Measurement While Drilling (MWD) Signal Analysis, Optimization and Design E-Book

Wilson C. Chin

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 512

Veröffentlichungsjahr: 2014

Beschreibung

Trade magazines and review articles describe MWD in casualterms, e.g., positive versus negative pulsers, continuous wavesystems, drilling channel noise and attenuation, in very simpleterms absent of technical rigor. However, few trulyscientific discussions are available on existing methods, let alonethe advances necessary for high-data-rate telemetry. Withouta strong foundation building on solid acoustic principles, rigorousmathematics, and of course, fast, inexpensive and efficient testingof mechanical designs, low data rates will impose unacceptablequality issues to real-time formation evaluation for years tocome. This book promises to change all of this. The lead authorand M.I.T. educated scientist, Wilson Chin, and Yinao Su,Academician, Chinese Academy of Engineering, and other teammembers, have written the only book available that developsmud pulse telemetry from first principles, adapting sound acousticprinciples to rigorous signal processing and efficient wind tunneltesting. In fact, the methods and telemetry principlesdeveloped in the book were recently adopted by one of theworld's largest industrial corporations in its mission toredefine the face of MWD.The entire engineering history for continuous wave telemetry iscovered: anecdotal stories and their fallacies, original hardwareproblems and their solutions, different noise mechanisms and theirsignal processing solutions, apparent paradoxes encountered infield tests and simple explanations to complicated questions, andso on, are discussed in complete "tell all" detail forstudents, research professors and professional engineersalike. These include signal processing algorithms, signalenhancement methods, and highly efficient "short" and"long wind tunnel" test methods, whose results can bedynamically re-scaled to real muds flowing at any speed. Amust read for all petroleum engineering professionals!

Leseprobe

Contents

Cover

Half Title page

Title page

Copyright page

Opening Message

Preface

Acknowledgements

Chapter 1: Stories from the Field, Fundamental Questions and Solutions

1.1 Mysteries, Clues and Possibilities

1.2 Paper No. AADE-11-NTCE-74 – “High-Data-Rate MWD System for Very Deep Wells”

1.3 References

Chapter 2: Harmonic Analysis: Six-Segment Downhole Acoustic Waveguide

2.1 MWD Fundamentals

2.2 MWD Telemetry Concepts Re-examined

2.3 Downhole Wave Propagation Subtleties

2.4 Six-Segment Downhole Waveguide Model

2.5 An Example: Optimizing Pulser Signal Strength

2.6 Additional Engineering Conclusions

2.7 References

Chapter 3: Harmonic Analysis: Elementary Pipe and Collar Models

3.1 Constant area drillpipe wave models

3.2 Variable area collar-pipe wave models

3.3 References

Chapter 4: Transient Constant Area Surface and Downhole Wave Models

Method 4-1. Upgoing wave reflection at solid boundary, single transducer deconvolution using delay equation, no mud pump noise (software reference, XDUCER*.FOR).

4.2 Method 4-2. Upgoing wave reflection at solid boundary, single transducer deconvolution using delay equation, with mud pump noise (software reference, HYBRID*.FOR).

4.3 Method 4-3. Directional filtering – difference equation method requiring two transducers (software reference, 2XDCR*.FOR).

4.4 Method 4-4. Directional filtering – differential equation method requiring two transducers (software reference, SAS14D*.FOR, option 3 only).

4.5 Method 4-5. Downhole reflection and deconvolution at the bit, waves created by MWD dipole source, bit assumed as perfect solid reflector (software reference, DELTAP*.FOR).

4.6 Method 4-6. Downhole reflection and deconvolution at the bit, waves created by MWD dipole source, bit assumed as perfect open end or zero acoustic pressure reflector (software reference, DPOPEN*.FOR).

4.7 References

Chapter 5: Transient Variable Area Downhole Inverse Models

5.1 Method 5-1. Problems with acoustic impedance mismatch due to collar-drillpipe area discontinuity, with drillbit assumed as open-end reflector (software reference, collar-pipe-open-16.for).

5.2 Method 5-2. Problems with collar-drillpipe area discontinuity, with drillbit assumed as closed end, solid drillbit reflector (software reference, collar-pipe-closed-*.for).

5.3 References

Chapter 6: Signal Processor Design and Additional Noise Models

6.1 Desurger Distortion

6.2 Downhole Drilling Noise

6.3. Attenuation Mechanisms (software reference, Alpha2, Alpha3, MWDFreq, datarate).

6.4 Drillpipe Attenuation and Mudpump Reflection (software reference, PSURF-1.FOR).

6.5 Applications to Negative Pulser Design in Fluid Flows and to Elastic Wave Telemetry Analysis in Drillpipe Systems

6.6 LMS Adaptive and Savitzky-Golay Smoothing Filters (software reference, all of the filters in Sections 6 and 7 are found in C:\MWD-06)

6.7 Low Pass Butterworth, Low Pass FFT and Notch Filters

6.8 Typical Frequency Spectra and MWD Signal Strength Properties

6.9 References

Chapter 7: Mud Siren Torque and Erosion Analysis

7.1 The Physical Problem

7.2 Mathematical Approach

7.3 Mud Siren Formulation

7.4 Typical Computed Results and Practical Applications

7.5 Conclusions

7.6 References

Chapter 8: Downhole Turbine Design and Short Wind Tunnel Testing

8.1 Turbine Design Issues

8.2 Why Wind Tunnels Work

8.3 Turbine Model Development

8.4 Software Reference

8.5 Erosion and Power Evaluation

8.6 Simplified Testing

8.7 References

Chapter 9: Siren Design and Evaluation in Mud Flow Loops and Wind Tunnels

9.1 Early Wind Tunnel and Modern Test Facilities

9.2 Short wind tunnel design

9.3 Intermediate Wind Tunnel for Signal Strength Measurement

9.4 Long Wind Tunnel for Telemetry Modeling

9.5 Water and Mud Flow Loop Testing

Chapter 10: Advanced System Summary and Modern MWD Developments

10.1 Overall Telemetry Summary

10.2 MWD Signal Processing Research in China

10.3 MWD Sensor Developments in China

10.4 Turbines, Batteries and Closing Remarks

10.5 References

Cumulative References

Index

About the Authors

Measurement While Drilling (MWD) Signal Analysis, Optimization and Design

Scrivener Publishing100 Cummings Center, Suite 541JBeverly, MA 01915-6106

Publishers at ScrivenerMartin Scrivener ([email protected])Phillip Carmical ([email protected])

Copyright © 2014 by Scrivener Publishing LLC. All rights reserved.

