Model-based analysis of mass transfer limitations in microreactors

Timothy Van Daelea, David Fernandes del Pozoa, Daan Van Hauwermeirena,

Krist V. Gernaeyb, Ingmar Nopensa,*

aBIOMATH, Dept. of Mathematical Modeling, Statistics and Bioinformatics,

Faculty of Bioscience Engineering, Ghent University, 9000 Ghent, Belgium

bCAPEC-PROCESS, Dept. of Chemical and Biochemical Engineering,

Technical University of Denmark, 2800 Kongens Lyngby, Denmark

Introduction

Mass transfer limitations occur when the diffusion rate of the molecules is lower than the reaction rate, leading to a decrease in reactorproductivity.The latter leads to higher processing costs and should thus be avoided [1]. Moreover, reaction kinetics cannot be calibrated properly when mass transfer limitations occur, since the data will reflect the mass transfer limitation, not the reaction kinetics of the system. Under these conditions, the values of the underlying kinetic model process parameters are obscured [2]. Therefore, mass transfer limitations should always be evaluated to ensure that these mass transfer effects are negligible. We hereby present a generic methodology to evaluate whether and to which extent mass transfer limitations are present andcomparedthis with the traditional approach relying ondimensionless numbers.

Approach

A simple enzymatic model was defined, in which substrate S is irreversibly converted to product P by an enzyme E. The corresponding reaction rate was defined as:

/ (1)

with r the reaction rate, kcat the turnover number, [E] the enzyme concentration and substrate concentration [S].Four different degrees of freedom wereevaluated with respect to impact on mass transfer limitation: diffusion coefficient D, channel width W, residence time τ and maximum reaction rateVmax:

/ (2)

with [S]in the inlet concentration of [S]. To quantify mass transfer limitations,a framework was developed as shown in Figure 1.

/ Figure 1: The proposed framework to quantify mass transfer limitations. The degrees of freedom are changed to the values of interest. After simulating both the ideal plug flow and Computational Fluid Dynamics (CFD) model, the results are compared by using a relative difference. A high relative difference represents high mass transfer limitations.

First, the values of the different degrees of freedom are chosen and these values are set for both ideal plug flow and CFD simulations. The diffusion coefficient D and the microreactor width W only affect the CFD simulations(the ideal plug flow model assumes perfect mixing in the transverse direction). Finally, the product concentrations leaving the reactorsare compared and a relative difference is calculated. The underlying idea is that high differences between the ideal plug flow and the CFD demonstrate that mass transfer limitation is important for reactor productivity.

Results

The presented approach was applied for a microreactor configuration with enzyme immobilized on the wall. The result for a channel width of 200 μm and a residence time of 10 min are given in Figure 2. About 150 CFD simulations were required to generate this plot(i.e. large computational effort). Three regions can be defined: at low Vmax and high D, no mass transfer limitation occurs (kinetically controlled reaction). At high Vmax and low D, mass transfer limitation is important. At high Vmax and high D, no conclusion can be drawn, because the reaction has already reached full conversion.

/ Figure 2: The approach to quantify the mass transfer limitation was applied to a microreactor with enzyme immobilized on the wall (channel width 200 μm and residence time 10 min). The grayscale colormap represents the relative difference between the ideal plug flow and the CFD model. The dashed lines (--) represent the amount of substrate which has been converted to product.

The second Damköhler number (DaII), which is the ratio between the reaction rate and diffusion rate(Equation 3), proved to be a reliable way to describe the transition from the kinetic limitation region to the mass transfer limitation region (Figure 3).

/ (3)

It can be noticed that the different DaII values correspond with a certain level of mass transfer, e.g. the DaII value of 0.10 corresponds with a relative difference of 1%. This illustrates that the dimensionless numbers are powerful, but also that the generic simulation-based approach proposed here yields reliable results.

/ Figure 3: The transition from the kinetic limitation region to the mass transfer limitation region can be predicted well by using the second Damköhler number (represented by dashed lines).

Conclusions

The presented approach allows evaluating and quantifyingmass transfer limitations. This is achieved by comparing CFD with ideal plug flow simulations. The presented approach is computationally demanding, but allows an in-depth study of the mass transfer phenomena which occur in microreactors. Dimensionless numbers, in particular the second Damhköhler number, are useful to quantify mass transfer limitations and results correspond well with the presented approach.

References

[1] P. Tufvesson., J. Lima-Ramos, J.S. Jensen, N. Al-Haque, W. Neto, J.M. Woodley, Process considerations for the asymmetric synthesis of chiral amines using transaminases,Biotechnol. Bioeng. 108 (2011) 1479–1493.

[2] A. Pohar and I. Plazl, Process Intensification through Microreactor Application, Chem. Biochem. Eng. Q. 23 (2009) 537–544.