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Enhanced Oil Recovery Scrivener Publishing 100 Cummings Center, Suite 541J Beverly, MA 01915-6106 Publishers at Scrivener Martin Scrivener (martin@scrivenerpublishing.com) Phillip Carmical (pcarmical@scrivenerpublishing.com) O. R. Ganiev, R. F. Ganiev and L. E. Ukrainsky Resonance Macro- and Micro-Mechanics of Petroleum Reservoirs Enhanced Oil Recovery Copyright © 2017 by Scrivener Publishing LLC. All rights reserved. Co-published by John Wiley & Sons, Inc. Hoboken, New Jersey, and Scrivener Publishing LLC, Beverly, Massachusetts. Published simultaneously in Canada. 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For general information on our other products and services or for technical support, please contact our Customer Care Department within the United States at (800) 762-2974, outside the United States at (317) 572-3993 or fax (317) 572-4002. Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic formats. For more information about Wiley products, visit our web site at www.wiley.com. For more information about Scrivener products please visit www.scrivenerpublish- ing.com. Cover design by Kris Hackerott Library of Congr ess Cataloging-in-Publication Data: ISBN 978-1-119-29382-8 Printed in the United States of America 10 9 8 7 6 5 4 3 2 1 Abstract Th is monograph discusses the scientifi c fundamentals of resonance macro- and micro-mechanics of petroleum reservoirs and its petroleum industry applications. It contains an overview of the research and engi- neering results of resonance macro- and micro-mechanics of petroleum reservoirs, which provides the scientifi c and applied foundations for the creation of groundbreaking wave technologies for production stimulation and enhanced oil recovery. Th e monograph is intended for a wide audience: students, teachers, scientists and practitioners who are interested in the fundamentals, the development and application of leading-edge technologies in the petro- leum industry and other industrial sectors. vii Contents Preface xiii Introduction: A Brief Historical Background and Description of the Problem xvii 1 Scientifi c Foundation for Enhanced Oil Recovery and Production Stimulation 1 1.1 Th e Practical Results of Near-Wellbore Formation Cleaning by Wave Stimulation 1 1.2 Th e Scientifi c Fundamentals of the First-Generation Wave Technology for Stimulation of Production Processes 7 1.2.1 Large-Scale Laboratory Experiments at Shell Test Facilities 8 1.2.2 Resonances in Near-Wellbore Formation. Resonances in Perforations 12 1.2.3 Excitation of Oscillations in Micro-Pores by One- Dimensional Longitudinal Macro-Waves in a Medium. Resonances. Transformation of Micro-Oscillations in Pores to Macro-Flows of Fluid. Th e Capillary Eff ect 15 1.2.4 Cleaning of Horizontal Wells 18 1.2.5 Preliminary Results 20 1.3 Stimulation of Entire Reservoirs by First-Generation Wave Methods for Enhanced Oil Recovery. Resonance Macro- and Micro-Mechanics of Petroleum Reservoirs: A Scientifi c Foundation for Enhanced Oil Recovery 21 2 Remove Micro-Particles by Harmonic External Actions 27 2.1 An Analysis of the Forces Acting on Pore-Contaminating Particles under a Harmonic External Action 27 2.2 Conditions for the Detachment of a Solid Particle from the Wall of a Pore under Harmonic External Action 30 2.3 Th e Criterion of Successful Harmonic Wave Stimulation. Criterion Determination Procedure 39 2.4 Summary 43 3 Remove Micro-Particles by Impact Waves 45 3.1 Determining Flow Parameters behind an Impact Wave 46 3.2 Assessing the Forces Th at Act on a Particle as the Front of an Impact Wave Is Passing 51 3.3 Conditions for the Detachment of a Solid Particle from the Wall of a Pore under the Action of a Passing Impact Wave 53 3.4 Th e Criterion for Successful Wave Stimulation by Impact Waves. Criterion Determination Procedure 58 3.5 Summary 61 4 Th e Wave Mechanisms of Motion of Capillary-Trapped Oil 63 4.1 Th e Conditions for the Detachment of a Droplet from the Wall of a Pore 64 4.2 Th e Case of Harmonic Action on a Capillary-Trapped Droplet 66 4.3 Th e Case of Impact Wave Action on a Capillary-Trapped Droplet 70 4.4 Summary 72 5 Action of Wave Forces on Fluid Droplets and Solid Particles in Pore Channels 73 5.1 Th e Mechanism of Trapping of Large Oil Droplets in a Waterfl ooded Reservoir. Propulsion of Droplets by One-Dimensional Nonlinear Wave Forces 73 5.2 Th e Average Flow of Fluid Caused by Oscillations in a Saturated Porous Medium with a Stationary Matrix and Inhomogeneous Porosity 76 5.2.1 Th e Statement of the Problem 76 5.2.2 Calculation Results 79 viii Contents 5.3 Fluid Flows Caused by Oscillations in Cone-Shaped Pores 84 5.3.1 Th e Statement of the Problem 84 5.3.2 Calculation Results 88 6 Th e Mobilization of Droplets and Blobs of Capillary-Trapped Oil from Microcavities 91 6.1 Th e Mathematical Statement of the Problem 91 6.2 Th e Natural Frequency of Gravity-Capillary Waves on Oil-Water and Oil-Surfactant Interfaces in Pores 95 6.3 Interface Instability Range 97 6.4 Oil-Water Interface Instability 98 6.5 Oil-Surfactant Interface Instability 102 7 Statements and Substantiations of Waveguide Mechanics of Porous Media 105 7.1 Resonance Mechanisms Possible in Fluid-Saturated Porous Media 105 7.2 Resonance of Two-Dimensional Axially Symmetric Waves in Horizontal Layers of Reservoir. Effi cient and Directed Excitation of Wave Energy in Target Sub-Layers 108 7.3 Resonance of Two-dimensional Plane Waves in Reservoir Compartmentalizing Strike-Slip Faults and Fractured Zones 114 7.3.1 Th e Mathematical Model of a Fluid-Saturated Porous Medium 115 7.3.2 Th e Statement of the Problem and Solution Procedure 118 7.3.3 Damping Decrements of Waves in a Natural Vertical Waveguide 121 7.3.4 Statement of a Resonance Waveguide Problem and Its Substantiation for Porous Media. Introduction 127 7.3.5 Resonances. Waveguide Processes in Porous Media with Heterogeneities. Th e Distribution of Forces Acting on Pore-Contaminating Solid Particles and Capillary-Trapped Oil Droplets in a Waveguide 132 Contents ix 7.4 Linked Waveguides in Compartmentalized Reservoirs. Th e Transfer of Oscillations into Reservoir Inner Zones under Multidimensional Resonance Conditions 141 7.4.1 Th e Statementof the Problem of Forced One- Dimensional Oscillations in Linked Sections of a Multi-Phase Medium under Resonance Conditions 142 7.4.2 Th e Results of Mathematical Simulation 144 7.5 Experimental Determination of Resonant Frequencies of a Reservoir. Practical Recommendations for Selecting Controlled Means and Oscillation/Wave Generators 145 8 Th e Resonant and Waveguide Characteristics of a Well 151 8.1 Selecting Wave Parameters for Stimulation of Horizontal Wells 153 8.1.1 Scientifi c Fundamentals 153 8.1.2 Practical Recommendations on Stimulation of Horizontal Wells 158 8.2 Near-Wellbore Stimulation. Th e Induction of Resonance 159 8.2.1 Resonances in the Wellbore Section between the Oscillation Generator and the Bottom. Using Waves to Transfer Wave Energy 159 8.2.2 Practical Recommendations for Stimulation of the Near-Wellbore Formation Zone 162 9 Experimental Study of Wave Action on a Fluid-Filled Porous Medium 165 9.1 Experimental Study of the Potential to Clean up the Near-Wellbore Formation Zone from Contamination using Wave Stimulation 165 9.1.1 Test Equipment and Methodology 166 9.1.2 Th e Results of Cleanup from Clay Mud 169 9.1.3 Th e Results of Cleanup from Clay-Polymer Mud 171 9.1.4 Summary 173 9.2 Th e Experimental Study of the Eff ect of Shock Waves on the Displacement of Hydrocarbons by Water in a Porous Medium. Connected Wells 173 9.2.1 Th e Test Equipment 174 x Contents 9.2.2 A Th eoretical Analysis of the Propagation of Waves Generated by a Shock-Wave Valve in the Test Facilities and Evaluation of the Forces Caused by the Wave Action 177 9.2.3 Th e Methodology of Tests 180 9.2.4 Results of Flow Acceleration Tests 181 9.2.5 Th e Eff ect of Wave Stimulation on Connected Wells 185 9.2.6 Summary 186 Conclusion 189 References 195 Index 201 Contents xi xiii Preface Th is monograph discusses one of the most important present-day research and engineering problems that aff ect the growth of the country’s economy: cost-eff ective oil production stimulation and enhanced oil recovery. Th e authors and other scientists at the Scientifi c Center for Nonlinear Wave Mechanics and Technologies of the Russian Academy of Sciences (NC NVMT RAN) have developed the scientifi c and applied foundations for what is known as resonance macro- and micro-mechanics of petroleum reservoirs, a novel and challenging path to effi cient oil recovery enhance- ment, which in some cases may incorporate and amplify the eff ects of other well-known conventional enhanced oil recovery methods (chemical, thermal, hydraulic fracturing, horizontal wells, etc.). Th e truth of this statement is backed by the results of both theoretical research at the leading edge of the theory of nonlinear oscillations and experimental studies conducted in laboratories and in the fi eld. Th is is described in detail in the introduction and in the following chapters of the monograph. Resonance macro- and micro-mechanics of petroleum reservoirs is a new area of fundamental and applied research in nonlinear wave mechanics, ahead of the international state-of-the-art and led by Russia. Th e proposed fi eld of resonance mechanics of petroleum reservoirs is based on the recently discovered multi-dimensional largescale resonance phenomena in heterogeneous oil reservoirs that have signifi cant eff ect on the motion of various