Development of a Sizing Equation for a Multi-Stage Choke Valve Trim by Andrew Grace Submitted

221 Pages·2011·5.85 MB·English

Development of a Sizing Equation for a Multi-Stage Choke Valve
Trim

by
Andrew Grace

Submitted for the award of Doctor of Philosophy at the
University of Limerick
February 2011

Supervisor:
Dr. Patrick Frawley
Department of Mechanical and Aeronautical Engineering
University of Limerick

i
CONFIDENTIALITY RESTRICTION

A confidentiality restriction has been placed on this thesis at the request of Cameron Flow
Control Ireland. This restriction limits the distribution of this report to Cameron Flow Control
Ireland and internal / external examiners. This restriction will remain in place until the year
ending 2016

ii
Abstract
Choke valves are used to regulate the pressure from natural gas reservoirs. Traditional choke
valves control the reservoir pressure drop using a single variable orifice. At choked flow
conditions a shock wave forms in the vena contracta in the valve creating high downstream
velocities and shock cell turbulence interaction. The high velocities increase erosion when
there are sand particles in the gas. Shock cell turbulence interaction is a highly efficient noise
generation mechanism and can create noise far in excess of industrial limits.

Multistage (MS) technology is used to reduce high pressure in stages within a valve. Instead
of a single port the MS valve uses a flow path of sequential restrictions and expansions. The
segmenting of the pressure drop eliminates the presence of shock waves. This reduces the
velocity (and hence erosion) and changes the primary noise generation mechanism to less
efficient turbulent shear. A new MS valve geometry was developed by Cameron Flow
Control. As part of this development a flow equation was required to determine the restrictive
area in the valve (referred to as valve coefficient or C ) which is necessary to control a set of
v
reservoir conditions. The C of the valve is a function of its internal geometry and is
v
complicated by the nature of the MS flow path.

A mathematical model of flow through the MS path was constructed based on a series of
sequential thick walled orifice plates. The choked flow conditions for the single stage
geometries were investigated and linked to the gas expansion factor (G ) and critical pressure
y
drop ratio (τ ). Experimental data and theory taken from (Rhode, 1969) was used to estimate
c
a C value for the overall flow path for a series of different pressure differentials. The fluid
v
properties were modelled using a suitable gas compressibility equation (Peng et al, 1976) and
a Joule Thomson relationship (Bessieres et al, 2006) to account for changes in the expansion
zones. The mathematical model did not produce a choked flow condition.

Experimental tests were conducted using a model of the MS flow path, a mass flow loop and
a Laser Doppler Anemometry (LDA) measurement system. The mass flow rate tests showed
that the rate of change of flow rate reduced significantly at high pressure drops without the
gas becoming choked. The LDA velocity measurements indicated the existence of three flow
phenomena within the MS path. Computational Fluid Dynamics (CFD) was used to
investigate the mechanism that caused the reduction in flow rate. Both the mass flow rate and
LDA velocity measurements were used to benchmark the CFD simulations. Three large
vortices were proven to exist in the restrictive channels and their size and location were
shown to ultimately limit the effective flow area.

A full flow test was conducted on the MS valve to finalise the sizing equation and account for
any upstream or downstream geometrical effects caused by the valve body. At the outlet of
the MS paths, which exited into the same volume, further vortices were seen. These proved to
further reduce the overall flow rate of the valve.

The primary outcomes of this research were the design of an effective MS valve (EU Patent
Number: IB2008053368). As part of this, a new limiting flow mechanism was described and
included as part of the sizing equation. In addition, a specific case where high inlet pressures
created shock waves at the outlet was presented. Furthermore this research detailed the first
use of LDA velocities measurements taken within a MS valve with a full scale design.

This research expands on the state of the art knowledge of valve sizing and design.
iii
DECLARATION

This thesis is presented in partial fulfillment of the requirements for the degree of Doctor of
Philosophy in Engineering. The substance of this thesis is the original work of the author and
due reference and acknowledgement has been made, when necessary, to the work of others.
No part of thesis has previously been accepted for any degree nor has it been submitted for
any other award.

