TRANSPORT AND RETENTION IN FRACTURED ROCK - CONSEQUENCES OF A POWER-LAW DISTRIBUTION FOR FRACTURE LENGTHS

A probabilistic model for the transport of a reacting species in fract ured rock is presented. Particles are transported by advection through a series of n rock fractures, and also diffuse and react chemically i n the surrounding porous medium. The fracture attributes are unobserve d with predefined statistical distribution. The time of arrival t(phi) of a given fraction phi of an initial solute pulse, a key quantity us ed in a variety of applications, is related to the statistics for frac ture apertures and lengths. A classification scheme is developed for t he large n asymptotics of t(phi). The expected value and variance of t (phi) are available explicitly if the aperture and length distribution have finite variance. The expected t(phi) is infinite, and its probab ility distribution is related to asymmetrical Levy distributions in th e case of a power-law distribution for lengths. The most probable time of arrival is proposed as a robust alternative to the expected value. A scaling transition in the most probable t(phi) versus n is found as the power-law exponent changes. These results suggest that risks asso ciated with migrating contaminants may be misrepresented by convention al stochastic analyses.