Radioactive chain decay
Is it possible to simulate radioactive chain decay (i.e parents produce daughter elements) in TOUGHREACT?
It is more complicated than the simple decay equation, as it needs to generate other species based on the decayed amount. The governing equation is Bateman equation. https://en.wikipedia.org/wiki/Bateman_equation
Yes, radioactive decay chains in the aqueous phase can be modeled using the "Aqueous Kinetics" option in chemical.inp. I've attached an example of 226Ra going to 222Rn. An entire decay chain could be simulated by starting with 238U. Note that the concentrations of some isotopes can be extremely small so chemical tolerances may have to be set smaller (tolch <= 1e-8).
1 ! Total number of kinetic aqueous reactions
2 -1.0 ra+2 1.0 rn(aq) ! Consumption: negative; production positive
1 1 ! rate model index, No.mechanism
1.37195E-11 ! decay constant (mol/kg water/s), Ra-226 decay to Rn-222 half-life = 1601 yrs
1 ra+2 2 1.0 ! species in product term
I would remind that if one is interested to an isotope decay chain only, but not to model water-rock equilibria with TOUGHREACT, a generic isotope decay chain or even multiple chains could be in principle simulated using TMVOCBio (Battistelli, 2004; Jung and Battistelli, 2017).
It's enough to set at a very large value the half saturation constant in the Monod equation to obtain a first order rate. Then using the stoichiometric coefficients of simulated degradation reaction (parent decay), the generation of the daughter can be simulated.
TMVOCBio allows to simulate not only VOCs and NCGs mixtures, but also dissolved solids (in trace amounts). VOCs, NCGs and dissolved solids can be all subject to degradation, or in this case to decay.
A possible limitation is that TMVOCBio assumes that only the component's fraction dissolved in the aqueous phase is directly degraded.
Hi Alfredo and Eric,
Thanks for your replies.
What you proposed seems to represent dc/dt = k, which is the zero order decay - while the decay indeed is first order. What came to my mind was to use the Monod equation (as in TMVOCBio), with KS being a large value and noticed that Alfredo has also came to the same conclusion. I tested my approach versus Hydrus and also the Bateman analytical solution for decay chains and seems it works