ONE-DIMENSIONAL SOLUTION OF THE TRANSPORT-EQUATION IN POROUS-MEDIA INTRANSIENT STATE BY A NEW NUMERICAL-METHOD FOR THE MANAGEMENT OF PARTICLE TRACK

For the last fifteen years or so, the random-walk methods have proved their worth in solving the transport equation in porous and fractured media. Their principal shortcomings remain their relatively slow calcu lation speed and their lack of precision at low concentrations. This p aper proposes a new code which eliminates these disadvantages by manag ing the particles not individually but in the form of numerical values (representing the number of particles in each phase, mobile and immob ile) assigned to each cell in a 1-D system. The calculation time then is short, and it is possible to introduce as many particles as desired into the model without increasing the calculation time. A large numbe r of injection types can be simulated, and to the classical convection -dispersion phenomenon can be added a process of exchange between the mobile and immobile phase according to first-order kinetics. Because t he particles are managed as numbers, the analytical solution obtained for the exchange during a time step reduces the calculation to a simpl e assignation of numerical values to two variables, one of which repre sents the mobile and the other the immobile phase; the calculation is then almost instantaneous. Because the program is developed in C, it l eaves much room for graphic interaction which greatly facilitates the fitting of tracer experiments with a limited set of parameters.