Co-published by John Wiley & Sons, Inc. Hoboken, New Jersey, and Scrivener Publishing LLC, Salem, Massachusetts.Published simultaneously in Canada.

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Library of Congress Cataloging-in-Publication Data:

ISBN 978-1-118-83168-7

Opening Message

Yinao Su, Ph.D., AcademicianChinese Academy of Engineering

In modern oil and gas exploration, drilling offers many engineering challenges. Multiple economical objectives are targeted, among them rapid penetration rates and productive payzones. To achieve this, high-data-rate MWD systems are urgently needed for detailed and accurate downhole characterization, real-time information being central to control, optimization and safety. But the downhole environment is not forgiving: high noise levels, strong signal distortion and interference, together with severe attenuation, impede data transmission rate. To overcome these difficulties, completely new systems oriented designs are required to replace simple fixes to existing tools.

Several approaches are available, e.g., electromagnetic wave, intelligent wired pipe and drillpipe acoustics, each possessing its unique shortcomings. Here we have asked, “Is it possible to improve mud pulse telemetry, the most popular and by far least intrusive operationally?” The answer is, “Yes!” We have applied wave propagation principles to hardware development, telemetry design and surface signal processing, treating our challenge from an integrated systems perspective. With research guided by theory and experiment, we have shown that basic transmission rates can be increased significantly, with further improvements possible through data compression.

At China National Petroleum Corporation, through its Drilling Research Institute, new technology, research and innovation aim at responsibly providing society with clean, safe and reliable energy. In this book, we wish to share our experiences with the industry in achieving our goal for “Developing Energy, Creating Harmony.” We hope that the methods we have pioneered, described in detail, will contribute to finding oil and gas more safely and efficiently.

Beijing, China

Preface

The physical theories behind Measurement-While-Drilling design should be rich in scientific challenges, engineering principles and mathematical elegance. To develop the next generation of high-data-rate tools, these must be understood and applied unfailingly without compromise. But one does not simply peruse the latest petroleum books, state-of-the-art reviews, or the most recent patents to understand their teachings. Most descriptions are just wrong. The science itself does not exist. All simply rehash hearsay and misconceptions that have proliferated for more than three decades – recycled street narratives and folklore about sirens, positive and negative pulsers, and yes, mud attenuation; over-simplified product brochures from oil service companies that monopolize the industry; and, unfortunately, all preach the same complaints about low data rates and industry’s failure to address modern logging needs.

The truth is, there have been no substantive developments in MWD telemetry and design over the years. Not one paper has appeared that deals with telemetry in a manner worthy of scientific publication. New tools, more like muscle-machines than intelligent instruments, are designed without regard for acoustic concepts, while signal optimization and surface processing, more often than not based on “hand-waving” arguments, proceed without guidance from wave equation models. True, tools are better engineered; mechanical parts erode less, pulser modulation is controlled more reliably, high-powered microprocessors have replaced simple circuit boards, electronic components survive higher temperatures and pressures, and overall reliability is impressive, all of which enables the logging industry to reach deeper targets. However, these are incremental improvements unlikely to change the big picture. And the big picture is bleak: unless conceptual breakthroughs are made, the present low data-rate environment is likely to persist.

Through this rapid progress, several disturbing problems are apparent. The first author, having consulted for established as well as start-up companies over the past ten years, is aware of no comprehensive theory addressing MWD acoustics. There are no university courses developed to educate the next generation of telemetry designers. The one-dimensional wave propagation models that are available are no more sophisticated that organ acoustics formulas from Physics 101. And tight-lipped service companies have been reluctant to publicize their failings, for obvious reasons, a business decision that has stymied progress in an important commercial endeavor. But unless companies are willing to share ideas and experiences, no one will benefit.

All of this is not new to science and certainly not unique to the commercialization of new products. The aerospace industry, decades ago just as subdued and secretive, suffered from similar failings. In that era though, just as the first author completed his Ph.D. from the Massachusetts Institute of Technology in aerospace engineering, companies like Boeing, Lockheed and McDonnell-Douglas, for instance, finally recognized that the best way forward was free dissemination of scientific methods. Engineers openly carried their Fortran decks from one company to the next, published their findings in open journals and debated their ideas with new-found colleagues near and far. Increased employment mobility only increased idea dissemination more rapidly. The rest is history: the Space Shuttle, the Space Station, the 767, 777 and 787. It is in this spirit that the present book is written: intellectual curiosity and honesty and a genuine interest to see MWD data rates improve.

The author, no new-comer to MWD, earned his stripes at Schlumberger and Halliburton, managing MWD telemetry efforts that developed and refined new hardware concepts and signal processing techniques. However, research funding was fragmented and scientific objectives were unclear. Knowing the right questions, it is understood, solves half the problem. But it was not until the new millenium that progress in the formulation and solution of rigorous wave equation models took hold. Numerical models, notorious for artificial dissipation and dispersion, that is, phase error, were abandoned in favor of more challenging exact analytical solutions. Physical principles could, for once, be clearly understood. New methods to model acoustic sources were developed and special studies were initiated to define broad classes of noise together with the requirements for their elimination. New experimental procedures based on acoustics models were designed, as were special “short” and “long wind tunnels” that accommodated subtle physical mechanisms newly identified.

Theories and models, even the most credible, can be incorrect. In the final analysis, well designed experiments are needed to validate or disprove new ideas. In this regard, China National Petroleum Corporation (CNPC) offered to build laboratory facilities, test siren designs, educate staff and evaluate new telemetry methods, and importantly, to share its results and technology openly with the petroleum industry.

A comprehensive project overview was first presented by the authors in “High-Data-Rate Measurement-While-Drilling System for Very Deep Wells,” Paper No. AADE-11-NTCE-74, at the American Association of Drilling Engineers’ 2011 AADE National Technical Conference and Exhibition, Houston, Texas, April 12-14, 2011. The paper summarized key ideas and results, but given page limits, could not provide details. All of our theoretical and experimental methods are now explained and summarized in this book, with numerous examples, providing useful tools to students and designers alike – our signal processing methods, dealing with signal reflection, distortion and optimization, are formulated, solved, validated and described for the first time. In addition, we offer a new prototype road-map for high-data-rate MWD that has found strong support from knowledgeable industry professionals.

