Conventional parameter estimation methods used in pressure transient analysis assume specific analytical probability distributions of error and use corresponding likelihood functions to estimate the key parameters such as reservoir permeability, wellbore storage, skin and distance to reservoir boundary. The most commonly used method is that of least squares, which assumes that measurement errors follow a Gaussian distribution. Lack of a priori information regarding the nature of these measurement errors have made the ordinary least squares method (OLS) the most common method for parameter estimation. In this study, on examination of multiple field data sets, the assumption of Gaussian errors was found to be weak. The use of OLS in such cases leads to biased estimates of reservoir parameters. A general method based on the framework of likelihood maximization that is inherent to parameter estimation was developed. This method does not require a prior assumption regarding the nature of the distribution of the underlying errors in the data. A hybrid variation was developed to improve the convergence properties of this method. The accuracy and convergence properties of this method were compared to that of OLS for field and synthetic datasets and found to be superior to OLS for arbitrary error distributions, while still maintaining accuracy in cases with truly Gaussian errors.
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