In the modern age of sustainability, computational studies have become key players in the optimal protection of the environment. In particular, mathematical models that describe the dynamic behavior of complex seepage processes play a crucial role in “protecting underground waters from pollution by toxic substances”--the salty waste products of the mining or chemical industry--“contained in surface sewage (sludge and tailing) ponds.” Protecting underground water is an issue of universal importance because of the decreasing levels of drinking water worldwide.

In this paper, Bulavatsky introduces a novel mathematical model of “the dynamics of the nonisothermal seepage of salt solutions in a geoporous medium under strong time nonlocality.” The consideration of “the dynamics of locally nonequilibrium seepage processes” clearly sets this model apart from its forerunners. The model is based on an accurate nonlinear system of fractional equations for the local pressure, the salt concentration in the liquid, and the temperature, with appropriate boundary conditions.

In addition to a comprehensive introduction to the model, the author suggests a highly appreciated numerical approach for deriving solutions to the boundary-value problem, which dramatically increases the value of the paper. However, the weak presentation of the numerical results and the lack of geophysical interpretations may frustrate the reader’s expectations and consign the paper to the category of great methodological papers, which is far below the potential of this study. Therefore, I strongly recommend it to experts in geophysics or other relevant fields.