  An accurate implementation of wetting and pressure drop is crucial to
correctly reproducing fluid displacement processes in porous media. Although
several strategies have been proposed in the literature, a systematic
comparison of them is needed to determine the most suitable for practical
applications. Here, we carried out numerical simulations to investigate the
performance of two widely used wettability schemes in the lattice Boltzmann
color gradient model, namely the geometrical wetting scheme by Leclaire et al.
(Scheme-I) and the modified direction of the color gradient scheme by Akai et
al. (Scheme-II). We showed that Scheme-II was more accurate in simulating
static contact angles of a fluid droplet on a solid surface. However, Scheme-I
was more accurate in simulating a dynamic case of a binary fluid flow in a
horizontal capillary tube described by the Washburn equation. Moreover, we
investigated the performance of two popular pressure gradient implementation
types. Type-I used the so-called Zou-He pressure boundary conditions at the
inlet and the outlet of the domain, while Type-II used an external body force
as a pressure gradient. We showed that the Type-I implementation was slightly
more accurate in simulating a neutrally wetting fluid in a horizontal capillary
tube described by the Washburn equation. We also investigated the differences
between the two types of pressure gradient implementation in simulating two
fluid displacement processes in a Bentheimer sandstone rock sample: the primary
drainage and the imbibition displacement processes.