Signed: Date: 14/4/2011
Andrew Grace, C.Eng (Candidate)
Dept. of Mechanical & Aeronautical Engineering
University of Limerick

Signed:_______________ Date:_____________
Dr. Patrick Frawley (Supervisor)
Dept. of Mechanical & Aeronautical Engineering
University of Limerick

iv
ACKNOWLEDGEMENTS

Ultimately this work was possible due to the patience of my wife Jill, who sacrificed many, many,
many weekends so I could spend time learning new things. I know I will spend every weekend
henceforth making it up to her.
I would also like to thank my parents, Greta and Mick, who started this all 30 years ago. Their support
throughout my life gave me all the tools I needed to understand the work I have undertaken. In turn I
can only hope to pass on their knowledge.
Pat Frawley deserves a special mention for his efforts in expanding my horizons. At times it must
have seemed like he was steering a rather large, unwieldy tug boat.
Also all my colleagues in Cameron who have come and gone over the years need mentioning. Some
gave good technical advice, some bought the drinks, others gave direction when none was apparent
and all have some part in this work. In no particular order; Britt Schmidt, Dave Quin, Martin
O’Donnell, Declan Elliot, Martin Meehan, Collin Matthews, Stephen Chambers, Eddie McHugh, and
Ray Smyth.

v
Contents

Tables of Contents
Page
Confidentiality Restriction ii
Abstract iii
Declaration iv
Acknowledgements v
Table of Contents
vi
List of Figures
ix
List of Tables
xiii
Nomenclature
xv
Abbreviations
xx

Section Title Page
Chapter 1- Introduction
1.1 Introduction 1
1.2 Control Choke Location and Function 1
1.3 Control Choke Anatomy 2
1.4 MS Trim Technology 4
1.5 Definitions and Service Conditions 5
1.6 CFD Modelling 7
1.7 LDA Benchmarking and C Flow Test 8
v
1.8 Objectives 8
1.9 Methodology 9

Chapter 2- Empirical Analysis
2.1 Introduction 11
2.2 Ideal Restriction and Quasi One Dimensional Flow 11
Valve Coefficient (C ) and the Orifice Plate Meter Coefficient
2.3 v 15
(C )
m
2.4 Single Stage- Gas Expansion Factor, G 18
y
2.5 Multistage Flow Path Model Simplification and Assumptions 22
2.6 First Pass Calculation 25
vi
Contents

2.6.1 MS Path C 26
d
2.6.2 Compressibility Factors 33
2.6.3 Temperature Variation Due to Expansion 36
2.6.4 Calculations and Discussion 40
2.7 Summary 42

Chapter 3- Experimental Investigation and Benchmark Data
3.1 Introduction 44
3.2 LDA Overview 44
3.3 Experimental Analysis 49
3.3.1 LDA Apparatus 49
3.3.2 MS Flow Oath Models 54
3.3.3 Flow Rig Components 60
3.4 LDA Literature Review 61
3.5 Non-Dimensional Analysis 65
3.6 Mass Flow Rate Measurements and Discussion 66
3.7 LDA Velocity Measurements and Discussion 68
3.8 Summary 77

Chapter 4- Computational Fluid Dynamics and Turbulence Model
4.1 Introduction 78
4.2 Turbulence Model 78
4.3 Turbulence Model Application Review 79
SST Turbulence Model Closure Equations and Near Wall
4.4 86
Treatment
4.5 CFX EOS Equations 89
4.6 Grid Independence 89
4.7 Heat Transfer Model 91
4.8 Boundary Conditions and Convergence Criteria 91
4.9 Mass Flow Rate and LDA Benchmark Results 94
4.10 Mesh Independence Results 103
4.11 Mass Rate Discussion 104
4.12 LDA Benchmark Discussion 105
vii
Contents

4.13 Choked Flow Mechanism 111
4.13.1 Choked Flow at Experimental Conditions 112
4.13.2 Choked Flow at Reservoir Conditions 115
4.14 Conclusions 119
4.15 Summary 119

Chapter 5- MS Trim Flow Tests
5.1 Introduction 121
5.2 Flow Test Literature Review 121
5.3 MS Valve Flow Test 132
5.3.1 Test Apparatus 132
5.3.2 Flow Test Procedure 134
5.3.3 Flow Test Results and Conclusions 138
5.4 Summary 142

Chapter 6- Discussion and Conclusions
6.1 Introduction 143
6.2 Summary and Discussion 143
6.3 Conclusions 150
6.4 Original Contributions 153
6.5 Potential for Further Work 154

