Abstract

A capillary equilibrium equation has been derived for porous rock. The basisfor the derivation is thermodynamic equilibrium, accounting for hydrostaticequilibrium phase equilibrium and minimization of Gibbs free energy. Theequation provides a relationship between oil saturation, pore size and heightin the reservoir, relative to the oil-water contact. In the lateral directionthe saturation in one pore call be related to another of a different size.Given the pore size distribution, the average saturation in a rock sample canbe found at an elevation above the oil water contact. Furthermore, the equationprovides insights into the laboratory imbibition and drainage pressurecurves.

The equation is developed for a water wet, oil-water reservoir. A similar derivation could be carried out for differentsystems.

Introduction

Virgin oil saturations within a reservoir increase rapidly with height from thebase of the oil column. This rapid change is the transition zone, which in mostreservoirs is less than 6 metres thick. The transition zone is followed byconstant water (and therefore constant oil) saturation with height, called theirreducible water saturation (Swirr). Capillary pressure defines thewater (and oil) saturation versus height, lso referred to as the initialequilibrium state apillary pressure is also an important element of flow, causing crossflow between beds, crossflow between fractures and the matrix, mitigating the formation of lingers and other factors affecting the ature ofthe flow.

Capillary pressure is not a fundamental potential of nature and as such must bethe sum of other fundamental potentials. If we consider these other potentialsto be pressure potentials, it would be possible to carry out a force (pressure)balance to etermine the initial equilibrium state_ However, the pressurebalance becomes very complex, when trying o balance pressure in pores ofdifferent sizes, shapes, oil saturations and at different heights. On the otherhand if we work in the realm of energy and entropy the problem becomestractable. The total energy entropy balance about a pore is the methodologyused here to derive capillary pressure for a water-wet

A derived capillary equilibrium equation, based on an energy-entropy balanceabout a pore is provided in detail in Appendix A. This equation in the form ofthe water pressure is:

swgh = Equation (1) Available in full reading text

To understand the various terms in the equation, five elements need to bedefined: I) Adsorption Potential, H, represents the interaction between thewater and the rock. The adsorption potential arises from the unbalancedelectrostatic charge density at the surface of the solid. Water's polar natureallows the dissipation of this electrostatic energy by aligning with the porewall. The dissipating of the surface energy releases heat, called the heat ofadsorption. The effect of the heat of adsorption on the water phase is to alignthe water molecules into a more ordered state (a decrease in entropy). Themeasured heat of adsorption of pure water onto a ilica gel or a glass surfaceis approximately 0.070 N/m at room temperature 1.

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