A high order method for solving the black-oil problem in porous media

•We solve a three-phase three-component problem (classical black-oil).•We use the sequential implicit discontinuous Galerkin method up to degree four.•We consider both saturated and undersaturated cases.•We use realistic input data for fluid properties and reservoir characteristics.

A high order method is formulated for solving the compressible black-oil problem with capillary effects in one-dimensional domains. The sequential implicit formulation combined with the interior penalty discontinuous Galerkin method is employed. The contribution of this work is to show convergence and robustness of high order polynomial approximations (up to fourth order) for saturated and undersaturated reservoirs.