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- Equations of State and PVT Analysis
- Equations of State and PVT Analysis: Applications for Improved Reservoir Modeling
- Applications of Equations of State in the Oil and Gas Industry

*In the literature there are several studies comparing the accuracy of various models in describing the PvT behavior of polymers. However, most of these studies do not provide information about the quality of the estimated parameters or the sensitivity of the prediction of thermodynamic properties to the parameters of the equations.*

By Tarek Ahmed. PVT pressure-volume-temperature reports are one way to achieve better parameters, and Equations of State and PVT Analysis, Second Edition, helps engineers to fine tune their reservoir problem-solving skills and achieve better modeling and maximum asset development. Resources are maximized with this must-have reference. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher.

This book and the individual contributions contained in it are protected under copyright by the Publisher other than as may be noted herein. Knowledge and best practice in this field are constantly changing. As new research and experience broaden our understanding, changes in research methods, professional practices, or medical treatment may become necessary.

Practitioners and researchers must always rely on their own experience and knowledge in evaluating and using any information, methods, compounds, or experiments described herein. In using such information or methods they should be mindful of their own safety and the safety of others, including parties for whom they have a professional responsibility. In , Dr. Ahmed has authored or coauthored several textbooks, including Reservoir Engineering Handbook and Hydrocarbon Phase Behvior , among others.

The primary focus of this book is to present the basic fundamentals of equations of state and PVT laboratory analysis, and their practical applications in solving reservoir engineering problems.

The book is arranged so it can be used as a textbook for senior and graduate students, or as a reference book for practicing petroleum engineers. Chapter 1 reviews the principles of hydrocarbon phase behavior and illustrates the use of phase diagrams in characterizing reservoirs and hydrocarbon systems. Chapter 2 presents numerous mathematical expressions and graphical relationships that are suitable for characterizing the undefined hydrocarbon-plus fractions.

Chapter 3 provides a comprehensive and updated review of natural gas properties and the associated, well-established correlations that can be used to describe the volumetric behavior of gas reservoirs.

Chapter 4 discusses the PVT properties of crude oil systems and illustrates the use of laboratory data to generate the properties of crude oil that can be used to perform reservoir engineering studies. Chapter 5 reviews developments and advances in the field of empirical cubic equations of state, and demonstrates their practical applications in solving phase equilibria problems. It is my hope that the information presented in this textbook will improve the understanding of the subject of equations of state and phase behavior.

Much of the material on which this book is based was drawn from the publications of the Society of Petroleum Engineers, the American Petroleum Institute, and the Gas Processors Suppliers Associations. Tribute is paid to the educators and authors who have made numerous and significant contributions to the field of phase equilibria. I would like to especially acknowledge the significant contributions that have been made to the field of phase behavior and equations of state to Donald Katz, M.

Special thanks to the editorial and production staff of Elsevier, in particular, Anusha Sambamoorthy, Kattie Washington, and Katie Hammon. Hydrocarbon phase behavior is an integral and important part of petroleum engineering. Reservoir and production engineers rely on phase behavior and pressure-volume-temperature for reserves, calculations, and surface facilities design.

This chapter provides the basic principles of hydrocarbon phase behavior and reviews the basic classifications of hydrocarbon systems through the use of phase diagrams. A phase is defined as any homogeneous part of a system that is physically distinct and separated from other parts of the system by definite boundaries. For example, ice, liquid water, and water vapor constitute three separate phases of the pure substance H2O, because each is homogeneous and physically distinct from the others; moreover, each is clearly defined by the boundaries existing between them.

Whether a substance exists in a solid, liquid, or gas phase is determined by the temperature and pressure acting on the substance.

It is known that ice solid phase can be changed to water liquid phase by increasing its temperature and, by further increasing the temperature, water changes to steam vapor phase. This change in phases is termed phase behavior. Hydrocarbon systems found in petroleum reservoirs are known to display multiphase behavior over wide ranges of pressures and temperatures. The most important phases that occur in petroleum reservoirs are a liquid phase, such as crude oils or condensates, and a gas phase, such as natural gases.

