Designing Microreactors in Chemical
Synthesis –Residence-time Distribution
of Microchannel Devices
KLAUS GOLBIG
ANSGAR KURSAWE
MICHAEL HOHMANN
SHAHRIYAR TAGHAVI-MOGHADAM
THOMAS SCHWALBE
CPC-Cellular Process Chemistry Systems GmbH,
Mainz,Germany
This contribution deals with the application of numerical methods in CPC-Systems’
microreaction development process and demonstrates the feasibility and significant
benefits for the suggested design method.It is focused on the design of capillary resi-
dence tubes,which is necessary if the residence time provided by the original micro-
reactor is not sufficient to complete the reaction.The residence time distribution is
calculated from a straightforward numerical model based on the common assump-
tion that axial gradients can be neglected.The results can be adapted easily to other
capillary diameters or reaction conditions.As an example,the method is applied to
the case of sequential synthesis.
Keywords :Microreactor;Residence time distribution;Sequential synthesis;
Dispersion;Fluid dynamics
Introduction
Synthesis via Microreactors
Microreaction devices are beneficial innovative tools in the improvement and opti-mization of reactions as well as in fast supply of sufficient quantities of target com-pounds.This exciting new technology improves control of reaction parameters such as temperature and concentration equipartition and thus allows in many cases higher yields,fewer by-products,and higher selectivities.Therefore it has become increas-ingly interesting for small-scale production and mobile reaction ,for automotive applications (Wegeng and Drost,1998).
In order to realize these benefits a proper design of the microreaction system is crucial:heat transfer area,mixing channel dimensions,and flow capillaries must be sized very carefully to achieve,for example,reasonable mixing,pressure drops,and
Received 2March 2001;in final form 19June 2003.
Address correspondence to Klaus Golbig,CPC-Systems GmbH,Hanauer Landstrasse 526,G58III,Frankfurt,Mainz 60343,Germany.E-mail:wille@cpc-net
620
Chem.Eng.Comm.,192:620–629,2005
Copyright #Taylor &Francis Inc.
ISSN:0098-6445print =1563-5201online
DOI:10.1080=
00986440590495197
Designing Microreactors in Chemical Synthesis621 flow equipartition(Ehrfeld et al.,1997).To open the field of general application of microreactors in chemical synthesis,a comprehensive analysis of the requirements for such a microreactor has to be performed.Such an analysis identifies the design parameters for multipurpose microreactors,based on a feed rate corresponding to a typical bench-scal
e synthesis.The resulting solution should be suitable for a variety of applications with reactions or transformations of miscible liquids.
Microreactor Approach to a Better Chemistry
CPC-Systems,Cellular Process Chemistry Systems GmbH,located in Mainz (Germany),is engaged in the development and optimization of standardized modu-lar microreaction systems as well as in their application to organic synthesis.This approach is based on the idea of shortening development periods of new active substances by consequent numbering-up.This means that the same microreactor units are used in laboratory and in pilot plant,thus avoiding the scale-up risk.
Numerous microreactor applications are stated in the current literature that can be considered as proof of the principle of microreaction technology in general. Microreactors have been used in commodity ,ethylene oxide(Richter et al.,1998),the preparation of hydrocyanic acid(Hessel et al.,1999)and for poly-merizations.CPC-Systems’modular microreaction system,based on the CYTOS1 microreactor,can be applied to promising fields in drug discovery and development processes.For instance,chemical syntheses of different targets like quinoline acid derivates(Ciprofloxacin1)and the Paal-Knorrpyrrole synthesis have been investi-gated(Taghavi-Moghadam et al.,2001).Further example
s from our day-to-day microreactor lab experience could be found in Schwalbe et al.(2002)and Autze et al.(2000);they cover the complete range from common nitrations over rearrange-ments to Suzuki couplings and Wittig-Horner reactions.Furthermore,the CYTOS1 modular microreaction system can be used in a setup for sequential synthesis to generate compound libraries.
In comparison to conventional parallel synthesizers,sequential synthesis offers higher flexibility because the reaction conditions can be controlled independently and individually for each reaction sequence.Compared to the limited reaction vol-ume in a reaction block of a parallel synthesizer,access to variable amounts of target compounds is ensured by a system running continuously,even if the reaction sequence is demanding or divergent.The automation of the system,which can be established by using an auto-feed-sampler and a fraction collector,leads to perform-ing a maximum of chemistry with minimum effort.
