
Reservoir Simulation and Well Interference
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Charged in the 1990s with solving some of petroleum engineering's biggest problems that the industry deemed "unsolvable," the authors of this innovative new volume solved those problems, not just using a well-published math model, but one optimized to run rapidly, the first time, every time. This not only provides numerical output, but production curves and color pressure plots automatically. And each in a single hour of desk time.
Using their Multisim software that is featured in this volume, secondary school students at the Aldine Independent School District delivered professional quality simulations in a training program funded by some of the largest energy companies in the world. Think what you, as a professional engineer, could do in your daily work. Valuable with or without the software, this volume is the cutting-edge of reservoir engineering today, prefacing each chapter with a "trade journal summary" followed by hands-on details, allowing readers to replicate and extend results for their own applications.
This volume covers parent-child, multilateral well, and fracture flow interactions, reservoir flow analysis, many other issues involving fluid flow, fracturing, and many other common "unsolvable" problems that engineers encounter every day. It is a must-have for every engineer's bookshelf.
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Wilson C. Chin, PhD, is an experienced petroleum engineer with over twenty books published by Wiley-Scrivener and other leading publishers and over a hundred articles published in scientific journals. He holds four dozen domestic and international patents and has received five major awards with the United States Department of Energy. Mr. Chin's interests include reservoir simulation, measurement while drilling, borehole electromagnetics, managed pressure drilling, formation testing, downhole vibrations, and drilling and cementing rheology.
Xiaoying Zhuang has almost a decade of experience in borehole rheology and reservoir fluid mechanics. From 2009 to 2011, she served as Co-Investigator for the United States Department of Energy in their sponsored research into well control, leading to a well-received book appearing in English and Chinese on the subject. "Jenny" has co-authored ten papers in her areas of technical interest.
Content
Preface xi
Acknowledgements xv
1 Parent-Child, Multilateral Well and Fracture Flow Interactions 1
Additional questions raised 1
Problem identified 2
Why call them frac hits? 5
Is a frac hit model possible? 5
1.1 Reference 7
2 Reservoir Flow Analysis - Concise and Rigorous Summary 9
2.1 Governing Equations and Numerical Formulation 9
Steady flows of liquids 10
Difference equation formulation 10
The iterative scheme 12
Modeling well constraints for liquids 13
Steady and unsteady nonlinear gas flows 15
Steady gas flows 16
Well constraints for gas flows 18
Transient, compressible flows 19
Compaction, consolidation and subsidence 22
Boundary conforming grids 23
Stratigraphic meshes for layered media 24
Modeling wellbore storage 25
2.2 References 27
3 Reservoir Simulation - Strengths, Limitations and Strategies 28
Deficiencies affecting all simulators 28
3.1 Rectangular versus Curvilinear Coordinates 29
3.2 Fracture Simulations and Analytical Subtleties 33
Aerodynamic analogies 33
3.3 A Digression - Advances in Geometric Modeling 35
3.3.1 Airfoil and three-dimensional wing flows 35
3.3.2 Two dimensional planar reservoir flows 36
3.4 Formulation Errors in Commercial Simulators 40
Commingled reservoirs 40
Unit mobility flow 40
Well constraints, pressures and rates, kh products 40
Upscaling methods and averaging 41
Geometric gridding 42
Input/output issues and 3D color graphics 42
Matrix solvers and numerical inversion 42
Meaning of farfield boundary conditions 43
Grid density 43
Simulator design philosophy 44
3.5 References 45
4 Parent-Child Well and Fracture Flow - A Simple Steady-State Example 46
4.1 A Simple Example - Steady Flow Parent-Child Well and Fracture Interactions 46
Reference examples 47
More interesting calculations 47
Closing remarks 53
4.2 Two Reference Single-Well Analyses 54
Reference Example A 54
Reference Example B 57
4.3 Detailed Two-Well and Fracture Flow Analyses 59
Run 1 - Two wells, different pressure constraints, homogeneous medium 59
Run 2 - Two wells, identical pressure constraints in homogeneous isotropic medium 81
