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font, font size, single or double column, landscape or portrait mode, and figures that you can click or tap to enlarge. For additional information about the settings and features on your reading device or app, visit the device manufacturer’s Web site. Many titles include programming code or configuration examples. To optimize the presentation of these elements, view the eBook in single-column, landscape mode and adjust the font size to the smallest setting. In addition to presenting code and configurations in the reflowable text format, we have included images of the code that mimic the presentation found in the print book; therefore, where the reflowable format may compromise the presentation of the code listing, you will see a “Click here to view code image” link. Click the link to view the print-fidelity code image. To return to the previous page viewed, click the Back button on your device or app.APPLIED PETROLEUM RESERVOIR ENGINEERING THIRD EDITION Ronald E. Terry J. Brandon Rogers Upper Saddle River, NJ • Boston • Indianapolis • San Francisco New York • Toronto • Montreal • London • Munich • Paris • Madrid Capetown • Sydney • Tokyo • Singapore • Mexico CityMany of the designations used by manufacturers and sellers to distinguish their products are claimed as trademarks. Where those designations appear in this book, and the publisher was aware of a trademark claim, the designations have been printed with initial capital letters or in all capitals. The authors and publisher have taken care in the preparation of this book, but make no expressed or implied warranty of any kind and assume no responsibility for errors or omissions. No liability is assumed for incidental or consequential damages in connection with or arising out of the use of the information or programs contained herein. For information about buying this title in bulk quantities, or for special sales opportunities (which may include electronic versions; custom cover designs; and content particular to your business, training goals, marketing focus, or branding interests), please contact our corporate sales department at firstname.lastname@example.org or (800) 382-3419. For government sales inquiries, please contact email@example.com. For questions about sales outside the U.S., please contact firstname.lastname@example.org. Visit us on the Web: informit.com/ph Library of Congress Cataloging-in-Publication Data Terry, Ronald E. Applied petroleum reservoir engineering / Ronald E. Terry, J. Brandon Rogers.—Third edition. pages cm Original edition published: Applied petroleum reservoir engineering / by B.C. Craft and M.F. Hawkins. 1959. Includes bibliographical references and index. ISBN 978-0-13-315558-7 (hardcover : alk. paper) 1. Petroleum engineering. 2. Oil reservoir engineering. I. Rogers, J. Brandon. II. Craft, B. C. (Benjamin Cole) III. Title. TN870.C88 2014 622'.338—dc23 2014017944 Copyright © 2015 Pearson Education, Inc. All rights reserved. Printed in the United States of America. This publication is protected by copyright, and permission must be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. To obtainpermission to use material from this work, please submit a written request to Pearson Education, Inc., Permissions Department, One Lake Street, Upper Saddle River, New Jersey 07458, or you may fax your request to (201) 236-3290. ISBN-13: 978-0-13-315558-7 ISBN-10: 0-13-315558-7 Text printed in the United States on recycled paper at Courier in Westford, Massachusetts. First printing, August 2014 Executive Editor Bernard Goodwin Managing Editor John Fuller Project Editor Elizabeth Ryan Copy Editor Scribe Inc. Indexer Scribe Inc. Proofreader Scribe Inc. Technical Reviewers Christine Economides Kegang Ling Editorial Assistant Michelle Housley Cover Designer Alan Clements Compositor Scribe Inc.To Rebecca and JaLeenContents Preface Preface to the Second Edition About the Authors Nomenclature Chapter 1 Introduction to Petroleum Reservoirs and Reservoir Engineering 1.1 Introduction to Petroleum Reservoirs 1.2 History of Reservoir Engineering 1.3 Introduction to Terminology 1.4 Reservoir Types Defined with Reference to Phase Diagrams 1.5 Production from Petroleum Reservoirs 1.6 Peak Oil Problems References Chapter 2 Review of Rock and Fluid Properties 2.1 Introduction 2.2 Review of Rock Properties 2.2.1 Porosity 2.2.2 Isothermal Compressibility 2.2.3 Fluid Saturations 2.3 Review of Gas Properties 2.3.1 Ideal Gas Law 2.3.2 Specific Gravity 2.3.3 Real Gas Law 2.3.4 Formation Volume Factor and Density 2.3.5 Isothermal Compressibility 2.3.6 Viscosity 2.4 Review of Crude Oil Properties 2.4.1 Solution Gas-Oil Ratio, Rso2.4.2 Formation Volume Factor, Bo 2.4.3 Isothermal Compressibility 2.4.4 Viscosity 2.5 Review of Reservoir Water Properties 2.5.1 Formation Volume Factor 2.5.2 Solution Gas-Water Ratio 2.5.3 Isothermal Compressibility 2.5.4 Viscosity 2.6 Summary Problems References Chapter 3 The General Material Balance Equation 3.1 Introduction 3.2 Derivation of the Material Balance Equation 3.3 Uses and Limitations of the Material Balance Method 3.4 The Havlena and Odeh Method of Applying the Material Balance Equation References Chapter 4 Single-Phase Gas Reservoirs 4.1 Introduction 4.2 Calculating Hydrocarbon in Place Using Geological, Geophysical, and Fluid Property Data 4.2.1 Calculating Unit Recovery from Volumetric Gas Reservoirs 4.2.2 Calculating Unit Recovery from Gas Reservoirs under Water Drive 4.3 Calculating Gas in Place Using Material Balance 4.3.1 Material Balance in Volumetric Gas Reservoirs 4.3.2 Material Balance in Water-Drive Gas Reservoirs 4.4 The Gas Equivalent of Produced Condensate and Water 4.5 Gas Reservoirs as Storage Reservoirs 4.6 Abnormally Pressured Gas Reservoirs 4.7 Limitations of Equations and Errors ProblemsReferences Chapter 5 Gas-Condensate Reservoirs 5.1 Introduction 5.2 Calculating Initial Gas and Oil 5.3 The Performance of Volumetric Reservoirs 5.4 Use of Material Balance 5.5 Comparison between the Predicted and Actual Production Histories of Volumetric Reservoirs 5.6 Lean Gas Cycling and Water Drive 5.7 Use of Nitrogen for Pressure Maintenance Problems References Chapter 6 Undersaturated Oil Reservoirs 6.1 Introduction 6.1.1 Oil Reservoir Fluids 6.2 Calculating Oil in Place and Oil Recoveries Using Geological, Geophysical, and Fluid Property Data 6.3 Material Balance in Undersaturated Reservoirs 6.4 Kelly-Snyder Field, Canyon Reef Reservoir 6.5 The Gloyd-Mitchell Zone of the Rodessa Field 6.6 Calculations, Including Formation and Water Compressibilities Problems References Chapter 7 Saturated Oil Reservoirs 7.1 Introduction 7.1.1 Factors Affecting Overall Recovery 7.2 Material Balance in Saturated Reservoirs 7.2.1 The Use of Drive Indices in Material Balance Calculations 7.3 Material Balance as a Straight Line 7.4 The Effect of Flash and Differential Gas Liberation Techniques and Surface Separator Operating Conditions on Fluid Properties7.5 The Calculation of Formation Volume Factor and Solution Gas-Oil Ratio from Differential Vaporization and Separator Tests 7.6 Volatile Oil Reservoirs 7.7 Maximum Efficient Rate (MER) Problems References Chapter 8 Single-Phase Fluid Flow in Reservoirs 8.1 Introduction 8.2 Darcy’s Law and Permeability 8.3 The Classification of Reservoir Flow Systems 8.4 Steady-State Flow 8.4.1 Linear Flow of Incompressible Fluids, Steady State 8.4.2 Linear Flow of Slightly Compressible Fluids, Steady State 8.4.3 Linear Flow of Compressible Fluids, Steady State 8.4.4 Permeability Averaging in Linear Systems 8.4.5 Flow through Capillaries and Fractures 8.4.6 Radial Flow of Incompressible Fluid, Steady State 8.4.7 Radial Flow of Slightly Compressible Fluids, Steady State 8.4.8 Radial Flow of Compressible Fluids, Steady State 8.4.9 Permeability Averages for Radial Flow 8.5 Development of the Radial Diffusivity Equation 8.6 Transient Flow 8.6.1 Radial Flow of Slightly Compressible Fluids, Transient Flow 8.6.2 Radial Flow of Compressible Fluids, Transient Flow 8.7 Pseudosteady-State Flow 8.7.1 Radial Flow of Slightly Compressible Fluids, Pseudosteady-State Flow 8.7.2 Radial Flow of Compressible Fluids, Pseudosteady-State Flow 8.8 Productivity Index (PI) 8.8.1 Productivity Ratio (PR) 8.9 Superposition 8.9.1 Superposition in Bounded or Partially Bounded Reservoirs 8.10 Introduction to Pressure Transient Testing8.10.1 Introduction to Drawdown Testing 8.10.2 Drawdown Testing in Pseudosteady-State Regime 8.10.3 Skin Factor 8.10.4 Introduction to Buildup Testing Problems References Chapter 9 Water Influx 9.1 Introduction 9.2 Steady-State Models 9.3 Unsteady-State Models 9.3.1 The van Everdingen and Hurst Edgewater Drive Model 9.3.2 Bottomwater Drive 9.4 Pseudosteady-State Models Problems References Chapter 10 The Displacement of Oil and Gas 10.1 Introduction 10.2 Recovery Efficiency 10.2.1 Microscopic Displacement Efficiency 10.2.2 Relative Permeability 10.2.3 Macroscopic Displacement Efficiency 10.3 Immiscible Displacement Processes 10.3.1 The Buckley-Leverett Displacement Mechanism 10.3.2 The Displacement of Oil by Gas, with and without Gravitational Segregation 10.3.3 Oil Recovery by Internal Gas Drive 10.4 Summary Problems References Chapter 11 Enhanced Oil Recovery 11.1 Introduction11.2 Secondary Oil Recovery 11.2.1 Waterflooding 11.2.2 Gasflooding 11.3 Tertiary Oil Recovery 11.3.1 Mobilization of Residual Oil 11.3.2 Miscible Flooding Processes 11.3.3 Chemical Flooding Processes 11.3.4 Thermal Processes 11.3.5 Screening Criteria for Tertiary Processes 11.4 Summary Problems References Chapter 12 History Matching 12.1 Introduction 12.2 History Matching with Decline-Curve Analysis 12.3 History Matching with the Zero-Dimensional Schilthuis Material Balance Equation 12.3.1 Development of the Model 12.3.2 The History Match 12.3.3 Summary Comments Concerning History-Matching Example Problems References Glossary IndexPreface As in the first revision, the authors have tried to retain the flavor and format of the original text. The text contains many of the field examples that made the original text and the second edition so popular. The third edition features an introduction to key terms in reservoir engineering. This introduction has been designed to aid those without prior exposure to petroleum engineering to quickly become familiar with the concepts and vocabulary used throughout the book and in industry. In addition, a more extensive glossary and index has been included. The text has been updated to reflect modern industrial practice, with major revisions occurring in the sections regarding gas condensate reservoirs, waterflooding, and enhanced oil recovery. The history matching examples throughout the text and culminating in the final chapter have been revised, using Microsoft Excel with VBA as the primary computational tool. As an introduction to the material balance approach of Applied Petroleum Reservoir Engineering, Third Edition, the purpose of the book has been and continues to be to prepare engineering students and practitioners to understand and work in petroleum reservoir engineering. The book begins with an introduction to key terms and an introduction to the history of reservoir engineering. The material balance approach to reservoir engineering is covered in detail and is applied in turn to each of four types of reservoirs. The latter half of the book covers the principles of fluid flow, water influx, and advanced recovery techniques. The last chapter of the book brings together the key topics in a history matching exercise that requires matching the production of wells and predicting the future production from those wells. In short, the book has been updated to reflect current practices and technology and is more reader friendly, with introductions to vocabulary and concepts as well as examples using Microsoft Excel with VBA as the computational tool. —Ronald E. Terry and J. Brandon RogersPreface to the Second Edition Shortly after undertaking the project of revising the text Applied Petroleum Reservoir Engineering by Ben Craft and Murray Hawkins, several colleagues expressed the wish that the revision retain the flavor and format of the original text. I am happy to say that I have attempted to do just that. The text contains many of the field examples that made the original text so popular and still more have been added. The revision includes a reorganization of the material as well as updated material in several chapters. The chapters were reorganized to follow a sequence used in a typical undergraduate course in reservoir engineering. The first chapters contain an introduction to reservoir engineering, a review of fluid properties, and a derivation of the general material balance equation. The next chapters present information on applying the material balance equation to different reservoir types. The remaining chapters contain information on fluid