Slug initiation and prediction using high accuracy methods

333 Pages·2012·15.4 MB·English

Cran(cid:12)eld University
School of Engineering
Applied Mathematics and Computing Group
Engineering Doctorate
THESIS
Slug initiation and prediction using
high accuracy methods -
applications with (cid:12)eld data
by
Stamatis Kalogerakos
Supervisors:
Prof. Chris Thompson
Dr. Mustapha Gourma
This thesis is submitted in partial ful(cid:12)lment of the requirements for
the degree of Doctor of Engineering.
Cran(cid:12)eld, 2011
© Cran(cid:12)eld University 2011. All rights reserved. No part of this publication may be
reproduced without the written permission of the copyright holder.
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Acknowledgements
I would like first of all to thank Prof. Chris Thompson for giving me the
opportunity of doing this EngD study and research in Cranfield University. I
would like to thank also EPSRC for the funding provided, and BP for the funding
as well as the data shared.
MoreoverIwouldliketothankDr. MustaphaGourmaforhispatience,motivation,
help and guidance, including many interesting discussions and also arguments!
I want also to thank Ninghong Jia and the other colleagues in the Applied
MathematicsandComputingGroupformakingmystudiesinCranfieldUniversity
a great experience. My sincere thanks go also to Kath Tipping for her supporting
role in all matters regarding administration of EngD.
Last, but not least, I would like to thank my wife for her understanding, support
and love during all these years. My parents receive also my deepest gratitude for
the many years of support during my early study years, and my thanks go also
to my brother for the good discussions we had.
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This is dedicated to my dearest wife and daughter
and also to my parents and my brother.
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Executive Summary
The sponsoring company of the project is BP. The framework within which the
research is placed is that of the Transient Multiphase Flow Programme (TMF-4),
a consortium of companies that are interested in phenomena related to flow
of liquids and gases, in particular with relevance to oil, water and air. The
deliverables agreed for the project were:
• validatingEMAPSthroughsimulationsofknownproblemsandexperimental
and field data concerning slug flow
• introducing numerical enhancements to EMAPS
• decreasing computation times in EMAPS
• using multi-dimensional methods to investigate slug flow
The outcome of the current project has been a combination of new product
development(1DmultiphasecodeEMAPS)andamethodologicalinnovation(use
of 2D CFD for channel simulations of slugs). These are:
• New computing framework composed of:
– Upgraded version of 1D code EMAPS
– Numerical enhancements with velocity profile coefficients
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– Validation with wave growth problem
– Parallelisation of all models and sources in EMAPS
– Testing suite for all sequential and parallel cases
– Versioningcontrol(SVN)andautomatictestinguponcodesubmission.
• Use of 2D CFD VOF for channel simulation with:
– Special initialisation techniques to allow transient simulations
– Validation with wave growth problem
– Mathematical perturbation analysis
– Simulations of 92 experimental slug flow cases
The cost of uptake of the above tools is relatively small compared to the benefits
that are expected to follow, regarding predictions of hydrodynamic slugging.
Dependingonthetimescalesinvolved,itisalsopossibletouseexternalconsultancies
in order to implement the solutions proposed, as these are software based and
their uptake could be carried out in a small time-frame. Moreover it may not be
necessary to build a parallel hardware infrastructure as it is now possible to have
easy access to large parallel clusters and pay rates depending on use.
