Traditional well logging methods, such as resistivity, acoustic, nuclear and NMR, provide indirect information related to fluid and formation properties. The "formation tester," offered in wireline and MWD/LWD operations, is different. It collects actual downhole fluid samples for surface analysis, and through pressure transient analysis, provides direct measurements for pore pressure, mobility, permeability and anisotropy. These are vital to real-time drilling safety, geosteering, hydraulic fracturing and economic analysis.
Methods for formation testing analysis, while commercially important and accounting for a substantial part of service company profits, however, are shrouded in secrecy. Unfortunately, many are poorly constructed, and because details are not available, industry researchers are not able to improve upon them. This new book explains conventional models and develops new powerful algorithms for "double-drawdown" and "advanced phase delay" early-time analysis - importantly, it is now possible to predict both horizontal and vertical permeabilities, plus pore pressure, within seconds of well logging in very low mobility reservoirs. Other subjects including inertial Forchheimer effects in contamination modeling and time-dependent flowline volumes are also developed. All of the methods are explained in complete detail. Equations are offered for users to incorporate in their own models, but convenient, easy-to-use software is available for those needing immediate answers.The leading author is a well known petrophysicist, with hands-on experience at Schlumberger, Halliburton, BP Exploration and other companies. His work is used commercially at major oil service companies, and important extensions to his formation testing models have been supported by prestigious grants from the United States Department of Energy. His new collaboration with China National Offshore Oil Corporation marks an important turning point, where advanced simulation models and hardware are evolving side-by-side to define a new generation of formation testing logging instruments. The present book provides more than formulations and solutions: it offers a close look at formation tester development "behind the scenes," as the China National Offshore Oil Corporation opens up its research, engineering and manufacturing facilities through a collection of interesting photographs to show how formation testing tools are developed from start to finish.
Single-Phase Flow Forward and Inverse Algorithms
Because the authors' prior book Formation Testing: Pressure Transient and Contamination from John Wiley & Sons is relatively new, appearing only in 2014, it is fitting to provide a concise summary of the methods and algorithms introduced there so that the contributions of the present book can be viewed and quickly understood in context. The work provided in this chapter sets the stage for the advanced drawdown-buildup and phase delay models discussed in Chapters 3 and 4.
We describe a comprehensive set of integrated formation testing forward and inverse analysis tools developed for wireline and "formation testing while drilling" (FTWD) applications in hardware design and pressure transient interpretation. The methods, based on rigorous Darcy flow formulations, are solved analytically in closed form whenever possible and cross-checked in different limits to ensure physical consistency and accuracy.
The transient problem for formation tester liquid pressure response in anisotropic media with flowline storage and skin at arbitrary dip, earlier solved in exact, closed analytical form assuming ellipsoidal sources (using complex complementary error functions), is used to derive exact solutions to several inverse problems where permeabilities are sought when dip angle and source and observation probe pressure drops are given.
First, the zero-skin forward solution is evaluated in the steady-state limit for constant rate pumping. Explicit inverse formulas are derived for all horizontal and vertical permeabilities and dip angles. With pressure drops computed at various dip angles from the forward simulation, derived formulas are used to predict both assumed permeabilities, demonstrating their utility in field interpretation. Neglect of dip angle can lead to significant errors in anisotropy prediction. Moreover, multi-valued inverse solutions exist: for a given set of pressure drops, three permeability pairs are found which require resolution from additional logging data.
Second, the "with-skin" forward solution is evaluated at steady-state for constant rate pumping to develop formulas relating source and observation probe pressure drop, vertical and horizontal permeabilities and skin factor. An algorithm giving possible solutions for both permeabilities and skin at any dip angle when both pressure drops are known is derived. Because only two pressure data points are assumed, additional logging information is needed to render a unique determination.
Third, short-duration "pulse interactions" at the observation probe are used to determine anisotropy (analogous to the pulses emanating from acoustic tools). These are strongest and most advantageous at low permeabilities where diffusion predominates. Short pulses, high in frequency content, provide detailed information. Multi-pulse wave-trains with different flow rates, pulse durations and separations enable multiple fast test suites at the rigsite without requiring new hardware. They are accurate, economical and reduce tool sticking risks in tight zones.
Fourth, "phase delay" approaches for permeability prediction analogous to electromagnetic logging methods are described. Sinusoidal pressure transients are created at the pumping probe. Their amplitudes and phases are measured at one or more observation probes. These are interpreted using Darcy analysis models. As with pulse interaction methods, phase delay approaches allow short-duration tests that are economical, safe and characterized by high signal-to-noise ratios.
