Wilson C Chin - Böcker

Managed Pressure Drilling Operations is a significant technology worldwide and beginning to make an impact all over the world. Often reservoir and drilling engineers are faced with the decision on how best to construct a well to exploit zones of interest while seeking to avoid drilling problems that contribute to reservoir damage or cause loss of hole. The decision to pursue a MPD operation is based on the intent of applying the most appropriate technology for the candidate and entails either an acceptance of influx to the surface or avoidance of influx into the wellbore.In today's exploration and production environment, drillers must now drill deeper, faster and into increasingly harsher environments where using conventional methods could be counter-productive at best and impossible at worst. Managed Pressure Drilling (MPD) is rapidly gaining popularity as a way to mitigate risks and costs associated with drilling in harsh environments. If done properly, MPD can improve economics for any well being drilled by reducing a rig's nonproductive time. Written for engineers, drilling managers, design departments, and operations personnel, Managed Pressure Drilling Modeling is based on the author's on experience and offers instruction on planning, designing and executing MPD projects. Compact and readable, the book provides a step by step methods for understanding and solve problems involving variables such as backpressure, variable fluid density, fluid rheology, circulating friction, hole geometry and drillstring diameter. All MPD variations are covered, including Constant Bottomhole Pressure, Pressurized MudCap Drilling and Dual Gradient Drilling. Case histories from actual projects are designed and analyzed using proprietary simulation software online.With this book in hand drilling professionals gain knowledge of the various variations involved in managed pressure drilling operations; understand the safety and operational aspects of a managed pressure drilling project; and be able to make an informed selection of all equipment required to carry out a managed pressure drilling operation. Case histories from actual projects are designed and analyzed using proprietary simulation software online Clearly explains the safety and operational aspects of a managed pressure drilling project Expert coverage of the various variations involved in managed pressure drilling operations Numerical tools and techniques needed for applying MPD principles and practices to individual projects

Quantitative Methods in Reservoir Engineering, Second Edition, brings together the critical aspects of the industry to create more accurate models and better financial forecasts for oil and gas assets. Updated to cover more practical applications related to intelligent infill drilling, optimized well pattern arrangement, water flooding with modern wells, and multiphase flow, this new edition helps reservoir engineers better lay the mathematical foundations for analytical or semi-analytical methods in today's more difficult reservoir engineering applications.

Authored by a worldwide expert on computational flow modeling, this reference integrates current mathematical methods to aid in understanding more complex well systems and ultimately guides the engineer to choose the most profitable well path. The book delivers a valuable tool that will keep reservoir engineers up-to-speed in this fast-paced sector of the oil and gas market.

Stay competitive with new content on unconventional reservoir simulation Get updated with new material on formation testing and flow simulation for complex well systems and paths Apply methods derived from real-world case studies and calculation examples

Multiprobe Pressure Testing and Reservoir Characterization: Pressure Transient, Contamination, Liquid and Gas Pumping Analysis provides much-needed three-dimensional, pressure transient simulators for job planning and data interpretation in well logging. First, discussions on fundamental concepts present fluid sampling, pressure transient and contamination analysis; physical concepts and numerical approaches; and multiprobe model formulations and validations. Other sections cover four-probe algorithms including conventional, overbalanced, and underbalanced drilling applications. The final section addresses triple-probe algorithms, which includes coupled models for pressure and contamination convergence acceleration. Notably, Chapter 10 explains how the multiprobe tool’s focus on characterizing permeability will promote better use of the reservoir as well as assist with energy storage in underground rock, demonstrating how multiprobe tools also facilitate the energy transition from fossil fuels to sustainable geothermal energy. The book's mathematical methods are described in a straightforward manner with numerous example calculations and applications demonstrating the practical utility of the approaches. This book is an invaluable reference for petroleum geologists and engineers involved in geothermal and conventional reservoir characterization and simulation.

