The paper describes a method of analyzing data from permanent downhole gauges, even in the presence of noise, gaps and outliers. The data mining approach developed allows for the revelation of the underlying data signal, and as a useful corollary also achieves deconvolution to compute the reservoir model – even with the existence of significant noise in the data.
The convolution kernel was initially invented and applied in the domain of natural language machine learning. In the original linguistic study, the convolution kernel detected the relationship between words by decomposing words into parts, and evaluating the parts using a simple kernel function. The success of the convolution kernel method inspired us to apply it to data from permanent downhole gauges (PDG). In this study, the data mining process was conducted in two stages, namely learning and prediction processes. In the learning process, the PDG data that were decomposed into a series of pressure responses to the previous flow rate change events were used to train the convolution-kernel-based data mining algorithm until the convergence. After convergence, the reservoir model was obtained implicitly in the form of polynomials in the high-dimensional Hilbert space defined by the convolution kernel function. In the prediction process, a pressure prediction was made by the reservoir model (obtained in the learning process) to an arbitrary given flow rate history (usually a constant flow rate history for simplicity). This flow rate history and the corresponding pressure prediction revealed the reservoir model underlying the variable PDG data.
In the previous work, a series of synthetic cases and real field cases have been used to test this approach. The method recovered the reservoir model successfully in all cases. In this paper, the method was tested under problematic data situations, including the existence of significant outliers and aberrant segments, incomplete production history, and unknown initial pressure. The results suggested that: 1) the method tolerated a moderate level of outliers and aberrant segments without any preprocessing; 2) the method could reveal the reservoir model with effective rate correction when the production history was incomplete; 3) the method could reveal the reservoir model and discover the appropriate initial pressure by using an optimization on initial pressure value when the initial pressure was unknown.