Abstract
The tanks-in-series model (TIS) is a popular model to describe the residence time distribution (RTD) of non-ideal continuously stirred tank reactors (CSTRs) with limited back-mixing. In this work, the TIS model was generalised to a cascade of n CSTRs with non-integer non-negative n. The resulting model describes non-ideal back-mixing with n > 1. However, the most interesting feature of the n-CSTR model is the ability to describe short recirculation times (bypassing) with n < 1 without the need of complex reactor networks. The n-CSTR model is the only model that connects the three fundamental RTDs occurring in reactor modelling by variation of a single shape parameter n: The unit impulse at n→0, the exponential RTD of an ideal CSTR at n = 1, and the delayed impulse of an ideal plug flow reactor at n→∞. The n-CSTR model can be used as a stand-alone model or as part of a reactor network. The bypassing material fraction for the regime n < 1 was analysed. Finally, a Fourier analysis of the n-CSTR was performed to predict the ability of a unit operation to filter out upstream fluctuations and to model the response to upstream set point changes.
Highlights
The pharmaceutical industry is currently transforming batch production processes to continuous manufacturing
The n-continuously stirred tank reactors (CSTRs) model is the only model that connects the three fundamental residence time distribution (RTD) occurring in reactor modelling by variation of a single shape parameter n: The unit impulse at n→0, the exponential RTD of an ideal CSTR at n = 1, and the delayed impulse of an ideal plug flow reactor at n→∞
ReactorThese typesreactor are too types idealised to correctly model the behaviour of a behaviour ofHowever, a real reactor. If these models are combined in itreactor networks, it is real reactor. If these basic models are basic combined in reactor networks, is possible to describe possible to describe the behaviour of a real unit operation, including effects such as deadback zones, nonthe behaviour of a real unit operation, including effects such as dead zones, non-ideal mixing, ideal back mixing, and/or bypassing effects
Summary
The pharmaceutical industry is currently transforming batch production processes to continuous manufacturing. Residence time distribution modelling is used to describe a complete continuous manufacturing line; it is utilised to describe the complex behaviour of single unit operations within reactor networks. If these basic models are basic combined in reactor networks, is possible to describe possible to describe the behaviour of a real unit operation, including effects such as deadback zones, nonthe behaviour of a real unit operation, including effects such as dead zones, non-ideal mixing, ideal back mixing, and/or bypassing effects This approach is not limited to pharmaceutical processes, and/or bypassing effects. Non-integer value of n > 1 allows tuning the RTD shape for varying degrees limited. Comparison parameter range of tanks-in-series (TIS), diffusion, and generalised of n continuous stirred tank reactor (n-CSTR).
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