flow in reservoirs and methods to predict hydrocarbon recoveries as a function of time. There were some problems in the original text with units. I have attempted to eliminate these problems by using a consistent definition of terms. For example, formation volume factor is expressed in reservoir volume/surface condition volume. A consistent set of units is used throughout the text. The units used are ones standardized by the Society of Petroleum Engineers. I would like to express my sincere appreciation to all those who have in some part contributed to the text. For their encouragement and helpful suggestions, I give special thanks to the following colleagues: John Lee at Texas A&M; James Smith, formerly of Texas Tech; Don Green and Floyd Preston of the University of Kansas; and David Whitman and Jack Evers of the University of Wyoming. —Ronald E. TerryAbout the Authors Ronald E. Terry worked at Phillips Petroleum researching enhanced oil recovery processes. He taught chemical and petroleum engineering at the University of Kansas; petroleum engineering at the University of Wyoming, where he wrote the second edition of this text; and chemical engineering and technology and engineering education at Brigham Young University, where he cowrote the third edition of this text. He received teaching awards at all three universities and served as acting department chair, as associate dean, and in Brigham Young University’s central administration as an associate in the Office of Planning and Assessment. He is past president of the Rocky Mountain section of the American Society for Engineering Education. He currently serves as the Technology and Engineering Education program chair at Brigham Young University. J. Brandon Rogers studied chemical engineering at Brigham Young University, where he studied reservoir engineering using the second edition of this text. After graduation, he accepted a position at Murphy Oil Corporation as a project engineer, during which time he cowrote the third edition of this text.NomenclatureChapter 1. Introduction to Petroleum Reservoirs and Reservoir Engineering While the modern petroleum industry is commonly said to have started in 1859 with Col. Edwin A. Drake’s find in Titusville, Pennsylvania, recorded history indicates that the oil industry began at least 6000 years ago. The first oil products were used medicinally, as sealants, as mortar, as lubricants, and for illumination. Drake’s find represented the beginning of the modern era; it was the first recorded commercial agreement to drill for the exclusive purpose of finding petroleum. While the well he drilled was not commercially successful, it did begin the petroleum era by leading to an intense interest in the commercial production of petroleum. The petroleum era had begun, and with it came the rise of petroleum geology and reservoir engineering. 1.1 Introduction to Petroleum Reservoirs Oil and gas accumulations occur in underground traps formed by structural and/or stratigraphic features.1* Figure 1.1 is a schematic representation of a stratigraphic trap. Fortunately, the hydrocarbon accumulations usually occur in the more porous and permeable portion of beds, which are mainly sands, sandstones, limestones, and dolomites; in the intergranular openings; or in pore spaces caused by joints, fractures, and solution activity. A reservoir is that portion of the trapped formation that contains oil and/or gas as a single hydraulically connected system. In some cases the entire trap is filled with oil or gas, and in these instances the trap and the reservoir are the same. Often the hydrocarbon reservoir is hydraulically connected to a volume of water bearing rock called an aquifer. Many reservoirs are located in large sedimentary basins and share a common aquifer. When this occurs, the production of fluid from one reservoir will cause the pressure to decline in other reservoirs by fluid communication through the aquifer. *References throughout the text are given at the end of each chapter. Figure 1.1 Schematic representation of a hydrocarbon deposit in a stratigraphic trap.Hydrocarbon fluids are mixtures of molecules containing carbon and hydrogen. Under initial reservoir conditions, the hydrocarbon fluids are in either a single-phase or a two phase state. A single-phase reservoir fluid may be in a liquid phase (oil) or a gas phase (natural gas). In either case, when produced to the surface, most hydrocarbon fluids will separate into gas and liquid phases. Gas produced at the surface from a fluid that is liquid in the reservoir is called dissolved gas. Therefore, a volume of reservoir oil will produce both oil and the associated dissolved gas at the surface, and both dissolved natural gas and crude oil volumes must be estimated. On the other hand, liquid produced at the surface from a fluid that is gas in the reservoir is called gas condensate because the liquid condenses from the gas phase. An older name for gas condensate is gas distillate. In this case, a volume of reservoir gas will produce both natural gas and condensate at the surface, and both gas and condensate volumes must be estimated. Where the hydrocarbon accumulation is in a two-phase state, the overlying vapor phase is called the gas cap and the underlying liquid phase is called the oil zone. There will be four types of hydrocarbon volumes to be estimated when this occurs: the free gas or associated gas, the dissolved gas, the oil in the oil zone, and the recoverable natural gas liquid (condensate) from the gas cap. Although the hydrocarbons in place are fixed quantities, which are referred to as the resource, the reserves depend on the mechanisms by which the reservoir is produced. In the mid-1930s, the American Petroleum Institute (API) created a definition for reserves. Over the next several decades, other institutions, including the American Gas Association (AGA), the Securities and Exchange Commissions (SEC), the Society of Petroleum Engineers (SPE), the World Petroleum Congress (now Council; WPC), and the Society of Petroleum Evaluation Engineers (SPEE), have all been part of creating formal definitions of reserves and other related terms. Recently, the SPE collaborated with the WPC, the American Association of Petroleum Geologists (AAPG), and the SPEE to publish the Petroleum Resources Management System (PRMS).2 Some of the definitions used in the PRMS publication are presented in Table 1.1. The amounts of oil and gas in these definitions are calculated from available engineering and geologic data. The estimates are updated over the producing life of the reservoir as more data become available. The PRMS definitions are obviously fairly complicated and include many other factors that are not discussed in this text. For more detailed information regarding these definitions, the reader is encouraged to obtain a copy of the reference.Table 1.1 Definitions of Petroleum Terms from the Petroleum Resources Management System2 1.2 History of Reservoir Engineering Crude oil, natural gas, and water are the substances that are of chief concern to petroleum engineers. Although these substances can occur as solids or semisolids such as paraffin, asphaltine, or gas-hydrate, usually at lower temperatures and pressures, in the reservoir and in the wells, they occur mainly as fluids, either in the vapor (gaseous)or in the liquid phase or, quite commonly, both. Even where solid materials are used, as in drilling, cementing, and fracturing, they are handled as fluids or slurries. The separation of well or reservoir fluid into liquid and gas (vapor) phases depends mainly on temperature, pressure, and the fluid composition. The state or phase of a fluid in the reservoir usually changes with decreasing pressure as the reservoir fluid is being produced. The temperature in the reservoir stays relatively constant during the production. In many cases, the state or phase in the reservoir is quite unrelated to the state of the fluid when it is produced at the surface, due to changes in both pressure and temperature as the fluid rises to the surface. The precise knowledge of the behavior of crude oil, natural gas, and water, singly or in combination, under static conditions or in motion in the reservoir rock and in pipes and under changing temperature and pressure, is the main concern of reservoir engineers. As early as 1928, reservoir engineers were giving serious consideration to gas energy relationships and recognized the need for more precise information concerning physical conditions in wells and underground reservoirs. Early progress in oil recovery methods made it obvious that computations made from wellhead or surface data were generally misleading. Sclater and Stephenson described the first recording bottom-hole pressure gauge and a mechanism for sampling fluids under pressure in wells.3It is interesting that this reference defines bottom-hole data as measurements of pressure, temperature, gas-oil ratio, and the physical and chemical natures of the fluids. The need for accurate bottom-hole pressures was further emphasized when Millikan and Sidwell described the first precision pressure gauge and pointed out the fundamental importance of bottom-hole pressures to reservoir engineers in determining the most efficient oil recovery methods and lifting procedures.4 With this contribution, the engineer was able to measure the most important basic data for reservoir performance calculations: reservoir pressure. The study of the properties of rocks and their relationship to the fluids they contain in both the static and flowing states is called petrophysics. Porosity, permeability, fluid saturations and distributions, electrical conductivity of both the rock and the fluids, pore structure, and radioactivity are some of the more important petrophysical properties of rocks. Fancher, Lewis, and Barnes made one of the earliest petrophysical studies of reservoir rocks in 1933, and in 1934, Wycoff, Botset, Muskat, and Reed developed a method for measuring the permeability of reservoir rock samples based on the fluid flow equation discovered by Darcy in 1856.5,6 Wycoff and Botset made a significant advance in their studies of the simultaneous flow of oil and water and of gas and water in unconsolidated sands.7 This work was later extended to consolidated sands and other rocks, and in 1940 Leverett and Lewis reported research on the three-phase flow of oil, gas, and water.8 It was recognized by the pioneers in reservoir engineering that before reservoirvolumes of oil and gas in place could be calculated, the change in the physical properties of bottom-hole samples of the reservoir fluids with pressure would be required. Accordingly, in 1935, Schilthuis described a bottom-hole sampler and a method of measuring the physical properties of the samples obtained.9 These measurements included the pressure-volume-temperature relations, the saturation or bubble-point pressure, the total quantity of gas dissolved in the oil, the quantities of gas liberated under various conditions of temperature and pressure, and the shrinkage of the oil resulting from the release of its dissolved gas from solution. These data enabled the development of certain useful equations, and they also provided an essential correction to the volumetric equation for calculating oil in place. The next significant development was the recognition and measurement of connate water saturation, which was considered indigenous to the formation and remained to occupy a part of the pore space after oil or gas accumulation.10,11 This development further explained the poor oil and gas recoveries in low permeability sands with high connate water saturation and introduced the concept of water, oil, and gas saturations as percentages of the total pore space. The measurement of water saturation provided another important correction to the volumetric equation by considering the hydrocarbon pore space as a fraction of the total pore volume. Although temperature and geothermal gradients had been of interest to geologists for many years, engineers could not make use of these important data until a precision subsurface recording thermometer was developed. Millikan pointed out the significance of temperature data in applications to reservoir and well studies.12 From these basic data, Schilthuis was able to derive a useful equation, commonly called the Schilthuis material balance equation.13 A modification of an earlier equation presented by Coleman, Wilde, and Moore, the Schilthuis equation is one of the most important tools of reservoir engineers.14It is a statement of the conservation of matter and is a method of accounting for the volumes and quantities of fluids initially present in, produced from, injected into, and remaining in a reservoir at any stage of depletion. Odeh and Havlena have shown how the material balance equation can be arranged into a form of a straight