Empirical measures of wettability in porous media and the relationship between them derived from pore-scale modelling

The wettability of a crude oil/brine/rock system is of central importance in determining the oil recovery efficiency of water displacement processes in oil reservoirs. Wettability of a rock sample has traditionally been measured using one of two experimental techniques, viz. the United States Bureau of Mines and Amott tests. The former gives the USBM index, I(USBM), and the latter yields the Amott-Harvey index, I(AH). As there is no well-established theoretical basis for either test, any relationship between the two indices remains unclear. Analytical relationships between I(AH) and I(USBM) for mixed-wet and fractionally-wet media have been based on a number of simplifying assumptions relating to the underlying pore-scale displacement mechanisms. This simple approach provides some guidelines regarding the influence of the distribution of oil-wet surfaces within the porous medium on I(AH) and I(USBM). More detailed insight into the relationship between I(AH) and I(USBM) is provided by modelling the pore-scale displacement processes in a network of interconnected pores. The effects of pore size distribution, interconnectivity, displacement mechanisms, distribution of volume and of oil-wet pores within the pore space have all been investigated by means of the network model. The results of these analytical calculations and network simulations show that I(AH) and I(USBM) need not be identical. Moreover, the calculated indices and the relationship between them suggest explanations for some of the trends that appear in experimental data when both I(USBM) and I(AH) have been reported in the literature for tests with comparable fluids and solids. Such calculations should help with the design of more informative wettability tests in the future.