industrial waste, mathematical modelling, depth and level of soil salinity.


Purpose. The goal of the article is to develop a method for identifying hazards and predicting the possibility of a technogenic emergency caused by the spread of compounds with heavy metals in the soil during long-term storage of galvanic sludge in open areas.

Methodology. The method is developed on the basis of a mathematical model that allows estimating changes in the depth of distribution and level of soil salinity over time using initial information about soil structure and its characteristics (molecular diffusion coefficient, volume humidity), annual volumes and conditions of sludge storage in the enterprise. Restrictions are set: the presence of harmful substances on the soil surface with a concentration that exceeds the permissible level; inadmissibility of harmful substances to aquifers.

Results. The practical use of the method made it possible to identify the main dangers and predict the possibility of an emergency situation with negative environmental consequences during long-term storage of galvanic waste in open areas. The dynamics of soil salinity levels and the depth of penetration of heavy metals increase over twenty years of conservation has been determined, as well as the possibility of hazardous compounds entering groundwater has been assessed.

Originality. The non-linear, non-stationary mathematical model is based on the theory of physico-chemical hydrodynamics of cellular media. The process of motion of metal salts has been described by the differential equation of motion and conservation of mass of matter for vertical mass transfer of matter.

Practical value. Formalization of information about the hazards arising during the storage of industrial waste with chemically active elements allows to consider the subject area as a complex dynamic system consisting of objects of different nature, the totality of which determines the level of danger of emergencies with environmental consequences. The developed method makes it possible to transfer the obtained results to decision-making support systems, predicting possible consequences and material costs associated with post-emergency measures, motivating the management to take measures in advance.


Directive 2000/60/EC of the European Parliament and of the Council of 23 October 2000 establishing a framework for Community action in the field of water policy. Official Journal of the European Communities. L. 327, vol.43, 22.12.2000. 72 p.

On Decision of the National Security and Defence Council of Ukraine of 19 March 2021 "On Measures to Improve Chemical Safety on the Territory of Ukraine". Decree of the President of Ukraine № 104/2021. [Online]. Available:

National report on the state of the environment in Ukraine in 2020. [Online]. Available:

Polevoy A.M., Gutsal A.I., Dronova O.A. Soil Science: textbook. Odessa: Ecology, 2013.

National report on the state of the environment in Ukraine in 2018, 2019. [Online]. Available:

Report on the main results of the State Emergency Service of Ukraine in 2019. [Online]. Available:

Loboichenko, V. Development of a hazard identification procedure for low-tonnage chemical production facilities. Problems of emergencies, No 2(30), pp. 176-186, 2019.

Adamu C.I., Nganje T.N., Edet A. (2014). Heavy Metal Contamination and Health Risk Assessment Associated with Abandoned Barite Mines in Cross River State, Southeastern Nigeria. Journal of Environmental Nanotechnology, Monitoring & Management, 3, pp. 10-21, 2014

Toxicological Profile for Lead. The Agency for Toxic Substances and Disease Registry (ATSDR). 2020. [Online]. Available::

Ali H. Khan E. Trophic Transfer, Bioaccumulation and Biomagnification of Non-Essential Hazardous Heavy Metals and Metalloids in Food Chains. Concepts and Implications for Wildlife and Human Health. Human and Ecological Risk Assessment, 25, pp. 1353-1376, 2018. URL:

Chen Y., Yuan L., Xu C. The Accumulation Characteristics and Potential Health Risks of Heavy Metals in Vegetables from Reclaimed Area of China. Human and Ecological Risk Assessment: An International Journal, 24, pp. 949-960, 2018. URL:

Khan K., Khan H., Lu Y., Ihsanullah I., Nawab J. Evaluation of Toxicological Risk of Foodstuffs Contaminated with Heavy Metals in Swat, Pakistan. Ecotoxicology and Environmental Safety, 108, pp. 224-232, 2014. URL:

Kornelyuk N.M., Khomenko O.M. Bioaccumulation of heavy metals by the urban trees around Cherkassy thermal power plant. Ukrainian Journal of Ecology, 8(1), pp. 953–960, 2018. doi: 10.15421/2018_298.

Ayantobo O.O., Awomeso J.A., Oluwasanya G.O., Bada B. S., Taiwo A. M. Non-Cancer Human Health Risk Assessment from Exposure to Heavy Metals in Surface and Groundwater in Igun-Ijesha, Southwest, Nigeria. American Journal of Environmental Sciences, 10, pp. 301-311, 2014. URL:

Lemos D.H., Camargo C.A., Camargo M.A., Landgraf M.D. Evaluation on the Concentration of Heavy Metals in Surface Waters in the Municipality of Pratápolis-MG. Open Access Library Journal, 6(5), pp. 1–12. 2019. doi: 10.4236/oalib.1105427.

