A new time discretization scheme for the numerical simulation of two-phase flow governed by a thermo dynamically consistent diffuse interface model is presented. The scheme is consistent in the sense that it allows for a discrete in time energy inequality. An adaptive spatial discretization is proposed that conserves
the energy inequality in the fully discrete setting by applying a suitable post processing step to the adaptive cycle. For the fully discrete scheme a quasi-reliable error estimator is derived which estimates the error both of the flow velo city, and of the phase field. The validity of the energy inequality in the fully discrete setting is numerically investigated.