Various uncertainty quantication methodologies are presented using a combination of several deterministic decline curve analysis models and two bootstrapping algorithms. The bootstrapping algorithms are the conventional bootstrapping method (CBM) and the modied bootstrapping method (MBM). The combined deterministic-stochastic combination models are applied to 126 sample wells from the Permian basin. Results are presented for 12 to 72 months of production hindcast given an average well production history of 120 months. Previous researchers used the Arps model and both conventional and modied bootstrapping with block re-sampling techniques to reliably quantify uncertainty in production forecasts. In this work, we applied both stochastic techniques to other decline curve analysis models|namely, the Duong and the Stretched Exponential Production Decline (SEPD) models. The algorithms were applied to sample wells spread across the three main sub-basins of the Permian. A description of how both the deterministic and stochastic methods can be combined is provided. Also, pseudo-codes that describes the methodologies applied in this work is provided to permit readers to replicate results if necessary. Based on the average forecast error plot in the Permian Basin for 126 active wells, we can also conclude that the MBM-Arps, CBM-Arps, and MBM-SEPD combinations produce P50 forecasts that match cumulative production best regardless of the sub-basin and amount of production hindcast used. Regardless of concerns about the coverage rate, the CBM-Arps, MBM-Arps, CBM-SEPD, and MBMSEPD algorithm combinations produce cumulative P50 predictions within 20% of the true cumulative production value using only a 24-month hindcast. With a 12 month-hindcast, the MBM-Arps combined model produced cumulative P50 predictions with a forecast error of approximately 20%. Also, the CBM-SEPD and MBM-SEPD models were within 30% of the true cumulative production using a 12- month hindcast. Another important result is that all the deterministic-stochastic method combinations studied under-predicted the true cumulative production to varying degrees. However, the CBM-Duong combination was found to severely under-predict cumulative production, especially for the 12-month hindcast. It is not a suitable model combination based on forecast error, especially when hindcast fractions on the low end of the spectrum are used. Accordingly, the CBM- Duong combination is not recommended, especially if production history of no more than 24 months is available for hindcasting. As expected, the coverage rate increased, and the forecast error decreased for all the algorithm combinations with increasing hindcast duration. The novelty of this work lies in its extension of the bootstrapping technique to other decline curve analysis models. The software developed can also be used to analyze many wells quickly on a standard engineering computer. This research is also important because realistic estimates of reserves can be estimated in plays like the Permian basin when uncertainty is correctly quantied.

A hallmark of unconventional reservoirs is characterization uncertainty. Assisted History Matching (AHM) methods provide attractive means for uncertainty quantification (UQ), because they yield an ensemble of qualifying models instead of a single candidate. Here we integrate embedded discrete fracture model (EDFM), one of fractured-reservoirs modeling techniques, with a commercial AHM and optimization tool. We develop a new parameterization scheme that allows for altering individual properties of multiple wells or fracture groups. The reservoir is divided into three types of regions: formation matrix; EDFM fracture groups; and stimulated rock volume (SRV) around fracture groups. The method is developed in a sleek, stand-alone form and is composed of four main steps: (1) reading parameters exported by tool; (2) generating an EDFM instance; (3) running the instance on a simulator; and (4) calculating a pre-defined objective function. We present two applications. First, we test the method on a hypothetical case with synthetic production data from two wells. Using 20 history-matching parameters, we compare the performance of five AHM algorithms. Two of which are based on Bayesian approach, two are stochastic particle-swarm optimization (PSO), and one is commercial DECE algorithm. Performance is measured with metrics, such as solutions sample size, total simulation runs, marginal parameter posterior distributions, and distributions of estimated ultimate recovery (EUR). In the second application, we assess the effect of natural fractures on UQ of a single horizontal well in the middle Bakken. This is achieved by comparing four AHM scenarios with increasingly varying natural-fracture intensity. Results of the first study show that, based on pre-set acceptance criteria, DECE fails to generate any satisfying solutions. Bayesian methods are noticeably superior to PSO, although PSO is capable to generate large number of solutions. PSO tends to be focused on narrow regions of the posteriors and seems to significantly underestimate uncertainty. Bayesian Algorithm I, a method with a proxy-based acceptance/rejection sampler, ranks first in efficiency but evidently underperforms in accuracy. Results from the second study reveal that, even though varying intensity of natural fractures cam significantly alter other model parameters, that appears not to have influence on UQ (or long-term production)

Reservoir Characterization is a collection of papers presented at the Reservoir Characterization Technical Conference, held at the Westin Hotel-Galleria in Dallas on April 29-May 1, 1985. Conference held April 29-May 1, 1985, at the Westin Hotel—Galleria in Dallas. The conference was sponsored by the National Institute for Petroleum and Energy Research, Bartlesville, Oklahoma. Reservoir characterization is a process for quantitatively assigning reservoir properties, recognizing geologic information and uncertainties in spatial variability. This book contains 19 chapters, and begins with the geological characterization of sandstone reservoir, followed by the geological prediction of shale distribution within the Prudhoe Bay field. The subsequent chapters are devoted to determination of reservoir properties, such as porosity, mineral occurrence, and permeability variation estimation. The discussion then shifts to the utility of a Bayesian-type formalism to delineate qualitative ""soft"" information and expert interpretation of reservoir description data. This topic is followed by papers concerning reservoir simulation, parameter assignment, and method of calculation of wetting phase relative permeability. This text also deals with the role of discontinuous vertical flow barriers in reservoir engineering. The last chapters focus on the effect of reservoir heterogeneity on oil reservoir. Petroleum engineers, scientists, and researchers will find this book of great value.

