№85-3
Mathematical modeling of vibrating screen dynamics for efficient drilling mud cleaning in oil and gas well drilling
M. Voita1, https://orcid.org/0009-0001-4801-0406
1Dnipro University of Technology, Dnipro, Ukraine
Coll.res.pap.nat.min.univ. 2026, 85:30–44
Full text (PDF)
https://doi.org/10.33271/crpnmu/85.030
ABSTRACT
Purpose. Calculation of the efficiency of vibrating screen operation for drilling mud cleaning from drill cuttings by developing a comprehensive mathematical model that accounts for the non-Newtonian rheology of the drilling fluid, the dynamics of the vibrating screen panel, and the probabilistic nature of particle separation.
The methods. The calculation is performed using the developed mathematical model, which integrates the equations of particle motion on a vibrating surface (considering viscous drag, adhesion, and inertial forces), the Herschel-Bulkley rheological model for the drilling fluid, and a stochastic model for the probability of particles passing through the screen apertures. The system of differential equations was solved numerically using the 4th-order Runge-Kutta method with an adaptive step size in Python with NumPy and SciPy libraries. Extensive parametric numerical simulations were conducted across a wide range of technological and design parameters.
Findings. The cleaning efficiency values range from 68.4% to 84.7% within the studied frequency range of 20–30 Hz and amplitudes of 2.0–4.0 mm. The optimal operating range of the vibrating screen was determined: oscillation frequency of 24–28 Hz, amplitude of 3.0–4.5 mm, and screen inclination angle of 8–12°. It is shown that an increase in the dynamic yield stress above 7 Pa reduces separation efficiency by 6–12%, while a lower flow behavior index improves cuttings transport along the screen.
The originality. Dependences of cleaning efficiency on the amplitude-frequency characteristics of the vibrating screen were established with consideration of the non-Newtonian properties of the drilling fluid. A comprehensive mathematical model was developed that for the first time combines the dynamics of the elastic screen panel, the rheological behavior of the drilling mud, and the probabilistic mechanism of particle passage. New dimensionless similarity criteria for the separation process on vibrating screens in non-Newtonian fluids were determined.
Practical implementation. The obtained calculation results allow drilling engineers to select optimal operating modes of vibrating screens based on the type of drilling fluid and the granulometric composition of drill cuttings. Implementation of the developed recommendations can increase drilling mud cleaning efficiency, reduce the risk of technological complications during well drilling, and lower costs associated with solids control equipment.
Keywords: mathematical modeling, vibrating screen, drilling fluid, non-Newtonian fluid, particle separation, cleaning efficiency, rheological properties.
References
1. Rastsvietaiev, V. O., Haddad, J., Aziukovskyi, O. O., Pashchenko, O. A., Babenko, M. V., & Vasylchenko, D. O. (2026). Development and evaluation of combined methods for cleaning paraffin wax deposits in pipelines oil and gas industry. Naukovyi Visnyk Natsionalnoho Hirnychoho Universytetu, (1), 50–57. https://doi.org/10.33271/nvngu/2026-1/050
2. Abbas, A. K., Alsaba, M. T., & Al Dushaishi, M. F. (2021). Improving hole cleaning in horizontal wells by using nanocomposite water-based mud. Journal of Petroleum Science and Engineering, 203, 108619. https://doi.org/10.1016/j.petrol.2021.108619
3. Muratova, S., Pashchenko, O., Khomenko, V., & Zhailiev, A. (2025). Application of machine learning for wellbore stability assessment. In Engineering for Rural Development (Vol. 24). Latvia University of Life Sciences and Technologies, Faculty of Engineering and Information Technologies. 24th International Scientific Conference Engineering for Rural Development. https://doi.org/10.22616/erdev.2025.24.tf109
4. Zakeri, A., Alizadeh Behjani, M., & Hassanpour, A. (2024). Fully Coupled CFD–DEM Simulation of Oil Well Hole Cleaning: Effect of Mud Hydrodynamics on Cuttings Transport. Processes, 12(4), 784. https://doi.org/10.3390/pr12040784
5. Gbadamosi, A. O., Junin, R., Abdalla, Y., Agi, A., & Oseh, J. O. (2019). Experimental investigation of the effects of silica nanoparticle on hole cleaning efficiency of water-based drilling mud. Journal of Petroleum Science and Engineering, 172, 1226–1234. https://doi.org/10.1016/j.petrol.2018.09.097
