REMARKS ON NUMERICAL AND ANALYTICAL METHODS TO CALCULATE DIFFUSION INWATER-SEDIMENT SYSTEMS

Diffusion plays an important role in the exchange processes between la ke sediments and the overlying water. Compounds entering the sediments usually have to penetrate through a certain mud thickness, where a re action may then occur, while compounds being released have to diffuse through the interstitial water before escaping into the lake water. In this article mathematical functions are given which describe certain cases. They are all based on the differential diffusion equation of Fi ck, but for different boundary conditions different mathematical solut ions of partial differential equations are needed. Four of these are p resented in this paper, covering the cases of a compound diffusing int o the sediments, with or without a chemical reaction occurring in the sediments, combined with either a constant or a non-constant concentra tion in the water. Furthermore a numerical approach is proposed in whi ch the calculations are made by an iteration process over time and spa ce. The results are presented as a series of concentrations as a funct ion of time and depth in the sediment layer. It is shown in the first place that the time and the space steps must be sufficient small in ag reement with the dimensions and time scale of the processes studied in order to obtain a satisfactory precision. The results can be fitted t o a simplified exponential equation of the form (A . e(-alpha . tb) - B), which can be used for a quick assessment of special cases. a depen ds on porosity, ratio between water and mud height; b approximate to 0 .667. Furthermore this equation can be used to extrapolate from labora tory experiments with the sediments of a specific lake to results vali d for the lake itself. The numerical model has also been used to descr ibe the backward diffusion of an eventual product of a chemical reacti on, which will diffuse further downward, but also upward. This is e.g. the case for the N2O production during denitrification experiments wh en acetylene is applied as an inhibitor. Finally, the application of s o called peepers and benthic chambers is discussed, while many of thei r disadvantages are explained.