Robust and fast FORTRAN and MATLAB (R) libraries to calculate pH distributions in marine systems
Three "easy-to-use solvers are presented for the approximation of pH acid the concentrations of protolytic species in marine aqueous systems. The first one is based on the conservation of alkalinity, the second one describes the progress (advancement) of a chemical reaction towards its state of equilibrium. and the third one is based on the conservation of the charges in the system (charge balance). They are developed for steady state or nun-steady state modelling, but they are also useful for pH calculations from measured data sets. To demonstrate their numerical stability over a wide range of pH, the solvers are tested with random input values. Internal consistency is checked by mass and charge conservation and by comparing the results of each solver. In closed systems, equilibrium calculations lead to identical pH values and species concentrations, as expected. The three approaches are also tested in a non-steady-state transport-reaction model that simulates early diagenesis in oxic deep-sea sediments as well as in reactive sediments from the deep Arabian Sea. In the model, dissolved carbonate species are either transported as individual species (CO2, HCO3-, CO32-) or as summed variables (TCO2, alkalinity). In the first case, the species are transported according to their individual molecular diffusion coefficients and concentration gradients. In the second case, protolytic species are transported along the gradient of summed concentrations using weighted overage diffusion coefficients. The advancement approach is coupled with transport of the individual species, whereas the alkalinity conservation and the charge balance approaches are applied to transport of summed variables. The model results show that the approaches lead to non-negligible differences in the species distribution and the pH. With intensive calcium carbonate dissolution, the thermodynamically-controlled dissolution rates dominate the system: in this case, the differences in the species distribution between the three solvers and the two transport schemes can be neglected, but strong differences in the calculated fluxes between sediment and bottom water can be observed. (C) 2001 Elsevier Science Ltd. All rights reserved.
ph calculation transport-reaction model thermodynamic equilibrium calculation transport in porous media