Artificial neural network model for predicting drill cuttings settling velocity

Abstract

The traditional method of using the coefficient of drag -Reynolds number relationship to predict cuttings settling velocity involves an implicit procedure that requires repeated, time-consuming and tedious iterations using Newtonian or mostly non-Newtonian correlations. Usually, these correlations are limited to certain fluid flow regimes. Besides, most of the explicit and direct cuttings settling velocity models that exist are based on the assumption that the cuttings are spherical particles. However, in the field, the cuttings are a mixture of various shapes and are hardly spherical, hence these models when applied to field conditions come off with huge errors. The objective of this work was to use a nature-inspired algorithm (artificial neural network -ANN) to develop a model for estimating cuttings settling velocity that would be robust and useful in the field that would take into account the shape of the cuttings. The data used for this work was obtained from research experiments in the literature. The model was then evaluated using four performance metrics namely: mean squared error (MSE), root mean square error (RMSE), sum of squares error (SSE) and goodness of fit (R²). It was found that the model's predictions obtained in this work agreed with experimental evidence. Furthermore, the developed model possesses the capacity to generalize across new input datasets and can be applied to particles of any shape, hence, defining the novelty of this research and bridging the gap between theory and practice. When compared with state-of-the-art models, the developed models show a high degree of robustness, as the ANN model performed reasonably well with an MSE of 7.5 × 10⁻⁴, an R² of 0.978, RMSE of 0.0274 and SSE of 0.25. To generalize the results across new input datasets, the developed model was cross-validated with new data that was not part of the training process. It was found that the ANN model had an MSE value 0.00807, RMSE of 0.0898, MAE of 0.065, SSE of 2.74 and MAPE of 0.675%. To ensure the replicability of the ANN model, the weights and biases for the inputs, hidden and output layers are presented in this work unlike other artificial intelligence-based models in the literature. The range of application for the developed ANN model is 0.0001 < Particle Reynolds's number <100 and 0.471 < cuttings sphericity <1. With the model developed in this work, the cuttings settling velocity can be predicted with minimal errors in a quick, less cumbersome, non-iterative manner and is not limited by cuttings shapes' factor and fluid flow regimes.

Keywords

Drill cuttings / Artificial neural network / Mud / Cuttings settling velocity

References

[1] A. Zakerian, S. Sarafraz, A. Tabzar, N. Hemmati, S.R. Shadizadeh, Numerical modeling and simulation of drilling cutting transport in horizontal wells, J.Pet.Explor. Prod. Technol. 8 (2) (2018) 455-474, https://doi.org/10.1007/s13202-018-0435-6.

[2] A.Z. Noah, Optimizing drilling fluid properties and flow rates for effective hole cleaning at high-angle and horizontal wells, J. Appl. Sci. Res. 9 (1) (2013) 705-718.

[3] B. Busahmin, N.H. Saeid, U.H.B.H. Hasan, G. Alusta, Analysis of hole cleaning for a vertical well, Open Access. Libr. J. 4 (2017) 1-10.

[4] D.I. Graham, T.E.R. Jones, Settling and transport of spherical particles in power-law fluids at finite Reynolds number, J. Non-Newtonian Fluid Mech. 54 (1994) 465-488.

[5] Z.A.R. Aswad, A. Rashid, The combined effect of irregular shape particles and fluid rheology on settling velocity measurement, 10th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics Held in Orlando, Florida from 14th -16th July 2014, 2014, p. 6.

[6] F. Zhang, S. Miska, M. Yu, E. Ozbayoglu, N. Takach, R.E. Osgouei, Is well clean enough? A fast approach to estimate hole cleaning for directional drilling, SPE/ICoTA Coiled Tubing and Well Intervention Conference and Exhibition Held in Texas, United States of America from 24th -25th March 2015, 2015, p. 16.