micro-inclusions, such as solid particles and droplets of fl uids (water, oil, etc.) in the micro-pores of an oil forma- tion (both near and far from the wellbore). In turn, the motion of micro- inclusions can drastically change the macro-mechanics of the porous medium. Th erefore, there are dynamically linked resonance macro- and micro-processes in petroleum reservoirs (porous media), which can be controlled for the purposes of both oil production stimulation and enhanced oil recovery. xiv Preface What is totally new and important about it is the theoretical and prac- tical discovery of the phenomenon of signifi cant amplifi cation of multi- dimensional waves in porous media as the waves propagate and are transmitted over long distances (which is the second aspect of the discov- ery), which permits stimulation of large areas of reservoirs with various heterogeneities, contaminated by solid particles both near and far from the wellbores or containing capillary-trapped oil, for enhanced oil recov- ery purposes. Th ese factors are the most common causes of declining production and recovery of oil in many cases, and it is diffi cult to select an economical stimulation method for their removal. Th e undertaken research and fi eld trials have shown that the reservoir damage control methods proposed in this monograph (based on the science of nonlinear resonance mechanics of porous media) may be more effi cient and econo- mical than others. To be able to create such multi-dimensional resonance conditions in the fi eld, various controlled appliances and devices, broadband oscilla- tion and wave generators with instrumentation and mathematical control systems have been developed. Th e corresponding soft ware packages for typical fi eld applications are constantly improved and updated depending on the geological settings of specifi c oil fi elds. Th is scientifi c base is used to design and build petroleum industry-oriented controlled appliances and devices that form a fi eld of the so-called wave machine engineer- ing sector. Wave machine engineering has also been founded by the NC NVMT RAN team and is rapidly evolving to the benefi t of various indus- tries [1, 2, 3, 4]. Th is book mostly discusses the fundamentals of resonance macro- and micro-mechanics of petroleum reservoirs, substantiation of its scientifi c and applied aspects, and prospects of its use in petroleum industry appli- cations. However, it should be noted that the initial research and devel- opment base for the statement and solution of the problem of resonance macro- and micro-mechanics of petroleum reservoirs was formed by earlier results of the so-termed wave technology. Th e wave technology, created by the NC NVMT RAN team for a wide range of applications in various industries including oil and gas, was quickly acclaimed by experts. As far back as in 1990 it was approved by a panel of experts of the USSR Ministry of Petroleum Industry for use at Soviet oil fi elds for production stimulation purposes. At the initial stage of wave technology development by the academic research team as a new fi eld of mechanics (the theory of nonlinear oscillations and waves and their technological applications), it was actively and specifi cally supported by the leaders of the USSR and by eminent Preface xv progressive statesmen. It was their idea to set up a research council (in 1984–1985) within the USSR Ministry of Petroleum Industry on the subject matter of using wave and vibrational processes in the petroleum industry (the council was chaired by R. F. Ganiev, then a professor and now a Member of the Russian Academy of Sciences) whose aim was to coordinate the research eff orts of teams in various sectors of the indus- try. A trial site was established at Nizhnevartovsknefnegas Oil Production Association and about 100 wells were provided for tests by various sub- sidiaries of the association. Th e tests involved various aspects of the wave technology, including gas-lift applications (for a lower gas consumption), drilling applications (for cleaner reservoir penetration through the use of bridging capabilities), etc. It was fi rst-generation wave technology, devel- oped and extensively tested by the industry in 1985–1990. More than 3,000 wells located in diff erent regions of the USSR, mainly in Western Siberia, were stimulated with very good results. As mentioned above, the wave technology was acclaimed by oil indus- try experts (including refi ning and petrochemical) and was also actively copied by various empirical inventors(not always petroleum engineers), especially aft er 1991. Unfortunately, when some of these people started using the science-driven wave technology without understanding its sci- entifi c fundamentals and principles, it resulted in incorrect use, nega- tive results in some cases, and even partial damage to reputation of the technology (as explained in more detail in the Introduction and the fi rst chapter of the book). R. Kh. Muslimov, a prominent scientist and a practicing expert in geology, a professor and a member of the Academy of Sciences of Tatarstan, reasonably and impartially wrote in his monograph that experts in oscil- lation mechanics, reservoir engineers and geologists should all joint their eff orts to implement this high-end and promising technology [5]. Meanwhile, the NC NVMT RAN team continued to invest eff ort in the wave technology on a broad scale. A number of wave resonance eff ects in near-wellbore formation zones were found, wave capillary eff ects of mul- tiple acceleration (by 100s to 1,000s times or more) of fl uids (water and oil) in micro-pores were identifi ed, along with other wave phenomena in porous media. First-generation wave technology was then quite fully developed and verifi ed by practice, progressing further on a new scientifi c basis. Cooperation (contracts) with Western oil companies, such as British Petroleum, Shell, Smith International (a drilling company) also played an important role in the development and perfection of the wave technology. Field trials of the enhanced oil recovery technique were conducted in xvi Preface Alaska, the North Sea, the Sultanate of Oman (drilling improvement), and laboratory tests were carried out at the highly valuable and unique Shell test facilities in the company’s research center in Holland. Th eoretical determinations of nonlinear dynamic characteristics of oscillation and wave generators were verifi ed at these facilities in conditions as close as possible to real wells. Effi cient removal of various types of contaminants from near-wellbore formation zones and multiple acceleration of fl ow processes in porous media were confi rmed. It should be noted that these results were obtained on full-size models of near-wellbore formation, rather than on quite small core samples (as it is usually done). Th e main results (scientifi c and practical) were published in various periodicals, backed by dozens of patents (including overseas patents) and inventors’ certifi cates of NC NVMT RAN scientists, and summarized in the authors’ monographs [6, 7, 8, 9, 10, 11]. Th at is why the Introduction and the fi rst chapter contain only a brief overview of the principal scientifi c fundamentals and some results (scientifi c and practical) of wave technology application, as needed to sub- stantiate the formulation of the main problem discussed here, resonance macro- and micro-mechanics of petroleum reservoirs, as a research and practical basis for oil production stimulation and enhanced oil recovery. Several problems of resonance macro- and micro-mechanics of petro- leum reservoirs and the wave technology have been solved in collabora- tion with our colleague I. G. Ustenko, an NC NVMT RAN staff member and senior research scientist (references to these studies are provided in the corresponding chapters of the book). NC NVMT RAN researchers Yu. S. Kuznetsov, D.Sc. (Eng.), N. A. Shamov D.Sc. (Eng.), S. A. Kostrov, Ph.D. (Eng.), G. A. Kalashnikov, Ph.D. (Eng.), Yu. B. Malykh, Ph.D. (Eng.), and others, as well as many reservoir engineers and production geologists from Western Siberia took active participation in fi eld trials of drilling improvement and production stimulations techniques at the initial stage of wave technology use. A. I. Petrov, D.Sc. (Geo.), a prominent expert in geol- ogy and mineralogy, was our consultant in this area throughout our work. In preparing this monograph, the authors drew upon petroleum industry knowledge provided in the generalizing monographs of renown petroleum geologists R. Kh. Muslimov, D.Sc. (Geo.) [5] and R. S. Khisamov, D.Sc. (Geo.) [12]. Th e authors are very grateful to all those who are mentioned above. Th e authors would like to thank R. I. Nigmatullin, a Member of the Academy of Sciences, for his review of this book and helpful advice. Th e authors xvii Introduction: A Brief Historical Background and Description of the Problem Th e state of the Russian economy depends, to a large extent, on the effi - cient and stable functioning of the petroleum industry, one of few sectors able to meet the demands of both the internal market and exports. In the present and coming decades, the task of increasing hydrocarbon recovery effi ciency, ultimate oil (for oil fi elds) and component (for gas condensate and gas condensate/oil fi elds) recovery factors is and will be one of the key challenges in achieving the country’s energy security. For this reason, an effi cient use of various improved recovery techniques along with a science-based search for novel enhanced oil recovery methods