Download or read book Accelerating Oil water Subsurface Flow Simulation Through Reduced order Modeling and Advances in Nonlinear Analysis written by Rui Jiang and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Reservoir simulation is an important tool for understanding and predicting subsurface flow and reservoir performance. In applications such as production optimization and history matching, thousands of simulation runs may be required. Therefore, proxy methods that can provide approximate solutions in much shorter times can be very useful. Reduced-order modeling (ROM) methods are a particular type of proxy procedure that entail a reduction of the number of unknown variables in the nonlinear equations. This dissertation focuses on two of the most promising proper orthogonal decomposition (POD)-based ROM methods, POD-TPWL and POD-DEIM. A separate (non-ROM) technique to accelerate nonlinear convergence for oil-water problems is presented in the appendix.

Download or read book Confessio de sancta trinitate contra eos qui ecclesias minoris Poloniae Arrianismi et pluralitatis Deorum accusant written by and published by . This book was released on 1562 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Reduced order Modeling for Oil water and Compositional Systems with Application to Data Assimilation and Production Optimization written by Jincong He and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Reservoir simulation of realistic systems can be computationally demanding because of the large number of system unknowns and the intrinsic nonlinearity of typical problems. Compositional simulation, in which multiple components and complex phase behavior are present, can be particularly challenging. The high computational cost of reservoir simulation represents a substantial issue for applications such as production optimization and history matching, in which hundreds or thousands of simulation runs must be performed. Reduced-order modeling represents a promising approach for accelerating the simulations required for these important applications. In this work, we focus on the development and application of a reduced-order modeling technique called POD-TPWL, which combines trajectory piecewise linearization (TPWL) and proper orthogonal decomposition (POD) to provide highly efficient surrogate models. The POD-TPWL method expresses new solutions in terms of linearizations around states generated (and saved) during previously simulated "training" runs. High-dimensional states (e.g., pressure and saturation in every grid block in an oil-water problem) are projected optimally into a low-dimensional subspace using POD. We first consider the application of POD-TPWL for data assimilation (or history matching) in oil-water systems. The POD-TPWL model developed for this application represents simulation results for new geological realizations in terms of a linearization around training cases. Geological models are expressed in reduced terms using a Karhunen-Loeve expansion of the log-transmissibility field. Thus, both the reservoir states (represented using POD) and geological parameters are described very concisely. The reduced-order representation of flow and geology is appropriate for use with ensemble-based data assimilation procedures, and here it is incorporated into an ensemble Kalman filter (EnKF) framework to enrich the ensemble at relatively low cost. The method is able to reconstruct full-order states, which are required by EnKF, whenever necessary. The combined technique enables EnKF to be applied using many fewer high-fidelity reservoir simulations than would otherwise be required to avoid ensemble collapse. For two and three-dimensional example cases, EnKF results using 50 high-fidelity simulations along with 150 POD-TPWL simulations are shown to be much better than those using only 50 high-fidelity simulations (for which ensemble collapse is observed) and are, in fact, generally comparable to the results achieved using 200 high-fidelity simulations. We next develop a POD-TPWL methodology for oil-gas compositional systems. This model is based on the molar formulation in Stanford's General Purpose Research Simulator with Automatic Differentiation, AD-GPRS, which uses pressure and overall component mole fractions as the primary unknowns. Several new features, including the application of a Petrov-Galerkin projection to reduce the number of equations (rather than the Galerkin projection, which was used previously), and a new procedure for determining which saved state to use for linearization, are incorporated into the method. Results are presented for heterogeneous three-dimensional reservoir models with up to six hydrocarbon components. Reasonably close agreement between full-order reference solutions and compositional POD-TPWL simulations is demonstrated for the cases considered. Construction of the POD-TPWL model requires preprocessing overhead computations equivalent to about three to four full-order runs. Runtime speedups using POD-TPWL are, however, very significant -- about a factor of 500-800 for the cases considered. The POD-TPWL model is thus well suited for use in computational optimization, in which many simulations must be performed, and we present examples demonstrating its application for such problems. Finally, we investigate the accuracy and stability of different constraint reduction treatments for POD-TPWL models. Following an error analysis of the general POD-TPWL representation, two projection methods, namely Galerkin projection and Petrov-Galerkin projection, are derived by minimizing the constraint reduction error under different norms. These projection methods are assessed computationally for oil-water and compositional systems. For oil-water systems, Galerkin projection combined with a stabilization procedure is generally more accurate than Petrov-Galerkin projection, though even with this stabilization Galerkin projection is not guaranteed to be stable at all time steps. For compositional systems, the POD-TPWL model with Galerkin projection exhibits poor stability, while Petrov-Galerkin provides a consistently stable and robust POD-TPWL model. A hybrid procedure for oil-water systems, which applies different projections at different time steps to achieve both accuracy and stability, is presented. Two other constraint reduction methods, referred to as inverse projection and weighted inverse projection, are also formulated and tested. These approaches are computationally more expensive but do offer some theoretical advantages, and may be useful in realistic problems following further development.

