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**Thermodynamic Models: Fundamentals and Computational Aspects - Comprehensive Overview**
**1. Foundational Concepts:**
- **Thermodynamic Potentials:** Gibbs energy, Helmholtz free energy, internal energy, and enthalpy, emphasizing their roles in phase equilibria.
- **Fugacity and Chemical Potential:** Core concepts for determining phase equilibrium, with fugacity coefficients derived from equations of state (EoS).
- **Phase Rules:** Gibbs phase rule application to determine degrees of freedom in multicomponent systems.
**2. Equations of State (EoS):**
- **Cubic EoS:** Peng-Robinson and Soave-Redlich-Kwong models for vapor-liquid equilibria, including volume roots and phase stability.
- **Advanced Models:** SAFT (Statistical Associating Fluid Theory) for associating fluids and electrolytes, addressing hydrogen bonding and ion interactions.
- **Mixing Rules:** Van der Waals, Huron-Vidal, and Wong-Sandler rules for extending EoS to mixtures.
**3. Phase Equilibrium Calculations:**
- **Vapor-Liquid (VLE) & Liquid-Liquid (LLE) Equilibria:** Gamma-phi (activity coefficients + EoS) and phi-phi (EoS for both phases) approaches.
- **Flash Calculations:** Rachford-Rice equation for two-phase splits, extended to three-phase with complex iteration schemes.
- **Stability Analysis:** Tangent Plane Distance Criterion to test phase stability, involving Gibbs energy minimization.
**4. Computational Techniques:**
- **Numerical Methods:** Newton-Raphson for solving nonlinear equations, successive substitution for fugacity updates.
- **Algorithm Design:** Pseudocode for stability testing, phase split computation, and handling multiple roots in cubic EoS.
- **Convergence Strategies:** Initial guess selection, damping techniques, and hybrid methods to ensure robustness.
**5. Advanced Topics:**
- **Critical Points and Multicomponent Systems:** Calculation of critical loci and retrograde phenomena.
- **Reactive and Multiphase Equilibria:** Integration of chemical reactions and handling of solid-fluid equilibria.
- **Parameter Estimation:** Regression of EoS/activity model parameters using optimization algorithms (e.g., Levenberg-Marquardt).
**6. Practical Applications:**
- **Process Simulation:** Link to software like Aspen Plus, emphasizing EoS implementation in distillation, extraction, and refrigeration.
- **Case Studies:** Industry-relevant examples (e.g., hydrocarbon systems, CO capture) illustrating model selection and troubleshooting.
**7. Challenges and Solutions:**
- **Numerical Stability:** Addressing convergence issues in ill-conditioned systems (e.g., near-critical points).
- **Non-Ideality Handling:** Combining EoS with activity models for highly non-ideal mixtures.
- **Code Implementation:** Strategies for efficient Jacobian matrix computation, leveraging automatic differentiation.
**Structure of the Book:**
- **Theory to Practice:** Begins with thermodynamic principles, progresses to model formulation, and culminates in computational algorithms.
- **Second Edition Updates:** Expanded coverage of SAFT, electrolyte solutions, and modern optimization techniques.
- **Pedagogical Tools:** Derivations, worked examples, and pseudocode to bridge theory and implementation.
**Key Takeaways:**
- Mastery of thermodynamic fundamentals is essential for effective model application.
- Computational proficiency requires understanding both numerical methods and thermodynamic theory.
- Real-world problems demand careful model selection, parameter tuning, and convergence management.
This structured approach equips readers to tackle complex thermodynamic modeling challenges in both academic and industrial settings.
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发表于 2025-3-14 10:50:22
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