Formation Testing: Supercharge, Pressure Testing, and Contamination Models

By Wilson C Chin

This third volume in the "Formation Testing" series further develops new methods and processes that are being developed in the oil and gas industry. In the 1990s through 2000s, the author co-developed Halliburton’s commercially successful GeoTapTM real-time LWD/MWD method for formation testing, and also a parallel method used by China Oilfield Services, which enabled the use of data taken at early times, in low mobility and large flowline volume environments, to support the important estimation of mobility, compressibility and pore pressure, which are necessary for flow economics and fluid contact boundaries analyses (this work was later extended through two Department of Energy Small Business Innovation Research awards).

While extremely significant, the effect of high pressures in the borehole could not be fully accounted for – the formation tester measures a combination of reservoir and mud pressure and cannot ascertain how much is attributed to unimportant borehole effects. The usual approach is "simply wait" until the effects dissipate, which may require hours – which imply high drilling and logging costs, plus increased risks in safety and tool loss. The author has now modeled this "supercharge" effect and developed a powerful mathematical algorithm that fully accounts to mud interations. In short, accurate predictions for mobility, compressibility and pore pressure can now be undertaken immediately after an interval is drilled without waiting.

This groundbreaking new work is a must-have for any petroleum, reservoir, or mud engineer working in the industry, solving day-to-day problems that he or she encounters in the field.

• Language: English
• Publisher: Wiley
• Release date: Mar 14, 2019
• ISBN: 9781119284581

Wilson C Chin

Wilson C. Chin, PhD MIT, MSc Caltech, fluid mechanics, physics, applied math and numerical methods, has published twenty-five research books with John Wiley & Sons and Elsevier; more than 100 papers and 50 patents; and won 5 awards with the US Dept of Energy. He founded Stratamagnetic Software, LLC in 1997, an international company engaged in multiple scientific disciplines.

Book preview

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 GeoTap™ 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 shows two books; the first two volumes of Formation Testing i.e. Chin et al. (2014) and Chin et al. (2015).

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 shows FT-00 (Main Interactive)liquid simulator displaying all the required inputs for the “main, interactive” mode.

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

Figure shows FT-00 (Batch Mode)simulator with setup box to define parameter ranges and increments for physical variables of interest.

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

Figure shows FT-00 (depth of investigation)simulator that supplies pressure results and plots predetermined separation distances between zero and the “maximum probe separation”.

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 applications where, for example, numerous kh, kv, ϕ or other values need to be varied systematically to match calculated pressure responses to probe measurements. As shown in Figure 1.2.1b, our FT-00 software also supports an exact batch mode calculator. Here, at the bottom left, a convenient setup box can be called to define parameter ranges and increments for physical variables of interest. Line plots and tables can be displayed during batch calculations, or more conveniently, suppressed to the very end, at which time a single large tabulation is offered to the user.

In other applications, depth of investigation (DOI) is important in job planning and interpretation error assessment. Consider, for example, a low mobility situation – will the assumed pump rate, or the maximum mechanical rate the system is capable of, result in a measurable signal at the observation probe? Will pressure diffusion (smearing) be excessive?

Rather than defining this quantity abstractly, as is commonplace in resistivity and electromagnetic logging, we use our ability to calculate probe responses at any distance from the source to advantage. Clicking the DOI button leads to the simplified menu in Figure 1.2.1c, which automatically supplies exact pressure results and plots at predetermined separation distances between zero and the maximum probe separation distance requested. Example calculations are offered in Chapter 4.

FT-01 model. It is known that numerical methods, e.g., Ansys, Comsol, and others, whether they are finite difference or finite element based, are influenced by truncation and round-off errors. In the historical context, these act as artificial viscosities in fluids problems. In formation testing applications hosted by Darcy’s equations, the calculated pressure response for a given inputted mobility may correspond to a different mobility whose value or even qualitative effect may be difficult to quantify. This is not acceptable for forward calculations. But the consequences are worse for the development in inverse methods because they cannot be properly validated.

We noted that SPE Paper 64650 provided equations for kh and kv determination for dual probe tools, although using steady-state pressure drops in vertical wells. At the time, only Ansys synthetic data was available and applications were deferred. The book Chin et al. (2014) provides the exact, analytical, closed form solution for kh and kv determination assuming dual probe tools where steady-state, liquid assumptions are in place. However, any dip angle is permitted. The screen for FT-01 is shown in Figure 1.2.2. The method is validated by using synthetic pressure data generated by the fully transient FT-00 code (which does not suffer from truncation or roundoff error), transferred to the first two boxes in Figure 1.2.2, and showing that predicted anisotropic permeabilities are consistent with those used in FT-00 to generate the pressure data. Example calculations appear in Chapter 4.

Figure shows FT-01 simulator,displaying anisotropic permeabilities by using synthetic pressure data.

Figure 1.2.2. FT-01, exact inverse liquid simulator.