Download or read book Subsurface Flow Management and Real time Production Optimization Using Model Predictive Control written by Thomas Jai Lopez and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the key challenges in the Oil & Gas industry is to best manage reservoirs under different conditions, constrained by production rates based on various economic scenarios, in order to meet energy demands and maximize profit. To address the energy demand challenges, a transformation in the paradigm of the utilization of "real-time" data has to be brought to bear, as one changes from a static decision making to a dynamical and data-driven management of production in conjunction with real-time risk assessment. The use of modern methods of computational modeling and simulation may be the only means to account for the two major tasks involved in this paradigm shift: (1) large-scale computations; and (2) efficient utilization of the deluge of data streams. Recently, history matching and optimization were brought together in the oil industry into an integrated and more structured approach called optimal closed-loop reservoir management. Closed-loop control algorithms have already been applied extensively in other engineering fields, including aerospace, mechanical, electrical and chemical engineering. However, their applications to porous media flow, such as - in the current practices and improvements in oil and gas recovery, in aquifer management, in bio-landfill optimization, and in CO2 sequestration have been minimal due to the large-scale nature of existing problems that generate complex models for controller design and real-time implementation. Their applicability to a realistic field is also an open topic because of the large-scale nature of existing problems that generate complex models for controller design and real-time implementation, hindering its applicability. Basically, three sources of high-dimensionality can be identified from the underlying reservoir models: size of parameter space, size of state space, and the number of scenarios or realizations necessary to account for uncertainty. In this paper we will address type problem of high dimensionality by focusing on the mitigation of the size of the state-space models by means of model-order reduction techniques in a systems framework. We will show how one can obtain accurate reduced order models which are amenable to fast implementations in the closed-loop framework .The research will focus on System Identification (System-ID) (Jansen, 2009) and Model Predictive Control (MPC) (Gildin, 2008) to serve this purpose. A mathematical treatment of System-ID and MPC as applied to reservoir simulation will be presented. Linear MPC would be studied on two specific reservoir models after generating low-order reservoir models using System-ID methods. All the comparisons are provided from a set of realistic simulations using the commercial reservoir simulator called Eclipse. With the improvements in oil recovery and reductions in water production effectively for both the cases that were considered, we could reinforce our stance in proposing the implementation of MPC and System-ID towards the ultimate goal of "real-time" production optimization.