[7] S. Rushd, I. Hassan, R.A. Sultan, V.C. Kelessidis, A. Rahman, H.S. Hasan, A. Hasan, Terminal settling velocity of a single sphere in drilling fluid, J.Part.Sci. Technol. 23 (2) (2018) 34-46.

[8] A. Holzer, M. Sommerfeld, New simple correlation formula for the drag coefficient of non-spherical particles, J.Powder Technol. 184 (2007) 361-365.

[9] M.E. Clift, R. Grace, J.R. Weber, Bubbles, Drops and Particles, third ed., Academic Press, New York, United States of America, 1978, p. 380p.

[10] F. Concha, A. Barrientos, Settling velocities of particulate systems: three powerseries expansion for the drag coefficient of a sphere and prediction of the settling velocity, Int. J. Miner. Process. 9 (2) (1982) 167-172.

[11] K. Ceylan, A. Altunbas, C. Kelbaliyev, A new model for estimation of drag force in the flow of Newtonian fluids around rigid or deformable particles, J.Powder Technol. 119 (2001) 250-256.

[12] J. Almedeij, Drag coefficient of flow around a sphere: matching asymptotically the wide trend, J.Powder Technol. 186 (1) (2008) 218-223.

[13] F.A. Morrison, Data Correlation for Drag Coefficient for Sphere, A Report Submitted to the Department of Chemical Engineering, Michigan Technological University, Houghton, Michigan, 2013, p. 86.

[14] R. Barati, S.A.A.S. Neyshabouri, G. Ahmadi, Development of empirical models with high accuracy for estimation of drag coefficient of flow around a smooth sphere: an evolutionary approach, J.Powder Technol. 257 (1) (2014) 11-19.

[15] A.R. Khan, J.F. Richardson, The resistance to motion of a solid sphere in a fluid, Chem. Eng. Commun. 62 (1) (1987) 135-150.

[16] A. Terfous, A. Hazzab, A. Ghenaim, Predicting the drag coefficient and settling velocity of spherical particles, J.Powder Technol. 239 (2) (2013) 12-20.

[17] R. Concha, E.R. Almendra, Settling velocities of particulate systems: settling velocities of individual spherical particles, Int. J. Miner. Process. 5 (1979) 349-367.

[18] G. Saha, N.K. Purohit, A.K. Mitra, Spherical particle terminal settling velocity and drag in Bingham liquids, Int. J. Miner. Process. 36 (2) (1992) 273-281.

[19] K. Ceylan, S. Herdem, T. Abbasov, A theoretical model for estimation of drag force in the flow of non-Newtonian fluids around spherical solid particles, J.Powder Technol. 103 (1999) 286-291.

[20] L.B. Torobin, W.H. Gauvin, Fundamental aspects of solids-gas flow: accelerated motion of a particle in a fluid, Can. J. Chem. Eng. 37 (6) (1959) 224-236.

[21] U.P. Ganguly, On the prediction of terminal settling velocity of solids in liquid -solid systems, Int. J. Miner. Process. 29 (3) (1990) 235-247.

[22] G.V. Madhav, R.P. Chhabra, Drag on non-spherical particles in viscous fluids, Int. J. Miner. Process. 43 (2) (1995) 15-29.

[23] K.G. Tsakalakis, G.A. Stamboltzis, Prediction of the settling velocity of irregularly shaped particles, J.Miner. Eng. 14 (3) (2001) 349-357.

[24] S.N. Shah, Y. El Fadili, R.P. Chhabra, New model for single spherical particle settling velocity in power law (visco-inelastic) fluids, Int. J. Multiph. Flow 33 (1) (2007) 51-66.

[25] Z.A.R. Aswad, M.A. Khaliq, New drag coefficient charts for settling spherical and disk particles in shear thinning fluids, 7th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics Held in Antalya, Turkey from 19th -21st July 2010, 2010, p. 6.

[26] S. Baldino, R.E. Osgouei, E. Ozbayoglu, S. Miska, N. Takach, R. May, D. Clapper, Cuttings settling and slip velocity evaluation in synthetic drilling fluids, 12th Offshore Mediterranean Conference and Exhibition Held in Ravenna, Italy from 25th -27th March 2015, 2015, p. 15.

