Short-time pressure response during the start-up of a constant-rate production of a high pressure gas well

The start-up flow of a constant-rate production of a high pressure gas well is studied, with emphasis on the effect of gas acceleration. Gas acceleration is important in the near wellbore region for a high pressure gas in a high permeability formation. It is shown that when gas acceleration is important, the system of governing equations for the porous media flow becomes hyperbolic. In response to an impulsively imposed mass flow-rate, a steep pressure front is created at the wellbore and it propagates into the formation. This steep pressure front is trailed by large amplitude pressure waves. As they travel away from the wellbore, the pressure front becomes less steep and the amplitude of the trailing waves decreases due to viscous damping. It is found that the pressure drawdown experiences a rapid increase followed by an oscillatory behavior in short times before approaching the classical logarithmic rise regime. The pressure gradient at the wellbore wall can grow to a large magnitude in the early times, which can cause a tensile failure of the rock materials near the wellbore.