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.}