Solving the equations governing multiphase flow in geological formations involves the generation of a mesh that faithfully represents the structure of the porous medium. This challenging mesh generation task can be greatly simplified by the use of unstructured (tetrahedral) grids that conform to the complex geometric features present in the subsurface. However, running a million-cell simulation problem using an unstructured grid on a real, faulted field case remains a challenge for two main reasons. First, the workflow typically used to construct and run the simulation problems has been developed for structured grids and needs to be adapted to the unstructured case. Second, the use of unstructured grids that do not satisfy the K-orthogonality property may require advanced numerical schemes that preserve the accuracy of the results and reduce potential grid orientation effects. These two challenges are at the center of the present paper. We describe in detail the steps of our workflow to prepare and run a large-scale unstructured simulation of a real field case with faults. We perform the simulation using four different discretization schemes, including the cell-centered Two-Point and Multi-Point Flux Approximation (respectively, TPFA and MPFA) schemes, the cell- and vertex-centered Vertex Approximate Gradient (VAG) scheme, and the cell- and face-centered hybrid Mimetic Finite Difference (MFD) scheme. We compare the results in terms of accuracy, robustness, and computational cost to determine which scheme offers the best compromise for the test case considered here.