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February 8, 2012 11:51am UTC

Time-step dependent reaction rates

Hi,

Help me how to set a "time-step" dependent "reaction-rate constant" for a time-dependent solver.

Regards,

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February 8, 2012 9:23pm UTC in response to Francois Gregoire

Re: Time-step dependent reaction rates

Hi,
Thanks for your guidance. I run number of simulations for two species; one with initial concentration of 10mol/m3 and the other with 0mol/m3 in reaction engineering(re) interface. I tried different relationships between reaction rate constant(k) and the timestep. Below are some of the results of simulations;

a) Simulation works if k=1/sqrt(timestep)[s^2], one specie is converted completely into the other in 0.4s but thereafter is seen the convergence problem(very slow simulation).

b) For a timestep=0.01s(just an example) simulation does not work for reaction rate (k) greater than nearly 16 (1/timestep^0.6=15.8489). Although at this value of k one species is converted into the other in about 0.0025s but there is seen the convergence problem as the timestep becomes constant with convergence around 3.6e5 and thus the simulation becomes very slow. For lower values of k the simulation works faster but with slow rate of conversion from one specie to the other.

c) For k=0.1*timestep[1/s], the reaction (conversion) is slower but the simulation is relatively faster. Convergence touches to about 6.9 (becomes flat after about 3500 iterations= about 200s) and conversion of one specie to the other is about 90% in 200s.

d) For k=0.01*timestep[1/s], the reaction (conversion) is further slower but the simulation is relatively faster. Convergence touches to about 2.2 (becomes flat after about 3500 iterations= about 600s) and conversion of one specie to the other is about 100% at 1400s.

e) For k=0.001*timestep[1/s], the reaction (conversion) is further slower but the simulation is relatively faster. Convergence touches to about 0.71 (becomes flat after about 3500 iterations= about 1700s) and conversion of one specie to the other is about 80% at 1700s.

f) For k=0.0001*timestep[1/s], the reaction (conversion) is further slower but the simulation is relatively faster. Convergence touches to about 0.21 (becomes flat after about 3500 iterations= about 5800s) and conversion of one specie to the other is about 70% at 5800s.

g) For k=0.00001*timestep[1/s], the reaction (conversion) is further slower but the simulation is relatively faster. Convergence touches to about 0.070 (becomes flat after about 3500 iterations= about 1.6e4s) and conversion of one specie to the other is about 70% at 1.6e4s.

FINDINGS: Linking reaction rate with timestep seems not beneficial as it slows down the simulation very badly if we want rapid conversion (fast reaction rate).

QUESTIONS:

i) I am studying flow and transport of species in dissolved form in a vertical column.

Initial conditions:Initial concentration values of both the species is zero in the column.

Boundary Conditions:One of the species(sepcie 1) is given saturation concentration at the inlet(bottom boundary) and the other(specie2) is given as 0mol/m3 at the inlet (bottom boundary).

Saturation value of specie 1 depends on the column height and therefore during the flow in the column the rising concentration from bottom of specie 1 exceeds the saturation concentration level for the specific height. The difference of concentration (dissolved concentration-saturation concentration) needs to be converted immediately into specie 2 as soon as this difference arises.

What is specific advice about setting up this conversion reaction.

ii) What type of solvers are helpful for reaction simulations.

Best Regads,

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February 11, 2012 10:58am UTC in response to Francois Gregoire

Re: Time-step dependent reaction rates

Dear Francois Gregoire

Thanks for your guidance.

Regards

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