## Mathematical modelling of oil infiltration into soil for Assessment of undersurface water pollution

We have applied mathematical models describing oil penetration into soils as a result of accidents on railway and pipeline routes in the general case and for special conditions taking into account the specific properties of several types of soils found along the routes (Davitashvili and Komurjishvili, 2002; Davitashvili, 2004). The calculations were made for meadow-alluvial, sandy and sub-sandy soils. Numerical calculations were carried out during 180 days. Numerical calculations have shown that the process of oil filtration into soils from the pits varied for different period of the numerical integration. In particular, it was possible to distinguish three stages during the numerical calculations.

The first stage contained intensive processes of oil evaporation and oil filtration in the soil. This process continued for about 1.8 days until the ground surface was clear of the spilled oil, with the exception of the pit areas. For the first stage, the distribution of oil in the soil was almost the same both in the vertical and in the horizontal directions. Although we can note that oil penetration in the soil in the vertical direction was more intensive than in the horizontal direction in the areas around the lower border of the pit. During the second stage, two processes occurred: oil filtration and evaporation from the soil, and oil infiltration into the soil from the areas around the pit, until the pit was clear of the spilled oil. Numerical calculations have shown that this stage continued about 31 days. The second stage was mainly characterized by oil propagation into the soil from the edges of the pits, but we note that during the second stage we have used non-stationary boundary conditions at the lateral borders of the pit, taking into account oil filtration and evaporation processes simultaneously, until the pit clearing process was accomplished. Numerical calculations have shown that the pit clearing process was accomplished in 31 days and the maximum depth of oil penetration in soil reached 2.1 m. The third stage of oil infiltration into soil was less intensive than the first and second stages. We have kept the process of oil infiltration into the soil under our observation until the velocity of the front of oil distribution into the soil was infinitesimal, i.e. until the process became almost stable. Numerical calculations have shown that the third stage continued about 147 days. We note that this process in the vertical direction was more intensive than in the horizontal direction and in

180 days the line of the front of oil distribution in the soil was not very well distinguished, but had a sinusoidal character. The maximum depth of the front of oil distribution in the soil was observed on the depth 3.9 m, almost along the symmetric axes of the pit, and the maximum distance of oil penetration in the horizontal direction were observed to be about 2.8 m from the symmetric axes of the pit for the meadow-alluvial soils.

As underground water in flat areas adjacent to the River Kura with pseudo-clay, sandy and marshy wet soils comes close to the surface about 3-4 m below surface in East Georgia, and underground water comes close to the surface about 2-3 m below surface in hilly regions and about 1 m below in the flat areas in West Georgia, so possibility of underground water pollution owing to accidents along oil pipeline and railway routes is high.

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