Development of tensile stress near a wellbore in radial porous media flows of a high pressure gas

The development of tensile stress near a wellbore in steady radial porous media flows is examined in detail, in particular for high pressure gas flows. It is shown that poroelasticity induced radial stress is always tensile for any pore pressure distribution. This induced tensile stress reaches a maximum value at the interior point where the local pore pressure equals the average pore pressure. It is also shown that no effective tensile stress can develop in Darcy flows of a liquid, while effective tensile stress can appear in Darcy flows of a gas when the drawdown pressure is large. The smallest flow-rate for the appearance of effective tensile stress occurs when gas acceleration effects become important in high pressure, high speed gas flows. For the flow beyond the critical condition for the occurrence of effective tensile stress, the tensile stress level depends strongly on the gas acceleration.