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Contents
Executive Summary v
List of Tables xxiv
Chapter 1: Project Description 1
1.1 Aim of the Research . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.3 Tasks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.4 Courses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.5 Articles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.6 Relevance of research to industry . . . . . . . . . . . . . . . . . . 7
1.7 Relevance of research to doctoral project . . . . . . . . . . . . . . 8
References 9
Chapter 2: Methodology 11
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2 EMAPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.3 Imperial College Data . . . . . . . . . . . . . . . . . . . . . . . . 13
2.4 BP Field Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.5 FLUENT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.6 Industrial analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
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CONTENTS
References 17
Chapter 3: Literature Review 19
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.2 Fluids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.3 Variables and definitions . . . . . . . . . . . . . . . . . . . . . . . 20
3.4 Equations of fluid motion . . . . . . . . . . . . . . . . . . . . . . 22
3.4.1 Mass Equation . . . . . . . . . . . . . . . . . . . . . . . . 23
3.4.2 Momentum Equation . . . . . . . . . . . . . . . . . . . . . 23
3.4.3 Stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.5 1-D Conservation Equations for two-phase flow . . . . . . . . . . . 25
3.5.1 Mass Conservation Equation . . . . . . . . . . . . . . . . . 26
3.5.2 Momentum Conservation Equation . . . . . . . . . . . . . 27
3.5.3 Closure Laws . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.5.3.1 Pressure Terms . . . . . . . . . . . . . . . . . . . 29
3.5.3.2 Interfacial Stress Terms . . . . . . . . . . . . . . 31
3.5.3.3 Wall Shear Stress Terms . . . . . . . . . . . . . . 31
3.6 Burger Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.7 Watson model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.8 Single Pressure Model . . . . . . . . . . . . . . . . . . . . . . . . 34
3.9 Numerical solver for one-dimensional two-phase flow model . . . . 35
3.9.1 Convective flux discretisation . . . . . . . . . . . . . . . . 37
3.9.2 Pressure flux discretisation . . . . . . . . . . . . . . . . . . 38
3.9.2.1 Source terms discretisation . . . . . . . . . . . . 39
3.9.3 AUSMDV∗ numerical scheme . . . . . . . . . . . . . . . . 40
3.10 Summary of slug characteristics . . . . . . . . . . . . . . . . . . . 40
3.10.1 Slug Translational Velocity . . . . . . . . . . . . . . . . . . 41
3.11 Slug initiation models . . . . . . . . . . . . . . . . . . . . . . . . . 43
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CONTENTS
3.12 Slug Stability Models . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.13 Slug Frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.14 VOF Model in Ansys FLUENT . . . . . . . . . . . . . . . . . . . 50
3.14.1 Modified HRIC Scheme . . . . . . . . . . . . . . . . . . . . 52
3.14.2 Density and other material properties . . . . . . . . . . . . 54
3.14.3 Momentum Equation . . . . . . . . . . . . . . . . . . . . . 54
3.14.4 Energy Equation . . . . . . . . . . . . . . . . . . . . . . . 55
3.14.5 Surface Tension . . . . . . . . . . . . . . . . . . . . . . . . 55
3.14.6 Turbulence . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.14.6.1 The standard k −ϵ model . . . . . . . . . . . . . 57
3.14.6.2 The Reynolds stress model . . . . . . . . . . . . . 57
3.15 Parallelisation concepts . . . . . . . . . . . . . . . . . . . . . . . . 58
3.15.1 Execution model . . . . . . . . . . . . . . . . . . . . . . . 60
3.15.2 Memory architecture . . . . . . . . . . . . . . . . . . . . . 61
3.15.2.1 Shared memory . . . . . . . . . . . . . . . . . . . 61
3.15.2.2 Distributed memory . . . . . . . . . . . . . . . . 62
3.15.3 MPI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
3.15.3.1 Single Program, Multiple Data . . . . . . . . . . 64
3.15.4 OpenMP . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.15.4.1 Shared & private memory . . . . . . . . . . . . . 65
3.15.4.2 Communication between threads . . . . . . . . . 66
3.16 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
References 69
Chapter 4: EMAPS 77
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.2 New Version . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
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CONTENTS
4.3 Adaptive Mesh Refinement (AMR) . . . . . . . . . . . . . . . . . 80
4.4 Restarting EMAPS simulations . . . . . . . . . . . . . . . . . . . 81
4.5 Parallelisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4.5.1 Profiling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4.5.2 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
4.5.3 Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
4.5.4 Continuous integration . . . . . . . . . . . . . . . . . . . . 90
4.5.5 MPI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
4.5.6 OpenMP . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
4.5.6.1 New grid structure . . . . . . . . . . . . . . . . . 92
4.5.7 Simulations with parallel version of EMAPS . . . . . . . . 95
4.5.8 Summary of Parallelisation work . . . . . . . . . . . . . . 97
4.6 SPM4s for hydrodynamic slug flow cases . . . . . . . . . . . . . . 98
4.7 BP Field Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
4.7.1 Simulation of X-Pad . . . . . . . . . . . . . . . . . . . . . 104
4.7.2 Simulation of R-Pad . . . . . . . . . . . . . . . . . . . . . 108
4.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
References 113
Chapter 5: Velocity Profile Coefficients 115
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
5.2 Velocity Profile Coefficients - EMAPS . . . . . . . . . . . . . . . . 116
5.3 Evolution of slug frequency . . . . . . . . . . . . . . . . . . . . . . 125
5.4 Distribution of slug interval times . . . . . . . . . . . . . . . . . . 127
5.5 Analysis with flow variables . . . . . . . . . . . . . . . . . . . . . 132
5.6 Simulation of Manolis cases with flow variable dependent C . . . 134
V
5.7 X-Pad Simulation with modified C . . . . . . . . . . . . . . . . . 137
V
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