SIZING SAFETY VALVES FOR SUPERCRITICAL STEAM BOILERS
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1 SIZING SAFETY VALVES FOR SUPERCRITICAL STEAM BOILERS J A Hare 1,3 and G Hawkins 2 1 Health and Safety Laboratory, Process Safety Section 2 Health and Safety Executive, Hazardous Installations Directorate, Chemical Industries 3 Contact details: HSL, Harpur Hill, Buxton, Derbyshire, SK17 9JN, UK; Tel.: þ44 (0) , john.hare@hsl.gov.uk There is considerable interest in the improved efficiency afforded by the operation of steam boilers at supercritical steam temperatures and pressures i.e. pressures above 220 bar and temperatures above 3748C. Steam boilers are normally fitted with safety valves to protect the boiler from over-pressurisation and standard methods are available for the sizing of safety valves for steam flow, using either gas flow equations with property data for steam or using simplified steam flow equations. The methods are documented in the following standards: BS EN ISO , various German standards and API 520. What methods should be used to size the safety valve for a supercritical steam boiler? The available literature on supercritical pressure relief, particularly involving steam, will be reviewed. Safety valve sizing calculations were performed at various supercritical pressures and temperatures. Reference methods were available using the rigorous Homogeneous Equilibrium Method (HEM) calculation method and the HEM using the Omega method (simple Equation of State). These methods were compared with the methods outlined in the standards with various assumptions. Recommendations are made for the sizing of safety valves for supercritical steam boilers. KEYWORDS: safety valve sizing, supercritical steam, steam boilers, standards INTRODUCTION There is considerable interest in the improved efficiency afforded by the operation of steam boilers at supercritical steam temperatures and pressures i.e. pressures above 220 bar and temperatures above 3748C. Steam boilers are normally fitted with safety valves to protect the boiler from over-pressurisation and standard methods are available for the sizing of safety valves for steam flow, using either gas flow equations with property data for steam or using simplified steam flow equations. The methods are documented in the various standards. This paper considers what methods should be used to size the safety valve for a supercritical steam boiler. In this paper, to avoid any confusion between terms, supercritical always refers to the thermodynamic state and choked conditions correspond to the maximum mass flow rate. BASIC THERMODYNAMICS AND FLUID MECHANICS Flow a supercritical fluid through a safety valve will be dependent on a number of factors. It will normally reach a condition whereby lowering the downstream pressure for a given fluid pressure and temperature at the safety valve inlet will not lead to an increase in velocity of the escaping fluid. Under these conditions the flow is known as choked flow and the safety valve acts as the choke point in the system. Determining the maximum mass flux along an isentropic path identifies the choke. For supercritical fluids, the choke conditions may occur in the superheated vapour region or the sub-cooled liquid region. Where the relieving pressure and temperature lie relative to the saturated vapour and liquid lines on an entropy/temperature plot determines where the choke will lie (see Figure 1). As the pressure falls the fluid will follow a line of constant entropy. For supercritical steam there will generally be only one phase: the supercritical fluid (choke in superheated vapour region) or the liquid phase (choke in sub cooled liquid region). Isentropic expansions of sub-critical superheated steam can give chokes in the two-phase region. What follows is generally applicable to cases where the choke is in the superheated vapour region. The use of the isentropic coefficient k or similar term is only valid where the choke is in the superheated region. The supercritical fluid is effectively being treated as a non-ideal high temperature and pressure gas. Therefore where the choke lies relative to the boundary between the two-phase and supercritical region is of vital importance. For water/ steam, thermodynamic data in the form of tables and entropy temperature diagrams are readily available, which allow the boundary between regions to be identified. The section on Gas Flow and Standard Methods discusses how the choke temperature and choke pressure ratios may be estimated from the isentropic coefficient. HEM METHODS The Homogeneous Equilibrium Model (HEM) (Fisher 1992) assumes uniform mixing across the flow area and. This article is published with the permission of the controller of HMSO and the Queen s Printer for Scotland 1