[27] F. Dioguardi, D. Mele, A new shape dependent drag correlation formula for nonspherical rough particles: experiments and results, J.Powder Technol. 277 (2015) 222-230.

[28] R. Elgaddafi, R. Ahmed, F. Growcock, Settling behaviour of particles in fiber-containing Herschel Bulkley fluid, J.Powder Technol. 301 (2016) 782-793.

[29] X. Song, Z. Xu, G. Li, Z. Pang, Z. Zh, A new model for predicting drag coefficient and settling velocity of spherical and non-spherical particle in Newtonian fluid, J.Powder Technol. 10 (1) (2017) 12-19.

[30] G. Dazhi, R.I. Tanner, The drag on a sphere in a power-law fluid, J. Non-Newtonian Fluid Mech. 17 (1985) 1-12.

[31] M.B. Bush, On the stagnation flow behind a sphere in a shear-thinning viscoelastic liquid, J. Non-Newtonian Fluid Mech. 55 (1994) 229-247.

[32] J. Blackery, E. Mitsoulis, Creeping motion of a sphere in tubes filled with a Bingham plastic material, J. Non-Newtonian Fluid Mech. 70 (1) (1997) 59-77.

[33] K.A. Missirlis, D. Assimacopoulos, E. Mitsoulis, R.P. Chhabra, Wall effects for motion of spheres in power-law fluids, J. Non-Newtonian Fluid Mech. 96 (6) (2001) 459-471.

[34] S.D. Dhole, R.P. Chhabra, V. Eswaran, Flow of power-law fluids past a sphere at intermediate Reynolds numbers, J. Ind.Eng. Chem. Res. 45 (2006) 4773-4781.

[35] J.J.D. Prashant, Direct simulations of spherical particle motion in Bingham liquids, J. Comput. Chem. Eng. 35 (2) (2009) 1200-1214.

[36] A.A. Zaidi, T. Tsuji, T. Tanaka, Hindered settling velocity and structure formation during particle settling by direct numerical simulation, Procedia Engineering Journal 102 (2) (2015) 1656-1666.

[37] J.K. Comer, C. Kleinstreuer, A numerical investigation of laminar flow past nonspherical solids and droplets, Transactions-ASME J. Fluids Eng 117 (1) (1995) 170-175, https://doi.org/10.1115/1.2816807 Mar 1995.

[38] E.I. Epelle, D.I. Gerogiorgis, CFD modelling and simulation of drill cuttings transport efficiency in annular bends: effect of particle sphericity, J. Pet. Sci. Eng. 170 (2018) 992-1004, https://doi.org/10.1016/j.petrol.2018.06.041.

[39] Baker Hughes INTEQ, Drilling Engineering Workbook. A Distributed Learning Course, (1995) 80270H Rev. B December 1995.

[40] M.R. Osborne, R.O. Watts, Simulation and Modelling. Chapter 8: Artificial Intelligence, Simulation and Modelling, (1977).

[41] S. Alnuaim, The technology arm of sustainability, J. Pet. Technol. 71 (3) (2019) 10.

[42] O.E. Agwu, J.U. Akpabio, S.B. Alabi, A. Dosunmu, Settling velocity of cuttings in drilling muds: a review of experimental, numerical simulations and artificial intelligence studies, J.Powder Technol. 339 (2018) 728-746.

[43] R. Rooki, F.D. Ardejani, A. Moradzadeh, V.C. Kelessidis, M. Nourozi, Prediction of terminal velocity of solid spheres falling through Newtonian and non-Newtonian pseudoplastic power law fluid using artificial neural network, Int. J. Miner. Process. 110 (2) (2012) 53-61.

[44] M. Li, G. Zhang, J. Xue, Y. Li, S. Tang, Prediction of the wall factor of arbitrary particle settling through various fluid media in a cylindrical tube using artificial intelligence, 2014, Sci. World J. (2014) 1-10.

