A UNIFIED APPROACH TO STOCHASTIC-CONVECTIVE TRANSPORT PROBLEMS

A stochastic-convective transport process is one in which solute is advected in isolated stream tubes that do not exchange mass during the time of transport. As a field scale model, It has certain advantages compared with a convective-dispersive model formulation, which requires complete mixing of regions with different velocity. Use of a stochastic-convective model formulation has been limited, in part because the theory has not been developed sufficiently to unify the description of initial value and boundary value problems. This study develops the complete theory for a vertically homogeneous soil by creating a stochastic-convective medium made up of stream tubes that do not exchange solute during transport. Each tube has uniform properties within it, but the properties vary from one tube to the next. By creating a field-scale medium made up of an ensemble of such tubes, we were able to derive both solute travel time and travel distance probability density functions (pdfs) for the stochastic-convective problem, thereby producing a consistent description of both the initial value and boundary value problems. With this description, it is possible to perform a single calibration of a travel time or travel distance pdf and use it as the foundation for all subsequent transport modeling. We show that there are two possible formulations of the pdfs, depending on the way in which mass is introduced to the solute transport volume during the time of calibration. After development of the theory, we use three examples to illustrate the application of the principles of stochastic-convective modeling to practical problems of interest in solute transport research.