Since publication of the above paper, numerous commercial drivers have made high-data-rate telemetry needs increasingly urgent. In the “old days,” conventional well logging data, e.g., resistivity, sonic or positioning, was simply transmitted to the surface for monitoring and evaluation. However, recent trends call for near-bit geosteering and rotary-steerable capabilities, in support of real-time economic and pore and annular pressure measurements. Despite their importance, few industry publications or websites provide “behind the scenes” descriptions of tool and software development processes, offering little to newer engineers eager to understand the technology – an unfortunate circumstance occurring even as the industry’s “great crew change” takes place.

To fill this need, China National Petroleum Corporation (CNPC) has encouraged us to document in detail its engineering processes, new tools and well logging sensors, in a comprehensive collection of laboratory and field photographs. Much of this work parallels ongoing developments in the West and sheds considerable insight into the country’s efforts to embrace high technology, e.g., stealth fighters, moon missions, fast computers and deep-sea submersibles, and its new-found open-ness in sharing its intellectual property. This book also captures the spirit of MWD engineering in China – we have provided recent paper abstracts and described advanced sensor development activities. It is the authors’ hope that the new technologies offered in the following chapters will contribute to the industry’s continuing need and increasing demand for real-time data as deeper, higher potential and more dangerous wells are drilled.

Wilson C. Chin, Ph.D., M.I.T.Houston, TexasEmail: [email protected]: [phone]

Acknowledgements

The lead author gratefully acknowledges the insights, experiences and friendships he acquired during his early MWD exposure at Schlumberger, Halliburton and other companies – pleasant memories that much more than compensate for the frustrations and sleepless nights brought upon by the challenges of high data rate telemetry. All of the authors are indebted to China National Petroleum Corporation for its support and encouragement throughout this project, and in particular, for its willingness and desire to share its results and activities with the petroleum engineering and well logging community.

Phillip Carmical, Acquisitions Editor and Publisher, has been extremely supportive of this book project and others in progress. His philosophy, to explain scientific principles the way they must be told, with equations and algorithms, is refreshing in an environment often shrouded in secrecy and commercialism. The authors are optimistic that their story-telling will advance the technology and explain why “black boxes” aren’t so mysterious after all.

Finally, the authors thank Xiaoying “Jenny” Zhuang for her hard work and commitment to ably working both sides of the language barrier (the lead author neither speaks nor reads Chinese, while the CNPC team is newly conversant in English). Without her interpretation skills and willingness to learn and understand MWD design issues, our efforts would not have yielded the successes they have and would not have led to friendships and lasting memories. And without Jenny’s personal devotion to a cause, this book would never have seen publication – and who knows, low data rates may remain just that.

Chapter 1

Stories from the Field, Fundamental Questions and Solutions

This chapter might aptly be entitled “Confessions of a confused, high-tech engineer.” And here’s why. In 1981, I was Manager, Turbomachinery Design, at Pratt & Whitney Aircraft, United Technologies Corporation, the company that supplied the great majority of the world’s commercial jet engines. Prior to that, I had served as Research Aerodynamicist at Boeing, working with pioneers in computational fluid dynamics and advanced wing design. What qualified me for these enviable positions was a Ph.D. from the Massachusetts Institute of Technology in acoustic wave propagation – and I had joined a stodgy M.I.T. from its even stodgier cross-town rival, the California Institute of Technology. These credentials in acoustics and fluid mechanics design made me eminently qualified to advance the state-of-the-art in Measurement-While-Drilling (also known as, “MWD”) telemetry – or so I, and other companies, unknowingly thought. At this juncture in my life, the journey through the Oil Patch begins.

1.1 Mysteries, Clues and Possibilities

As a young man, I had dreaded the idea of forever making incremental improvements to aircraft systems, merely as a mainstay to the art of survival and paying the mortgage, sitting at the same desk, in the same building, for decades on end. That possibility, I believed, was a fate worse than death. Thus, in that defining year, I answered a Schlumberger employment advertisement in The New York Times for scientists eager to change the world – the petroleum world, anyway. But unconvinced that any normal company would hire an inexperienced aerospace engineer, and of all things, for a position chartered with high-tech underground endeavors, I was unwilling to give up one of my ten valuable, hard-earned vacation days. Still, the company was stubborn in its pursuit and, for better or worse, kindly accommodated my needs.

Carl Buchholz, the division president at the time, interviewed me that one fateful Saturday. “What do you know about oil?” he bluntly asked, giving me that honest Texan look in the eye. To be truthful, I did not know anything, zilch. “Nothing, but I’ve watched Jed Clampett shoot it out of the ground,” I confessed (Clampett was the hillbilly in the television sitcom who blasted his rifle into the ground, struck oil and moved to Los Angeles to live in his new mansion in “The Beverly Hillbillies”). Buchholz broke out in uncontrolled laughter. That type of honesty he appreciated. I got the job. And with that, I became Schlumberger’s Supervisor, MWD Telemetry, for 2nd generation mud siren and turbine design.

The company’s Analysts division, at the time responsible for an ambitious next-generation, high-data-rate MWD design program, had built ultra-modern office and flow loop facilities in southwest Houston. The metal pipe test section was housed in an air-conditioned room where engineers could work in a clean and comfortable environment away from the pulsations of the indoor mudpump that supplied our flow. A small section of the flow loop was accessible in this laboratory with the main plumbing carefully hidden behind a wall – details no self-respecting, white-collar Ph.D. cared for nor admitted an interest to.

My charter was simple. We were transmitting at 3 bits/sec in holes shallow by today’s standards with a 12 Hz carrier frequency. Our objective was N bits/sec, where N >> 3 (the value of N is proprietary). The solution seemed straightforward, as company managers and university experts would have it. Simply “crank up the carrier to (N/3) × 12 Hz and run.” I did that. But my transducers would measure only confusion, with new pressure oscillations randomly adding to old ones and results depending on mud type, pump speed and time of day. What happened “behind the wall” controlled what we observed but we were too naïve to know. Anecdotal stories told by different field hands about new prototypes were confusing and contradictory. One simply did not know what to believe. Thirty years later, the data rate is still comparable, a bit better under ideal conditions, as it was then. Clearly, there were physical principles that we did not, or perhaps were never meant to, fully comprehend.

