General solutions of the nonlinear PDEs governing the erosion kinetics (Q1876967)

The general solution of one-dimensional mathematical model of erosion kinetics is given. This process is related to the sand production in oil-production wells: the hydro-mechanical instabilities (due to the seepage forces) generate the particle transfer phenomenon. The mathematical model is a second-order partial differential system of Monge-type, which governs the porosity of the medium, together with a constitutive relation governing the filtration kinetics. The general analytical solution is obtained, according to the convenient initial and boundary conditions. An interesting numerical study is given in the last part, describing the time and space evolution of the porosity. The obtained results could be useful for engineering petroleum science.