0
Research Papers: Offshore Technology

Modeling of Wave Propagation in Drilling Fluid

[+] Author and Article Information
Mona Golbabaei-Asl

Mem. ASME
Mechanical Engineering Department,
University of Akron,
Akron, OH 44325-3903
e-mail: M.Golbabaie@gmail.com

Alex Povitsky

Mechanical Engineering Department,
University of Akron,
Akron, OH 44325-3903
e-mail: Alex14@uarkon.edu

Lev Ring

Weatherford International, Inc.,
Technology Development,
Houston, TX 77041-3000
e-mail: lev.ring@sbcglobal.net

1Corresponding author.

Contributed by the Ocean, Offshore, and Arctic Engineering Division of ASME for publication in the JOURNAL OF OFFSHORE MECHANICS AND ARCTIC ENGINEERING. Manuscript received October 11, 2016; final manuscript received February 25, 2018; published online April 24, 2018. Assoc. Editor: Theodoro Antoun Netto.

J. Offshore Mech. Arct. Eng 140(4), 041304 (Apr 24, 2018) (9 pages) Paper No: OMAE-16-1124; doi: 10.1115/1.4039565 History: Received October 11, 2016; Revised February 25, 2018

The study presents a one-dimensional (1D) numerical model of wave propagation as well as transmission/reflection phenomena in Newtonian and non-Newtonian drilling mud flow associated with oil/gas drilling activities. Propagation of wave formed due to back pressure changes by means of a choke is investigated. In general, the reflection and transmission of pressure waves at intersection of conduits with different cross sections or in case of partial blockage typical of drilling practices is multidimensional and caused by nonuniform boundary conditions over the cross section. The 1D approach is investigated to approximate the multidimensional reflection and transmission of pressure pulse at areal discontinuity in conduit. The approach is facilitated by introduction of a local force exerted by solid wall on the fluid at the intersection of the conduits into conservative form of the equation for momentum conservation. In addition, nonconservative formulation of momentum equation was explored. To solve the differential equations, MacCormack numerical scheme with second-order accuracy is applied to the nonlinear Euler and 1D viscous conservation equations. A grid refinement study is performed. It is shown that nonconservative form of the conservation laws results in more accurate prediction of transmission and reflection in case of areal discontinuity. The results of the numerical modeling are presented in terms of pressure wave propagation and attenuation upon reflection and transmission at consequent interfaces.

FIGURES IN THIS ARTICLE
<>
Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.