Run 3 - Return to Run 1 well constraints, with Wells 1 and 2 joined using uniform fracture 84
Run 4 - Incomplete fracture penetration at Well 1 91
Closing remarks 96
4.4 References 96
5 Hydraulic Fracture Flow for Horizontal Wells in Anisotropic Media 97
5.1 Horizontal or Multilateral Wells Intersected by General Hydraulic Fractures in Fully Transient Flow 97
Run 1 99
Runs 2, 3 and 4 101
5.2 Detailed Software Analysis 105
5.2.1 Run 1. No fractures along vertical-to-horizontal well (for reference baseline comparisons) 105
5.2.2 Run 2. Horizontal well intersected by a single hydraulic fracture 142
5.2.3 Run 3. Horizontal well intersecting two fracture planes 147
5.2.4 Run 4. Horizontal well intersecting three fractures 149
5.2.5 Runs 5-6. Effects of anisotropy and fracture orientation 153
Run 5 153
Run 6 155
5.3 References 157
6 Cube Models in Reservoir Development 158
6.1 Well Spacings, Parent-Child Effects and Reservoir Strategy in Modern Drilling 158
6.1.1 Basic optimization problems 158
6.1.2 Reservoir flow simulation versus statistical modeling approaches 160
6.1.3 Cube model set-up and computed results 161
6.1.4 Reservoir optimization and cost effectiveness 166
6.1.5 Closing remarks 168
6.1.6 References 169
6.2 Detailed Software Analysis 170
6.3 A More Optimal Production Method 197
6.4 References 200
7 Simulating While Drilling - Extending a Vertical Well Horizontally During Transient Production 201
7.1 Declining Production with Horizontal Lateral Solution 201
7.2 Detailed Software Analysis 207
7.3 References 236
8 Simulating While Drilling - Adding a Complicated Multilateral Well During Transient Production from a Vertical 237
8.1 Vertical and Subsequent Multilateral Neighboring Well 238
8.2 Detailed Software Analysis 243
8.3 References 264
9 Heterogeneous, Anisotropic, Layered Reservoir with Finite Tilted Fracture Plane Produced by Multilateral Wells 265
9.1 Five Comparative Production Scenarios 266
Run 1. Uniform isotropic reservoir (base reference) 267
Run 2. Effect of high permeability fracture on Run 1 272
Run 3. Highly heterogeneous three layer reservoir, isotropic flow within each sub-domain, no fracture planes 274
Run 4. Effect of anisotropy on Run 1 (again, uniform kx, ky, with kz 50% smaller), no fractures 276
Run 5. Nonlinear gas flows, results compared with Run 1 liquid baseline, assuming uniform kx, ky and kz, no fractures 278
Closing remarks 279
9.2 Detailed Software Analysis 280
Run 1. Uniform isotropic reservoir (base reference) 281
Layered geological description 281
Software caution 283
Layered drilling description 287
Layer results and flow decline curves 300
Run 2. Effect of high permeability fracture on Run 1 308
Run 3. Highly heterogeneous three layer reservoir, isotropic flow within each sub-domain, no fracture planes 312
Run 4. Effect of anisotropy on Run 1 (again, uniform kx, ky, with kz 50% smaller), no fractures 316
Run 5. Nonlinear gas flows, results compared with Run 1 liquid baseline, assuming uniform kx, ky and kz, no fractures 321
9.3 Closing Remarks 328
9.4 References 328
10 Advanced Reservoir Modeling with Multisim 329
10.1 Features 330
Reservoir Description 330
Well System Modeling 330
Additional Simulator Features 330
10.2 Licensing Options 331
Multisim 331
Complementary Models 331
4D TurboView 331
Fluid Tracer 331
Formation Testing Suite 331
10.3 Disclaimer 332
End-User License Agreement (EULA) 332
Grant of license 332
Descriptions of other rights and limitations 333
Termination 334
Copyright 334
No warranties 334
Limitation of liability 334
Further disclaimers 335
Additional restrictions 335
End of EULA 335
Cumulative References 336
Index 351
About the Authors 359
Wilson C. Chin 359
Xiaoying Zhuang 376
1
Parent-Child, Multilateral Well and Fracture Flow Interactions
Our industry is confronting headwinds driven by uncertainty, confusion and fear, and quite likely, will be prone to act before all the facts are in. Drillers and field engineers believe that they have uncovered new physical phenomena. Rapid production declines, unlike those in past decades, certainly point to new possibilities in petrophysics - governances of Nature that we have little time to explore and tackle. The evidence is there. Just look around. The town folk are amassing. The consequences are disastrous. But big data, machine learning and artificial intelligence just might mine deeper insight. Problem solved. And the lone cowboy rides off into the sunset.