line and solved.15 When production of oil or gas underlain by a much larger aquifer volume causes the water in the aquifer to rise or encroach into the hydrocarbon reservoir, the reservoir is said to be under water drive. In reservoirs under water drive, the volume of water encroaching into the reservoir is also included mathematically in the material balance on the fluids. Although Schilthuis proposed a method of calculating water encroachment using the material-balance equation, it remained for Hurst and, later, van Everdingen and Hurst to develop methods for calculating water encroachment independent of the material balance equation, which apply to aquifers of either limited or infinite extent, ineither steady-state or unsteady-state flow.13,16,17 The calculations of van Everdingen and Hurst have been simplified by Fetkovich.18 Following these developments for calculating the quantities of oil and gas initially in place or at any stage of depletion, Tarner and Buckley and Leverett laid the basis for calculating the oil recovery to be expected for particular rock and fluid characteristics.19,20 Tarner and, later, Muskat21 presented methods for calculating recovery by the internal or solution gas drive mechanism, and Buckley and Leverett20 presented methods for calculating the displacement of oil by external gas cap drive and water drive. These methods not only provided means for estimating recoveries for economic studies; they also explained the cause for disappointingly low recoveries in many fields. This discovery in turn pointed the way to improved recoveries by taking advantage of the natural forces and energies, by supplying supplemental energy by gas and water injection, and by unitizing reservoirs to offset the losses that may be caused by competitive operations. During the 1960s, the terms reservoir simulation and reservoir mathematical modeling became popular.22–24 These terms are synonymous and refer to the ability to use mathematical formulas to predict the performance of an oil or gas reservoir. Reservoir simulation was aided by the development of large-scale, high-speed digital computers. Sophisticated numerical methods were also developed to allow the solution of a large number of equations by finite-difference or finite-element techniques. With the development of these techniques, concepts, and equations, reservoir engineering became a powerful and well-defined branch of petroleum engineering. Reservoir engineering may be defined as the application of scientific principles to the drainage problems arising during the development and production of oil and gas reservoirs. It has also been defined as “the art of developing and producing oil and gas fluids in such a manner as to obtain a high economic recovery.”25 The working tools of the reservoir engineer are subsurface geology, applied mathematics, and the basic laws of physics and chemistry governing the behavior of liquid and vapor phases of crude oil, natural gas, and water in reservoir rocks. Because reservoir engineering is the science of producing oil and gas, it includes a study of all the factors affecting their recovery. Clark and Wessely urged a joint application of geological and engineering data to arrive at sound field development programs.26 Ultimately, reservoir engineering concerns all petroleum engineers, from the drilling engineer who is planning the mud program, to the corrosion engineer who must design the tubing string for the producing life of the well. 1.3 Introduction to Terminology The purpose of this section is to provide an explanation to the reader of the terminology that will be used throughout the book by providing context for the terms and explaining the interaction of the terms. Before defining these terms, note Fig. 1.2, which illustratesa cross section of a producing petroleum reservoir. Figure 1.2 Diagram to show the occurrence of petroleum under the Earth’s surface. A reservoir is not an open underground cavern full of oil and gas. Rather, it is section of porous rock (beneath an impervious layer of rock) that has collected high concentrations of oil and gas in the minute void spaces that weave through the rock. That oil and gas, along with some water, are trapped beneath the impervious rock. The term porosity (φ) is a measure, expressed in percent, of the void space in the rock that is filled with the reservoir fluid. Reservoir fluids are segregated into phases according to the density of the fluid. Oil specific gravity (γo) is the ratio of the density of oil to the density of water, and gas specific gravity (γg) is the ratio of the density of natural gas to the density of air. As the density of gas is less than that of oil and both are less than water, gas rests at the top of the reservoir, followed by oil and finally water. Usually the interface between two reservoir fluid phases is horizontal and is called a contact. Between gas and oil is a gas-oil contact, between oil and water is an oil-water contact, and between gas and water is a gas-water contact if no oil phase is present. A small volume of water called connate (or interstitial) water remains in the oil and gas zones of the reservoir. The initial amount of fluid in a reservoir is extremely important. In practice, thesymbol N (coming from the Greek word naptha) represents the initial volume of oil in the reservoir expressed as a standard surface volume, such as the stock-tank barrel (STB). G and W are initial reservoir gas and water, respectively. As these fluids are produced, the subscript p is added to indicate the cumulative oil (Np), gas (Gp), or water (Wp) produced. The total reservoir volume is fixed and dependent on the rock formations of the area. As reservoir fluid is produced and the reservoir pressure drops, both the rock and the fluid remaining in the reservoir expand. If 10% of the fluid is produced, the remaining 90% in the reservoir must expand to fill the entire reservoir void space. When the hydrocarbon reservoir is in contact with an aquifer, both the hydrocarbon fluids and the water in the aquifer expand as hydrocarbons are produced, and water entering the hydrocarbon space can replace the volume of produced hydrocarbons. To account for all the reservoir fluid as pressure changes, a volume factor (B) is used. The volume factor is a ratio of the volume of the fluid at reservoir conditions to its volume at atmospheric conditions (usually 60°F and 14.7 psi). Oil volume at these atmospheric conditions is measured in STBs (one barrel is equal to 42 gallons). Produced gases are measured in standard cubic feet (SCF). An M (1000) or MM (1 million) or MMM (1 billion) is frequently placed before the units SCF. As long as only liquid phases are in the reservoir, the oil and water volume factors (Bo and Bw) will begin at the initial oil volume factors (Boi and Bwi) and then steadily increase very slightly (by 1%–5%). Once the saturation pressure is reached and gas starts evolving from solution, the oil volume factor will decrease. Gas (Bg) volume factors will increase considerably (10-fold or more) as the reservoir pressure drops. The change in volume factor for a measured change in the reservoir pressure allows for simple estimation of the initial gas or oil volume. When the well fluid reaches the surface, it is separated into gas and oil. Figure 1.3 shows a two-stage separation system with a primary separator and a stock tank. The well fluid is introduced into the primary separator where most of the produced gas is obtained. The liquid from the primary separator is then flashed into the stock tank. The liquid accumulated in the stock tank is Np, and any gas from the stock tank is added to the primary gas to arrive at the total produced surface gas, Gp. At this point, the produced amounts of oil and gas are measured, samples are taken, and these data are used to evaluate and forecast the performance of the well.Figure 1.3 Schematic representation of produced well fluid and a surface separator system. 1.4 Reservoir Types Defined with Reference to Phase Diagrams From a technical point of view, the various types of reservoirs can be defined by the location of the initial reservoir temperature and pressure with respect to the two-phase (gas and liquid) envelope as commonly shown on pressure-temperature (PT) phase diagrams. Figure 1.4 is the PT phase diagram for a particular reservoir fluid. The area enclosed by the bubble-point and dew-point curves represents pressure and temperature combinations for which both gas and liquid phases exist. The curves within the two phase envelope show the percentage of the total hydrocarbon volume that is liquid for any temperature and pressure. At pressure and temperature points located above the bubble-point curve, the hydrocarbon mixture will be a liquid phase. At pressure and temperature points located above or to the right of the dew-point curve, the hydrocarbon mixture will be a gas phase. The critical point, where bubble-point, dew-point, and constant quality curves meet, represents a mathematical discontinuity, and phase behavior near this point is difficult to define. Initially, each hydrocarbon accumulation will have its own phase diagram, which depends only on the composition of the accumulation.Figure 1.4 Pressure-temperature phase diagram of a reservoir fluid. Consider a reservoir containing the fluid of Fig. 1.4 initially at 300°F and 3700 psia, point A. Since this point lies outside the two-phase region and to the right of the critical point, the fluid is originally in a one-phase gas state. Since the fluid remaining in the reservoir during production remains at 300°F, it is evident that it will remain in the single-phase or gaseous state as the pressure declines along path . Furthermore, the composition of the produced well fluids will not change as the reservoir is depleted. This is true for any accumulation with this hydrocarbon composition where the reservoir temperature exceeds the cricondentherm, or maximum two-phase temperature (250°F for the present example). Although the fluid left in the reservoir remains in onephase, the fluid produced through the wellbore and into surface separators, although the same composition, may enter the two-phase region owing to the temperature decline, as along line . This accounts for the production of condensate liquid at the surface from a single-phase gas phase in the reservoir. Of course, if the cricondentherm of a fluid is below approximately 50°F, then only gas will exist on the surface at usual ambient temperatures, and the production will be called dry gas. Nevertheless, even dry gas may contain valuable liquid fractions that can be removed by low-temperature separation. Next, consider a reservoir containing the same fluid of Fig. 1.4 but at a temperature of 180°F and an initial pressure of 3300 psia, point B. Here the fluid is also initially in the one-phase gas state, because the reservoir temperature exceeds the critical-point temperature. As pressure declines due to production, the composition of the produced fluid will be the same as reservoir A and will remain constant until the dew-point pressure is reached at 2700 psia, point B1. Below this pressure, a liquid condenses out of the reservoir fluid as a fog or dew. This type of reservoir is commonly called a dew point or a gas-condensate reservoir. This condensation leaves the gas phase with a lower liquid content. The condensed liquid remains immobile at low concentrations. Thus the gas produced at the surface will have a lower liquid content, and the producing gas-oil ratio therefore rises. This process of retrograde condensation continues until a point of maximum liquid volume is reached, 10% at 2250 psia, point B2. The term retrograde is used because generally vaporization, rather than condensation, occurs during isothermal expansion. After the dew point is reached, because the composition of the produced fluid changes, the composition of the remaining reservoir fluid also changes, and the phase envelope begins to shift. The phase diagram of Fig. 1.4 represents one and only one hydrocarbon mixture. Unfortunately, this shift is toward the right and further aggravates the retrograde liquid loss within the pores of the reservoir rock. Neglecting for the moment this shift in the phase diagram, for qualitative purposes, vaporization of the retrograde liquid occurs from B2to the abandonment pressure B3. This revaporization aids liquid recovery and may be evidenced by decreasing gas-oil ratios on the surface. The overall retrograde loss will evidently be greater (1) for lower reservoir temperatures, (2) for higher abandonment pressures, and (3) for greater shift of the phase diagram to the right—the latter being a property of the hydrocarbon system. The retrograde liquid in the reservoir at any time is composed of mostly methane and ethane by volume, and so it is much larger than the volume of stable liquid