Multiprobe Pressure Testing and Reservoir Characterization: Pressure Transient, Contamination, Liquid and Gas Pumping Analysis provides much-needed three-dimensional pressure transient simulators for job planning and data interpretation in well logging. Discussions cover fundamental concepts, present fluid sampling, pressure transient and contamination analysis; physical concepts and numerical approaches; and multiprobe model formulations and validations. Other sections cover four-probe algorithms, including conventional, overbalanced, and underbalanced drilling applications. The final section addresses triple-probe algorithms, which includes coupled models for pressure and contamination convergence acceleration.Notably, a further chapter explains how the multiprobe tool’s focus on characterizing permeability will promote better use of the reservoir as well as assist with energy storage in underground rock, demonstrating how multiprobe tools also facilitate the energy transition from fossil fuels to sustainable geothermal energy.

Reviews present day needs, tool operations, and analysis methods, along with numerous practical examples and applicationsDevelops a suite of mathematical models, algorithms, and software from first principlesExplains, in detail, how multiprobe pressure logging is superior to using conventional sensors because direct, accurate reservoir characteristics support energy-efficient geothermal designsProvides an alternative look at the investigation of unconventional reservoirs, not only in terms of hydrocarbon production, but also with carbon and energy storage in mind

For the practitioner, this volume is a valuable tool for predicting reservoir flow in the most efficient and profitable manner possible, using quantitative methods rather than anecdotal and outdated methods. For the student, this volume offers insight not covered in other textbooks.

Too many approaches in traditional petroleum engineering are based on "ad hoc" and "common sense" methods that have no rigorous mathematical basis. Most textbooks dealing with reservoir engineering do not go into the necessary mathematical detail and depth. This new book by Wilson Chin, a revision of two earlier books published by Gulf Publishing, Modern Reservoir Flow and Well Transient Analysis and Formation Invasion, integrates rigorous mathematical methods for simulating and predicting reservoir flow both near and away from the well.

Predicts reservoir flow to maximize resources, time, and profits Includes problems and solutions for students Presents mathematical models in an easy-to-understand and easy-to-simulate format

Computational Rheology for Pipeline and Annular Flow develops and applies modern analytical and computational finite difference methods for solving flow problems in drilling and production. It also provides valuable insights into flow assurance analysis in subsea pipeline design. Using modeling techniques that simulate the motion of non-Newtonian fluids, e.g., power law, Bingham plastic, and Herschel-Bulkley flows, this book presents proven annular flow methodologies for cuttings transport and stuck pipe analysis based on detailed experimental data obtained from highly deviated and horizontal wells. These methods are applied for highly eccentric borehole geometries to the design of pipeline bundles in subsea applications, where such annular configurations arise in velocity and thermal modeling applications.Also covered extensively are the design and modeling of pipelines having non-circular cross-sections, where deviations from ideal circular geometries arise from plugging due to wax deposition and the presence of hydrates and asphaltenes. As in the case of annular flows, the new algorithms apply to fluids with general rheological description; for example, the methods show very precisely how flow rate and pressure gradient vary nonlinearly in practical problem situations. Provides valuable insights into flow assurance analysis. Contains new algorithms on annular flows and fluids with general rheological descriptions supply solutions to practical problems.

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 designAlmost 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.

The only book available for the reservoir or petroleum engineer covering formation testing—with algorithms for wireline and LWD reservoir analysis developed for transient pressure, contamination modeling, permeability, and pore pressure prediction.Traditional well logging methods, such as resistivity, acoustic, nuclear, and NMR, provide indirect information relating to fluid and formation properties. However, the "formation tester" offered in wireline and MWD/LWD operations is different. It collects actual downhole fluid samples for surface analysis, and through pressure transient analysis, provides direct measurements for pore pressure, mobility, permeability, and anisotropy. These are vital to real-time drilling safety, geosteering, hydraulic fracturing, and economic analysis.Methods for formation testing analysis, while commercially important and accounting for a substantial part of service company profits, are shrouded in secrecy. Many are poorly constructed, and because details are not available, industry researchers are not able to improve on them. Formation Testing explains conventional models and develops new, more powerful algorithms for early-time analysis. More importantly, it addresses a critical area in sampling related to "time required to pump clean samples," using rigorous multiphase flow techniques. All of the methods are explained in complete detail. Equations are offered for users to incorporate in their own models, but, for those needing immediate answers, convenient, easy-to-use software is available.The lead author is a well-known petrophysicist with hands-on experience at Schlumberger, Halliburton, BP Exploration, and other companies. His work is used commercially at major oil service companies, and important extensions to his formation testing models have been supported by prestigious grants from the U.S. Department of Energy. His latest collaboration with China National Offshore Oil Corporation marks an important turning point, where advanced simulation models and hardware are evolving side-by-side, defining a new generation of formation testing logging instruments. Providing more than formulations and solutions, this book offers a close look at "behind the scenes" formation tester development, as the China National Offshore Oil Corporation opens up its research, engineering, and manufacturing facilities through a collection of never-before-seen photographs, showing how formation testing tools are developed from start to finish.

