We propose a simple model of flow in a partially filled wormhole, where layers of oil, Slurry and immobile sand can coexist. The slurry at the bottom or the wormhole is assumed to behave as a Bingham material, i.e., it yields when the shear stress exceeds the yield stress. The yield stress is assumed to increase; with depth due to the weight of the overlying sand. A Mohr-Coulomb equation is used to calculate the yield stress thin the slurry and immobile sand layers. Linearized Navier-Stokes equations are solved to calculate the oil and mobile sand flow rates. Different characteristic oil and sand flow patterns are studied. Oil and sand flow rates through the wormhole are calculated as functions of pressure gradient and rheological parameters. This simple model could be used to estimate sand transport in a partially filled wormhole, complementing a sand transport model for uniformly filled wormholes((4)). These wormhole flow models can be incorporated into a field scale model for cold production.