution interactions affecting retention of solution at high electrolyte concentrations. Previous researchers assumed that at high solution concentrations clays did not swell sufficiently to affect hydraulic properties.

Effect of Temperature Level upon Capillary Pressure Curves

Abstract A number of recent studies of drainage relative permeability ratio by dynamic displacement have permeability ratio by dynamic displacement have indicated temperature sensitivity. Poston et al. found that the irreducible water saturation appeared to increase significantly with temperature-level increase and speculated that capillary pressure saturation data would also change to show this effect. Although there have been capillary pressure-saturation studies which show important pressure-saturation studies which show important differences between laboratory and reservoir conditions (presumably higher temperatures), the effects have usually been attributed to adsorption and desorption of polar components from the liquid phases. There appears to be no systematic studies phases. There appears to be no systematic studies of the effect of temperature level upon capillary pressure. pressure. Equipment was constructed to permit measuring capillary pressures for simple systems at temperatures ranging from room temperature to about 350 deg. F. Drainage and imbibition capillary pressure curves were measured for three consolidated pressure curves were measured for three consolidated sandstones and one limestone sample, at either three or four temperature levels form 70 deg to 325 deg F. Fluid used were a filtered white oil and distilled water. Results for the sandstone samples were similar. The practical irreducible water saturation increased significantly as temperature was raised from 70 deg F to the maximum temperature studies - about 325 deg F. Surprisingly, the hysteresis between drainage and imbibition cycles decreased as temperature increased and was nearly absent at 300 deg F. Results indicated that the sandstone samples became markedly more water-wet as temperature level increased. Results for the limestone sample were quite different. All capillary pressure-saturation curves for the various isotherms were found to lie within the envelope of the room-temperature drainage and imbibition curves. The main objective of this study was to determine whether the supposition of Poston et al. was correct. Results are in agreement with the previous dynamic displacement work. Introduction In 1967, Poston et al reported displacement experiments on unconsolidated sands at elevated temperatures and found that the irreducible water saturation increased with temperature increase. The oil viscosity appeared to have had no real effect on their results. Although less conclusive, practical residual oil saturations (to a producing practical residual oil saturations (to a producing water-oil ratio of 100) appeared to decrease with temperature increase. The results also indicated important increases in both oil and water relative permeabilities as temperature increased. This led permeabilities as temperature increased. This led Poston et al. to suggest that temperature affects. Poston et al. to suggest that temperature affects. the sand wettability. Sessile-drop contact angle measurements indicated that the water-oil-glass contact angle decreased with temperature increase. The results of Poston et al. regarding an increase in irreducible water saturation with temperature increase and the nondependence of this finding on the viscosity ratio deserve more attention. it is a well established concept in the literature that increasing water wetness of sands is reflected in an increase in the irreducible water saturation and an increase in oil recovery efficiency. The effect on a capillary pressure-saturation curve would be to cause a shift toward increasing irreducible wetting-phase saturation. if this is the case, then the studies of McNiel and Moss and Willman et al. should give partial credit for the added oil recovery efficiency involved in hot water flooding to the effect of temperature level upon wettability. In view of the potential importance of hot fluid injection for improving oil recovery and the lack of an adequate description of the flow process and thermodynamics involved, it was decided to study the speculation of Poston et al. that capillary pressure-saturation curves should be temperature pressure-saturation curves should be temperature dependent. This study concerns the effect of temperature level upon capillary pressure-saturation relationships for consolidated porous media. SPEJ p. 13

A MATHEMATICAL FUNCTION FOR DESCRIBING CAPILLARY PRESSURE-DESATURATION DATA

Synopsis The equations of Brooks and Corey for relating effective saturation S e to capillary pressure p e describe experimental data quite well for small values of S e but overestimate p e as S e approaches unity. Using assumed functions for the distribution of pore volume with respect to pore radius, Brutsaert was able to describe experimental data satisfactorily provided that constants such as mean pore radius and the standard deviation of pore radius were determined from distribution functions derived from experimental data rather than from the assumed functions. White developed a mathematical model which described experimental data of S(p e ) satisfactorily but the technique required the determination of thirteen constants describing the relationship. In this paper, a pore-volume probability density function is introduced which permits the development of a function for describing effective saturation in terms of dimensionless capillary pressure p e , that is, capillary pressure scaled in terms of bubbling pressure. The capillary pressure-saturation data on the drainage cycle are described better by the new function than by the equations of Brooks and Corey. The correspondence between experiment and theory is better at small values of Se than for values approaching unity. The relationship between S e and p. is characterized by three constants, each of which is, in turn, a function of the pore-size distribution index. Two of these constants are related to mean pore radius and to the standard deviation of the pore-volume distribution.

THE GAS HYDRATE OF BROMOCHLORODIFLUOROMETHANE

An experimental study has been made of the saturation pressure – temperature lines of liquid bromochlorodifluoromethane, liquid bromochlorodiflucromethane – water, bromochlorodifluoromethane hydrate – water, and bromochlorodifluoromethane hydrate – ice systems, for which the characteristic equations are given. Two quadruple points for the hydrate systems have been located and solubilities of water in bromochlorodifluoromethane and bromochlorodifluoromethane in water determined. A systematic treatment of gas hydrate saturation pressure data to yield thermodynamic equations is indicated, and the thermodynamic functions for bromochlorodifluoromethane hydrate and its phase reactions are tabulated. Bromochlorodifluoromethane hydrate is shown to be a stoichiometric compound, and its thermodynamic functions are considered in relation to those of other gas hydrates.