Fast-forward to 1992 at Halliburton Energy Services, an eternity later, where I had been hired as Manager, FasTalk MWD. Again, mass confusion prevailed. Some field engineers had reported excellent telemetry results in certain holes, while others had reported poor performance under seemingly identical conditions. The company had acquired several small companies during that reign of corporate acquisitions in the oil service industry. It would turn out that “good versus bad” depended, with all other variables constant, on whether the signal valve was a “positive” or a “negative” pulser. No one really distinguished between the two: because the MWD valve was simply viewed as a piston located at the end of the drillpipe, exciting the drilling fluid column residing immediately above, it didn’t matter if it was pushing or pulling. Sirens were a different animal; no one, except Schlumberger, it seemed, understood them. But nobody really did.

Additional dependencies on drilling conditions only added to the confusion. Industry consensus at the time held that MWD telemetry characteristics depended on drillbit type and nozzle size and, perhaps, rock properties, to some extent. It also appeared that whether or not the drillbit was off-bottom mattered. Very often, common sense dictated that the drillbit acted as a solid reflector, since nozzle cross-sectional areas were “pretty small” compared to pipe dimensions. Yet, this line of reasoning was contradictory and had its flaws; strong MWD signals by then had been routinely detected in the borehole annulus, where their existence or lack of was used to infer gas influx. It became clear that what the human eye visually perceived as small may not be small from a propagating wave’s perspective.

Lack of controlled experiments also pervaded the industry and still does. Whenever any service company design team was lucky enough to find a test well, courtesy of obliging operating company customers, engineering “control” usually meant installing the same pressure transducer in the same position on the standpipe. New tools that were tested in one field situation would perform completely differently in others: standpipe measurements had lives of their own, it seemed, except at very low data rates of 1 bit/sec or less, barring mechanical tool failure, which was often. Details related to surface plumbing, bottomhole assembly, bit-box geometry, drilling motor details and annular dimensions, were not recorded and were routinely ignored. The simple “piston at the end of pipe model” didn’t care – and neither did most engineers and design teams.

By the mid-1990s, the fact that higher data rate signaling just might depend on wave propagation dawned upon industry practitioners. This revelation arose in part from wave-equation-based seismics – new then, not quite understood, but successful. I began to view my confusion as a source of inspiration. The changing patterns of crests and troughs I had measured had to represent waves – waves whose properties had to depend on mud sound speed and flow loop geometry. At Halliburton, I would obtain patents teaching how to optimize signals by taking advantage of wave propagation, e.g., signal strength increase by downhole constructive wave interference (without incurring erosion and power penalties), multiple transducer array signal processing to filter unwanted signals based on direction and not frequency, and others.

Still, the future of mud pulse telemetry was uncertain, confronting an unknowing fate – a technology held hostage by still more uncontrolled experiments and their dangerous implications. At the time, industry experts had concluded that mud pulse telemetry’s technology limits had been attained and that no increases in data rate would be forthcoming. At Louisiana State University’s ten-thousand-feet flow loop, researchers had carefully increased MWD signal frequencies from 1 to 25 Hz, and measured, to their dismay, continually decreasing pressures at a second faraway receiver location. At approximately 25 Hz, the signal disappeared. Completely. That result was confirmed by yours truly, at the same facility, using a slightly different pulser system. Enough said – the story was over. Our MWD research efforts were terminated in 1995 and I resigned from the company in 1999.

The key revelation would come years later as I watched children play “jump rope” in the park. A first child would hold one end of the rope, while a second would shake the opposing end at a given frequency. Transverse waves on a rope are easy to visualize, but the ideas apply equally to longitudinal waves. The main idea is this. At any given frequency, a standing wave system with nodes and antinodes is created that depends on material properties. If the frequency changes, the nodal pattern changes and moves. If one fixes his attention at one specific location, the peak-to-peak displacement appears to come and go. Node and anti-node positions move: what may be interpreted as attenuation may in fact be amplitude reduction due to destructive wave interference – a temporary effect that is not thermodynamically irreversible loss.

This was exactly the situation in the 10,000 feet LSU flow loop. At one end is a mudpump whose pistons act like solid reflectors, assuming tight pump seals, while at the opposite end, a reservoir serves as an open-end acoustic reflector. Pressure transducers were located at fixed positions along the length of the acoustic path. Unlike the jump-rope analogy, the MWD pulser was situated a distance from one of the ends, adding some complexity to the wave field since waves with antisymmetric pressures traveled in both directions from the source. The exact details are unimportant for now. However, the main idea drawn from the jump rope analogy applies: increasing frequency simply changes the standing wave pattern and we (and others) were measuring nothing more than expected movements nodes and antinodes. Attenuation results were buried in the mass of resulting data. This is easy to understand in hindsight. Recent calculations, in fact, show that large attenuation is impossible over the length of the flow loop for the mud systems used.

One crucial difference was suggested above. Whereas, in our jump rope example, excitations originated at the very end of the waveguide (i.e., “at the bit”), the excitations in the LSU flow loop occurred within the acoustic path, introducing subtleties. For example, when a positive pulser or a mud siren closes, a high-pressure signal is created upstream while a low-pressure signal is formed downstream, with both signals propagating away from the valve; the opposite occurs on closure. These long waves travel to the ends of the acoustic channel, reflect accordingly as the end is a solid or open, and travel back and forth through the valve (which never completely closes) to set up a standing wave patterns whose properties depend on mud, length and source.

Had our pulser created disturbance pressure fields that were symmetric with respect to source position, as opposed to being antisymmetric – that is, had we tested a “negative pulser,” our results and conclusions would have been completely different. Any theory of wave propagation applicable to MWD telemetry had to accommodate end boundary conditions, acoustic impedance matching conditions at area (pipe and collar junctions) or material discontinuities (rubber interfaces in mud motors), and importantly, signal source “dipole” or “monopole” properties. Fortunately, such a general theory is now available for signal prediction and inversion and forms, in part, the subject matter of this book. Using the six-segment-waveguide model in Chapter 2, one can confirm the LSU findings. Importantly, one can show that MWD signals can survive well beyond published 25 Hz limits and explain why the industry’s very slow pulsers always create strong signals. In fact, in Chapter 10, the method is used to design a conceptual prototype system capable of transmitting more than 10 bits/sec without data compression in very deep wells.