6. Muratova, S., Ratov, B., Khomenko, V., Pashchenko, O., & Kamyshatskyi, O. (2025). Improvement of the methodology for measuring plastic viscosity and dynamic shear stress of drilling fluids. IOP Conference Series: Earth and Environmental Science, 1491(1), 012026. https://doi.org/10.1088/1755-1315/1491/1/012026
7. Jimmy, D., Wami, E., & Ogba, M. I. (2022). Cuttings Lifting Coefficient Model: A Criteria for Cuttings Lifting and Hole Cleaning Quality of Mud in Drilling Optimization. In SPE Nigeria Annual International Conference and Exhibition. SPE. SPE Nigeria Annual International Conference and Exhibition. https://doi.org/10.2118/212004-ms
8. Hummert, E., & Pataki-Hundt, A. (2010). Technical Note: Ultrasonic Cleaning of Mud Encrustations from Flood Damaged Woodcuts. Restaurator, 31(1). https://doi.org/10.1515/rest.2010.004
9. Dong, J., Lindeman, S., Autin, J., Gluszko, P., Goodyear, D., & Norman, J. (2025). Revolutionizing Offshore Drilling: The Robotic Enhanced Barite Recovery and Waste Reduction System for Mud Tank Cleaning. In Offshore Technology Conference. OTC. Offshore Technology Conference. https://doi.org/10.4043/35873-ms
10. Ji, Z., Feng, Q., Li, S., Li, Z., & Pan, Y. (2025). Design of Novel Hydraulic Drive Cleaning Equipment for Well Maintenance. Processes, 13(8), 2424. https://doi.org/10.3390/pr13082424
11. Al-Rubaii, M. M. (2025). Advisory Automated System for Wellbore Cleaning and Evaluation Improves Drilling Efficiency. In ADIPEC. SPE. ADIPEC. https://doi.org/10.2118/228970-ms
12. Gosavi, S. V., Adla, A., Sripada, S., Furey, K., Evans, A. M., & Degroot, A. K. (2025). Case Study - Efficient Drilling of High-Angle Wells: Overcoming Strength Anisotropy and Enhancing Hole Cleaning via Remote Real-Time Borehole Management. In SPE/IADC International Drilling Conference and Exhibition. SPE. SPE/IADC International Drilling Conference and Exhibition. https://doi.org/10.2118/223794-ms
13. Pashchenko, O., Sarbopeyeva, M., Kamyshatskyi, O., Arshidinova, M., & Petrenko, V. (2026). Comparative Analysis of Contact Stress Models for Optimizing Rock-Destroying Elements in Drilling Operations. In Advances in Science and Technology (Vol. 172, pp. 87–96). Trans Tech Publications Ltd. International Conference “Challenges of ensuring Ukraine’s mineral resources in the context of post-war reconstruction – 2025.” https://doi.org/10.4028/p-fbhdv2
14. Saihood, T., Al-Safran, E., & Nguyen, T. (2023). Modeling and Optimization of Mud Cap Drilling for Undrillable Wells Due to Loss of Circulation. In SPE Annual Technical Conference and Exhibition. SPE. SPE Annual Technical Conference and Exhibition. https://doi.org/10.2118/215040-ms
15. Badrouchi, F., Rasouli, V., & Badrouchi, N. (2022). Impact of hole cleaning and drilling performance on the equivalent circulating density. Journal of Petroleum Science and Engineering, 211, 110150. https://doi.org/10.1016/j.petrol.2022.110150
16. Pashchenko, O. A., Khomenko, V. L., Ratov, B. T., Koroviaka, Y. A., & Rastsvietaiev, V. O. (2024). Comprehensive approach to calculating operational parameters in hydraulic fracturing. IOP Conference Series: Earth and Environmental Science, 1415(1), 012080. https://doi.org/10.1088/1755-1315/1415/1/012080
17. Alhadi, A., & Magzoub, M. (2021). Treatment of Prodigious Reactive Shale in the Permian Basin Using High-Performance Drilling Fluid: A Successful Case Study. In SPE International Conference on Oilfield Chemistry. SPE. SPE International Conference on Oilfield Chemistry. https://doi.org/10.2118/204341-ms
18. Ruggiero, M., Meledeth, A., De Smedt, F., Kucs, R., Ripperger, G., Comotti, S., Cockram, L., & Colombo, I. (2024). Automated and Unmanned Shale Shaker Performance and Borehole Instability Monitoring Using Computer Vision and Artificial Intelligence. In ADIPEC. SPE. ADIPEC. https://doi.org/10.2118/222109-ms
19. Cai, Q., Yan, Y., Yang, Y., Yang, T., Shao, Y., & Guo, S. (2022). Discussion on Application of Fine Flow Splitting and Blocking Removal Technology in Low Permeability Horizontal Wells. In Springer Series in Geomechanics and Geoengineering (pp. 4730–4736). Springer Nature Singapore. https://doi.org/10.1007/978-981-19-2149-0_440
date of first submission of the article to the publication – 04/13/2026
date of acceptance of the article for publication after review – 05/21/2026
date of publication – 06/30/2026