that could be obtained from it at atmospheric temperature and pressure. The composition of this retrograde liquid is changing as pressure declines so that 4% retrograde liquid volume at, for example, 750 psia might contain as much surface condensate as 6% retrograde liquid volume at 2250 psia.If the initial reservoir fluid composition is found at 2900 psia and 75°F, point C, the reservoir would be in a one-phase state, now called liquid, because the temperature is below the critical-point temperature. This is called a bubble-point (or black-oil or solution-gas) reservoir. As pressure declines during production, the bubble-point pressure will be reached, in this case at 2550 psia, point C1. Below this pressure, bubbles, or a free-gas phase, will appear. When the free gas saturation is sufficiently large, gas flows to the wellbore in ever increasing quantities. Because surface facilities limit the gas production rate, the oil flow rate declines, and when the oil rate is no longer economic, much unrecovered oil remains in the reservoir. Finally, if the initial hydrocarbon mixture occurred at 2000 psia and 150°F, point D, it would be a two-phase reservoir, consisting of a liquid or oil zone overlain by a gas zone or cap. Because the composition of the gas and oil zones are entirely different from each other, they may be represented separately by individual phase diagrams that bear little relation to each other or to the composite. The liquid or oil zone will be at its bubble point and will be produced as a bubble-point reservoir modified by the presence of the gas cap. The gas cap will be at the dew point and may be either retrograde, as shown in Fig. 1.5(a), or nonretrograde, as shown in Fig. 1.5(b). Figure 1.5 Phase diagrams of a cap gas and oil zone fluid showing (a) retrograde cap gas and (b) nonretrograde cap gas. From this technical point of view, hydrocarbon reservoirs are initially either in a single-phase state (A, B, or C) or in a two-phase state (D), depending on their temperatures and pressures relative to their phase envelopes. Table 1.2 depicts a summary of these four types. These reservoir types are discussed in detail in Chapters4, 5, 6, and 7, respectively. Table 1.2 Summary of Reservoir Types Table 1.3 presents the mole compositions and some additional properties of five single-phase reservoir fluids. The volatile oil is intermediate between the gas condensate and the black, or heavy, oil types. Production with gas-oil ratios greater than 100,000 SCF/STB is commonly called lean or dry gas, although there is no generally recognized dividing line between the two categories. In some legal work, statutory gas wells are those with gas-oil ratios in excess of 100,000 SCF/STB. The term wet gas is sometimes used interchangeably with gas condensate. In the gas-oil ratios, general trends are noticeable in the methane and heptanes-plus content of the fluids and the color of the tank liquids. Although there is good correlation between the molecular weight of the heptanes plus and the gravity of the stock-tank liquid, there is virtually no correlation between the gas-oil ratios and the gravities of the stock-tank liquids, except that most black oil reservoirs have gas-oil ratios below 1000 SCF/STB and stock-tank liquid gravities below 45 °API. The gas-oil ratios are a good indication of the overall composition of the fluid, high gas-oil ratios being associated with low concentrations of pentanes and heavier and vice versa.Table 1.3 Mole Composition and Other Properties of Typical Single-Phase Reservoir Fluids The gas-oil ratios given in Table 1.3 are for the initial production of the one-phase reservoir fluids producing through one or more surface separators operating at various temperatures and pressures, which may vary considerably among the several types of production. The gas-oil ratios and consequently the API gravity of the produced liquid vary with the number, pressures, and temperatures of the separators so that one operator may report a somewhat different gas-oil ratio from another, although both produce the same reservoir fluid. Also, as pressure declines in the black oil, volatile oil, and some gas-condensate reservoirs, there is generally a considerable increase in the gas-oil ratio owing to the reservoir mechanisms that control the relative flow of oil and gas to the wellbores. The separator efficiencies also generally decline as flowing wellhead pressures decline, which also contributes to increased gas-oil ratios. What has been said previously applies to reservoirs initially in a single phase. The initial gas-oil ratio of production from wells completed either in the gas cap or in the oil zone of two-phase reservoirs depends, as discussed previously, on the compositions of the gas cap hydrocarbons and the oil zone hydrocarbons, as well as the reservoir temperature and pressure. The gas cap may contain gas condensate or dry gas, whereas the oil zone may contain black oil or volatile oil. Naturally, if a well is completed in both the gas and oil zones, the production will be a mixture of the two. Sometimes thisis unavoidable, as when the gas and oil zones (columns) are only a few feet in thickness. Even when a well is completed in the oil zone only, the downward coning of gas from the overlying gas cap may occur to increase the gas-oil ratio of the production. 1.5 Production from Petroleum Reservoirs Production from petroleum reservoirs is a replacement process. This means that when hydrocarbon is produced from a reservoir, the space that it occupied must be replaced with something. That something could be the swelling of the remaining hydrocarbon due to a drop in reservoir pressure, the encroachment of water from a neighboring aquifer, or the expansion of formation. The initial production of hydrocarbons from an underground reservoir is accomplished by the use of natural reservoir energy.27 This type of production is termed primary production. Sources of natural reservoir energy that lead to primary production include the swelling of reservoir fluids, the release of solution gas as the reservoir pressure declines, nearby communicating aquifers, gravity drainage, and formation expansion. When there is no communicating aquifer, the hydrocarbon recovery is brought about mainly by the swelling or expansion of reservoir fluids as the pressure in the formation drops. However, in the case of oil, it may be materially aided by gravitational drainage. When there is water influx from the aquifer and the reservoir pressure remains near the initial reservoir pressure, recovery is accomplished by a displacement mechanism, which again may be aided by gravitational drainage. When the natural reservoir energy has been depleted, it becomes necessary to augment the natural energy with an external source. This is usually accomplished by the injection of gas (reinjected solution gas, carbon dioxide, or nitrogen) and/or water. The use of an injection scheme is called a secondary recovery operation. When water injection is the secondary recovery process, the process is referred to as waterflooding. The main purpose of either a natural gas or water injection process is to repressurize the reservoir and then maintain the reservoir at a high pressure. Hence the term pressure maintenance is sometimes used to describe a secondary recovery process. Often injected fluids also displace oil toward production wells, thus providing an additional recovery mechanism. When gas is used as the pressure maintenance agent, it is usually injected into a zone of free gas (i.e., a gas cap) to maximize recovery by gravity drainage. The injected gas is usually produced natural gas from the reservoir in question. This, of course, defers the sale of that gas until the secondary operation is completed and the gas can be recovered by depletion. Other gases, such as nitrogen, can be injected to maintain reservoir pressure. This allows the natural gas to be sold as it is produced. Waterflooding recovers oil by the water moving through the reservoir as a bank of fluid and “pushing” oil ahead of it. The recovery efficiency of a waterflood is largely afunction of the macroscopic sweep efficiency of the flood and the microscopic pore scale displacement behavior that is largely governed by the ratio of the oil and water viscosities. These concepts will be discussed in detail in Chapters 9, 10, and 11. In many reservoirs, several recovery mechanisms may be operating simultaneously, but generally one or two predominate. During the producing life of a reservoir, the predominance may shift from one mechanism to another either naturally or because of operations planned by engineers. For example, initial production in a volumetric reservoir may occur through the mechanism of fluid expansion. When its pressure is largely depleted, the dominant mechanism may change to gravitational drainage, the fluid being lifted to the surface by pumps. Still later, water may be injected in some wells to drive additional oil to other wells. In this case, the cycle of the mechanisms is expansion, gravitational drainage, displacement. There are many alternatives in these cycles, and it is the object of the reservoir engineer to plan these cycles for maximum recovery, usually in minimum time. Other displacement processes called tertiary recovery processes have been developed for application in situations in which secondary processes have become ineffective. However, the same processes have also been considered for reservoir applications when secondary recovery techniques are not used because of low recovery potential. In this latter case, the word tertiary is a misnomer. For most reservoirs, it is advantageous to begin a secondary or a tertiary process before primary production is completed. For these reservoirs, the term enhanced oil recovery was introduced and has become popular in reference to any recovery process that, in general, improves the recovery over what the natural reservoir energy would be expected to yield. Enhanced oil recovery processes are presented in detail in Chapter 11. 1.6 Peak Oil Since oil is a finite resource in any given reservoir, it would make sense that, as soon as oil production from the first well begins in a particular reservoir, the resource of that reservoir is declining. As a reservoir is developed (i.e., more and more wells are brought into production), the total production from the reservoir will increase. Once all the wells that are going to be drilled for a given reservoir have been brought into production, the total production will begin to decline. M. King Hubbert took this concept and developed the term peak oil to describe not the decline of oil production but the point at which a reservoir reaches a maximum oil production rate. Hubbert said this would occur at the midpoint of reservoir depletion or when one-half of the initial hydrocarbon in place had been produced.28 Hubbert developed a mathematical model and from the model predicted that the United States would reach peak oil production sometime around the year 1965.28 A schematic of Hubbert’s prediction is shown in Fig. 1.6.Figure 1.6 The Hubbert curve for the continental United States. Figure 1.7 contains a plot of the Hubbert curve and the cumulative oil production from all US reservoirs. It would appear that Hubbert was fairly accurate with his model but a little off on the timing. However, the Hubbert timing looks more accurate when production from the Alaskan North Slope is omitted.Figure 1.7 US crude oil production with the Hubbert curve (courtesy US Energy Information Administration). There are many factors that go into building such a model. These factors include proven reserves, oil price, continuing exploration, continuing demand on oil resources, and so on. Many of these factors carry with them debates concerning future predictions. As a result, an argument over the concept of peak oil has developed over the years. It is not the purpose of this text to discuss this argument in detail but simply to point out some of the projections and suggest that the reader go to the literature for further information. Hubbert predicted the total world crude oil production would reach the peak around the year 2000. Figure 1.8 is a plot of the daily world crude oil production as a function of year. As one can see, the peak has not been reached—in fact, the production is continuing to increase. Part of the discrepancy with Hubbert’s prediction has to do withthe increasing amount of world reserves, as shown in Fig. 1.9. Obviously, as the world’s reserves increase, the time to reach Hubbert’s peak will shift. Just as there are several factors that affect the time of peak oil, the definition of reserves has several contributing factors, as discussed earlier in this chapter. This point was illustrated in a recent prediction by the International Energy Agency (IEA) regarding the oil and gas production