Parent-Child, Multilateral Well

and Fracture Interactions




Wilson C. Chin

Xiaoying Zhuang





You’re a petroleum engineer confronting that dreadful question, "Where to drill that next infill well?" Desperation sets in. Production has fallen big time. Management is unhappy. Shareholders are furious. A few months ago, the Wall Street Journal reported that, through 2017, one operator had spaced its wells 330 ft apart, then increased this to 500 ft (see "A Fracking Experiment Fails to Pump as Predicted, B. Olson, July 4, 2019). But the Journal of Petroleum Technology recently gave different numbers, now "450 ft or 600 ft" (see "Simple Well Spacing Calculations are Inaccurate and Costly," T. Jacobs, November 2019). Sometime back, the present author recalls a smaller 200 ft. Or something like that. Whatever the specifics, the consensus is clear – too close a spacing may be too bad and too late.

Now, let’s turn back the clock to Fluids 101. You’re sitting in your first well testing class absorbing the subtleties behind "pressure transient analysis." Changes in pressure in oil and gas reservoirs satisfy a so-called "diffusivity equation," also known as the "heat equation," a well understood pillar of mathematical physics whose inferences have withstood the test of time in numerous disciplines. Heat transfer, nuclear physics, contamination modeling, you name it. The instructor starts with a simple problem and, to be sure, invokes very limiting assumptions in order to get usable answers. For example, simplifications might include vertical well production in an infinite reservoir, isotropy, homogeneity without layering, liquids as opposed to gases, and so on. Eventually, the problems get tougher. In all cases, you recollect that it is not the time "t" or the radial position "r" alone that is important. In the simplest cases, it is the "lumped" combination "fmcr2/(kt)" that appears, where f is porosity, m is viscosity, c is compressibility and k is permeability.

Things can get complicated too. Other models account for square farfield boundaries. Eccentrically placed wells in circular domains. Effects of five-spot or nine-spot production patterns. Layering. All of these lead to more intimidating math functions. Not just "exponentials," but "error functions," "complex complementary error functions," Ei and Bessel symbols, and more. And so, to get simpler models involving quantities that can be easily plotted and interpreted, researchers employed "early time expansions" and late time "asymptotic approximations," with everything not falling between these two limits relegated to an ambiguous "middle time" twilight zone. So "early, middle and late times" are not absolutes like "1, 2 and 3 hours" or "100, 200 and 300 hours." Relative times must be defined with respect to the algebraic expansion parameter "fmcr2/(kt)" itself, and possibly more "dimensionless variables," depending on the complexity of the problem – clearly, fluid and formation properties dictate time separations.

Production from modern reservoirs likewise satisfies "diffusivity equations," although in their original, less simplified formats. Gone is the azimuthal symmetry expected from vertical wells. The radial "r" coordinate must be replaced by "x, y and z" so that any tools employed mathematically must escalate in sophistication. Because wells may be drilled in any manner dictated by geological concerns, in reservoirs that may be anisotropic and inhomogeneous at Nature’s discretion, simple solutions will not be possible. Artifacts like "fmcr2/(kt)" may be as ancient as childhood dreams. But the fact is, well testing and petroleum production are one and the same physical phenomena and identical ideas and approaches apply. Well separations, like early and late times, are not absolutes. They depend on formation and fluid properties. And on wellbore constraint types and levels utilized in production. On farfield drive models. And whether the produced fluid is liquid or gaseous. And in the latter case, on the thermodynamic process involved. Even then, optimal separations (or equivalently, numbers of wells) will depend on time – and different times for different reservoirs.

