Chapter 1
Formation Testing - Strategies, Capabilities and Solutions

1.1 Development Perspectives

During the mid-1990s, the present author, working with his colleague Mark Proett at Halliburton Energy Services, in Houston, focused his efforts on rapid and efficient formation tester pressure transient interpretation methods. Since the 1950s, flow rate and pressure drop data had been routinely used during sampling operations to predict "effective" or "spherical permeability" (or, more precisely, mobility) - this single-probe measurement provided reservoir characterization information complementing the retrieval and analysis of actual fluid samples. However, the interpretation made use of a steady-state formula requiring complete pressure equilibrium - that is, steady flows that, in the environment of the 1990s and beyond, possibly required hours of expensive wait times at the rigsite and increased the risk of lost tools.

We were tasked with the development of more rapid methods that would "roll out" with the introduction of our new formation tester. But disruptive technology is never easy. The obvious and economic use of early time data would be contaminated by pressure distortive effects associated with flowline storage volume, a problem compounded by tight zones, heavy oils, or both. An empirical method in use at the time seemed to work well; applications to synthetic and limited field data were successful, although why, unfortunately, was anyone's guess. But rigorous mathematics would come to the rescue. The complete initial-boundary value problem was formulated and laboriously solved exactly in its entirety. Closed form, analytical solutions for the "direct" or "forward problem," in which transient pressure histories were sought given fluid, formation, tool and flow rate properties, were obtained in terms of complex complementary error functions. A special "exponential" limit of this solution was studied, which explained why our empirical method worked, and importantly, how it could be improved. This limit formed the basis for a new "inverse" model, in which permeability (mobility), pore pressure and fluid compressibility could be predicted from a limited set of pressure measurement data.

Our research resulted in a number of publications and contributions, all of which were later summarized in "Advanced Permeability and Anisotropy Measurements While Testing and Sampling in Real-Time Using a Dual Probe Formation Tester," SPE Paper No. 64650, Seventh International Oil & Gas Conference and Exhibition, Beijing, China, November 2000 (for earlier related work, refer to "Cumulative References" and "About the Author" in this book). In summary, our work led to three significant contributions -

• A simpler "exponential" formula was developed which allowed rapid predictions of effective spherical permeability (or mobility) in tight zones, using early time data in the presence of strong flowline volume effects. Additional by-products of this approach included pore pressure and fluid compressibility. This method forms the basis of the company's real-time GeoTapT logging-while drilling service operable for single and also dual probe tools.
• A method to predict isotropic permeability (or mobility) using phase delay measurements was also developed. Basically, the travel time for sinusoidal waves created by an oscillating pump piston source and measured at a nearby observation probe would provide the desired predictions. However, while a patent award did result from this work, the method was not economically viable since two probes were required - unlike the drawdown-buildup approach above using the exponential formula and just a single source (or pumping) probe.
• For dual probe tools at zero dip angle (that is, operating in vertical wells), formulas were also given for kh and kv prediction using steady pressure drops obtained at source and observation probes - these measurements, of course, may require lengthy wait times.

In 2004, the United States Department of Energy (DOE), through its Small Business Innovation Research (SBIR) program, awarded two hundred awards nationally in areas such as plasma physics, nuclear energy, refining, waste remediation, building and ventilation, and so on. Four grants were made for fossil fuel and well logging research - two of these awards, both won by this author through his consulting firm Stratamagnetic Software, LLC, founded in 1999, related to formation tester interpretation and analysis. These grants, together with three additional DOE awards, carried stipends significant to any start-up organization and indirectly supported activities in Measurement-While-Drilling, reservoir engineering, drilling and cementing rheology and electromagnetic logging. The freedom that the awards provided led to new methodologies which would dominate the author's work for more than a decade. Many "loose ends" have been resolved, and over the past several years, our work has been disseminated through John Wiley & Sons; in formation testing, in three volumes, this representing our third.

Figure 1.1. Chin et al. (2014) and Chin et al. (2015).

In this last volume on formation testing, we summarize new industry capabilities applicable to all manufacturers' tools in Chapters 1. Chapter 2 highlights "supercharge" effects, where high overbalance pressures distort formation tester measurements - a new interpretation model, suitable for desktop or downhole use, is developed for early time mobility, pore pressure and compressibility prediction in the presence of flowline storage. Chapter 3 develops new inverse methods for multiple drawdown and buildup applications for reservoir characterization, formation treatment and hydrate production. Finally, Chapter 4, provides a broad range of examples for practical engineering application.

1.2 Basic Forward and Inverse Models

In this section, we discuss methods for forward and inverse analysis that employ "simple" logging techniques such as steady-state drawdown, unsteady drawdown, and drawdown-buildup. The "forward" or "direct" problem solves for the transient pressure response when fluid, formation, tool and flowrate parameters are given. On the other hand, the "inverse" or "indirect" formulation attempts to provide permeability (or, mobility), fluid compressibility and pore pressure when a limited number of time and pressure data points are given. With the exception of supercharge and multiple drawdown and buildup methods, the models discussed here are developed in detail in Chin et al. (2014) and Chin et al. (2015).

FT-00 model. Our (initial) flagship forward simulator, simply named "FT-00," is shown in Figures 1.2.1a,b,c. The underlying math model is the exact, analytical, closed form, analytical solution solving the complete initial-boundary value problem formulation for liquids originally published in "Advanced Permeability and Anisotropy Measurements While Testing and Sampling in Real-Time Using a Dual Probe Formation Tester," SPE Paper No. 64650, Seventh International Oil & Gas Conference and Exhibition, Beijing, China, November 2000.

Figure 1.2.1a. FT-00 (Main Interactive) exact forward liquid simulator.

Figure 1.2.1b. FT-00 (Batch Mode) exact forward liquid simulator.

Figure 1.2.1c. FT-00 (DOI) exact forward liquid simulator.

Although the solution is exact, the solution could not be used for real-time or even most desktop applications for two reasons. First, the "complex complementary error function" supplied in most scientific mathematical libraries was far too complicated for downhole use with microprocessors having limited capabilities. And second, transient pressure responses at observation probes could not be calculated for the entire range of logging applications because of very small and very large arguments. For these reasons, the "exponential model" was, and probably is currently, used, although the authors at the time were satisfied that its scientific basis had been clearly established. In the early 2000s, however, the author and other collaborators reworked the complex variables methods underlying the error function evaluation in order to render FT-00 fully functioning (details are offered in Chin et al. (2014)). As a result, the Windows program will perform dozens or more simulations per minute (in batch mode) depending on the microprocessor used, and importantly, will provide transient pressure responses at both source probe and distant observation probes. Figure 1.2.1a displays all the required inputs for the "main, interactive" mode. Standard outputs include line graphs for assumed volume flow rate versus time, source and observation probe pressure responses versus time, and finally, normalized plots showing both pressure and flow rate responses. In addition, detailed tabulations are offered to support other user applications like report generation and spreadsheet plotting.

While the "main, interactive" mode is useful insofar as establishing physical intuition for the flow variables at hand, it may be less convenient in history matching...