of the United States.29 Figure 1.8 World crude oil production plotted as a function of year. Figure 1.9 World crude oil reserves plotted as a function of year. In a recent report put out by the IEA, personnel predicted that the United States will become the world’s top oil producer in a few years.29 This is in stark contrast to what they had been predicting for years. The report states the following: “The recent reboundin US oil and gas production, driven by upstream technologies that are unlocking light tight oil and shale gas resources, is spurring economic activity... and steadily changing the role of North America in global energy trade.”29 The upstream technologies that are referenced in the quote are the increased use of hydraulic fracturing and horizontal drilling techniques. These technologies are a large reason for the increase in US reserves from 22.3 billion barrels at the end of 2009 to 25.2 at the end of 2010, while producing nearly 2 billion barrels in 2010. Hydraulic fracturing or fracking refers to the process of injecting a high-pressure fluid into a well in order to fracture the reservoir formation to release oil and natural gas. This method makes it possible to recover fuels from geologic formations that have poor flow rates. Fracking helps reinvigorate wells that otherwise would have been very costly to produce. Fracking has raised major environmental concerns, and the reservoir engineer should research this process before recommending its use. The use of horizontal drilling has been in existence since the 1920s but only relatively recently (1980s) reached a point where it could be used on a widespread scale. Horizontal drilling is extremely effective for recovering oil and natural gas that occupy horizontal strata, because this method offers more contact area with the oil and gas than a normal vertical well. There are endless possibilities to the uses of this method in hydrocarbon recovery, making it possible to drill in places that are either literally impossible or much too expensive to do with traditional vertical drilling. These include hard-to-reach places like difficult mountain terrain or offshore areas. Hubbert’s theory of peak oil is reasonable; however, his predictions have not been accurate due to increases in known reserves and in the development of technologies to extract the petroleum hydrocarbons economically. Reservoir engineering is the formulation of a plan to develop a particular reservoir to balance the ultimate recovery with production economics. The remainder of this text will provide the engineer with information to assist in the development of that plan. Problems 1.1 Conduct a search on the web and identify the world’s resources and reserves of oil and gas. Which countries possess the largest amount of reserves? 1.2 What are the issues involved in a country’s definition of reserves? Write a short report that discusses the issues and how a country might be affected by the issues. 1.3 What are the issues behind the peak oil argument? Write a short report that contains a description of both sides of the argument. 1.4 The use of hydraulic fracturing has increased the production of oil and gas from tight sands, but it also has become a debatable topic. What are the issues that are involved in the debate? Write a short report that contains a description of bothsides of the argument. 1.5 The continued development of horizontal drilling techniques has increased the production of oil and gas from certain reservoirs. Conduct a search on the web for applications of horizontal drilling. Identify three reservoirs in which this technique has increased the production of hydrocarbons and discuss the increase in both costs and production. References 1. Principles of Petroleum Conservation, Engineering Committee, Interstate Oil Compact Commission, 1955, 2. 2. Society of Petroleum Engineers, “Petroleum Reserves and Resources Definitions,” http://www.spe.org/industry/reserves.php 3. K. C. Sclater and B. R. Stephenson, “Measurements of Original Pressure, Temperature and Gas-Oil Ratio in Oil Sands,” Trans. AlME (1928–29), 82, 119. 4. C. V. Millikan and Carrol V. Sidwell, “Bottom-Hole Pressures in Oil Wells,” Trans. AlME (1931), 92, 194. 5. G. H. Fancher, J. A. Lewis, and K. B. Barnes, “Some Physical Characteristics of Oil Sands,” The Pennsylvania State College Bull. (1933), 12, 65. 6. R. D. Wyckoff, H. G. Botset, M. Muskat, and D. W. Reed, “Measurement of Permeability of Porous Media,” AAPG Bull. (1934), 18, No. 2, p. 161. 7. R. D. Wyckoff and H. G. Botset, “The Flow of Gas-Liquid Mixtures through Unconsolidated Sands,” Physics (1936), 7, 325. 8. M. C. Leverett and W. B. Lewis, “Steady Flow of Oil-Gas-Water Mixtures through Unconsolidated Sands,” Trans. AlME (1941), 142, 107. 9. Ralph J. Schilthuis, “Technique of Securing and Examining Sub-surface Samples of Oil and Gas,” Drilling and Production Practice, API (1935), 120–26. 10. Howard C. Pyle and P. H. Jones, “Quantitative Determination of the Connate Water Content of Oil Sands,” Drilling and Production Practice, API (1936), 171–80. 11. Ralph J. Schilthuis, “Connate Water in Oil and Gas Sands,” Trans. AlME (1938), 127, 199–214. 12. C. V. Millikan, “Temperature Surveys in Oil Wells,” Trans. AlME (1941), 142, 15. 13. Ralph J. Schilthuis, “Active Oil and Reservoir Energy,” Trans. AlME (1936), 118, 33. 14. Stewart Coleman, H. D. Wilde Jr., and Thomas W. Moore, “Quantitative Effectsof Gas-Oil Ratios on Decline of Average Rock Pressure,” Trans. AlME (1930), 86, 174. 15. A. S. Odeh and D. Havlena, “The Material Balance as an Equation of a Straight Line,” Jour. of Petroleum Technology (July 1963), 896–900. 16. W. Hurst, “Water Influx into a Reservoir and Its Application to the Equation of Volumetric Balance,” Trans. AlME (1943), 151, 57. 17. A. F. van Everdingen and W. Hurst, “Application of the LaPlace Transformation to Flow Problems in Reservoirs,” Trans. AlME (1949), 186, 305. 18. M. J. Fetkovich, “A Simplified Approach to Water Influx Calculations—Finite Aquifer Systems,” Jour. of Petroleum Technology (July 1971), 814–28. 19. J. Tarner, “How Different Size Gas Caps and Pressure Maintenance Programs Affect Amount of Recoverable Oil,” Oil Weekly (June 12, 1944), 144, No. 2, 32– 44. 20. S. E. Buckley and M. C. Leverett, “Mechanism of Fluid Displacement in Sands,” Trans. AlME (1942), 146, 107–17. 21. M. Muskat, “The Petroleum Histories of Oil Producing Gas-Drive Reservoirs,” Jour. of Applied Physics (1945), 16, 147. 22. A. Odeh, “Reservoir Simulation—What Is It?,” Jour. of Petroleum Technology (Nov. 1969), 1383–88. 23. K. H. Coats, “Use and Misuse of Reservoir Simulation Models,” Jour. of Petroleum Technology (Nov. 1969), 1391–98. 24. K. H. Coats, “Reservoir Simulation: State of the Art,” Jour. of Petroleum Technology (Aug. 1982), 1633–42. 25. T. V. Moore, “Reservoir Engineering Begins Second 25 Years,” Oil and Gas Jour. (1955), 54, No. 29, 148. 26. Norman J. Clark and Arthur J. Wessely, “Coordination of Geology and Reservoir Engineering—A Growing Need for Management Decisions,” presented before API, Division of Production, Mar. 1957. 27. R. E. Terry, “Enhanced Oil Recovery,” Encyclopedia of Physical Science and Technology, Vol. 5, 3rd ed., Academic Press, 2002. 28. M. K. Hubbert, “Nuclear Energy and the Fossil Fuels,” Proc. American Petroleum Institute Drilling and Production Practice, Spring Meeting, San Antonio (1956), 7–25; see also Shell Development Company Publication 95, June 1956. 29. International Energy Agency, “World Energy Outlook 2012 Executive Summary,” http://www.iea.org/publications/freepublications/publication/English.pdfChapter 2. Review of Rock and Fluid Properties 2.1 Introduction As fluid from a reservoir is produced and brought to the surface, the fluid remaining in the reservoir experiences changes in the reservoir conditions. The produced fluid also experiences changes as it is brought to the surface. The reservoir fluid typically sees only a decrease in pressure, while the produced fluid will experience decreases in pressure and in temperature. As the pressure decreases, it is common to observe gas that had been dissolved in the oil or water be liberated. Reservoir engineers use terms, such as the solution gas-oil ratio (Rso), to account for this. There are many variations on this term. R is generally used to denote any ratio, while the subscripts denote which ratio is being used. Rsoi, for example, is the initial gas-oil ratio, and Rsw is the solution gas water ratio. As the fluid is produced from the reservoir, the pressure on the rock from the overburden or the rock above it remains constant but the pressure of the fluid surrounding it is decreasing. This leads the rock to expand or the pores in the rock to be compressed. This change in pore volume due to pressure is called the pore volume compressibility (cf). The compressibility of the gas is also of interest. The gas compressibility (cg) involves a compressibility factor (z). The compressibility factor is simply a ratio of how the gas would behave ideally compared to how it behaves in actuality. The compressibility of oil (co) and water (cw) can also be determined, but their magnitude is far less than that of the gas. The determination of each of these properties, as well as those defined in Chapter 1, is critical in predicting the performance of a reservoir. This chapter contains a discussion of the pertinent rock and fluid properties with which a reservoir engineer will work. 2.2 Review of Rock Properties Properties discussed in this section include porosity, isothermal compressibility, and fluid saturation. Although permeability is a property of a rock matrix, because of its importance in fluid flow calculations, a discussion of permeability is postponed until Chapter 8, in which single-phase fluid flow is considered. 2.2.1 Porosity As discussed in Chapter 1, the porosity of a porous medium is given the symbol of φ and is defined as the ratio of void space, or pore volume, to the total bulk volume of the rock. This ratio is expressed as either a fraction or a percentage. When using a value of porosity in an equation, it is nearly always expressed as a fraction. The termhydrocarbon porosity refers to that part of the porosity that contains hydrocarbon. It is the total porosity multiplied by the fraction of the pore volume that contains hydrocarbon. Porosity values range from 10% to 40% for sandstone type reservoirs and 5% to 15% for limestone type reservoirs.1 The value of porosity is usually reported as either a total or an effective porosity, depending on the type of measurement used. The total porosity represents the total void space of the medium. The effective porosity is the amount of the void space that contributes to the flow of fluids. This is the type of porosity usually measured in the laboratory and used in calculations of fluid flow. The laboratory methods of measuring porosity include Boyle’s law, water saturation, and organic-liquid saturation methods. Dotson, Slobod, McCreery, and Spurlock have described a porosity-check program made by 5 laboratories on 10 samples.2 The average deviation of porosity from the average values was ±0.5% porosity. The accuracy of the average porosity of a reservoir as found from core analysis depends on the quality and quantity of the data available and on the uniformity of the reservoir. The average porosity is seldom known more precisely than to 1% porosity (e.g., to 5% accuracy at 20% porosity). The porosity is also calculated from indirect methods using well log data, often with the assistance of some core measurements. Ezekwe discusses the use of various types of well logs in the calculation of porosity.3 Logging techniques have the advantage of averaging larger volumes of rock than in core analysis. When calibrated with core data, they should provide average porosity figures in the same range of accuracy as core analysis. When there are variations in porosity across the reservoir, the average porosity should be found on a volume-weighted basis. In highly fractured, rubblized, or vuggy carbonate reservoirs, the highest porosity rock may be neither cored nor logged, and hydrocarbon volumes based on core or log porosity averages may be grossly underestimated. 