Production Data Analysis by Machine Learning

In this dissertation, I will present my research work on two different topics. The first topic is production data analysis of low-permeability well. The second topic is a quantitative evaluation of key completion controls on shale oil production. In Topic 1, I propose and investigate two novel methodologies that can be applied to improve the results of low-permeability well decline curve analysis. Specifically, I first proposed an iterative two-stage optimization algorithm for decline curve parameter estimation on the basis of two-segment hyperbolic model. This algorithm can be applied to find optimal parameter results from the production history data. By making use of a useful relation that exits between material balance time (MBT) and the original production profile, we propose a three-step diagnostic approach for the preliminary analysis of production history data, which can effectively assist us in identifying fluid flow regimes and increase our confidence in the estimation of decline curve parameters. The second approach is a data-driven method for primary phase production forecasting. Functional principal component analysis (fPCA) is applied to extract key features of production decline patterns on basis of multiple wells with sufficiently long production histories. A predictive model is then built using principal component functions obtained from the training production data set. Finally, we make predictions for the test wells to assess the quality of prediction with reference to true production data. Both methods are validated using field data and the accuracy of production forecasts gives us confidence in the new approaches. In Topic 2, generalized additive model (GAM) is applied to investigate possibly nonlinear associations between production and key completion parameters (e.g., completed lateral length, proppant volume per stage, fluid volume per stage) while accounting for the influence of different geological environments on hydrocarbon production. The geological cofounding effect is treated as a random clustered effect and incorporated in the GAM model by means of a state-of-the-art statistical machine learning method graphic fused LASSO. We provide several key findings on the relation between completion parameters and hydrocarbon production, which provide guidance in the development of efficient completion practices

Production Data Analysis by Machine Learning

In this dissertation, I will present my research work on two different topics. The first topic is production data analysis of low-permeability well. The second topic is a quantitative evaluation of key completion controls on shale oil production. In Topic 1, I propose and investigate two novel methodologies that can be applied to improve the results of low-permeability well decline curve analysis. Specifically, I first proposed an iterative two-stage optimization algorithm for decline curve parameter estimation on the basis of two-segment hyperbolic model. This algorithm can be applied to find optimal parameter results from the production history data. By making use of a useful relation that exits between material balance time (MBT) and the original production profile, we propose a three-step diagnostic approach for the preliminary analysis of production history data, which can effectively assist us in identifying fluid flow regimes and increase our confidence in the estimation of decline curve parameters. The second approach is a data-driven method for primary phase production forecasting. Functional principal component analysis (fPCA) is applied to extract key features of production decline patterns on basis of multiple wells with sufficiently long production histories. A predictive model is then built using principal component functions obtained from the training production data set. Finally, we make predictions for the test wells to assess the quality of prediction with reference to true production data. Both methods are validated using field data and the accuracy of production forecasts gives us confidence in the new approaches. In Topic 2, generalized additive model (GAM) is applied to investigate possibly nonlinear associations between production and key completion parameters (e.g., completed lateral length, proppant volume per stage, fluid volume per stage) while accounting for the influence of different geological environments on hydrocarbon production. The geological cofounding effect is treated as a random clustered effect and incorporated in the GAM model by means of a state-of-the-art statistical machine learning method graphic fused LASSO. We provide several key findings on the relation between completion parameters and hydrocarbon production, which provide guidance in the development of efficient completion practices

Representing complex data using localized principal components with application to astronomical data

Often the relation between the variables constituting a multivariate data space might be characterized by one or more of the terms: ``nonlinear'', ``branched'', ``disconnected'', ``bended'', ``curved'', ``heterogeneous'', or, more general, ``complex''. In these cases, simple principal component analysis (PCA) as a tool for dimension reduction can fail badly. Of the many alternative approaches proposed so far, local approximations of PCA are among the most promising. This paper will give a short review of localized versions of PCA, focusing on local principal curves and local partitioning algorithms. Furthermore we discuss projections other than the local principal components. When performing local dimension reduction for regression or classification problems it is important to focus not only on the manifold structure of the covariates, but also on the response variable(s). Local principal components only achieve the former, whereas localized regression approaches concentrate on the latter. Local projection directions derived from the partial least squares (PLS) algorithm offer an interesting trade-off between these two objectives. We apply these methods to several real data sets. In particular, we consider simulated astrophysical data from the future Galactic survey mission Gaia.Comment: 25 pages. In "Principal Manifolds for Data Visualization and Dimension Reduction", A. Gorban, B. Kegl, D. Wunsch, and A. Zinovyev (eds), Lecture Notes in Computational Science and Engineering, Springer, 2007, pp. 180--204, http://www.springer.com/dal/home/generic/search/results?SGWID=1-40109-22-173750210-

Another look at principal curves and surfaces

© . This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/Principal curves have been defined as smooth curves passing through the “middle” of a multidimensional data set. They are nonlinear generalizations of the first principal component, a characterization of which is the basis of the definition of principal curves. We establish a new characterization of the first principal component and base our new definition of a principal curve on this property. We introduce the notion of principal oriented points and we prove the existence of principal curves passing through these points. We extend the definition of principal curves to multivariate data sets and propose an algorithm to find them. The new notions lead us to generalize the definition of total variance. Successive principal curves are recursively defined from this generalization. The new methods are illustrated on simulated and real data sets.Peer ReviewedPostprint (author's final draft

Principal arc analysis on direct product manifolds

We propose a new approach to analyze data that naturally lie on manifolds. We focus on a special class of manifolds, called direct product manifolds, whose intrinsic dimension could be very high. Our method finds a low-dimensional representation of the manifold that can be used to find and visualize the principal modes of variation of the data, as Principal Component Analysis (PCA) does in linear spaces. The proposed method improves upon earlier manifold extensions of PCA by more concisely capturing important nonlinear modes. For the special case of data on a sphere, variation following nongeodesic arcs is captured in a single mode, compared to the two modes needed by previous methods. Several computational and statistical challenges are resolved. The development on spheres forms the basis of principal arc analysis on more complicated manifolds. The benefits of the method are illustrated by a data example using medial representations in image analysis.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS370 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org