3 replies to this topic

[samin_chemeng]

Hello,

 

I’ve encountered a process modeling problem involving the mixing of two incompressible liquid streams with different pressures and pipe diameters. While it seems straightforward, I haven’t found a clear analytical solution or theoretical justification for how the pressure behaves at the mixing node. Most process simulators (e.g., Aspen HYSYS) assume that the pressure at the mixing point is equal to the minimum of the two inlet pressures, but I would like to understand whether this is physically justified or just a modeling convention.

 

Here’s the setup:

• Stream C1:
  Volumetric flow rate: Gv1 = 200 m³/h
  Pressure: P1 = 10.5 barg
  Pipe diameter: D1 = 200 mm, L1 = 400 m;

• Stream C2:
  Volumetric flow rate: Gv2 = 100 m³/h
  Pressure: P2 = 3.5 barg
  Pipe diameter: D2 = 100 mm, L2 = 10 m;

• The two streams mix at node N1, forming stream C3 with:
  Flow rate: Gv3 = Gv1 + Gv2 = 300 m³/h
  Pressure: P3 = ?
  Pipe diameter: D3 = 200 mm, L3 = 85 m;

• The mixed stream flows to a discharge point U1 (e.g., a tank) with pressure:
  P4 = 1.03 barg (hydrostatic)

In the simulator, the pressure at the mixing node appears to be P3 = min(P1, P2) = 3.5 barg, and the excess energy seems to be reflected in a slight increase in fluid temperature. I attempted to apply Bernoulli’s equation, but I’m unsure whether it’s valid in this context, especially since the mixing occurs at a junction and not along a single streamline. Also, I’m not sure if I’ve accounted correctly for the energy losses or the state functions of the fluid (incompressible liquid in this case).

 

In my analysis, I used the following energy balance:

Before mixing:
Gv1 × (h1 - F1) + Gv2 × (h2 - F2) = Gv3 × h3

After mixing and before discharge:
Gv3 × (h3 - F3) = Gv4 × h4 → h3 - F3 = h4

Where:
Gv = volumetric flow rate [m³/h]
P = pressure [barg]
D = pipe diameter [mm]

L = pipe length [m]
h = specific enthalpy [kJ/kg]
F = specific energy loss due to friction [kJ/kg]
η = kinematic viscosity [cP]
ρ = density [kg/m³]

 

My question is:
Is there a theoretical basis for assuming that the pressure at the mixing node is equal to the lower of the two inlet pressures, especially when the pipe diameters differ? Or is this simply a modeling simplification used in simulators?

Any references to literature, textbooks, or articles that address this type of hydraulic mixing behavior would be greatly appreciated.

Thank you in advance!

[Pilesar]

Fluid pressure at the mixing node is calculated backwards from the sink. There is just one combined stream after mixing. If you know the flow rate and the final sink pressure, it is just a matter of determining the pressure drop to the sink to find the pressure at the node.

  In every case I have seen, fluid moves from high pressure to low pressure unless mechanically acted upon (for example, by a pump or compressor.)

  Your pressure at P3 will NOT be as high as P1 or P2. There will be pressure drop caused by the piping between the source and the mixing node. Do not ignore the pipe lengths!

  Your problem statement is really over specified with at least three equations. Any one of the three streams can be used to calculate the pressure at the mixing node. They should each give the same answer since there is only one unique pressure at P3. When calculating pressure drop through a pipe, there are additional unstated parameters that matter. Elevation change and pipe roughness are not given. In real life, pipe roughness is assumed or backwards calculated from measured pressure drop as a tuning parameter. I suggest you calculate the pressure drop of all three streams separately as if they were completely independent as an exercise even though just the stream from P3 to P4 is adequate to find the solution.

[katmar]

I agree completely with Pilesar. About the only thing that correlates with the minimum of the two supply pressures is that if the pressure at the node is higher than the minimum of the two inlet pressures then the flow in the line from the lower pressure source will reverse and flow towards the source (assuming that there are no changes in elevation).

[latexman]

When two liquids are mixed, the pressure at the mixing point will equalize and, in a continuous flow system, the resulting pressure will be at or below the lowest pressure of the incoming streams.

The simulator rule is spot on.