Wave propagation is central to all areas of petroleum engineering, e.g., drilling vibrations, MWD mud pulse telemetry, swab-surge, geophysical ray tracing, ocean and current interactions, electromagnetic wave and sonic applications in the borehole, but rarely treated rigorously or described in truly scientific terms, even for a single discipline. Wilson Chin, an MIT and Caltech educated scientist who has consulted internationally, provides an integrated, comprehensive, yet readable exposition covering all of the cited topics, offering insights, algorithms and validated methods never before published. A must on every petroleum engineering bookshelf! In particular, the book: Delivers drillstring vibrations models coupling axial, torsional and lateral motions that predict rate-of-penetration, bit bounce and stick-slip as they depend on rock-bit interaction and bottomhole assembly properties,Explains why catastrophic lateral vibrations at the neutral point cannot be observed from the surface even in vertical wells, but providing a proven method to avoid them,Demonstrates why Fermat's "principle of least time" (used in geophysics) applies to non-dissipative media only, but using the "kinematic wave theory" developed at MIT, derives powerful methods applicable to general attenuative inhomogeneous media,Develops new approaches to mud acoustics and applying them to MWD telemetry modeling and strong transients in modern swab-surge applicagtions,Derives new algorithms for borehole geophysics interpretation, e.g., Rh and Rv in electromagnetic wave and permeability in Stoneley waveform analysis, andOutlines many more applications, e.g., wave loadings on offshore platforms, classical problems in wave propagation, and extensions to modern kinematic wave theory.These disciplines, important to all field-oriented activities, are not treated as finite element applications that are simply gridded, "number-crunched" and displayed, but as scientific disciplines deserving of clear explanation. General results are carefully motivated, derived and applied to real-world problems, with results demonstrating the importance and predictive capabilities of the new methods.

Traditional well logging methods, such as  resistivity, acoustic, nuclear and NMR, provide indirect information related to fluid and formation properties.  The “formation tester,” offered in wireline and MWD/LWD operations, is different.  It collects actual downhole fluid samples for surface analysis, and through pressure transient analysis, provides direct measurements for pore pressure, mobility, permeability and anisotropy.  These are vital to real-time drilling safety, geosteering, hydraulic fracturing and economic analysis.Methods for formation testing analysis, while commercially important and accounting for a substantial part of service company profits, however, are shrouded in secrecy.  Unfortunately, many are poorly constructed, and because details are not available, industry researchers are not able to improve upon them.  This new book explains conventional models and develops new powerful algorithms for “double-drawdown” and “advanced phase delay” early-time analysis - importantly, it is now possible to predict both horizontal and vertical permeabilities, plus pore pressure, within seconds of well logging in very low mobility reservoirs.  Other subjects including inertial Forchheimer effects in contamination modeling and time-dependent flowline volumes are also developed.  All of the methods are explained in complete detail.  Equations are offered for users to incorporate in their own models, but convenient, easy-to-use software is available for those needing immediate answers.The leading author is a well known petrophysicist, with hands-on experience at Schlumberger, Halliburton, BP Exploration and other companies.  His work is used commercially at major oil service companies, and important extensions to his formation testing models have been supported by prestigious grants from the United States Department of Energy.  His new collaboration with China National Offshore Oil Corporation  marks an important turning point, where advanced simulation models and hardware are evolving side-by-side to define a new generation of formation testing logging instruments.  The present book provides more than formulations and solutions: it offers a close look at formation tester development “behind the scenes,” as the China National Offshore Oil Corporation opens up its research, engineering and manufacturing facilities through a collection of interesting photographs to show how formation testing tools are developed from start to finish.

