The current work presents a mathematical model to simulate “viscoplastic fluid hammer”-overpressure caused by sudden viscoplastic fluid deceleration in pipelines. The flow is considered one-dimensional, isothermal, laminar, and weakly compressible and the fluid is assumed to behave as a Bingham plastic. The model is based on the mass and momentum balance equations and solved by the method of characteristics (MOC). The results show that the overpressures taking place in viscoplastic fluids are smaller than those occurring in Newtonian fluids and also that two pressure gradients-one negative and one positive-are possibly noted after pressure stabilization. The pressure stabilizes nonuniformly on the pipeline because viscoplastic fluids present yield stresses. Overpressure magnitudes depend not only on the ratio of pressure wave inertia to viscous effect but also on the Bingham number. The pipeline designer should take into account the viscoplastic fluid behavior reported in this paper when engineering a new pipeline system.
Issue Section:
Multiphase Flows
References
1.
Streeter
, V. L.
, and Wylie
, E. B.
, 1974
, “Waterhammer and Surge Control
,” Annu. Rev. Fluid Mech.
, 6
, pp. 57
–73
.2.
Mitsoulis
, E.
, 2007
, “Flows of Viscoplastic Materials: Models and Computations
,” Rheol. Rev.
, pp. 135
–178
.3.
Ghidaoui
, M. S.
, Zhao
, M.
, McInnis
, D. A.
, and Axworthy
, D. H.
, 2005
, “A Review of Water Hammer Theory and Practice
,” ASME Appl. Mech. Rev.
, 58
(1
), pp. 49
–76
.4.
Bergant
, A.
, Simpson
, A. R.
, and Tijsseling
, A. S.
, 2006
, “Water Hammer With Column Separation: A Historical Review
,” J. Fluids Struct.
, 22
(2
), pp. 135
–171
.5.
Brunone
, B.
, Karney
, B. W.
, Mecarelli
, M.
, and Ferrante
, M.
, 2000
, “Velocity Profiles and Unsteady Pipe Friction in Transient Flow
,” ASCE J. Water Resour. Plann. Manage.
, 126
(4
), pp. 236
–244
.6.
Brunone
, B.
, Ferrante
, M.
, and Cacciamani
, M.
, 2004
, “Decay of Pressure and Energy Dissipation in Laminar Transient Flow
,” ASME J. Fluid. Eng.
, 126
(6
), pp. 928
–934
.7.
Wahba
, E. M.
, 2013
, “Non-Newtonian Fluid Hammer in Elastic Circular Pipes: Shear-Thinning and Shear-Thickening Effects
,” J. Non-Newtonian Fluid Mech.
, 198
, pp. 24
–30
.8.
Bird
, R. B.
, Armstrong
, R. C.
, and Hassager
, O.
, 1987
, Dynamics of Polymeric Liquids
, 2nd ed., Vol. 1
, Wiley
, New York
, Chap. 2.9.
Oliveira
, G. M.
, Negrão
, C. O. R.
, and Franco
, A. T.
, 2012
, “Pressure Transmission in Bingham Fluids Compressed Within a Closed Pipe
,” J. Non-Newtonian Fluid Mech.
, 169–170
, pp. 121
–125
.10.
Sestak
, J.
, Cawkwell
, M. G.
, Charles
, M. E.
, and Houskas
, M.
, 1987
, “Start-Up of Gelled Crude Oil Pipelines
,” J. Pipelines
, 6
(1
), pp. 15
–24
.11.
Cawkwell
, M. G.
, and Charles
, M. E.
, 1987
, “An Improved Model for Start-Up of Pipelines Containing Gelled Crude Oil
,” J. Pipelines
, 7
(1
), pp. 41
–52
.12.
Chang
, C.
, Rønningsen
, H. P.
, and Nguyen
, Q. D.
, 1999
, “Isothermal Start-Up of Pipeline Transporting Waxy Crude Oil
,” J. Non-Newtonian Fluid Mech.
, 87
(2–3
), pp. 127
–154
.13.