2.2.2 Isothermal Compressibility The isothermal compressibility for a substance is given by the following equation: where c = isothermal compressibility V = volume p = pressure The equation describes the change in volume that a substance undergoes during a change in pressure while the temperature is held constant. The units are in reciprocal pressure units. When the internal fluid pressure within the pore spaces of a rock, which issubjected to a constant external (rock or overburden) pressure, is reduced, the bulk volume of the rock decreases while the volume of the solid rock material (e.g., the sand grains of a sandstone) increases. Both volume changes act to reduce the porosity of the rock slightly, of the order of 0.5% for a 1000-psi change in the internal fluid pressure (e.g., at 20% porosity to 19.9%). Studies by van der Knaap indicate that this change in porosity for a given rock depends only on the dif erence between the internal and external pressures and not on the absolute value of the pressures.4 As with the volume of reservoir coils above the bubble point, however, the change in pore volume is nonlinear and the pore volume compressibility is not constant. The pore volume compressibility (cf) at any value of external-internal pressure difference may be defined as the change in pore volume per unit of pore volume per unit change in pressure. The values for limestone and sandstone reservoir rocks lie in the range of 2 × 10–6to 25 × 10–6 psi–1. If the compressibility is given in terms of the change in pore volume per unit of bulk volume per unit change in pressure, dividing by the fractional porosity places it on a pore volume basis. For example, a compressibility of 1.0 × 10–6 pore volume per bulk volume per psi for a rock of 20% porosity is 5.0 × 10–6 pore volume per pore volume per psi. Newman measured isothermal compressibility and porosity values in 79 samples of consolidated sandstones under hydrostatic pressure.5 When he fit the data to a hyperbolic equation, he obtained the following correlation: This correlation was developed for consolidated sandstones having a range of porosity values from 0.02 < φ < 0.23. The average absolute error of the correlation over the entire range of porosity values was found to be 2.60%. Newman also developed a similar correlation for limestone formations under hydrostatic pressure.5 The range of porosity values included in the correlation was 0.02 < φ < 0.33, and the average absolute error was found to be 11.8%. The correlation for limestone formations is as follows: Even though the rock compressibilities are small figures, their effect may be important in some calculations on reservoirs or aquifers that contain fluids of compressibilities in the range of 3 to 25(10)–6 psi–1. One application is given in Chapter 6 involving calculations above the bubble point. Geertsma points out that when the reservoir is not subjected to uniform external pressure, as are the samples in thelaboratory tests of Newman, the effective value in the reservoir will be less than the measured value.6 2.2.3 Fluid Saturations The ratio of the volume that a fluid occupies to the pore volume is called the saturation of that fluid. The symbol for oil saturation is So, where S refers to saturation and the subscript o refers to oil. Saturation is expressed as either a fraction or a percentage, but it is used as a fraction in equations. The saturations of all fluids present in a porous medium add to 1. There are, in general, two ways of measuring original fluid saturations: the direct approach and the indirect approach. The direct approach involves either the extraction of the reservoir fluids or the leaching of the fluids from a sample of the reservoir rock. The indirect approach relies on a measurement of some other property, such as capillary pressure, and the derivation of a mathematical relationship between the measured property and saturation. Direct methods include retorting the fluids from the rock, distilling the fluids with a modified American Society for Testing and Materials (ASTM) procedure, and centrifuging the fluids. Each method relies on some procedure to remove the rock sample from the reservoir. Experience has found that it is difficult to remove the sample without altering the state of the fluids and/or rock. The indirect methods use logging or capillary pressure measurements. With either method, errors are built into the measurement of saturation. However, under favorable circumstances and with careful attention to detail, saturation values can be obtained within useful limits of accuracy. Ezekwe presents models and equations used in the calculation of saturation values for both direct and indirect methods.3 2.3 Review of Gas Properties 2.3.1 Ideal Gas Law Relationships that describe the pressure-volume-temperature (PVT) behavior of gases are called equations of state. The simplest equation of state is called the ideal gas law and is given by where p = absolute pressure V = total volume that the gas occupies n = moles of gas T = absolute temperatureR′ = gas constant When R′ = 10.73, p must be in pounds per square inch absolute (psia), V in cubic feet (ft3), n in pound-moles (lb-mols), and T in degrees Rankine (°R). The ideal gas law was developed from Boyle’s and Charles’s laws, which were formed from experimental observations. The petroleum industry works with a set of standard conditions—usually 14.7 psia and 60°F. When a volume of gas is reported at these conditions, it is given the units of SCF (standard cubic feet). As mentioned in Chapter 1, sometimes the letter M will appear in the units (e.g., MCF or M SCF). This refers to 1000 standard cubic feet. The volume that 1 lb-mol occupies at standard conditions is 379.4 SCF. A quantity of a pure gas can be expressed as the number of cubic feet at a specified temperature and pressure, the number of moles, the number of pounds, or the number of molecules. For practical measurement, the weighing of gases is difficult, so gases are metered by volume at measured temperatures and pressures, from which the pounds or moles may be calculated. Example 2.1 illustrates the calculations of the contents of a tank of gas in each of three units. Example 2.1 Calculating the Contents of a Tank of Ethane in Moles, Pounds, and SCF Given A 500-ft3tank of ethane at 100 psia and 100°F. Solution Assuming ideal gas behavior, Pounds = 8.32 × 30.07 = 250.2 At 14.7 psia and 60°F, SCF = 8.32 × 379.4 = 3157 Here is an alternate solution using Eq. (2.4): 2.3.2 Specific Gravity Because the density of a substance is defined as mass per unit volume, the density ofgas, ρg, at a given temperature and pressure can be derived as follows: where Mw = molecular weight Because it is more convenient to measure the specific gravity of gases than the gas density, specific gravity is more commonly used. Specific gravity is defined as the ratio of the density of a gas at a given temperature and pressure to the density of air at the same temperature and pressure, usually near 60°F and atmospheric pressure. Whereas the density of gases varies with temperature and pressure, the specific gravity is independent of temperature and pressure when the gas obeys the ideal gas law. By the previous equation, the density of air is Then the specific gravity, γg, of a gas is Equation (2.6) might also have been obtained from the previous statement that 379.4 ft3 of any ideal gas at 14.7 psia and 60°F is 1 mol and therefore a weight equal to the molecular weight. Thus, by definition of specific gravity, If the specific gravity of a gas is 0.75, its molecular weight is 21.7 lbs per mol. 2.3.3 Real Gas Law Everything up to this point applies to a perfect or ideal gas. Actually there are no perfect gases; however, many gases near atmospheric temperature and pressure approach ideal behavior. All molecules of real gases have two tendencies: (1) to fly apart from each other because of their constant kinetic motion and (2) to come together because of electrical attractive forces between the molecules. Because the molecules are quite far apart, the intermolecular forces are negligible and the gas behaves close toideal. Also, at high temperatures, the kinetic motion, being greater, makes the attractive forces comparatively negligible and, again, the gas approaches ideal behavior. When the volume of a gas will be less than what the ideal gas volume would be, the gas is said to be supercompressible. The number, which measures the gas’s deviation from perfect behavior, is sometimes called the supercompressibility factor, usually shortened to the gas compressibility factor. More commonly it is called the gas deviation factor (z). This dimensionless quantity usually varies between 0.70 and 1.20, with a value of 1.00 representing ideal behavior. At very high pressures, above about 5000 psia, natural gases pass from a supercompressible condition to one in which compression is more difficult than in the ideal gas. The explanation is that, in addition to the forces mentioned earlier, when the gas is highly compressed, the volume occupied by the molecules themselves becomes an appreciable portion of the total volume. Since it is really the space between the molecules that is compressed and there is less compressible space, the gas appears to be more difficult to compress. In addition, as the molecules get closer together (i.e., at high pressure), repulsive forces begin to develop between the molecules. This is indicated by a gas deviation factor greater than unity. The gas deviation factor is by definition the ratio of the volume actually occupied by a gas at a given pressure and temperature to the volume it would occupy if it behaved ideally, or These theories qualitatively explain the behavior of nonideal or real gases. Equation (2.7) may be substituted in the ideal gas law, Eq. (2.4), to give an equation for use with nonideal gases, where Vais the actual gas volume. The gas deviation factor must be determined for every gas and every combination of gases and at the desired temperature and pressure— for it is different for each gas or mixture of gases and for each temperature and pressure of that gas or mixture of gases. The omission of the gas deviation factor in gas reservoir calculations may introduce errors as large as 30%.7 Figure 2.1 shows the gas deviation factors of two gases, one of 0.90 specific gravity and the other of 0.665 specific gravity. These curves show that the gas deviation factors drop from unity at low pressures to a minimum value near 2500 psia. They rise again to unity near 5000 psia and to values greater than unity at still higher pressures. In the range of 0 to 5000 psia, the deviation factors at the same temperature will be lower for the heavier gas, and for the same gas, they will be lower at the lower temperature.Figure 2.1 Effect of pressure, temperature, and composition on the gas deviation factor. When possible reservoir fluid samples should be acquired at the formation level, such samples are termed bottom-hole fluid samples, and great care must be taken to avoid sampling the reservoir fluid below bubble-point or dew-point pressure. Without a bottom-hole fluid sample, produced wet gas or gas condensate may be recombined at the surface. This may be accomplished by recombining samples of separator gas, stock tank gas, and stock-tank liquid in the proportions in which they are produced. The deviation factor is measured at reservoir temperature for pressures ranging from reservoir to atmospheric. For wet gas or gas condensate, the deviation factor may be measured for differentially liberated gas below the dew-point pressure. For reservoir oil, the deviation factor of solution gas is measured on gas samples evolved from solution in the oil during a differential liberation process. The gas deviation factor is commonly determined by measuring the volume of a sample at desired pressures and temperatures and then measuring the volume of the same mass of gas at atmospheric pressure and at a temperature sufficiently high so that all the material remains in the vapor phase. For example, a sample of the Bell Field gas has a measured volume of 364.6 cm3 at 213°F and 3250 psia. At 14.80 psia and 82°F, it has a volume of 70,860 cm3. Then, by Eq. (2.8), assuming a gas deviation factor of unity at the lower pressure, the deviation factor at 3250 psia and 213°F is If the gas deviation factor is not measured, it may be estimated from its specificgravity. Example 2.2 shows the method for estimating the gas deviation factor from its specific gravity. The method uses a correlation to estimate pseudocritical temperature and pressure values for a gas with a given specific gravity. The correlation was developed by Sutton on the basis of over 5000 different gas samples.8 Sutton developed a correlation for two distinct types of gases—one being an associated gas and the other being a condensate gas. An associated gas is defined as a gas that has been liberated from oil and typically contains large concentrations of ethane through pentane. A condensate gas typically contains a vaporized hydrocarbon liquid, resulting in a high concentration of the heptanes-plus fractions in the gas phase. For the associated gases, Sutton conducted a regression analysis on the raw data and obtained the following equations over the range of specific gas gravities with which he worked—0.554 < γg< 1.862: Sutton found the following equations for the condensate gases covering the range of gas gravities of 0.554 < γg< 2.819: Both sets of these correlations were derived for gases containing