Using the Gibbs Ensemble Monte Carlo (GEMC) simulation technique, we examine the liquid-liquid phase behavior for a symmetric binary LJ fluid confined in a disordered solid matrix. Increasing the matrix packing fraction and adsorption strength, and lowering the ratio of adsorbent to adsorbate particle size reduces the magnitude of the miscibility gap. We also employ Voronoi tessellations to analyze the distribution of cavity sizes in mono- and polydisperse matrices to help explain the observed phase behavior.