In a saturated solution with dispersed clusters of a second phase, the mechanism by which the larger clusters grow at the expense of the smaller ones is called Ostwald Ripening. Although the mechanism is well understood in situations where multiple clusters of gas exist in a liquid solution, evolution is much more complicated to predict when the two phases interact with a solid matrix, since the solid plays a significant role in determining the shape of the interface. In this paper, we study capillary dominated regimes in porous media where the driving force is inter-cluster diffusion. By decomposing the Ostwald ripening mechanism into two processes that operate on different time scales – the diffusion of solute gas in the liquid and the readjustment of the shape of the gas- liquid interface to accommodate a change in mass – we develop a sequential algorithm to solve for the evolution of systems with multiple gas ganglia. In the absence of a solid matrix, thermodynamic equilibrium is reached when all of the gas phase aggregates to form one large bubble. In porous media on the other hand, we find that ripening can lead to equilibrium situations with multiple disconnected ganglia, and that evolution is highly dependent on initial conditions and the structure of the solid matrix. The fundamental difference between the two cases is in the relationship between mass and capillary pressure.