In this simulation, liquid propane or liquid toluene is injected into an evacuated 2-L spherical tank that is held at constant temperature. When propane is injected, it either vaporizes completely or forms two phases in vapor-liquid equilibrium (VLE), depending on the number of moles injected and the temperature (control both with sliders). Because toluene has a much lower saturation pressure, only a small amount of injected toluene liquid vaporizes. When the component is in VLE, the tank pressure equals the saturation pressure; otherwise, the pressure is calculated using the ideal gas law. The pressure is displayed at the top of the tank. Click the "inject" button to inject liquid into the tank. Press "reset" at any time to start from the beginning. The intensity of the blue color of the vapor is proportional to the vapor density. The liquid volume in the tank is exaggerated relative to the vapor volume for better visualization. The bar graph on the right shows the number of moles of liquid and vapor in the tank.
When propane or toluene is in vapor-liquid equilibrium (VLE), the pressure in the tank is the saturation pressure, which is calculated using the Antoine equation:
$$ [1] \quad P_{i}^{sat} = 10^{\left( A_{i} - \frac{ B_{ i } }{ T + C_{ i } } \right)} $$
where \( P_{i}^{sat} \) is the saturation pressure (bar), \( A_i \), \( B_i \), and \( C_i \) are Antoine constants, and \( T \) is temperature (K). When only vapor is present, the ideal gas law is used to calculate the pressure \( P \):
$$ [2] \quad P = \frac{ n R T }{ V } $$
where \( n \) is the total moles (moles of vapor in this case), \( R \) is the ideal gas constant [(L bar) / (mol K)], and \( V \) is the total volume (L). When the component is in VLE, the sum of the liquid \( V_L \) and vapor \( V_V \) volumes equal the volume of the tank \( V \):
$$ [3] \quad V = V_L + V_V $$
and the liquid volume is determined using the liquid density \( \rho_{ L } \):
$$ [4] \quad V_L = \frac{ n_L }{ \rho_L } $$
The vapor volume is determined using the ideal gas law:
$$ [5] \quad V_V = \frac{ n_V R T }{ P^{sat} } $$
where the total moles (moles injected) equals the sum of the liquid \( n_L \) and vapor \( n_V \) moles:
$$ [6] \quad n = n_L + n_V $$
To solve for \( n_{L} \), substitute equation [4] and [5] into equation [3],
$$ [7] \quad V = \frac{ n_L }{ \rho_L } + \frac{ ( n - n_L ) R T }{ P^{sat} } $$
and bring \( n_{L} \) to the left-hand side of the equation:
$$ [8] \quad n_L = \frac{ \rho_L (P^{sat} V - n R T) }{ P^{sat} - R T \rho_L } $$
From here we can calculate the volume of vapor by solving equation [6] for \( n_{V} \) and plugging it into equation [5].
This simulation was created in the Department of Chemical and Biological Engineering, at University of Colorado Boulder for LearnChemE.com by Neil Hendren under the direction of Professor John L. Falconer. This simulation was prepared with financial support from the National Science Foundation. Address any questions or comments to learncheme@gmail.com. All of our simulations are open source, and are available on our LearnChemE Github repository.
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