Single Phase Liquid Mixer Help

posted in: Help, SPL Mixer 0

This page explains how the Single Phase Liquid Mixer Unit Op works.

Unit Op Symbol and Dialogs

Input Dialog

SPL Mixer requires 5 input values.

Valid impeller types are:

  1. Six blade disc
  2. Four blade flat
  3. Four blade 45 degree pitched
  4. Three blade high efficiency

Output Dialog

100% uniformity is not achievable because there is always a measurable layer of clear liquid at the top of the batch.  Mixing time 95% is the time required to achieve 95% mixing quality. Mixing rate constant (km) is a function of impeller type, speed of the impeller (N) and geometry.

Pumping rate (Q) is a measure of pumping ability of the impeller, which is a function of speed of the impeller and geometry.

Scale of Agitation (SA) is a relative measure for assessing agitation intensity. SA is a linear function of characteristic velocity (v). SA value of 1 represents a low level, and 10 a high level of agitation intensity.

Power of the agitator is the power required to rotate the impeller, which is the function of impeller diameter, speed of the impeller and Newton number. Newton number is also known as power number in some regions.

 

Single Phase Liquid Mixer Equations

Notations

Notation Description
N Speed of the impeller
B Tank diameter
z Tank height
d Impeller diameter
a, b Impeller constants
ρ Density
μ Viscosity
Vdot Volumetric flowrate

Equation System

No. Quantity Formulae
1. Pumping rate Q=Nq\cdot N\cdot (d)^{3}
2. Mixing rate constant km=a\cdot N\cdot (\frac{d}{B})^{b}\cdot (\frac{B}{z})^{0.5}
3. Tank volume V=\frac{\pi\cdot z\cdot (B)^{2}}{4}
4. Volumetric flowrate outlet Vdot_{out}=Vdot_{i=1}+Vdot_{i=2}
5. Residence time \tau =\frac{V}{Vdot_{out}}
6. Percent volume added V_{add}=(\frac{(Vdot_{i=2}\cdot \tau )}{V})\cdot 100
7. Mixing time 95% t=\frac{\ln(0.05)}{-km\cdot d1}
8. Newton number Ne=\frac {P}{\rho_{i=3}\cdot (N)^{3}\cdot (d)^{5}}
9. Reynolds number Re=\frac{N\cdot (d)^{2}\cdot \rho _{i=3}}{\mu _{i=3}}
10. Froude number Fr=\frac{(N)^{2}\cdot d}{g}
11. Galilei number Ga=\frac{(Re)^{2}}{Fr}
12. Area of the tank A=\frac{\pi\cdot (B)^{2}}{4}
13. Characteristic velocity v=\frac{Q}{A}
14. Scale of agitation S_{A}=32.8\cdot v
15. Mixing number N_{m}=\tau\cdot N

 

For the equations 1 and 8, constants Nq and Np can be found from Reynolds number using the following graphs. Reynolds number is calculated in SPL Mixer model with the inputs such as speed of the impeller (N), impeller diameter (d), outlet density (ρ) and outlet viscosity (μ). Y-axis title “Np” on the left hand side graph, also known as Newton number, corresponds to the equation number 1. Reynolds number in the following graphs corresponds to equation 9. Equation 1 is the equation for the pumping number on the right hand side graph.

 

 

 

 

 

 

 

 

 

 

 

 

Example

Here is an example how to use the SPL Mixer.

Ethanol and glycerol are mixed in the SPL Mixer with a user defined molar flow rate at atmospheric pressure and ambient temperature (P=1 atm, T=20°C).

The user defines the impeller type and its diameter. The user also defines the tank height, tank diameter and speed of the impeller.

The SPL Mixer unit op calculates Newton number, pumping number, flow characteristics (Reynolds, Galilei, Froude and Mixing numbers), scale of agitation, mixing rate constant, power required and uniformity of mixing.

Importance of thermodynamic models and property database is evident from the following graphs. It can be seen from graphs that changing temperature of the stream changes Reynolds number, Newton number and power of the impeller.

 

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Download a free CHEMCAD flowsheet and use the Single Phase Liquid (SPL) Mixer!

SPL Mixer.cc7

 

Limitations

The SPL Mixer model operates for a homogeneous liquid-liquid system. If one of the components is gaseous, choose bubble column (for gas-liquid).

The SPL Mixer can handle 2 input streams. The volumetric flowrate of second stream should not be more than 5% of the volume of the tank.

 

Roadmap

Current version: 1.0

The following enhancements are currently planned:

SPL Mixer 1.1

  1. Versions for 5, 25 and more components.
  2. Cost estimation
  3. Reports

SPL Mixer 1.2

  1. Different sets of input parameters

SPL Mixer 2.0

  1. Multi-phase mixers

 


We want your feedback!

Unit Op Rating
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References

1. James R. Couper, W. Roy Penney, James R. Fair, Stanley M. Walas (Eds.). (2012). Chemical Process Equipment: Selection and design. Butterworth - Heinemann.