Phase Equilibrium & Flas Calculations

VLE Diagram Types:
- Pxy (Pressure-Composition): Assumes a constant temperature.
- Txy (Temperature-Composition): Assumes a constant pressure.

Definitions:
- Dew Line: Represents the first point of liquid introduced into an all-gas system.
- Bubble Line: Represents the first point of gas introduced into an all-liquid system.
Phase Envelope:
- Encountering either the bubble or dew line places the system in the phase envelope.
- Position in Diagrams:
- In a Txy Diagram, the dew line is above the bubble line (higher temperature is vapor phase).
- In a Pxy Diagram, the bubble line is above the dew line (higher pressure supports liquid phase).

Previous Class Discussions:
- Spent time generating Txy and Pxy diagrams with corresponding XY curves.
- Discoveries: The bubble point curve and dew point line produce similar curves on the XY plot as long as the XY relationship is maintained.
Homework Focus: Majority aligns with Friday’s class work on VLE diagrams (80% of homework).

Ideal Mixtures:
- Ideal behavior is assumed for most examples in this course.
- Key Model:
- Distribution Coefficient (K): Relates the vapor and liquid compositions of a component.
- Raoult’s Law:
- For ideal mixtures: $Y_i = X_i P_i^{sat}$
- Where:
  - $Y_i$ : Mole fraction in vapor
  - $X_i$ : Mole fraction in liquid
  - $P_i^{sat}$ : Saturation pressure of component i.

Definition of Flash Units:
- Flash units are single-stage distillation columns operating based on boiling points for vapor-liquid separation.
Operational Principles:
- Mixtures are fed into the flash unit at specific temperature and pressure conditions.
- Either the temperature is increased or pressure is reduced, leading to phase separation into vapor and liquid.
Equilibrium:
- Vapor (B) is rich in volatile components; liquid (L) is rich in less volatile components.

System Type:
- Open system with mass transfer (flows in and out).
- Steady-state conditions (no accumulation in the unit), rigid walls (volume remains constant).
Energy Balance:
- When changing temperature or pressure, an energy balance must be conducted, accounting for heat duty.

Data Provided:
- Molar flow rates and compositions of the feed.
- Operating conditions (flash pressure and temperature).
Goals of Flash Calculations:
- Calculate the molar flows for both vapor and liquid streams as well as their compositions.
Types of Flash Calculation Problems:
1. Given flash temperature and flash pressure, calculate vapor and liquid amounts and compositions.
2. Given one stream's composition, solve for operating temperature and pressure.

Mass Balances Equation:
- Total system balance: $F = L + V$ , where F = total feed, L = liquid flow, V = vapor flow.
Independent Equations:
- If n components:
- Can write n + 1 equations.
- Only n of them are independent due to overall mass balance.
Equilibrium Condition:
- For binary mixtures, write Raoult's Law for each component.
- $Y_i = K_i X_i$ , where $K_i = \frac{P_i^{sat}}{P}$ .

Flash Calculation Example:
- Mixture: Benzene and Para-xylene; Equimolar feed of 50% each.
- Reaction Conditions: Feed at 30°C and 1 bar, determine results at 107°C still at 1 bar.
Heats of Vaporization:
- Heat duty must be positive due to energy input for vaporization.
Heat Duty Calculation:
- Use energy balance equation that consists of the heat leaving the unit through vapor and liquid and the heat entering through the feed, formatted accordingly.

Use Antoine’s Equation for saturation pressure calculations.
Watson's Equation for finding latent heat changes at specified temperatures (critical temp calculations).

Split tasks effectively among members: can include areas for diagram generation, flash calculations, report organization, etc.
Collaborative work is encouraged for group project delivery and integration of respective outcomes.

Time allocated for team discussions on project distribution.
Class ends with availability for questions on spreadsheet-related calculations and flash calculations.