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.

References

References
1.
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.
2.
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.
3.
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
.
4.
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
.
5.
Povitsky
,
A.
,
2002
, “
Numerical Study of Wave Propagation in a Compressible Non-Uniform Flow
,”
Phys. Fluids
,
14
(
8
), pp.
2657
2672
.
6.
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.
7.
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
.
8.
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
.
9.
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
.
10.
Wahba
,
E. M.
,
2008
, “
Modelling the Attenuation of Laminar Fluid Transients in Piping Systems
,”
Appl. Math. Modell.
,
32
(
12
), pp.
2863
2871
.
11.
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.
12.
Jovic
,
V.
,
2013
,
Analysis and Modeling of Non-Steady Flow in Pipe and Channel Networks
,
Wiley
,
West Sussex, UK
, Chap. 4.
13.
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.
14.
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
.
15.
Gray
,
G. R.
, and
Darley
,
H. C. H.
,
1980
,
Composition and Properties of Oilwell Drilling Fluids
,
Gulf Publishing
,
Houston, TX
, Chap. 5.
16.
Shames
,
I. H.
,
1992
,
Mechanics of Fluids
,
McGraw-Hill
,
New York
, Chap. 8.
17.
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
18.
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
.
19.
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.
20.
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.
21.
Pletcher
,
R. H.
,
Tannehill
,
J. C.
, and
Anderson
,
D. A.
,
2013
,
Computational Fluid Mechanics and Heat Transfer
,
CRC Press
,
Boca Raton, FL
, Chap. 4.
22.
Golbabaei-Asl
,
M.
,
Povitsky
,
A.
, and
Ring
,
L.
,
2015
, “
CFD Modeling of Fast Transient Processes in Drilling Fluid
,”
ASME
Paper No. IMECE2015-52482.
23.
Lele
,
S. K.
,
1992
, “
Compact Finite Difference Schemes With Spectral-Like Resolution
,”
J. Comput. Phys.
,
103
(
1
), pp.
16
42
.
24.
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
.
25.
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
.
26.
MATLAB
,
2014
, “
Documentation
,” The MathWorks Inc., Natick, MA.
27.
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
.
28.
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
.
29.
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
30.
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
.
31.
Chapra
,
S. C.
,
2012
,
Applied Numerical Methods With MATLAB for Engineers and Scientists
,
3rd ed.
,
McGraw-Hill
,
New York
, pp.
528
529
.
You do not currently have access to this content.