History Matching With Cumulative Production Data
- Ted A. Watson (Texas A & M U.) | Scott H. Lane (Texas A & M U.) | J. Michael Gatens III (S.A. Holditch and Assocs. Inc.)
- Document ID
- Society of Petroleum Engineers
- Journal of Petroleum Technology
- Publication Date
- January 1990
- Document Type
- Journal Paper
- 96 - 100
- 1990. Society of Petroleum Engineers
- 1.2.3 Rock properties, 5.5 Reservoir Simulation, 5.6.4 Drillstem/Well Testing, 5.8.6 Naturally Fractured Reservoir, 5.5.8 History Matching, 5.8.2 Shale Gas, 5.4.2 Gas Injection Methods
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A measurement-error model is formulated and an appropriate weighted-least-squares (WLS) performance index is developed for history matching with cumulative production data. This performance index provides more accurate estimates of the unknown reservoir properties than the usual ordinary-least-squares (OLS) performance index.
The use of numerical reservoir simulators to predict well performance is an important acid well-established process in reservoir engineering. The reliability of these predictions is limited by the accuracy with which the input reservoir properties are determined. The reservoir properties can be estimated by history matching measured pressure or production data, whereby parameters in a numerical reservoir simulator are adjusted so that the resulting calculated quantities m some sense match the measured data. These adjustments can be made with automatic history-matching algorithms.
Most automatic history-matching algorithms determine parameter estimates that minimize an OLS performance index given by the sum of squared differences between the measured data and the corresponding values calculated with the reservoir simulator. Knowledge of the data-measurement process, however, can be used to develop a WLS performance index that may provide more accurate estimates of the reservoir properties.
In this paper, we formulate a measurement-error model and develop a WLS performance index appropriate for history matching with cumulative production data. Residual analysis is introduced as a means for checking the validity of the measurement-error model, and two useful tests are presented for analyzing history-matching residuals.
Two key steps are involved in obtaining accurate estimates of reservoir properties from history matching measured pressure or production data. The first step is to select an appropriate reservoir model for describing the physical process. The reservoir model need not describe the process exactly, but it is desirable that the differences between measured and calculated quantities (for an appropriate set of reservoir parameters) be reasonably described as random error. (The problem of model selection is considered elsewhere I and is not discussed in detail here.) The second step is to estimate unknown parameters (i.e., reservoir rock properties) within the reservoir model by minimizing an appropriate performance index so that the resulting parameter estimates are, statistically, the best estimates for the unknown reservoir properties.
|File Size||333 KB||Number of Pages||5|