If your flow is in a helicoid, there will be scondary forces that will also increase mixing and heat trasnfer.

Please refer to helical flow in literature, as the Reynolds number needs to be adjusted using the tube diameter (d), coil diameter (D) also known as Dean Number = N_Re*(d/D)

Check Mori and Nakayama (1967 a and b) for further studies on this heat transfer

and Ali (2000) for pressure drop and fluid dynamics

As i think you are converting batch process into a continuous process.

your calculation for Re is correct. But in case of Coil reactor your surface to volume ratio for reactant will be drastically changed, so for same rate of heat transfer you will have fine tune flow rate of reactants. Furthermore form yield point of view you can play with reaction also.

Hello Thiago, from the heat ransfer point of view I think you are correct. Concerning the other boundary conditions I am sure that if the reaction has not got a selectivity of 100% you will sure end up with something different but in any case better than in the stirred vessel. In tube reactors selectivity will rise due to the narrower residence time spectrum (Bodenstein number). Control of temperature will become easier due to the increased surface to volume ratio. Scale up will become easier as in strirred tanks it becomes tricky to maintain the temperature unless you work at the vaporization temperature of the solvent.

In addition to Frank point I like to suggest to pay attention on the problem of flow in gap between two concentric cylinders. This is not so complex flow than in stirring vessel but the only classic Reynolds number is not sufficient. Two different dimensionless compexes is needing. One for axial flow, and one more for angular flow.

If your flow is in a helicoid, there will be scondary forces that will also increase mixing and heat trasnfer.

Please refer to helical flow in literature, as the Reynolds number needs to be adjusted using the tube diameter (d), coil diameter (D) also known as Dean Number = N_Re*(d/D)

Check Mori and Nakayama (1967 a and b) for further studies on this heat transfer

and Ali (2000) for pressure drop and fluid dynamics

Dear Pablo, can you provide more specific reference for Mori and Nakayama (1967 a and b) ?

Sure:

Study of forced convective heat transfer in curved pipes (2nd report, turbulent region) Y Mori, W Nakayama - International journal of heat and mass transfer, 1967a - Elsevier

Study on forced convective heat transfer in curved pipes:(3rd report, theoretical analysis under the condition of uniform wall temperature and practical formulae)

Y Mori, W Nakayama - International journal of heat and mass transfer, 1967b - Elsevier

These may also help:

Fully developed laminar convection from a helical coil

RL MANLAPAZ, SW CHURCHILL - Chemical Engineering …, 1981 - Taylor & Francis

Heat transfer in tube coils with laminar and turbulent flow

RA Seban, EF McLaughlin - International journal of heat and mass transfer, 1963

Comparison of heat transfer rates between a straight tube heat exchanger and a helically coiled heat exchanger

DG Prabhanjan, GSV Raghavan, TJ Rennie - … in Heat and Mass Transfer, 2002

Dear Pablo, thanks for sharing those useful references with us. They were quit informative.

The flow regime is a function of both the Reynolds number and the geometry, therefore you cannot transfer a Reynolds number directly from one geometry to another. Even with a stirred vessel the flow regime (at the same Re value) will depend on things like the shape of the stirrer, that of the vessel and number and geometry of the baffles. If you choose the length scale judiciously then to obtain a similar flow regime Re will probably have to be of the same order but there's no guarantee the values will be the same or near.

I agree with Tuan. It sounds like you are attempting to use the Buckingham-Pi method or similar to recreate your reaction in the coil. But Buckingham-Pi requires geometric similarity, which you do not have.

A lot depends on the type of reaction you're running. If it is a fairly simple chemical reaction that isn't really affected by rheology and hydrodynamics, then you just need to worry about the temperature and concentration. Why not start by using the rate constants you got from the CSTR and model the coil as a plug flow reactor? On the other hand, if you're working with some kind of viscoelastic polymer or a biological reaction, the hydrodynamics become very important and you may want to try and maintain shear forces. In this case, the CSTR and coil will never be similar, since the CSTR has definite regions of high an low shear, whereas the coil will have similar shear forces throughout.

Either way, instead of just trying to find the "right" Reynolds number, try to determine how the change in reactor type affects your reaction and focus on keeping those things as similar as possible. Maybe the diffusion is so great the secondary forces don't even affect mixing... It all depends on the type of reaction you're working with.