Centrifuge Measurements of Capillary Pressure: Part 2 – Cavitation

Abstract

Centrifuge air/water capillary pressure measurements made at one atmosphere ambient pressure can have the liquid in tension (negative absolute pressure) and cavitation in the liquid saturated region should not occur with water-wet rocks having capillary entry pressure less than three atmospheres. Thermodynamics argue that water that is in hydrostatic equilibrium in the pore space that has been invaded by a gas that is also in hydrostatic equilibrium can be in chemical equilibrium with the water vapor in the gas. An experiment showed no evidence of cavitation in rocks with a capillary entry pressure of 50 psi. Introduction In part I we discussed the outflow boundary condition of zero capillary pressure. It was shown that some of the problems that have been attributed at the outflow boundary condition or cavitation could have been due to inadequate core cleaning or lack of equilibrium. For example, a core that was not adequately cleaned has a low capillary entry pressure and significant trapped water saturation in an air-brine centrifuge capillary pressure measurement. Conditions for the violation of the outflow boundary condition were defined. In Part 2 we discuss the question of cavitation of the liquid when the liquid is in tension. Cavitation is of concern with air-liquid capillary pressure measurements when the air pressure is one atmosphere and the capillary pressure exceeds one atmosphere. The liquid is then in tension (negative absolute pressure), and it is known that bulk liquid is not stable with respect to its vapor when it is in tension. If cavitation was to occur in the 100% liquid saturated region, the liquid production would occur before the capillary entry pressure was reached. This would result in an apparent capillary entry pressure that is less that the actual value. The question of cavitation in the liquid saturated region is addressed in the first section. If cavitation was to occur in the gas invaded region whenever the liquid was in tension, then the liquid could become discontinuous until the hydrostatic pressure in the continuous bodies of liquid is positive. The second section shows that liquid and gas that is in hydrostatic equilibrium can also be in thermodynamic equilibrium. The final section presents experimental results which show that a rock with a capillary entry pressure of 50 psi has the same capillary pressure curve regardless of whether the air pressure is one atmosphere or 300 psi, i.e., whether the liquid was in tension or not. The Appendix contains the derivations required to describe the nucleation of a bubble in a cavity. These results are used to describe cavitation in a liquid saturated region. The existence of water in tension in porous media is a common occurrence with the water vapor desorption method for determination of capillary pressure. Melrose has reviewed the literature on the negative pressures of liquids. Water can exist under greater negative pressures than is encountered in capillary pressure measurements made by the water vapor desorption, centrifuge, and porous plate methods and showed that the results were in agreement even though the water was under significant tension. It remains to prove that in porous media that liquid in tension exists as a stable state rather than a metastable state which is subject to random disturbances.

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“…Similar experiments using glass micromodels were recently reported [28]. Theoretical issues ofnucleation in the liquid-to-vapor transition in porous media were addressed in recent studies by Parlar and Yortsos [80], and by Hirasak.i et al [59], in the contexts of vapor desorption and cavitation in a capillary centrifuge. Both works emphasize the importance of heterogeneous nucleation in porous media.…”

“…Figure 2 qualitatively portrays such a relationship for a hydrophilic cavity (~-a< 1rl2), that satisfies the relation Wlr < cos(9-a). Hydrophobic cavities, first introduced by Harvey et al [54], were considered by Hirasaki et al [59]. To proceed further, we will assume that a self-similarity exists between the maximum size cavity and the size of the host pore body.…”

“…Consider now the nucleation process_ in a conical cavity, with curvature corresponding to the equilibrium value given by (56). The stability of mechanical equilibrium in gas-liquid interfaces in cavities was examined by various authors [46,59,111]. A quit~ general result is obtained: mechanically stable interfaces ( £1-ll.F I dVJ > 0) require configurations such that dr I dV < 0, while mechanically unstable interfaces (£1-ll.FidVJ < 0) correspond to drldV > 0.…”

“…. 59 Profile of Si concentration vs. length for set 1. 60 · Effluent pH vs. PV injected for set 2. 61 Profile of pH vs. length for set 2 . .…”

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“…For this, liquid pressure has to decrease below vapor pressure without appearance of cavitation. Hirasaki et al [13] estimate that liquid absolute pressure in a porous medium could decrease to À4 bar without appearance of cavitation at large scale (liquid phase remains stable), due to pores geometry. They also provide experimental drainage capillary curves obtained by centrifugation with two levels of air pressure: atmospheric pressure (leading to negative liquid pressure) and high pressure (liquid pressure remains above vapor pressure).…”