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