Statistical Rethinking: A Bayesian Course with Examples in R and Stan builds readers’ knowledge of and confidence in statistical modeling. Reflecting the need for even minor programming in today’s model-based statistics, the book pushes readers to perform step-by-step calculations that are usually automated. This unique computational approach ensures that readers understand enough of the details to make reasonable choices and interpretations in their own modeling work. The text presents generalized linear multilevel models from a Bayesian perspective, relying on a simple logical interpretation of Bayesian probability and maximum entropy. It covers from the basics of regression to multilevel models. The author also discusses measurement error, missing data, and Gaussian process models for spatial and network autocorrelation. By using complete R code examples throughout, this book provides a practical foundation for performing statistical inference. Designed for both PhD students and seasoned professionals in the natural and social sciences, it prepares them for more advanced or specialized statistical modeling. Web Resource The book is accompanied by an R package (rethinking) that is available on the author’s website and GitHub. The two core functions (map and map2stan) of this package allow a variety of statistical models to be constructed from standard model formulas.

The fundamental mathematical tools needed to understand machine learning include linear algebra, analytic geometry, matrix decompositions, vector calculus, optimization, probability and statistics. These topics are traditionally taught in disparate courses, making it hard for data science or computer science students, or professionals, to efficiently learn the mathematics. This self-contained textbook bridges the gap between mathematical and machine learning texts, introducing the mathematical concepts with a minimum of prerequisites. It uses these concepts to derive four central machine learning methods: linear regression, principal component analysis, Gaussian mixture models and support vector machines. For students and others with a mathematical background, these derivations provide a starting point to machine learning texts. For those learning the mathematics for the first time, the methods help build intuition and practical experience with applying mathematical concepts. Every chapter includes worked examples and exercises to test understanding. Programming tutorials are offered on the book's web site.

Rock masses are initially stressed in their current in situ state of stress and to a lesser natural state. Whether one is interested in the extent on the monitoring of stress change. formation of geological structures (folds, faults, The subject of paleostresses is only briefly intrusions, etc. ), the stability of artificial struc discussed. tures (tunnels, caverns, mines, surface excava The last 30 years have seen a major advance our knowledge and understanding of rock tions, etc. ), or the stability of boreholes, a in the in situ or virgin stress field, stress. A large body of data is now available on knowledge of along with other rock mass properties, is the state of stress in the near surface of the needed in order to predict the response of rock Earth's crust (upper 3-4km of the crust). masses to the disturbance associated with those Various theories have been proposed regarding structures. Stress in rock is usually described the origin of in situ stresses and how gravity, within the context of continuum mechanics. It is tectonics, erosion, lateral straining, rock fabric, defined at a point and is represented by a glaciation and deglaciation, topography, curva second-order Cartesian tensor with six compo ture of the Earth and other active geological nents. Because of its definition, rock stress is an features and processes contribute to the current enigmatic and fictitious quantity creating chal in situ stress field.

The process of user-centered innovation: how it can benefit both users and manufacturers and how its emergence will bring changes in business models and in public policy. Innovation is rapidly becoming democratized. Users, aided by improvements in computer and communications technology, increasingly can develop their own new products and services. These innovating users—both individuals and firms—often freely share their innovations with others, creating user-innovation communities and a rich intellectual commons. In Democratizing Innovation, Eric von Hippel looks closely at this emerging system of user-centered innovation. He explains why and when users find it profitable to develop new products and services for themselves, and why it often pays users to reveal their innovations freely for the use of all.The trend toward democratized innovation can be seen in software and information products—most notably in the free and open-source software movement—but also in physical products. Von Hippel's many examples of user innovation in action range from surgical equipment to surfboards to software security features. He shows that product and service development is concentrated among "lead users," who are ahead on marketplace trends and whose innovations are often commercially attractive. Von Hippel argues that manufacturers should redesign their innovation processes and that they should systematically seek out innovations developed by users. He points to businesses—the custom semiconductor industry is one example—that have learned to assist user-innovators by providing them with toolkits for developing new products. User innovation has a positive impact on social welfare, and von Hippel proposes that government policies, including R&D subsidies and tax credits, should be realigned to eliminate biases against it. The goal of a democratized user-centered innovation system, says von Hippel, is well worth striving for. An electronic version of this book is available under a Creative Commons license.