Numerical Solutions for Diagenetic Models

The previous section demonstrated that the analytical solutions of Pick s Second Law of Diffusion can only be applied to a very limited number of cases. Frequently, highly simplified boundary conditions have to be assumed which actually cannot be found in a natural environment. Additionally, the effort is almost always limited to merely one component dissolved in pore water, or to its behavior in space and/or time. Any complex relations between the numerous dissolved components, or even concentrations of complexes and ion pairs which become variable due to reaction sequences, or accordingly taking into account the difference between concentrations and activities, all are simply not regarded in the mathematical 

The solution to this problem consists in the application of numerical solutions when diagenetic processes are modeled. Such numerical solutions always divide the continuum of reaction space and reaction time into discrete cells and discrete time intervals. If one divides up the continuum of space and time to a sufficient degree into discrete cells and time steps (which is not the decisive problem with the possibilities given by today s computers), one will be able to apply much simpler and better manageable conditions within the corresponding cells, and with regard to the expansion of a time interval, so that, in their entirety, they still will describe a complex system. Thus, it is possible, for example, to apply the two-step-procedure (Schulz and Reardon 1983), in which the individual observation of physical transport (advection, dispersion, diffusion) or any geochemical multiple component reaction is made feasible within one interval of time. 

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