Correlation for the effect of fluid viscosities on counter-current spontaneous imbibition

Counter-current imbibition occurs when brine spontaneously displaces oil from a water-wet porous rock. In experiments that attempt to simulate the production of oil from fractured reservoirs, the cumulative production of oil is measured as a function of time. Even with wetting properties fixed, usually at very strong wetting by water, there are many variables, including the basic rock properties, the size and shape of the core, which faces are open, and the water and oil viscosities. Experimental production versus time curves have been correlated for many of the variables involved (Ma, S., Morrow, N.R. and Zhang, X., 1997, J. Pet. Sci. Eng., 18, 165–178). The origin of most of the terms in the correlation is theoretically understood and only the viscosity term is essentially empirical. However, this term is significant when relating laboratory experiments to reservoir behaviour. Since the development of the Ma et al. correlation, data with a wider range of viscosity ratio has been obtained by increasing the viscosity of the aqueous phase. Sequential developments in the mathematical analysis of the effect of viscosity ratio in other correlations and their ease of application are reviewed. A modification of the viscosity term in the Ma et al. correlation is presented that gives close correlation of data for four orders of magnitude variation in liquid/liquid viscosity ratio and is physically consistent with the extreme case when one phase is inviscid.In mathematical modelling of spontaneous imbibition, it is often assumed when using the standard analysis, that the effective relative permeabilities for each phase do not depend on viscosity ratio. Such an assumption leads to a correlation that only fits the data for a limited range of viscosity ratios. However, the correlation of data over four orders of magnitude variation in viscosity ratio by a function that only contains the viscosities implies that there is a consistent dependency of effective relative permeabilities on viscosity ratio. The improved correlation is shown to perform better than the standard analysis even with the relative permeability ratio optimized to give the closest fit to the experimental data. An assessment of how the relative permeability ratio varies with viscosity is obtained by matching the standard mathematical model to the new empirical correlation.