Transient Material Balances

Initial volume of solution

500

L

Inlet flow rate (𝜈_{0})

27.7

L/s

Inlet concentration A (C_{A,0})

1.0

mol/L

Reaction rate constant (k)

0.050

s^{-1}

Directions

Details

About

Start simulation

Reset

Simulation speed

1.0

s/s

Plot:

A draining tank with a continuous feed is simulated; a chemical reaction takes place in the tank. To observe how concentration in the tank changes without a reaction, set the rate constant slider to zero. Adjust the inlet flow rate and concentration using sliders, then press "Start simulation". The volume, concentration of A in the tank, or outlet flow rate can be plotted, depending on which is selected from the Plot drop-down menu. To speed up the graph plot, increase the simulation speed using the slider. Reset the simulation to initial conditions by pressing "Reset".

Because the liquid is constant density, the overall material balance is:

$$ [1] \quad \frac{ dV }{ dt } = \nu_{0} - \nu_{out} $$where \( V \) is volume of liquid in the tank, \( \nu_{0} \) is volumetric flow rate in, and \( \nu_{out} \) is volumetric flow rate out. The velocity of the outlet \(( u_{out} )\) is:

$$ [2] \quad u_{out} = \sqrt{ 2 g h } $$where \( g \) is gravitational acceleration (9.81 m/s^{2}) and \( h \) is the height of liquid in the tank:

where \( A_{tank} \) is the cross-sectional area of the tank. Thus, the outlet volumetric flow rate is:

$$ [4] \quad \nu_{out} = u_{out} A_{out} $$where \( A_{out} \) is the cross-sectional area of the outlet pipe. Combining equations [1] -[4] yields:

$$ [5] \quad \frac{ dV }{ dt } = \sqrt{ \frac{ 2 g V }{ A_{tank} } } A_{ out } - \nu_{0} $$The first-order rate of reaction [\( r_{A} \), mol/(L s)] is

$$ [6] \quad r_{ A } = - k C_{ A } $$where \( k \) is the reaction rate constant (s^{-1}). The equation for number of moles of component \( A \) in the tank is:

where \( N_{A} \) is number of moles of \( A \) in the tank and \( C_{ A, 0 } \) is the concentration \( A \) in the inlet stream (mol/L). In this simulation, equations [5] and [7] were solved numerically using Euler's Method.

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. 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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