Wave Propagation in Drilling, Well Logging and Reservoir Applications


Wilson C. Chin, Ph.D., M.I.T.

Stratamagnetic Software, LLC

Houston, Texas and Beijing, China


I was a troubled young man haunted by ghosts of unsolved problems. Everywhere I traveled, questions without answers plagued me. They were petroleum in nature, originating from oilfields far and near, following engineers to home offices and balance sheets, lingering on flatbeds and electronic beacons. Many phenomena were real and repeatable but could not be explained. And what was inexplicable could not be solved, improved or optimized.

Take drilling vibrations – many issues here. For one, almost all drillstring failures are blamed on resonance; yet, drillers could not drill at resonance (to enhance penetration rates) even if they tried. Or catastrophic lateral vibrations occurring at the neutral point – why can’t these violent events be detected at the surface even in vertical wells? And why have researchers not yet modeled stick-slip vibrations, bit-bounce and rate-of-penetration as they depend on BHA and lab-derived rock-bit interaction data in their simulation tools?

Or consider the most urgent problem in MWD mud pulse telemetry. Strong signal strength is needed to overcome attenuation in deep wells, typically achieved by tightening valve clearances, which implies severe power and erosion penalties. But what about harnessing nature itself – phasing downward traveling waves from the pulser, which ultimately reflect upwards, to superpose in-phase with upgoing waves created a split-second later? Or, in physics parlance, employ "constructive wave interference" where one literally amplifies signals for free? Problem is, if the conventional solid piston pulser model is applied, waves that initially travel in opposite directions can never interact after reflection, making reinforcement and modeling impossible. So what now?

Fast forward to geophysical ray tracing. Almost all studies employ the three-dimensional wave equation and Fermat’s "Principle of Least Time." This "must" be correct, after all, who can argue with Fermat? The Fermat, no less. However, this well known principle applies to conservative media only. When attenuation exists, least times for travel along rays do not apply. And worse, what if wave dissipation were only known empirically, say as an "imaginary frequency" function and not from differential equations? How do we model phase distortions due to amplitude? And what about heterogeneities?

Then there’re Stoneley waves. Most borehole studies have us believe that numerically intensive processing is required to hunt for elusive tidbits lurking in unsuspecting waveforms – this means, naturally, service company fees. The truth is, almost all of the physical properties identified in well known studies can be summarized in a few equations derived from the "kinematic wave theory" pioneered at Caltech and M.I.T. Moreover, permeability can be accurately predicted using rather simple formulas. Inexpensively. The list goes on and on.

Over the years, I have collected numerous examples of wave propagation problems that seemingly defied explanation and solution – however, applying innovative methods, we have solved all of them through analysis and logic. But rather than communicate these results in dry, abstract and esoteric scientific papers, I have chosen to motivate our tools and results in one comprehensive volume focusing on several key unifying themes, a book which may ultimately serve more purposes than those intended.

On this launch of John Wiley’s new Advances in Petroleum Engineering series, we are pleased to present the solutions to all of the above problems and more. Originally, the publisher and I discussed the possibility of starting with a math-oriented project, one that I had endorsed. However, math books already proliferate and still another would be hopelessly lost among thousands. Thus, we decided to include only the most germane approaches, together with a concise exposition of "kinematic wave" ideas, then of "displacement sources," and finally, address the insurmountable petroleum challenges cited earlier.

No other quote from classical literature is more appropriate to this effort than one from Sherlock Holmes, in The Stock-Broker’s Clerk, by Sir Arthur Conant Doyle – "I am afraid that I rather give myself away when I explain. Results without causes are much more impressive." And to those who enjoy a good mystery or an exasperating puzzle, dutifully examine the following page. Carefully peruse the bow, the way it’s held and executed. What effect does its position and velocity have on the sound created? How do waves that reflect from the ends behave at the contact itself and how do they travel afterwards? What changes when the environment changes? The key to our models can be found in this photograph, and in this book, one which we hope will stand on its math and engineering merits for many years.

Wilson C. Chin, Ph.D., M.I.T.

Houston, Texas and Beijing, China

Email: wilsonchin@aol.com

Phone: (832) 483-6899



The author gratefully acknowledges the contributions of numerous colleagues who have added to his experiences, perspectives and insights over the years – friends and individuals who studied perplexing situations through their scientific curiosity and who have, through their collective efforts, shown how seemingly disparate phenomena share more in common than their apparent differences. In particular, I thank Boeing, Schlumberger, Halliburton, British Petroleum, China National Petroleum Corporation, China National Offshore Oil Corporation, GE Oil & Gas and others, for motivating many of the problems considered in this book and contributing to the scientific literature as a result.

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. In a world increasingly dominated by finite element models where monotonous gridding and computer graphics substitute for physics and progress, the need for true engineering insight is now more important than ever, particularly in the race for economic superiority. Some will disagree, but mathematics will always have the first word, and more often than not, the last. So Phil, thanks again.