Interval Computing Method for Analyzing Field-Scale Solute Transport

Abstract

The stochastic-convective model of solute transport was analyzed using interval arithmetic. An interval distribution function was developed to facilitate the identification of appropriate intervals to be used in the proposed interval computing method. Results obtained from a field-scale tracer experiment were used for a relative comparison of three methods (interval computing method, Monte Carlo simulations, and stochastic theories) for predicting travel time distributions and field-scale mean solute concentrations. Interval computations yielded results that agreed well with stochastic approaches and predicted general trends of the observed data. The field-scale solute breakthrough curves were well reproduced by the interval computing method; however, the standard deviations of the travel times were slightly overestimated. The interval computing technique was shown to be computationally efficient and may be viewed as an alternative to the use of stochastic differential equations and Monte Carlo simulations. It was further demonstrated that the interval distribution function possesses all the attributes of a membership function, and, therefore, offers an attractive method for combining probabilistic and fuzzy information in a single application.