Influence of Fluid Viscosity On Mass Transfer Between Rock Matrix And Fractures
Authors: Ma S. , Zhang X. , Morrow N.R. 
Published: March 2010

Abstract
Scaling of spontaneous imbibition measurements is important to characterization of wetting properties and to modelling mass transfer between rock matrix and fractures. A scaling equation proposed by Mattax and Kyte(ll) has been widely applied to prediction of field-scale oil recovery from fractured reservoirs. The scaling equation involves many assumptions including identical core-sample shapes and viscosity ratios.
In this paper, the effect of viscosity and viscosity ratio on rate of spontaneous imbibition is investigated. Imbibition data is reported for systems with two orders of magnitude variation in viscosity ratio. The results show, for systems of similar geometry, that the imbibition time is proportional to the square root of viscosity ratio. This observation combined with a new definition of characteristic length is used to define a modified scaling group which allows for differences in viscosity ratio, and the shapes and boundary conditions of the core samples.

Introduction
Spontaneous imbibition is a natural physical process driven by capillary forces whereby a nonwetting phase is displaced by a wetting phase from a porous medium(l). Examples of practical significance may be found in civil and chemical engineering, soil science, and numerous other areas. In petroleum engineering, imbibition is considered especially important in oil recovery from fractured reservoirs, where the rate of mass transfer between rock matrix and the associated fractures controls the oil production. However, much remains to be learned about the combined effect of imbibition, gravity, and both microscopic and macroscopic fluid distribution on oil recovery from fractured systems.
Development of analytical functions or other computational schemes which account for mass transfer between rock matrix and fractures is of special importance to mathematical modelling of fractured reservoirs(2–6). Scaling of spontaneous imbibition phenomena is a critical step in this development. Provided that gravity effects can be safely neglected, capillary pressure is the driving force for spontaneous imbibition. Permeability and relative permeabilities in the two phase region of flow determine the rate of imbibition. Both capillary pressure and relative permeability are functions of saturation. Thus many factors enter into scaling of imbibition rates. The effect of fluid viscosity is of primary concern in this study. The effect of core sample shapes and boundary conditions will also be discussed.

Imbibition in Tubes
Most analyses of imbibition consider behaviour in cylindrical tubes. For a cylindrical tube of radius r, the Laplace equation gives the capillary pressure, Pc
Equation 1–8 (available in full paper)
Analysis of imbibition behaviour in cylindrical tubes provides guidance to studies of imbibition in porous media. However, direct applications of the conclusions drawn from the tube models to porous media should not be expected because spontaneous imbibition in porous media is usually dominated by countercurrent flow.

Scaling of Imbibition in Porous Media
From Equations (1) and (2), capillary pressure is inversely proportional to pore size, and permeability is proportional to the pore size squared. Thus, although capillary pressure decreases with increasing permeability [Equation (3)], the more permeable the porous media, the faster the imbibition rate [Equations (5) and (6)]. This conclusion was verified experimentally by Handy for water displacing air(8).