Abstract:
The recording of pressure data by permanent downhole gauges (PDGs) is much like
the conventional well tests—in the sense that both of these record pressure response
in a well following a flow rate change. The bottleneck of handling PDG data is,
unlike conventional well tests, they include highly convoluted pressures reflecting unrestricted
fluctuations in a producing well. Moreover, these data are noisy, and large
in volume. These difficulties make the PDG data impossible to interpret by familiar
conventional analysis techniques. Some recent attempts looked at the problem from
a data mining point of view, which revealed the potential of this approach for interpreting
PDG data. Among them, a convolution-kernel-based data mining method
was relatively more successful. However, expensive computational cost, and some
inaccuracy and lack of interpretability in prediction leave room for improving the
approach.
Data mining is a nonparametric regression technique that involves two stages,
namely, training and prediction. During training, the available data are used to teach
the algorithm, and upon convergence it is expected to unveil the hidden pattern
in data. The trained algorithm then can be used for prediction. However, a mere
convergence does not always guarantee a useful correlation between the independent
input data and observations. In fact, the success of any kernelized data mining lies in
the combination of correct kernel function and appropriate feature selection. Because
of the aforementioned method’s relative success in variable flow-rate situations, it was
closely inspected to get an insight of the reasons behind its success. The investigation
led to three important observations. One, the same complex convolution kernel can
be computed using an alternatively formulated method based on the simplest linear
kernel. Two, in terms of prediction accuracy, a linear kernel performs better than
a polynomial kernel, and therefore should be preferred. Three, empirical nonlinear
features can have significant impact on a data mining method’s ability in capturing
pressure transient details. Following these observations, a total of 1275 new data mining methods were constructed in present work. A linear kernel was used in these
methods, and the feature vectors were constructed by combining some empirically
chosen nonlinear terms with the recognized dominant terms pertinent to common
reservoir behaviors. The quality of these methods was evaluated on 12 synthetic
cases that were carefully designed to mimic the most common real situations.
The basis of the quality measurement was simple, how a given method predicts
on new data that are totally different from the data it was trained with. Based
on the performance analysis, the best method was identified. This method clearly
outperforms the aforementioned convolution kernel method, and predictions made by
the method on all synthetic cases were very close to the true reservoir behavior—
which proves its ability in exploring underlying reservoir models. The method also
performed well on real data. Furthermore, the deployment of linear kernel decreases
the computational demand significantly.
