Peng Robinson Equation of State

5 Key excerpts on "Peng Robinson Equation of State"

• 

  eBook - ePub

  Equations of State and PVT Analysis

  Applications for Improved Reservoir Modeling

  • Tarek Ahmed(Author)
  • 2016(Publication Date)
  • Gulf Professional Publishing

    (Publisher)

  The Peng-Robinson Equation of State

  Peng and Robinson (1976a) conducted a comprehensive study to evaluate the use of the SRK equation of state for predicting the behavior of naturally occurring hydrocarbon systems. They illustrated the need for an improvement in the ability of the equation of state to predict liquid densities and other fluid properties, particularly in the vicinity of the critical region. As a basis for creating an improved model, Peng and Robinson (PR) proposed the following expression:

  p =

  R T

  V – b

  –

  a α

  V + b

  2

  – c

  b 2

  where a , b , and α have the same significance as they have in the SRK model, and parameter c is a whole number optimized by analyzing the values of the terms Z c and b/V c as obtained from the equation. It is generally accepted that Z c should be close to 0.28 and b/V c should be approximately 0.26. An optimized value of c  = 2 gives Z c  = 0.307 and (b/V c ) = 0.253. Based on this value of c , Peng and Robinson proposed the following equation of state (commonly referred to as PR EOS):

  p =

  R T

  V – b

  –

  a α

  V

  V + b

  + b

  V – b

    (5.110)

  Imposing the classical critical point conditions [Eq. (5.48) ] on Eq. (5.110) and solving for parameters a and b yields

  a =

  Ω a

  R 2

  T c 2

  p c

    (5.111)

  b =

  Ω b

  R

  T c

  p c

    (5.112)

  where

  Ω a

  = 0.45724

  Ω b

  = 0.07780

  This equation predicts a universal critical gas compressibility factor, Z c , of 0.307, compared to 0.333 for the SRK model. Peng and Robinson also adopted Soave’s approach for calculating parameter α :

  α =

  1 + m

  1 –

  T r

  2

    (5.113)

  where m  = 0.3796 + 1.54226ω  − 0.2699ω 2 .

  Peng and Robinson (1978) proposed the following modified expression for m that is recommended for heavier components with acentric values ω  > 0.49:

  m = 0.379642 + 1.48503 ω − 0.1644

  ω 2

  + 0.016667

  ω 3

    (5.114)

  Rearranging Eq. (5.110)

  Sign up to read

  Learn more about book
• 

  eBook - PDF

  Fundamentals of Chemical Engineering Thermodynamics, SI Edition

  • Kevin Dahm, Donald Visco(Authors)
  • 2014(Publication Date)
  • Cengage Learning EMEA

    (Publisher)

  Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 560 Fundamentals of Chemical Engineering Thermodynamics Once again, the predictions using the binary interaction parameter optimized at the lower temperature are better than predictions without any binary interaction param-eter (the dashed curve). However, the predictions are not as accurate as that realized in Example 11-5 and shown in Figure 11.7. The reasons that both the correlations at 323.15 K and the subsequent predictions at 338.15 K using the Peng-Robinson equation of state are not accurate are varied. The main reason stems from the fact that the Peng-Robinson equation of state was de-signed for non-polar substances (its utility for non-polar mixtures is demonstrated in Example 12-2), while the system in Example 12-4 has two polar compounds and has hydrogen-bonding interactions. We do have choices, though, if we would like to use an equation of state approach (phi-phi modeling) for mixtures that contain polar compounds. Example approaches currently in use in this field of research include: A change in how the a parameter in the Peng-Robinson equation of state is cal-culated by bringing in an additional, compound-specific parameter. A change in the mixing rule that uses excess molar Gibbs free energy modeling information. The addition of a hydrogen-bonding term to a cubic equation of state. Equations of state that are not cubic, but are based on theories from statistical mechanics. Any and all of these approaches have been used to improve the accuracy, both from a correlative and predictive standpoint, when working with equations of state for the vapor–liquid equilibrium of mixtures.

  Sign up to read

  Learn more about book
• 

  eBook - PDF

  Thermodynamics

  Kinetics of Dynamic Systems

  • Juan Carlos Moreno Piraján(Author)
  • 2011(Publication Date)
  • IntechOpen

    (Publisher)