Resistivity logging represents the cornerstone of modern petroleum exploration, providing a quantitative assessment of hydrocarbon bearing potential in newly discovered oilfields. Resistivity is measured using AC coil tools, as well as by focused DC laterolog and micro-pad devices, and later extrapolated, to provide oil saturation estimates related to economic productivity and cash flow. Interpretation and modeling methods, highly lucrative, are shrouded in secrecy by oil service companies – often these models are incorrect and mistakes perpetuate themselves over time.This book develops math modeling methods for layered, anisotropic media, providing algorithms, validations and numerous examples. New electric current tracing tools are also constructed which show how well (or poorly) DC tools probe intended anisotropic formations at different dip angles. The approaches discussed provide readers with new insights into the limitations of conventional tools and methods, and offer practical and rigorous solutions to several classes of problems explored in the book.Traditionally, Archie's law is used to relate resistivity to water saturation, but only on small core-sample spatial scales. The second half of this book introduces methods to calculate field-wide water saturations using modern Darcy flow approaches, and then, via Archie's law, develops field-wide resistivity distributions which may vary with time. How large-scale resistivity distributions can be used in more accurate tool interpretation and reservoir characterization is considered at length. The book also develops new methods in "time lapse logging," where timewise changes to resistivity response (arising from fluid movements) can be used to predict rock and fluid flow properties.

Mysterious "supercharge effects," encountered in formation testing pressure transient analysis, and reservoir invasion, mudcake growth, dynamic filtration, stuck-pipe remediation, and so on, are often discussed in contrasting petrophysical versus drilling contexts.  However, these effects are physically coupled and intricately related. The authors focus on a comprehensive formulation, provide solutions for different specialized limits, and develop applications that illustrate how the central ideas can be used in seemingly unrelated disciplines. This approach contributes to a firm understanding of logging and drilling principles. Fortran source code, furnished where applicable, is listed together with recently developed software applications and conveniently summarized throughout the book. In addition, common (incorrect) methods used in the industry are re-analyzed and replaced with more accurate models, which are then used to address challenging field objectives.Sophisticated mathematics is explained in "down to earth" terms, but empirical validations, in this case through Catscan experiments, are used to "keep predictions honest." Similarly, early-time, low mobility, permeability prediction models used in formation testing, several invented by one of the authors, are extended to handle supercharge effects in overbalanced drilling and near-well pressure deficits encountered in underbalanced drilling. These methods are also motivated by reality. For instance, overpressures of 2,000 psi and underpressures near 500 psi are routinely reported in field work, thus imparting a special significance to the methods reported in the book.This new volume discusses old problems and modern challenges, formulates and develops advanced models applicable to both drilling and petrophysical objectives. The presentation focuses on central unifying physical models which are carefully formulated and mathematically solved. The wealth of applications examples and supporting software discussed provides readers with a unified focus behind daily work activities, emphasizing common features and themes rather than unrelated methods and work flows. This comprehensive book is "must" reading for every petroleum engineer.

Co-written by a world-renowned petroleum engineer, this breakthrough new volume teaches engineers how to configure, place and produce horizontal and multilateral wells in geologically complicated reservoirs, select optimal well spacings and fracture separations, and how to manage factors influencing well productivity using proven cost-effective and user-friendly simulation methods.Charged in the 1990s with solving some of petroleum engineering's biggest problems that the industry deemed "unsolvable," the authors of this innovative new volume solved those problems, not just using a well-published math model, but one optimized to run rapidly, the first time, every time. This not only provides numerical output, but production curves and color pressure plots automatically. And each in a single hour of desk time.Using their Multisim software that is featured in this volume, secondary school students at the Aldine Independent School District delivered professional quality simulations in a training program funded by some of the largest energy companies in the world. Think what you, as a professional engineer, could do in your daily work. Valuable with or without the software, this volume is the cutting-edge of reservoir engineering today, prefacing each chapter with a "trade journal summary" followed by hands-on details, allowing readers to replicate and extend results for their own applications.This volume covers parent-child, multilateral well, and fracture flow interactions, reservoir flow analysis, many other issues involving fluid flow, fracturing, and many other common "unsolvable" problems that engineers encounter every day. It is a must-have for every engineer's bookshelf.

