Effects of Capillary Forces and Adsorption on Reserves Distribution
Authors: Shapiro A.A. , Stenby E.H. 
Published: December 2007

Abstract
The purpose of this study is to evaluate the effects of capillary forces and adsorption on the distribution of a hydrocarbon mixture in an oil-gas-condensate reservoir. These effects consist in the precipitation of the liquid phase in thin pores and on the internal surface of the reservoir rock. To estimate the amount of the dispersed liquid condensate, analytical methods based on the generalization of the Kelvin equation and on the potential theory of adsorption have been developed. Sample calculations show significant role of adsorption, especially, in the neighborhood of the critical point of a mixture.

Introduction
Characterization and development of a petroleum reservoir can be highly affected by the fact that the behavior of hydrocarbon fluids in the reservoir differs from that in the PVT experiments. Such a difference is caused by the action of capillary forces and adsorption. The capillary forces can lead to precipitation of dispersed liquid phase containing valuable intermediate and heavy hydrocarbons and to its entrapment in macro- and mesopores. Due to the phenomenon of adsorption, significant amount of the reservoir fluid can be "caught" by the internal surface of the porous matrix and by the micropores.
The effect of capillary forces on reserves distribution was extensively studied. Especial attention was paid to the coupled effect of gravity and capillary forces. In thick low permeable oil-gas-condensate reservoirs, the capillary forces lead to spreading the gas-oil contact into the transition zone. Such zone can be as thick as hundred meters, however the pressure in it is still close to the dew point. The condensate saturation in this zone may non-monotonously vary with depth, due to reservoir heterogeneity. Recent studies show that the mutual action of the capillary forces and thermal gradient breaks the equilibrium state in the transition zone, which results in formation of the diffusion fluxes.
The internal surface of many reservoir rocks is quite large (up to 107 m2/m3) and completely wetting which shows its high capability to accumulate adsorbate. However the adsorption of hydrocarbons in gas-condensate reservoirs has not attained considerable attention, at least, compared to the effects of capillary forces. Only nitrogen adsorption as a method of determining the internal surface (in couple with capillary pressure data), adsorption in specific conditions of Devonian shale formations, and adsorption of asphaltenes have been studied.
Any study of the surface effects in reservoir conditions must take into account the following peculiarities of reservoir thermodynamics:Bulk phases (vapor and liquid condensate) are highly non-ideal, multicomponent mixtures;The reservoir mixture shows retrograde behavior, condensation occurs when the pressure decreases;The effects of capillary forces and adsorption are especially significant in the neighborhood of a dew point (or, geometrically, close to the gas-oil contact).
These peculiarities plague studies of the capillary effects, making it impossible to apply usual tools (such like the classical Kelvin equation) without their thorough modification. Additionally, the capillary pressure behaves as a singular small parameter in the governing system of equations for capillary equilibrium, which results in some difficulties and instabilities in numerical and analytical methods for solution of this system.
An application of the existing adsorption theories to reservoir conditions is even more difficult, since, to the best of our knowledge, the great majority of these theories describes adsorption from a one-component ideal fluid, or from a dilute solution. Only few concepts are related to the mixture adsorption (the most well-known of them being IAS and RAS theories). However, the adsorbed mixture is still supposed to be far from the dew point. Extrapolation of the existing schemes onto the neighborhood of the dew point is a non-trivial problem because, when this neighborhood is approached, the properties of the adsorbed mixture must be continuously transformed to the properties of the bulk liquid condensate, at least in the case when the last one is completely welling.
P. 441