Calculation of safety valve reaction force and stress analysis

Thread Content

I. What is the exhaust reaction force? A safety valve is a device used for overpressure protection of pressure vessels, pressure pipelines, and other pressurized equipment in chemical processing plants. When the system pressure exceeds the set tripping pressure of the safety valve, the safety valve opens its valve disc to allow pressure to be released, thereby achieving the purpose of protecting the system by reducing pressure. During the steam discharge and pressure relief process of a safety valve, a certain reaction force is generated on the pipes connected to it as well as on its supporting structures; this force is known as the steam discharge reaction force. II. What is a safety valve? Open and closed systems of safety valves: In an open system and a closed system, when the system pressure exceeds the maximum allowable operating pressure, the safety valve releases air to reduce the system pressure, thereby ensuring the safety of the system. When a safety valve opens, and the gas is discharged directly into the atmosphere or into a vent pipe that is not connected to the safety valve, it is called an open system. When the safety valve opens, the gas is discharged into a closed system through an exhaust pipe directly connected to the safety valve; such a system is known as a closed system. In a closed discharge system, the fluid is discharged while in a state of steady flow; when the discharged fluid enters the closed discharge system, the pressure relief device generally exerts no significant force or torque on the discharge system. Only at the point of rapid expansion is there a significant reaction force that needs to be calculated. However, simple analysis methods are not suitable for closed discharge systems; complex analyses of their piping systems over time are required to obtain the actual values of reaction forces and bending moments. The following theoretical analyses and calculations in accordance with the specifications are all carried out for open systems. III. Standard specifications for calculating the exhaust reaction force. The calculation of the gas discharge reaction force of safety valves is usually provided by the safety valve manufacturers. If the manufacturer does not provide relevant data, the calculations can be carried out according to the following standards: API RP520-2003 \"Selection and Installation of Pressure Relief Devices in Refineries\", SY/T 10044-2002 \"Recommended Practices for Determining, Selecting, and Installing Pressure Relief Devices in Refineries\" (this standard is largely based on the aforementioned American standard API RP 520), HG/T 20570.2-1995 \"Installation and Selection of Safety Valves\", and ASME B31.1-2022 \"Power Piping\". The reactive force exerted at the elbow due to the steady-state flow after the safety valve opens is directed vertically downward (as shown in the diagram above). There are generally three methods for calculating the magnitude of this force, namely those described in API 520, HG/T 20570—1995, and the ASME B31.1 standards. IV. Calculation Method and Comparison: During the pressure relief process of the safety valve, the outlet pressure of the exhaust pipe is always greater than the backpressure; flow under such conditions is referred to as critical flow, and therefore the parameters at the end of the exhaust pipe in this case are critical parameters. The calculation formulas in the three standards are all derived from critical parameters, but the critical parameters for API 520 are determined by stagnation pressure and stagnation specific volume, while those for ASME B31.1 are determined by stagnation enthalpy. Based on the principles of gas dynamics, when an airflow is brought to a state of zero velocity through adiabatic and isentropic stagnation from a certain state, it is referred to as a stagnated state; the flow parameters in this corresponding state are known as stagnation parameters. Before discharge, the flow velocity of the medium through the safety valve is almost zero; this state can be considered a stagnation state. The discharge pressure is the stagnation pressure, and the discharge temperature is the stagnation temperature. Subsequently, the corresponding stagnation specific volume and stagnation enthalpy values are determined. In engineering, for the calculation of the exhaust reaction force in safety valve systems where the medium can be approximated as an ideal gas, it is correct to use the formulas provided by both standards. For the sake of saving time on reading the article and facilitating organization, the corresponding formulas are provided directly below. The entire derivation process is covered in the relevant explanations and descriptions in various standards; care should be taken to review these standards during implementation. 