A Mathematical Model for Dispersion in the Direction Of Flow in Porous Media

Abstract

A three-parameter mathematical model for onedimensional flow in porous media is developed. The objective of the model is to predict accurately the longitudinal dispersion associated with the flow of either ga-'!!s or liquids over a wide range of Reynolds number.A qualitative analysis of the model parameters is given. Published experimental pulse-response curves are compared with results predicted by the model. Several general types of problems are given for which the model can be used.

A dual‐domain mass transfer approach for modeling solute transport in heterogeneous aquifers: Application to the Macrodispersion Experiment (MADE) site

“…The hydraulic conductivity interpolation algorithm of ordinary kriging generates a unique hydraulic conductivity field, preserves local accuracy near data points but smoothens data in areas of sparse sampling, and provides no measure of uncertainty. Stochastic geostatistical simulation generates alternative, equally probable realizations, retains heterogeneities and large spatial variability, and provides variance as a measure of uncertainty [Deutsch and Journel, 1998]. For this study, more of the observed plume characteristics are preserved when the hydraulic conductivity field is generated using fBm as a conditional geostatistical simulator.…”

“…Measured hydraulic conductivity distributions need to be incorporated into models by assigning a different hydraulic conductivity value to each model node using interpolation. Interpolation methods, such as the method of ordinary kriging used for simulation 1, generate a unique hydraulic conductivity field and only preserve local accuracy near data points while smoothing data in areas of sparse sampling [Deutsch and Journel, 1998]. Second, even with a more sophisticated hydraulic conductivity generation methodology, it may still be impossible to achieve a sufficiently accurate representation of the true hydraulic conductivity vari- By simulating a mobile and immobile domain, the dualdomain mass transfer model allows for advective transport to occur in the mobile region at velocities increased inversely proportional to the ratio of mobile/immobile porosities thus providing a mechanism for rapid spreading of a certain amount of mass downstream while retaining a bulk of mass near the source area.…”

Simulating solute transport in an aggregated soil with the dual-porosity model: measured and optimized parameter values

“…aggregates, macropores) can cause non-ideal transport of solutes, as exemplified by asymmetrical breakthrough curves and 'preferential' transport. Several mathematical models have been developed to simulate solute transport in structured systems, the most widely used being the first-order, dualporosity model developed by Deans (1963) and Coats and Smith (1964), and extended to sorbing solute by Van Genuchten and Wierenga (1976).…”

Absorption-Delay Models of Heat Transport

“…W. Munk [13] made similar observations through a different argument. Also see [6] for a related application to the flow of a concentration pulse in a porous medium.…”

“…Solutions are compared to those given in [15]. (See [6] and [10] for corresponding problems of a concentration pulse in a porous medium flow. )…”