2 Figure 1. Entropy temperature graph for water/steam both thermodynamic and mechanical equilibrium. The rigorous HEM calculation uses physical property data to evaluate the isentropic expansion from an initial supercritical pressure and supercritical temperature. The mass flux (G) when calculated using equation (1) goes through a maximum at the choke pressure (P choke ). This maximum flux is the choke mass flux (G choke ). G ¼ ((2(h o h)) 1=2 )=v (1) The safety valve area (A) is then calculated using equation (2), which includes the required mass flow rate (Q m ). Note in safety valve sizing, Q m is normally given in (kg h 21 ) and A in (mm 2 ). The discharge coefficient (K dr ) is the actual flow capacity divided by the theoretical flow capacity. In the example calculations in this paper the discharge coefficient was taken to be 1.0. A ¼ Q m 10 6 ={3600 K dr G choke } (2) The HEM can be evaluated approximately using the Omega method (Leung 1996). The value of Omega (v) can be calculated at any pressure (P) using an Equation of State (3). A single isentropic expansion is required to generate the Equation of State; generally the expansion is to 0.9 or 0.7 of the original pressure. v ¼ ((v=v o ) 1)=((P o =P) 1) (3) The Omega method, implemented using a spreadsheet, can then be used to calculate the choke pressure ratio (h c ), hence the choke pressure (P choke ) and also the choke mass flux (G choke ). To obtain h c, its value is varied using a solver so that equation (4) is satisfied. P choke is then obtained using equation (5). G choke is obtained using equation (6) and G choke with equation (7). The safety valve area (A) is then calculated using equation (2). Note that equation (7) can be used to back calculate an equivalent dimensionless mass flux value (G choke ) for the rigorous HEM calculation. h 2 c þ (v2 2v)(1 h c ) 2 þ 2v 2 lnh c þ 2v 2 (1 h c ) ¼ 0 (4) P choke ¼ P o h c (5) G choke ¼(h c =v 1=2 ) (6) G choke ¼ (P o =v o ) 1=2 G choke (7) GAS FLOW AND STANDARD METHODS For gas flow, a dimensionless mass flux (G choke ) can be defined similar to that used in the Omega method. G choke can be estimated from the isentropic coefficient k using equation (8). Similar terms, to the dimensionless mass flux, occur in various standards. The terms can all be calculated from G choke or k. The sizing equations from ISO standard are given in the next subsection, including an equation for the compressibility factor Z. G choke ¼{k(2=(k þ 1)) (kþ1)=(k 1) } 1=2 (8) Working with a k value enables the choke pressure ratio (h c ) and choke temperature ratio (u c ) to be estimated using equations (9) and (10) based on gas flow theory (Lapple 1943). The values of both ratios and G choke are listed in Table 1 for k values of (for saturated Isentropic coefficient (k) Table 1. Choke pressure and temperature ratios Choke pressure ratio (h c ) Choke temperature ratio (u c ) Dimensionless mass flux (G choke )
3 steam) and 1.3 (for superheated steam). Some standards (BS 6759 and API 520) also give specific methods for steam flow in which some of the steam properties are incorporated in the sizing equations. h c ¼ (2=(k þ 1)) (k=(k 1)) (9) u c ¼ 2=(k þ 1) (10) ISO STANDARD (BS EN : 2004) Two equations (11 and 12) are provided in section of the standard for calculating the flow area of a safety valve for gaseous media at critical flow. The compressibility factor Z is obtained from its definition in equation (13) using the specific volume (v). It could also be obtained from charts, showing Z as a function of the reduced temperature (T r ) and reduced pressure (P r ). The function C is obtained from the isentropic coefficient (k) using equation (14). A ¼ Q m ={P o CK dr (M=Z T o ) 1=2 } (11) A ¼ Q m ={0:2883 C K dr (P o =v o ) 1=2 } (12) Z ¼ 10 5 P o Mv o =RT o (13) C ¼ 3:948{k(2=(k þ 1)) (kþ1)=(k 1) } 1=2 ¼ 3:948 G choke (14) EXAMPLE CALCULATIONS Safety valve relief sizing calculations (see results in table 2) were performed at four relieving pressures (400, 500, 600 and 700 bara) and four relieving temperatures (400, 500, 600 and 7008C) for a required mass flow rate of kg h 21. The Rigorous HEM Calculation method (using data from the PPDS database (PPDS 2004)) and the Omega method (using a simple Equation of State) were used. Figure 1, the entropy versus temperature diagram for steam/water, shows isobars for all 4 pressures. Isentropic