Mixing of fluids having different densities

[paddy1385]

Hi,

I am doing a pressure drop calculation for my project where there is a mixing of two fluids having densities of 980 Kg/m3 & 850 Kg/m3. Flow rates are 400 m3/hr & 120 m3/hr respectively. I am unsure of what the outlet flow rate will be. If we consider the volumetric flow rate, the outlet should be 520 m3/hr, but if we convert these into mass flow, then the flow rate will be 392000 + 102000 = 494000 Kg/hr which comes to 504 m3/hr. So how should I calculate the outlet flow rate & what will be the density of the mixed fluid that I should consider as this will also impact the pressure drop.

 

[Latexman]

It depends on the nature of the two fluids and how they interact (any reaction, heat effects, etc.), if at all. Do you expect any interaction, or do expect the fluids to mix together with no interactions?

Good luck,
Latexman

Technically, the glass is always full - 1/2 air and 1/2 water.

 

[paddy1385]

Hi Latexman,

I think the fluids will mix together without any reaction or heat effect, the fluids are Fuel oil & Diesel, can you advise on this?

 

[Latexman]

I would assume the volumetric flows are additive, thus 520 m3/hr.

The mixture density would be 494,000 Kg/hr / 520 m3/hr = 950 kg/m3.



Good luck,
Latexman

Technically, the glass is always full - 1/2 air and 1/2 water.

 

[zdas04]

Latexman is completely correct.

I was interested in where your 504 m[sup]3[/sup]/hr came from. If I divide the mass flow rate by your 504 m[sup]3[/sup]/hr I get 980 kg/m[sup]3[/sup]. Did you really think that the mixed stream would have the density of the predominant component? That the minor component would somehow be promoted to that density? You have to use a weighted average density. If you use a density of:

(980*400+850*120)/(400+120) = 950 kg/m[sup]3[/sup]

Then the mass flow rate of the incompressible fluid matches the volume flow rate as required.

David Simpson, PE
MuleShoe Engineering

In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. Galileo Galilei, Italian Physicist

 

[LittleInch]

Somewhere in this calc "392000 + 102000 = 494000 Kg/hr which comes to 504 m3/hr" there is an error. What combined density did you use to get 504? If you just add the mixtures in proportion to the flow and get latexmans 950 kg/m3 (like I do), you get 520 m3/hr.

Note, this only works when the two mixtures are being pumped BEFORE mixing. once you mix it, your pump will react differently as will your system curve which will change depending on the combined viscosity. The density of the mixture will affect the pressure exerted by the same head, but directly shouldn't affect the pressure drop per se.



Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[BigInch]

It is going to take a lot more diluent to get the viscosity lower; about 40% diluent to get a blend viscosity = mean of the two.

 

[georgeverghese]

In addition to getting the right mix density, the mix viscosity also has to be estimated for the pressure drop calc. See mixing rules in Perry Chem Engg Handbook in the chapter on physical property estimation methods for mixtures of similar chemical composition.
Also account for temp changes if these 2 streams are not at the same temp; for which Cp mix is a weight averaged sum of the 2 streams, assuming the mix remains at below bubble point temp.
Any temp changes may have some slight effect on mix density.

 

[BigInch]

And BTW adding volumes of HC doesn't give exactly the sum of each component's volume. There is a shrinkage effect (API equation 12.3) here of 0.24% = 519.8m3/h

 

[zdas04]

BigInch,
Your post got me interested in learning more about the mechanism of the shrinkage. I looked in Shrinkage Losses Resulting from Liquid Hydrocarbon Blending and found

Even though mixing two crude oils is far more complex than the sand filling the void space between the marbles, it still really helped me get my head around the concept. The equations from The Manual of Petroleum Measurement Standards Chapter 12 Section 3 were illuminating as well. It is so easy to forget that crude is not water.

The linked article also explains how to calculate mixture density (which is close, but not exactly the number you get from the weighted average approach that you would use for two liquids that were less complex).

Thanks for sharing.



David Simpson, PE
MuleShoe Engineering

In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. Galileo Galilei, Italian Physicist

 

[BigInch]

If this was a 50/50 mix the shrinkage would be 0.5%
It is far more important to consider that then compressibility for example.