# Plug flow for pipe flow

1. Aug 26, 2010

### colen212

I am trying to formulate a plug flow for section of my model. In my model, I've series of CSTR that are linked with the plug flow. The output of the plug flow model is the CSTR model. My main focus is blending CSTR and plug to replicate a residenc time distribution. However, i need a plug flow at the begining so as to delay the process and not alter the shape of the CTSR.

2. Aug 26, 2010

### MichielM

Hi Colen
Could you give a little more detail of what you're trying to do exactly. What do you mean by 'the output of the plug flow model is the CSTR model', do you mean that this is physically the case, i.e. you have a PFR connected to a CSTR, or do you only use the PFR to 'model' a time delay of your input signal?

The basic equation for an RTD-model in a PFR is the transient convection model (in 1D):
$$\frac{\partial C}{\partial t}=u\frac{\partial C}{\partial x}$$

By the way, I'm guessing you're a chemical engineer (like I am), on a forum like this it might be smart to explain what a CSTR is, I'm not sure whether that is common knowledge outside the chemical engineering community.

Regards,

Michiel

3. Aug 26, 2010

### colen212

You got the problem description. I am trying to use the plug flow as a delay signal. I want to delay the flow out of the system so I had to use the plug flow. I've used the equation you posted but the mass is not conserved. As expected, my input flowrate should be the same value of output flow. I suspected my boundary conditons or the numerical analysis are the issues:
Here are boundary conditions that I used:

m(0) = Flowrate_in/u
u*(Partial(m(L)) = u *m(L)

where u is the velocity which is L/t, and L is the length and t = time
m is the mass(kg)
m(0) is the mass at the inlet
m(L) is the mass at the outlet.