American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc.
This paper was prepared for the Rocky Mountain Regional Meeting of the Society of Petroleum Engineers of AIME, to be held in Denver, Colo., April 7–9, 1975. Permission to copy is restricted to an abstract of not more than 300 words. Illustrations may not be copied. The abstract should contain conspicuous acknowledgment of where and by whom the paper is presented. Publication elsewhere after publication in the JOURNAL paper is presented. Publication elsewhere after publication in the JOURNAL OF PETROLEUM TECHNOLOGY or the SOCIETY OF PETROLEUM ENGINEERS JOURNAL is usually granted upon request to the Editor of the appropriate journal provided agreement to give proper credit is made. provided agreement to give proper credit is made. Discussion of this paper is invited. Three copies of any discussion should be sent to the Society of Petroleum Engineers office. Such discussion may be presented at the above meeting and, with the paper, may be considered for publication in one of the two SPE magazines.
The main purpose of gas reservoir simulation is to predict the future performance of the reservoir under Alternate 1 production policies. The successful prediction of reservoir performance requires accurate parameters such as performance requires accurate parameters such as permeability, porosity and reservoir boundaries. permeability, porosity and reservoir boundaries. These parameters are normally estimated from well tests where the pressure and flow-rate measurements are subject to errors. As a result of the measurement error, the predicted performance will also be subject to error. performance will also be subject to error. This paper shows that statistical limits can be placed on such estimates. placed on such estimates. The parameter estimation procedure from noisy well-test data has been studied. Several drawdown and buildup tests for a radial homogeneous gas reservoir were simulated. "Noise" (measurement error) was superimposed on the test data. Nonlinear least-squares regression was used to estimate the mean values and standard deviations of the reservoir parameters (permeability, porosity and drainage parameters (permeability, porosity and drainage radius) from the "observed" well pressures. At the end of each test statistical confidence limits were established on the estimated parameters. parameters. The estimated parameters and their confidence limits were used to predict the future pressure behavior of the reservoir. Confidence pressure behavior of the reservoir. Confidence limits were also established on the pressure behavior. Several different tests were studied to determine the effect of the well-test method on the confidence limits of the future pressure predictions. predictions. The confidence limits theory (reliability theory) was also applied to gas-in-place estimation from a drawdown test. A Monte-Carlo simulator was used to calculate the standard error in the estimated gas in place.
For a natural gas producer or gas transmission company, the accurate prediction of gas well or reservoir performance is of primary importance. Currently, it is likely that the performance of a gas reservoir is predicted by performance of a gas reservoir is predicted by using a mathematical model (simulator) of the reservoir. As an example, the mathematical description of a one-well radial gas reservoir is given by the following nonlinear partial differential equation, initial condition, and boundary conditions.
(1)
