Most clastic reservoirs contain discontinuous shales that act as barriers or baffles to fluid flow and can not be correlated between wells. To our knowledge, there are no published studies on the effect of discontinuous shales on First Contact Miscible Water Alternating Gas (FCMWAG) processes and how they might alter the sweep efficiency. This work aims to remedy this deficiency. A series of well-characterized laboratory experiments in two-dimensional homogeneous and heterogeneous beadpacks were carried out. Both simultaneous and slug FCMWAG displacement experiments were performed in the porous media containing discontinuous shale. Simultaneous injection was conducted at WAG ratios of 1:1, 4:1 and 1:4. Slug flooding were carried out at a WAG ratio of 1:1 with slug sizes of 5% PV and 50% PV. All experiments were then modelled using IMPES finite difference simulator without using history matching (all simulations used directly measured porous media properties as inputs) to quantify the accuracy of the simulation when modelling the FCMWAG displacements in a porous media with a discontinuous shale. For simultaneous injection, experiments and simulations have demonstrated that there is an optimal WAG ratio, at which oil recovery is maximized. Additionally, the simulator predicted fairly the location of the bypassed oil which was mainly downstream of the shale unit. However, a poor match was found between measured and predicted water and solvent cuts because in the simulation it is assumed that the injected water and gas flow simultaneously whereas the experiments show that: solvent and water prefer to flow in segregated paths rather than flowing simultaneously across the whole porous media, and due to the segregate flow, water laterally blocks solvent from contacting the bypassed oil which reduces FCMWAG efficiency. In slug injection, the large water slug (50% PV) displacement outperformed the 5% PV slug process because the large water slug injected ahead of solvent significantly reduced the extent of fingering and the bypassed oil around the shale barrier. Simulation of the slug WAG experiments showed good agreement for the oil recovery. However, a discrepancy in the physics of the fluid flow during the displacements especially downstream and upstream of the shale barrier was observed in the fluid cut curves. Simulation predicted less fingering and fewer breakdowns of the injected slugs.