In the analysis of a hydrocarbon production performance, empirical techniques have been applied over time; extrapolating the historical behavior of the observations under the assumption that the past, present and future continue under the same trend, not subject to interventions.
In order to extract the greatest amount of information from this time serie, this work applied the Box Jenkins and Reinsel methodology, to decompose its trend, into additional elements, such as seasonality and randomness, once the stationarity condition has been achieved. A model representing the 70.22% of the information was defined as SARIMA(0,1,1)(1,0,0)12. Its predictions were linear, unbiased, and of minimal variance, however, this model did not match the nature of the time serie, due to the fact that the regular component of the serie could not be modeled as autoregressive. In contrast, this was only modeled as a linear function of the actual and previous errors (p = 0 and q = 1), and the computed residuals were not normal.
Finally, the convenience of the use of geostatistical techniques was demonstrated. A forecast step comprised from 01/01/2008 to 12/01/2008, and considering that data was observed from January to July of that same year, these served as a comparison estimating an absolute average percentage error of the estimates (MAPE) of 5%. On the same way, this technique was applied to predict missing values from the internal structure of the time serie, along two seasonal cycles. Observations between 01/01/2001 and 12/01/2002 were removed from the total oil production historical data. Results showed a MAPE of 7.15%, not only demonstrating the efficiency of the geostatistical technique but also, that the methodology honored the seasonality and trend of the time serie. Errors were normal, identically distributed, and uncorrelated.
Audience take away:
- Faced with the accelerated and inevitable decline in fluid production, the Oil and Gas industry is interested in modeling the productive behavior of reservoirs. Therefore, numerical models are calibrated based on historical pressure and production data and the omission of any input data generates uncertainty in the results of their predictions.
- Given the absence of information in some periods of time, specifically in mature fields, the convenience of using geostatistical techniques, an area of petroleum engineering that has been little explored in the time domain, is proposed as an alternative for the prediction of missing data in the time series of the decline in production of fluids in the reservoir of an oil field.
- Results showed that the geostatistical estimation reproduces the trend and the seasonal component of the data that was not evidenced in the application of the conventional analysis methodology for time series.
- This research could be expanded considering new variogram types, to improve the accuracy of the predictions.