[45] E.B. Goldstein, G. Coco, A machine learning approach for the prediction of settling velocity, J. Water Resour. Res. 50 (2014) 3595-3601.

[46] M. Kamyab, R. Dawson, P. Farmanbar, A new method to determine friction factor of cuttings slip velocity calculation in vertical wells using neural networks, SPE Asia Pacific Oil and Gas Conference and Exhibition Held in Perth, Australia from 25th -27th October 2016, 2016, p. 7.

[47] No date S.M. Sadat-Helbar H. Shirazi D. Zare, Estimating the Fall Velocity of Sediment Particles in Water Reservoir, 10p http://www.cbdb.org.br/documentos/IR%C3%83-3%20ANN.doc, Accessed date: 2 September 2017.

[48] G. Shafabakhsh, H. Naderpour, R. Noroozi, Determining the relative importance of parameters affecting concrete pavement thickness, J. Rehabil. Civ. Eng. 3-1 (2015) (2015) 61-73.

[49] H. Fazeli, R. Soleimani, M.A. Ahmadi, R. Badrnezhad, A.H. Mohammadi, Experimental study and modelling of ultrafiltration of refinery effluents using a hybrid intelligent approach, J. Energy.Fuels 27 (6) (2013) 3523-3537.

[50] A. Ghaffari, H. Abdollahi, M.R. Khoshayand, B.I. Soltani, A. Dadgar, M. Rafieetehrani, Performance comparison of neural network training algorithms in modelling of bimodal drug delivery, Int. J. Pharm. 327 (1) (2006) 126-138.

[51] E. Jorjani, C.S. Chehreh, S.H. Mesroghli, Application of artificial neural networks to predict chemical desulfurization of Tabas coal, J. Fuel. Technol. 87 (12) (2008) 2727-2734.

[52] F. Mekanik, M. Imteaz, S. Gato-Trinidad, A. Elmahdi, Multiple regression and artificial neural network for long term rainfall forecasting using large scale climate modes, J. Hydrol. 503 (2) (2013) 11-21.

[53] Mathworks, MATLAB Neural Network Toolbox: User's Manual, Mathworks Inc., Natick, Massachusetts, USA, 2015, p. 375p V-rsion 8.5.0.197613 (R2015a).

[54] M.M.A. Alel, M.R.A. Upom, R.A. Abdullah, M.H.Z. Abidin, Estimating SPT-N value based on soil resistivity using hybrid ANN-PSO algorithm, J. Phys. 995 (1) (2018) 1-14.

[55] J.D. Olden, M.K. Joy, R.G. Death, An accurate comparison of methods for quantifying variable importance in artificial neural networks using simulated data, Ecol. Model. 178 (2004) 389-397.

[56] M.J. Watts, S.P. Worner, Using artificial neural networks to determine the relative contribution of abiotic factors influencing the establishment of insect pest species, Ecol. Inf. 3 (2008) 64-74.

[57] J.D. Olden, D.A. Jackson, Illuminating the “black box”: understanding variable contributions in artificial neural networks, J.Ecol. Model. 154 (2002) 135-150.

[58] D.L.J. Alexander, A. Tropsha, D.A. Winkler, Beware of R2: simple, unambiguous assessment of the prediction accuracy of QSAR and QSPR models, J. Chem. Inf. Model. 55 (7) (2015) 1316-1322.

[59] R.M. Turian, T.F. Yuan, G. Mauri, Pressure drop correlation for pipeline flow of solid-liquid suspensions, J. Am.Inst. Chem. Eng. 17 (4) (1971) 809-817.

[60] K.C. Wilson, R.R. Horsley, T. Kealy, J.A. Reizes, M. Horsley, Direct prediction of fall velocities in non-Newtonian materials, Int. J. Miner. Process. 71 (1) (2003) 17-30.

