The two-layer Quasi-Geostrophic equations are a very simple model of the ocean on large lateral scales. Vortex solutions to these equations exist, and have been used to model heat transport in areas of the ocean affected by convection. We will review these results and discuss their applicability to convective patches. Then we will derive a new set of equations valid for lateral scales more applicable to ocean convection. These Intermediate Quasi-Geostrophic equations have a two-layer form that also has vortex solutions, similar to those that exist for the Quasi-Geostrophic equations.