is critical for the oil industry to grow in the current conditions. Reservoir fl ow characteristics (porosity and permeability), pore space contamination, reservoir fl uid composition, its viscosity and capillary properties at the fl uid-rock interface are among the key factors controlling oil recovery processes. Th e most common cause for declining fl ow rates of oil and gas produc- tion wells is contamination of the pore space in near-wellbore formation zones. Pore space contamination may occur from various causes such as invasion of drilling mud clay particles into the formation while drilling; mobilization of rock fi nes with the extracted reservoir fl uids while pro- ducing; deposition of resins, asphaltenes and paraffi nes in the pore space; chemical processes in the rock, etc. Traditionally, a number of techniques have been used to remediate near- wellbore formation damage: injection of special solutions, thermochemical and electro-chemical stimulation. In heavily contaminated lowperme- ability rocks, performance of these methods depends on the chemistry of contaminants and on the correct selection of treatment fl uids. xviii Introduction In 1984–85, a near-wellbore cleanup method using oscillations and waves was proposed by the A. A. Blagonravov Institute of Machines Science of the Academy of Sciences of the USSR (reorganized later into the Scientifi c Center for Nonlinear Wave Mechanics and Technologies of the Russian Academy of Sciences (NC NVMT RAN)). Th e method consists in placing a purpose-designed oscillation generator that excites pressure waves in the near-wellbore formation region into a well close to perforations. Passing through contaminated pores in near-wellbore formation, the waves act upon the contaminating particles stuck to pore walls and, provided they are of a suffi ciently high power, can detach the particles from pore walls thereby ensuring cleanup. Th e success of wave stimulations obviously depends on the magnitude by which the force acting on a particle stuck to a pore wall is greater than the force of adhesion of the particle to the pore wall. Th ese stimulations are called fi rst-generation wave technologies. Th ey have become quite common. Such stimulation jobs have been performed in Western Siberia, Tataria, Bashkiria and other regions of Russia, as well as in Oman, USA (in Alaska), Norway (on a North Sea platform), and in China. More than 3,000 wells have been treated. As a result of the stimulations, fl ow rates of production wells increased by 70–80% (in some cases, 2 to 5-fold); injectivity of injection wells increased by 80–90% (documents issued by the Ministry of Petroleum Industry are available to confi rm the performance of the wave technology). In the 1990s, fi rst- generation wave stimulations were accepted by the Ministry of Petroleum Industry of the USSR asa technology recommended for application throughout the Soviet Union. A detailed review of the results obtained during the application of fi rst-generation wave technology is provided in Chapter 1 below. Th anks to its widespread use in the country, the fi rst-generation wave tech- nology was soon acclaimed enthusiastically by many inventors specializing in well workovers. Th ey tried to modify the original technology that was built around the use of vortex and cavitation generators of various designs, run- ning within certain operating envelopes dictated by the properties of the near- wellbore zone to be treated; the operating envelopes were defi ned through complex research aimed at determining the rates of fl uid fl ow through the generator, input pressures, and geometric arrangements. A distinctive feature of these generators is a wide range of frequencies and the high amplitude of the excited pressure oscillations. For example, tests conducted at Shell test facilities in the Netherlands showed that pressure amplitudes of some spectral components in the 2–5 kHz band were greater than 15 atmospheres. Attempts were made, most of which failed, to replace the proposed generator with other types such as rotary-pulse or ultrasonic generators, because radiation from rotary-pulse sources is mono-harmonic, while Introduction xix the amplitude of ultrasonic generators is not high enough and, moreover, ultrasonic waves attenuate very quickly in near-wellbore formation. Even vortex cavitation generators, if running outside of pre-determined operat- ing envelopes or not in a precise geometric arrangement, did not always bring positive results due to insuffi cient pressure wave amplitudes within a reservoir’s formation damage zone. To summarize: the fi rst-generation wave technology invented at NC NVMT RAN proved to be effi cient in multiple fi eld tests, however, a num- ber of superfi cially similar near-wellbore formation wave stimulation tech- niques appeared under the name of “wave technology”. In most cases, these techniques fail to bring positive results because they either use inadequate generators or their generators run outside of the operating envelopes that ensure success. Either way, they fail to take into account the scientifi c basis of the technology. Meanwhile, the originators of the fi rst-generation wave technology continued to improve it. To date, they have made signifi cant progress, capitalizing on recent advances in the science of resonance eff ects. Th e next step in the development of this technology was the idea of using near-wellbore resonance phenomena to amplify wave amplitudes, thereby augmenting wave cleanup processes in the near-wellbore forma- tion zone. In its simplest form, the idea was implemented for resonances at perforations [13]. As far as we know, the simple idea of using resonant and waveguide properties of near-wellbore formation zones has not been previously contemplated by anyone. Although, as mentioned in [14], the cleaning effi ciency and cleaning rate are improved signifi cantly with increased wavefi eld amplitude. And it is exactly resonance that allows achieving the highest amplitude with minimum energy, while waveguid- ing properties point to the wave excitation frequencies at which their amplitudes decay with distance slower than at others. Apparently, the fact that no one has tried to look at the problem at this angle can be explained by the prevailing opinion that the structure of a reservoir as a whole or even only of the near-wellbore zone is so complex that it is practically impossible to determine, with a suffi cient accuracy, its reso- nant frequencies and to build a wave excitation source (generator) that can generate exactly one of these frequencies. However, as studies con- ducted at NC NVMT RAN have shown, the use of vortex cavitation gen- erators with a wide multi-harmonic (practically continuous) radiation spectrum permits coverage of entire frequency bands, including near- wellbore formation resonant frequencies. As far as approximate deter- mination of resonant frequency values is concerned, it was shown in [13] that they can be found quite accurately if every perforation hole that xx Introduction is fi lled with a fl uid interacting with a porous medium at the interfaces is considered to be a resonator. It was later discovered that resonant frequencies, as well as the so-called critical waveguiding frequencies that ensure the lowest attenuation, can be approximated not only for the near-wellbore formation zone (covering the entire thickness of the formation) but for entire formations having a certain structure. As shown below, the new generation wave technology is based upon this discovery. Th e next step in the evolution of fi rst-generation wave technology became possible thanks to the development of drilling techniques. To be more specifi c, the enabling method behind this step was the creation in near-wellbore formation of networks of extended perforation tunnels providing reliable connectivity between the reservoir and the wells. In particular, it is proposed to use a perforation drilling system to create small-diameter perforation tunnels/waveguides, extending deep into the formation from the wellbore, followed by wave stimulation with a cavitation wave generator whose frequency band is within the pass- band of the created network of perforations/waveguides. Testbed trials have confi rmed the feasibility of drilling deep perforation tunnels [15]. It should be noted that, unlike the near-wellbore resonant wave stimu- lation where the geometry of the perforations and hence the resonant frequencies of wave stimulation are fi xed, this method opens up totally new possibilities. For example, it becomes possible to create a system of perforations with desired resonant frequencies, selecting the frequencies from a range close to the most powerful emissions in the spectrum of the available generator. On the other hand, fi rst-generation wave technology was tested in com- bination with chemical cleaning methods, i.e. injection of various chemi- cal agents that react with near-wellbore contaminants and transform them into easily removable solutions. Combined application of wave technology and chemical methods has produced some techniques that perform much better than each initial method alone [9]. A combination of near-wellbore wave stimulation with jet pump operation laid the groundwork for yet another method of near-well- bore formation remediation called “Overbalanced/underbalanced wave cleaning of near-wellbore formation”. Th e method permits sig- nifi cant improvement of the cleaning of near-wellbore formation zones around the main borehole and side tracks, as well as