Engineers even today give overly simplified explanations for MWD signal generation; these physical inadequacies are reflected in models which do not, and cannot, extrapolate the full potential of mud pulse telemetry. We describe some of these fallacies. First, many believe that an “obvious” pressure drop, or “delta-p” (denoted by Δp), created by a valve is essential for MWD signal generation. Very often, this is incorrectly measured in laboratory flow loops using slowly opening and closing pulsers and orifices. This unfortunately measures pressure drops associated with viscous losses about blunt valves – and has nothing to do with the acoustic water hammer pulses associated with high data rate – that is, the “banging” of the mud column that brings it to a near stop. This dynamic element of the testing cannot be ignored or compromised.

But even more troublesome is the Δp explanation itself. Viewed as an essential requirement for MWD signal generation, the concept is completely inapplicable to negative pulsers. For positive pulsers and sirens, the created acoustic pressures are antisymmetric with respect to source location, and a nonzero pressure differential always exists. But while it is true that such pulsers create acoustic Δp’s that excite the telemetry channel, Δp’s are not necessary for all MWD systems. A negative pulser on opening (or closing) creates acoustic disturbance pressure fields that are symmetric with respect to source position. As such, the corresponding Δp is identically zero; for such systems, it is the (nonzero) discontinuity in axial velocity across the source position that is directly correlated to the signal. The formulation differences between acoustic “dipoles” (that is, positive pulsers and mud sirens) and “monopoles” (negative pulsers) are carefully distinguished in this book. Because negative pulsers can damage or even fracture underground formations, and are therefore a liability in deepwater applications, we will not focus on their design in this book.

Competent engineering requires one to distinguish between length scales that are relevant and those that are not. As will become clear in Chapter 2, and as suggested in our discussion on drillbit geometry, the ratio between nozzle and drillpipe diameters is one such measure that is mostly irrelevant to long wave acoustics. Another meaningless measure is the ratio of the pulser-to-drillbit distance to drillpipe length. The extreme smallness of this dimensionless number is often used to justify, for modeling purposes, the placement of the pulser at the bottom end of an idealized drilling channel. In effect, this reduces the formulation to a simple “piston at the end of a pipe” model which can be solved by most graduate engineers. But as we will demonstrate, this simplification amounts to “throwing out the baby with the bath water.”

And why is this? Piston models are unable to deal with source properties: they cannot distinguish between created pressures that are antisymmetric with respect to source position and those that are symmetric. Thus they predict like physics for both dipoles and monopoles. What’s worse, the possibility that upgoing waves can interact constructively with those that travel downward and then reflect up cannot be addressed – this potential application is extremely important to signal enhancement by constructive wave interference, which is achievable by tailoring the telemetry scheme to take advantage of phase properties associated with the mud sound speed and bottomhole assembly.

Moreover, the simple piston model precludes signal propagation up the borehole annulus, which as discussed, has proven to be useful in gas influx detection while drilling. When the complete waveguide – to include the annulus and bit-box as essential elements – is treated as an integrated system, as will be done in Chapter 2, it becomes clear that our simple description of the drillbit as a solid or an open reflector – offered only for illustrative purposes – is too simplified. By extending our formulation to allow pulsers to reside within the drill collar and not simply at the drillbit, we will demonstrate a wealth of physical phenomena and engineering advantages previously unknown.

The subject of surface signal processing and reflection cancellation is similarly shrouded in mystery. An early patent for “dual transducer, differential detection” draws analogies with electric circuit theories, however, using methods with sinusoidal eiωt dependencies. But why time periodicity is relevant at all in systems employing randomly occurring phase shifts is never explained. Rules-of-thumb related to quarter-wavelength interactions, appropriate only to steady-state waves (which do not convey information) used in the patent, prevail to this day for transient situations. They can’t possibly work and they don’t.

Just as troubling are more recent company patents on multiple transducer surface signal processing which sound more like accounting recipes than scientific algorithms, e.g., “subtract this, delay that, add to the shifted value,” when, in fact, formal methods based on the wave equation (derived later in this book) yield more direct, rigorous and generalizable results. We take our cues directly from wave-equation-based seismic processing where all propagation details, including those related to source properties, are treated in their full generality. With this approach, new multiple transducer position and multiple time level reflection cancellation schemes can be inferred straightforwardly from finite difference discretizations of a basic solution to the wave equation.

As if all of this were not bad enough, we take as our final example, the infamous “case of the missing signal,” the mystery which had stymied many of the best minds one too many times – a situation in which MWD tools of all kinds refused to yield discernible standpipe pressures despite their near-perfect mechanical condition. It turned out that, of all things, operators were using inexpensive centrifugal (as opposed to positive displacement) pumps. This illustration offers the strongest, most compelling evidence supporting the wave nature underlying MWD signals. Pistons on positive displacement mud pumps function as solid reflectors, which double the upgoing signal at the piston face; centrifugal pumps with open ends, to the contrary, enforce “zero acoustic pressure” constraints which destroy signals. An understanding of basic acoustics would have reduced frustration levels greatly and saved significantly on time and money.

For those who have forgotten, one-dimensional acoustics is taught in high school and amply illustrated with organ pipe examples. Classical mathematics books give the general solution “f(x + ct) + g(x − ct)” showing that any solution is the sum of left and right-going waves; books on sound discuss impedance mismatches and conservation laws applicable at such junctions. Basic frequency-dependent attenuation laws have been available for over a hundred years. In this sense, the field is well developed. But in other respects the field offers fertile ground for nurturing new and practically useful ideas.

These new ideas include, for example, (1) formal derivations for receiver array reflection and noise cancellation based on the wave equation, (2) model development for elastic distortions of MWD signal at desurgers, (3) constructive and destructive wave interference in waveguides with multiple telescoping sections, (4) downhole signal optimization by constructive wave interference, (5) reflection deconvolution of multiple echoes created within the downhole MWD drill collar, and so on. All of these topics are addressed in this book. In fact, forward models are developed which create transient pressure signals when complicated waveguide geometries and telemetering schemes are specified, and complementary inverse models are constructed that extract position-encoded signals from massively reverberant fields under high-data-rate conditions, with mathematical consistency between the two demonstrated in numerous examples.

