Model 4 (Expert)

Because the microreactor operates in laminar flow, the flow profile is not uniform but rather curved (see figure below). The zero-velocity condition at the walls results in a parabolic flow profile. The smaller the distance between the two walls, the more exaggerated the parabolic nature of the flow profile becomes (assuming the flowrate remains constant). Since the reaction is happening only at the walls of the reactor, this difference in duration could have a big effect on the temperature and concentration profiles across the channel. Diffusion of chemicals and heat conduction act to equilibrate the fluid at the center of the channel with the fluid at the walls. Since the fluid in the center of the channel spends so much less time in the reactor than the fluid at the walls, the center fluid has less time to equilibrate with the wall fluid.

Assuming uniform flow profile Parabolic flow profile
   

Channel geometry drawing

IMPORTANT: Notice that we are modeling only half the height of the reactor, so make the model run faster.

Accounting for effects of flow:

Since we model a laminar system, the full Navier-Stokes equations are solved for each element in the model. Convective terms are included to allow for consideration of heat convection between the fluid in the reactor and the walls of the reactor.

Limitations:

• The modeling package used (FIDAP) does not have any pre-existing code for handling reactors. Therefore, the code was modified by Dr.Bruce Finlayson to perform a single reaction (oxidation of ammonia to nitric acid) at the walls.
• Only one species, ammonia, is tracked throughout the model run. For the purposes of calculating the rate of ammonia consumption, the oxygen concentration is assumed to be proportional to the local pressure.
• Linking the heat generation term with the reaction term was not possible, so the heat generation was modeled as a constant flux at the walls.

A pressure drop along the channel was included.

As can be seen in the figure on the general page, we neglect any variation in the ‘x’ direction. We assume that the microreactor is symmetric with respect to the plane defined by y=0.5 and perpendicular to the bottom and top walls of the device, so to save time in running the model we include only half the height of the device.

In addition, to facilitate incorporation of the boundary and initial conditions, we extend the geometry of the device to include –0.53<z<7 and –0.82<y<0.5.

We solved for a steady-state solution.

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