New efficient algorithm for solving thermodynamic chemistry

Parameter estimation for reactive transport by a Monte‐Carlo approach

“…3 For nonlinear relations, such as equilibrium chemical equations, their efficiency decreases strongly. It has been well established 4,5 that gradient methods are sometime unable to solve some batch equilibrium problems. For batch equilibrium, nonconvergence of gradient method is due to local minima, flat zone of the error function or infinite loop phenomena.…”

The semismooth Newton method for the solution of reactive transport problems including mineral precipitation-dissolution reactions

“…Since mineral X 7 is not present any more the forward reaction 2X 2 + 1X 7 −→ 1X 4 + 3X 6 can not go on anymore (the backward reaction is still possible). Therefore the concentrations c 4 and c 6 are (possibly) smaller than in dynamic equilibrium.…”

“…For each of these 4 matrices there are 7 3 = 35 submatrices and the same number of determinants. Since the Tracer is not involved in chemical reactions we can reduce this to 6 3 = 20 submatrices (the last row of S 1 min and S 1 mob vanishes). Summarizing all calculations we get The same work has to be done for all other subsetsĴ ⊂ {1, .…”

“…In the computational geoscience community there is a very popular way to solve the PDE-ODE-AE-CC system [3,6]: In the current time step, for each mineral and each discretization point, an assumption is made (usually based on the previous time step) whether saturation or complete dissolution will hold. Through this assumptions the complementary conditions are replaced by AEs.…”

Computing multi-species chemical equilibrium with an algorithm based on the reaction extents

“…In summary, numerical strategies for computing chemical equilibrium problems are classified into two main groups: stoichiometric and non-stoichiometric algorithms (van Baten & Szczepanski, 2011;Blomberg & Koukkari, 2011;Brassard & Bodurtha, 2000;Carrayrou et al, 2002). Stoichiometric algorithms converge on the solution of a set of simultaneous mass balance and mass action equations at each iteration, while non-stoichiometric algorithms aim a direct minimization of the Gibbs energy functions of the chemical species constrained by mass balances.…”