special completion screens. Unique equipment for these operations has been designed and successfully tested in the fi eld [16]. It has been prepared for extensive commercial use. Introduction xxi Along with the aforementioned studies that have signifi cantly advanced near-wellbore formation wave stimulations, NC NVMT RAN scientists have made a major, groundbreaking step forward and have actually come up with new generation wave technologies that are an alternative to the best enhanced oil recovery methods (including hydraulic fracturing and other leading-edge techniques). Th is step in wave technology advancement became possible thanks to the discov- ery of multi-frequency resonances and critical waveguiding frequen- cies associated with a formation’s natural waveguiding properties that are controlled by its structural heterogeneities: horizontal and vertical stratifi cation or compartmentalization. Moreover, multi-dimensional spatial resonance forms are capable of multi-fold amplifi cation and critical waveguiding forms propagate in formations to considerable dis- tances. Th e discovery of multi-frequency spatial resonance waveforms and critical waveguiding formsof motion in formations has allowed us to broaden signifi cantly the wave technology’s potential for improving production rates and enhancing oil recovery. NC NVMT RAN possesses unique soft ware for computing resonances and critical waveguiding fre- quencies for formations with known structural heterogeneities. Optimal designs of wave stimulation devices and oscillation generators have been developed. One of such approaches was tested on fi elds operated by Tomskneft in Russia, as well as on fi elds in Texas and California and proved to be many times less expensive than hydraulic fracturing, with an on-par perfor- mance but without the risk of reservoir fl ooding. In order to use natural resonant and waveguiding properties of forma- tions, controlled by their structural heterogeneities including horizon- tal and vertical stratifi cation or compartmentalization caused by vertical naturally-fractured zones and faults, it is proposed to conduct wave stim- ulations in a frequency band corresponding to the resonant frequencies of formations with structural heterogeneities. Th anks to the use of wave- guiding properties of formations and the discovery of the resonant wave amplifi cation phenomenon in spatial structures, it has become possible to stimulate much larger areas, to transmit resonant wave energy accurately to a predetermined zone containing capillary-trapped oil, and to mobilize capillary-trapped oil into the fl uid fl ow stream towards production wells. In fi eld conditions, this translates to a higher oil recovery and a lower water cut of fl uid produced from a particular reservoir. Th e unique equipment (and corresponding soft ware) that has been developed to create resonant multi-frequency waves in rock formations, accompanied by signifi cant changes in velocities and pressures of the xxii Introduction reservoir fl uid and the rock matrix, permits effi cient stimulation of large areas within an oilfi eld. In addition to the mobilization of capillarytrapped oil, near-wellbore formation zones around wells located far from the wave source within a treatment site can be stimulated too. Th e results obtained show that this technology is a cost eff ective and environmentally friendly alternative to hydraulic fracturing and other leading edge enhanced oil recovery methods. Th ese results have provided a basis for the creation of resonance macro- and micro-mechanics of petroleum reservoirs. Th is is a groundbreaking new method of enhanced oil recovery that can be combined with other well-known techniques such as chemical, ther- mal, horizontal well and other stimulations to signifi cantly improve their performance. 1 1 Scientific Foundation for Enhanced Oil Recovery and Production Stimulation First-Generation Wave Technologies for Improving Near-Wellbore Fluid-Flow Capacity of Oil-Bearing Formations and Enhanced Oil Recovery. Resonances in Near-Wellbore Formation. Large-Scale Laboratory Effects. The Statement and Substantiation of the Problem of Resonance Macro- and Micro-Mechanics of Petroleum Reservoirs: A Scientific Foundation for Enhanced Oil Recovery and Production Stimulation 1.1 The Practical Results of Near-Wellbore Formation Cleaning by Wave Stimulation The wave technology that was introduced in the 1980s by NC NVMT RAN has been used for many years to remediate near-wellbore damage in productive reservoirs. A wide range of field tests of wave principle-based devices has been conducted, mostly on oil fields operated by Nizhnevartovskneftegas, Yuganskneftegas, Langepasneftegas, Kogalymneft and Tomskneft, as well as on fields located in the Republics of Bashkortostan and Tatarstan, in the Perm Territory [9], and others. These tests have been conducted on both injection and production wells. In a number of cases, the tests were performed on several dozens of injection wells while monitoring response in offset production wells. Increased injectivities of injection wells as well as increased flow rates and lower water cuts of the responding production wells indirectly indicate that oil recovery can be enhanced by wave stimulation of remote and stagnant reservoir zones. Enhanced Oil Recovery: Resonance Macro- and Micro-Mechanics of Petroleum Reservoirs. O. R. Ganiev, R. F. Ganiev and L. E. Ukrainsky. © 2017 Scrivener Publishing LLC. Published 2017 by John Wiley & Sons, Inc. 2 Enhanced Oil Recovery Most of the tests were conducted on oil fields operated by Nizhnevar- tovskneftegas, where a total of about 400 wells (injection and production) were subjected to wave stimulation by the end of 1987. An analysis of the results of the 1986 field tests of wave principle-based equipment has shown that the equipment is quite efficient in terms of stimulation of near-wellbore formation zones of production and injec- tion wells. Average incremental injectivity and flow rate after wave stimulation jobs was 255 m3/day of water and 23.4 t/day of oil per well, respectively (from a report dated 1 January 1987 on wave stimulation performance at Nizhnevartovskneftegas oil production facilities in April/December 1986). It has been noted that the best performance is provided by combined well stimulation that includes hydrochloric acid treatment and the use of a downhole hydro-impact generator tool devel- oped at NC NVMT RAN, with acid injection through the oscillation generator. An analysis of the results of production well stimulations has shown that oil flow rates increased by an average of 15-20 t/day after combined well stimulation jobs (i.e. flow rates increased by 1.5–2.5 times). Downhole hydro-impact generator treatments account for 50–60% of the increase, i.e. 8–11 t/day of oil. This conclusion is confirmed by data on the wells that were stimulated using only downhole hydro-impact gen- erators without any other stimulation methods. To hone the wave stimu- lation procedure, a dedicated program of injection and production well treatments was designed and implemented. The purpose of the program was to identify response to downhole hydro-impact tool stimulations only, without effects from other treatments such as acidizing, acid pick- ling, cleaning circulation, etc. The program involved a package of logs run into the stimulated wells. A bulk of the research scope was completed by the mid-June, 1987. An analysis of the results of production well stimulations shows that the flow rates of all the tested wells increased. For example, one well (No. 12104) demonstrated an increase in the oil flow rate from 90 to 147 t/day; another well (No. 297) showed an increase in total fluid flow rate from 86 to 150 m3/day with an unchanged water cut; while yet another well (No. 12397) showed an increase in total fluid flow rate from 38 to 48 m3/day with the water cut dropping from 5% to 1–2%. These results along with results of several other tests allowed us to con- firm the earlier conclusion that wave stimulations are an efficient method of near-wellbore formation treatment. The near-wellbore cleanup field tests were conducted on the basis of the authors’ theoretical studies. The results are described in [8, 9, 10, 11]. Scientific Foundation for Enhanced Oil Recovery 3 Fig. 1.1 shows a typical production history of a production well. A pro- duction well operated by Priobye oil company is taken as an example. Fig. 1.1. Priobye Oil Company Production Well Wave Stimulation Results As we see, the oil flow rate was declining and by the time of the stimu- lation job it had dropped more than 2 times below its initial value. It is an indication of near-wellbore formation damage. After the treatment which consisted in placing a source of pressure oscillations (with frequencies matching the estimated resonant frequencies for a particular well in order to drive contaminating particles from the near-wellbore zone into the wellbore) close to perforations infront of the productive reservoir, flow rates were practically restored to their initial levels and remained stable during the observation period (10 months). These results are typical for the proposed technology. Many such tests were conducted in different regions of the Russian Federation and abroad. Based on results of the stimulation jobs conducted in Russia, this technology was officially accepted (a certificate of acceptance by the USSR Ministry of Petroleum Industry dated 1990 is available). Let us cite some of the data available on two stimulation jobs per- formed on West Siberian production wells. 