[61] S.F. Chien, Settling velocity of irregularly shaped particles, Journal of SPE Drilling and Completion 4 (1994) 281-289.

[62] M.T. Ityokumbul, A non-parametric method for particle settling velocity determination in a slurry bubble column, Chem. Eng. J. 54 (1994) 1-6.

[63] N.S. Cheng, Simplified settling velocity formula for sediment particle, J. Hydraul. Eng. 123 (2) (1997) 149-152.

[64] J. Guo, Logarithmic matching and its applications in computational hydraulics and sediment transport, J. Hydraul. Res. 40 (5) (2002) 555-565.

[65] S. Zhiyao, W. Tingting, X. Fumin, L. Ruijie, A simple formula for predicting settling velocity of sediment particles, J. Water Sci.Eng. 1 (1) (2008) 37-43.

[66] K. She, L. Trim, D. Pope, Fall velocities of natural sediment particles: a simple mathematical presentation of the fall velocity law, J. Hydraul. Res. 43 (2) (2005) 189-195.

[67] J.P. Ahrens, A fall velocity equation, J. Waterw. Port, Coast. Ocean Eng. 126 (2) (2000) 99-102.

[68] P.P. Brown, D.F. Lawler, Sphere drag and settling velocity revisited, J. Environ. Eng. 129 (3) (2003) 222-231.

[69] R. Turton, N. Clark, An explicit relationship to predict spherical particle terminal velocity, J.Powder Technol. 53 (1987) 127-129.

[70] D. Zigrang, N. Sylvester, An explicit equation for particle settling velocities in solid -liquid systems, J. Am.Inst. Chem. Eng. 27 (6) (1981) 1043-1044.

[71] A. Haider, O. Levenspiel, Drag coefficient and terminal velocity of spherical and non-spherical particles, J.Powder Technol. 58 (1989) 63-70.

[72] N.S. Cheng, Comparison of formulas for drag coefficient and settling velocity of spherical particles, J.Powder Technol. 189 (2009) 395-398.

[73] A.N. Singh, K.C. Roychowdhury, Study of the effects of orientation and shape on the settling velocity of non-isometric particles, J. Chem. Eng.Sci. 24 (1969) 1185-1186.

[74] J.M. Peden, Y. Luo, Settling velocity of variously shaped particles in drilling and fracturing fluids, SPE Drilling Engineering Journal 2 (4) (1987) 1-7.

[75] C.L. Briens, Correlation for the direct calculation of the terminal velocity of spherical particles in Newtonian and pseudo plastic (power law fluids), J.Powder Technol. 67 (1991) 87-91.

[76] A.V. Nguyen, H. Stechemesser, G. Zobel, H.J. Schulze, An improved formula for terminal velocity of rigid spheres, Int. J. Miner. Process. 50 (2) (1997) 53-61.

[77] D.S. Bharagava, K. Rajagopal, An integrated expression for settling velocity of particles in water, Journal of Water Research 26 (7) (1992) 1005-1008.

[78] T.N. Smith, A model of settling velocity, J. Chem. Eng.Sci. 53 (2) (1998) 315-323.

[79] S.M. Sadat-Helbar, E. Amiri-Tokaldany, S. Darby, A. Shafaie, Fall velocity of sediment particles, 4th IASME/WSEAS International Conference on Water Resources, Hydraulics and Hydrology Held in Tokyo, Japan, from 17th -23rd January 2009, 2009, p. 17.

[80] V.C. Kelessidis, An explicit equation for the terminal velocity of solid spheres falling in pseudoplastic liquids, Chem. Eng.Sci.J 59 (1) (2004) 4437-4447.

[81] J.C. Alcerreca, R. Silva, E. Mendoza, Simple settling velocity formula for calcareous sand, J. Hydraul. Res. 51 (2) (2013) 215-219.

[82] J. Faitli, Continuity theory and settling model for spheres falling in non-Newtonian one and two phase media, Int. J. Miner. Process. 169 (2017) 16-26.