Physics-Informed Neural Networks for the Prediction of Critical Sand Transport Velocity in Oil and Gas Pipelines
Abstract
Poorly consolidated reservoir formations make the generation of sand alongside hydrocarbons unavoidable. The condition of petroleum pipelines can be seriously compromised by the rapid generation of sand or by sand deposition at low velocities, leading to degradation and reduced capacity. Consequently, it is essential to investigate the minimum transport velocity needed to prevent pipeline sand accumulation. This study employed two predictive modelling tools, a physics-informed neural network (PINN) and a multilayer perceptron (MLP) regressor, to estimate the minimum transport conditions in a solid-liquid-gas pipeline. The models were developed using 182 experimental data sets, which included variables such as superficial velocity, pipe diameter, particle diameter, sand density, sand concentration, liquid density, viscosity, pipe angle of inclination, and critical velocity parameters. The results indicated that the physics-informed neural network outperformed the MLP regressor, achieving an R² coefficient of 0.9999 and a root mean square error (RMSE) of 0.00465. In comparison, the MLP regressor attained an R² coefficient of 0.9992 and an RMSE of 0.0295. Both models were evaluated alongside existing empirical and data-driven models and demonstrated superior performance in predicting minimum transport velocity, with the PINN yielding the best results. A sensitivity analysis revealed that the superficial velocity is the most influential parameter for predicting minimum transport velocity, followed by pipe diameter, sand concentration, and pipe angle. This research highlights the potential of effectively integrating physical laws into the machine learning training process to estimate minimum transport velocity in multiphase pipelines better
References
Al-Mutahar, F. (2006). Modeling of critical deposition velocity of sand in horizontal and inclined pipes (Master's thesis). The University of Tulsa, Tulsa, OK.
Archibong-Eso, A., Aliyu, A. M., Yan, W., Okeke, N. E., Baba, Y. D., Fajemidupe, O., & Yeung, H. (2020). Experimental study on sand transport characteristics in horizontal and inclined two-phase solid-liquid pipe flow. Journal of Pipeline Systems Engineering and Practice, 11(1), 04019050. doi:10.1061/(asce)ps.1949-1204.0000427. https://doi.org/10.1061/(ASCE)PS.1949-1204.0000427
Bhattacharya, B., Price, R. K., & Solomatine, D. P. (2007). Machine learning approach to modeling sediment transport. Journal of Hydraulic Engineering, 133(4), 440-450. https://doi.org/10.1061/(ASCE)0733-9429(2007)133:4(440)
Danielson, T. J. (2007, April). Sand transport modeling in multiphase pipelines. In Offshore Technology Conference (pp. OTC-18691). https://doi.org/10.4043/18691-MS
Dabirian, R., Mohan, R. S., Shoham, O., & Kouba, G. (2016, July). Sand flow regimes in slightly upward inclined gas-liquid stratified flow. In Fluids Engineering Division Summer Meeting (Vol. 50299, p. V01BT28A003). American Society of Mechanical Engineers.