1. The production method was an electric submersible pump. Dura- tion of well stimulation treatment: 14 hours. After the stimulation job, oil flow rate increased from 8 t/day to 25.6 t/day, while water cut dropped from 89% down to 66%. Incremental oil production during a 3-month period amounted to 2,219.0 tons. 4 Enhanced Oil Recovery 2. The production method was gas lift. Duration of the well stimu- lation treatment: 13 + 3 = 16 hours. After stimulation, the payzone net thickness increased from 4.4 m to 5.4 m due to addition of a reservoir layer. Oil flow rate increased from 11.1 t/day to 12 t/day. Water cut decreased from 40% to 10%. Incremental oil production during a 3- month period amounted to 100 tons. Gas consumption for gas lift operation was the same before and after the stimulation job: 8,000 nm3/day. Provided below are well log curves for a number of injection wells that underwent wave treatment in different regions of Russia. The most typical West Siberian and Bashkirian were chosen as examples. In all of the cases, injectivity profiles before and after the stimulation are shown. As can be seen, the stimulations helped improving conformance in some cases, opened non-contributing sub-layers and cleaned near-wellbore reservoir zones. Fig. 1.2 shows injectivity profiles of two injection wells operated by Chernogorneft. After the wave stimulation treatment, their injection capacity Q increased from 101 m3/day to 493 m3/day and from 350 m3/day to 580 m3/day, respectively. The vertical columns of figures are the distances from the wellheads in meters. The intervals marked by arrows are perforated intervals. P is the wellhead injection pressure. As can be seen, wave stimulations in both wells opened new sub-layers and increased sweep efficiencies sweepK by 1.65 and 2.18 times, respectively. Fig. 1.3 and Fig. 1.4 show injectivity profiles of two wells operated by Kogalymneft. After the wave stimulation treatment, their injection capac- ity increased from 175 m3/day to 418 m3/day and from 350 m3/day to 740 m3/day, respectively. We can see improved conformance after the wave stimulation treat- ment in the first case, and activation of new sub-layers (injection along the entire perforated interval) in the second case. The perforated interval on Fig. 1.4 is marked by horizontal dash lines. Fig. 1.5 shows injectivity profiles before and after wave stimulation of a well operated by Samotlorneft. After the wave stimulation treatment, its injection capacity increased from 239 m3/day to 668 m3/day. Fig.1.6 shows injectivity profiles of a well operated by Arlanneft, a sub- sidiary of Bashneft Oil Company, before and after wave stimulation, at different wellhead pressures. As we can see, the injection capacity in- creased in all cases. The active section of the perforated interval became much longer, and injectivity of the most permeable sub-layer increased noticeably. Scientific Foundation for Enhanced Oil Recovery 5 Fig. 1.2. Chernogorneft Oil Company Injection Well Stimulation Fig. 1.3. Kogalymneft Oil Company Injection Well Stimulation 6 Enhanced Oil Recovery Fig. 1.4. Kogalymneft Oil Company Injection Well Stimulation Fig. 1.5. Samotlorneft Oil Company Injection Well Stimulation Fig. 1.6. Arlanneft Oil Company Injection Well Stimulation Scientific Foundation for Enhanced Oil Recovery 7 Fig. 1.7. Arlanneft Oil Company Injection Well Stimulation Fig.1.7 shows injectivity profiles for another well operated by Arlanneft. Its injection capacity increased from 38 m3/day to 137 m3/day. As the selected data indicate, stimulation of near-wellbore formation zones provides a significant positive effect in various geological conditions. Provided below is a broader selection of data on typical near-wellbore stimulations of injection wells. 1. Duration of well stimulation: 5.5 hours. As a result of the stimula- tion job, diffusivity increased from 1495 to 4150 cm2/sec, permeability increased from 0.021 to 0.058 D, transmissibility increased from 40 to 109.9 D*cm/cP, and injectivity increased from 755 m3/day (at reservoir pressure maintenance pressure P = 97 atm) to 894 m3/day (P = 98 atm). 2. Duration of well stimulation: 6 hours. As a result of the stimulation job, injectivity increased from 303 m3/day (at P =120 atm) to 600 m3/day. It should be noted that injection well stimulations can bring about higher production rates just as good as production well stimulations. For instance, an analysis of displacement parameters for the two aforemen- tioned injection wells has shown that four production wells responded to the injectivity increase. Incremental oil production from these wells after the stimulation treatment of the two aforementioned injection wells reached 600 tons over a period of two months. The results of some stimulation jobs performed on West Siberian wells are summarized in Table 1.1. 1.2 The Scientific Fundamentals of the First- Generation Wave Technology for Stimulation of Production Processes Provided below is a brief overview of the results that form the basis of the first-generation wave technology for near-wellbore stimulation. In great- er detail they are described in [8, 9, 10, 11]. 8 Enhanced Oil Recovery Table 1.1 It em N o . W el l N o . N et O il T h ic k n es s (m ) R es er vo ir P re ss u re P ro d u ct io n M et h o d W at er C u t (% ) Flow Rate (t/day) Well Status after 9 Months in Operation In cr em en ta l O il P ro d u ct io n ( t) Before Stimu- lation After Stimu- lation Flow Rate (t/day) Water Cut (%) Produc- tion Method Luginets Field It is a gas / oil field; Jurassic sediments (the target reservoir is J1/З); tight sandstones (average permeability is 20 mD, porosity is 16%). The reservoir has interlayers of shales and siltstones. 1 64 9.4 195 inactive 0 0 13 6.4 0 SRP 1,585 2 875 4.8 189 nat. flow 20 0.8 3 4.2 20 nat. flow 1,511 3 1,219 6 220 nat. flow 15 1.7 5 5.2 15 nat. flow 719 4 1,102 12 216 nat. flow 15 1.7 4 10.6 15 SRP 1,975 5 885 8 205 nat. flow 0 1 4.2 4.2 0 SRP 965 Total: 6,755 Tevlin Field 6 7,778 10 215 SRP 0 12 40 50 0 ESP 4,800 7 7,660 9.2 190 SRP 0 5 35 30 0 SRP 3,800 Total: 8,600 Kogalym Field Medium- to fine-grained sandstones and coarse-grained siltstones. Arkose, shaly, heterogeneous. Shaly sandstone cement, occasionally interlayers with shaly/carbonate cement. Low permeability: 25 mD on average, porosity: 20%. 8 5,519 5 270 injector 100 80 490 230 100 45,000 9 2,063 7.3 275 injector 100 250 540 400 100 41,500 Total: 86,500 Pokomasov Field Polymictic sandstones; porosity: 20.7%; permeability: 50–150 mD 10 263 7 262 inactive 58 7.6 18.75 1.9 45 SRP 171 Total: 171 First, we would like to present the results of experiments conducted at Shell test facilities in Rijswijk, the Netherlands. 1.2.1 Large-Scale Laboratory Experiments at Shell Test Facilities Here below is a description of an experimental program in which a hydro-impact generator was used. A test drilling apparatus capable of simulating the processes that take place near an oil well (with real-life Scientific Foundation for Enhanced Oil Recovery 9 operating parameters) was usedin the experiments. A schematic of the apparatus is shown in Fig. 1.8 and its general view is provided in Fig. 1.9. Fig. 1.8 Fig. 1.9 10 Enhanced Oil Recovery The test procedure was as follows. Upon completion of drilling, the rate of flow of fluid through the zone of rock adjacent to the drilled hole and the differential pressure across the zone were measured. After that, the drill bit was replaced with a hydro-impact tool and wave stimulation of the walls of the drilled hole was conducted. Then, the rate of fluid flow through the same rock zone and the differential pressure across it were re-measured. A plot of measured flow rate versus differential pressure is provided in Fig. 1.10. Judging by the slope of the curves, initial permeability of invad- ed specimens is estimated to be around 300 mD, while after the wave treatment it is about 1000 mD (with a 20% accuracy). Initial permeability of clean specimens was 800–900 mD. Therefore, the wave stimulation brought about a roughly 4-fold increase in permeability. Fig. 1.10 Tests were also conducted on mud-invaded hexagonal sandstone blocks measuring 39 cm by 80 cm. A hole was drilled through the center of the blocks. A conventional bit was used to drill the hole under condi- tions that were as close as possible to field drilling conditions. In particu- lar, the pressure of drilling mud near the bit was 45 bar. The diameter of the drilled hole was about 22 cm. In the process of drilling, the drilling mud invaded the near-wellbore zone and clay particles contained in the mud, apart from precipitating on the surface of the rock specimen, pene- trated inside the block to a certain depth. Upon completion of drilling, the rock specimen was removed from the high-pressure vessel and was cut up along a plane intersecting its axis. After that, near-wellbore zone Scientific Foundation for Enhanced Oil Recovery 11 wave cleanup tests were conducted on the drilled rock specimen. For this purpose, the test drilling apparatus was rearranged. The drill bit was removed and the hydro-impact generator was installed in its place at the end of the supply pipe. The supply pipe was connected to a tank filled with water. Water was pumped through the generator as described above. The generator was positioned at a distance of 12 cm from the bottom of the hole in the block. The flow rate was increased to 300 liters per mi- nute. Fig. 1.11 After the wave treatment the rock specimen was cut up. A photograph of the cut is provided in Fig. 1.11 (right). For comparison, a sample that was cut up after drilling without wave treatment is shown on the left side. This sample was drilled under exactly the same conditions as the one that underwent wave stimulation. A layer (3–4 cm thick) of a lighter color than the rest of the invaded zone was found around the borehole. As we can see, the contamination has disappeared. Therefore, a conclusion can be drawn that the waves cleaned the near-wellbore zone from the invad- ing drilling mud clay particles. The results of these experiments have provided the foundation for the development of first-generation wave technology for petroleum industry applications. 