1) The calculation formula in API 520 standard: 2) ASME B31.1 uses stagnation enthalpy in the formula for calculating the reaction force at the discharge elbow in open-type discharge systems; the formulas for critical pressure, critical velocity, and discharge reaction force are as follows: (These are the formulas given in the American standard; a version in metric units is provided below.) A —— Cross-sectional area of the exhaust pipe, in mm2; a, b —— Gas constants, which can be found in Table II-2.2.1 of Appendix II of ASME B31.1 standard; h0 —— Enthalpy of the gas at the inlet of the safety valve, in J/kg; p —— Critical pressure (absolute pressure) at the discharge outlet during release, in MPa; pa —— Atmospheric pressure (absolute pressure), in MPa; V —— Critical velocity at the discharge outlet during release, in m/s; W —— Mass flow rate of the medium, in kg/s. 3) In HG/T 20570.2—1995 “Installation and Selection of Safety Valves”, the formula for calculating the reaction force is as follows: 4) Differences and connections among the above three formulas: a) The formulas for calculating the reaction force when a safety valve releases pressure, as specified in API 520, HG/T 20570—1995, and ASME B31.1, are all derived based on critical parameters; only the calculation methods differ. The calculation results of API 520 and ASME B31.1 are essentially the same, and both can be applied in engineering practice. However, HG/T 20570—1995 differs significantly from API 520. b) ASME B31.1 introduces thermodynamic parameters such as the stagnation enthalpy of superheated and saturated steam, thereby enabling more accurate calculation results. API520 uses the ideal gas law to convert stagnation pressure and stagnation specific volume into formulas related to stagnation temperature; however, it may lead to certain inaccuracies in calculations for non-ideal gases. V. Stress on the pipeline caused by the exhaust reaction force: When a safety valve discharges, the flow of fluid generates a reaction force (acting vertically downward). Unless a special design is employed, this force will be transmitted to the pressure relief device itself, as well as to the fixed supports or to the walls of the containers connected to the equipment. The exact values of the load and the stresses it induces depend on the magnitude of the reaction force and the installation of the piping system. As a designer, it is responsible to analyze the discharge system to determine whether the reaction forces and associated bending moments will cause excessive stress on any components within the system. The magnitude of the reaction force depends on whether the discharge is open or closed. If a elbow is to be installed in the drainage system to direct the fluid into the vent pipe, the location of the elbow and the installation of the supports are important factors to consider when analyzing the bending moments. VI. Flexible design of the safety valve pipeline When designing the outlet pipeline for a safety valve, many factors need to be taken into account, such as meeting the requirements regarding the flow rate of the medium, preventing excessive back pressure from affecting the operation of the safety valve, ensuring that the reaction forces generated by the safety valve do not cause damage to the valve or the pipeline, and avoiding the accumulation of liquid in the pipeline. The focus is on analyzing the rational design of the outlet pipeline to ensure that the reaction force from the safety valve does not cause damage. Many people who design vent pipes prefer to add two 90-degree elbows at the pipe outlet, so that the final outlet of the vent pipe faces downward ； Or add a 90-degree elbow to keep the pipe outlet horizontal. First, analyze the left diagram: the horizontal outlet of the vent pipe means that, during venting, a horizontal thrust is exerted on the pipe outlet. Since there are no reverse supports on the pipe to withstand this reaction force, this force inevitably acts on the safety valve and the pipe ends in the form of a torque. When this reaction force becomes sufficiently large, it can even cause the flanges to deform or the pipe ends to tear. The outlet of the safety valve discharge pipe, which is discharged into the atmosphere with its opening facing upward, should be cut to have a flat edge, and rain protection measures should be installed. Care must be taken to avoid excessive impact forces during discharge, which could cause the rain protection devices to fall off and injure people. When the safety valve discharge pipe is installed horizontally, its outlet should be cut at a 45° angle to prevent rainwater from entering; care must be taken to ensure that the cut is not oriented in such a way that the discharged fluid sprays onto the platform. Analyzing the diagram on the right again, the outlet of the vent pipe points downward; therefore, when discharge occurs, the reaction force at the outlet acts upward. Since there are no supports at the elbow at the top to bear this reaction force, it inevitably acts on the safety valve and the pipe outlet in the form of forces and moments, which can easily cause damage to the safety valve, the pipe outlet, and the flanges. For the reasons mentioned above, due to the reaction force generated when the safety valve discharges, as well as forces such as the weight of the outlet pipe, vibration, and thermal expansion, appropriate supports should be installed at the outlet of the safety valve. In cases where the discharge pressure difference of the safety valve is high, shock-absorbing supports may be necessary (the placement of these supports should be determined based on calculations of the reaction force exerted by the safety valve). For more details, follow the WeChat official account---Yi Peiguan