Transport of Cryptosporidium parvum in porous media:: Long-term elution experiments and continuous time random walk filtration modeling

Complex transport behavior other than advection-dispersion, simple retardation, and first-order removal has been observed in many biocolloid transport experiments in porous media. Such nonideal transport behavior is particularly evident in the late time elution of biocolloids at low concentrations. Here we present a series of saturated column experiments that were designed to measure the breakthrough and long-term elution of Cryptosporidium parvum in medium sand for a few thousand pore volumes after the initial source of oocysts was removed. For a wide range of ionic strengths, I, we consistently observe slower-than-Fickian, power law tailing. The slope of the tail is flatter for higher I. At very high ionic strength the slope decays to a rate slower than t(-1). To explain this behavior, we propose a new filtration model based on the continuous time random walk (CTRW) theory. Our theory upscales heterogeneities at both the pore-scale geometry of the flow field and the grain surface physicochemical properties that affect biocolloid attachment and detachment. Pore-scale heterogeneities in fluid flow are shown to control the breakthrough of a conservative tracer but are shown to have negligible effect on oocyst transport. In our experiments, C. parvum transport is dominated by the effects of physicochemical heterogeneities. The CTRW model provides a parsimonious theory of nonreactive and reactive transport. The CTRW filtration process is controlled by three parameters, Lambda, beta, and c, which are related to the overall breakthrough retardation (R = 1 + Lambda), the slope of the power law tail (beta), and the transition to a slower than t(-1) decay (c).