Evaluation of confidence intervals in well test interpretation results

Abstract

Abstract Uncertainty in well test analysis results from errors in pressure and rate measurements, from uncertainties in basic well and reservoir parameters; from the quality of the match with the interpretation model; and from the non-uniqueness of the interpretation model. Yet, well test analysis results are usually reported as unique values, often with unrealistic precision. Most well test interpretation software programmes use non-linear regression to determine the reservoir parameters that provide the best match between actual rate and pressure data and a given interpretation model. The non-linear regression evaluates the match quality as a standard correlation between each parameter. This, however, only estimates the match errors, and does not incorporate the other errors that must be accounted for to understand the overall uncertainty on the analysis. The paper presents a practical methodology for the determination of error bounds in well test analysis and illustrates its application with well tests from an oil reservoir and a gas condensate reservoir in the North Sea in order to evaluate typical error bounds for the most common parameters such as permeability-thickness, permeability, skin effect, fracture, horizontal well lengths and distances to boundaries. Differences in error bounds between hand and computer analysis are also discussed. Introduction Uncertainty in well test analysis results from errors in pressure and rate measurements, from uncertainties in basic well and reservoir parameters; from the quality of the match with the interpretation model; and from the non-uniqueness of the interpretation model (Horne 1994). Yet, well test analysis results are usually reported as unique values, often with unrealistic precision. This has been exacerbated by the use of hand calculators and, later on, computers and well test interpretation software for performing well test analysis calculations, because engineers, students and professionals alike, seem to believe that because the tools they use display eight decimal places, all eight places are accurate. Consequently, distances to boundaries are often reported with a resolution of a tenth of a foot, skin with two decimal digits, and permeabilities greater than 100 mD within 0.1 mD, i.e. with resolutions better than 0.1%, which is utterly ridiculous.