Unsteady-State Gas Flow into Gas Wells

Abstract

Abstract The theory for unsteady radial flow of gas, as simplified by Aronofsky and Jenkins, has been reviewed and compared with actual well performance. This study indicated that the theory should be modified by the introduction of an empirical "rate of flow" function "Y(q)". The expansion of the theory on the flow of gas to include a Y(q) term bridges the gap between the theory of unsteady-state flow of gas and actual gas-well behavior. Apparently, the Y(q) term is a function only of the rate of flow for a given well. The completion factor or skin effect is associated with the Y(q) function in such a manner that at least two or more sets of drawdown or pressure build-up tests are needed to separate the Y(q) function and the completion factor. Since the Y(q) function used in this report represents an energy loss dependent on rate of flow near the well-bore of a gas well which is in addition to the loss required by Darcy's law, the Y(q) function is related to the exponent of the back-pressure curve for a gas well. Techniques and equations are presented which permit the estimation of stabilized and "short-time" deliverabilities. Introduction The published theory of radial unsteady-state flow of gas through porous media may be divided into papers which use Darcy's law as a premise and other papers, which recognize that Darcy's law may not hold for flow into gas wells. Miller compared theory based on Darcy's law with actual gas-well behavior and concluded that flow into gas wells deviates from Darcy's law. Houpeurt in a thorough investigation of flow into gas wells concluded that the flow rate into a gas well is proportional to the difference between the squares of upstream and downstream pressures elevated to a power between 1.0 and 0.5. Houpeurt also concluded that the deviation from Darcy's law is caused by irreversible, kinetic energy exchange between the flowing gas and the porous media. Tek presented a complete evaluation of the flow problem in gas wells. Several investigators state that the inclusion of gas compressibility into flow equations based on Darcy's law does not begin to explain the flow problems suggested by gas-well behavior.