is a sink/source term that models homogeneous chemical reactions [39], i.e., reactions that solely involve the aqueous phase, as for instance:Two terms appear in Eq. (84) to account for chemical reactions.
The term
is a sink/source term that models homogeneous chemical reactions [39], i.e., reactions that solely involve the aqueous phase, as for instance:
| Ca(aq)2++2OH(aq)−↔Ca(OH)2(s) | (95) |
In most cases, chemical reactions are modeled by assuming that they are faster than ionic transport. A dimensional analysis by Barbarulo et al. [40] showed that this local equilibrium assumption (LEA) is valid in most situations for ionic transport in cementitious materials. Under LEA, chemical reactions are modeled by algebraic mathematical relationships [39]. Following a paper published in 1989 by Yeh and Tripathi [41], the current trend for solving ionic transport problems in reactive materials is to separate the transport and chemical reaction parts. The partial differential equations describing ionic transport are solved with the finite difference or finite element method, whereas a Newton algorithm is used to solve the nonlinear algebraic system of equation associated with the chemical reactions. Depending on the type of chemical reactions involved in a problem, different algorithms can be used to split transport and chemistry, as reviewed in Refs. [42] and [43].
When the local equilibrium assumption is not valid, chemical reactions are modeled with kinetic expressions [39] involving reaction rate. This case arises for problems in groundwater ionic transport where large pressure head gradients can be at the origin of high fluid velocity. Kinetically controlled reaction modeling is discussed in Refs. [44], [45] and [46].