Continuous stirred-tank reactor

The continuous stirred-tank reactor (CSTR), also known as vat- or backmix reactor, mixed flow reactor (MFR), or a continuous-flow stirred-tank reactor (CFSTR), is a common model for a chemical reactor in chemical engineering and environmental engineering. A CSTR often refers to a model used to estimate the key unit operation variables when using a continuous agitated-tank reactor to reach a specified output. The mathematical model works for all fluids: liquids, gases, and slurries. The behavior of a CSTR is often approximated or modeled by that of an ideal CSTR, which assumes perfect mixing. In a perfectly mixed reactor, reagent is instantaneously and uniformly mixed throughout the reactor upon entry. Consequently, the output composition is identical to composition of the material inside the reactor, which is a function of residence time and reaction rate. The CSTR is the ideal limit of complete mixing in reactor design, which is the complete opposite of a plug flow reactor (PFR). In practice, no reactors behave ideally but instead fall somewhere in between the mixing limits of an ideal CSTR and PFR. A continuous fluid flow containing non-conservative chemical reactant A enters an ideal CSTR of volume V. Assumptions: perfect or ideal mixing steady state , where NA is the number of moles of species A closed boundaries constant fluid density (valid for most liquids; valid for gases only if there is no net change in the number of moles or drastic temperature change) nth-order reaction (r = kCAn), where k is the reaction rate constant, CA is the concentration of species A, and n is the order of the reaction isothermal conditions, or constant temperature (k is constant) single, irreversible reaction (νA = −1) All reactant A is converted to products via chemical reaction NA = CA V Integral mass balance on number of moles NA of species A in a reactor of volume V: where, FAo is the molar flow rate inlet of species A FA is the molar flow rate outlet of species A vA is the stoichiometric coefficient rA is the reaction rate Applying the assumptions of steady state and νA = −1, Equation 2 simplifies to: The molar flow rates of species A can then be rewritten in terms of the concentration of A and the fluid flow rate (Q): Equation 4 can then be rearranged to isolate rA and simplified: where, is the theoretical residence time () CAo is the inlet concentration of species A CA is the reactor/outlet concentration of species A Residence time is the total amount of time a discrete quantity of reagent spends inside the reactor.