While innovative use of physical principles is emphasized for downhole telemetry design and signal processing, testing and evaluation of hardware and tool concepts are equally important, but often viewed as extremely time-consuming, labor-intensive and, simply, expensive. This need not be – and is not – the case. In “Flow Distribution in a Tricone Jet Bit Determined from Hot-Wire Anemometry Measurements,” SPE Paper No. 14216, by A.A. Gavignet, L.J. Bradbury and F.P. Quetier, presented at the 1985 SPE Annual Technical Conference and Exhibition in Las Vegas, and in “Flow Distribution in a Roller Jet Bit Determined from Hot-Wire Anemometry Measurements,” by A.A. Gavignet, L.J. Bradbury and F.P. Quetier, SPE Drilling Engineering, March 1987, pp. 19–26, the investigators, following ideas suggested by the lead author, who had by then routinely used wind tunnels to study sirens and turbines, showed how more detailed flow properties can be obtained using aerospace measurement methods in air. The scientific justification offered was the “highly turbulent nature of the flow.” This counter-intuitive (but correct) approach to modeling mud provides a strategically important alternative to traditional testing that can reduce the cost of developing new MWD systems. Wind tunnel use in the petroleum industry was, by no means, new at the time. For instance, Norton, Heideman and Mallard (1983), with Exxon Production Research Company, and others, had published studies employing wind tunnel use in offshore platform design, extrapolating air-based results dimensionlessly to water flows using standard Strouhal and Reynolds number normalizations.

Additionally, a common normalization given in turbomachinery books can be used to reduce static and dynamic torque properties for various flow rates and densities to a single dimensionless performance curve – simply plot torque (normalized by a dynamic head) against the velocity swirl or “tip speed” ratio. This also motivates intelligent test matrix design: by judiciously choosing widely separated test points, everything there is to know about torque can be inferred – there is no need to perform hundreds of tests for different flow rates, rotation speeds and mud weights. Taken together, the two recipes just discussed allow simple and rigorous characterization of siren and turbine properties over the entire operating envelope with a minimum of labor, time and expense!

The subject matter of this monograph represents years of both mental satisfaction and endless frustration, that is, continuing “love-hate” conflicts in confronting imposing challenges. These chapters summarize key ideas and highlight new theoretical results, physical insights, and testing and evaluation strategies that were developed in thinking “outside the box.” But the endeavor would not come full circle until the suggestions were put to real tests in real engineering design and field testing programs.

Under the leadership of Dr. Yinao Su, Director of CNPC’s Downhole Control Institute, comprehensive wind tunnel facilities were developed, and procedures, algorithms and theories were tested. The recent work described in “High-Data-Rate Measurement-While-Drilling System for Very Deep Wells,” Paper No. AADE-11-NTCE-74 presented at the American Association of Drilling Engineers’ 2011 National Technical Conference and Exhibition in Houston, summarizes findings aimed at an MWD system architecture that provides at least 10 bits/sec (without data compression) in very deep wells with lengths up to 30,000 ft. An updated version concludes the present chapter, providing an overview of current MWD project results and objectives. We emphasize that all of the theoretical and experimental methods in this book are available to the industry. The authors hope that, by openly identifying and discussing problems, solutions and strategies, petroleum exploration can be made more efficient with greater emphasis on safety, while reducing economic and exploration risk and educating the next generation of engineers.

1.2 Paper No. AADE-11-NTCE-74 – “High-Data-Rate MWD System for Very Deep Wells”

Significantly expanded with photographs and detailed annotations …

1.2.1 Abstract.

Measurement-While-Drilling systems presently employing mud pulse telemetry transmit no faster than one or two bits/sec from deep wells containing highly attenuative mud. The reasons – “positive pulsers” create strong signals but large axial flow forces impede fast reciprocation, while “mud sirens” provide high data rates but are lacking in signal strength. China National Petroleum Corporation research in MWD telemetry focuses on improved formation evaluation and drilling safety in deep exploration wells. A high-data-rate system providing 10 bits/sec and operable up to 30,000 ft is described, which creates strong source signals by using downhole constructive wave interference in two novel ways. First, telemetry schemes, frequencies and pulser locations in the MWD drill collar are selected for positive wave phasing, and second, sirens-in-series are used to create additive signals without incurring power and erosion penalties. Also, the positions normally occupied by pulsers and turbines are reversed. A systems design approach is undertaken, e.g., strong source signals are augmented with new multiple-transducer surface signal processing methods to remove mudpump noise and signal reflections at both pump and desurger, and mud, bottomhole assembly and drill pipe properties, to the extent possible in practice, are controlled to reduce attenuation. Special scaling methods developed to extrapolate wind tunnel results to real muds flowing at any downhole speed are also given. We also describe the results of detailed acoustic modeling in realistic drilling telemetry channels, and introduce by way of photographs, CNPC’s “short wind tunnel” for signal strength, torque, erosion and jamming testing, “very long wind tunnel” (over 1,000 feet) for telemetry evaluation, new siren concept prototype hardware and also typical acoustic test results. Movies demonstrating new test capabilities will be shown.

1.2.2 Introduction.

The petroleum industry has long acknowledged the need for high-data-rate Measurement-While-Drilling (MWD) mud pulse telemetry in oil and gas exploration. This need is driven by several demand factors: high density logging data collected by more and more sensors, drilling safety for modern managed pressure drilling and real-time decision making, and management of economic risk by enabling more accurate formation evaluation information.

Yet, despite three decades of industry experience, data rates are no better than they were at the inception of mud pulse technology. To be sure, major strides in reliability and other incremental improvements have been made. But siren data rates are still low in deeper wells and positive pulser rates also perform at low levels. Recent claims for data rates exceeding tens of bits/sec are usually offered without detailed basis or description, e.g., the types of mud used and the corresponding hole depths are rarely quoted.

From a business perspective, there is little incentive for existing oil service companies to improve the technology. They monopolize the logging industry, maintain millions of dollars in tool inventory, and understandably prefer the status quo. Then again, high data rates are not easily achieved. Quadrupling a 3 bits/sec signal under a 12 Hz carrier wave, as we will find, involves much more than running a 48 Hz carrier with all else unchanged. Moreover, there exist valid theoretical considerations (via Joukowski’s classic formula) that limit the ultimate signal possible from sirens. Very clever mechanical designs for positive pulsers have been proposed and tested in the past. Some offer extremely strong signals, although they are not agile enough for high data rates. But unfortunately, the lack of complementary telemetry schemes and surface signal processing methods renders them hostage to strong reverberations and signal distortions at desurgers.

One would surmise that good “back of the envelope” planning, from a systems engineering perspective underscoring the importance of both downhole and surface components, is all that is needed, at least in a first pass. Acoustic modeling in itself, while not trivial, is after all a well-developed science in many engineering applications. For example, highly refined theoretical and numerical models are available for industrial ultrasonics, telephonic voice filtering, medical imaging, underwater sonar for submarine detection, sonic boom analysis for aircraft signature minimization, and so on, several dealing with complicated three-dimensional, short-wave interactions in anisotropic media.

