MULTIPROBE PRESSURE TESTING

AND RESERVOIR CHARACTERIZATION -

PRESSURE TRANSIENT, CONTAMINATION,

LIQUID AND GAS PUMPING ANALYSIS

by

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

Stratamagnetic Software, LLC

Beijing and Houston

Preface

In the early 1990s, a multiprobe formation tester was introduced by a major oil service company that was innovative in its design. This tool, consisting of an active “sink” probe and a passive “horizontal” observation probe displaced azimuthally 180 deg from the sink, would offer predictions for both kh and kv permeabilities. However, at low mobilities, measured pressure drops at the latter were significantly less than those at the sink. The same was true of the “vertical” probe, located several feet away, coincident with the sink azimuth. These limitations reduced the versatility and usefulness of the multiprobe design, substantially decreasing the accuracy behind many tester predictions.

Petroleum manufacturers have since improved formation tester capabilities by positioning multiple probes azimuthally about the tool body, say three, four and possibly more, and additionally, introducing more probe rows at more axial locations. But engineering design, job planning, and predictions for permeability, anisotropy, pore pressure and compressibility would require fully three-dimensional pressure models that are lacking even to this day. And while commercial finite element solvers can simulate liquid pressure transients to some extent, it is still not possible to model the effects of mudcake buildup, invasion and supercharge – plus the nonlinearly coupled pressure and convective-diffusive processes that control miscible multiphase flow mixing and contamination. Furthermore, commercial solvers provide only sparse documentation on the algorithms used and even fewer validations. Many computed results are awash with excessive round-off and truncation errors to the extent that “artificial viscosity” and fictitious diffusion dominate the actual consequences of true permeabilities and viscosities.

Thus, important “what if” questions related to pressure interpretation, cleaning efficiency and sampling could not be answered, leaving many field issues unresolved. Even newer idealized source models, many including supercharge capabilities, are not useful since modern multiprobe tools function in a fully three-dimensional environment. Moreover, practical solvers must be portable, run inexpensively on standard computers, and importantly, produce and display accurate and reliable answers rapidly with minimal user expertise and intervention. In this light, we have successfully addressed the most challenging formation testing problems in pressure transient analysis and fluid sampling. These problems, their formulations, mathematical solutions and applications, form the subject of this book.

We considered three, four and up to twelve-probe tools with nozzles distributed azimuthally about the mandrel – nozzles that may differ in size and shape, which may operate independently (with different flow rates, start and stop times) or in concert with others in pressure tests, and whose solutions were subjected to exhaustive physical tests and programming validations. Once we were satisfied with their performance in terms of accuracy and numerical stability, they were nonlinearly coupled to convective-diffusive concentration equations, plus invasion, supercharge and dynamic mudcake filtration models to simulate in-situ fluid contamination processes that control the integrity of fluid sampling operations. Only with such models can we optimize oilfield activities.

We did not stop here. We also implemented convergence acceleration methods for steady flow analyses to perform calculations as much as twenty times more rapidly than straightforward transient numerical schemes. Their purpose was real-time creation of massive databases in “DP versus kh and kv” useful for history matching field data at the rigsite to theory – and, in particular, to solving the full three-dimensional inverse problem exactly, also addressed in this book. That’s right – determining all the possible (kh, kv) datasets that are consistent with measured pressure drops at one or more pumping nozzles located azimuthally about the wellbore – to support inverse solutions.

And further, we considered fully transient nonlinear gas pumping, again for three and four probe tools whose nozzles may be round, oval or slotted. No approximations, for instance, like linearizing “average pressure” methods, were used that would compromise accuracy. We started with Muskat’s time-tested exact gas formulation (assuming general thermodynamic conditions) and transformed it exactly to a form similar to that for linear liquid flow equations – and made use of the stable pressure transient solvers developed early on in this book. As if this were not enough, we also extended methods to study traditional “dual probe” tools, that is, formation testers with two axially separated probes, to newer instruments with larger arrays of axially separated probes. In this endeavor, we drew upon physical analogies found in array resistivity or electromagnetic logging interpretation.

All in all, the author hopes that this new body of knowledge, together with the idealized source models he has developed in five prior books with John Wiley & Sons over the past decade, will bring greater efficiencies to the industry and more accurate well logging. This being said, one might believe that interest in permeability research would soon peak in an industry that has strived over decades to overcome challenges posed by unknown underground formations. However, the advent of newer azimuthal tools should instead bring greater accuracy and more applications to peameability anisotropy and heterogeneity mapping.

One beneficiary of the new technology – joining traditional oil and gas exploration and drilling – is modern geothermal and sustainable energy development. A quick Google or Bing search on reservoir characterization in these subject areas reveals several recurring themes – permeability, permeability and more permeability. While the main text of this new book from Elsevier focuses on physical principles, mathematical models and computational approaches, we have shared our excitement by welcoming these new applications in a final chapter that highlights perspectives offered by leaders in geotechnical modeling. We emphasize that the equations and the methods remain unchanged. However, development aims and objectives between conventional and newer applications will differ. Toward this end, selected Abstracts are discussed with a view toward broadening and motivating our use of the tools described here in new and important applications.

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

Beijing and Houston

Email: stratamagnetic.software@outlook.com

Acknowledgements

The author wishes to thank the numerous persons and organizations that have contributed to his interests and successes in formation testing research. Among these are Mark Proett, colleague and friend, who guided his initial investigations years ago; Yongren Feng at China Oilfield Services, who motivated many of the methods, ideas and applications in this book; and Xiaoying “Jenny” Zhuang, without whose interpretation skills the author would not have understood the many exciting conversations and debates conducted in a foreign language.

He also expresses his gratitude to the United States Department of Energy, which has supported his research in multiple fields over the years; but, especially, in two formation testing research awards in 2004 offered through its Small Business Innovation Research (SBIR) program. The author is additionally grateful to his colleagues at BP Exploration, Schlumberger, Halliburton, BakerHughes and GE Oil and Gas who have contributed immeasurably to his understanding of the geosciences over decades of exciting professional activity.

Last but not least, the author is indebted to Jennette McClain, Elsevier Acquisitions Editor, for highlighting newer emphases in geothermal and sustainable development applications, and for suggesting improvements to the manuscript. All conclusions represent the author’s exclusive opinions and views. The research and software development work in this book was supported entirely by Stratamagnetic Software internal funding. Hardware capabilities and characteristics of industry tools described, representing features that may not correspond to those of actual tools, are offered for discussion purposes only.

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

Beijing and Houston

Email: stratamagnetic.software@outlook.com