# Reservoir description via statistical and machine-learning approaches

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Description of subsurface reservoirs is important for decision-making in the development of hydrocarbon resources. Reservoir description concerns (1) geophysical interpretation: prediction of rock properties from geophysical measurements such as borehole and seismic amplitude data, and (2) reservoir modeling: modeling of the spatial distribution of rock properties conditioned by geophysical interpretations (geological modeling), and simulation of fluid-transport, elastic, mechanical, and electromagnetic phenomena, among others, taking place in a geological model (reservoir simulation). Reservoir description based on stochastic reservoir modeling and conditioned by fluid production history enables uncertainty estimation for hydrocarbon reserves and fluid production forecast. Accurate reservoir description assists the management of risk and profit during the exploration and development of hydrocarbon production resources.
As one of the most important components of reservoir description, the interpretation of well logs provides high-resolution estimations of in situ rock properties around the wellbore, such as lithology, porosity, fluid saturation, permeability, and elastic moduli. However, conventional petrophysical models are often too simplistic to reproduce the complex relationship between well logs and rock properties, especially permeability. Therefore, data-driven inferential methods, such as machine learning modeling, are needed for more accurate permeability prediction in spatially complex rocks. The accurate prediction of permeability across multiple wells is even more challenging because of variable borehole environmental conditions (e.g., drilling fluid and borehole size), different logging instruments (e.g., induction vs. lateral resistivity logs), and their vintage (e.g., logging-while-drilling vs. wireline logs). To mitigate biases introduced by both variable borehole environmental conditions and borehole instruments, well-log normalization is commonly implemented prior to performing multi-well interpretation projects. However, conventional well-log normalization methods ignore the correlation among different well logs and require much effort and expertise by the interpreter.
The first objective of this dissertation is to develop a data-driven interpretation workflow that uses machine-learning methods to perform automatic well-log normalization by considering the correlation among different well logs and to accurately estimate permeability from the normalized well logs. The workflow consists of four steps: (1) identifying well-calibrated wells (type wells) for the wells that need correction (test wells), based on the statistical distance of the associated well logs. (2) Obtaining training data from type wells to train the machine-learning model to minimize the mean-squared error (MSE) of permeability prediction. (3) Performing well-log normalization for the test well logs by minimizing the divergence to the type-well well logs. (4) Predicting the permeability of test wells using normalized well logs.
The new interpretation workflow is applied to predict the permeability of 30 wells in the Seminole San Andres Unit (SSAU). Compared to the permeability prediction model without well-log normalization, the new workflow decreases the mean-squared error (MSE) of permeability prediction by 20-50% and greatly accelerates well-log preprocessing with the automatic well-log normalization step.
Stochastic reservoir models conditioned by petrophysical and geophysical interpretations are important for uncertainty management during reservoir exploration and development. Conventional geostatistical methods, such as Kriging and multiple-point simulation, are commonly used for conditional reservoir modeling. However, it is difficult to use these methods to construct reservoir models that reproduce long-range geological patterns that are important for fluid-transport prediction, such as the continuity of channels in a turbidite channel sedimentary system.
The second objective of this dissertation is to develop a new machine learning method to construct stochastic reservoir models that reproduce important long-range patterns and are conditioned by the interpretation of well logs and seismic amplitude data. This method consists of three steps: (1) calculating training images of a depositional system, such as a turbidite channel or a deepwater lobe system, with rule-based modeling methods. (2) Training a new conditional generative adversarial model, referred to as the stochastic pix2pix model, to generate reservoir model realizations that reproduce patterns in the training images and are conditioned by well logs and seismic amplitude data. (3) Using the trained model to generate conditional reservoir model realizations. However, limitations on computer memory make it difficult for the new method to generate reservoir model realizations with over millions of voxels, such as models with multi-scale architectural elements. To further improve the computational efficiency to generate large and detailed reservoir models, a hierarchical modeling workflow is developed which uses the stochastic pix2pix model to simulate architectural elements from the largest to the smallest scale.

The stochastic pix2pix method is verified by comparing the generated lobe and fluvial channel model realizations to reservoir models constructed with the rule-based modeling method. Comparisons indicate that conditioning data, such as rock facies interpreted from well logs and depositional surfaces identified from seismic amplitude data, are well reproduced in model realizations generated with the new method. Statistical metrics, such as semi-variogram, multiple-point histogram (MPH), compensational stacking index, geometrical probability map, and rock facies histogram were calculated to confirm that model realizations accurately reproduce the patterns observed in the training images. Metrics of performance indicate a good reproduction of patterns, for example, the mean-absolute error of geometrical probability is below 2%, while the MPH difference is below 5%.
The combination of well-log normalization and interpretation workflow with machine learning-based stochastic reservoir modeling enables more accurate formation evaluation and better estimates of uncertainties associated with rock property distributions than possible with standard modeling approaches.