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The similarity solution of the longitudinal dispersion phenomenon of miscible fluids in porous media

The longitudinal dispersion phenomenon of miscible fluids in porous media is discussed by regarding the cross- sectional flow velocity as time dependent in a specific form. The mathematical formulation of the phenomenon yields a non-linear partial differential equation. This partial differential equation is transformed into ordinary differential equation by using infinitesimal transformations group technique of similarity analysis. An analytical solution of the later is derived in terms of error function.The solution obtained is physically consistent with the results of earlier re- searchers and which is also more classical than other results obtained by various researchers.This type of phenomenon has been of great concern to hydrologists who have been studying the problem of displacement of fresh water by sea water in coastal areas. The oil industry has also become involved in miscible displacement studies in connection with the possibility of flushing oil by solvents from reservoirs.