Davidson
, M. R.
, Nguyen
, Q. D.
, Chang
, C.
, and Rønningsten
, H. P.
, 2004
, “A Model for Restart of a Pipeline With Compressible Gelled Waxy Crude Oil
,” J. Non-Newtonian Fluid Mech.
, 123
(2–3
), pp. 269
–280
.14.
Oliveira
, G. M.
, Rocha
, L. L. V.
, Franco
, A. T.
, and Negrão
, C. O. R.
, 2010
, “Numerical Simulation of the Start-Up of Bingham Fluid Flows in Pipelines
,” J. Non-Newtonian Fluid Mech.
, 165
(19–20), pp. 1114
–1128
.15.
Vinay
, G.
, Wachs
, A.
, and Agassant
, J. F.
, 2006
, “Numerical Simulation of Weakly Compressible Bingham Flows: The Restart of Pipeline Flows of Waxy Crude Oils
,” J. Non-Newtonian Fluid Mech.
, 136
(2–3
), pp. 93
–105
.16.
Vinay
, G.
, Wachs
, A.
, and Frigaard
, I.
, 2007
, “Start-Up Transients and Efficient Computation of Isothermal Waxy Crude Oil Flows
,” J. Non-Newtonian Fluid Mech.
, 143
(2–3), pp. 141
–156
.17.
Wachs
, A.
, Vinay
, G.
, and Frigaard
, I.
, 2009
, “A 1.5d Numerical Model for the Start Up of Weakly Compressible Flow of a Viscoplastic and Thixotropic Fluid in Pipelines
,” J. Non-Newtonian Fluid Mech.
, 159
(1–3
), pp. 81
–94
.18.
Negrão
, C. O. R.
, Franco
, A. T.
, and Rocha
, L. L. V.
, 2011
, “A Weakly Compressible Flow Model for the Restart of Thixotropic Drilling Fluids
,” J. Non-Newtonian Fluid Mech.
, 166
(23–24
), pp. 1369
–1381
.19.
Anderson
, J. D.
, 1990
, Modern Compressible Flow: With Historical Perspective
, 2nd ed., McGraw-Hill
, New York
, Chaps. 1 and 3.20.
Swamee
, P. K.
, and Aggarwal
, N.
, 2011
, “Explicit Equations for Laminar Flow of Bingham Plastic Fluids
,” J. Pet. Sci. Eng.
, 76
(3–4
), pp. 178
–184
.21.
Melrose
, J. C.
, Savins
, J. G.
, Foster
, W. R.
, and Parisha
, E. R.
, 1958
, “A Practical Utilization of the Theory of Bingham Plastic Flow in Stationary Pipes and Annuli
,” Pet. Trans. AIME
, 213
, pp. 316
–324
.22.
Wylie
, E. B.
, Streeter
, V. L.
, and Suo
, L.
, 1993
, Fluid Transients in Systems
, Prentice Hall
, NJ
, Chap. 3.23.
Wahba
, E. M.
, 2008
, “Modeling the Attenuation of Laminar Fluid Transients in Piping Systems
,” Appl. Math. Modell.
, 32
(12
), pp. 2863
–2871
.24.
Oliveira
, G. M.
, Franco
, A. T.
, Negrão
, C. O. R.
, Martins
, A. L.
, and Silva
, R. A.
, 2013
, “Modeling and Validation of Pressure Propagation in Drilling Fluids Pumped Into a Closed Well
,” J. Pet. Sci. Eng.
, 103
, pp. 61
–71
.25.
Holmboe
, E. L.
, and Rouleau
, W. T.
, 1967
, “The Effect of Viscous Shear on Transients in Liquid Lines
,” ASME J. Basic Eng.
, 89
(1
), pp. 174
–180
.26.
Sobey
, R. J.
, 2004
, “Analytical Solutions for Unsteady Pipe Flow
,” J. Hydroinf.
, 6
, pp. 187
–207
.Copyright © 2016 by ASME
You do not currently have access to this content.