Al-Musharafi S.K , Mahmoud I. Y., Al-Bahry S. N. Environmental Contamination by Industrial Effluents and Sludge Relative to Heavy Metals. Journal of Geoscience and Environment Protection, Vol. 2, No. 2, pp. 22-28, 2014. doi: 10.4236/gep.2014.22003.

Children's health and the environment in Europe: a baseline assessment. European Environment and Health Information System (ENHIS). 2007. Fact Sheet No. 4.4. CODE. RPG4_Food_EXI, World Health Organization. [Online]. Available:

Baseline Human Health Risk Assessment. US Environmental Protection Agency (USEPA). 2001. Vasquez Boulevard and 1-70 Superfund Site, Denver. [Online]. Available:

Zarazúa G., Girón-Romero K., Tejeda S., Carreño-De León C., Ávila-Pérez P. Total Reflection X-Ray Fluorescence Analysis of Toxic Metals in Fish Tissues. American Journal of Analytical Chemistry, 5 (12). pp. 806–811, 2014. doi: 10.4236/ajac.2014.512089

Rumana S, Nazimah M, Bader-Un-Nisa. Vulnerability of Sunflower Germination and Metal Translocation under Heavy Metals Contamination. American Journal of Plant Sciences, Vol. 10, No. 5, 2019. doi: 10.4236/ajps.2019.105054.

Nester A.A., Nikitin O.O., Romanishina O.V., Mitiuk L.O., Polukarov Yu.O. Achieving environmental security with economic impact. Journal of Naukovyi Visnyk Natsionalnoho Hirnychoho Universytetu, No 6. pp. 115–120, 2020. URL:

Zhongchen H., Jianwu Li, Hailong W., Zhengqian Ye, Xudong W., Yongfu Li, Dan L., Zhaoliang S. Soil Contamination with Heavy Metals and Its Impact on Food Security in China. Journal of Geoscience and Environment Protection, Vol. 7, No. 5, 2019. doi: 10.4236/gep.2019.75015

Myslyuk О., Khomenko О., Yehorova О. Ecological assessment for the acid-base properties of urban soils in cherkasy city. Bulletin of Kremenchuk Mykhailo Ostohradskyi State Polytechnic University, Vol. 4 (117), pp. 53-59, 2019. doi: 10.30929/1995-0519.2019.4.53-59

Nasirova N. K., Mukhamedov K. G., Mutalov Sh. A., Mukhamedov J. K. Electroplating sludge utilization. Universum: technical sciences, 12 (93), 2021. URL:[15.12.2021]/Nasirova1.pdf

Tretiakova L, Mitiuk L. Prediction of soil salinity from galvanic sludge. Actual Problems of Renewable Power Engineering, Construction and Environmental Engineering: IV International Scientific-Technical Conference, 6-8 February 2020, Kielce (Poland, Ukraine, Croatia, Slovakia, Sweden, USA): Book of Abstracts. Kielce, Politechnika Świętokrzyska, pp. 150-153, 2020. [Online]. Available:

Loboichenko V. Methodology for identifying prerequisites for the expansion of emergencies resulting from the accumulation of hazardous substances in chemical facilities. Urban Public Utilities, 1(154), pp. 298-30, 2020. URL:

Shevchenko O.L., Bublias V.M., Kolomiets S.S. Bases of transference of moisture are in the zone of suspend water. Kyiv: A Publishing-polydiene center is the "Kyiv university", 2014. URL: https:// › lib › moisture_transfer.

Nester A.A., Tretiakova L, Mitiuk L, Prakhovnіk N, Husiev A. Remediation of Soil Containing Sludge Generated by Printed Circuit Board Production and Electroplating. Journal of Environmental Research, Engineering and Management, Vol. 76, No. 4, pp. 68–75, 2020. doi: 10.5755/j01.erem.76.4.25460

Baliuk S.A., Drozd O.M. Assessment of production eco-system services of the salted and solonetzic soils of South of Ukraine. Visnik agrarnoyi nauki, 1, pp. 60–67, 2019.

Tretiakova L., Mitiuk L., Panasiuk I., Rebuel E. Mathematical model building for predicting the dissemination of hazardous substances in the soil. EUREKA: Physics and Engineering, No. 1 (38), pp. 12-22, 2022. doi: 10.21303/2461-4262.2022.002231