Continuous stirred-tank reactor
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.
A continuous fluid flow containing non-conservative chemical reactant A enters an ideal CSTR of volume V. Assumptions: Integral mass balance on number of moles NA of species A in a reactor of volume V:
, is always equal to the reactor volume divided by the fluid flow rate.
[2] See the next section for a more in-depth discussion on the residence time distribution of a CSTR.
Equation 6 can be solved by integration after substituting the proper rate expression.
The table below summarizes the outlet concentration of species A for an ideal CSTR.
The exit age distribution (E(t)) defines the probability that a given fluid particle will spend time t in the reactor.
[2] More commonly, the reactor hydraulics do not behave ideally or the system conditions do not obey the initial assumptions.
Non-ideal hydraulic behavior is commonly classified by either dead space or short-circuiting.
The presence of corners or baffles in a reactor often results in some dead space where the fluid is poorly mixed.
If dead space or short-circuiting occur in a CSTR, the relevant chemical or biological reactions may not finish before the fluid exits the reactor.
[7] To model systems that do not obey the assumptions of constant temperature and a single reaction, additional dependent variables must be considered.
CSTRs are known to be one of the systems which exhibit complex behavior such as steady-state multiplicity, limit cycles, and chaos.
[8] As seen in the graph with one CSTR, where the inverse rate is plotted as a function of fractional conversion, the area in the box is equal to
When the same process is applied to a cascade of CSTRs as seen in the graph with three CSTRs, the volume of each reactor is calculated from each inlet and outlet fractional conversion, therefore resulting in a decrease in total reactor volume.
Optimum size is achieved when the area above the rectangles from the CSTRs in series that was previously covered by a single CSTR is maximized.
For an isothermal first order, constant density reaction in a cascade of identical CSTRs operating at steady state For one CSTR:
At steady state, the general equation for an isothermal zeroth order reaction at in a cascade of CSTRs is given by
For an isothermal second order reaction at steady state in a cascade of CSTRs, the general design equation is
As seen above, an increase in the number of CSTRs in series will decrease the total reactor volume.
The largest decrease in cost, and therefore volume, occurs between a single CSTR and having two CSTRs in series.
From a rearrangement of the equation given for identical isothermal CSTRs running a zeroth order reaction:
Therefore the total reactor volume is independent of the number of CSTRs for a zeroth order reaction.
When considering parallel reactions, utilizing a cascade of CSTRs can achieve greater selectivity for a desired product.
and B is the desired product, the cascade of CSTRs is favored with a fresh secondary feed of
and B is the desired product, a cascade of CSTRs with an inlet stream of high
[3] Therefore, CSTRs are typically larger than PFRs, which may be a challenge in applications where space is limited.
However, one of the added benefits of dilution in CSTRs is the ability to neutralize shocks to the system.
As opposed to PFRs, the performance of CSTRs is less susceptible to changes in the influent composition, which makes it ideal for a variety of industrial applications:
