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 transport, and the occurrence of lag in reaction systems are some areas of hydrogeology that involve exposure time in an important way. A general balance equation for accounting for such effects is provided through an extended transport operator that incorporates generalized exposure time as an additional independent coordinate. Evolution of material distributions over exposure time appears within this transport operator as a convective process that represents space- and time-dependent generalized exposure of material constituents undergoing physical transport and nonequilibrium chemical and microbiological mass transformations. The general equation is derived from basic mass balance arguments by treating the constituents as a mixture of overlapping continue and developing evolution equations for the mixture material densities in the new dimensions of space, time, and exposure time. Example applications of the approach to each of the three examples above are described.