  We explore their strengths and weaknesses and to examine the predictive capability of these equations. A brief introduction to Soave-Redlich-Kwong (SRK), Peng-Robinson (PR), Patel-Teja (PT), Schmit-Wenzel (SW), and Esmaeilzadeh-Roshanfekr (ER) equations of state has been provided with intention to compare their efficiency in predicting different reservoir fluids properties. The Progress in developing EOS for the calculation of thermodynamic data and phase behavior is also reviewed. Effect of characterization on VLE predictions as well as advances in application of equations of state for heavy hydrocarbons has been considered in this work. Finally, as a case-study, phase behavior of a typical Omani crude oil as well as application of EOS with proper characterization method for this real oil sample has been examined. 2. Overview of EOS Consider the plot of pressure versus total volume of a pure substance shown in Fig.1. An equation of state (EOS) is desired to represent the volumetric behavior of the pure substance in the entire range of volume both in the liquid and in the gaseous state. Thermodynamics – Kinetics of Dynamic Systems 166 Fig. 1. Pressure volume diagram of a pure component An EOS can represent the phase behavior of the fluid, both in the two-phase envelope (i.e., inside the binodal curve), on the two-phase envelope, and outside the binodal curve. Numerous EOS have been proposed to represent the phase behavior of pure substances and mixtures in the gas and liquid states since Van der Waals introduced his expression in 1873. These equations were generally developed for pure fluids and then extended to mixtures through the use of mixing rules. The mixing rules are simply a means of calculation mixture parameters equivalent to those of a pure substance. The equations of state are divided into two main groups: cubic and noncubic.

  Sign up to read

  Learn more about book
• 

  eBook - ePub

  Petroleum Engineering: Principles, Calculations, and Workflows

  • Moshood Sanni(Author)
  • 2018(Publication Date)
  • American Geophysical Union

    (Publisher)

  4 Equations of States As discussed in Chapter 3, important Equation of State (EOS) models for predicting hydrocarbon phase properties are the: Redlich–Kwong Equation of State [ Redlich and Kwong, 1949 ], shown in equation (4.1) ; Soave–Redlich–Kwong Equation of State [ Soave, 1972 ], shown in equation (4.2) ; and the Peng Robinson Equation of State [ Peng and Robinson, 1976 ], shown in equation (4.3). These EOS models can be generally represented in the form that describes the pressure of a system as a difference between repulsive and attractive pressure terms: p = p repulsive ‐ p attractive. (4.1) (4.2) (4.3) where specific volume = volume/number of moles: Consistent units for parameters in EOS calculations were summarized in Table 3.3. EOS models defined by equations (4.1) – (4.3) are termed two‐parameter equations of state; they depend on two characteristic parameters, a and b, determined experimentally or derived from other fluid component properties. Two‐parameter equations of state were originally formulated to deal with the limitation of the ideal gas equation and, subsequently, extended to calculate state properties of liquid hydrocarbons. 4.1. GENERALIZED REPRESENTATION OF EOS MODELS Martin [ 1979 ] showed that all cubic equations of state can be expressed in terms of the compressibility factor (Z): (4.4) where where m 1 and m 2 depend on the EOS model as summarized in Table 4.1 and Z is defined as: (4.5) Table 4.1 Parameters a(T), b, m 1, m 2, E 2, E 1, and E 0 for Different EOS Models [Adapted from Martin, 1979 ; Coats, 1980 ]. EOS m 1 m 2 E 2 E 1 E 0 a(T) b Redlich–Kwong (RK) 0 1 −1 A − B − B 2 ‐AB Soave–Redlich–Kwong (SRK) 0 1 −1 A − B − B 2 ‐AB Peng Robinson (PR) −1 + B A − 2B − 3B 2 −AB+

  Sign up to read

  Learn more about book
• 

  eBook - PDF

  Advanced Thermodynamics Engineering

  • Kalyan Annamalai, Ishwar K. Puri, Milind A. Jog(Authors)
  • 2011(Publication Date)
  • CRC Press

    (Publisher)

  Otherwise, the relations between these properties must be derived using physical principles. First, we will discuss the simplest equation of state (i.e., the ideal gas relation). This relation will be extended to consider real gases and other fluids in terms of two- and three-parameter equations of state. Finally, approximate equations of state for liquids and solids are discussed. THERMOLAB 306 ◾ Advanced Thermodynamics Engineering, Second Edition software is available to solve for v given P and T and vice versa for various state equations. (for which spreadsheet software is also available at www.crcpress.com, download and update page, Advanced Thermodynamics Engineering, download thermolab-1.zip) 6.2 Equations of State The ideal gas equation of state is also considered to be a thermally or mechanically perfect state equation. In Chapter 1 we presented a simple derivation of this equation by using microscopic thermodynamic considerations and neglecting intermolecular forces and the molecular body vol-ume. The resulting relation was Pv RT 0 = . (6.1) The subscript 0 in this chapter and Chapter 7 implies that the gas is ideal at the given conditions. If the measured gas volume at given P and T values is identical to that calculated by using Equation 6.1, the gas is said to be an ideal gas. However, if the measured specific volume at the same pres-sure and temperature differs from that determined using Equation 6.1, the gas is considered to be a real gas. If so, the actual specific volume v – (T, P) can be determined from experiments and tabulate them for many species of interest just like steam and R134a tables. However this requires tabulation of a vast amount of data for many species. A way to avoid tabulation is to the use com-pressibility factor Z, which is defined as Z(T, P) = v – (T, P)/v – 0 (T, P), (6.2) while v – 0 can be determined using ideal gas law.

  Sign up to read

  Learn more about book