On the distribution of multicomponent mixtures over generalized exposure time in subsurface flow and reactive transport: Foundations, and formulations for groundwater age, chemical heterogeneity, and biodegradation

The fate of materials undergoing transport and reactions in natural porous media sometimes depends on the time of exposure of the conveyed material to other materials present in the system. The distribution of groundwater age , the effects of mineral chemical heterogeneity on reactive solute transpor t, and the occurrence of lag in reaction systems are some areas of hydrogeo logy that involve exposure time in an important way. A general balance equa tion for accounting for such effects is provided through an extended transp ort operator that incorporates generalized exposure time as an additional i ndependent coordinate. Evolution of material distributions over exposure ti me appears within this transport operator as a convective process that repr esents space- and time-dependent generalized exposure of material constitue nts undergoing physical transport and nonequilibrium chemical and microbiol ogical mass transformations. The general equation is derived from basic mas s balance arguments by treating the constituents as a mixture of overlappin g continue and developing evolution equations for the mixture material dens ities in the new dimensions of space, time, and exposure time. Example appl ications of the approach to each of the three examples above are described.