Formation Testing:

Low Mobility Pressure Transient Analysis

Wilson C. Chin, Ph.D., MIT

Stratamagnetic Software, LLC,

Yanmin Zhou, Yongren Feng and Qiang Yu

China Oilfield Services Limited, Beijing



Just two years ago, the authors published Formation Testing Pressure Transient and Contamination Analysis with John Wiley & Sons, focusing on advanced forward models and inverse solutions pertinent to modern interpretation and job planning. Many of the new models were exact analytical solutions. For example, the flagship module FT-00 solved a general formulation allowing for anisotropic media, skin effects and flowline storage pressure distortions; inverse models complementing this solution were able to provide horizontal and vertical permeabilities at any dip angle for both linear liquid and nonlinear gas flows. We could have stopped with these very satisfying results, but the "bug" that haunts researchers is a terrible beast which never sleeps.

Our results required steady-state pressure drop data at both source and observation probes, a limitation that restricted their applicability to medium-to-high mobility applications. For modern low-mobility reservoirs, this could mean hour-long wait times or more, implying low efficiencies, high costs and increasing risks of lost tools. So the authors asked, "Are there physical processes that take advantage of low mobilities – providing spherical permeability predictions within seconds?" Later, this took an even more ambitious focus. "Is it possible to predict both horizontal and vertical permeability, also within seconds, using only standard dual-probe tools?"

It is well known that fast transient drawdown-buildup methods employing single probes could, at best, provide only the "spherical permeability" kh2/3kv1/3. Because the two perms can vary by a factor of ten in anisotropic media, spherical predictions are limited in usefulness – a serious issue since both are crucial to hydraulic fracturing, borehole stability, and so on. A second equation was required to uniquely provide two numbers – ideally, one that could be rapidly evaluated from early time data. We successfully followed one important clue. In resistivity logging, where time delays and amplitude decays between transmitter and receiver coils are used to determine formation resistivity, the quantity "sin2 d /Rh + cos2 d /Rv" always appeared, where d is the dip angle. In fact, the more conductive (diffusive) the medium, the better the well log. Finding an estimate for "sin2 d /kh + cos2 d /kv" would surely help predict the relative values of horizontal and vertical permeability for a known kh2/3kv1/3. This observation motivated us to develop formation testing analogies to electromagnetic logging – our key results are reported in Chapters 3 and 4.

The authors are pleased to present these important new results, and the present book, which completely explains the ideas, methods, equations and algorithms, also provides detailed calculations and applications examples. At the present time, we are developing sophisticated test fixtures to validate our methods and calibrate new tools. This is surely an exciting time for formation tester development and for petroleum exploration well logging.

It is important to emphasize that the approaches developed here did not materialize overnight – they required a long-term commitment to understanding the fundamental physics, developing analogies between seemingly different disciplines like fluid dynamics and electromagnetics, and an obsession with solving important problems that ultimately benefit everyone in society. The authors recognize that creative work requires continuing motivation and investment in people – so our endeavors will continue, whether or not oil prices drop further – we won’t be the ones turning out the lights.

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

Houston, Texas


Phone: (832) 483-6899



The lead author gratefully acknowledges the insights, experiences and friendships he acquired during his early exposure to formation testing at Halliburton Energy Services in the 1990s; and in particular, the contributions of his colleague and friend Mark Proett, now with Saudi Aramco, who shaped his initial thinking and approach to pressure transient and contamination analysis.

In 2004, the United States Department of Energy, through its Small Business Innovation Research (SBIR) program, awarded approximately two-hundred grants in support of high-risk efforts in all areas of energy, e.g., nuclear fusion, plasma physics, batteries, green energy, and so on. Four were allocated to fossil fuels – and, of these, two would support the lead author’s projects, entitled "Formation Tester Permeability Prediction in Tight Gas Sands" and "Formation Tester Immiscible Flow Response in Horizontally Layered Media." The insights acquired in these researches no doubt fueled further innovations. For these past opportunities, the lead author is very appreciative.

All of the authors are indebted to China National Offshore Oil Corporation (CNOOC) and its subsidiary China Oilfield Services Limited (COSL) for its support and encouragement throughout our work in formation testing. Without the open access that we were granted to its tools, plans, staff and insights, we would not have been able to focus on the problems that really mattered. The authors appreciate the company’s permission to publish significant portions of an internal report documenting our new low mobility inverse methods.

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 CNOOC/COSL team is newly conversant in English). Without Jenny’s interpretation skills and willingness to learn the technology, progress would have slowed and this formation testing monograph – the second in two years – may not have seen publication.