Applying Machine-Learning Techniques To Interpret Flow-Rate, Pressure, and Temperature Data From Permanent Downhole Gauges

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Summary Permanent downhole gauges (PDGs) provide a continuous record of pressure, temperature, and, sometimes, flow rate during well production. The continuous record provides rich information about the reservoir and makes PDG data a valuable source for reservoir analysis (e.g., pressure-rate deconvolution for reservoir-model identification). It has been shown in previous work that the convolution-kernel (CK) -based data-mining approach is a promising tool to interpret flow-rate and pressure data from PDGs. The CK method denoises and deconvolves the pressure signal successfully without an explicit-breakpoint detection. However, the bottlenecks of computational efficiency and the incomplete recovery of reservoir behaviors limit the application of the method to interpret real-PDG data. In this paper, three different machine-learning techniques were applied to flow-rate/pressure interpretation. We formulated the machine-learning techniques into a linear regression (LR) on parameters that connect the nonlinear flow-rate features with pressure targets. Such a formulation leads to a closed-form solution, which speeds up the computation dramatically. The machine-learning algorithms that were formulated using LR were shown to have the same learning quality as the CK method, and they outperformed it with much less computational effort. Next, the kernel method was applied to address the issue of the incomplete recovery of reservoir behaviors, because it efficiently expanded the dimension of the feature space without an explicit representation of the features, but it led to overfitting. Finally, kernel ridge regression (KRR) used the expanded features given by the kernel function to capture the more detailed reservoir behaviors, while controlling the prediction error using ridge regression (RR). It was shown that KRR recovers the full reservoir behaviors successfully (e.g., wellbore-storage effect, skin effect, infinite-acting radial flow, and boundary effect). Some potential uses of temperature data from PDGs are also discussed in this paper. Machine learning was shown to be able to model the temperature and pressure data recorded by PDGs, even if the actual physical model is complex. This originates from the fact that, by using features as an approximation of model characteristics, machine learning does not require a perfect knowledge of the physical model. The modeling of pressure using temperature data was extended to two promising applications: pressure-history reconstruction using temperature data, and the cointerpretation of temperature and pressure data when flow-rate data are not available.