Chapter 7- References 155
Appendix A 166
Appendix B 178
Appendix C 180
Appendix D 185
Appendix E 195

viii
Contents

List of Figures
Figure No. Title Page
Chapter 1- Introduction
1.1 Photograph of a typical low pressure surface x-tree (Cameron FLC)
3
1.2 Overview of major valve components (Cameron FLC)
3
1.3 Trim details for a single stage valve (Cameron FLC)
4
1.4 Sectional view of a multistage stack trim (Cameron FLC)
4
1.5 FLC two plane multistage flow path with expansion zone (Cameron
5
FLC)
1.6 Required C valves plotted on various inherent flow characteristics
v 7
1.7 Research methodology
10

Chapter 2- Empirical Analysis
2.1 Convergent-divergent nozzle with M varying with area (Anderson
12
2003)
2.2 Convergent-divergent nozzle with equations 2.2 - 2.4 plotted and
13
values at the throat noted (Anderson 2003)
2.3 Thin lip orifice plate with converging and diverging flow stream
14
2.4 Thick walled orifice plate VC location (Perry, 1949)
14
2.5 Barrel shock / under-expanded jet formed below the critical break
15
pressure point (Crist et al, 1966)
2.6 Change in C based on varying orifice geometry defined by β
m 17
(Essom, 2007)
2.7 Distance to VC in pipe diameters defined by β (North
17
American Manufacturing, 1989)
2.8 Plot of gas expansion factor (Y) versus pressure drop ratio (x) for a
21
number of valves with the limit of Y = 0.667 (IEC 60534-2-1)
2.9 Early Prototype models for the MS path
22
2.10 Multistage Path Geometry with throttling sections and expansion
23
zones
2.11 Simplified multistage flow path with increasing throttling and
24
expansion sections
2.12 Flow chart of theoretical calculations for C
v 26
2.13 Thick walled orifice plate test specimen as used by (Rhode, 1969)
26
2.14 Plot of Discharge Coefficient Versus Velocity Head for θ = 1.05,
28
1.6, 2.0, 2.83 and 4.0
2.15 Plot of C versus τ, for θ = 4.0, up to the choked flow point
d 30
2.16 Plot of C versus τ, for θ = 1.0, up to the choked flow point
d 31
ix
Contents

2.17 Nelson-Obert compressibility plot based on 25 different pure gases,
34
reproduced and simplified for clarity from (Cengel et al, 2004)
2.18 Curves for gas mixture GC1L (92% methane) plotted for both PR
38
and SRK EOS (Kortekass, 1997)
2.19 Temperature variations for all natural gas mixtures against pressure
38
drop for a fixed upstream pressure of 1,000 bar (Kortekass, 1997)
2.20 Comparison of JTIC obtained for; experimental, Monte Carlo and
40
other EOS Models (Bessieres et al, 2006)
2.21 Mass flow rate versus pressure drop ratio, τ, using mathematical
41
analysis

Chapter 3- Experimental Investigation and Benchmark Data
3.1 Light intensity scattered from a small particle, (Durst et al, 1976) 45
3.2 Burst signal for a single particle in a LDA probe volume with 45
Gaussian intensity pedestal and Doppler signal (Drain, 1980)
3.3 Dantec Fiber-Flow system with Spectra-Physics 4W Argon-Ion 50
laser
3.4 Dantec BSA-F70 LDA Signal Processer 50
3.5 Fringe pattern for two component velocity measurement formed by 51
blue and green light (Drain, 1980)
3.6 LDA Apparatus with Test Model In-Situ 51
3.7 Optical Layout and Resultant Beam Angle (Dantec Dynamics) 52
3.8 Details of Probe Volume (Dantec Dynamics) 53
3.9 Multi-plane MS Flow Path 55
3.10 Trigonometric relations for refractive index and probe volume shift 55
3.11 Refraction of Laser and resultant probe volume location 56
3.12 Test Model A- MS Path Lower Section 57
3.13 Test Model B- MS Path Upper Section 57
3.14 Test Model Assembly 58
3.15 Test Model Assembly continued 58
3.16 TMA Throttling Sections and Measurement Locations 59
3.17 TMB Throttling Sections and Measurement Locations 59
3.18 Valve Flow Rig (IEC 60534-2-3) 60
3.19 Calibration Data for Annubar 61
3.20 Optical Layout of Ruggerini four stroke piston with optical access 62
(Amato, 1990)
3.21 Variation in tangential velocity, RMS and Turbulence Intensity at 63
measurement point 15mm for varying crank angle (Amato, 1990)
3.22 Variation in velocity RMS across cylinder radius (encompassing the 64
5 measurement points) (Amato, 1990)
x