less than 10% of H2S, CO2, and N2. If concentrations of these gases are larger than 10%, the reader is referred to the original work of Sutton for corrections. Having obtained the pseudocritical values, the pseudoreduced pressure and temperature are calculated. The gas deviation factor is then found by using the correlation chart of Fig. 2.2.Figure 2.2 Compressibility factors for natural gases (after Standing and Katz, trans. AlME).9 Example 2.2 Calculating the Gas Deviation Factor of a Gas Condensate from Its Specific Gravity Given Gas specific gravity = 0.665 Reservoir temperature = 213°F Reservoir pressure = 3250 psia Solution Using Eqs. (2.11) and (2.12), the pseudocritical values are ppc = 744 – 125.4(0.665) + 5.9(0.665)2 = 663 psia Tpc = 164.3 + 357.7(0.665) – 67.7(0.665)2 = 372°R For 3250 psia and 213°F, the pseudoreduced pressure and temperature are Using the calculated values in Fig. 2.2, z = 0.918. In many reservoir-engineering calculations, it is necessary to use the assistance of a computer, and the chart of Standing and Katz then becomes difficult to use. Dranchuk and Abou-Kassem fit an equation of state to the data of Standing and Katz in order to estimate the gas deviation factor in computer routines.10 Dranchuk and Abou-Kassem used 1500 data points and found an average absolute error of 0.486% over ranges of pseudoreduced pressure and temperature of 0.2 < ppr< 30 1.0 < Tpr< 3.0 and forppr< 1.0 with 0.7 < Tpr< 1.0 The Dranchuk and Abou-Kassem equation of state gives poor results for Tpr = 1.0 and ppr> 1.0. The form of the Dranchuk and Abou-Kassem equation of state is as follows: where Because the z-factor is on both sides of the equation, an iterative method is necessary to solve the Dranchuk and Abou-Kassem equation of state. Any one of a number of techniques can be used to assist in the iterative method.11 The Excel solver function is a common computer tool to solve these types of iterative problems, and instructions on its use are available in the Help section of the Excel program. A more accurate estimation of the deviation factor can be made when the analysis of the gas is available. This calculation assumes that each component contributes to the pseudocritical pressure and temperature in proportion to its volume percentage in the analysis and to the critical pressure and temperature, respectively, of that component. Table 2.1 gives the critical pressures and temperatures of the hydrocarbon compounds and others commonly found in natural gases.12It also gives some additional physical properties of these compounds. Example 2.3 shows the method of calculating the gas deviation factor from the composition of the gas.Table 2.1 Physical Properties of the Paraffin Hydrocarbons and Other Compounds (after Eilerts12) Example 2.3 Calculating the Gas Deviation Factor of the Bell Field Gas from Its Composition Given The composition column 2 and the physical data columns 3 to 5 are taken from Table 2.1.Solution The specific gravity may be obtained from the sum of column 6, which is the average molecular weight of the gas, The sums of columns 7 and 8 are the pseudocritical pressure and temperature, respectively. Then, at 3250 psia and 213°F, the pseudoreduced pressure and temperature are The gas deviation factor using Fig. 2.2 is z = 0.91. Wichert and Aziz have developed a correlation to account for inaccuracies in the Standing and Katz chart when the gas contains significant fractions of carbon dioxide (CO2) and hydrogen sulfide (H2S).13 The Wichert and Aziz correlation modifies the values of the pseudocritical constants of the natural gas. Once the modified constants are obtained, they are used to calculate pseudoreduced properties, as described in Example 2.2, and the z-factor is determined from Fig. 2.2 or Eq. (2.13). The Wichert and Aziz correlation equation is as follows: where A = sum of the mole fractions of CO2 and H2S in the gas mixtureB = mole fraction of H2S in the gas mixture The modified pseudocritical properties are given by Wichert and Aziz found their correlation to have an average absolute error of 0.97% over the following ranges of data: 154 < p (psia) < 7026 and 40 < T (°F) < 300. The correlation is good for concentrations of CO2 < 54.4% (mol %) and H2S < 73.8% (mol %). 2.3.4 Formation Volume Factor and Density The gas formation volume factor (Bg) relates the volume of gas in the reservoir to the volume on the surface (i.e., at standard conditions psc and Tsc). It is generally expressed in either cubic feet or barrels of reservoir volume per standard cubic foot of gas. Assuming a gas deviation factor of unity for the standard conditions, the reservoir volume of 1 std ft3 at reservoir pressure p and temperature T by Eq. (2.8) is where pscis 14.7 psia and Tscis 60°F: The constants in Eq. (2.16) are for 14.7 psia and 60°F only, and different constants must be calculated for other standards. Thus for the Bell Field gas at a reservoir pressure of 3250 psia, a temperature of 213°F, and a gas deviation factor of 0.910, the gas volume factor is These gas volume factors mean that 1 std ft3(at 14.7 psia and 60°F) will occupy 0.00533 ft3 of space in the reservoir at 3250 psia and 213°F. Because oil is usually expressed in barrels and gas in cubic feet, when calculations are made on combination reservoirs containing both gas and oil, either the oil volume must be expressed in cubic feet or the gas volume in barrels. The foregoing gas volume factor expressed in barrels is 0.000949 bbl/SCF. Then 1000 ft3 of reservoir pore volume in the Bell Field gas reservoir at 3250 psia containsG = 1000 ft3 ÷ 0.00533 ft3/SCF = 188 M SCF Equation (2.8) may also be used to calculate the density of a reservoir gas. An expression for the moles of gas in 1 ft3 of reservoir gas pore space is p/zRT. By Eq. (2.6), the molecular weight of a gas is 28.97 × γglb per mol. Therefore, the pounds contained in 1 ft3—that is, the reservoir gas density (ρg)—is For example, the density of the Bell Field reservoir gas with a gas gravity of 0.665 is 2.3.5 Isothermal Compressibility The change in volume with pressure for gases under isothermal conditions, which is closely realized in reservoir gas flow, is expressed by the real gas law: Sometimes it is useful to introduce the concept of gas compressibility. This must not be confused with the gas deviation factor, which is also referred to as the gas compressibility factor. Equation (2.17) may be differentiated with respect to pressure at constant temperature to give Finally, because for an ideal gas, z = 1.00 and dz/dp = 0, and the compressibility is simply the reciprocal of the pressure. An ideal gas at 1000 psia, then, has a compressibility of 1/1000 or 1000 × 10–6 psi–1. Example 2.4 shows the calculation of the compressibility of a gas from thegas deviation factor curve of Fig. 2.4 using Eq. (2.18). Example 2.4 Finding the Compressibility of a Gas from the Gas Deviation Factor Curve Given The gas deviation factor curve for a gas at 150°F is shown in Fig. 2.3. Figure 2.3 Gas compressibility from the gas deviation factor versus pressure plot (see Example 2.4). Solution At 1000 psia, the slope dz/dp is shown graphically in Fig. 2.3 as –127 × 10–6. Note that this is a negative slope. Then, because z = 0.83At 2500 psia, the slope dz/dp is zero, so the compressibility is simply At 4500 psia, the slope dz/dp is positive and, as shown in Fig. 2.3, is equal to 110 × 10–6psi–1. Since z = 0.90 at 4500 psia, Trube has replaced the pressure in Eq. (2.18) by the product of the pseudocritical and the pseudoreduced pressures, or p = ppc(ppr) and dp = ppcdppr.14 This obtains Multiplying through by the pseudocritical pressure, the product cg(ppc) is obtained, which Trube defined as the pseudoreduced compressibility (cr): Mattar, Brar, and Aziz developed an analytical expression for calculating the pseudoreduced compressibility.15 The expression is Taking the derivative of Eq. (2.13), the equation of state developed by Dranchuk and Abou-Kassem,10the following are obtained: andUsing Eqs. (2.21) to (2.23) and the definition of the pseudoreduced compressibility, the gas compressibility can be calculated for any gas as long as the gas pressure and temperature are within the ranges specified for the Dranchuk and Abou-Kassem correlation. Using these equations, Blasingame, Johnston, and Poe generated Figs. 2.4 and 2.5.16In these figures, the product of crTpris plotted as a function of the pseudoreduced properties, ppr and Tpr. Example 2.5 illustrates how to use these figures. Because they are logarithmic in nature, better accuracy can be obtained by using the equations directly.Figure 2.4 Variation in crTprfor natural gases for 1.05 ≤ Tpr ≤ 1.4 (after Blasingame).16Example 2.5 Finding Compressibility Using the Mattar, Brar, and Aziz Method Given Find the compressibility for a 0.90 specific gravity gas condensate when the temperature is 150°F and pressure is 4500 psia. Solution From Eq. (2.11) and (2.12), ppc = 636 psia and Tpc = 431°R. Thus, From Fig. 2.5, crTpr = 0.088. Thus,Figure 2.5 Variation in crTprfor natural gases for 1.4 ≤ Tpr ≤ 3.0 (after Blasingame).162.3.6 Viscosity The viscosity of natural gas depends on the temperature, pressure, and composition of the gas. It has units of centipoise (cp). It is not commonly measured in the laboratory because it can be estimated with good precision. Carr, Kobayashi, and Burrows have developed correlation charts, Figs. 2.6 and 2.7, for estimating the viscosity of natural gas from the pseudoreduced temperature and pressure.17 The pseudoreduced temperature and pressure may be estimated from the gas specific gravity or calculated from the composition of the gas. The viscosity at 1 atm and reservoir temperature (Fig. 2.6) is multiplied by the viscosity ratio (Fig. 2.7) to obtain the viscosity at reservoir temperature and pressure. The inserts of Fig. 2.6 are corrections to be added to the atmospheric viscosity when the gas contains nitrogen, carbon dioxide, and/or hydrogen sulfide. Example 2.6 illustrates the use of the estimation charts. Figure 2.6 The viscosity of hydrocarbon gases at 1 atm and reservoir temperature, with corrections for nitrogen, carbon dioxide, and hydrogen sulfide (after Carr, Kobayashi, and Burrows, trans. AlME).17Figure 2.7 Viscosity ratio as a function of pseudoreduced temperature and pressure (after Carr, Kobayashi, and Burrows, trans. AlME).17 Example 2.6 Using Correlation Charts to Estimate Reservoir Gas Viscosity Given Reservoir pressure = 2680 psia Reservoir temperature = 212°F Well fluid specific gravity = 0.90 (Air = 1.00) Pseudocritical temperature = 420°R Pseudocritical pressure = 670 psia Carbon dioxide content = 5 mol %Solution μ1 = 0.0117 cp at 1 atm (Fig. 2.6) Correction for CO2 = 0.0003 cp (Fig. 2.6, insert) μ1 = 0.0117 + 0.0003 = 0.0120 cp (corrected for CO2) μ/μ1 = 1.60 (Fig. 2.7) μ = 1.60 × 0.0120 = 0.0192 cp at 212°F and 2608 psia Lee, Gonzalez, and Eakin developed a semiempirical method that gives an accurate estimate of gas viscosity for most natural gases having specific gravities less than 0.77 if the z-factor has been calculated to include the effect of contaminants.18 For the data from which the correlation was developed, the standard deviation in the calculated gas viscosity was 2.69%. The ranges of variables used in the correlation were 100 < p (psia) < 8000, 100 < T (°F) < 340, 0.55 < N2(mol %) < 4.8, and 0.90 < CO2(mol %) < 3.20. In addition to the gas temperature and pressure, the method requires the z-factor and molecular weight of the gas. The following equations are used in the calculation for the gas viscosity in cp: where where ρg = gas density from Eq. (2.5), g/cc p = pressure, psia T = temperature, °R Mw = gas molecular weight2.4 Review of Crude Oil Properties The next few sections contain information on crude oil properties, including several correlations that can be used to estimate values for the properties. McCain, Spivey, and Lenn present an excellent review of these correlations in their book, Reservoir Fluid Property Correlations.19 However, these crude oil property correlations are, in general, not as reliable as the correlations that have been presented earlier for gases. There are two main reasons for the oil correlations being less reliable. The first is that oils usually consist of many more components than gases. Whereas gases are mostly made up of alkanes, oils can be made up of several different classes of compounds (e.g., aromatics and paraffins). The second reason is that mixtures of liquid components exhibit more nonidealities than mixtures of gas components. These nonidealities can lead to errors in extrapolating correlations that have been developed for a certain database of samples to particular applications outside the database. Before using any of the correlations, the engineer should make sure that the application of interest fits within the range of parameters for which a correlation was