12 Enhanced Oil Recovery 1.2.2 Resonances in Near-Wellbore Formation. Resonances in Perforations As mentioned above, near-wellbore formation wave stimulation intensi- fies when resonance modes of wave motion are achieved. In the general case, resonance occurs when frequencies of external wave action coincide with the natural frequencies of objects exposed to the action. In actual field conditions, various sources of resonances can be found both at the bottom of a production well and in the near-wellbore formation zone. We can investigate the onset of resonance in an individual perforation hole at the bottom of a well as one of such sources [13]. Let the perforation hole be a fluid-filled horizontal channel in the shape of a straight circular cylinder with a cross-section radius R0 and a length l. One end of the channel connects to the wellbore, while the other end and the enveloping surface, together with the impermeable plane z = 0, are the boundaries of the fluid-saturated porous medium that fills the semi-space z > 0. The channel occupies a volume measuring r < R0, 0 < z < l (Fig. 1.12). Fig. 1.12. Wave Resonance in a Perforation Hole at the Bottom of a Well. The Model Setup Steady-state oscillations in such a system caused by the action of har- monic pressure oscillations at the end of a channel connected to the wellbore are studied in [13]. The computed results are shown in Figs. 1.13–1.14. Fluid parameters correspond to crude oil parameters while porous medium parameters correspond to in-situ oil saturated sandstone. Scientific Foundation for Enhanced Oil Recovery 13 Fig. 1.13 shows channel wall oscillation amplitude versus distance to the wellbore. The curves differ in frequency ω. As can be seen from the plot, the shape of wall boundary oscillation and its amplitude depend essentially on bottomhole pressure oscillation frequency. The resonant nature of channel wall oscillations is demonstrated by the curves on Fig.1.14. These curves are channel wall oscillation amplitudes at mid- point z = l/2 (curve 1) and at channel end z = l (curve 2) versus pressure oscillation frequency for an l = 0.3 m. Fig. 1.13 Fig. 1.14 Let us call the frequency that corresponds to the main peak of the curves in Fig. 1.14 the main resonant frequency ωres. At this frequency, the maximum oscillation of the channel wall is almost an order of magni- tude greater than at other frequencies. In order to achieve resonant oscillation of the channel wall, bottomhole pressure oscillation frequency needs to be chosen very precisely. This requirement follows from the behavior of the curve near the main resonant frequency. Thus, the presence of a finite-length channel near the wellbore signifi- cantly increases the amplitude of oscillations. The main resonant frequency depends on the parameters of the porous medium and the geometry of the channel. However, numerical simula- tion has shown that changing the parameters of the porous medium and the radius of the channel within a wide range of values has little effect on the main resonant frequency. In the course of simulation, the channel radius R0 was changed in the range from 2 mm to 10 mm. Significant oscillations of the channel wall are observed at other fre- quencies as well, but their amplitude is much lower than at the main resonant frequency. Permeability has the largest spread in values. Permeabilities between layers can differ by an order of magnitude or more. Fig.1.15 shows the 14 Enhanced Oil Recovery main resonant frequency versus channel length. Curve 1 corresponds to a permeability k = 1 10–10 m2, and curve 2 corresponds to a permeability k = 5 10–12 m2. Curve 1 permeabilities are typical for Bashkirian oilfield formations, whole curve 2 permeabilities are commonly observed in West Siberian formations. As we can see, there is almost no difference between the values of resonant frequencies for perforation channels of the same length. Fig. 1.15 Fig. 1.16 The main resonant frequency mostly depends on the length of the channel. As can be seen from Fig. 1.15, the smaller the channel length, the higher the frequency. Fig. 1.16 shows the amplitude of porous medium matrix oscillations versus the distance to the channel axis r at the main resonant frequencies for various channel lengths. The mutual arrangement of the curves indicates that for oscillations at the main resonant frequency the affected zone grows with the length of the channel. Therefore, a frequency of bottomhole pressure oscillations corre- sponding to the highest amplitude of oscillations in the near-wellbore zone can be chosen. There is a weakdependence between this pressure oscillation frequency and the parameters of the porous medium but a strong dependence on the length of the channel. We note that the foregoing problem involves only a single perforation hole. However, several or even all perforation holes of a well may reso- nate simultaneously. This happens when a generator’s radiation frequen- cies are resonant for all of the perforation holes. Besides, in this case the entire near-wellbore formation zone may be involved in resonance. In practical terms, this is the most preferable case for near-wellbore wave stimulation. Scientific Foundation for Enhanced Oil Recovery 15 1.2.3 Excitation of Oscillations in Micro-Pores by One- Dimensional Longitudinal Macro-Waves in a Medium. Resonances. Transformation of Micro-Oscillations in Pores to Macro-Flows of Fluid. The Capillary Effect This sub-section describes the results achieved by the authors in coopera- tion with S. A. Korneyev and published in [10, 11, 17]. We investigated the possibility of transforming the wave motions of a porous fluid-saturated medium into a unidirectional monotonous motion of fluid such as the flow of fluids from a productive reservoir to a wellbore. These types of motions can be realized in porous fluid- saturated media because in heterogeneous wave fields an impulse trans- ferred from the matrix to the fluid during a period of oscillation can be non-zero. This is caused by various nonlinearities as well as by heteroge- neities of wave fields inside the pores. When macro-waves propagate in a porous fluid-saturated medium, they excite oscillations inside each pore. If certain conditions are met, the oscillatory motions in the micro- pores transform into strong unidirectional monotonous macro-motions of the fluid. We studied the simplest one-dimensional wave field (a compressional wave) in a porous fluid- saturated medium, located on a segment 0 < x < L and defined as follows. The left end of the segment is described by the fictitious tension 0f and the pressure in the fluid as the sum of the constant pressure component p0 and disturbance in the form of harmonic oscillations; the right end of the segment is described by the absence of matrix shifts and a pressure that is equal to its undisturbed value p0. The conditions at the left end correspond to a wellbore with an oscillation generator, while on the right end they correspond, for instance, to a boundary between reser- voir zones with highly different matrix porosities and densities, or to another wellbore. The solution of the linearized equations is a standing compressional wave. In addition to nonlinearities such as convection terms commonly ob- served in hydrodynamic systems, unidirectional seepage flows are also controlled by nonlinearities specific to porous fluid-saturated media and associated with porosity oscillations in wave fields. The thing is that porosity oscillations are a superposition of terms whose frequencies and phases coincide with the oscillations of densities and pressures in the fluid. Therefore, situations are possible when superposition of porosity oscillations with fluid pressure and density oscillations in a wave field 16 Enhanced Oil Recovery leads to the initiation of unidirectional motion of fluid in the pores of a fluid-saturated porous medium. Mathematically, it is described by nonlinear terms in equations of motion that contain products of cyclic in time porosity disturbances by cyclic disturbances of pressure gradients in the fluid and fictitious tension in the matrix, or by cyclic disturbances of fluid flows and matrix in interfacial interaction forces, in particular in equations for frictional forces and forces of added masses. From the applied point of view, the most interesting thing is to find out whether waves can be used to achieve directional motions, in particular a fluid flow that is nonzero in time on the average. The relationship between fluid flow and frequency shows that there are frequency bands within which considerable fluid flows may occur. It is caused by resonances of the initial compressional standing macro-wave. Fig. 1.17 shows fluid flow velocities versus the excitation frequency ω for certain values of parameters of the porous medium. As we can see (Fig. 