Three-dimensional model and procedures for prediction of sand production in gas reservoirs

Based on the principle of effective stress and nonlinear Darcy’s law for gas, three-dimensional elasto-plastic model for sand production with coupled stress and pressure is established, which is solved by the nonlinear finite element method. According to results obtained with the numerical code, distributions of effective plastic strain, pressure, and velocity are investigated. The maximum effective strain occurs at the top and bottom of the starting position of perforations; the stable pressure looks like irregular funnel, and the gas velocity increases dramatically with the its maximum value occurring at the end of perforations. From the distributions of effective plastic strain and velocity, sand production in gas reservoirs is controlled by the effective stress; and steep increase in gas velocity due to pressure dependency is the important affecting factor. Meanwhile, high formation pressure will reduce the possibility of sand production. For gas reservoirs with high pressure, to maintain high formation pressure, to stabilize the bottom hole pressure and to keep this pressure below the limit value would help to reduce the amount of sand production.