Time Series Analysis for Reservoir Zonation
- D.W. Bennion (U. Of Calgary)
- Document ID
- Society of Petroleum Engineers
- Journal of Petroleum Technology
- Publication Date
- September 1968
- Document Type
- Journal Paper
- 913 - 914
- 1968. Society of Petroleum Engineers
- 5.5 Reservoir Simulation
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- 157 since 2007
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A time series is a set of data of which each element is associated with a moment of time. In this report the elements of the set are denoted by x(t). If two time series are used, the second will be denoted by y(t). Well logs can be considered to be time series and can be analyzed using time series techniques. Methods for analyzing time series have been discussed by Weiner and Bendat and Piersol, and have been employed in geophysical studies. The cross-correlation function is used for two time series whose elements are x(t) and y(t). It is used to determine the dependence of the two series on each other. The cross-correlation function is given by the following equation:
Rsy = cross-correlation function for time series x(t) lagging y(t) by lag number r Ryx = cross-correlation function for times series y(t) lagging x(t) by lag number r N = number of data points in each time series r = lag number r = 0, 1, 2, . . . . m m = maximum lag number, usually 10 to 15 percent of N.
If each time series is normalized so that it has a mean of zero and a variance of one, the cross-correlation function will range from minus one to plus one. A perfect correlation between two time series yields the value plus one. Filtering is used to remove noise from time series and thus helps to increase the cross-correlation function. Many techniques to filter out noise have been proposed. For this report a simple smoothing method proposed by Healy and Bogert was used.
Si = smoothing data, i = I to F Xk = unsmoothed time series Wj = weighting series G = a given selection interger; for example, G=3 applies weight to every third item of the time series N = number of sample points in time series M = number of weights, must be odd k = j . G - G + r r = i - I + 1
F = N - .
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