The conditions under which these phases exist are a matter of considerable practical importance. The experimental or the mathematical determinations of these conditions are conveniently expressed in different types of diagrams, commonly called phase diagrams. The objective of this chapter is to review the basic principles of hydrocarbon phase behavior and illustrate the use of phase diagrams in describing and characterizing the volumetric behavior of single-component, two-component, and multicomponent systems.

The simplest type of hydrocarbon system to consider is that containing one component. The word component refers to the number of molecular or atomic species present in the substance.

A single-component system is composed entirely of one kind of atom or molecule. We often use the word pure to describe a single-component system.

The qualitative understanding of the relationship between temperature T , pressure p , and volume V of pure components can provide an excellent basis for understanding the phase behavior of complex petroleum mixtures. This relationship is conveniently introduced in terms of experimental measurements conducted on a pure component as the component is subjected to changes in pressure and volume at a constant temperature.

The effects of making these changes on the behavior of pure components are discussed next. Suppose a fixed quantity of a pure component is placed in a cylinder fitted with a frictionless piston at a fixed temperature T 1.

Furthermore, consider the initial pressure exerted on the system to be low enough that the entire system is in the vapor state. This initial condition is represented by point E on the pressure-volume phase diagram p - V diagram as shown in Fig. Consider the following sequential experimental steps taking place on the pure component:. The pressure is increased isothermally by forcing the piston into the cylinder. Consequently, the gas volume decreases until it reaches point F on the diagram, where the liquid begins to condense.

The corresponding pressure is known as the dew point pressure , p d, and defined as the pressure at which the first droplet of liquid is formed. The piston is moved further into the cylinder as more liquid condenses. This condensation process is characterized by a constant pressure and represented by the horizontal line FG. At point G , traces of gas remain and the corresponding pressure is called the bubble point pressure , p b, and defined as the pressure at which the first sign of gas formation is detected.

A characteristic of a single-component system is that, at a given temperature, the dew point pressure and the bubble point pressure are equal. As the piston is forced slightly into the cylinder, a sharp increase in the pressure point H is noted without an appreciable decrease in the liquid volume. That behavior evidently reflects the low compressibility of the liquid phase. By repeating these steps at progressively increasing temperatures, a family of curves of equal temperatures isotherms is constructed as shown in Fig.

The dashed curve connecting the dew points, called the dew point curve line FC , represents the states of the saturated gas. The dashed curve connecting the bubble points, called the bubble point curve line GC , similarly represents the saturated liquid. These two curves meet a point C , which is known as the critical point. The corresponding pressure and volume are called the critical pressure , p c, and critical volume , V c, respectively.

Note that, as the temperature increases, the length of the straight-line portion of the isotherm decreases until it eventually vanishes and the isotherm merely has a horizontal tangent and inflection point at the critical point.

This isotherm temperature is called the critical temperature , T c, of that single component. This observation can be expressed mathematically by the following relationship:. Referring to Fig. Within this defined region, vapor and liquid can coexist in equilibrium. Outside the phase envelope, only one phase can exist. The critical point point C describes the critical state of the pure component and represents the limiting state for the existence of two phases, that is, liquid and gas.

In other words, for a single-component system, the critical point is defined as the highest value of pressure and temperature at which two phases can coexist. A more generalized definition of the critical point, which is applicable to a single- or multicomponent system, is this: The critical point is the point at which all intensive properties of the gas and liquid phases are equal. An intensive property is one that has the same value for any part of a homogeneous system as it does for the whole system; that is, a property independent of the quantity of the system.

Pressure, temperature, density, composition, and viscosity are examples of intensive properties. Many characteristic properties of pure substances have been measured and compiled over the years. These properties provide vital information for calculating the thermodynamic properties of pure components as well as their mixtures.

The most important of these properties include. Those physical properties needed for hydrocarbon phase behavior calculations are presented in Table 1. Note : Numbers in this table do not have accuracies greater than 1 part in ; in some cases extra digits have been added to calculated values to achieve consistency or to permit recalculation of experimental values. Another means of presenting the results of this experiment is shown in Fig. As shown in the illustration, line AC terminates at the critical point point C and can be thought of as the dividing line between the areas where liquid and vapor exist.