Additional questions raised. But the evidence is circumstantial. What is real are advances in hydraulic fracturing that have supported resurgences in oilfield activity. High permeability conduits created in the formation have accelerated the production of oil just about everywhere. Reserve estimates were predicted to escalate. But these increases would suddenly drop, much to the consternation of producers and bankers, destroying cash flow forecasts and independents' ability to continue loan payments. However, all of this would not be unexpected.
Unless an underground reservoir is continuously replenished by pressure drives charged by additional pools of oil (and these do, by the way, exist - e.g., see Mahfoud and Beck (1995)), any production must result from "sealed reservoirs" with initially high pressure. Thus, the amount of recoverable oil or gas is limited. Much of the reservoir is occupied by matrix rock and immovable fluids. The volume that remains is finite. Fractures remove movable fluids rapidly and leave the reservoir high and dry quickly. And so, fast declines will remain a fact of life.
In 2014, the senior author attended a meeting at a large oil service company where one of its clients was asked, "How do you determine fracture density?" This individual, a well respected industry spokesman, reluctantly admitted, "If your neighbor does 'N' number of fracs, you do '2N.'" So there was little after-thought in making operational decisions. There was neither time nor leeway to analyze. If your choice increased production, if only for a short duration, that was fine. And that's human nature, until the unavoidable reality sets in.
Problem identified. In recent years, there has been a proliferation of papers addressing the issues cited above. We will not offer any comprehensive summaries or reviews. Readers are encouraged to search for relevant case studies using keywords identified below. To highlight present industry confusion, several publications are discussed, with our comments, if only to illustrate the degree of confusion.
An interesting analysis appears in "To Solve Frac Hits, Unconventional Engineering Must Revolve Around Them," T. Jacobs, Journal of Petroleum Technology, April 2019, pp. 27 - 31. Noting that "the U.S. shale sector is expected to drill about 20,000 horizontal wells in 2019," the author observes that, "The impetus for an engineering overhaul is being forced by the prevalent well-to-well fracture interactions known as frac hits. These events are the subject of intensifying study by U.S. and Canadian shale producers that have attributed them to lowering oil recovery factors from new child wells by 20 - 40% while inflicting even higher losses on older, yet less productive, parent wells."
And a scientific overhaul is seriously needed. The senior author, an experienced reservoir engineer with major operating and oil service company experience, has never seen a comprehensive reservoir engineering assessment addressing production issues. For instance, "What well constraints were applied to parent wells, before and after, and in child wells after development? Details about drive mechanisms, well layouts, intervention activities, initial reservoir pressures?" What of supporting numerical simulations? Most computer models are difficult to use, require highly trained personnel, and unfortunately, are limited in the complexity of the physical features that can be easily described.
