Spontaneous potential (SP) well-logging is one of the most common and useful well-logging techniques in petroleum exploitation. This monograph is the first of its kind on the mathematical model of spontaneous potential well-logging and its numerical solutions. The mathematical model established in this book shows the necessity of introducing Sobolev spaces with fractional power, which seriously increases the difficulty of proving the well-posedness and proposing numerical solution schemes. In this book, in the axisymmetric situation the well-posedness of the corresponding mathematical model is proved and three efficient schemes of numerical solution are proposed, supported by a number of numerical examples to meet practical computation needs.

Mathematically rigorous, computationally fast, and easy to use, this new approach to electromagnetic well logging gives the reservoir engineer a new dimension to MWD/LWD interpretation and tool design Almost all publications on borehole electromagnetics deal with idealizations that are not acceptable physically. On the other hand, “exact models” are only available through detailed finite element or finite difference analysis, and more often than not, simply describe case studies for special applications. In either case, the models are not available for general use and the value of the publications is questionable. This new approach provides a rigorous, fully three-dimensional solution to the general problem, developed over almost two decades by a researcher familiar with practical applications and mathematical modeling. Completely validated against exact solutions and physics-based checks through over a hundred documented examples, the self-contained model (with special built-in matrix solvers and iteration algorithms) with a “plain English graphical user interface” has been optimized to run extremely fast – seconds per run as opposed to minutes and hours – and then automatically presents all electric and magnetic field results through integrated three-dimensional color graphics. In addition to state-of-the-art algorithms, basic "utility programs" are also developed, such as simple dipole methods, Biot-Savart large diameter models, nonlinear phase and amplitude interpolation algorithms, and so on. Incredibly useful to oilfield practitioners, this volume is a must-have for serious professionals in the field, and all the algorithms have undergone a laborious validation process with real use in the field.

Venice-1 symposium on applied and industrial mathematics, 1989

Modeling of Resistivity and Acoustic Borehole Logging Measurements Using Finite Element Methods provides a comprehensive review of different resistivity and sonic logging instruments used within the oil industry, along with precise and solid mathematical descriptions of the physical equations and corresponding FE formulations that govern these measurements. Additionally, the book emphasizes the main modeling considerations that one needs to incorporate into the simulations in order to obtain reliable and accurate results. Essentially, the formulations and methods described here can also be applied to simulate on-surface geophysical measurements such as seismic or marine controlled-source electromagnetic (CSEM) measurements. Simulation results obtained using FE methods are superior. FE methods employ a mathematical terminology based on FE spaces that facilitate the design of sophisticated formulations and implementations according to the specifics of each problem. This mathematical FE framework provides a highly accurate, robust, and flexible unified environment for the solution of multi-physics problems. Thus, readers will benefit from this resource by learning how to make a variety of logging simulations using a unified FE framework. - Provides a complete and unified finite element approach to perform borehole sonic and electromagnetic simulations - Includes the latest research in mathematical and implementation content on Finite Element simulations of borehole logging measurements - Features a variety of unique simulations and numerical examples that allow the reader to easily learn the main features and limitations that appear when simulating borehole resistivity measurements

Hydrocarbon exploration and production incorporate great technology challenges for the oil and gas industry. In order to meet the world's future demand for oil and gas, further technological advance is needed, which in turn requires research across multiple disciplines, including mathematics, geophysics, geology, petroleum engineering, signal processing, and computer science. This book addresses important aspects and fundamental concepts in hydrocarbon exploration and production. Moreover, new developments and recent advances in the relevant research areas are discussed, whereby special emphasis is placed on mathematical methods and modelling. The book reflects the multi-disciplinary character of the hydrocarbon production workflow, ranging from seismic data imaging, seismic analysis and interpretation and geological model building, to numerical reservoir simulation. Various challenges concerning the production workflow are discussed in detail. The thirteen chapters of this joint work, authored by international experts from academic and industrial institutions, include survey papers of expository character as well as original research articles. Large parts of the material presented in this book were developed between November 2000 and April 2004 through the European research and training network NetAGES, "Network for Automated Geometry Extraction from Seismic". The new methods described here are currently being implemented as software tools at Schlumberger Stavanger Research, one of the world's largest service providers to the oil industry.

This book constitutes the refereed post-proceedings of the Second International Conference on High Performance Networking, Computing, and Communication systems, ICHCC 2011, held in Singapore in May 2011. The conference was held together with the Second International Conference on Theoretical and Mathematical Foundations of Computer Science, ICTMF 2011, which proceedings are published in CCIS 164. The 84 revised selected papers presented were carefully reviewed and selected for inclusion in the book. The topics covered range from computational science, engineering and technology to digital signal processing, and computational biology to game theory, and other related topices.