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

Abstract

Abstract. 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 continua 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. IntroductionThe fate of materials undergoing transport in porous media sometimes depends on the time of exposure of the conveyed material to other materials present in the system. Such dependency appears in diverse ways, three of which are introduced here as example phenomena that will be analyzed in this article. In the case where the conveyed material is the water itself and the other material is the aquifer solid phase, the exposure time is the groundwater age [e.g., Goode, 1996; Varni and Cartera, 1998]. This quantity is important in recharge source

Processes in Microbial Transport in the Natural Subsurface

“…This limitation is noted in Johnson et al [61] who provide a heuristic accounting of the effects of residence time on reversibility by zeroing the detachment rate for microbes whose residence time exceeds a particular threshold. A new theoretical approach allows the tracking of residence time effects on arbitrary reaction terms [153]. This approach supports both variable methods of accounting of residence time (e.g., cumulative vs. contiguous) as well as arbitrary specification of the effect of residence time on the overall partitioning kinetics.…”

“…For example, the process of metabolic lag [131,153] may be experimentally indistinguishable from a substrate diffusion limitation through a biofilm. Both processes result in a delay in the onset of degradation, and the correct labeling of the process may or may not have an effect on the ultimate amount of contaminant degraded.…”

“…Tan et al [120], Lindqvuist et al [69], and Saiers and Hornberger [105] all introduce the classical site-saturation limiting factor on the attachment rate coefficient, in order to account for potential depletion of available surface sites as attached microbe densities increase, which may occur when aqueous microbes cannot attach to attached microbes. Ginn [43] modeled non-Markovian (i.e., residence-time dependent) attachment/detachment kinetics apparent in experiments of McCaulou et al [165] using the exposure-time approach of Ginn [153], as described below.…”

“…In [153] a reformulation of the conventional fate and transport mass balance (our Eq. (7)) is developed that allows distributions of solutes such as biomass over space x and time t, and generalized exposure-time (here residence time) x on surfaces, so that C mm is C mm ðx; t; xÞ.…”

Partial ages: diagnosing transport processes by means of multiple clocks

“…The full Eulerian description of the age field requires the introduction of a distribution of the ages of these particles. The appropriate framework is therefore five-dimensional, i.e., space × time × age (Bolin and Rodhe 1973;Hall and Plumb 1994;Delhez et al 1999;Ginn 1999;Haine and Hall 2002). While special techniques can be used to work in this five-dimensional space Cornaton 2012), this complexity is avoided in most Eulerian studies by resorting to the steady state hypothesis (e.g., Holzer and Hall 2000;Khatiwala et al 2009) or by considering only the mean value of the ages of the particles in a water parcel.…”