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The [[design equation]] for a chemical reactor is based directly on the [[general balance equation]]
The [[design equation]] for a chemical reactor is based directly on the [[general balance equation]]
:<math>F_{j0} - F_j + \int^V{r_jdV} = \frac{dN_j}{dt}</math>
:<math>F_{j0} - F_j + \int^V{r_jdV} = \frac{dN_j}{dt}</math><ref name="fogler">Fogler, H. Scott. ''Elements of Chemical Reaction Engineering, 4e''. Pearson Education: 2006.</ref>
where
where
:F<sub>j0</sub> is the molar flow rate into the system of species j
:F<sub>j0</sub> is the molar flow rate into the system of species j
:F<sub>j</sub> is the molar flow rate out of the system of species j
:F<sub>j</sub> is the molar flow rate out of the system of species j
:r<sub>j</sub> is the [[rate equation|rate of dissapearance]] of species j
:r<sub>j</sub> is the [[rate equation|rate of appearance]] of species j<ref>Since the design equation is performed on a reactant, the rate of appearance is actually negative. For this reason -r<sub>j</sub> is often substituted, to represent dissapearance of the reactant.</ref>
:V is [[volume]] in which the reactor takes place
:V is [[volume]] in which the reactor takes place
:N<sub>j</sub> is the number of [[mole]]s of species j
:N<sub>j</sub> is the number of [[mole]]s of species j
The design equation is always performed on the [[limiting reactant]] of a reaction.
The design equation is typically performed on the [[limiting reactant]] of a reaction.
==Batch Reactor==
A ''batch reactor'' is the simplest form of a chemical reactor. A batch reactor is simply a vessel of fixed or variable volume which has no material flows into or out of the system. A batch reactor could be as small as a [[beaker]] in a chemistry lab, or as large as a 1,000 gallon fermenter in a large scale [[beer|brewery]].
===Design Equation===
Since batch reactors have no in or out flows, F<sub>j0</sub> and F<sub>j</sub> are both equal to 0. If the reactor is assumed to be [[well mixed]], then there are no spacial variations of r<sub>j</sub> (in other words, r<sub>j</sub> is a constant and can be taken outside of the [[integral]]. Thus, the design equation for a batch reactor is
:<math>r_jV = \frac{dN_j}{dt}</math>.
===Uses===
Batch reactors are useful for
*small-scale operations
*testing new processes
*manufacturing expensive products
*very slow processes (such as [[biology|biological]] reactions)
==Notes==
<references />
[[Category:Chemical Engineering]]
[[Category:Chemical Engineering]]