Computational Rheology for Pipeline and Annular Flow

268 Pages·2001·1.716 MB·English

by  Wilson C. Chin PhD

Computational Rheology for Pipeline and
Annular Flow

by Wilson C. Chin, Ph.D.

Boston Oxford Auckland Johannesburg Melbourne New Delhi
Gulf Professional Publishing is an imprint of Butterworth-Heinemann
Copyright © 2001 by Butterworth–Heinemann
A member of the Reed Elsevier group
All rights reserved.
No part of this publication may be reproduced, stored in a retrieval system, or trans-
mitted in any form or by any means, electronic, mechanical, photocopying, record-
ing, or otherwise, without the prior written permission of the publisher.
Recognizing the importance of preserving what has been written,
Butterworth–Heinemann prints its books on acid-free paper whenever possible.
Butterworth–Heinemann supports the efforts of American Forests and
the Global ReLeaf program in its campaign for the betterment of trees,
forests, and our environment.
Library of Congress Cataloging-in-Publication Data
Chin, Wilson C.
Computational rheology for pipline and annular flow/ by Wilson C. Chin.
p. cm. Includes index
ISBN 0-88415-320-7 (alk. Paper)
1. Oil well drilling 2. Petroleum pipleines--fluid dynamics--mathematical models
3. Wells--fluid dynamics--mathematical models. I. Title.
TN871.C49535 2000
622'.3382--dc21 00-06176
British Library Cataloguing-in-Publication Data
Acatalogue record for this book is available from the British Library.
The publisher offers special discounts on bulk orders of this book.
For information, please contact:
Manager of Special Sales
Butterworth–Heinemann
225 Wildwood Avenue
Woburn, MA01801–2041
Tel: [phone]
Fax: [phone]
For information on all Gulf Professional Publishing publications available, contact
our World Wide Web home page at: http://www.gulfpp.com
10 9 8 7 6 5 4 3 2 1
Printed in the United States of America
n o-itaci d- eD
:oT
MarAkP. r oett,
Frienda ndC olleague
v
iv
Contents
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
1. Introduction: Basic Principles and Applications . . ..... 1
WhSyt udRyh eology? , 5
Review of Analytical Results , 7
Overview of Annular Flow , 11
iveR ewo fP riorA nnularM odels , 13
ThNee Cwo mputationaMlo dels , 41
PracticaAlp plications , 71
Philosophoyf Nu mericaMlo deling , 02
References, 22
2. Eccentric, Nonrotating, Annular Flow . . . . . . . . . . . . . . . 25
Theory and Mathematical Formulation , 26
Boundary Conforming Grid Generation , 33
Numerical Finite Difference Solution , 35
Detailed Calculated Results , 73
Examp1l.e Fully Concentric Annular Flo w , 37
Examp2l.e ConcentriPci paen Bdo reholietn h e
PresencoeCaf u ttingBse d , 34
Examp3l.e Highly Eccentric Circular Pipe and
Borehole , 48
Examp4l.e SquareD rillC ollari na C irc ulaHro le , 50
Examp5l.e Small Hole, Bingham Plastic Model , 52
Examp6l.e Small Hole, Power Law Fluid , 57
Examp7l.e Large Hole, Bingham Plastic , 59
Examp8l.e Large Hole, Power Law Fluid , 16
Examp9l.e L arge Hole with Cuttings Bed , 65
References, 86
iiv
3. Concentric, Rotating, Annular Flow . . . . . . . . . . . . . . . . . 69
General Governing Equations , 96
Exact Solution for Newtonian Flows , 72
Narrow Annulus Power Law Solution , 67
Ana lytical Validation , 80
DifferenceBse tweeNn ewtonian and Power Law Flows , 81
MorAep plica tionFso rmulas, 83
DetaileCda lcu lated Results, 58
Examp1l.e aE st Greenbriar No. 2, 86
Examp2l.e DetaiSled patial Properties Versus “r”, 87
Examp3l.e Mor e of East Greenbriar, 96
References, 99
4. Recirculating Annular Vortex Flows . . . . . . . . . . . . . . . . . 100
WhatA lucriceR er ating Vortex Flows?, 101
MotivatinIgd eaasn Cdo n trolling Variables, 201
DetaileCda lcu lated Results, 401
tHow oA void StagnanBtu bbles, 011
PAr actica l ,elpmaxE 111
Reference1s1,2
5. ApplicationtDsor illinagnP dr oduction . . . . . . . . . . . . . . 113
Cuttings Transport iDn e viateWde lls , 115
Discussio1n . Water- BaseM uds , 115
Discussio2n. Cutt ingTsr ansporDta tabase , 120
Discussio3n. InverEt mulsionVse rsu“sA lOli lM”u ds, 221
Discussio4n. Effect of Cutting sB edT hickness, 521
Discussio5n. Wh4y5 o 6–0 o In clinationAsr Weo rst, 821
Discussio6n. KeIys sueisCn u ttingTsr ansport, 921