expansion involves reducing the temperature (and pressure) while maintaining the same entropy; i.e. a vertical line downwards on Figure 1. For relieving temperatures of 5008C and above the chokes were found to lie in the superheated vapour region (right portion of the graph above the saturated vapour line). Here, there was excellent agreement between the rigorous HEM and the Omega method in terms of the calculated vent areas. This is because the linear equation of state (EOS) used in the Omega method is adequately predicting the pressure specific volume relationship i.e. Omega remains relatively constant during the isentropic expansion. For a relieving temperature of 4008C the chokes were found to lie in the sub-cooled liquid region (left portion of the graph above the saturated liquid line). There was less agreement between the rigorous HEM and the Omega method in terms of the calculated vent areas. This is because a linear EOS is not representing the pressure specific volume relationship accurately i.e. Omega varies considerably during the isentropic expansion. When the chokes were found to lie in the superheated vapour region, the standard methods (BS EN ISO , AD Merkblatt A2, DIN 3320, TRD 421, BS 6759 and API 520) could also be evaluated (see results in Table 2). The gas flow methods require an expression to characterise the pressure specific volume relationship for the fluid. The specific volume was either used directly or calculated from ideal gas theory modified with a compressibility factor. The specific volume was obtained from steam tables (e.g. Harvey (1995) or Rogers and Mayhew (1980)) and in good agreement with the PPDS data. Spirax Sarco (2005) suggested two k values for steam work: k ¼ 1.3 for superheated steam and k ¼ for saturated steam. There was excellent agreement between all the gas flow methods, using a particular k value, in terms of the calculated vent area. Use of either k value does not imply that supercritical steam is either saturated or superheated, but that the k value could represent the isentropic behaviour Table 2. Vent sizes (mm 2 ) calculated at various relieving pressures and relieving temperatures Relieving temperature Method Relieving pressure 4008C 5008C 6008C 7008C Rigorous HEM 400 bara bara bara bara Gas flow k ¼ bara N/A bara N/A bara N/A bara N/A Gas flow k ¼ bara N/A bara N/A bara N/A bara N/A
4 IChemE SYMPOSIUM SERIES NO. 153 Figure 2. Dimensionless mass flux with pressure and decreases with temperature. Gchoke values could be obtained using either the rigorous HEM or the Omega method. For relieving temperatures of 5008C and above, using a k value of 1.3 in the gas flow equations, is more representative of Gchoke than using a k value of The reason for the k ¼ 1.3 predictions being more accurate is now clear. For a relieving temperature of 4008C, the Gchoke values (obtained using the rigorous HEM) were much higher, this causes the calculated vent sizes to be much smaller. Gas flow equation methods would not be valid for this relieving temperature; clearly the choke is in the sub-cooled liquid region. Gchoke seems to be still increasing with pressure and decreasing with temperature. The graph also shows the Gchoke for liquid flow; use of a liquid flow equation would over-predict the dimensionless mass flux. Figure 3 shows the choke pressure ratio (hc) versus relieving pressure for a range of relieving temperatures. of the fluid. Using any of the gas flow methods with accurate specific volume data and a k value of 1.3, the calculated flow areas were slightly higher than the reference methods. With accurate specific volume data and a k value of 1.135, the calculated flow areas were higher than the reference methods but were not unduly conservative. Steam flow methods rely on the relief pressure and a superheat correction factor. These methods were not used in the calculations, as superheat makes little sense for supercritical steam, as there is no saturation temperature. DISCUSSION AND RECOMMENDATIONS Figure 2 shows the dimensionless mass flux (Gchoke ) versus relieving pressure for a range of relieving temperatures. For relieving temperatures of 5008C and above, there is less Gchoke variation at low pressure and also Gchoke increases Figure 3. Choke pressure ratio 4