The automated microreaction system also opens up an easy way to automatic reaction optimization.For this purpose a mathematical software generates a statisti-cal design of experiments and evaluates the results automatically via inline analytical sensors.Therefore CPC-Systems’microreaction systems are suited for the pro-duction of specimens as well as for the process development.
reaction diffusion
Design Model for Capillary Flows
The Problem
CPC-Systems’CYTOS1microreaction system,shown in Figure1,is composed of a pumping module,an exchangeable microreaction unit,and an optional
residence-time providing module,all connected by a convenient bayonet coupling.The residence-time providing unit,for example,a stainless steel capillary,is required for realization of larger reaction times.
For sequential operations the residence-time distributions (RTD)of the micro-reactor and the residence module have to be considered carefully because they may suffer from the laminar flow regime in the capillary tubing,especially if dead volumes are present.On the other hand,diffusive mixing can be very fast on a small scale,so that laminar flow is not necessarily considered a drawback.If more than one capillary is operated in parallel,flow equipartition also becomes an important issue.However,laminar flow regime is known to be modeled very precisely with minor effort.
In our microreaction system corrosion-resistant ceramic piston pumps are used,in contrast to some micro-analytic ,electrophoresis,which are based on electroosmotically driven flows.The vel
ocity profiles differ in both cases.In a pressure-driven capillary,the laminar velocity profile in Figure 2shows a pro-nounced parabolic shape,where the liquid at the wall is nearly stagnant.Influenced by such a velocity profile a concentration peak injected at the inlet will soon
be
Figure 1.CYTOS 1
microreaction system,the first commercial turn-key microreaction system.622K.Golbig et al.
dispersed,yielding a broad residence-time distribution at the outlet.Nevertheless,the molecular diffusion in radial direction limits this peak broadening.In this article design rules consider both effects.
Modeling
There are only a few sources available on this particular problem.In the engineering literature usually only an axial dispersion process is considered (Levenspiel,1958,1999),which was shown first by Taylor (1953)to be sufficient.He developed an analytical solution of the interaction between radial diffusion and axial convection in tubes.On the assumption that axial concentration gradients can be neglected in comparison to radial gradients and the introduction of a relative coordinate system moving with the mean velocity of the fluid,he was successful in reformulating the original problem into a simpler unidimensional axial dispersion process.The role of this process in the case of heterogeneous gas-phase reactions was investigated by Matlosz and coworkers (Commenge et al.,2001).
In order to uncover the details of this peak-broadening phenomenon,a numerical approach was developed that is more flexible regarding geometry and boundary con-ditions.The model uses finite volume balances as well as the following assumptions:
.
Fully developed parabolic velocity profile .
Restriction to radial diffusion .
Conservation of mass (no reaction).
Discretization in axial and radial direction .
Limitation of maximum concentration change to 10%by appropriate choice of D t .Length of one axial discretization element D l
D l ¼D t Áu max
The program computes the diffusive
c i ;j ;k þ1¼c i ;j ;k þ
D n i À1;k ÀD n i ;j ;k p D l ðr i Àr i À1Þwith D n i ;k ¼2p D D l r i c i ;j ;k Àc i þ1;j ;k r i þ1Àr i
and the convectional mass transport from cell i,j À1to cell i,j
c i ;j ;k þ1¼ð1Àg i Þc i ;j ;k þg i c i ;j À1;k
in an alternating mode.In the equations n denotes amount of moles,c the cell concen-tration,D the diffusion coefficient,r i the outer radial position of the cell i ,and g i
the
Figure 2.Velocity profile and peak broadening inside a capillary tube due to combination of axial convection and radial diffusion.
Designing Microreactors in Chemical Synthesis 623
velocity weighting factor of cell i.The velocity weighting factor g i represents the ratio of fluid leaving cell i,j À1into the next cell i,j downstream during the time period D t .
g i ¼1Àr 2i þr 2i À12R 2
where R denotes to the inner radius of the capillary.The subscripts contain infor-mation about the radial and axial position of the cell,and the last subscript indicates the numeric operation step.
Simulation Results
As presented in Figure 3,the resulting residence-time distribution of a short capillary for each individual radial position clearly shows that material is short cutting through the center whereas the RTD curves near the wall are delayed.
Generalized RTD Diagram.To avoid time-consuming calculations,the fact is used that,simply put,the calculation procedure is just computing the same figures of dimensionless concentrations in each run.Only the scaling of the time steps differs depending on the diffusion time constants d 2=D .Thus,the resulting dimensionless RTD curve is dependent on only one parameter,the dimensionless di
ffusion time or Fourier number Fo d :
Fo d ¼t mean D
d wher
e t mean is mean residence time,D is diffusivity,and d 2is tube diameter is
1.Figure    3.Residence-time distribution for capillary with 5min mean residence time and
1.75mm inner diameter (D ¼6.9Á10À10m 2=s).624K.Golbig et al.

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