XVI International Conference on Computational Methods in Water Resources (CMWRXVI) Ingeniørhuset  

Reactive transport models without mathematical solution  Paper   

Author:  Maarten W. Saaltink <maarten.saaltink@upc.edu> (Dep. of Geotechnical Engineering and GeoSciences, Technical University of Catalonia) 
 Jesús Carrera <jesus.carrera@upc.edu> (Dep. of Geotechnical Engineering and GeoSciences, Technical University of Catalonia) 
Presenter:  Maarten W. Saaltink <maarten.saaltink@upc.edu> (Dep. of Geotechnical Engineering and GeoSciences, Technical University of Catalonia) 
Date:
 20060618
Track:
Special Sessions
Session:
MultiDisciplinary Approaches To Reactive Transport Simulation In Aquifer Systems 
DOI:  10.4122/1.1000000434 
DOI:  10.4122/1.1000000435 

It is well known that not all mathematical equations have a mathematical solution.
Also reactive transport models, being actually mathematical equations, may lack a
mathematical solution or may have it only in a domain not applicable to the variable
(for instance, negative concentrations). Obviously such models cannot represent
reality, hence are wrong and should be avoided. Nevertheless, in reactive transport
studies the possibility of nonexistence of a solution is seldom taken into account.
A reason may be that detection of the existence or nonexistence of a solution is far
from obvious, especially for complex models.
We studied the existence of a mathematical solution for a number of types of
reactive transport models. We found that there are rate laws for kinetic reactions
that may lead to models without a solution. Moreover, these are typical rate laws
obtained from laboratory experiments. We also propose modifications to these rate
laws so that they can be applied to reactive transport models without problems. 