Abstract:

The continuous record of pressure, temperature, and sometimes flow rate by Permanent Downhole Gauges (PDGs) contains rich information about the reservoir. Due to the different conditions where data are collected, PDG data have unique characteristics that require different interpretation approaches than conventional well testing. One of the machine learning approaches developed earlier was the convolution-kernel-based data mining (Liu and Horne, 2013a, 2013b). The method was shown to be promising for pressure-rate deconvolution on noisy data. However, the bottlenecks of computation efficiency and incomplete recovery of reservoir behaviors limit the application of the convolution kernel method to interpret real PDG data. In this work, two classes of methods were applied for PDG data interpretation. One was the machine learning approach with feature handcrafting based on physics, the other was the deep learning approach by using recurrent neural networks to learn on raw PDG measurements. Both approaches were shown effective to extract the patterns containing the reservoir information from PDG data. The extracted patterns were demonstrated to be useful in three ways: one was deconvolution by predicting the pressure corresponding to a constant rate history; the other two were to predict pressure in the future with given rate control, and vice versa. Three feature-based machine learning techniques were explored to interpret PDG data, namely, the linear approach, the kernel method, and kernel ridge regression. First the linear approach was proved to learn with the same features as the previous convolution kernel method, while it required much lower computational cost. The linear approach was used further for pressure-rate deconvolution and it outperformed two conventional deconvolution methods when noise or outliers were contained in the data. Next the kernel method and kernel ridge regression were utilized to adjust the machine learning model capability and to model the pressure behaviors covering early-transient until late-transient periods. Additional machine learning models were developed for the problems of rate reconstruction and multiwell testing, by handcrafting new set of features. Recurrent neural networks were investigated for PDG data interpretation with a focus on nonlinear autoregressive exogenous models (NARX). It was shown that NARX learned the patterns behind PDG time series data with its uniquer recurrent architecture, by feeding the memory of previous computations back into the model. NARX was also applied for pressure-rate deconvolution and it identified different reservoir models successfully. One key advantage of NARX is that it learns on raw data, although thought and effort are needed to tune the neural network. A case study on temperature transient analysis demonstrated NARX`s advantage over feature-based machine learning when feature handcrafting was difficult because of limited knowledge of the physics.

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