Arch Failure in Sandstone in the Case of Nonlinear Flow

A mathematical model of elastic--plastic deformations and stability of sand in a compacted zone around a perforation with a nonlinear flow is developed for a gas well. Laser processing of porous materials is accompanied by similar problems too. The stresses in porous material and the effect of flowing fluids have been analyzed theoretically. The criteria describing stability of sand arches are given. Critical rates of production are found that do not result in destruction of the reservoir near the perforation opening by tensile and shear stresses. The influence of variable permeability on the stability of the arches around the perforations has been studied. The significant influence of water on elastic–plastic deformation and destruction of sand arches is shown within the approach of constant saturation. The results are obtained for both fluid production from the well and gas injection into the reservoir. The conditions of arch stability near the perforated opening are always fulfilled with fluid injection.