Machining learning may uncover the relevant parameters with enough statistical analysis, and perhaps, will help us better understand a reservoir’s underlying geology – but it will almost certainly rediscover Darcy’s diffusivity equation and re-establish the importance of simulation in a world driven by deterministic events. What we need now are better simulators, more rapid calculations, highly visual output, and lower computer and labor costs – and importantly, validated physical models that credibly simulate downhole physics while maintaining a user-friendly working interface. In thought-provoking discussions with domestic operators, and marketing staff of leading oil service companies, one surprising and unexpected response was all-too-often encountered. Simulators were too difficult to use, required excessive computing resources and training, and in any event, needed data that was simply unavailable. Company staff either had little or no access to these tools or were unfamiliar with their operation. Thus, rules of thumb like "200 ft" or "400 ft" would proliferate. Issues related to "parent-child, multilateral well and fracture flow interference," the subject of this book, now dominate our headlines – and will be the focus of our MultiSim model.

The author, an experienced reservoir engineer, mathematician and software developer, has refined this simulator over the past two decades, outlined in detail in Reservoir Engineering in Modern Oilfields: Vertical, Deviated, Horizontal and Multilateral Well Systems (John Wiley, 2016) and Quantitative Methods in Reservoir Engineering, 2nd Edition (Elsevier, 2017). In the present book, we have devised six very difficult flow problems based on client suggestions, which are described in Chapters 4 – 9, and have shown how usable solutions can be obtained in two or less hours of desk time. Our approach models only controlling parameters like multilateral topology, macroscopic reservoir properties, well constraints and drive models. Further, we do not promise forecasts accurate to the last percent – not an unfavorable assessment given that reservoir simulator inputs are rarely known with precision anyway.

And we’ll explain why many competing models, despite their high costs and resource intensive requirements, actually deliver much less. But our simulator is accurate and easy to use. It will most likely recommend the better choice in comparative runs and describe how production will respond to changes in well position, type and trajectory. If one drilling scenario predicts 15% more production, you’re probably in luck and won’t lose. We have taken a presentation approach where problems and solutions are summarized early on, as if written for trade journal publication, with details available later to interested readers. This provides a rapid, "bird’s eye" perspective of our technology and capabilities, and will prove useful to those anxious to duplicate our results and test drive a new simulation engine that’s programmed to roar.


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

Houston, Texas




The Fourth of July will long remain my day of revelation for 2019. I awoke from an overseas trip to the Wall Street Journal article, "A Fracking Experiment Fails to Pump as Predicted," describing one company’s experience with production problems arising from wells drilled too closely together.

Two years ago, a major supersize fracking operation that many said would represent the future of the U.S. drilling boom was initiated. To reduce costs and avoid problems that can occur when single shale wells are spaced too closely together, an experiment was begun where as many as sixty oil and natural-gas wells would be completed from one location. While many looked promising in 2017, their performance had fallen off very significantly (e.g., compare Figures 9.1.6 and 9.1.7).

It turned out the problem afflicted an entire industry. Magic rules of thumb, many lacking in reservoir engineering rigor, proliferated. Two hundred feet, then three hundred, then ever increasing separations would be key to productivity. But this was nothing new. In 2014, the senior author attended an industry seminar where one company expert, asked how fracture densities were selected, replied, "If a competitor adopted a hundred fracs, we’d go two hundred."

The WSJ article was not the first to warn of such problems. But it was key to highlighting industry issues that I was unaware of. I would research and study the literature. Spend sleepless nights dreading nightmares. Worry about unknowns rapidly becoming reality. About "frac hits," "parent-child interference, the need for new petrophysics, and how complexities with multilaterals defied analysis.

And "analytical versus ‘data driven’ approaches," as if statistics could replace predictive models ground in physical principles. This book shows how difficult problems can be simply studied using rapid, interactive, but rigorous methods. Over several weeks, the authors devised challenging scenarios showing that key features can be modeled, solved and understood . . . plus carefully documenting our findings.

And so, thank you, Brad Olson, for writing an excellent and enlightening piece; to Xiaoying, for your diligence and hard work; and, as usual, Phil Carmical, Publisher and Acquisition Editor, for your support, interest and keeping the faith all these years.

Wilson C. Chin

Houston, Texas