Development and verification of new semi-analytical methods for the analysis and prediction of gas well performance

Abstract

The analysis of well performance behavior from natural gas reservoirs requires the rigorous solution of the real gas diffusivity equation in terms of the pseudopressure function. Combining this equation with the material balance equation (MBE) we can develop a closed form rate-time solution which predicts well performance. This formulation requires the development of a pseudotime function as a replacement for the time variable. Unfortunately, this pseudotime function requires knowledge of average reservoir pressure history as depletion progresses, which leads to an iterative (rather than direct) solution for well performance behavior. This work provides simplified solutions for the gas diffusivity equation by making convenient assumptions regarding gas properties (i.e., [] = constant, [] = constant, etc.), which eliminates the need for the pseudopressure and pseudotime functions. In particular, these new solutions should lend themselves to use for the analysis of low pressure gas reservoirs. We have developed two new relations (p² and (p/z)² results) that predict gas well rate-time performance within engineering accuracy of the rigorous solution. Unlike the pseudopressure-pseudotime relation, our new solutions require only knowledge of properties at initial and certain reference pressures, and do not require knowledge of the average reservoir pressure profile. The new flow equations are derived from the rigorous normalized pseudopressure formulation. Our model is that of a well centered in a circular reservoir producing at a constant buttonhole pressure during boundary-dominated flow conditions. We used this verification sequence to establish the ''reference'' pressure at which to evaluate the coefficients C and qi to be used in the new relations. Our new rate-time relations are shown to match the simulated well performance for a range of gas properties and are superior to all forms except the rigorous pseudopressure-pseudotime relation. In addition, our new relations are direct, and relatively simple to apply. In this sense, we conclude that our new rate-time relations can and should be used for the analysis, interpretation and prediction of gas well performance.