By contrast, MWD mud pulse telemetry can be completely described by a single partial differential equation, in particular, the classical wave equation for long wave acoustics. This is the same equation used, in elementary calculus and physics, to model simple organ pipe resonances and is subject of numerous researches reaching back to the 1700s. Why few MWD designers use wave equation models analytically, or experimentally, by means of wind tunnel analogies implied by the identical forms of the underlying equations, is easily answered: there are no physical analogies that have motivated scientists to even consider models that bear any resemblance to high-data-rate MWD operation. For instance, while it has been possible to model Darcy flows in reservoirs using temperature analogies on flat plates or electrical properties in resistor networks, such approaches have not been possible for the problem at hand.

1.2.3 MWD telemetry basics.

Why is mud pulse telemetry so difficult to model? In all industry publications, signal propagation is studied as a piston-driven “high blockage” system where the efficiency is large for positive pulsers and smaller for sirens. The source is located at the very end of the telemetry channel (near the drillbit) because the source-to-bit distance (tens of feet) is considered to be negligible when compared to a typical wavelength (hundreds of feet).

For low frequencies, this assumption is justified. However, the mathematical models developed cannot be used for high-data-rate evaluation, even for the crudest estimates. In practice, a rapidly oscillating positive pulser or rotating siren will create pressure disturbances as drilling mud passes through it that are antisymmetric with respect to source position. For instance, as the valve closes, high pressures are created at the upstream side, while low pressures having identical magnitudes are found on the downstream side. The opposite occurs when the pulser valve opens.

The literature describes only the upgoing signal. However, the equally strong downgoing signal present at the now shorter wavelengths will “reflect at the drillbit” (we will expand on this later) with or without a sign change – and travel through the pulser to add to upgoing waves that are created later in time. Thus, the effect is a “ghost signal” or “shadow” that haunts the intended upgoing signal. But unlike a shadow that simply follows its owner, the use of “phase-shift-keying” (PSK) introduces a certain random element that complicates signal processing: depending on phase, the upgoing and downgoing signals can constructively or destructively interfere. Modeling of such interactions is not difficult in principle since the linearity of the governing equation permits simple superposition methods. However, it is now important to model the source itself: it must create antisymmetric pressure signals and, at the same time, allow up and downgoing waves to transparently pass through it and interfere. It is also necessary to emphasize that wave refraction and reflection methods for very high frequencies (associated with very short wavelengths) are inapplicable. The solution, it turns out, lies in the use of mathematical forcing functions, an application well developed in earthquake engineering and nuclear test detection where long seismic waves created by local anomalies travel in multiple directions around the globe only to return and interfere with newer waves.

Wave propagation subtleties are also found at the surface at the standpipe. We have noted that (at least) two sets of signals can be created downhole for a single position-modulated valve action (multiple signals and MWD drill collar reverberations are actually found when area mismatches with the drill pipe are large). These travel to the surface past the standpipe transducers. They reflect not only at the mudpump, but at the desurgers. For high-frequency, low amplitude signals (e.g., those due to existing sirens), desurgers serve their intended purpose as the internal bladders “do not have enough time” to distort signals. On the other hand, for low-frequency, high amplitude signals (e.g., positive and negative pulsers), the effects can be disastrous: a simple square wave can stretch and literally become unrecognizable.

Thus, robust signal processing methods are important. However, most of the schemes in the patent literature amount to no more than crude “common sense” recipes that are actually dangerous if implemented. These often suggest “subtracting this, delaying that, adding the two” to create a type of stacked waveform that improves signal-to-noise ratio. The danger lies not in the philosophy but in the lack of scientific rigor: true filtering schemes must be designed around the wave equation and its reflection properties, but few MWD schemes ever are. Moreover, existing practices demonstrate a lack of understanding with respect to basic wave reflection properties. For example, the mud pump is generally viewed with fear and respect because it is a source of significant noise. It turns out that, with properly designed multiple-transducer signal processing methods, piston induced pressure oscillations can be almost completely removed even if the exact form of their signatures is not known. In addition, theory indicates that a MWD signal will double near a piston interface, which leads to a doubling of the signal-to-noise ratio. Placing transducers near pump pistons works: this has been verified experimentally and suggests improved strategies for surface transducer placement.

1.2.4 New telemetry approach.

This understanding prompts us to look for alternatives, both downhole and uphole. We first address downhole physics near the source. We have observed that up and downgoing waves are created at the siren, and that reflection of the latter at the drillbit and their subsequent interaction with “originally upgoing” waves can lead to “random” constructive or destructive wave interference that depends on the information being logged. This is certainly the case with presently used phase-shift-keying which position-modulates “at random” the siren rotor. However, if the rotor is turned at a constant frequency, random wave cancellations are removed. The uncertainty posed by reflections of phase-shifted signals, whose properties depend on nozzle size, wavelength, annular geometry, logging data, and so on, are eliminated in the following sense: a sinusoidal position modulation always creates a similar sinusoidal upgoing pressure wave without “kinks” and possible sign changes. In fact, depending on the location of the source within the MWD drill collar, the geometry of the bottomhole assembly, the transmission frequency and the mud sound speed, the basic wave amplitude can be optimized or de-optimized and controlled with relative ease. Pump and desurger reflections at the surface, of course, still require surface signal processing.

Information in the form of digital 0’s and 1’s can therefore be transmitted by changes in frequency, that is, through “frequency-shift-keying” (FSK). But, unlike conventional FSK, we select our high frequencies by using only those values that optimize wave amplitude by constructive interference. Neighboring low-amplitude waves need not be obtained by complete valve slowdown, as in conventional PSK. If, say, 60 Hz yields a locally high FSK amplitude, it is possible (and, in fact, we will show) that 50 Hz may yield very low amplitudes, thus fulfilling the basic premise behind FSK. The closeness in frequencies implies that mechanical inertia is not a limiting factor in high data rate telemetry because complete stoppage is unnecessary, so that power, torque and electronic control problems are minimal and not a concern. Eliminating complete stoppage also supports data rate increases because the additional time available permits more frequency cycles. In fact, using a frequency sequence like “60–50–70–80” would support more than 0’s and 1’s, suggesting “0, 1, 2 and 3” encoding.

