A UNIFIED APPROACH TO STOCHASTIC-CONVECTIVE TRANSPORT PROBLEMS

A stochastic-convective transport process is one in which solute is ad vected in isolated stream tubes that do not exchange mass during the t ime of transport. As a field scale model, It has certain advantages co mpared with a convective-dispersive model formulation, which requires complete mixing of regions with different velocity. Use of a stochasti c-convective model formulation has been limited, in part because the t heory has not been developed sufficiently to unify the description of initial value and boundary value problems. This study develops the com plete theory for a vertically homogeneous soil by creating a stochasti c-convective medium made up of stream tubes that do not exchange solut e during transport. Each tube has uniform properties within it, but th e 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 b oth solute travel time and travel distance probability density functio ns (pdfs) for the stochastic-convective problem, thereby producing a c onsistent description of both the initial value and boundary value pro blems. With this description, it is possible to perform a single calib ration of a travel time or travel distance pdf and use it as the found ation for all subsequent transport modeling. We show that there are tw o possible formulations of the pdfs, depending on the way in which mas s is introduced to the solute transport volume during the time of cali bration. After development of the theory, we use three examples to ill ustrate the application of the principles of stochastic-convective mod eling to practical problems of interest in solute transport research.