Mathematical model for piping development considering fluid-solid interaction

Based on the law of conservation of mass, the conservation of mass of transporting particles in the cell body is determined, from which a continuity equation of the transporting particles is derived. Particle transporting is associated with the fluid flow. So the calculation should combine the continuity equation of flow in the seepage field. Then a fluid-solid interaction model is proposed. Based on the relations between the particle loss and the change of the seepage field, the relationship among the permeability coefficient, losses quantity, porosity and other parameters is quantified. The coupled model can be solved combined with the initial conditions and boundary conditions. Finally, a one-dimensional piping problem is simulated by means of the proposed model. Decoupled by a time-step method, the model is solved successfully by use of the finite difference method. From the calculated results, the variations of the particle loss, seepage velocity, porosity and the remaining particle volume in the piping proceeding are analyzed. The impact of the hydraulic gradient is discussed as well with repeated calculation under different hydraulic gradients.