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Theory-guided data science-based reservoir prediction of a North Sea oil field

Data science-based methods, such as supervised neural networks, provide powerful techniques to predict reservoir properties from seismic and well data without the aid of a theoretical model. In these supervised learning approaches, the seismic-to-rock property relationship is learned from the data. One of the major factors limiting the success of these methods is whether there exists enough labeled data, sampled over the expected geology, to train the neural network adequately. To overcome these issues, this paper explores hybrid theory-guided data science (TGDS)-based methods. In particular, we build a two-component model in which the outputs of the theory-based component are the inputs in the data science component. First, we simulate many pseudowells based on the well statistics in the project area. The reservoir properties, such as porosity, saturation, mineralogy, and thickness, are all varied to create a well-sampled data set. Elastic and synthetic seismic data are then generated using rock physics and seismic theory. The resulting collection of pseudowell logs and synthetic seismic data, called the synthetic catalog, is used to train the neural network. The derived operator is then applied to the real seismic data to predict reservoir properties throughout the seismic volume. This TGDS method is applied to a North Sea data set to characterize a Paleocene oil sand reservoir. The TGDS results better characterize the geology and well control, including a blind well, compared to a solely theory-based approach (deterministic inversion) and a data science-based approach (neural network using only the original wells). These results suggest that theory and data science can complement each other to improve reservoir characterization predictions. Introduction Machine learning algorithms employing neural networks have been used for some time in geophysics to quantitatively predict elastic and rock properties from seismic data (Hampson et al., 2001). These supervised learning techniques derive a statistical relationship between the log and seismic data at the well locations. This relationship is then applied to the seismic data to estimate the log properties at other locations in the seismic survey. The limiting factor in performing this analysis is that sufficient labeled data (i.e., well control) are needed to train and validate the relationship. More recent neural network architectures, such as deep neural networks (DNNs) (Goodfellow et al., 2016), have been adapted for geophysical reservoir characterization. Downton and Hampson (2018) use a DNN, while Zheng and Zhang (2018) and Das et al. (2019) use convolutional neural networks (CNNs) Jonathan E. Downton1, Olivia Collet2, Daniel P. Hampson1, and Tanya Colwell1 to predict elastic parameters. These networks place even greater demands on the amount of data necessary to perform the analysis. The image-recognition CNN of Krizhevsky et al. (2012) is trained using millions of labeled images. The training wells available in typical geophysical reservoir characterization projects number in the tens rather than millions. Halevy et al. (2009) show that increasing the amount of data is often more important than the choice of algorithm, which is why this paper focuses on how to deal with this lack of training data. Many different approaches have been taken to increase the amount of training data. K. Wang et al. (2019) perform a series of transformations on the labeled data to increase the amount available. Y. Wang et al. (2019) use a 1D cycle-consistent generative adversarial network to help stabilize the problem. Downton and Hampson (2018), Zheng and Zhang (2018), and Das et al. (2019) all generate synthetic data to increase the amount of training data. A number of important considerations determine whether there is enough training data. First, there needs to be sufficient data to calculate statistically reliable operators in the presence of noise. Second, in order to derive relationships that generalize satisfactorily, the well data need to sample the range of the expected geology for the project area. For example, to predict the fluid saturation, both hydrocarbonand brine-filled training examples are needed. If only brine-filled reservoir examples are available, an interpreter might perform fluid substitution and amplitude variation with offset (AVO) modeling to understand the seismic response to the other fluid. Other important variables such as the reservoir thickness, porosity, and mineralogy can also be varied to understand their responses. These all complicate the mapping between the seismic and the desired reservoir properties, often in a nonlinear and nonunique manner. In this way, rock physics and seismic theory can be used to create training data that span the range of the expected geology. This is the approach of Downton and Hampson (2018) and of this paper. Methods that solely transform the original labeled data or are based on the statistics of the original labeled data do not address this second consideration. This use of theory to generate training data within a data science methodology is a form of hybrid theory-guided data science (TGDS) (Karpatne et al., 2017) and hence is the terminology adopted by this paper. The theory component consists in using rock-physics relationships to simulate a large idealized set of pseudowell logs and AVO modeling to generate synthetic gathers, which we will refer to as the synthetic catalog (Dvorkin et al., 2014). This synthetic catalog, which contains both the target log 1CGG GeoSoftware, Calgary, Alberta, Canada. E-mail: jon.downton@cgg.com; dan.hampson@cgg.com; tanya.colwell@cgg.com. 2CGG GeoSoftware, Massy, France. E-mail: olivia.collet@cgg.com. https://doi.org/10.1190/tle39100742.1