In order to make constructive interference work, the time delay between the downgoing waves and their reflections, with the newer upgoing waves, must be minimized. This is accomplished by placing the siren as close to the drillbit as possible, with the downhole turbine now positioned at the top of the MWD drill collar. This orientation is disdained by conventional designers because “the turbine may block the signal.” However, this concern is unfounded and disproved in all field experiments. This is obvious in retrospect. The “see through area” for turbines is about 50% of the cross-section. If signals can pass through siren rotor-stator combinations with much lower percentages, as they have time and again, they will have little difficulty with turbines.

1.2.5 New technology elements.

The above discussion introduces the physical ideas that guided our research. An early prototype single-siren tool designed for downhole testing is shown assembled and disassembled in Figures 1.1a and 1.1b. Multiple siren tools have been evaluated. To further refine our approach and understanding of the scientific issues, math models and test facilities were developed to fine-tune engineering details and to obtain “numbers” for actual design hardware and software. We now summarize the technology.

Figure 1.1a. Prototype single-siren tool (assembled).

Figure 1.1b. Prototype single-siren tool (disassembled).

1.2.5.1 Downhole source and signal optimization.

As a focal point for discussion, consider the hypothetical MWD drill collar shown in Figure 1.2a. Here, physical dimensions are fixed while siren frequency and position are flexible. Up and downgoing signals (with antisymmetric pressures about the source) will propagate away from the pulser, reflect at the pipe-collar intersection, not to mention the interactions that involve complicated wave transfer through the drillbit and in the borehole annulus.

Figure 1.2a. Example MWD collar used for siren frequency and source placement optimization analysis.

A six-segment acoustic waveguide math model was formulated and solved, with the following flow elements: drillpipe (satisfying radiation conditions), MWD drill collar, mud motor or other logging sub, bit box, annulus about the drill collar, and finally, annulus about the drillpipe (also satisfying radiation conditions). The “mud motor” in Figure 1.2a could well represent a resistivity-at-bit sub. At locations with internal impedance changes, continuity of pressure and mass was invoked. The siren source was modeled as a point dipole using a displacement formulation so that created pressures are antisymmetric. Numerical methods introduce artificial viscosities with unrealistic attenuation and also strong phase errors to traveling waves. Thus, the coupled complex wave equations for all six sections were solved analytically, that is, exactly in closed form, to provide uncompromised results.

Calculated results were interesting. Figure 1.2b displays the actual signal that travels up the drillpipe (after all complicated waveguide interferences are accounted for) as functions of transmission frequency and source position from the bottom. Here, “Δp” represents the true signal strength due to siren flow, i.e., the differential pressure we later measure in the short wind tunnel. For low frequencies less than 2 Hz, the red zones indicate that optimal wave amplitudes are always found whatever the source location. But at the 12 Hz used in present siren designs, source positioning is crucial: the wrong location can mean poor signal generation and, as can be seen, even “good locations” are bad.

Figure 1.2b. Drillpipe p/Δp to 12 Hz.

These calculations are repeated for upper limits of 50 Hz and 100 Hz in Figures 1.2c and 1.2d. In these diagrams, red means optimal frequency-position pairs for hardware design and signal strength entering the drillpipe. Our objective is p/Δp >> 1 (Δp is separately optimized in hardware and wind tunnel analysis). That present drilling telemetry channels support much higher data rates than siren operations now suggest, e.g., carrier waves exceeding 50 Hz, is confirmed by independent research at www.prescoinc.com/science/drilling.htm (see Figure 10.5). In our designs, we select the frequencies and siren positions, or for sirens-in-tandem, in such a way that high amplitudes are achieved naturally without power or erosion penalties (mud siren signal amplitudes are typically increased by decreasing rotor-stator gap, which leads to higher resistive torques and local sand-convecting flow velocities).

Figure 1.2c. Drillpipe p/Δp to 50 Hz.

Figure 1.2d. Drillpipe p/Δp to 100 Hz.

1.2.5.2 Surface signal processing and noise removal.

Downhole signal optimization, of course, has its limits. To complement efforts at the source, surface signal processing and noise removal algorithms must be developed that are robust. Our approach is based on rigorous mathematics from first principles. The classic wave equation states that all “solutions (measured at some point “P” along the standpipe) are superpositions of upgoing “f” and downgoing “g” waves. A differential equation for “f” is constructed. It is then finite differenced in space and time as if a numerical solution were sought. However, it is not. The Δz and Δt in the discretized result are re-interpreted as sensor spacing (in a multiple transducer array) and time step, whose pressure parameters are easily stored in surface data acquisition systems. The solution for the derivative of the signal was given in U.S. Patent 5,969,638 or Chin (1999). At the time, it was erroneously believed that telemetered data could be retrieved from spatial derivatives but this proved difficult. In recent work, the method was corrected by adding a robust integrator that handles abrupt waveform changes. The successful recovery of “red” results to match “black” inputs, using the seemingly unrelated green and blue transducer inputs, is shown in Figures 1.3a and 1.3b. Mudpump generated noise can be almost completely removed. Experimental validations are given later.

Figure 1.3a. Three step pulse recovery from noisy environment.

Figure 1.3b. Three step pulse recovery (very noisy environment).

1.2.5.3 Pressure, torque and erosion computer modeling.

The mud siren, conceptualized in Figure 1.4a, is installed in its own MWD drill collar and consists of two parts, a stationary stator and a rotor that rotates relative to the stator. The rotor periodically blocks the oncoming mud flow as the siren valve opens and closes. Bi-directional pressure pulses are created during rotation. At the very minimum, the cross-sectional flow area is half-blocked by the open siren; at worst, the drill collar is almost completely blocked, leaving a narrow gap (necessary for water hammer pressure signal creation) between stator and rotor faces for fluid passage. This implies high erosion by the sand-laden mud and careful aerodynamic tailoring is needed. Because there are at least a dozen geometric design parameters, testing is expensive and time-consuming. Thus, the computational method in Chin (2004), which solves the three-dimensional Laplace equation for the velocity potential in detail, is used to search for optimal designs. Computed results, displayed for various degrees of valve closure, are shown in Figures 1.4b and 1.4c. Other results include “resistive torque vs angle of closure” important to the design of fast-action rotors. Results are validated and refined by “short wind tunnel” analyses described later.

Figure 1.4a. Early 1980s “stable closed’ siren and improved 1990s “stable-opened” downstream rotor design.

Figure 1.4b. Streamline traces for erosion analysis.

Figure 1.4c. Velocities for erosion and pressure analysis.