The curve is commonly called the vapor pressure curve or the boiling point curve. The corresponding pressure at any point on the curve is called the vapor pressure , p v, with a corresponding temperature termed the boiling point temperature. The vapor pressure curve represents the conditions of pressure and temperature at which two phases, vapor and liquid, can coexist in equilibrium.

Systems represented by a point located below the vapor pressure curve are composed only of the vapor phase. Similarly, points above the curve represent systems that exist in the liquid phase. These remarks can be conveniently summarized by the following expressions:. It should be pointed out that these expressions are valid only if the system temperature is below the critical temperature T c of the substance.

The lower end of the vapor pressure line is limited by the triple point A. This point represents the pressure and temperature at which solid, liquid, and vapor coexist under equilibrium conditions. The line AB is called the sublimation pressure curve of the solid phase, and it divides the area where solid exists from the area where vapor exists. Points above AB represent solid systems, and those below AB represent vapor systems.

The line AD is called the melting curve or fusion curve and represents the change of melting-point temperature with pressure. The fusion melting curve divides the solid phase area from the liquid phase area, with a corresponding temperature at any point on the curve termed the fusion or melting-point temperature. Note that the solid-liquid curve fusion curve has a steep slope, which indicates that the triple point for most fluids is close to their normal melting-point temperatures. For pure hydrocarbons, the melting point generally increases with pressure so the slope of the line AD is positive.

Water is the exception in that its melting point decreases with pressure, so in this case, the slope of the line AD is negative. Each pure hydrocarbon has a p - T diagram similar to that shown in Fig. In addition, each pure component is characterized by its own vapor pressures, sublimation pressures, and critical values, which are different for each substance, but the general characteristics are similar.

If such a diagram is available for a given substance, it is obvious that it could be used to predict the behavior of the substance as the temperature and pressure are changed. For example, in Fig.

Thermodynamics - Kinetics of Dynamic Systems. Reservoir fluids contain a variety of substances of diverse chemical nature that include hydrocarbons and nonhydrocarbons. Hydrocarbons range from methane to substances that may contain carbon atoms. The chemistry of hydrocarbon reservoir fluids is very complex. In spite of the complexity of hydrocarbon fluids found in underground reservoirs, equations of state have shown surprising performance in the phase-behavior calculations of these complex fluids.

PrefaceThe primary focus of this book is to present the basic fundamentals of equations of state and PVT laboratory analysis and their practical applications in.

Petroleum Geoscience ;; 7 2 : — Simulation of improved recovery processes from gas condensate and volatile oil reservoirs is significantly affected by the match of experimental PVT data. Therefore, a proper characterization of the mixture composition and tuning of the equation of state used are crucial for the accuracy of the reservoir model. This paper presents an efficient method for phase behaviour matching by non-linear regression. The constraints introduced by the boundaries of the regression variables are eliminated by a suitable change of variables.

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PVT pressure-volume-temperature reports are one way to achieve better parameters, and Equations of State and PVT Analysis, Second Edition, helps engineers to fine tune their reservoir problem-solving skills and achieve better modeling and maximum asset development. Resources are maximized with this must-have reference. Tarek is currently a Founder of Tarek Ahmed and Associates, Ltd, a consulting firm that specializes in in-house petroleum engineering courses and consulting services worldwide. Ahmed has authored numerous papers and several successful Elsevier books, including Advanced Reservoir Engineering and Reservoir Engineering Handbook, 4th Edition We are always looking for ways to improve customer experience on Elsevier.

Именно. Танкадо рассудил, что, если он погибнет, деньги ему не понадобятся, - так почему бы не вручить миру маленький прощальный подарок. Оба замолчали.

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Merkaba11 02.04.2021 at 18:02This title covers a wide range of topics related to the Pressure Volume Temperature PVT behavior of complex hydrocarbon systems and documents the ability of Equations of State EOS in modeling their behavior.

OcГ©ane A. 03.04.2021 at 03:01Equations of state and PVT analysis: applications for improved reservoir modeling / Tarek Ahmed. p. cm. Includes bibliographical references and index.