I am trying to find the volume of a PFR reactor. For this purpose I have written the rate expression as a function of conversion, and stuffed it in to an integral. I am using the AutomaticUnits package by Jon McLoone.
The problem is that when I execute the equation containing the integral, Mathematica starts working, but returns no result. I abort the operation after waiting what I would call suffcient time :-) My setup is seen below:
rA[X_] := k*((1 - X)/(1 + 2* X)*P/(R T) - (
X/(1 + 2 *X)*P/(R T)*((2*X)/(1 + 2 *X) *P/(R T))^2)/
kc) /. {k -> 0.0440238 Minute^-1,
kc -> 0.025 Mol^2* Liter^-2} //. {P -> 10 Atmosphere,
T -> 127 Kelvin + 273.15 Kelvin,
R -> 0.08205746 (Liter*Atmosphere)/(Kelvin*Mol)}
V == FA0*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(0\), \( .9*0.512618\)]\(
\*SuperscriptBox[\(rA[X]\), \(-1\)] \[DifferentialD]X\)\) /. {FA0 ->
2.5 Mol Minute^-1}
I have investigated it for a long time now, and have found out the following:
- If I remove the Units, the expression Evaluates as it is supposed to.
- If I keep the units, and take the reciprocal of 1/rA ( so just rA ), it evaluates. Not with the correct answer of course.
- I have done the exact same operations once before, but with a much smaller function rA, which worked!
I am pretty much on bare ground, and hope someone can help me by pointing out my mistakes. I am afraid the answer is obvious, but I have stared too much at the same two lines of code, and have hence become immune toward finding a solution.
I am using Mathematica 9.
Best Regards
Simon P.
