A model for the velocity of proppant particles in slot flow is presented. The proppant is either retarded or accelerated relative to the fluid depending on the ratio of the proppant size to the fracture width. It has been found that when this ratio is small, the proppant travels faster than the average fluid velocity at that location because the proppant tends to be confined to the center of the flow channel where the fluid velocity is higher. As the proppant size increases, the effect of the fracture walls becomes more important and the proppant is retarded by the walls. The retardation of particle relative to the fluid is greater for larger particles and greater proximities to the fracture walls due to the hydrodynamic stress exerted on the sphere by the walls in the narrow gap. A higher proppant concentration restricts the area available to flow and increases the drag forces on the particles.

A model is presented for the effect of fracture walls and proppant concentration on proppant transport. The effect of this increased drag force is accounted for by modifying the wall - particle interaction. The influence of the surrounding proppant spheres on the drag force on a particle is estimated from the effect of a wall on the drag force acting on a single particle. The equivalent hydraulic diameter is then used to determine the proppant retardation. The effects of wall roughness and fluid leakoff are discussed. Models are suggested that capture these first order effects.

The new model for proppant retardation has been incorporated into a 3D fracture simulator. Results show that the proppant placement is substantially different when proppant retardation/acceleration is considered. Comparisons of propped fracture lengths obtained with the new model agree much better with propped and effective fracture lengths reported in the field.