Download or read book New Techniques for Reduced order Modeling in Reservoir Simulation written by Zhaoyang Jin and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Reservoir simulation is widely applied for the management of oil and gas production and CO2 storage operations. It can be computationally expensive, however, particularly when the flow physics is complicated and many simulation runs must be performed. This has motivated the development of reduced-order modeling (ROM) procedures, where the goal is to achieve high degrees of computational speedup along with reasonable solution accuracy. In this work we develop and apply two types of ROM methods -- one based on proper orthogonal decomposition (POD) and piecewise linearization, and one based on deep learning. We first develop a POD-based ROM, referred to as POD-TPWL, to simulate coupled flow-geomechanics problems. In POD-TPWL, proper orthogonal decomposition, which enables the representation of solution unknowns in a low-dimensional subspace, is combined with trajectory piecewise linearization (TPWL), where solutions with new sets of well controls are represented via linearization around previously simulated (training) solutions. The over-determined system of equations is projected into the low-dimensional subspace using a least-squares Petrov-Galerkin procedure. The states and derivative matrices required by POD-TPWL, generated by an extended version of Stanford's Automatic-Differentiation-based General Purpose Research Simulator, are provided in an offline (pre-processing or training) step. Offline computational requirements correspond to the equivalent of 5-8 full-order simulations, depending on the number of training runs used. Runtime (online) speedups of O(100) or more are achieved for new POD-TPWL test-case simulations. The POD-TPWL model is tested extensively for a 2D coupled problem involving oil-water flow and geomechanics. It is shown that POD-TPWL provides predictions of reasonable accuracy, relative to full-order simulations, for well-rate quantities, global pressure and saturation fields, global maximum and minimum principal stress fields, and the Mohr-Coulomb rock failure criterion, for the cases considered. A systematic study of POD-TPWL error is conducted using various training procedures for different levels of perturbation between test and training cases. The use of randomness in the well bottom-hole pressure profiles used in training is shown to be beneficial in terms of POD-TPWL solution accuracy. The procedure is also successfully applied to a prototype 3D example case. We next apply the POD-TPWL reduced-order modeling framework to simulate and optimize the injection stage of CO2 storage operations. The use of multiple derivatives, meaning that the linearizations are performed around different training solutions at different time steps, is described and assessed. Two example cases are presented, and the ability of the POD-TPWL model to accurately capture bottom-hole pressure, when time-varying CO2 injection rates are prescribed, is demonstrated. It is also shown that, for these examples, the reduced-order models can provide accurate estimates of CO2 molar fraction at particular locations in the domain. The POD-TPWL model is then incorporated into a mesh adaptive direct search optimization framework where the objective is to minimize the amount of CO2 reaching a target layer at the end of the injection period. The POD-TPWL model is shown to be well suited for this purpose and to provide optimization results that are comparable to those obtained using full-order simulations. POD-TPWL preprocessing computations entail a (serial) time equivalent of about 6.7 full-order simulations, though the resulting runtime speedups, relative to full-order simulation, are about 100--150 for the cases considered. Finally, we develop a new deep-learning-based ROM for reservoir simulation. The reduced-order model is based on an existing embed-to-control (E2C) framework and includes an auto-encoder, which projects the system to a low-dimensional subspace, and a linear transition model, which approximates the evolution of the system states in low dimension. In addition to the loss function for data mismatch considered in the original E2C framework, we introduce a physics-based loss function that penalizes predictions that are inconsistent with the governing flow equations. The loss function is also modified to emphasize accuracy in key well quantities of interest (e.g., fluid production rates). The E2C ROM is shown to have interesting parallels with POD-TPWL. The new ROM is applied to oil-water flow in a 2D heterogeneous reservoir. A total of 300 high-fidelity training simulations are performed in the offline stage, and the network training requires 10-12~minutes on a Tesla V100 GPU node. Online (runtime) computations achieve speedups of O(1000) relative to full-order simulations. Extensive test case results, with well controls varied over large ranges, are presented. Accurate ROM predictions are achieved for global saturation and pressure fields at particular times, and for injection and production well responses as a function of time. Error is shown to increase when 100 or 200 (rather than 300) training runs are used to construct the E2C ROM.

Download or read book An Introduction to Reservoir Simulation Using MATLAB GNU Octave written by Knut-Andreas Lie and published by Cambridge University Press. This book was released on 2019-08-08 with total page 677 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents numerical methods for reservoir simulation, with efficient implementation and examples using widely-used online open-source code, for researchers, professionals and advanced students. This title is also available as Open Access on Cambridge Core.

Download or read book Computational Methods for Multiphase Flows in Porous Media written by Zhangxin Chen and published by SIAM. This book was released on 2006-04-01 with total page 551 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a fundamental and practical introduction to the use of computational methods. A thorough discussion of practical aspects of the subject is presented in a consistent manner, and the level of treatment is rigorous without being unnecessarily abstract. Each chapter ends with bibliographic information and exercises.

Download or read book Introduction to Derivative Free Optimization written by Andrew R. Conn and published by SIAM. This book was released on 2009-04-16 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first contemporary comprehensive treatment of optimization without derivatives. This text explains how sampling and model techniques are used in derivative-free methods and how they are designed to solve optimization problems. It is designed to be readily accessible to both researchers and those with a modest background in computational mathematics.

Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1985 with total page 1346 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Reservoir Characterization written by Larry Lake and published by Elsevier. This book was released on 2012-12-02 with total page 680 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book The Mathematics of Reservoir Simulation written by Richard E. Ewing and published by SIAM. This book was released on 2014-12-01 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes the state of the art of the mathematical theory and numerical analysis of imaging. Some of the applications covered in the book include computerized tomography, magnetic resonance imaging, emission tomography, electron microscopy, ultrasound transmission tomography, industrial tomography, seismic tomography, impedance tomography, and NIR imaging.

Download or read book Data Analytics in Reservoir Engineering written by Sathish Sankaran and published by . This book was released on 2020-10-29 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: Data Analytics in Reservoir Engineering describes the relevance of data analytics for the oil and gas industry, with particular emphasis on reservoir engineering.

Download or read book Advanced Modeling with the MATLAB Reservoir Simulation Toolbox written by Knut-Andreas Lie and published by Cambridge University Press. This book was released on 2021-11-25 with total page 625 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many leading experts contribute to this follow-up to An Introduction to Reservoir Simulation using MATLAB/GNU Octave: User Guide for the MATLAB Reservoir Simulation Toolbox (MRST). It introduces more advanced functionality that has been recently added to the open-source MRST software. It is however a self-contained introduction to a variety of modern numerical methods for simulating multiphase flow in porous media, with applications to geothermal energy, chemical enhanced oil recovery (EOR), flow in fractured and unconventional reservoirs, and in the unsaturated zone. The reader will learn how to implement new models and algorithms in a robust, efficient manner. A large number of numerical examples are included, all fully equipped with code and data so that the reader can reproduce the results and use them as a starting point for their own work. Like the original textbook, this book will prove invaluable for researchers, professionals and advanced students using reservoir simulation methods. This title is available as Open Access on Cambridge Core.

Download or read book Applied Mechanics Reviews written by and published by . This book was released on 1987 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Petroleum Abstracts Literature and Patents written by and published by . This book was released on 1987 with total page 1348 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Hydrogeophysics written by Yorum Rubin and published by Springer Science & Business Media. This book was released on 2006-05-06 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt: This ground-breaking work is the first to cover the fundamentals of hydrogeophysics from both the hydrogeological and geophysical perspectives. Authored by leading experts and expert groups, the book starts out by explaining the fundamentals of hydrological characterization, with focus on hydrological data acquisition and measurement analysis as well as geostatistical approaches. The fundamentals of geophysical characterization are then at length, including the geophysical techniques that are often used for hydrogeological characterization. Unlike other books, the geophysical methods and petrophysical discussions presented here emphasize the theory, assumptions, approaches, and interpretations that are particularly important for hydrogeological applications. A series of hydrogeophysical case studies illustrate hydrogeophysical approaches for mapping hydrological units, estimation of hydrogeological parameters, and monitoring of hydrogeological processes. Finally, the book concludes with hydrogeophysical frontiers, i.e. on emerging technologies and stochastic hydrogeophysical inversion approaches.

Download or read book Produced Water written by Kenneth Lee and published by Springer Science & Business Media. This book was released on 2011-09-18 with total page 601 pages. Available in PDF, EPUB and Kindle. Book excerpt: A state-of-the-art review of scientific knowledge on the environmental risk of ocean discharge of produced water and advances in mitigation technologies. In offshore oil and gas operations, produced water (the water produced with oil or gas from a well) accounts for the largest waste stream (in terms of volume discharged). Its discharge is continuous during oil and gas production and typically increases in volume over the lifetime of an offshore production platform. Produced water discharge as waste into the ocean has become an environmental concern because of its potential contaminant content. Environmental risk assessments of ocean discharge of produced water have yielded different results. For example, several laboratory and field studies have shown that significant acute toxic effects cannot be detected beyond the "point of discharge" due to rapid dilution in the receiving waters. However, there is some preliminary evidence of chronic sub-lethal impacts in biota associated with the discharge of produced water from oil and gas fields within the North Sea. As the composition and concentration of potential produced water contaminants may vary from one geologic formation to another, this conference also highlights the results of recent studies in Atlantic Canada.