This new volume, the third in Wiley-Scrivener's series on formation testing, reviews pressure transient interpretation and contamination analysis methods, providing numerous practical discussions and examples with rigorous formulations solved through exact, closed form, analytical solutions.This new volume in the "Formation Testing" series further develops new methods and processes that are being developed in the oil and gas industry. In the 1990s through 2000s, the author co-developed Halliburton's commercially successful GeoTapTM real-time LWD/MWD method for formation testing, and also a parallel method used by China Oilfield Services, which enabled the use of data taken at early times, in low mobility and large flowline volume environments, to support the important estimation of mobility, compressibility and pore pressure, which are necessary for flow economics and fluid contact boundaries analyses (This work was later extended through two Department of Energy Small Business Innovation Research awards.).While extremely significant, the effect of high pressures in the borehole could not be fully accounted for. The formation tester measures a combination of reservoir and mud pressure and cannot ascertain how much is attributed to unimportant borehole effects. The usual approach is "simply wait" until the effects dissipate, which may require hours, which imply high drilling and logging costs, plus increased risks in safety and tool loss. The author has now modeled this "supercharge" effect and developed a powerful mathematical algorithm that fully accounts for mud interations. In short, accurate predictions for mobility, compressibility and pore pressure can now be undertaken immediately after an interval is drilled without waiting.This groundbreaking new work is a must-have for any petroleum, reservoir, or mud engineer working in the industry, solving day-to-day problems that he or she encounters in the field.

Real-world reservoirs are layered, heterogeneous and anisotropic, exposed to water and gas drives, faults, barriers and fractures. They are produced by systems of vertical, deviated, horizontal and multilateral wells whose locations, sizes, shapes and topologies are dictated "on the fly, at random"by petroleum engineers and drillers at well sites. Wells may be pressure or rate-constrained, with these roles re-assigned during simulation with older laterals shut-in, newer wells drilled and brought on stream, and so on. And all are subject to steady and transient production, each satisfying different physical and mathematical laws, making reservoir simulation an art difficult to master and introducing numerous barriers to entry. All of these important processes can now be simulated in any order using rapid, stable and accurate computational models developed over two decades.And what if it were further possible to sketch complicated geologies and lithologies, plus equally complex systems of general wells, layer-by-layer using Windows Notepad? And with no prior reservoir simulation experience and only passing exposure to reservoir engineering principles? Have the user press "Simulate," and literally, within minutes, produce complicated field-wide results, production forecasts, and detailed three-dimensional color pressure plots from integrated graphics algorithms?Developed over years of research, this possibility has become reality. The author, an M.I.T. trained scientist who has authored fifteen original research books, over a hundred papers and forty patents, winner of a prestigious British Petroleum Chairman's Innovation Award in reservoir engineering and a record five awards from the United States Department of Energy, has delivered just such a product, making real-time planning at the well-site simple and practical. Workflows developed from experience as a practicing reservoir engineer are incorporated into "intelligent menus" that make in-depth understanding of simulation principles and readings of user manuals unnecessary.  This volume describes new technology for down-to-earth problems using numerous examples performed with our state-of-the-art simulator, one that is available separately at affordable cost and requiring only simple Intel Core i5 computers without specialized graphics boards. The new methods are rigorous, validated and well-documented and are now available for broad petroleum industry application.