FT-02 model. In our description of FT-01, our exact inverse model for liquid flows using steady pressure data, we emphasized that it was validated by running forward liquid transient simulator FT-00 until steady-state conditions were achieved in order to obtain steady pressure inputs for inverse calculations. FT-02 represents our exact inverse method for nonlinear gas flows based on exact, closed form, analytical solutions (details are offered in Chin et al. (2014)). Whereas FT-00 for liquids was constructed from simple exact solutions using linear superposition methods, an analogous forward simulator for nonlinear gas flows cannot be developed because superposition methods do not apply. Thus, a different validating forward simulator for gases was developed, in this case an exact one for steady-state nonlinear gas flows. This complementary pair of steady forward and inverse gas simulators is shown in Figure 1.2.3. The method allows simultaneous for kh and kv determination for dual probe tools using steady-state pressure drop data. It applies to all dip angles plus a range of thermodynamic effects, for instance, isothermal and adiabatic processes, and so on. We emphasize that inverse solutions need not be unique. In other words, more than a single horizontal and vertical permeability pair may be found for a given set of dual probe pressure drops. Additional logging information (outside the realm of formation tester analysis) is required to render the solution unique. Example calculations are offered in Chapter 4.

Figure shows FT-02, exact, steady forward and inverse gas simulators allowing simultaneous for Kh and Kv determination for dual probe tools using steady-state pressure drop data for all dip angles plus a range of thermodynamic effects.

Figure 1.2.3. FT-02, exact, steady forward and inverse gas simulators.

FT-06 and FT-07 models. Our exact FT-00 forward simulator for liquid motions is based on closed form, analytical solutions, and its versatile flowrate capabilities are founded on general linear superposition principles. For mathematical expediency, these required piecewise constant rate specifications, say +1 cc/s for two sec, + 5 cc/s for six sec, – 10 cc/s for three sec, and so on. In many practical applications, pumps cannot achieve such constant rates because of excessive formation resistance or mechanical issues. In fact, timewise volume flowrate functions may take the form of triangles, trapezoids or non-ideal shapes. Thus, the need for a numerically based simulator capable of handling more general volume flowrate functions is apparent.

A numerical option is also required for general transient nonlinear gas flows, for which closed form analytical solutions are not available, and for which, in any event, linear superposition methods are inapplicable. Our FT-06 numerical finite difference simulator serves two combined functions. First, it solves liquid flow problems subject to arbitrarily defined flowrates, as is apparent from the flowrate schedule in Figure 1.2.4a. In fact, as shown, a numerical file read in by the user is also possible. Second, the computational engine is extended to nonlinear gas flows for a wide range of thermodynamic situations, e.g., isothermal, adiabatic or other processes of interest. Furthermore, anisotropy may be specified via kh, kv or effective spherical permeability and kv/kh. The same computational outputs as FT-00 are offered, that is, line plots for source and observation probe pressures, flowrate, and pressure-rate superposed plots versus time, plus detailed numerical tabulations. Example flowrate functions are displayed in Figure 1.2.4b.

Figure shows FT-06, numerical liquid and gas forward simulator that solves liquid flow problems subject to arbitrarily defined flowrates.

Figure 1.2.4a. FT-06, numerical liquid and gas forward simulator.

Figure shows FT-06, general flowrate functions, forward simulator that shows line plots for source and observation flowrate versus time with detailed numerical tabulations.

Figure 1.2.4b. FT-06, general flowrate functions, forward simulator.

FT-06 assumes that flowline storage volume is constant for the duration of the simulation. In other applications, those focusing on hardware development efforts, the need for time-varying flowline volume simulation arises. It is known that when formations are low in mobility and flowline volumes are not small, pressure responses can be distorted or smeared. The need to dynamically tune flowline volume allows the field engineer to adjust the resolution in his pressure curve and permit more accurate interpretation using inverse prediction methods such as those offered in this book. Our FT-07 numerical simulator provides a general means to define time-varying flowline volumes, as suggested in the bottom left menu shown in Figure 1.2.4c. Examples using FT-06 are offered in Chapter 4, while applications using FT-07 are provided in Chin et al. (2015).

Figure shows FT-07 numerical simulator, a FT-06 extension supporting general time-varying flowline volume.

Figure 1.2.4c. FT-07, a FT-06 extension supporting general time-varying flowline volume.

FT–PTA–DDBU model. Previously, we introduced two inverse models, namely FT-01 for liquids and FT-02 for gases, both requiring steady pressure drops from dual probe data. These models were based on exact, close form, analytical solutions of the respective steady Darcy formulations, and while impractical, do offer horizontal and vertical mobility predictions. In contrast, the FT-PTA-DDBU inverse model, for drawdown-buildup applications using buildup data, supports early time data usage for low mobility applications with non-negligible flowline storage effects. This model rapidly (within seconds) predicts the effective or spherical mobility kh²/³kv¹/³/µ where μ is the viscosity.

