Highly Compressible Porous Media Flow near a Wellbore: Effect of Gas Acceleration

A fundamental study on porous medium flow of a highly compressible gas near a wellbore is carried out. The effect of gas acceleration is assessed quantitatively. It is shown that gas acceleration induced by the converging flow introduces a quadratic drag on the flow; acceleration due to volumetric-expansion causes the pressure curve to steepen near the wellbore and the flow to become choked at high flow-rates. When the flow is choked, the pressure gradient at the wellbore wall becomes unbounded. It is also shown that for any given mass flow-rate, the well pressure predicted from the model considering acceleration effect is significantly below that calculated from the Darcy-Forchheimer model. Implications of these results to petroleum engineering are discussed.