This report outlines progress in the third quarter of the second year of the DOE project ''High Resolution Prediction of Gas Injection Process Performance for Heterogeneous Reservoirs''. High order finite difference schemes for one-dimensional, two-phase, multicomponent displacements are investigated. Numerical tests are run using a three component fluid description for a case when the interaction between phase behavior and flow is strong. Some currently used total variation diminishing (TVD) methods produce unstable results. A third order essentially non-oscillatory (ENO) method captures the effects of phase behavior for this test case. Possible modifications to ensure stability are discussed along with plans to incorporate higher order schemes into the 3DSL streamline simulator.