Confidence Limits of Reservoir Parameters By Material Balance

Abstract Material balance methods of determining reservoir parameters such as the original oil in place are sensitive to uncertainties in the input data. Traditionally, regression techniques have been used to determine the "best-fit" values of the reservoir parameters and these have been used as a good representation of the "true" values. The effect of errors in the reservoir pressure measurements on the Havlena-Odeh4 method are examined using a gas cap drive reservoir as an example. The errors in the measured pressures are estimated from the available data. These errors are propagated through the calculations and show that the resulting error bars vary with the size of the relative pressure drop. Weighted linear regression is used to determine both the best fit values and the standard deviation, which serves as a measure of the statistical confidence limits. An alternative approach using the material balance method is to calculate the expected pressures from a model and vary the parameters of the model until the pressures match the observed pressures. Minimization of a suitable objective function by non-linear regression provides the best estimates of the reservoir parameters and the confidence limit contours can be derived. These are then used to draw correct inferences from the results - in the example, the possible communication between two oil pools is investigated. The 95% confidence limits are found to cover a wide range in the OOIP and gas cap fraction, thus the "best fit" has limited usefulness. The confidence limits can be used to compare the results of volumetric calculations and to restrict the range of variables used in subsequent reservoir studies.- e.g., numerical simulation. The methods outlined in this paper are general and are not limited to two parameters thus they can be used for any material balance problem. Introduction Material balance is one of the fundamental tools of reservoir engineering.In essence, measurements of the pressure changes in a reservoir as fluids are withdrawn are used to derive the reservoir parameters such as OOIP, gas cap fraction and the water influx characteristics. The significant effect of errors in the data on the derived parameters, such as the OOIP, gas cap fraction and aquifer characteristics was recognized early in the development of the subject, and the equation has been examined by numerous authors1,5. Random errors are present in all the input parameters: the average reservoir pressure at any time, the total withdrawals from the reservoir and the PVT properties of the reservoir fluids. Usually, errors in reservoir pressure are the most significant, and only these will be addressed in this paper. Systematic errors (as opposed to random) are also present. These arise from numerous sources e.g., the PVT data not representing the reservoir fluids accurately, a single pressure not representing the reservoir (due to lack of continuity). These will not be discussed in this work, although corrections applied for reservoir pressures in the field example are an example of reducing a set of systematic errors arising from insufficient shut-in time. In this paper a general method for assessing the uncertainties is described.