EvaluatioonSf p otting F luidsf orS tuckP ipe, 131
CementinAg pplications, 531
Examp1l.e EccentriNco nrotatinFgl owB,a seline
Concentric Case, 631
Examp2l.e Eccentric Nonrotating Flow, Eccentric
Circular Case, 139
Examp3l.e EccentriNco nrotatinFgl oSwA, evere
Washout , 141
Examp4l.e EccentriNco nrotatinFgl owC,a sing
with Centralizers, 241
Examp5l.e Concentric Rotating Flows,
S tationarBya seline , 146
Exa 6.mple Concentric Rotating Flows,
RotatinCga sing , 150
CoileTdu bing Return Flows , 153
iiiv
HeavilCyl ogg ed Stuck Pipe, 351
Conclus ions , 155
Reference1s5,6
6. BundlePdi pelines : Coupled Annular Velocity
dnaT emperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
Computer Visualization a ndS peechS ynthesis, 061
Coupled Velocity and Temperature Fields , 361
Reference1s6,7
7. Pipe Flow Model ing in General Ducts . . . . . . . . . . . . . . . . 168
NewtoniaFnl oiwn Circular Pipes , 169
FiniDtief fe renceM ethod, 071
NewtoniFalnio w n Rectangular Ducts, 471
ExacAtn alytic al Series Solution, 471
FiniDtief fe rencSeo lution, 177
xE ample Calculation, 971
GeneraBlo undary Conforming Grid Systems, 081
Recapitulation, 183
Two Examp lCea lculations, 381
CloggedA nnulusa nd Stuck Pipe Modeling, 681
Reference1s8,9
8. SolidDse pos ition Modeling . . . . . . . . . . . . . . . . . . . . . . . . . 190
MudcakBeu ild up on Porous Rock, 191
Deposition Me chanics, 591
Sedimentary Tr ansport, 591
TrSlurry ansport, 691
Waxeasn d Paraffins, Basic Ideas, 791
Hydra te Control2,0 1
ModelinCgo ncept asn Idn tegration , 203
WaBxu ilduDpu teo TemperaturDei fferences , 203
Depositioann Fdl o wfield Interaction, 402
DetaiClaeld culated Examples, 502
Simulation 1. WaDxe positiowni tNhe wtonian
F low in Circular Duct, 502
Simulation 2. Hydrate Plug with Newtonian Flow
nicriC ular Duct (Velocity Field), 012
Simulation 3. Hydrate Plug with Newt onianF low
nialucriC Dru c(tV iscouSst resFsi eld), 213
Simulation 4. Hydrate Plug with Power Law Flow
in Circular Duct, 512
Simulation 5. Hydrate Plug, Herschel-Bulkley Flow
in Circular Duc t, 812
xi
Simulation 6. Eroding a Clogged Bed, 222
Reference2s2,8
9. Pipe Bends, Secondary Flows, Fluid Heterogeneities . . . . 231
ModelinNgo n-Newton ian Duct Flow in Pipe Bends, 232
Straight, Cl osedD ucts, 232
Hagen-P oiseuille Flow Between Planes , 233
Flow Between C oncentriPcl ates, 332
Flows in Clos eCdu rveDdu cts, 632
FluHiedt erogeneiti es and Secondary Flows, 832
Reference2s4,0
10. Advanced M odeling Methods . . . . . . . . . . . . . . . . . . . . . . . 241
Complicated Problem Domains, 142
Singly-Con nectedR egions , 242
Doubly-Co nnecteRde gions, 342
Triply-Con nectedR egions , 245
Convergence Acceleration , 246
FastS olutionst o Laplace’s Equation, 742
SpeRchieaoll ogical Models, 942
Software Notes, 252
Reference2s5,3
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255
AuthoBri ography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257
x
Preface
It has been a decade since Borehole Flow Modeling first appeared,
integrating modern finite difference methods with advanced techniques in
curvilinear grid generation, and applying powerful computational algorithms to
annular flow problems encountered in drilling and producing horizontal and
deviatedw ellsT. h ee arlyw orkc ombinede ssentiale lementso fm athematicsa nd
numerical analysis, also paying careful attention to empirical results obtained
from field and laboratory observation, and importantly, always driven by a
stronegm phasio“snr eawlo rldo”p erationaplr oblems.
Prio r to BFM , workers invoked “slot flow,” “parallel plate,” and “narrow
annulus” assumptions to model non-Newtonian flows in eccentric annuli, with
little success in correlating experimental data. With the new methods, which
solved the complete flow equations exactly, at least to the extent permitted by
numerical discretization, it was possible to explain the University of Tulsa’s
detailecdu ttingtsr anspordta tabasietn e rmossf i mplpeh ysicaplr inciples.
Fast forward to the new millennium . Cuttings transport, stuck pipe, and
annular flow are even more important because deep subsea drilling imposes
