6: PT Behavior and Equations of State (EOS) I
- Page ID
- 7509
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Module Goal: To introduce you to quantification in fluid phase behavior.
Module Objective: To quantitatively and qualitatively compare ideal and real gas behavior.
The ultimate purpose of this text is to build a firm knowledge of the phase behavior of fluids. With this understanding, we will be able to establish the basis and rationale upon which phase behavior applications in production systems are grounded. We are using the word production in a generic sense, that is, where it pertains to reservoir, pipeline, and the surface production (of any produced fluid).
- 6.1: Introduction
- This page discusses the importance of understanding phase behavior via phase diagrams to predict system behavior under different conditions. It highlights thermodynamic processes in petroleum production, especially gas cycling for optimizing recovery. The limitations of laboratory and field measurements for phase behavior data are noted, emphasizing the use of Equations of State (EOS) as predictive models to analyze system properties and maintain equilibrium during production.
- 6.2: P-V-T Behavior
- This page discusses the complexities of predicting fluid behavior under different pressure, temperature, and volume conditions (P-V-T). It highlights the need to simplify real behaviors into an idealized model, known as the "ideal gas," and outlines the process of creating assumptions for this model. Corrections are then applied to account for deviations from ideal behavior in real scenarios, providing a foundation for further exploration of fluid dynamics.
- 6.3: Ideal Behavior
- This page discusses the ideal gas model, which assumes negligible molecular interactions and volume, allowing for perfectly elastic collisions. Although no real gas perfectly fits this model, it serves as a useful approximation at low pressures and high temperatures. Key principles include Boyle's Law and Charles' Law, leading to the ideal gas equation \( Pv = nRT \). The model illustrates two extremes: infinite volume at low pressure and the difficulties posed by high pressure and low volume.
- 6.4: Real Gases
- In reality, no gas behaves ideally. Therefore, the ideal EOS is not useful for practical applications, although it is important as the basis of our understanding of gas behavior. Even though the ideal model is not reliable for real engineering applications, we have to keep in mind that the ideal gas EOS is the starting point of all modern approaches.
- 6.5: Summary
- This page discusses the limitations of the ideal gas equation of state (EOS), which inaccurately predicts gas behavior by suggesting that ideal gases won’t condense and often gives higher pressures and volumes than real gases. These shortcomings demonstrate the need for more accurate models to account for real gas behavior in various conditions.