A Solute Transport in Stratified Media

Two-dimensional and steady solute transport in a stratified porous formation is analysed under assumption that the effect of pore-scale dispersion is negligible. The longitudinal dispersion produced as a result of the vertical variation of hydraulic conductivity is analysed by averaging the variability of a solute flux concentration and conductivity. The evolution of the solute flux concentration is expressed with respect to the correlated variable, that is the travel (arrival) time at a fixed location and the averaging procedure is constructed to satisfy the boundary condition where the inlet concentration is a known function of time. In such a statement, a velocity-averaged solute flux concentration is described by a conventional dispersion model (CDM) with a dispersion coefficient which is a function of the arrival time. It is demonstrated that such CDM satisfies the assumption that hydraulic conductivity of the layers is gamma distributed with the parameter of distribution which is chosen to represent a reasonable value of the field scale solute dispersion. The overall behaviour of the model is illustrated by several examples of two-dimensional mass transport.     

Unsteady Flow to Wells Partially Penetrating in Two-Layered Aquifers

The unsteady flow of water to well in a layered aquifer with an interlayer flow is examined in this paper. The system studied comprises an aquifer consisting of two productive layers of finite thickness that are in a perfect hydraulic contact and a well which partially penetrates in one of the layers. Each layer is assumed to be homogeneous and isotropic and the water contained in the aquifer is of identical physical properties and small compressibility.The analytical solutions are derived for the case when the system is characterised by equality of hydraulic diffusivity of layers. These solutions give the results accurate enough for practical applications and allow to estimate the effects of partial penetration and contrast in parameters of formation on distribution of the flow potential both at large distances from wells and at the wells.The obtained solutions also provide a basis for predicting the interlayer flow arising from the performance of a pumping well as well as between a pair of wells which have an open interval located in different layers of the aquifer. Two cases have been analysed: (1) a pumping pair of wells which is used to prevent water inflow to the productive well, and (2) a pumping-injection pair of wells providing the demanded mixing of water from adjacent layers. Some examples of flow patterns and specially computed diagrams are given to illustrate the operation of such systems.