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Reservoir Modeling - Background and Overview

Overview

Reservoir simulation is as old as petroleum exploration itself - it is essential to the profession because it supports cash flow analysis and economic planning. Its beginnings in the 1930s were humble and easily summarized. Let Rw and Rres denote wellbore and farfield reservoir radii, Pw and Pres their corresponding pressures, k the isotropic permeability, µ the liquid viscosity and H the thickness of the circular field. When this field is produced at the center by a fully penetrating vertical well, the steady-state pressure distribution is given by P = Pw + (Pres - Pw) (log r/Rw)/log(Rres/Rw) while the corresponding volume production flow rate is Q = - (2pKH/µ) (Pres - Pw)/log(Rres/Rw) where "r" is the radial coordinate. For transient compressible flows, analogous time-dependent formulas are found which depend on farfield boundary conditions - these models importantly predict production decreases with time and assist companies with investment and corporate planning. For the first several decades, these simple methods sufficed for most purposes, and quite literally, the entire field of reservoir engineering could be explained in a few volumes using equations and charts that did not require any computer access or modeling expertise.

Reservoir modeling landscape. All of that changed starting with the early 1990s. Horizontal wells emerged on the scene. These evolved into multilateral well systems drilled from offshore platforms. Reservoirs were no longer uniform and thick. Heterogeneities, anisotropy and layering were the rule. Produced fluids evolved from liquid to multiphase. Gas flows that were produced required thermodynamic descriptions and difficult nonlinear solutions not amenable to classical analysis methods. And finally, the vertical wells that penetrated ideal reservoirs were replaced by general wellbore topologies and multilateral systems (decided by drillers and geologists at the well site) and which penetrated formations that were as complicated as Nature and geology would allow. All of this made reservoir simulation challenging - but extremely frustrating in spite of the fastest computing machines.

Reflections on simulation and modeling. I began my career in reservoir modeling in the early 1990s, and being the "closet mathematician" that I knew myself to be, I was elated to work on anything resembling of Laplace's equation - a formulation close to my prior comfort zone in theoretical aerodynamics. I expected the rigor and excitement that I had experienced, first in obtaining my Doctorate from the Massachusetts Institute of Technology (in mathematics and fluid dynamics), and later, as Research Scientist at Boeing, then the industry's leader in computational fluids. However, practical reservoir simulation in oil company settings was not exactly research and not quite very exciting.

We ran massive simulations on Crays and IBM mainframes. Computations, accurate models we were told, crunched along for hours and days over evenings and weekends with unerring accuracy. But the methods were "black boxes" because the technology was proprietary - we could not assess the methods since the underlying equations and algorithms were off-limits. Graphical user interfaces were non-existent. Three-dimensional color plots were outputs required additional days of processing on dedicated graphics computers. Jobs were submitted using "keyword inputs" that replaced the Fortran decks that engineers had grown accustomed to. And these inputs included "matrix solver selection," a nightmare even to Ph.D. mathematicians, since the optimal solver actually depended on the (evolving) reservoir being modeled.

Because getting simulators to operate properly required reading countless user manuals, reservoir engineers were often happy to get any output, right or wrong. At one leading company, in fact, results were almost always wrong. In an age when computer memory actually cost money, megabytes were allocated according to employee status - lower seniority personnel were allocated fewer memory blocks than their higher ranking peers. But they were not aware of nor privy to this policy - no one knew except middle management. And so, our expensive computers would overwrite recent results over and over, in the process generating absolutely useless numbers and just as garbled graphics.

Extrapolating core level rock properties to grid blocks that were literally hundreds of feet long in each direction required an incredible leap of faith that few engineers would admit to. Throw in the additional shale streak or fault that more than likely hides beneath the surface and one wonders what geology is really being modeled. Geostatistics, the new game in town at the time, was viewed with skepticism since modeled rocks did not look like rocks. Common sense dictated that a good geologist could probably produce a better picture of the underground reservoir than the best workflows exploration companies developed. With time, this author understood more the limitations behind the methods and algorithms used. These ideas are discussed in Chapter 2, which is essential reading for those who wish to understand the fundamental differences between our simulator and many commonly used. However, our explanations are not required for those who simply want to use our software - in fact, this Handbook is written with practitioners in mind and is very results oriented.

Reservoir Flow Algorithms for Petroleum Engineers

The author's ideas behind reservoir flow modeling were strongly influenced by his background in mathematics and fluids, developed and honed at M.I.T. and Caltech, and later at Boeing and United Technologies, where advanced methods were put to use in modeling complicated three-dimensional effects. Early applications of these methods to reservoir engineering led to a Chairman's Innovation Award at British Petroleum in 1990 (refer to Figure 1-1). New approaches to horizontal and multilateral well modeling were later marketed as 3D/SIMTM by Gulf Publishing Company (e.g., see Figure 1-2), and offered as (the original) StrataSimT by StrataModel, Inc. in 1992 (Figure 1-3). A comprehensive theoretical monograph, namely, Modern Reservoir Flow and Well Transient Analysis (Chin, 1993) appeared soon thereafter, and was followed a decade later by Quantitative Methods in Reservoir Engineering, First Edition (Chin, 2002) - a Second Edition, offered by Elsevier Science, will appear in late 2016. The methods described in the earlier publications are highlighted in Figures 1-4 to 1-6. Readers interested in these methods, or wishing to pursue research or develop related software, are encouraged to consult these publications. In this book, we focus primarily on practical matters and insights that guided our development of a unique product - MultisimT.

Figure 1-1. British Petroleum Chairman's Innovation Award (1990).

Figure 1-2. Multilateral well simulator, Gulf Publishing (1990s).

Figure 1-3. Original StrataSimT (1992) from StrataModel, Inc.

Figure 1-4. 3D/SIMTM from Society of Petroleum Engineers (1995).

Figure 1-5. Author's reservoir monograph in Gulf's "ebook Collection."

Figure 1-6. 4D TurboviewT color graphics (O&G Journal, 1990s).

MultisimT Features - Advanced Interactive Reservoir Modeling

In this section, we summarize the modeling capabilities and user interface features incorporated into MultisimT Mathematically rigorous theory and advanced numerical algorithms offering accurate, rapid and stable computations provide the underlying foundation - these are described in Chin (2002, 2016) and briefly summarized in Chapter 2 of this book. A description of the software system is given below, and detailed validations are given in Chapters 2, 3 and 4.

MultisimT was designed to be easy to use, requiring minimal hardware and software resources - a Windows computer with an Intel Core i5 processor is suggested and special graphics cards or accelerators are not needed. Because interactive sessions are anticipated, with typical "what if" studies taking approximately thirty minutes, the system was built to support a nine layer reservoir with up to 31 × 31 grids per layer, implying 8,649 or about 10,000 pressure unknowns. The 10,000 × 10,000 equation system is solved in seconds "behind the scenes" and pressure fields are automatically displayed in three-dimensional color plots with highly integrated graphical output. Our approach is "memory-conserving," using advanced "in place" calculations where possible.

Because the author served several years as a senior reservoir engineer with operating companies, the workflow used in these organizations is embedded in our menu structures - software manuals are not required, although prospective users are encouraged to peruse this book to gain some insight into our modeling philosophy and versatility. Reservoir engineering relies on accurate descriptions of heterogeneities, anisotropies, layers, geological structures, and of course, the...