Scaling of spontaneous imbibition measurements is important to characterizationof wetting properties and to modelling mass transfer between rock matrix andfractures. A scaling equation proposed by Malrax and Kyre (1962) has beenwidely applied to prediction of field-scale oil recovery rom fracturedreservoirs. The scaling equation involves many assumptions including identicalcore-sample shapes and viscosity ratios. In this paper, the effect o/viscosityand viscosity ratio on rate of spontaneous imbibition is investigated.Imbibition data is reported for systems with two orders of magnitude variationin viscosity ratio. The results show, for systems of similar geometry, that theimbibition time is proportional to the square root of viscosity ratio. Thisobservation combined with a new definition of characteristic length is used todefine a modified scaling group which allows for differences in viscosityratio, and the shapes and boundary conditions of the coresamples.
Spontaneous imbibition is a natural physical process driven by capillary forceswhereby a nonwetting phase is displaced by a wetting phase from a porous medium(Morrow, 1970). Examples of practical significance may be found in civil andchemical engineering, soil science, and numerous other areas. In petroleumengineering, imbibition is considered especially important in oil recovery fromfractured eservoirs, where the rate of mass transfer between rock matrix andthe associated fractures controls the oil production. However, much remains tobe learned about the combined effect of imbibition, gravity, and bothmicroscopic and macroscopic fluid distribution on oil recovery from fracturedsystems. Development of analytical functions or other computational schemeswhich account for mass transfer between rock matrix and fractures is of specialimportance to mathematical modelling of fractured reservoirs (Aronofsky et al.,1958; Warren and Root, 1963; Kazemi et al., 1976; Kazemi et al., 1992, Chen etal., 1995) Scaling of spontaneous imbibition henomena is a critical step inthis development. Provided that gravity effect can be safely neglected, capillary pressure is the driving force for spontaneous imbibition.Permeability and relative permeabilities in the two phase region of flowdetermine the rate of imbibition. Both capillary pressure and relativepermeability are functions of saturation. Thus many factors enter into scalingof imbibition rates. The effect of fluid viscosity is of primary concern inthis study. The effect of core sample shapes and boundary conditions will alsobe discussed.
Most analyses of imbibition consider behavior in cylindrical tubes. For acylindrical tube of radius r, the Laplace equation gives the capillarypressure, PC
PC = Equation (1) Available in full Paper
where s is the interfacial tension and ? is the contact angle.
The relationship between permeability, k, porosity, f and tortuosity, tfor aparallel bundle of equal size cylindrical tubes with radius r is given by Leverett (1939).
r = Equation (2) Available in full Paper
Thus the capillary pressure, Eq 1, can be expressed as
PC = Equation (3) Available in full Paper
The ratio of permeability to pore size gives a characteristic pore structurelength