Numerical solutions for 2-D dispersion with variable inputs through porous media

Analytical Solutions for Hydrodynamic dispersion in aquifers involve numerous simplifying assumptions seldom realised in practice. Various numerical techniques are being developed to improve the dispersion modeling. Hitherto the studies have been generally limited to steady continuous inputs of pollutants, while variable inputs are more common in field cases. In the present study, an attempt has been made to develop numerical solutions incorporating some variable input conditions for better relevance to field conditions. The algorithms for the numerical solutions have been developed for Bar diagram and Sine wave variable inputs. A 2-D experimental setup has been fabricated for generating the experimental results and to verify the numerical models developed in this work. Experimental results have been generated for conservative pollutant with steady and Bar diagram inputs in a laboratory setup. An attenuation factor has been defined to model the relative fluctuations of the output concentration profiles, corresponding to those of varying inputs. Multiple regressions have been fitted to obtain the functional relationships of the attenuation factors with the physical parameters, namely U(average pore velocity), X(axial distance from pollutant input point), P(periodicity of varying pollutant) and alpha x (longitudinal dispersivity). Nonlinear models have been found to be superior, when compared with the corresponding numerical solutions. The numerical solutions developed in this work are in good agreement with the corresponding experimental concentration profiles, at 99.5% probability level of the chi-square test. Attenuation factor has the maximum influence on U. The factor decreases with U and P, and increases with X and alpha x.