tighter demands on safety and efficiency. Rheology is more important than ever
since drilling fluid characteristics now depend on temperature and pressure. To
make matters worse, the same subsea applications introduce operational
problems with severe economical consequences on the “delivery” side. More
often than not, thick waxes will deposit unevenly and large hydrate plugs will
form in mile-long pipelines. The harsh ocean environment and the lack of
accessibility make every flow stoppage event a very serious matter involving
millionodsfo llars.
While current industry interests focus on the thermodynamics of wax and
hydrate crystallization and formation, and to some extent, on the altered
properties of affected crudes, new rheological models will not be useful until
they can be used with simulators to study macroscopic flow processes. For
example, knowing “n” and “k” does not give the flow rate associated with a
known pressure drop when large hydrate plugs or crescent-shaped wax deposits
impede flow within the pipeline. This book uses the methods of BFM to model
non-Newtonian flow in ducts with arbitrary geometrical cross-sections, e.g.,
different classes of blockages associated with different modes of wax
depositionh,y dratfeo rmationa,nd de briasc cumulation.
ix
As in BFM , our advanced curvilinear grids adapt exactly to the cross-
sectional geometry, and allow highly accurate numerical models to be
formulated and solved … in seconds . I will focus on practical results. For
example,w ew ills howt hati ti sn otu nusualf or“ 25%a reab lockages”t or educe
volumetric flow by 60% to 80% or more. However, our new approaches
provide more than “flow rate versus pressure drop” relationships. We will take
advantage of new simulation capabilities to design dynamic, time-dependent
models that show how wax, hydrates, and debris grow or erode with
continuously changing duct cross-sections, where these changes are imposed by
thvee locitayn sdt resesn vironmenotgf e neranlo n-Newtoniafnl uids.
Other applications are possible. For example, natural gas hydrates may
become an economically viable energy source if potential logistical problems
can be addressed satisfactorily. Some have suggested mixing ground hydrates
with refrigerated crudes to form transportable pipeline slurries. How finely
these solids are ground will affect rheology on the “n and k” level, but
simulation provides actual velocity profiles, power requirements, and pressure
levels for scale-up. Off-design plugging and “start-up conditions” are important
in pipeline operations. The same simulations also produce “snapshots” of
viscous stress fields that tend to erode these structures; thus, for the first time, a
tool that allows risk evaluation is available. Detailed understanding of the flow
enablesb etterc haracterizationo fw axa ndh ydratef ormationa ndd eposition.
I am indebted to many organizations and individuals that have shaped my
technical skills, professional interests, and personal perspectives over the years.
In particular, I express my gratitude to the Massachusetts Institute of
Technology, for providing a solid foundation in physics and mathematical
analysis, and the Boeing Commercial Airplane Company, for the opportunity to
learn modern grid generation and finite difference methods.
I also wish to acknowledge Halliburton Energy Services, particularly Steve
Almond, Ron Morgan, and Harry Smith, and Brown & Root Energy Services,
notably Raj Amin, Gee Fung, Tin Win, and Jeff Zhang, for their support in
developing advanced rheological models, and especially for an environment that
encourages fundamental studies and physical understanding. I am also grateful
to the United States Department of Energy for its support in computer
visualization, convergence acceleration, and duct geometry mapping research,
provided under Grant No. DE-FG03-99ER82895. The encouragement offered
by Timothy Calk, John Wilson, and James Wright, Gulf Publishing, is also
kindlyn oted.F inally,I a mi ndebtedt om yf rienda ndc olleagueM arkP roett,f or
lendingac riticala nds ympathetice art oa llm y“ crazyi deas”o vert hey ears.
WilsoCCn.h inP,h .D.M,. I.T.
HoustonT,e xas
Emai l: [email protected]
xii