Calculation of Viscosity Scaling Groups for Spontaneous Imbibition of Water Using Average Diffusivity Coefficients

Abstract

Spontaneous imbibition is an important driving mechanism for oil recovery in fractured water-wet reservoirs. Reliable scaling relationships have to be used to scale laboratory test results to the field. This work addresses the scaling law described by Ma et al. (J. Pet. Sci. Eng. 1997, 18, 165.), with emphasis on the fluid viscosity term. Oil recovery curves versus time are generated using a mathematical expression, which has been shown to reproduce laboratory results very well for spontaneous imbibition of water into chalk cores (Standnes, D. C. J. Pet. Sci. Eng. 2006, 50, 151.). The expression includes an average constant diffusivity coefficient, which is calculated as an average value over the water saturation range. Calculated oil recovery rates versus time are then scaled using the Ma et al. scaling law describing mass transfer between matrix blocks and fractures. This law includes a geometrical mean term of the fluid viscosities found empirically to account for variation in oil and water viscosities...