Justifying the experimental method for determining the parameters of liquid infiltration in bulk material

Abstract

The object of this study is the process of impregnation of liquid into the bulk material, in particular, into the soil. Determining the impregnation parameters is a relevant task when assessing the consequences of an emergency spill of a hazardous liquid. Infiltration of liquid into the soil leads to pollution of water resources. However, the greatest danger is the ignition of the spill of a combustible liquid. Based on the Green-Ampt model, a mathematical description of the impregnation of liquid into bulk material was built. It is a system of two ordinary differential equations of the first order, one of which describes the reduction of the thickness of the liquid layer on the surface, and the other describes the dynamics of the impregnation of liquid into depth. The solution to the system was derived in the form of time dependence on the depth of impregnation. An experimental study was conducted on the example of impregnation of crude oil in the sand. To this end, sand was poured into a vertical measuring glass cylinder. After that, the liquid was poured and a video recording of the impregnation process was carried out. By processing the video recording, the depth of impregnation and the corresponding time were determined. The results of the study show that the relationship between the thickness of the liquid layer on the surface of the sand and the depth of impregnation is linear in nature: the relative deviation of linear approximation from experimental data does not exceed 3.5. By expanding the logarithmic function contained in the solution to the system of differential equations into the Taylor series, a polynomial dependence of time on the depth of impregnation was established. To determine the coefficients of the polynomial based on the experimental data, the least squares method was used. In this case, the approximation error after the first minute after spilling does not exceed 10 %. The proposed method could be used to account for seepage in the model of liquid spreading on the ground and the burning model of a flammable liquid spill