Question

Confirm Continuous-Flow Stirred Tank Reactors (CFSTRs) in-series approximate a Plug-Flow Reactor (PFR).

1) Assume steady-state and 1st order reaction kinetics

2) The total volume of the CSFTRs in-series is equal to the volume of the PFR.

3) Also, the total Hydraulic Retention time (HRT) of the CFSTRs in-series is equal to the HRT of the PFR.

Answer 1

The continuous stirred-tank reactor (CSTR), also known as vat- or backmix reactor, or a continuous-flow stirred-tank reactor (CFSTR)^[1][2], is a common model for a chemical reactor in chemical 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.^{[notes 1]} The mathematical model works for all fluids: liquids, gases, and slurries.

The behavior of a CSTR is often approximated or modeled by that of a Continuous Ideally Stirred-Tank Reactor (CISTR). All calculations performed with CISTRs assume perfect mixing. In a perfectly mixed reactor, the output composition is identical to composition of the material inside the reactor, which is a function of residence time and rate of reaction. If the residence time is 5-10 times the mixing time, this approximation is valid for engineering purposes. The CISTR model is often used to simplify engineering calculations and can be used to describe research reactors. In practice it can only be approached, in particular in industrial size reactors.

Continuous flow stirred-tank reactors are usually applied in waste water treatment processes. CSTRs facilitate rapid dilution rates which make them resistant to both high pH and low pH volatile fatty acid wastes. CSTRs are less efficient compared to other types of reactors as they require larger reactor volumes to achieve the same reaction rate as other reactor models such as Plug Flow Reactors.

The plug flow reactor model (PFR, sometimes called continuous tubular reactor, CTR, or piston flow reactors) is a model used to describe chemical reactions in continuous, flowing systems of cylindrical geometry. The PFR model is used to predict the behavior of chemical reactors of such design, so that key reactor variables, such as the dimensions of the reactor, can be estimated.

Fluid going through a PFR may be modeled as flowing through the reactor as a series of infinite thin coherent "plugs", each with a uniform composition, traveling in the axial direction of the reactor, with each plug having a different composition from the ones before and after it. The key assumption is that as a plug flows through a PFR, the fluid is perfectly mixed in the radial direction but not in the axial direction (forwards or backwards). Each plug of differential volume is considered as a separate entity, effectively an infinitesimally small continuous stirred tank reactor, limiting to zero volume. As it flows down the tubular PFR, the residence time ({\displaystyle \tau }) of the plug is a function of its position in the reactor. In the ideal PFR, the residence time distribution is therefore a Dirac delta function with a value equal to {\displaystyle \tau }.

Assumptions:

• Plug flow
• Steady state
• Constant density (reasonable for some liquids but a 20% error for polymerizations; valid for gases only if there is no pressure drop, no net change in the number of moles, nor any large temperature change)
• Single reaction occurring in the bulk of the fluid (homogeneously).