[1] Lorentzen, R.J., Fjelde, K.K., Froyen, J., Lage, A.C., Naevdal, G. and Vefring, E.H., 2001, January. Under-balanced drilling: Real time data interpretation and decision support. In SPE/IADC drilling conference. Society of Petroleum Engineers. https://doi.org/10.2118/67693-MS.
[2] Lorentzen, R.J., Fjelde, K.K., Froyen, J., Lage, A.C., Naevdal, G. and Vefring, E.H., 2001, January. Under-balanced and low-head drilling operations: Real time interpretation of measured data and operational support. In SPE Annual Technical Conference and Exhibition. Society of Petroleum Engineers. https://doi.org/10.2118/71384-MS.
[3] Lorentzen, R.J., Naevdal, G. and Lage, A.C., 2003. Tuning of parameters in a two-phase flow model using an ensemble Kalman filter. International Journal of Multiphase Flow, 29(8), pp.1283-1309. https://doi.org/10.1016/S0301-9322(03)00088-0.
[4] Vefring, E.H., Nygaard, G., Fjelde, K.K., Lorentzen, R.J., Naevdal, G. and Merlo, A., 2002, January. Reservoir characterization during underbalanced drilling: Methodology, accuracy, and necessary data. In SPE Annual Technical Conference and Exhibition. Society of Petroleum Engineers. https://doi.org/10.2118/77530-MS.
[5] Vefring, E.H., Nygaard, G.H., Lorentzen, R.J., Naevdal, G. and Fjelde, K.K., 2006. Reservoir characterization during underbalanced drilling (UBD): Methodology and active tests. SPE Journal, 11(02), pp.181-192. https://doi.org/10.2118/77530-MS.
[6] Fan, J., Gao, C., Taihe, S., Liu, H. and Yu, Z., 2001, January. A comprehensive model and computer simulation for underbalanced drilling in oil and gas wells. In SPE/ICoTA Coiled Tubing Roundtable. Society of Petroleum Engineers. https://doi.org/10.2118/68495-MS.
[7] Perez-Tellez, C., 2003. Improved Bottom Hole Pressure Control for Underbalance Drilling Operation (Ph. D. thesis). Louisiana State University.
[8] Perez-Tellez, C., Urbieta-Lopez, A., Miller, A. and Banda-Morato, R.G., 2003, January. Bottomhole Pressure Measurements: Indispensable Tool for Optimizing Underbalanced Drilling Operations. In Offshore Technology Conference. Offshore Technology Conference. https://doi.org/10.4043/15061-MS.
[9] Fadairo, A.S. and Falode, O.A., 2009, January. Effect of drilling cuttings transport on pressure drop in a flowing well. In Middle East Drilling Technology Conference & Exhibition. Society of Petroleum Engineers. https://doi.org/10.2118/125707-MS.
[10] Yan, T., Wang, K., Sun, X., Luan, S. and Shao, S., 2014. State-of-the-art cuttings transport with aerated liquid and foam in complex structure wells. Renewable and Sustainable Energy Reviews, 37, pp.560-568. https://doi.org/10.1016/j.rser.2014.05.047
[11] Ghobadpouri, S., Hajidavalloo, E. and Noghrehabadi, A.R., 2017. Modeling and simulation of gas-liquid-solid three-phase flow in under-balanced drilling operation. Journal of Petroleum Science and Engineering, 156, pp.348-355. https://doi.org/10.1016/j.petrol.2017.06.015.
[12] Wei, N., Xu, C., Meng, Y., Li, G., Ma, X. and Liu, A., 2018. Numerical simulation of gas-liquid two-phase flow in wellbore based on drift flux model. Applied Mathematics and Computation, 338, pp.175-191. https://doi.org/10.1016/j.amc.2018.03.067
[13] Li, X., Ma, H., Zhao, H., Gao, D., Lu, B., Ding, S., Gong, D. and Ma, Z., 2020. Study on the model for predicting maximum allowable measured depth of a horizontal well drilled with underbalanced operation. Journal of Petroleum Science and Engineering, 191, p.107104.https://doi.org/10.1016/j.petrol.2020.107104.
[14] Evje, S. and Flåtten, T., 2003. Hybrid flux-splitting schemes for a common two-fluid model. Journal of Computational Physics, 192(1), pp.175-210. https://doi.org/10.1016/j.jcp.2003.07.001.
[15] Hatta, N., Fujimoto, H., Isobe, M. and Kang, J.S., 1998. Theoretical analysis of flow characteristics of multiphase mixtures in a vertical pipe. International Journal of Multiphase Flow, 24(4), pp.539-561. https://doi.org/10.1016/S0301-9322(97)00074-8.
[16] Jahangiri, M. and Delbari, O., 2020. Heat Transfer Correlation for Two Phase Flow in a Mixing Tank. Journal of Heat and Mass Transfer Research, 7(1), pp.1-10. https://doi.org/10.22075/jhmtr.2020.17712.1232.
[17] Falavand Jozaei, A., Tayebi, A., Shekari, Y. and Ghafouri, A., 2017. Numerical simulation of transient natural gas flow in pipelines using high order DG-ADER scheme. Journal of Heat and Mass Transfer Research, 4(1), pp.35-43. https://doi.org/10.22075/jhmtr.2016.497.
[18] Dranchuk, P.M. and Abou-Kassem, H., 1975. Calculation of Z factors for natural gases using equations of state. Journal of Canadian
138 S.Ghobadpouri / JHMTR 8 (2021) 127- 138
Petroleum Technology, 14(03). https://doi.org/10.2118/75-03-03.
[19] Bratland, O., 2010. Pipe flow 2: multi-phase flow assurance.
[20] Boyun, G., William, C. and Ali Ghalambor, G., 2007. Petroleum production engineering: a computer-assisted approach.
[21] Khezrian, M., Hajidavalloo, E. and Shekari, Y., 2015. Modeling and simulation of under-balanced drilling operation using two-fluid model of two-phase flow. Chemical
Engineering Research and Design, 93, pp.30-37. https://doi.org/10.1016/j.cherd.2014.05.007.
[22] Lage, A.C. and Time, R.W., 2000, January. An experimental and theoretical investigation of upward two-phase flow in annuli. In SPE Asia Pacific Oil and Gas Conference and Exhibition. Society of Petroleum Engineers. https://doi.org/10.2118/64525-MS.