formation testing · 2019. 7. 18. · formation testing – strategies, capabilities and solutions...

Formation Testing Volume 3

Scrivener Publishing100 Cummings Center, Suite 541J

Beverly, MA 01915-6106

Publishers at ScrivenerMartin Scrivener ([email protected])

Phillip Carmical ([email protected])

Formation Testing Volume 3

Wilson C. Chin

Supercharge, Pressure Testing and Contamination Models

Th is edition fi rst published 2019 by John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, USA and Scrivener Publishing LLC, 100 Cummings Center, Suite 541J, Beverly, MA 01915, USA© 2019 Scrivener Publishing LLCFor more information about Scrivener publications please visit www.scrivenerpublishing.com.

All rights reserved No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or other-wise, except as permitted by law Advice on how to obtain permission to reuse material from this title is available at http://www.wiley.com/go/permissions.

Wiley Global Headquarters111 River Street, Hoboken, NJ 07030, USA

For details of our global editorial offi ces, customer services, and more information about Wiley products visit us at www.wiley.com.

Limit of Liability/Disclaimer of WarrantyWhile the publisher and authors have used their best eff orts in preparing this work, they make no representations or warranties with respect to the accuracy or completeness of the contents of this work and specifi cally disclaim all warranties, including without limitation any implied warranties of merchantability or fi tness for a particular purpose No warranty may be created or extended by sales representatives, written sales materials, or promotional statements for this work Th e fact that an orga-nization, website, or product is referred to in this work as a citation and/or potential source of further information does not mean that the publisher and authors endorse the information or services the organization, website, or product may provide or recommendations it may make Th is work is sold with the understanding that the publisher is not engaged in rendering professional services Th e advice and strategies contained herein may not be suitable for your situation You should consult with a specialist where appropriate Neither the publisher nor authors shall be liable for any loss of profi t or any other commercial damages, including but not limited to special, incidental, consequential, or other damages Further, readers should be aware that websites listed in this work may have changed or disappeared between when this work was written and when it is read.

Library of Congress Cataloging-in-Publication DataISBN 978-1-119-28377-5

Cover images courtesy of the authorCover design by: Kris Hackerott

Set in size of 11pt and Minion Pro by Exeter Premedia Services Private Ltd., Chennai, India

Printed in the USA

10 9 8 7 6 5 4 3 2 1

http://www.wiley.com/go/permissionshttp://www.wiley.com

v

Contents

Preface ix

Acknowledgements xi

1 Formation Testing – Strategies, Capabilities and Solutions 11.1 Development Perspectives 11.2 Basic Forward and Inverse Models 41.3 Supercharge Forward and Inverse Models 141.4 Multiple Drawdown and Buildup Inverse Models 201.5 Multiphase Cleaning and Supercharge Model 241.6 System Integration and Closing Remarks 291.7 References 30

2 Supercharging – Forward Models and Inverse Solutions 312.1 Supercharge and Math Model Development 312.2 Supercharge Pressure and Ultimate Decay 342.3 United States Patent 7,243,537 B2 372.4 Forward and Inverse Models with Supercharging –

Drawdown-Only and Drawdown-Buildup Applications and Illustrative Examples 692.4.1 General Ideas in Formation Testing Formulations 692.4.2 Mathematical Formulation 73

2.5 Drawdown Only Applications 782.5.1 Example DD-1, High Overbalance 782.5.2 Example DD-2, High Overbalance 842.5.3 Example DD-3, High Overbalance 882.5.4 Example DD-4, Qualitative Pressure Trends 922.5.5 Example DD-5, Qualitative Pressure Trends 95

vi Contents

2.5.6 Example DD-6, “Drawdown-Only” Data with Multiple Inverse Scenarios for 1 md/cp Application 97

2.5.7 Example DD-7, “Drawdown-Only” Data with Multiple Inverse Scenarios for 0.1 md/cp Application 102

2.6 Drawdown – Buildup Applications 1072.6.1 Example DDBU-1, Drawdown-Buildup, High

Overbalance 1072.6.2 Example DDBU-2, Drawdown-Buildup, High

Overbalance 1112.6.3 Example DDBU-3, Drawdown-Buildup, High

Overbalance 1142.6.4 Example DDBU-4, Drawdown-buildup, 1 md/cp

Calculations 1182.6.5 Example DDBU-5, Drawdown-buildup, 0.1 md/cp

Calculations 1222.7 Supercharged Anisotropic Flow Simulation Model 1272.8 References 131

3 Pressure Transient Analysis – Multirate Drawdown and Buildup 1323.1 Multirate Drawdown and Buildup Applications 133

3.1.1 Monitoring, Testing, Treatment and Retest 1343.1.2 Hydrate Characterization and Production 138

3.2 Detailed Validations with Exact Solutions 1423.2.1 Validation of PTA-App-01 Inverse Model 1443.2.2 Validation of PTA-App-02 Inverse Model 1483.2.3 Validation of PTA-App-03 Inverse Model 1563.2.4 Validation of PTA-App-04 Inverse Model 1633.2.5 Validation of PTA-App-05 Inverse Model 1723.2.6 Validation of PTA-App-06 Inverse Model 1773.2.7 Validation of PTA-App-07 Inverse Model 1823.2.8 Validation of PTA-App-08 Inverse Model 1873.2.9 Validation of PTA-App-09 Inverse Model 192

3.2.10 Validation of PTA-App-10 Inverse Model 1973.2.11 Validation of PTA-App-11 Inverse Model 202

3.3 References 219

Contents vii

4 Practical Applications and Examples 2214.1 Review Objectives 2214.2 Practical Applications and Examples 222

4.2.1 Isotropic Medium Pressure Testing 222 4.2.1.1 Steady-state method 222 4.2.1.2 Drawdown-buildup method 226 4.2.1.3 Drawdown only method 230

4.2.2 Anisotropic Media Pressure Testing (Using FT-01) 232

4.2.3 Supercharge Eff ects in Drawdown-Buildup 2404.2.4 Supercharge Mechanics in Detail – Reservoir

Fluid More Viscous Th an Mud 2504.2.5 Supercharge Mechanics in Detail –

Reservoir Fluid Less Viscous Th an Mud 2614.2.6 Supercharge Mechanics in Detail –

Reservoir Fluid Viscosity Equals Mud Viscosity 2644.2.7 Perfectly Balanced Well, Mechanics in Detail –

Reservoir Fluid Viscosity Equals Mud Viscosity 2664.2.8 Underbalance Mechanics in Detail –

Reservoir Fluid Viscosity Equals Mud Viscosity 2684.2.9 Comparing Overbalance vs Underbalance

Pressures for Same Reservoir and Tool Pumping Conditions 270

4.2.10 Consequences of Non-Performing Pump Piston 2844.2.11 Batch Processing Using FT-00 2914.2.12 Depth of Investigation Using FT-00

DOI Function 2964.2.13 History Matching Using FT-06 Batch Mode 306

4.2.13.1 Operating FT-06 batch simulator 308 4.2.13.2 Source code documentation

(color coded) 313 4.2.13.3 A fi nal example – concise operational

summary 3284.2.14 Gas Pumping 334

4.2.14.1 Several fi eld notes 334 4.2.14.2 Review of steady-state direct and

inverse methods 335 4.2.14.3 Transient gas calculations 338

4.3 References 342

5 Best Practices and Closing Remarks 3435.1 Best Practices 3435.2 Recommended Reading 351

Cumulative References 352

Index 363

About the Author 369

viii Contents

ix

Preface

Th is volume, possibly the third and fi nal of three, summarizes new and important methods and approaches for wireline and LWD/MWD for-mation tester pressure transient interpretation. Two prior monographs, Formation Testing: Pressure Transient and Contamination Analysis (2014) and Formation Testing: Low Mobility Pressure Transient Analysis (2015), had developed essential models and algorithms for exact forward analysis; rapid, real-time, inverse mobility and pore pressure prediction methods in low mobility environments with non-negligible fl owline volume eff ects; steady-state and transient forward and inverse techniques; miscible, multi-phase fl ow contamination modeling for sample quality control; fast “phase-delay” methods for realtime kh and kv prediction in tight zone applications, and other useful mathematical methods.

