Formation Testing

Preface

Well logging professionals understand that “the success of a job depends on pre-job planning.” This is most certainly true of formation testing, where numerous difficult-to-answer questions arise daily on a worldwide basis. For example, how long should the field engineer pump in order to obtain a clean sample? What procedures are needed to obtain good estimates for permeability and anisotropy from pressure transient measurements? Answers are challenging to obtain because the underlying physical problems are complicated. How mudcake grows (this differs significantly from permeable to tight formations) affects invasion depth and mixing near the well – and hence the pumping time required. But contamination and clean-up also depend on dip angle, flow rate, hardware (e.g., single-probe versus dual packer tools), and so on. Pressure transient analyses yield good estimates for permeability and anisotropy, at least in classical well testing. But in formation testing, the effects of flowline and annular storage introduce interpretation difficulties made worse by tight formations – in addition, the viscosity of the underlying flow may be uncertain if the degree of mixing is not well characterized. However, it is clear that simulation, while not perfect because all new formations are not well understood, is a necessary part of the job; fortunately, any recommendations will ultimately be refined and more important as additional data becomes available. So it is with reservoir characterization … progress builds upon prior progress.

Fine, then. “Let’s rock and roll.” But really, it’s not that easy. One might believe that many of the required mathematical formulations needed are already available, as had been the case with well testing, in classical British textbooks on heat transfer (e.g., Carslaw, H.S., and Jaeger, J.C., Conduction of Heat in Solids, Oxford University Press, London, 1946). This is so, at least with spherical source models in homogeneous isotropic media, modeling flowline storage but not skin effects. However, when the roles of dual-probes, dual packer extensions, dip angle, layering, skin effect, gas flow thermodynamics and other specialized oilfield variables must be understood, there is no substitute for original research and good mathematical description. A detailed literature search shows that the required models and software are simply nonexistent. And what is available is limited in usefulness – very often, models and services offered by commercial organizations are based on cursory analysis, lacking in scientific rigor and open discussion, and unfortunately shrouded in secrecy.

In 2004, the United States Department of Energy, through its Small Business Innovation Research program, awarded approximately two hundred awards nationally in diverse areas such as plasma physics, nuclear energy, refining, environmental waste remediation, and so on. Importantly, four grants were made for fossil fuel and well logging research – two of these awards, both won by the lead author, related to formation tester interpretation and analysis.

This author gratefully acknowledges Award DE-FG02-04ER84082, entitled “Formation Tester Permeability Prediction in Tight Gas Sands,” and Award DE-FG02-04ER84083, entitled “Formation Tester Immiscible Flow Response in Horizontally Layered Media.” Computational methods were funded by an earlier grant, Award DE-FG03-99ER82895, entitled “Irregular Grid Generation and Rapid Three-Dimensional Color Display Algorithm,” while extensions to deviated well applications were supported in part by DE-FG02-06ER84621 entitled “Borehole Seismic Modeling Using Curvilinear Boundary-Conforming Meshes.” These grants carried stipends significant to any startup organization and indirectly supported future activities in Measurement-While-Drilling and borehole electromagnetic logging.

This book serves multifaceted purposes: (i) it explains what the important fluid-dynamical problems are in formation testing, (ii) it surveys and critiques existing analysis and interpretation models, (iii) it develops key suites of mathematical models for software implementation, (iv) it provides detailed calculations and graphical results illustrating important physical concepts, and (v) it completely summarizes all new models made available for distribution to all industry-wide users. We importantly emphasize that all of the methods described in this book, with the exception of the axisymmetric contamination algorithms in Chapter 4, which are owned by Halliburton Energy Services and which were presented in detail earlier at the June 2005 SPWLA meeting in New Orleans, are available for use under flexible executable and source code licenses (the 2005 invasion models are now superseded by forthcoming nonaxisymmetric algorithms for horizontal wells which will be reported at a later date). Industry partners are encouraged to use the new methods – and even incorporate the new algorithms in company software and business models.

How does an engineer find his niche in, of all things, petroleum fluids modeling? I earned my Ph.D. at MIT and earlier degree from Caltech. My major areas were high-speed aerodynamics and wave propagation, which are synonymous with applied math and nonlinear differential equations – specialties that focus on rigorous solutions to practical problems. From MIT, I joined Boeing’s prestigious computational fluid dynamics group in Seattle and, three years later, headed up engine flow analysis at United Technologies’ Pratt and Whitney, the company that develops the world’s most powerful jet engines.

But the thrill of the hunt lost its allure, despite the thrill of being published in journals and attending high-tech conferences. Like all of you, I was attracted to the petroleum industry because of its excitement, the opportunities it offered and the challenges in confronting the truly unknown. That was just five years into my career, as I joined a new industry undergoing rapid change – a transition requiring me to learn anew the fluid-dynamics of flows as far underground as my prior learning was above ground. Since then, two decades have elapsed, in which I actively engaged in oilfield research and development. In that time, for example, with leading operating and service companies like British Petroleum, Schlumberger and Halliburton, I was fortunate to have been continuously challenged by new problems both mathematical and operational. These organizations taught how science was not only significant in its own right, but why math modeling, hardware design and good measurements go hand-in-hand – and with this, the importance of people, training and sound technology transfer in the long-awaited “great crew change” happening this very minute.

This flow analysis and simulation book is unique because it brings two decades of perspectives and experience on the fluid mechanics of Darcy flows to bear on the fundamental problems facing formation testing. Many commonly accepted “recipes” are critiqued and incorrect underlying assumptions are noted. We aim at a rigorous and scientifically correct approach to pressure transient and contamination modeling. For each of the important problems surveyed, the state-of-the-art is examined, and analytical or numerical solutions are offered – with the exact physical assumptions always stated precisely and the mathematical strategies clearly presented. Industry “common sense” approaches are avoided: once the correct model is formulated, the entire arsenal of analysis tools is brought to bear – and, in all cases, we strive to present usable tools to users in such a way that new results can be applied immediately and effectively. There are no secrets – all of our methods are fully disclosed, with only limited key algorithms falling under the scope of intellectual property protection.

Fortunately, this book does not require advanced mathematics or numerical analysis to understand. Great care was undertaken to explain and develop very advanced methods in simple terms that undergraduates can comprehend. This is essential to encouraging scientific curiosity and in promoting an atmosphere of credibility and open discussion. The great majority of the ideas and results presented here are new and have never been published. In order to communicate these ideas effectively, they are not presented all at once. Instead, the earlier chapters cover basic essentials – notions which are nonetheless state-of-the-art to the literature – new ideas that raise questions and issues that in turn motivate the need to develop even more methods as is done in the remaining six chapters. This book is amply illustrated with tables, pictures and line plots in order to provide the “physical feel” needed by field engineers, so that an understanding of the mathematics is not key – however, enough detail is provided so that oil company and university researchers desiring to extend the methods can do so with minimal up-front time investment.

We emphasize that our methods can be used for a variety of applications, in addition to forward and inverse modeling for formation evaluation, the main focus of this book. They can be used in new hardware design, say for improved permeability prediction or near-well clean-up; for faster real-time methods in downhole drilling applications; for optimizing new “sampling while drilling” tools; for training neural net simulators for flexible field and microprocessor application; or, for formation tester tool selection in different geological settings. The possibilities, we have found, are...