References

Bourgoyne, A. T., Jr. , Chenevert, M. E. , Millheim, K. K. , and Young, F. S., Jr. , 1986, Applied Drilling Engineering, Society of Petroleum Engineers, Richardson, TX, Chap. 4.
Medley, G. H. , Moore, D. , and Nauduri, S. , 2008, “Simplifying MPD: Lessons Learned,” SPE/IADC Managed Pressure Drilling and Underbalanced Operations Conference and Exhibition, Abu Dhabi, United Arab Emirates, Jan. 28–29, SPE Paper No. SPE-113689-MS.
Martins, M. N. , Soares, A. K. , Ramos, H. M. , and Cavos, D. I. , 2016, “CFD Modeling of Transient Flow in Pressurized Pipes,” Comput. Fluids, 126, pp. 129–140. [CrossRef]
Golbabaei-Asl, M. , and Knight, D. D. , 2014, “Numerical Characterization of High-Temperature Filament Interaction With Blunt Cylinder at Mach 3,” Shock Waves, 24(2), pp. 123–138. [CrossRef]
Povitsky, A. , 2002, “Numerical Study of Wave Propagation in a Compressible Non-Uniform Flow,” Phys. Fluids, 14(8), pp. 2657–2672. [CrossRef]
Zheng, T. , Vatistas, G. , and Povitsky, A. , 2007, “Sound Generation by Street of Vortices in a Non-Uniform Flow,” Phys. Fluids, 19(3), p. 037103.
Chaudhry, M. H. , and Hussaini, M. Y. , 1985, “Second-Order Accurate Explicit Finite-Difference Schemes for Waterhammer Analysis,” ASME J. Fluids Eng., 107(4), pp. 523–529. [CrossRef]
Chen, H. , Liu, H. , Chen, J. , and Wu, L. , 2013, “Chebyshev Super Spectral Viscosity Method for Water Hammer Analysis,” Propul. Power Res., 2(3), pp. 201–207. [CrossRef]
Amara, L. , Berreksi, A. , and Achour, B. , 2013, “Adapted MacCormack Finite-Differences Schemes for Water Hammer Simulation,” J. Civ. Eng. Sci., 2(4), pp. 226–233.
Wahba, E. M. , 2008, “Modelling the Attenuation of Laminar Fluid Transients in Piping Systems,” Appl. Math. Modell., 32(12), pp. 2863–2871. [CrossRef]
Onorati, A. , Ferrari, G. , Cerri, T. , Cacciatore, D. , and Ceccarani, M. , 2005, “1D Thermo-Fluid Dynamic Simulation of a High Performance Lamborghini V12 S.I. Engine,” SAE Paper No. 2005-01-0692.
Jovic, V. , 2013, Analysis and Modeling of Non-Steady Flow in Pipe and Channel Networks, Wiley, West Sussex, UK, Chap. 4.
Tikhonov, V. , Bukashkina, O. , Liapidevskii, V. , and Ring, L. , 2016, “Development of Model and Software for Simulation of Surge-Swab Process at Drilling,” SPE Russian Petroleum Technology Conference and Exhibition, Moscow, Russia, Oct. 24–26, SPE Paper No. SPE-181933-MS.
Hermoso, J. , Jofore, B. D. , Martinez-Boza, F. J. , and Gallegos, C. , 2012, “High Pressure Mixing Rheology of Drilling Fluids,” Ind. Eng. Chem. Res., 51(44), pp. 14399–14407. [CrossRef]
Gray, G. R. , and Darley, H. C. H. , 1980, Composition and Properties of Oilwell Drilling Fluids, Gulf Publishing, Houston, TX, Chap. 5.
Shames, I. H. , 1992, Mechanics of Fluids, McGraw-Hill, New York, Chap. 8.
Adeleke, N. A. , 2010, “Blockage Detection in Natural Gas Pipelines by Transient Analysis,” M.Sc. thesis, The Pennsylvania State University, State College, PA. https://etda.libraries.psu.edu/catalog/10022
Greyvenstein, G. P. , 2002, “An Implicit Method for the Analysis of Transient Flow in Pipe Networks,” Int. J. Numer. Methods Eng., 53(5), pp. 1127–1143. [CrossRef]
Zamora, M. , Roy, S. , Slater, K. , and Tronsco, J. , 2012, “Study on the Volumetric Behavior Oils, Brines, and Drilling Fluids Under Extreme Temperatures and Pressures,” SPE ATCE, San Antonio, TX, Oct. 8–10, SPE Paper No. SPE-160029-MS.
Quigley, M. C. , 1989, “Advanced Technology for Laboratory Measurements of Drilling Fluid Friction Coefficient,” SPE Annual Technical Conference and Exhibition, San Antonio, TX, Oct. 8–11, SPE Paper No. SPE-19537-MS.
Pletcher, R. H. , Tannehill, J. C. , and Anderson, D. A. , 2013, Computational Fluid Mechanics and Heat Transfer, CRC Press, Boca Raton, FL, Chap. 4.
Golbabaei-Asl, M. , Povitsky, A. , and Ring, L. , 2015, “CFD Modeling of Fast Transient Processes in Drilling Fluid,” ASME Paper No. IMECE2015-52482.
Lele, S. K. , 1992, “Compact Finite Difference Schemes With Spectral-Like Resolution,” J. Comput. Phys., 103(1), pp. 16–42. [CrossRef]
Nordstrom, J. , and Karpenter, M. H. , 1999, “Boundary and Interface Conditions for High-Order Finite-Difference Methods Applied to the Euler and Navier-Stokes Equations,” J. Comput. Phys., 148(2), pp. 621–645. [CrossRef]
Tam, C. K. W. , and Webb, J. C. , 1993, “Dispersion-Relation-Preserving Finite Difference Schemes for Computational Acoustics,” J. Comput. Phys., 107(2), pp. 262–281. [CrossRef]
MATLAB, 2014, “Documentation,” The MathWorks Inc., Natick, MA.
Bogey, C. , Cacqueray, N. , and Bailly, C. A. , 2009, “Shock-Capturing Methodology Based on Adaptative Spatial Filtering for High-Order Non-Linear Computations,” J. Comput. Phys., 228(5), pp. 1447–1465. [CrossRef]
Darian, H. M. , Esfahanian, V. , and Hejranfar, K. A. , 2011, “Shock-Detecting Sensor for Filtering of High-Order Compact Finite Difference Schemes,” J. Comput. Phys., 230(3), pp. 494–514. [CrossRef]
Carpenter, M. H. , Gottlieb, D. , and Abarbanel, S. , 1991, “The Stability of Numerical Boundary Treatments for Compact High-Order Finite-Difference Schemes,” NASA Langley Research Center, Hampton, VA, NASA Contractor Report No. 187628. https://searchworks.stanford.edu/view/2821728
Celik, I. B. , Ghia, U. , Roache, P. J. , and Christopher , 2008, “Procedure for Estimation and Reporting of Uncertainty Due to Discretization in CFD Applications,” ASME J. Fluids Eng., 130(7), p. 078001.
Chapra, S. C. , 2012, Applied Numerical Methods With MATLAB for Engineers and Scientists, 3rd ed., McGraw-Hill, New York, pp. 528–529.

