  We introduce a family of hybrid discretisations for the numerical
approximation of optimal control problems governed by the equations of
immiscible displacement in porous media. The proposed schemes are based on
mixed and discontinuous finite volume element methods in combination with the
optimise-then-discretise approach for the approximation of the optimal control
problem, leading to nonsymmetric algebraic systems, and employing minimum
regularity requirements. Estimates for the error (between a local reference
solution of the infinite dimensional optimal control problem and its hybrid
approximation) measured in suitable norms are derived, showing optimal orders
of convergence.
