Mathematical modeling of oil leakage dynamics from a pipeline into a po-rous medium considering soil filtration resistance
DOI:
https://doi.org/10.31471/2304-7399-2026-22(83)-222-233Keywords:
mathematical modeling, unsteady filtration, oil leakage, pipeline, porous medium, filtration resistance, piezoconductivity coefficient, Green’s function.Abstract
The paper addresses the problem of mathematical modeling of oil leakage dynamics from a main pipeline into a porous soil medium, taking into account filtration resistance. The relevance of the study is driven by the need to improve the accuracy of predicting the extent of contamination caused by emergency pipeline failures. The aim of the research is to develop an analytical model of unsteady filtration and to determine the influence of filtration back-pressure on the leakage rate. The governing equation is formulated in terms of excess pressure using the piezoconductivity coefficient, which ensures dimensional consistency of all terms.
To solve the problem, integral transform methods, namely the Laplace and Fourier transforms, are applied, resulting in an analytical solution in the form of a Green’s function for a half-space with a point source. To account for the nonlinear feedback effect of filtration back-pressure on the leakage rate, an iterative algorithm is proposed that ensures consistency between the pressure field dynamics and the source intensity. A comparative analysis for soils with different filtration properties demonstrates a significant dependence of the transient phase duration on the piezoconductivity of the medium.
The obtained results can be used to estimate oil loss volumes, predict the spread of contamination, and support engineering decision-making in the mitigation of emergency leakage events.
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