developed. As long as this is done, the correlations used for estimating liquid properties will be adequate and can be expected to yield accurate results. Correlations should only be used in the early stages of production from a reservoir when laboratory data may not be available. The most accurate values for liquid properties would come from laboratory measurements on a bottom-hole fluid sample. Ezekwe has presented a summary of various methods used to collect reservoir fluid samples and subsequent laboratory procedures to measure fluid properties.3 2.4.1 Solution Gas-Oil Ratio, Rso The amount of gas dissolved in an oil at a given pressure and temperature is referred to as the solution gas-oil ratio (Rso), in units of SCF/STB. The solubility of natural gas in crude oil depends on the pressure, temperature, and composition of the gas and the crude oil. For a particular gas and crude oil at constant temperature, the quantity of solution gas increases with pressure, and at constant pressure, the quantity decreases with increasing temperature. For any temperature and pressure, the quantity of solution gas increases as the compositions of the gas and crude oil approach each other—that is, it will be greater for higher specific gravity gases and higher API gravity crudes. Unlike the solubility of, say, sodium chloride in water, gas is infinitely soluble in crude oil, the quantity being limited only by the pressure or by the quantity of gas available. Crude oil is said to be saturated with gas at any pressure and temperature if, on a slight reduction in pressure, some gas is released from the solution. Conversely, if no gas is released from the solution, the crude oil is said to be undersaturated at that pressure. The undersaturated state implies that there is a deficiency of gas present andthat, had there been an abundance of gas present, the oil would be saturated at that pressure. The undersaturated state further implies that there is no free gas in contact with the crude oil (i.e., there is no gas cap). Gas solubility under isothermal conditions is generally expressed in terms of the increase in solution gas per unit of oil per unit increase in pressure (e.g., SCF/STB/psi or dRso/dp). Although for many reservoirs, this solubility figure is approximately constant over a considerable range of pressures, for precise reservoir calculations, the solubility is expressed in terms of the total gas in solution at any pressure (e.g., SCF/STB, or Rso). It will be shown that the reservoir volume of crude oil increases appreciably because of the solution gas, and for this reason, the quantity of solution gas is usually referenced to a unit of stock-tank oil and the solution gas-oil ratio (Rso) is expressed in standard cubic feet per stock-tank barrel. Figure 2.8 shows the variation of solution gas with pressure for the Big Sandy reservoir fluid at reservoir temperature 160°F. At the initial reservoir pressure of 3500 psia, there is 567 SCF/STB of solution gas. The graph indicates that no gas is evolved from the solution when the pressure drops from the initial pressure to 2500 psia. Thus the oil is undersaturated in this region, and there can be no free gas phase (gas cap) in the reservoir. The pressure 2500 psia is called the bubble-point pressure, for at this pressure bubbles of free gas first appear. At 1200 psia, the solution gas is 337 SCF/STB, and the average solubility between 2500 and 1200 psia isFigure 2.8 Solution gas-oil ratio of the Big Sandy Field reservoir oil, by flash liberation at reservoir temperature of 160°F. The data of Fig. 2.8 were obtained from a laboratory PVT study of a bottom-hole sample of the Big Sandy reservoir fluid using a flash liberation process that will be defined in Chapter 7. In Chapter 7, it will be shown that the solution gas-oil ratio and other fluid properties depend on the manner by which the gas is liberated from the oil. The nature of the phenomenon is discussed together with the complications it introduces into certain reservoir calculations. For the sake of simplicity, this phenomenon is ignored and a stock-tank barrel of oil is identified, with a barrel of residual oil following a flash liberation process, and the solution gas-oil ratios by flash liberation are used. Estimating a value for the solution gas-oil ratio, Rsob, at the bubble point requires information about the conditions at which the surface separator is operating. If the separator pressure and temperature are not available, then Valko and McCain propose the following equation to estimate Rsob20: where Rso,SP = solution gas-oil ratio at the exit of the separator When laboratory analyses of the reservoir fluids are not available, it is often possible to estimate the solution gas-oil ratio with reasonable accuracy. Velarde, Blasingame, and McCain give a correlation method from which the solution gas-oil ratio may be estimated from the reservoir pressure, the reservoir temperature, the bubble-point pressure, the solution gas-oil ratio at the bubble-point pressure, the API gravity of the tank oil, and the specific gravity of the separator gas.21 The correlation involves the following equations: whereRsob = solution gas-oil ratio at the bubble-point pressure, STB/SCF p = pressure, psia pb = pressure at the bubble-point, psia γg,SP = specific gravity of the separator gas ρo,API = gravity of the stock-tank oil, °API T = temperature, °F The gravity of the stock-tank oil is frequently reported as a specific gravity relative to water at 60°F. The equation used to convert from specific gravity to units of °API is If the density is reported in °API and is needed in lb/ft3, then rearrange Eq. (2.27) and solve for the specific gravity. The specific gravity is then multiplied by the density of water at 60°F, which is 62.4 lb/ft3. 2.4.2 Formation Volume Factor, Bo The formation volume factor (Bo), which is also abbreviated FVF, at any pressure may be defined as the volume in barrels that one stock-tank barrel occupies in the formation (reservoir) at reservoir temperature, with the solution gas that can be held in the oil at that pressure. Because both the temperature and the solution gas increase the volume of the stock-tank oil, the factor will always be greater than 1. When all the gas present is in solution in the oil (i.e., at the bubble-point pressure), a further increase in pressure decreases the volume at a rate that depends on the compressibility of the liquid. It was observed earlier that the solution gas causes a considerable increase in the volume of the crude oil. Figure 2.9 shows the variation in the formation volume factor of the reservoir liquid of the Big Sandy reservoir as a function of pressure at reservoir temperature of 160°F. Because no gas is released from solution when the pressure drops from the initial pressure of 3500 psia to the bubble-point pressure at 2500 psia, the reservoir fluid remains in a single (liquid) state; however, because liquids are slightly compressible, the FVF increases from 1.310 bbl/STB at 3500 psia to 1.333 bbl/STB at 2500 psia. Below 2500 psia, this liquid expansion continues but is masked by a much larger effect: the decrease in the liquid volume due to the release of gas from solution. At 1200 psia, the FVF decreases to 1.210 bbl/STB, and at atmospheric pressure and 160°F, the FVF decreases to 1.040 bbl/STB. The coefficient of temperature expansion for the 30°API stock-tank oil of the Big Sandy reservoir is close to 0.0004 per degrees Fahrenheit; therefore, one stock-tank barrel at 60°F will expand to about 1.04 bbl at 160°F, as calculated fromFigure 2.9 Formation volume factor of the Big Sandy Field reservoir oil, by flash liberation at reservoir temperature of 160°F. where β is the temperature coefficient of expansion of the oil. One obvious implication of the formation volume factor is that for every 1.310 bbl of reservoir liquid in the Big Sandy reservoir, only 1.000 bbl, or 76.3%, can reach the stock tank. This figure (76.3% or 0.763) is the reciprocal of the formation volume factor and is called the shrinkage factor. Just as the formation volume factor is multiplied by the stock-tank volume to find the reservoir volume, the shrinkage factor is multiplied by the reservoir volume to find the stock-tank volume. Although both terms are in use, petroleum engineers have almost universally adopted the formation volume factor. As mentioned previously, the formation volume factors depend on the type of gas liberation process—a phenomenon that we ignore until Chapter 7. In some equations, it is convenient to use the term two-phase formation volume factor (Bt), which is defined as the volume in barrels one stock-tank barrel and its initial complement of dissolved gas occupies at any pressure and reservoir temperature. In other words, it includes the liquid volume, Bo, plus the volume of thedif erence between the initial solution gas-oil ratio, Rsoi, and the solution gas-oil ratio at the specified pressure, Rso. If Bgis the gas volume factor in barrels per standard cubic foot of the solution gas, then the two-phase formation volume factor can be expressed as Above the bubble point, pressure Rsoi = Rso and the single-phase and two-phase factors are equal. Below the bubble point, however, while the single-phase factor decreases as pressure decreases, the two-phase factor increases, owing to the release of gas from solution and the continued expansion of the gas released from solution. The single-phase and two-phase volume factors for the Big Sandy reservoir fluid may be visualized by referring to Fig. 2.10, which is based on data from Figs. 2.8 and 2.9. Figure 2.10 (A) shows a cylinder fitted with a piston that initially contains 1.310 bbl of the initial reservoir fluid (liquid) at the initial pressure of 3500 psia and 160°F. As the piston is withdrawn, the volume increases and the pressure consequently must decrease. At 2500 psia, which is the bubble-point pressure, the liquid volume has expanded to 1.333 bbl. Below 2500 psia, a gas phase appears and continues to grow as the pressure declines, owing to the release of gas from solution and the expansion of gas already released; conversely, the liquid phase shrinks because of loss of solution gas to 1.210 bbl at 1200 psia. At 1200 psia and 160°F, the liberated gas has a deviation factor of 0.890, and therefore the gas volume factor with reference to standard conditions of 14.7 psia and 60°F is Figure 2.10 Visual conception of the change in single-phase and in two-phase formation volume factors for the Big Sandy reservoir fluid.Figure 2.8 shows an initial solution gas of 567 SCF/STB and, at 1200 psia, 337 SCF/STB, the difference of 230 SCF being the gas liberated down to 1200 psia. The volume of these 230 SCF is Vg = 230 × 0.01300 = 2.990 ft3 This free gas volume, 2.990 ft3 or 0.533 bbl, plus the liquid volume, 1.210 bbl, is the total FVF or 1.743 bbl/STB—the two-phase volume factor at 1200 psia. It may also be obtained by Eq. (2.28) as Bt = 1.210 + 0.002316 (567 – 337) = 1.210 + 0.533 = 1.743 bbl/STB Figure 2.10 (C) shows these separate and total volumes at 1200 psia. At 14.7 psia and 160°F (D), the gas volume has increased to 676 ft3 and the oil volume has decreased to 1.040 bbl. The total liberated gas volume, 676 ft3 at 160°F and 14.7 psia, is converted to standard cubic feet at 60°F and 14.7 psia using the ideal gas law, producing 567 SCF/STB as shown in (E). Correspondingly, 1.040 bbl at 160°F is converted to stock tank conditions of 60°F as shown in Eq. (2.28) to give 1.000 STB, also shown in (E). The single-phase formation volume factor for pressures less than the bubble-point pressure may be estimated from the solution gas-oil ratio, oil density, density of the stock-tank oil, and the weighted average specific gravity of the surface gas, using a correlation prepared by McCain, Spivey, and Lenn:19 where ρo,ST = density of stock-tank oil, lb/ft3 γg,S = weighted average specific gravity of the surface gas ρo = oil density The weighted average specific gravity of the surface gas should be calculated from the specific gravities of the stock-tank and the separator gases from the following equation:where γg,SP = specific gravity of the separator gas RSP = separator gas-oil ratio γg,ST = specific gravity of the stock-tank gas RST = stock-tank gas-oil ratio For pressures greater than the bubble-point pressure, Eq. (2.32) is used to calculate the formation volume factor: where Bob = oil formation volume factor at the bubble-point pressure co = oil compressibility, psi–1 Column (2) of Table 2.2 shows the variation in the volume of a reservoir fluid relative to the volume at the bubble point of 2695 psig, as measured in the laboratory. These relative volume factors may be converted to formation volume factors if the formation volume factor at the bubble point is known. For example, if Bob = 1.391 bbl/STB, then the formation volume factor at 4100 psig is