And catch-all terms like "frac hits" are coming under increased scrutiny. "We know they are entrenched, but honestly, they don't mean much," said George King, an industry expert, making a point that well interactions in question are not all the same. "Some are harmful, some are helpful, some are temporary, some are long-term." The paper also lists multiple strategies, e.g., "wider well spacing," "staggered wells (wine rack configuration)," "cube development," "rolling development," and "slowback," all of which should be studied using physics-based models evaluated under a wide combination of input parameters.
Another useful discussion is offered in "The Problem with Bigger Fracs in Tighter Spaces," S. Rassenfoss, Journal of Petroleum Technology, December 2017, pp. 28 - 31. The author identifies issues that should be addressed. "How does fracturing affect the reservoir between tightly spaced wells?" "How do we explain sudden drops in production?" "Could an existing well have produced the reserves without the infill well?" "How are surges of fluids flowing well-to-well through connected fracture systems described?" The paper also offers two self-explanatory visuals, reproduced in Figures 1.1 and 1.2. The last paragraph in Figure 1.2 is enlightening and supports the authors' contentions above, namely, that existing models are difficult to use, requiring inputs that are either difficult to obtain or simply non-existent. The present book hopes to convey two ideas - (1) the main influencers are available, and (2) simple, but rigorous, analyses are possible that address most physical effects, requiring minimal effort or specialized training, assuming the level of an undergraduate petroleum engineer.
The article "In the Battle Against Frac Hits, Shale Producers Go to New Extremes," T. Jacobs, Journal of Petroleum Technology, August 2018, pp. 35 - 38, interestingly describes one of the "new extremes" utilized in drilling practice. According to the author, "Most in the shale business know these projects as 'cube developments.' Their scope of work has moved operators away from developing wells one at a time to a half dozen or more at a time. Each cube project is done from supersized well pads that host four to six rigs, two pressure pumping fleets, and hundreds of people every day."
But just a year later, in "A Fracking Experiment Fails to Pump as Predicted," Wall Street Journal reporter Bradley Olson, on July 4, 2019, described how one company's supersized operation, one that two years earlier was thought to represent the future of the U.S. drilling boom, would lose its attractiveness. To reduce costs and avoid production problems when wells are spaced closely together, the company pioneered its "Cube Model" for reservoir development using numerous multilateral wells. Initial results were promising. However, subsequent results differed from those expected.
A more tractable idealization of this problem is presented later in Chapter 6 in which the development plan in Figure 1.3 is replaced by a nine multilateral well system with three wells residing in three separate rows. A full-field analysis is presented, requiring all but several minutes of simulation time on a Windows i5 computer - but just as important, a simpler, much less expensive drilling configuration using only two deviated wells, was identified offering the same production. Cube models do reduce drilling expenses through obvious economies of scale, but ultimately, the reservoir only contains as much oil as the volume holds. In this sense, careful cash flow management is still a must.
In the cautionary article "Factory Drilling is No Substitute for Formation Evaluation," E. Sprunt, World Oil, July 2014 warned, as early as five years ago, of the dangers behind methods that may not be grounded in physical principles. Ms. Sprunt, who holds a Doctorate from the Massachusetts Institute of Technology, is the president-elect of the American Geosciences Institute, and was the President of the Society of Petroleum Engineers (SPE) in 2006. In that article, she emphasizes that, "In a push to reduce costs in unconventional shale play reservoirs, some in the industry are racing to systematize development processes, even before understanding many of the aspects that play a role in shale production. This "manufacturing approach" is not a substitute for a comprehensive understanding of a formation."
The present authors agree - and, further, that "understanding of a formation" means reservoir modeling as much as it does petrophysical analysis. As emphasized earlier, a rigorous, easy-to-use Darcy flow simulator that allows rapid, convenient and rigorous model for problems containing heterogeneities, general drive models, arbitrary systems of vertical, horizontal and multilateral wells, liquids and gases, is not readily available in the industry, until now. This book, through detailed discussions in Chapters 4 - 9, will credibly fill this void.
A recent trade journal article "Physics-based or...
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