Isothermal tubular reactor with first order chemical reaction Problem description: In a tubular reactor, the fluid composition varies from position to position along its length route; consequently, the material balance for a reaction component must be made to a volume differential element Aδz, as shown in the figure. For systems where the reaction volume or volumetric rate v does not vary with the reaction, as is the case with liquid phase systems and some gas phase systems. For liquids, the variation volume with the reaction is negligible when there is no phase change. Consequently, we can to take: v=uA constant For A, we will have: Balance for component A in the differential element of the reactor: Enter = Exit - React Enter: uACA Out: uACA + d(uACA)δz/dz - rAδz React: rAAδz Substituting in the balance of A: uAc = uAC + d(uACA)δz/dz -r Aδz d(uACA)δz/dz -r Aδz = 0 d(uACA)/dz - rAA=0 uA*dCA/dz - rAA=0 u*dCA/dz-rAA=0 Defining the dimensionless distance: ? = z/L there is: ??/dz = 1/L So: dCA/dz = dCA/??* ??/dz dCA/dz=dCA/ ??*1/L Substituting into the differential equation: u*dCA/ ??*1/L - rA= 0 dCA/ ?? - L/u*rA=0 For a first order reaction, we have: rA = -kCA Substituting into the differential equation: dCA/ ??+kL/u*CA=0 The converted fraction XA of a given reactant A is defined as the fraction converted into product or: XA=FAi -FA/FAi If the volumetric velocity v does not change with the reaction, the conversion can be calculated by: XA=CAi -CA/CAi Numerical data: For a component A fed to a tubular reactor where the following reaction takes place, A -> B, the reaction is of first order, where the reaction rate measured with respect to A is given by: rA = -kCA Determine the conversion in a 10.000L reactor for the following data: CAi = 0,1 mol/L FAi = 200 mols/h k = 0,2 1/h What is the volume of the tubular reactor for a 50% conversion?
Isothermal tubular reactor with first order chemical reaction
Problem description: In a tubular reactor, the fluid composition varies from position to position along its length route; consequently, the material balance for a reaction component must be made to a volume differential element Aδz, as shown in the figure.
For systems where the reaction volume or volumetric rate v does not vary with the reaction,
as is the case with liquid phase systems and some gas phase systems. For liquids, the variation volume with the reaction is negligible when there is no phase change. Consequently, we can to take:
v=uA constant
For A, we will have:
Balance for component A in the differential element of the reactor:
Enter = Exit - React
Enter: uACA
Out: uACA + d(uACA)δz/dz - rAδz
React: rAAδz
Substituting in the balance of A:
uAc = uAC + d(uACA)δz/dz -r Aδz
d(uACA)δz/dz -r Aδz = 0
d(uACA)/dz - rAA=0
uA*dCA/dz - rAA=0
u*dCA/dz-rAA=0
Defining the dimensionless distance: ? = z/L
there is: ??/dz = 1/L
So: dCA/dz = dCA/??* ??/dz
dCA/dz=dCA/ ??*1/L
Substituting into the differential equation:
u*dCA/ ??*1/L - rA= 0
dCA/ ?? - L/u*rA=0
For a first order reaction, we have:
rA = -kCA
Substituting into the differential equation:
dCA/ ??+kL/u*CA=0
The converted fraction XA of a given reactant A is defined as the fraction converted into product or:
XA=FAi -FA/FAi
If the volumetric velocity v does not change with the reaction, the conversion can be calculated by:
XA=CAi -CA/CAi
Numerical data: For a component A fed to a tubular reactor where the following reaction takes place, A -> B, the reaction is of first order, where the reaction rate measured with respect to A is given by:
rA = -kCA
Determine the conversion in a 10.000L reactor for the following data:
CAi = 0,1 mol/L
FAi = 200 mols/h
k = 0,2 1/h
What is the volume of the tubular reactor for a 50% conversion?
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