Since the first publications by Hazlett (Transp Porous Med, 20:21-35, 1995) and Hilpert and Miller (Adv Water Res, 24:243-255, 2001), the pore-morphology-based method has been widely applied to determine the capillary pressure-saturation curves of porous media. The main advantage of the method is the simulation of a primary drainage process for large binary images using moderate computational time and memory compared to other two-phase flow simulations. Until now, the pore morphology model was restricted to totally wetting materials or those with a constant contact angle. Here, we introduce a similarly computationally efficient extension of the model that now enables the calculation of capillary pressure-saturation curves for porous media, where the contact angle varies locally within, due to a composite structure.