1.17a), fluid flow velocities are quite high in a number of narrow frequency bands. In what follows, the frequencies that correspond to maximum fluid flow velocities are referred to as resonant frequencies. Fig. 1.17 For comparison purposes, Fig. 1.17b shows pressure gradient versus Darcy steady-state fluid flow velocity for the medium. As we can see, to achieve a fluid flow velocity equal to the velocity achieved by external pressure oscillation stimulation with an amplitude of the first resonant frequency of just 1 bar, the steady-state case requires a pressure gradient of about 20 bar/m, while water injection through dedicated wells usually provides pressure gradients of 0.3–0.4 bar/m [18]. Therefore, wave stimula- tion is capable of initiating flows at such velocities that in the steady-state case require practically unreachable enormous pressure gradients. Scientific Foundation for Enhanced Oil Recovery 17 We note that resonant frequencies of the one-dimensional (in this case) wave strongly depend on the length of the interval .L As analyses have shown, the smaller L the higher the resonant frequency. For L = 1 m, the resonant frequency р is approximately 1.0 kHz. In summary, we can say that nonlinear wave mechanisms of motion have been found that can create additional fluid flows in porous fluid- saturated media. Velocities of such flows are similar to the velocities of steady-state flows that can be created in the same medium by significant steady-state pressure gradients. The magnitude of these gradients is such that it cannot be achieved by any other currently known method. As far as it is applicable to oil production, it means that wave fields created in a medium can be used to clean up near-wellbore formation zones, mobilize capillary-trapped oil, drive hydrodynamically uncon- nected hydrocarbon blobs towards wellbores, etc. A similar phenomenon of the transformation of micro-oscillations of pores into significant fluid macro-flows was found by the authors as far back as in 1989 [19]. It was demonstrated that traveling waves that propa- gate in the walls of a micro-capillary (Fig. 1.18) – a model of a pore in a porous medium – can cause non-oscillatory unidirectional motions of the fluid filling the capillary along its axis. The parameters of such flows are shown in Table 1.1. For instance, a traveling shear translational wave with an amplitude of just 10–2 μm propagating in the wall of a capillary with an undisturbed radius of 10 μm can cause steady-state flow inside the capillary with a cross-sectional average velocity of 4.5 cm/sec. To create the same flow by applying steady-state pressures at the ends of the capillary, a pressure gradient of 36 bar/m would be required [10, 11]. Such a gradient cannot be achieved in subsurface formations using conven- tional methods [18]. Fig. 1.18 18 Enhanced Oil Recovery Table 1.2 Capillary Radius (m) Wave Fre- quency (Hz) Average Velocity (m/s) Equivalent Steady-State Pressure Gradient (mPa/m) 10–2 550 0.39 0.312·10–4 10–3 5·104 0.344 0.275·10–2 10–5 2·107 0.045 3.6 1.2.4 Cleaning of Horizontal Wells It was proposed to use first-generation wave technology to clean sand control screens used in horizontal wells. Typical, commonly used screens are shown in Fig. 1.19. The one on the left is a pre-pack screen in which sand and gravel are used as the filtering components (here below this type of screens is referred to as S1), while on the right is a strata-pack screen that uses pre-perforated multilayer metal cylinders (hereinafter referred to as S2). A detaileddescription of the relevant experiments conducted by the authors in cooperation with NC NVMT RAN scientists I. G. Ustenko and V. N. Ivanov is provided in [10, 11]. In this paper, we offer only a brief overview of the results. Fig. 1.19 Sand control screens are commonly used in horizontal well comple- tion strings to prevent drilling mud solids and reservoir fluid solids from plugging the wellbore. To ensure reliable protection, it is important that the screens remain clean during and after the well completion process. It is obvious that the simplest method of cleaning is washing. In this case, the washing fluid is circulated through the screen’s polluted zone. Note that the polluted zone has to be isolated (for instance, by packers) for the duration of the washing job. The thing is that if the polluted zone is not isolated, the washing fluid would circulate only through clean sections of the screen, leaving the polluted section untouched. Scientific Foundation for Enhanced Oil Recovery 19 The wave method of cleaning screens in horizontal wells does not re- quire isolation of polluted zones as in this case cleaning is provided by waves and cavitation created by wave generators. A schematic of a screen-cleaning wave generator assembly in a horizontal well is shown in Fig. 1.20, where 1 is the reservoir, 2 is the screen, 3 is the tubing con- taining the washing fluid, 4 is the wave generator, 5 is the cavitation zone, 6 are the fluid flow lines downstream of the generator, 7 is the low- pressure zone, 8 are the pressure waves, 9 are the cavitation bubbles, 10 is the flow of the reservoir fluid through the screen, 11 is the flow of the washing fluid through the screen. Fig. 1.20 The washing fluid is pumped through the generator. If the flow rate and the pressure are high enough for the generator to operate, then waves and cavitation appear in the flow downstream of the generator. Cavita- tion bubbles collapse at a distance from the generator and create high- amplitude pressure pulses that do the cleaning. Figs. 1.21–1.22 show the results of screen washing tests. As can be seen, the wave cleaning method outperformed conventional washing with respect to both screen types. In the case of screen S1 (Fig. 1.21), it took less time to clean the screen with a better quality of cleaning. Screen S2 (Fig. 1.22) was cleaned even faster. Moreover, the conventional washing method was unable to clean this screen at all. It was determined that the screen’s permeability began to drop, and the test was stopped. We would like to note that although the upstream pressure in the wave cleaning case was higher than in the conventional washing case, the total energy consumption was lower due to a shorter duration of the cleaning job. The tests show that wave stimulation offers better performance and cost efficiency compared to conventional washing. This method allowed us to clean screen S1 two times faster. The final screen permeability 20 Enhanced Oil Recovery achieved by the wave cleaning method is much closer to the initial per- meability than the final permeability achieved by washing. It took even less time to clean screen S2 by the wave method than screen S1, while the washing method was unable to clean screen S2 at all. Fig. 1.21 Fig. 1.22 In summary, the wave screen cleaning technology has the following advantages of over conventional washing: 1) better quality of cleaning, 2) shorter procedure duration, 3) smaller power consumption, 4) no need to isolate the polluted zone with packers, 4) no invasion of the washing fluid into the productive reservoir. Therefore, the wave cleaning method has proven its high performance. 1.2.5 Preliminary Results However, despite numerous successes, there were some failures in the application of wave technologies for near-wellbore zone cleaning – mostly, as mentioned above, because the method was used incorrectly, without understanding its scientific basis, without inducing resonance in the near-wellbore zone, etc. Failures of first-generation wave stimulations had various causes. In some cases, they were caused by reservoir depletion, while in other cases they were caused by in-situ chemical processes that led to significant permeability impairment. In yet other cases, the wave forces acting on the contaminating particles in near-wellbore formation were not high enough to overcome the force of adhesion, etc. Even in cases where the matrix was contaminated by plugging solids, wave stimulation failure analysis was complicated by an inaccurate understanding of the mecha- nisms and criteria of near-wellbore formation cleaning by the wave method, etc. There was no accurate understanding of how the wave cleaning mechanism worked. What wave parameters are critical for the cleaning process? What governs the wave parameters critical for the Scientific Foundation for Enhanced Oil Recovery 21 cleaning action? This study is an attempt to find answers to these ques- tions that are linked to – as it will be shown below – the development of the so-called micro- and macro-mechanics of petroleum reservoirs. Accordingly, the first-generation wave methods designed mainly for near-wellbore formation stimulation will also advance significantly. 