Fifth, a full 3D horizontal well model for single-probe, dual-probe, dual-packer and elongated pad tools with real mandrels in layered media is given, with computations showing effects of azimuth and bed boundary on pressure response and their implications on permeability prediction. While source models require dual-probe data for inverse application, full 3D models can be used with single-probe FTWD tools (measuring azimuthal pressures) to provide clues related to permeability, anisotropy and bed thickness.
Finally, real-time FTWD pore pressure and mobility prediction is discussed. Such problems, key to drilling safety and rapid economic evaluation, involve transient data distorted by flowline storage effects. Accurate predictions are possible using a minimum of pressure data. We develop rational polynomial expansion methods that do not require exponential, real or complex complementary error functions, and moreover, do not use regression or least-squares smoothing filters that introduce diffusive assumptions beyond those implicit in Darcy's laws. Rapid analysis frees microprocessor resources for other important control and interpretation functions needed during drilling.
2.2 Basic Model Summaries
In formation tester pressure transient analysis, two general types of practical field applications arise, namely, "forward modeling," in which source and observation probe responses are sought when fluid, formation and tool parameters are specified, and "inverse modeling," in which kh and kv permeabilities (and possibly pore pressure) are required when all other parameters are given.
Forward models have been developed to a high degree of sophistication. Almost twenty years ago, Proett and Chin (1996) published the first full three-dimensional finite element analysis assuming realistic borehole environments with pad, probe, mandrel, flowline storage and bedding plane effects. These are reviewed in Formation Testing Pressure Transient and Contamination Analysis (Chin et al, 2014), which also cites extensions to include coupled dynamic mudcake growth and supercharge corrections.
Chin and Proett (2005) provided finite difference models that included multiphase miscible and immiscible effects. In downhole sampling, the time required to pump until clean in-situ fluids are obtained is important. This time scale differs from that used for pressure transient interpretation. Figures 2.1a,b illustrate capabilities that have been used to design new tools and interpret transient data obtained in complicated environments. Figure 2.1c shows Catscan experiments in which dynamic cake growth is measured in cores with different permeabilities. This is important to supercharge and contamination corrections.
Figure 2.1a. Finite element model, flow vectors near probe.
Figure 2.1b. Pressures for drawdown with two probes (left) and one (right).
Figure 2.1c. Catscan results (flow from top to bottom, darkening lines at center indicate cake growth in time).
While fully three-dimensional models are important in their own right, they do require complicated inputs, numerical simulation expertise, not to mention sophisticated and expensive computing environments that host high-overhead software and long calculations. Thus, fast methods that retain the basic elements of the physics are desirable, particularly for field office use and real-time downhole analysis. A number of simpler formulations are possible. These range from elementary point source models, which unfortunately "blow up" at the "r = 0" origin, to finite radius models, which apply flowline storage and skin boundary conditions at spherical source surfaces (ellipsoidal in transversely isotropic flow).
This chapter also introduces new physical concepts in pressure transient interpretation using innovative math models first described in Chin et al (2014). So that the ideas are clearly explained, math details are omitted in favor of examples, although shorter summaries are offered. For readers interested in analytical and numerical details, reference to the book is necessary. Several new capabilities and modules are available and, for convenience, are referred to by a "FT-" designation with "FT" referring to formation testing.
2.2.1 Module FT-00
This deals with exact transient liquid response in homogeneous anisotropic media. It solves for the unsteady Darcy pressure field about an ellipsoidal source surface immersed in a transversely isotropic infinite homogeneous medium allowing full skin effect and flowline storage boundary conditions. This "nonzero radius source" model is more powerful than limited point source approximations because it handles nearfield boundary conditions without becoming singular at the origin as do point source models. We emphasize that cylindrical borehole effects and drilling fluid invasion are not directly incorporated.
The earlier exact analytical solution, posed in terms of the complex complementary error function erfc(z), applied to a single drawdown or buildup and was limited to zero dip angles. To be effectively used for job planning and inverse applications, such as those considered here, improvements were needed. (1)
The erfc function in most scientific software libraries does not converge for certain ranges of complex arguments, and unfortunately, those associated with flowline storage effects on the order of those encountered in real formation testing tools (storage distorts pressure transients and its understanding is important to pressure and mobility interpretation). A new, fast and accurate subroutine is used which converges for a much wider range of complex arguments. Split-second response with fourteen digit accuracy guarantees robust and stable numerical performance. (2)
While the original work formally applied to pressures at all points, that is, all observation points in...