Figures

Grahic Jump Location
Fig. 1

Problem schematics: (a) drilling channel with controlled back pressure at the choke, (b) uniform channel with upward mud motion (shaded area on top view), and (c) nonuniform channel with upward mud motion (shaded area on top view)

Grahic Jump Location
Fig. 2

Transient pressure profile at the outlet boundary: (a) step pressure pulse, (b) saw pressure pulse, and (c) triangular pressure pulse

Grahic Jump Location
Fig. 3

Static pressure at tc/L=0 and the pressure wave (p/pinitial) at tc/L=0.5 generated by step increase of the back pressure in flow with: (a) normal viscosity and (b) enhanced viscosity

Grahic Jump Location
Fig. 4

Static pressure at tc/L=0 and the pressure wave (p/pinitial) at tc/L=5 generated by saw pulse at the back pressure: (a) normal viscosity and (b) enhanced viscosity

Grahic Jump Location
Fig. 5

Capability of wave capturing by compact versus MacCormack scheme

Grahic Jump Location
Fig. 6

Grid refinement study for step pulse initiated as back pressure: (a) normal viscosity (pressure profile depicted in Fig. 3(a)) and (b) enhanced viscosity (pressure profile depicted in Fig. 3(b))

Grahic Jump Location
Fig. 7

Triangular pressure pulse propagation: (a) Newtonian flow, μ=μwater, (b) non-Newtonian flow, power law: n=0.73 and K=0.1347lbf/100ft2·sn, and (c) non-Newtonian flow, yield power law: n=0.705,K=0.2318lbf/100ft2·sn, and τy=1.44lbf/100ft2

Grahic Jump Location
Fig. 8

Computational results for dimensionless triangular pulse pressure pwave/pinitial traveling across the areal discontinuity (tc/L denotes dimensionless time): (a) pressure contour plots subsequent to passage from narrow to the wide section of the conduit (top) and pressure profiles at different time intervals before, at, and after passage across areal discontinuity (bottom) and (b) pressure contour plots subsequent to passage from wide to the narrow section of the conduit (top) and pressure profiles at different time intervals before, at, and after passage across areal discontinuity (bottom)

Grahic Jump Location
Fig. 9

Pressure pulse interacting with partial blockage of drilling channel: (a) pressure wave pwave/pinitial contour plot when the pulse has traveled across the second areal discontinuity, (b) dimensionless wave pressure obtained from solution of conservative governing equations with forcing term (Eq. (4b)), and (c) dimensionless wave pressure obtained from solution ofnonconservative governing equation (Eq. (5)) (tc/L denotes dimensionless time)

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In