Analytical Solution of Mass Transport Equations

The analytical solution is possible only for the simplest cases. Usually it is accomplished in two stages. First, the hydrodynamic part of the problem for the determination of the field of rate and flow vectors is solved. 

Then the hydrogeochemical part for the distribution of individual components dissolved in ground water is solved. The analytical solution of mass transport problems includes the introduction of edge and initial conditions of the hydrochemical object and selection of advection-dispersion mass transport equations matching the assigned conditions and mathematical solution of the equation themselves. 

Edge conditions. At the base of an analytical solution lies reviewed above advective-dispersive mass transport equation. For its solution it is necessary to have boundary and initial conditions, i.e., conditions at which the process begins, operates and ends. 

Boundary conditions define the mass transport nature through object s boundaries in coordinates x, y, z for the entire studied period t. 

The first type of boundary conditions (or Dirichlet type) is set by the concentration values at the boundaries  

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