Evaluating Confidence Intervals in Well-Test-Interpretation Results
Authors: Denney Dennis 
Published: February 2015

This article, written by Senior Technology Editor Dennis Denney, contains highlights of paper SPE 113888, "Evaluation of Confidence Intervals in Well-Test- Interpretation Results," by A.C. Azi, SPE, and A. Gbo, SPE, Imperial College; T. Whittle, SPE, Baker Atlas; and A.C. Gringarten, SPE, Imperial College, prepared for the 2008 SPE Europec/ EAGE Annual Conference and Exhibition, Rome, 9-12 June. The paper has not been peer reviewed.
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 nonuniqueness of the interpretation model. Yet, well-test-analysis results often are reported as unique values, with unrealistic precision. A practical method is presented to determine error bounds in well-test analysis. An application with well tests from an oil reservoir and a gas-condensate reservoir in the North Sea evaluates typical error bounds for the most common parameters.

Introduction
Uncertainty in well-test analysis was made worse by the use of hand-held calculators and, later on, computers and well-test-interpretation software for performing well-test-analysis calculations because engineers, students, and professionals alike seem to accept that because the tools they use display eight decimal places, all eight places are accurate. Consequently, distances to boundaries often are reported with a resolution of tenths of a foot, skin values are reported with two decimal digits, and permeabilities greater than 100 md are reported to within 0.1 md (i.e., with resolutions finer than 0.1%).
It has been pointed out that the results of a well-test interpretation could never be more accurate than the values of applicable rock and fluid properties. An interactive, graphical method can describe the objective-function (a measure of the difference between model and data) behavior around the optimal solution to provide the interpreter with a range of solutions instead of a single value. The main objective of this paper is to provide uncertainty ranges derived from several tests in different reservoirs.

Method
This method uses four steps. It provides the uncertainty in well-test results associated with a specific match to a specific model as well as uncertainties in well- and reservoir-input parameters and in the match parameters. The uncertainty associated with the choice of model (which could imply a much larger uncertainty in results) is not taken into account.

Step 1 (Fig. 1): Well-Test Analysis.
The analysis yields values of match parameters [e.g., pressure match; time match; curve match, (CDe2s)match; and distance to the fault, dD] and a measure of the match quality expressed as a standard deviation. The equations defining the match parameters are expressed in terms of well- and reservoir-input data [i.e., flow rate, formation volume factor (FVF); viscosity; total compressibility; reservoir thickness, h; porosity; and wellbore radius] and they provide the analysis results (e.g., permeability-thickness product, kh; permeability, k; skin effect, S; wellbore-storage coefficient, C; and distance to the boundary, d).