Power Law Concept on Darcy's Flow Model: A New Approach for Analysing Gas/Condensate Well Deliverability

Abstract The productivity of gas and oil well plays an important role in gas and oil field development, particularly gas condensate well that is characterised by severe loss of well deliverability due to liquid drop out below the dew point, and for establishing field proration schedules and setting maximum allowable production rates for individual wells by regulatory agencies. Houpeurt equation and Rawlins-Schellhardt equation are the most widely used gas deliverability equations by engineers. Although the Houpeurt equation has a theoretical basis and is rigorously correct, the equation assumes that Darcy's law is still valid under high velocity of gas flow and that an additional term must be added to account for the increased pressure drop. The Rawlins-Schellhardt equation still continues to be used by the natural gas industry, however it was empirically formulated and the deliverability plot is traditionally reversed in order to estimate the deliverability exponent. In this work, a new gas/condensate well deliverability equation under pseudo-steady-state condition is developed using the power law concept on Darcy's model of flow: this is suitable in view of the fact that Darcy's law breaks down under conditions of high velocity flow which is proven to exist in gas/condensate wells. Thus this concept vehemently account for the non-linearity between gas flow rate and potential gradient due to inertial effects in the porous media. The formulation procedures are detailed. An illustrative example in which the new equation is applied to field data is included. Results comparison between the new equation and the traditional dry gas equations by Houpeurt, and Rawlins-Schellhardt is made to illustrate its capabilities, and the correlation between the three methods is shown. The new approach will provide a single and useful tool for estimating gas/condensate well productivity.