Conductivity of narrow fractures filled with a proppant monolayer

A simplified approach for calculating the conductivity of narrow fractures filled with a sparse monolayer of proppant particles is developed. The proppant particles are modelled as rigid spheres and the deformation of the fracture faces is assumed to be purely elastic. Hertz contact theory and the principle of superposition are utilised to obtain the fracture opening profile as a function of the proppant concentration and the value of confining stress. The conductivity of the deformed fracture channel is determined by using computational fluid dynamics. been demonstrated that some optimal proppant concentration exists, which maximises the fracture conductivity. Based on the simplified approach developed in this paper, the optimal concentration has been obtained as a function of the confining stress and the material properties of the fractured medium. The results are compared with previously published experimental data, which also indicate the existence of an optimal proppant concentration. A reasonable agreement between theoretical and experimental results is observed.