We investigate the displacement of one fluid through an inclined porous sheet by the injection of a second fluid of different density. Using numerical simulation we explore the role of the density contrast between the injected and the reservoir fluid on the displacement process, in the cases where the density contrast originates from either compositional contrasts and/or temperature contrasts between the fluids. In the case where the density contrast originates from compositional differences between the fluids, the density front moves with the fluid–fluid front, and gravity may accelerate or decelerate the time for the injected liquid to reach the sink. In the case where the density contrast originates from a temperature contrast between the injected fluid and the reservoir fluid, then the density front follows the thermal front. Therefore, owing to thermal inertia, it lags behind the fluid–fluid front. This has a quantitative impact on the time required for the injected liquid to reach the sink. If there are both thermal and compositional contrasts between the injected and reservoir fluid, then the thermal and compositional fronts become decoupled in space. The two fronts may lead to complementary or opposing density changes; the different cases lead to vastly different patterns of displacement and time at which the injected liquid reaches the sink, even if the net change in density between reservoir and the injected fluid is the same. We discuss the implications of these phenomena for water injection in sub-surface hydrocarbon and geothermal reservoirs. In an Appendix, we note how a viscosity across both the thermal front and the fluid–fluid front can also lead to a rich spectrum of flow patterns, especially if one front is stable and the other unstable to viscous instability.