As indicated in Figure 1.2.5, only three time-pressure data points are required, together with the time TDD1 at which drawdown ceases. Shown at the bottom right are pore pressure and mobility predictions. A drawdown only model, using drawdown data is also available. While both are still offered, they have been replaced by the more general inverse capabilities of the multiple drawdown and buildup system described later, which in addition to pore pressure and mobility, offers fluid compressibility. Note that our multiple drawdown and buildup options do not model supercharge due to overbalance effects, but a version of the code in Figure 1.2.5 with supercharge is available.

Figure shows FT-PTA-DDBU inverse model, a drawdown-buildup applications for pore pressure and spherical mobility at low mobilities with flowline storage effects.”

Figure 1.2.5. FT-PTA-DDBU, early time, low mobility, flowline volume non-negligible – for drawdown only, see Figure 1.4.4).

Classic inversion model. Finally, we cite for historical purposes the original single-probe model offering spherical mobility when steady pressure drops are available assuming a continuous constant flowrate fluid withdrawal. The method is based on an exact analytical solution, but the main drawback with this approach is the possibility of long waits in low mobility environments, required so that steady conditions are achievable and flowline storage effects dissipate.

Figure shows classic inverse model offering spherical mobility when steady pressure drops are available.

Figure 1.2.6. Classic inverse model.

1.3 Supercharge Forward and Inverse Models

In our prior discussion of inverse model FT-PTA-DDBU, we indicated that pore pressure, mobility and fluid compressibility were predicted from early time, single-probe, pressure transient data with non-negligible flowline storage effects. This zero-supercharge model, for drawdown-buildup applications utilizing buildup data, is again shown in the top of Figure 1.3.1. Mathematical details are offered in the formation testing book of Chin et al. (2014), explaining both exponential function as well as rational polynomial implementations (the latter, used in our work, is more robust, since exponentials are prone to compiler or microprocessor quality issues). This method is extended in Chapter 2 of this book to include supercharge effects due to overbalance in the well. The screen at the bottom of Figure 1.3.1 contains one additional input box Pover (psi) for the over-pressure due to overbalance. Again, pore pressure, mobility and compressibility are predicted.

Figure shows two software modules explaining drawdown-buildup applications utilizing buildup data. The top module with zero supercharge for explaining both exponential function as well as “rational polynomial” implementations whereas the bottom module strong supercharge or overbalance pressure contains one additional input box “Pover (psi)” for the over-pressure due to overbalance.

Figure 1.3.1. Both software modules apply to drawdown-buildup applications using buildup data. Pore pressure, mobility and compressibility predictions, zero supercharge (top), strong supercharge or overbalance pressure (bottom).

In addition to the supercharge inverse model shown at the bottom of Figure 1.3.1, which applies to drawdown-buildup applications using buildup data (as shown in the yellow screen), a complementary supercharge inverse model for drawdown applications using drawdown data is also available and is shown in Figure 1.3.2 with essentially identical inputs as in Figure 1.3.1, except that TDD1 (for the time when drawdown stops) is not requested. Note that all the black DOS screen software items shown in the figures below represent completed and fully validated algorithms, except that, as of this writing, more attractive Windows user interfaces have not been written – all of the results generated in Chapter 2 used the black screen interfaces below as temporary front ends. In addition to Model SC-DD-INVERSE-2 for inverse calculations, a complementary forward solver, which calculates transient drawdown pressure responses at the source probe when fluid and formation properties, tool characteristics, volume flowrates, pore pressure and overbalance pressure are given, is available and shown in Figure 1.3.3. In fact, the forward or direct solver in Figure 1.3.3 was run to create synthetic transient (supercharged) pressure data, which was inputted into the inverse model Figure 1.3.2. Here, inverse calculations recovered the known mobility, pore pressure and compressibility.

Figure shows Input screen for inverse model SC-DD-INVERSE-2 for low mobility, isotrophic, supercharged applications for “drawdown only” problems when flowline storage is not negligible.

Figure 1.3.2. Input screen for Model SC-DD-INVERSE-2.

Figure shows Input screen for Model SC-DD-FORWARD-3B, that calculates transient drawdown pressure responses at the source probe when fluid and formation properties, tool characteristics, volume flowrates, pore pressure and overbalance pressure are given.

Figure 1.3.3. Input screen for Model SC-DD-FORWARD-3B.

For drawdown only applications, a special forward simulator was also written to calculate and plot a baseline pore pressure and flowrate given run assuming different values of overbalance pressure. This program is shown in Figure 1.3.4a and calculated pressure responses (with automated graphics displays) are given in Figure 1.3.4b.

Figure shows Input screen for Model SC-DD-FORWARD-2-CREATE-TABLES-3B to calculate and plot a baseline “pore pressure and flowrate given” run assuming different values of overbalance pressure.