Written by a leading industry specialist, a must-have for drilling specialists, petroleum engineers, and field practitioners, this is the only book providing practical, rigorous and validated models for general annular flows, eccentric geometries, non-Newtonian fluids, yield stresses, multiphase effects, and transient motions and flow rates and includes new methods describing mudcake integrity and pore pressure for blowout assessment.Wilson C. Chin has written some of the most important and well-known books in the petroleum industry. These books, whose research was funded by the U.S. Department of Energy and several international petroleum corporations, have set very high standards. Many algorithms are used at leading oil service companies to support key drilling and well logging applications.For the first time, the physical models in these publications, founded on rigorous mathematics and numerical methods, are now available to the broader industry: students, petroleum engineers, drillers and faculty researchers. The presentations are written in easy-to-understand language, with few equations, offering simplified explanations of difficult problems and solutions which provide key insights into downhole physical phenomena through detailed tabulations and color graphics displays. Practical applications, such as cuttings transport, pressure control, mudcake integrity, formation effects in unconventional applications, and so on, are addressed in great detail, offering the most practical answers to everyday problems that the engineer encounters.The book does not stop at annular flow. In fact, the important role of mudcake growth and thickness in enabling steady flow in the annulus is considered, as is the role of (low) formation permeability in affecting mud filtration, cake growth, and fluid sealing at the sandface. This is the first publication addressing "the big picture," a "first" drawn from the author's related research in multiple disciplines such as drilling rheology, formation testing and reservoir simulation. A must-have for any petroleum engineer, petroleum professional, or student, this book is truly a groundbreaking volume that is sure to set new standards.

Trade magazines and review articles describe MWD in casual terms, e.g., positive versus negative pulsers, continuous wave systems, drilling channel noise and attenuation, in very simple terms absent of technical rigor. However, few truly scientific discussions are available on existing methods, let alone the advances necessary for high-data-rate telemetry. Without a strong foundation building on solid acoustic principles, rigorous mathematics, and of course, fast, inexpensive and efficient testing of mechanical designs, low data rates will impose unacceptable quality issues to real-time formation evaluation for years to come.This all-new revised second edition of an instant classic promises to change all of this. The lead author and M.I.T.-educated scientist, Wilson Chin, has written the only book available that develops mud pulse telemetry from first principles, adapting sound acoustic principles to rigorous signal processing and efficient wind tunnel testing. In fact, the methods and telemetry principles developed in the book were recently adopted by one of the world's largest industrial corporations in its mission to redefine the face of MWD.The entire engineering history for continuous wave telemetry is covered: anecdotal stories and their fallacies, original hardware problems and their solutions, different noise mechanisms and their signal processing solutions, apparent paradoxes encountered in field tests and simple explanations to complicated questions, and so on, are discussed in complete "tell all" detail for students, research professors and professional engineers alike. These include signal processing algorithms, signal enhancement methods, and highly efficient "short" and "long wind tunnel" test methods, whose results can be dynamically re-scaled to real muds flowing at any speed. A must read for all petroleum engineering professionals!

A powerful new monograph from an aerodynamicist reviewing modern conventional aerodynamic approaches, this volume covers aspects of subsonic, transonic and supersonic flow, inverse problems, shear flow analysis, jet engine power addition, engine and airframe integration, and other areas, providing readers with the tools needed to evaluate their own ideas and to implement the newer methods suggested in this book.This new book, by a prolific fluid-dynamicist and mathematician who has published more than twenty research monographs, represents not just another contribution to aerodynamics, but a book that raises serious questions about traditionally accepted approaches and formulations, providing new methods that solve longstanding problems of importance to the industry. While both conventional and newer ideas are discussed, the presentations are readable and geared to advanced undergraduates with exposure to elementary differential equations and introductory aerodynamics principles. Readers are introduced to fundamental algorithms (with Fortran source code) for basic applications, such as subsonic lifting airfoils, transonic supercritical flows utilizing mixed differencing, models for inviscid shear flow aerodynamics, and so on. These are models they can extend to include newer effects developed in the second half of the book. Many of the newer methods have appeared over the years in various journals and are now presented with deeper perspective and integration.This book helps readers approach the literature more critically. Rather than simply understanding an approach, for instance, the powerful "type differencing" behind transonic analysis, or the rationale behind "conservative" formulations, or the use of Euler equation methods for shear flow analysis when they are unnecessary, the author guides and motivates the user to ask why and why not and what if. And often, more powerful methods can be developed using no more than simple mathematical manipulations. For example, Cauchy-Riemann conditions, which are powerful tools in subsonic airfoil theory, can be readily extended to handle compressible flows with shocks, rotational flows, and even three-dimensional wing flowfields, in a variety of applications, to produce powerful formulations that address very difficult problems. This breakthrough volume is certainly a "must have" on every engineer's bookshelf.