Equation of State Overview

Introduction

Equations of State (EoS) provide a rigorous thermodynamic framework for predicting fluid phase behavior from composition. Unlike empirical PVT correlations that treat oil as a "black box," EoS methods model individual hydrocarbon components and their interactions.

EoS modeling is essential when:

• Compositional effects matter — gas injection, condensate reservoirs, volatile oils
• Phase boundaries are needed — bubble/dew point curves, phase envelopes
• Multiple phases coexist — vapor-liquid equilibrium (VLE), liquid-liquid equilibrium (LLE)
• Process simulation — separator optimization, pipeline transport
• PVT lab tuning — matching experimental data with thermodynamic models

When to Use EoS vs. Black Oil

---

Cubic Equations of State

General Form

All cubic EoS can be written as:

$$P = \frac{RT}{V - b} - \frac{a(T)}{(V + \delta_1 b)(V + \delta_2 b)}$$

Where:

• $a(T)$ = attraction parameter (temperature-dependent)
• $b$ = co-volume parameter (molecular size)
• $\delta_1, \delta_2$ = EoS-specific constants

Available Models

Best Practice: Peng-Robinson is the industry standard for petroleum applications. Use SRK when comparing with legacy studies or when vapor-phase accuracy is more important.

---

Key Concepts

Component Properties

Each component in an EoS model requires:

For well-defined components (C1-C10, CO2, N2, H2S), these are known from databases. For heavy fractions (C7+), they must be estimated using characterization correlations.

Binary Interaction Parameters ($k_

Binary interaction parameters correct the geometric mean mixing rule for unlike molecular interactions:

$$a_{ij} = \sqrt{a_i \cdot a_j} \cdot (1 - k_{ij})$$

Alpha Functions

The temperature dependence of the attraction parameter is modeled through alpha functions:

$$a(T) = a_c \cdot \alpha(T_r, \omega)$$

---

EoS Workflow

Complete Phase Behavior Analysis

---

Available Calculations

Component Data

Flash Calculations

📖 Full Documentation: Flash Calculations

Phase Properties

Phase Envelope

📖 Full Documentation: Phase Envelope

---

C7+ Characterization

Heavy fractions (C7+) are not pure components and must be characterized:

1. Property estimation — estimate $T_c$, $P_c$, $\omega$ from $M_w$ and $\gamma$ (specific gravity)
2. Splitting — divide C7+ into pseudo-components using distribution functions
3. Lumping — reduce component count for computational efficiency

Available characterization methods include Kesler-Lee, Twu, and Riazi-Daubert correlations.

📖 Full Documentation: C7+ Characterization

---

Viscosity Models

EoS provides volumetric properties but not transport properties. Separate viscosity models are needed:

📖 Full Documentation: Viscosity Models

---

Best Practices

Model Selection

1. Start with Peng-Robinson — industry standard, best liquid density
2. Use SRK only when comparing with legacy data or for vapor-dominated systems
3. Always specify $k_{ij}$ for non-hydrocarbon components (CO2, N2, H2S)

Validation

1. Match saturation pressure — tune $k_{ij}$ and C7+ properties to match measured $P_b$ or $P_{dew}$
2. Check density — compare calculated liquid density with measured values
3. Verify phase envelope — ensure critical point and cricondenbar are physically reasonable
4. Cross-check with PVT — black oil properties from EoS should agree with PVT correlations

Common Pitfalls

---

Related Documentation

EoS Details

• Peng-Robinson EoS — PR76 equation, mixing rules, parameters
• Flash Calculations — PT flash, Rachford-Rice, K-values
• Phase Envelope — Bubble/dew point curves, cricondenbar
• C7+ Characterization — Splitting, property estimation
• Viscosity Models — Lee-Gonzalez-Eakin, LBC, Pedersen

Supporting Topics

• PVT Overview — Empirical correlations for comparison
• VFP Overview — Multiphase flow requiring fluid properties

---

References

1. Peng, D.Y. and Robinson, D.B. (1976). "A New Two-Constant Equation of State." Industrial & Engineering Chemistry Fundamentals, 15(1), 59-64.

2. Soave, G. (1972). "Equilibrium Constants from a Modified Redlich-Kwong Equation of State." Chemical Engineering Science, 27(6), 1197-1203.

3. Whitson, C.H. and Brule, M.R. (2000). Phase Behavior. SPE Monograph Vol. 20.

4. Pedersen, K.S. and Christensen, P.L. (2007). Phase Behavior of Petroleum Reservoir Fluids. CRC Press.

5. Michelsen, M.L. and Mollerup, J.M. (2007). Thermodynamic Models: Fundamentals and Computational Aspects, 2nd Edition. Tie-Line Publications.