5 For the HEM, for relieving temperatures of 5008C and above, there is less h c variation at low pressure and also h c decreases with pressure and increases with temperature. For relieving temperatures of 5008C and above, using a k value of 1.3 in the gas flow equations is more representative of h c than using a k value of For a relieving temperature of 4008C, the h c values were significantly lower. Use of gas flow equation methods would not be valid for this relieving temperature; clearly the choke is in the sub-cooled liquid region. h c seems to be still decreasing with pressure and increasing with temperature. The graph also shows the h c for liquid flow, use of a liquid flow equation would under predict the choke pressure ratio. Figure 4 shows the choke temperature ratio (u c ) versus relieving pressure for a range of relieving temperatures. u c values were obtained using the rigorous HEM. There is more u c variation at low temperature: for a relieving temperature of 4008C u c decreases with pressure, whereas for a relieving temperature of 5008C u c increases with pressure. For relieving temperatures of 6008C and above, using a k value of 1.3, in the gas flow equations, is more representative of u c than using a k value of Supercritical steam boilers are finding increasing application in the power generation sector. They are used to achieve higher operating efficiencies. Pressures are typically in the range to 220 to 420 bara and mass flows around 150,000 kg h 21. Use of chrome containing steels allows steam temperature up to 6208C, whilst nickel based alloys can work up to 7208C. The recommended method of approach is to examine the relieving pressure and relieving temperature on the entropy temperature diagram:. If it lies above the saturated vapour line then the choke will occur in the superheated vapour region. For accurate work the rigorous HEM or the Omega method (based on an EOS) can be used to determine the mass flux. Reasonable predictions for the mass flux can also be achieved using gas flow equations with k ¼ 1.3 and accurate specific volume data.. If it lies above the saturated liquid line vapour then the choke will occur in the sub-cooled liquid region. The rigorous HEM is generally the only method available to predict the mass flux. Use of a liquid flow equation may over predict the mass flux.. If it lies directly above the critical point, or above the saturated vapour line but at a temperature below 5008C, it would be prudent to use the rigorous HEM. Further work is in progress to better define the applicability of different methods in this region. UNITS AND SYMBOLS A ¼ flow area of safety valve (mm 2 ) C ¼ function of isentropic coefficient G ¼ mass flux (kg m 22 s 21 ) G choke ¼ maximum mass flux at choke pressure (kg m 22 s 21 ) G choke ¼ dimensionless mass flux at choke pressure h o ¼ initial enthalpy at starting pressure (J kg 21 ) h ¼ enthalpy at current pressure (J kg 21 ) k ¼ isentropic coefficient K dr ¼ discharge coefficient M ¼ molar mass (kg kmol 21 ) P o ¼ starting/relieving pressure (bara) P ¼ current pressure (bara) P choke ¼ choke pressure (bara) P r ¼ reduced pressure Q m ¼ required mass flowrate (kg h 21 ) R ¼ universal gas constant T o ¼ relieving temperature (K) T ¼ inlet temperature (K) T choke ¼ choke temperature (K) T r ¼ reduced temperature v ¼ specific volume at current pressure (m 3 kg 21 ) Figure 4. Choke temperature ratio 5
6 v o ¼ initial specific volume at starting pressure (m 3 kg 21 ) Z ¼ compressibility factor v ¼ Omega parameter h c ¼ choke pressure ratio u c ¼ choke temperature ratio REFERENCES 1. AD Merkblatt A2 Pressure Vessel Equipment safety devices against excess pressure safety valves 2. API RP 520 Sizing, Selection, and Installation of Pressure-Relieving Devices in Refineries Part 1 Sizing and Selection 7 th edition January BSI EN ISO : 2004 Safety devices for protection against excessive pressure Part 1: Safety valves 4. BS 6759 Safety Valves Parts 1 3, DIN : 1984, Safety valves; safety shut-off valves; definitions, sizing, marking 6. Fisher HG et al Emergency Relief System Design using DIERS technology Chapter II, DIERS/AIChE, Harvey AH Thermodynamic Properties of Water: Tabulation from the IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use, NIST web guide, Lapple Isothermal and Adiabatic Flow of Compressible Fluids Trans AIChE Vol 39 p , Leung Easily Size Relief Devices and Piping for Two-Phase Flow Chemical Engineering Progress, p28 December Physical Property Data Service (PPDS) for Windows, v3.1.4 TUV NEL Ltd, Rogers GFC & Mayhew Thermodynamic and Transport Properties of Fluid 3 rd edition, Spirax Sarco, Steam Engineering Learning Modules Module 9.4 Safety Valve Sizing, TRD 421, Technical Equipment for Steam Boilers Safeguards against excessive pressure safety valves for boilers of groups I, III & IV 6
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