Davies, J. (1987). Calculation of critical velocities to maintain solids in suspension in horizontal pipes. Chemical Engineering Science, 42(7), 1667-1670. https://doi.org/10.1016/0009-2509(87)80171-9
Ehinmowo, A. B., Talabi, O. O., Ajala, E. O., Olamigoke, O. & Ojewumi, M. E. (2022). An Enhanced model for the prediction of Minimum Transport Conditions in Multiphase flow systems. FUOYE Journal of Engineering and Technology, 7(1). https://doi.org/10.46792/fuoyejet.v7i1.730
Ehinmowo, A. B., Ariyo, O. O., Ohiro, O. A., Fajemidupe, O. T., & Salam, K. K. (2021). An Improved Data-Driven Model for the Prediction of Minimum Transport condition for sand transport in Multiphase Flow Systems. FUOYE Journal of Engineering and Technology, 6(1). https://doi.org/10.46792/fuoyejet.v6i1.618
Fajemidupe, O. T., Aliyu, A. M., Baba, Y. D., Archibong-Eso, A., & Yeung, H. (2019). Sand minimum transport conditions in gas-solid-liquid three-phase stratified flow in a horizontal pipe at low particle concentrations. Chemical Engineering Research and Design, 143, 114-126. https://doi.org/10.1016/j.cherd.2019.01.014
Leporini, M., Marchetti, B., Corvaro, F., di Giovine, G., Polonara, F., & Terenzi, A. (2019). Sand transport in multiphase flow mixtures in a horizontal pipeline: An experimental investigation. Petroleum, 5(2), 161-170. https://doi.org/10.1016/j.petlm.2018.04.004
Li, Z., Bai, J., Ouyang, H., Martelli, S., Tang, M., Yang, Y., ... & Gu, Y. (2024). Physics-informed neural networks for friction-involved nonsmooth dynamics problems. Nonlinear Dynamics, 112(9), 7159-7183. https://doi.org/10.1007/s11071-024-09350-z
Mahmud, H. B., Leong, V. H., & Lestariono, Y. (2020). Sand production: A smart control framework for risk mitigation. Petroleum, 6(1), 1-13. https://doi.org/10.1016/j.petlm.2019.04.002
Oroskar, A. R., & Turian, R. M. (1980). The critical velocity in pipeline flow of slurries. AIChE Journal, 26(4), 550-558. https://doi.org/10.1002/aic.690260405
Salam, K. K., Arinkoola, A. O., & Aminu, M. D. (2018). Application of response surface methodology (RSM) for the modelling and optimization of sand minimum transport condition (MTC) in pipeline multiphase flow. Petroleum & Coal, 60(2).
Sarraf Shirazi, A., & Frigaard, I. (2021). SlurryNet: Predicting critical velocities and frictional pressure drops in oilfield suspension flows. Energies, 14(5), 1263. https://doi.org/10.3390/en14051263
Stachurska, B., Mahdavi-Meymand, A., & Sulisz, W. (2022). Machine learning methodology for determination of sediment particle velocities over sandy and rippled bed. Measurement, 197, 111332. https://doi.org/10.1016/j.measurement.2022.111332
Tebowei, R., Hossain, M., Islam, S. Z., Droubi, M. G., & Oluyemi, G. (2018). Investigation of sand transport in an undulated pipe using computational fluid dynamics. Journal of petroleum science and engineering, 162, 747-762. https://doi.org/10.1016/j.petrol.2017.11.003
Turian, R. M., Hsu, F. L., & Ma, T. W. (1987). Estimation of the critical velocity in pipeline flow of slurries. Powder Technology, 51(1), 35-47. https://doi.org/10.1016/0032-5910(87)80038-4
Vlasak, P., Chara, Z., Matousek, V., Konfrst, J., & Kesely, M. (2019). Effect of pipe inclination on flow behaviour of fine-grained settling slurry. In EPJ Web of Conferences (Vol. 213, p. 02094). EDP Sciences. https://doi.org/10.1051/epjconf/201921302094
Yan, W. (2010). Sand transport in multiphase pipelines. PhD Thesis, Cranfield University, UK.
Yao, R., Qi, D., Zeng, H., Huang, X., Li, B., Wang, Y., ... & Wang, Z. (2022). Study on Critical Velocity of Sand Transport in V-Inclined Pipe Based on Numerical Simulation. Water, 14(17), 2627. https://doi.org/10.3390/w14172627
Yao, R., Wang, Z., & Huang, X. (2023). Design Parameters Investigation on Sand Transportation Characteristics of V-Inclined Pipe Based on Eulerian-Eulerian Two-Phase Flow Model. Water, 15(24), 4266. https://doi.org/10.3390/w15244266
Zhang, L., Guan, J., Zhong, D., & Wang, Y. (2023). Effect of sediment particles on the velocity profile of sediment-water mixtures in open-channel flow. International Journal of Sediment Research, 38(3), 361-373. https://doi.org/10.1016/j.ijsrc.2022.11.005