Th e present book tackles two additional challenges. Th e fi rst deals with high overbalance pressures, which “supercharge” the pressure fi elds surrounding tool probes, and addresses specifi c questions. How do we extrapolate mobility, compressibility and pore pressure accurately in the presence of possibly overwhelming borehole eff ects which have not yet dissipated? How can we use this model to obtain error bounds on the usual downhole predictions? And how does supercharging evolve dynami-cally, as a function of formation, borehole and mud fi ltration properties? Second, we consider “multiple drawdown and buildup” sequences, actu-ally any combination of piecewise constant, positive, negative or zero fl ow-rates, calculate their exact pressure response, and importantly, show how any three time-pressure data points taken during the fi nal fl owrate cycle can be accurately inverted to produce mobility, compressibility and pore pressure – and that’s rapidly, in the presence of fl owline volume distortions and low mobility environments.

Detailed theory, validations and engineering applications are given for both new models. But just as important, the present book summarizes all of our collective results obtained over the years, and highlights their appli-cation to day-to-day activities. Th is perspective is invaluable especially to a

x Preface

researcher refl ecting on his path to discovery in dealing with what appeared to be an endless array of random challenges. Out of this, a number of “best practices” were developed which focus on uses of our models, which apply to all manufacturers’ formation testing tools. It is diffi cult to believe that almost two decades have elapsed since the author’s fi rst introduction to formation testing and sampling – it’s been immensely challenging and enjoyable, particularly in seeing these methods used in oil exploration – and, I suppose, an intellectual labor of love, that’s fi nally coasting to a sat-isfying ending. I think.

Wilson C. Chin, Ph.D., M.I.T.Houston, Texas

Email: [email protected]

xi

Acknowledgements

Th e author is indebted to his friends and colleagues at Halliburton Energy Services and China Oilfi eld Services who strongly shaped and infl uenced his initial approaches to formation testing. Over the past twenty years, the freedom to pursue new ideas and a continual exposure to state-of-the-art technology have led to innovative interpretation and oilfi eld planning methods that have positively impacted our industry. Th is third book in our trilogy on formation testing summarizes modeling approaches that address operational concerns raised by petroleum engineers, for example, interpretation in supercharged environments, modeling contamination under overbalanced pressures, gas pumping, and applications to reservoir treatment and enhanced hydrate production.

Th e author gratefully acknowledges the United States Department of Energy for its support through its Small Business Innovation Research (SBIR) program for Contracts DE-FG03-99ER82895, DE-FG02-04ER84082, DE-FG02-04ER84083 and DE-FG02-06ER84621, and through its Research Partnership to Secure Energy for America (RPSEA) Ultra-Deepwater Program, for assistance under Contract 08121-2502-01. Such programs are essential in supporting new, high-risk ideas that may make a diff erence – and, certainly, to entrepreneurs dedicated to science and wanting of the chance to make the world just a bit better. Finally, thanks to Mark Proett, formation testing guru, Xiaoying Zhuang, friend and facilitator, and last but not least, Phil Carmical, Acquisitions Editor and Publisher, for their interest and continuing support over the years. Without their unwavering faith and confi dence, this author’s frustrations and disappointments may have remained just that.

1

1Formation 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, SeventhInternational 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 GeoTapTM 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.

2 Formation Testing Volume 3

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.

Formation Testing 3

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).

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


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

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 liquidsoriginally 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.

Formation Testing 5

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, 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?


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

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.

Formation Testing 7

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 kvdetermination 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 kvdetermination assuming dual probe tools where steady-state, liquidassumptions 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 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 kvdetermination 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 1.2.3. FT-02, exact, steady forward and inverse gas simulators.

Formation Testing 9

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.

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


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

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.

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

Formation Testing 11

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 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” kh

2/3kv1/3/ where is the viscosity.

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

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.


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

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


formation testing · 2019. 7. 18. · formation testing – strategies, capabilities and solutions...

Documents