Semi-batch system modeling?

[ChemIncognito]

I have a batch reactor which contains a solid (a clathrate) that decomposes. The system is vented at constant pressure, so that there is no accumulation of gas in the system (anything generated flows out). I have a flowmeter attached to the outlet, such that I can measure the instantaneous venting rate (liters/sec), and I can measure total outlet volume. I'm trying to determine rate parameters for this system, and am having a hard time doing it.

If I start:

In - Out + Gen = Acc

I get to

Out=Gen

I'll just assume a first order reaction, so I have

Out = kCa V

Unfortunately, volume is not really constant (it'll be dV/dt) in this case. Can anyone point me in the right direction? It has been a while since I've done this, and all books usually treat semi-batches as inlet with no outlet, but I'm the other way around.

Thanks very much!
Mike

 

[babucher]

If you begin with an overall mass balance on a system consisting of the solid phase (is it a solid phase, or solids mixed in liquid?), you'll get an Acc = - Out term that looks like,

dM/dt = - m_dot_out

express dM/dt as d(rho*V)/dt and consider rho constant to get rho*dV/dt.

I'm not sure where I'd take this without more information, but the above can give you a rate equation for volume (of the solid phase).