Coupled model for simulating proppant distribution in extending fracture

•A new coupled model of fracture propagation with proppant transport is established.•Proppant settlement, proppant bed height, fluid flow velocity and fluid loss are considered in the model.•The finite difference method combined with boundary element method are used to make the model quickly solved.•Two different moving mesh systems are used to facilitate the moving boundary.•Results provide new insights for better understanding proppant transport and settling in water fracturing.