1.3 Stimulation of Entire Reservoirs by First- Generation Wave Methods for Enhanced Oil Recovery. Resonance Macro- and Micro- Mechanics of Petroleum Reservoirs: A Scientific Foundation for Enhanced Oil Recovery In a number of cases where near-wellbore wave stimulation jobs were conducted using a generator based on vortex flow effects, increases in flow rates were observed not only on the well in which the generator was installed but on offset wells too. Therefore, apart from wave stimulation of near-wellbore formation zones, this method can be used to stimulate entire reservoirs or large sections measuring several square kilometers. In this case the generator is installed in one of the wells within the se- lected field section, and the offset wells are influenced by the stimulation (Fig. 1.23). Fig. 1.23 22 Enhanced Oil Recovery As an example, Fig. 1.24 shows the results of a stimulation job con- ducted on a section of the Luginets oil field located in the Tomsk region. As we can see, production flow rates were restored not only on the stimu- lated well but on several offset wells too: the offset wells and the stimulat- ed well form a pattern. Fig. 1.24 We would also like to provide here some results of field tests conduct- ed at the Elk Hills oil field in California [20]. The responding wells were located within 800-meter radius circles whose centers were the wells in which the generators were installed. A map of the field is shown in Fig. 1.25. Fig. 1.25 Scientific Foundation for Enhanced Oil Recovery 23 The 73 responding wells were located within two circles as shown on the map. Stimulation results are shown in Fig. 1.26, which is the com- bined response of the 73 responding wells located inside the circles. The simulation program started in December 2003. By January 2005 combined flow rates of the 73 wells (oil production) increased by 42% compared to the initial level at the beginning of the stimulation cam- paign. Compared to trend-based January 2005 projected production, combined flow rates increased by 60%. According to the oil cut trend (a parameter inverse to water cut), the oil cut was expected to drop. However, a 28% increase in the oil cut compared to the initial level at the beginning of the stimulation program, or a 47% increase compared to the trend-projected value was observed. Fig. 1.26 Fig. 1.27 is a comparison of responses to two enhanced oil recovery methods: hydraulic fracturing and impact wave stimulation of a large section of an oil field. These jobs were conducted at the Lost Hill oil fieldin Texas. It is a di- atomite formation that has 0.1–2,000 mD permeability, 45–55% porosity, 700–1200 m productive depth, 30% water cut and 26o API oil gravity. In October 1999, a 7.2-point Richter scale earthquake took place. We can see on the diagram that the 7 wells that were fractured in November 1999 responded to the earthquake. In August 2000, a section of the field was stimulated using an impact wave generator. 24 Enhanced Oil Recovery Fig. 1.27 The response to hydraulic fracturing is obvious in terms of increases in oil production and oil cut. However, the response to wave stimulation is comparable to hydraulic fracturing. Note that the 7-well hydraulic frac- turing cost was US$2 million, while the hydro-impact wave stimulation cost only US$ 100,000. These data prove that in some cases stimulation of entire reservoirs can bring very good results. However, just like in the case of near- wellbore formation treatment, the stimulations were not always success- ful. Failures of first-generation wave stimulations of entire reservoirs had various causes, including the application of the method without a clear understanding of its scientific basis. In some cases, there was not enough residual oil in the stimulated section; in other cases, the wave forces acting on capillary-trapped oil droplets and reservoir-contaminating solids were not high enough to overcome the capillary forces and the force of adhesion, etc., just like it was mentioned above for the near- wellbore formation wave treatment case. Wave stimulation failure analy- sis was complicated by an inaccurate understanding of the causes behind oil recovery impairment in productive reservoirs, the lack of stimulation success or failure analyses, and the lack of a rigorous theory to explain the observations. Moreover, it was not clear until recently what wave param- eters are critical for the stimulation of entire reservoirs, etc. Summarizing, the principal mechanisms of oil production and oil re- covery impairment were not investigated thoroughly enough, the criteria (conditions) for enhancing the recovery of oil from heterogeneous reser- voirs were not identified, etc. The resonance macro- and micro-mechanics of petroleum reservoirs, which is the subject of this study, provides answers to the questions posed above. It serves as the scientific basis for the development of con- Scientific Foundation for Enhanced Oil Recovery 25 trolled machines and devices, including oscillation and wave generators with proper measuring and control systems, for stimulation of near- wellbore zones and entire reservoirs to increase production and to en- hance oil recovery. Wave stimulation equipment is based on mathemati- cal software products that have been created thanks to the development of the resonance macro- and micro-mechanics of a petroleum reservoir – a growing field of fundamental science. 27 2 Remove Micro-Particles by Harmonic External Actions The Micro-Mechanics of a Porous Medium and the Criterion for Successful Wave Stimulation to Remove Contaminating Micro-Particles Stuck to Pore Walls by Harmonic External Actions This chapter describes theoretical investigation of the phenomena that take place in the wave fields in fluid-saturated porous media. We consider the effect of these phenomena on fluid flow processes in productive reservoirs and on pore space cleaning, that is on the motion of micro- inclusions in the pores under the action of forces of the wave nature. 2.1 An Analysis of the Forces Acting on Pore-Contaminating Particles under a Harmonic External Action In this sub-section, we consider the case where the flow capacity of near- wellbore formation suffers from the precipitation in the near-wellbore zone of small rock particles that were either carried in from the reservoir with the produced fluids or invaded the near-wellbore zone during drilling. We assume that the contaminating solids are retained in the pore space by the action of adhesion forces that make the particles cling to rock walls. We consider the wave action to be monoharmonic. The main idea behind using wave stimulation to clean the pore space from any contaminants of this type is to use wave action to transmit oscillation motions to the solid particles that contaminate rock matrix pores, reservoir fluid and pore walls. It will result in the detachment of contaminating particles and oil droplets from pore walls and their mobi- lization with the seepage fluid flow towards production wells. Enhanced Oil Recovery: Resonance Macro- and Micro-Mechanics of Petroleum Reservoirs. O. R. Ganiev, R. F. Ganiev and L. E. Ukrainsky. © 2017 Scrivener Publishing LLC. Published 2017 by John Wiley & Sons, Inc. 28 Enhanced Oil Recovery Let Oxyz be a system of Cartesian coordinates with the origin at an arbitrary point O, fixed in the absolute space. Let the unit vectors of this system – ex, ey, ez – be also fixed, and let the unit vector ez be vertical. We consider an arbitrary pore with a solid particle retained on the sur- face of the pore by the force of adhesion. At the point of contact between the particle and the pore, let us introduce the normal to the surface of the pore np directed inside the pore, and the vectors τp1 and τp2 that form an orthonormal basis on the plane tangent to the surface of the pore at the point of contact with the retained particle. Fig. 2.1 We assume that the point on the boundary of the pore to which the contaminating particle is attached moves together with the matrix of the porous fluid-saturated medium with a velocity of x x y y z zw w w we e e . We also assume that the particle is acted upon by the following forces: 1) the sum of reservoir pressure gradients – grad P and the wave forces that occur in a wave field (such as those described in Section 1.2.3). We consider this sum to be independent of time; 2) the force of gravity and the force of buoyancy directed along ez; 3) the non-steady-state fluid pressure gradient due to wave action – grad p; 4) the force of inertia p dw dt , where p is the density of the particle; 5) a Stokes type force proportional to the difference between velocities of the fluid and the matrix: u w , where ηf is the viscosity of the fluid, α is a coefficient that depends on the shape and dimensions of the pore and the contaminating particle (in the simplest case 2 p4.5r , where rp is the mean radius of particles); we note that the Remove Micro-Particles by Harmonic External Actions 29 latter force does not have a non-zero component along the normal np due to the medium persistence assumption; 6) an added mass type force proportional to the difference between accelerations of the fluid and the particle: f dw du dt dt , where β is the added mass coefficient, f is the density of the fluid; 7) the force of adhesion Fad that retains the parti- cle on the pore wall. We assume that the force of adhesion Fad balances off any force f that is applied to the particle and tries to detach the particle from the wall, i.e. whose projection on the normal to the pore surface pn directed inside the pore is positive if the modulus of the force f does not exceed some limiting value lim F that depends on the force of cohesion between the particle and the pore surface and the normal pressure N that presses the particle to the pore surface. We assume that lim F MS kNS , where M is a coefficient of the force of cohesion that defines the maximum specific force of cohesion between the particle and the pore per a unit of the contact area that is independent of the normal pressure; S is the contact area between the particle and the pore wall; k is a coefficient of propor- tionality between the normal pressure that presses the particle to the pore wall and the increase in lim F . If limf F , then the particle is detached
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