Static Mixer Help

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This page explains how the Static Mixer Unit Op works.

Static Mixers are inline units that can be used to achieve mixing in continuous or semi-continuous systems. It serves several purposes ranging from the blending of components, thermal homogenization to various pipeline reactions. The important parameters that decide the type of mixer are,

  1. Fluid viscosities
  2. Viscosity ratios
  3. Flow ratios

Unit Op Symbol and Dialogs

Input Dialog

Static Mixer requires four input values, namely the mixer length, mixer diameter, user specified maximum pressure drop, and the roughness of the material used. Usually the static mixer is assembled by combining a number of mixer elements. The type of desired mixer could also be selected. The major types are:

  1. K-type or helicals
  2. S-type or corrugated

 

Output Dialog

The outputs are the Reynolds number, the pressure drop and the Co-efficient of mixing (CoV).  Reynolds number (Re) is the ratio of inertial to viscous force and this is used to determine whether the flow regime is in laminar or turbulent.

Pressure drop (dp) for the static mixer is determined based on the Reynolds number. The geometry of the mixer or the mixer type greatly influences the pressure drop across the static mixer.

Co-efficient of variance of mixing determines the radial uniformity of composition in the exit stream. Usually a CoV value of 0.05 or 5% is acceptable [1].

 

 

 

Static Mixer Equations

Notations

Notation Description
L Length of the mixer
D Diameter of the mixer
uavg Average inlet velocity
f Friction factor
Kout, Kmix  Mixer constants
ε Pipe roughness factor
ρ Density
μ Viscosity
Vdot Volumetric flowrate

Equation System

 

No. Quantity Formulae
1. Area A = \frac{\pi\cdot (D)^{2}}{4}
2. Average velocity u_{avg} = \frac{Vdot_{i=1}+Vdot_{i=2}}/A
3. Volume fraction \phi = \frac{Vdot_{i=1}}{Vdot_{i=1}+Vdot_{i=2}}
4. Reynolds number Re = \frac{D\cdot u_{avg}\cdot \rho_{i=3}}{\mu_{i=3}}
5. Fanning friction factor f = 2\cdot ((\frac{8}{Re})^{12}+((2.457\cdot \ln(((\frac{7}{Re})^{0.9} + 0.27\cdot (\frac{\epsilon}{D}))^{-1}))^{16} +(\frac{37350}{Re})^{16})^{-1.5})^{\frac{1}{12}}
6. Pipe Pressure drop dp_{norm} = \frac{4\cdot f\cdot L\cdot \rho_{i=3}\cdot (u_{avg})^{2}}{D}
7. Mixer Pressure drop dp_{mix} = K_{mix}\cdot dp_{norm}
8. Inlet CoV COV_{in} = \sqrt{\frac{1-\phi}{\phi}}
9. Relative CoV COV_{r} = (K_{out})^{L/D}
10. Outlet CoV COV_{out} = COV_{in}\cdot COV_{r}

 

It should be noted that the higher flow needs to be specified in the first port and the lower one in the second port respectively.

Normally, equation 6 is calculated from Moody’s chart given below or by other formulae depending on the operating regiment. Moody’s chart is a plot of Reynolds number (Re) against the Darcy friction factor for the corresponding relative roughness (ε/D) of the pipe. A Reynolds number of 2300  has been used for distinguishing between laminar flow and turbulent flow.

Static mixers cannot be considered for all flow rates and all components. The user has to consider the desired pressure drop and the mixing quality required before choosing the static mixer.

Note: Darcy’s friction factor is four times the Fanning friction factor.

 

Example

Here is an example how to use the Static Mixer.

Water and glycerol are mixed in the Static Mixer with user-defined specifications for flow rate, pressure, and temperature (P=1 bar, T=20°C). In this case, the first stream is water and the second one glycerol, with a water flow rate of 50,000 kg/h and glycerol flow rate of 27,000 kg/h. The viscosity ratio of this system is high (around 1:1300) making it a suitable example for blending.

The user defines the length, diameter, pipe roughness and the type of mixer. Since the maximum pressure drop lost depends on the service, this also needs to be specified by the user.

The Static Mixer unit op calculates the Reynolds number, pressure drop across the mixer and the outlet Coefficient of variance (CoV_{out}). Here the L/D ratio is 8 and the Reynolds number is 1770 making the stream laminar flow.

It can be seen from the graph that the best service for this flow ratio is the S-type 45 deg corrugated static mixer. Even though it has a higher pressure drop, it meets the 0.05 COV criteria required for industrial mixers.

For a turbulent case with a lower glycerol flow rate (2700 kg/hr) the results are as follows:

 


In this case, the focus should be more on the pressure drop across the mixer than the COV value, making the 3 tab mixer or the 30 deg corrugated S- type mixers as better choices.

Download a free CHEMCAD flowsheet and use the Static Mixer!

Static Mixer.cc7

Limitations

Static mixers have several limitations in their use. It is not suitable when there is no constant flow rate, processes with short residence times and also when the viscosity and flow ratios of the two streams are varying significantly. Since the flow regime between a Reynolds number of 2100 and 10000 is not defined properly by the available equations, the results in this flow region need to be scrutinized.

Roadmap

Current version: 1.0

The following enhancements are currently planned:

Static Mixer 1.1

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

Static Mixer 1.2

  1. Different sets of input parameters

Static Mixer 2.0

  1. Multi-phase mixers

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References

1. Paul, E. L., Atiemo-Obeng, V. A., & Kresta, S. M. (Eds.). (2004). Handbook of industrial mixing: science and practice. John Wiley & Sons.