The Lattice Boltzmann Method (LBM) is an elegant method to simulate fluid dynamics based on modelling distributions of particles moving and colliding on a lattice. We present examples of two phase flow using the Rothman and Keller (RK) colour gradient Lattice Boltzmann model to study phenomena associated with two phase immiscible fluid flow relevant to water being injected into an oil saturated sandstone. The model involves streaming and colliding two distribution functions (red and blue) representing the number densities of two fluids, where the collision step involves two terms which represents how particle distributions change in each time step due to collision while encouraging colour segregation. We conducted 2D numerical experiments to study the effect of wetting angle on the morphology of flow of a lower viscosity fluid being injected at the left of a simplified model rock matrix that was filled with a higher viscosity fluid. The cases studied involved the injected fluid being non-wetting (wetting angle = 180 degrees), neutral wetting (wetting angle = 90 degrees) and wetting (wetting angle = 0 degrees). These three cases show viscous fingering behaviour with different morphologies for the different wetting angles. For the case of the non-wetting fluid injection, a series of narrow fingers are observed. For the case of neutral wetting, broader and rounded fingers are observed. And for the case of injecting a wetting fluid, a broad but distorted front is observed approaching stable displacement. The results show the importance of the wetting angle on the morphology of viscous fingering. This study demonstrates that the multiphase Lattice Boltzmann Method can simulate phenomenology relevant to studies of enhanced oil recovery such as water injection, and hence, may lead to improved estimates of oil recovery factors.