Systematic oil flow modeling in the Quasi-3D approximation yields additional terms that allows for variable cross-section area tubing

Abstract

A systematic model development for oil flow in quasi-3D (1D + 2D) is presented. Our approach provides a unified modeling scheme. Besides, additional terms are obtained, which allows for tubing area variation along the flow direction. The area variation can be modeled as analytic function or random fluctuation, as it could be the result of deposits or tubing internal surface roughness. The proposed approach can be used to obtain analytic solutions which provide physical insight into the phenomena under scrutiny, including the validation of software tools, sensor development and sensor placement. One starts from conservation laws as given by kinetic theory and applies the transverse averaging technique (TAT) to extract the one-dimensional approximation in formal grounds. To demonstrate its application, the steady-state Ramey’s model, the Hasan’s transient model and a simple two-phase model are generated from the obtained equations.

Keywords

Conservation equation / Flow model / Two-phase flow / Ramey’s model / Hasan’s model

Acknowledgments

This work was partly funded by CNPq, Brazilian funding agency, and by PETROBRAS, Brazilian Oil Company. This work is dedicated to Prof. Anatoly A. Barybin of Saint-Petersburg State Electrotechnical University, in memoriam.

The author thanks CNPq for its continued support. He also thanks eng. Maurício Galasssi and eng. Manoel Feliciano da Silva Jr., both from PETROBRAS Brazilian Oil Company for bringing this problem to his attention.

References

[1] Henry J. Ramey Jr., Wellbore heat transmission J. Petrol. Technol. 14 (1962) 427-435, 04.

[2] A.R. Hasan, C.S. Kabir, X. Wang, Development and application of a wellbore/reservoir simulator for testing oil wells, SPE Form. Eval. 12 (1997) 182-188, 03.

[3] Octavio Cazarez-Candia, Mario A. Vaásquez-Cruz, Prediction of pressure, temperature, and velocity distribution of two-phase flow in oil wells, J. Petrol. Sci. Eng. 46 (2005) 195-208.

[4] Bulent Izgec,Transient Fluid and Heat Flow Modeling in Coupled Wellbore/reservoir Systems, Texas A& M University, PhD Thesis, 2008.

[5] A.R. Hasan, C.S. Kabir, Wellbore heat-transfer modeling and applications, J. Petrol. Sci. Eng. 86-87 (2012) 127-136.

[6] A.T. Singhe, J.R. Ursin, J. Henninges, G. Pusch, L. Ganzer, Modeling of temperature effects in CO₂ injection wells, Energy Procedia 37 (2013) 3927-3935.

[7] Effects of tripping and swabbing in drilling and completion operations, Final Report. Prepared for the Department of the Interior, Bureau of Safety and Environmental Enforcement Prepared by Bourgoyne Engineering LLC in Collaboration with Darryl Andrew Bourgoyne vol. 17, LLC and Bourgoyne Enterprises, Inc. July, 2017.

[8] Dan Sui, Vebjørn Haraldstad Langåker, Downhole temperature Modeling for non-Newtonian fluids in ERD wells, Model. Ident. Contr. 39 (2018) 131-149.

[9] Fengrui Sun, Yuedong Yao, Mingqiang Chen, Xiangfang Li, Lin Zhao, Ye Meng, Zheng Sun, Tao Zhang, Feng Dong, Performance analysis of superheated steam injection for heavy oil recovery and modeling of wellbore heat efficiency, Energy 125 (2017) 795-804.

[10] Fengrui Sun, Yuedong Yao, Guozhen Li, Xiangfang Li, Chengang Lu, Zhili Chen, A model for predicting thermophysical properties of water at supercritical state in offshore CDTW, Measurement 124 (2018) 241-251.

[11] B.K. Sinha, M.S. Patel, Recent developments in high precision quartz and langasite pressure sensors for high temperature and high pressure applications, IEEE International Frequency Control Symposium (IFCS) (2016) 1-13.

[12] Leonardo B. M. Silva, Edval J. P. Santos, FPGA-based smart sensor implementation with precise frequency to digital converter for flow measurement, 6th Southern Programmable Logic Conference, SPL 2010 -Proceedings 5483009, pp. 21-26,.

[13] Leonardo B. M. Silva, Edval J. P. Santos,Modeling quality factor in AT-cut quartzcrystal resonators, Chip in Curitiba 2013 -SBMicro 2013: 28th Symposium on Microelectronics Technology and Devices 6676121.

[14] Leonardo B.M. Silva, Edval J.P. Santos, Quartz and GaPO 4 pressure transducers for high resolution applications in high temperature: a simulation approach,in: 29th Symposium on Microelectronics Technology and Devices: Chip in Aracaju, SBMicro 2014 6940116, 2014.

[15] Leonardo B.M. Silva, Edval J.P. Santos, Modeling high-resolution downhole pressure transducer to achieve semi-distributed measurement in oil and gas production wells, Journal of Integrated Circuits and Systems 14 (2) (2019) 1-9.

[16] Jean-Noël Jaubert, Fabrice Mutelet, VLE predictions with the Peng-Robinson equation of state and temperature dependent kijcalculated through a group contribution method, Fluid Phase Equil. 224 (2004) 285-304.

[17] American Petroleum Institute. https://www.api.org/.

[18] Mamoru Ishii, Takashi Hibiki, 1sted, Springer Science,Thermo-Fluid Dynamics of Two-phase Flow, New York, 2006.

[19] Donald A. Drew, Stephen L. Passman, Springer,Theory of Multicomponent Fluids, Berlin, 1999.

[20] Richard L. Liboff, Kinetic Theory: Classical, Quantum and Relativistic Descriptions, 1990. Prentice-Hall.

[21] Anatoly. A. Barybin, Edval. J.P. Santos, Transverse averaging technique for the depletion capacitance of nonuniform PN-junctions, Semicond. Sci. Technol. 22 (2007) 312-319.

[22] Anatoly A. Barybin, Edval J.P. Santos, Large-signal and high-frequency analysis of nonuniformly doped or shaped pn-junction diodes, J. Appl. Phys. 109 (2011) 114510.

[23] Stephen Childress, An Introduction to Theoretical Fluid Dynamics, New York University, 2008.

[24] M.H. Chaudhry, Applied hydraulics transients, in: Chapter 2 Transient-Flow Equations. 3rd Ed, Springer-Verlag, New York, 2014.

[25] Reijo Kouhia,Brief Introduction to Continuum Mechanics, Lecture Notes to the Course Mechanics of Materials, 2016.