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Process Safety and Environmental Protection 133 (2020) 104–123

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Process Safety and Environmental Protection journal homepage: www.elsevier.com/locate/psep

A review on modeling and simulation of blowdown from pressurized vessels and pipelines Umar Shafiq a , Azmi M. Shariff a,∗ , Muhammad Babar a , Babar Azeem a , Abulhassan Ali b , Mohamad Azmi Bustam a a b

CO2 Research Centre (CO2RES), Universiti Teknologi PETRONAS, 32610 Bandar Seri Iskandar, Perak, Malaysia Department of Chemical and Materials Engineering, University of Jeddah, Jeddah, Saudi Arabia

a r t i c l e

i n f o

Article history: Received 14 February 2019 Received in revised form 24 September 2019 Accepted 31 October 2019 Available online 13 November 2019 Keywords: Blowdown High-pressure vessels Hazards Depressurization Simulation tools Modeling

a b s t r a c t In process industry, failure or rupture of pressurized vessel is very dangerous especially when there is an escape of flammable gaseous mixture that can cause potential fire or explosion. One of the scenarios that causes such accidents is the blowdown process. Therefore, it becomes crucial to control blowdown process to prevent such accidents. It is important to design optimally to make sure that blowdown valve is according to the requirements. For the safe use of a pressure relief system, some of the parameters are critical, for example, selection of construction material, sizing of relief valves, temperature, and pressure, etc. There is no literature currently available that discusses all the mathematical models or simulation tools for optimum design of the blowdown process. This subject matters because the available models or tools cover different aspects of blowdown process. A meticulous review is required to present the applications of these models and tools based on the accidental scenarios. Therefore, this paper critically reviews the models and tools that are developed purposely to calculate optimum blowdown parameters based on fluid and vessel conditions. Recommendations are given for the development of new simulation tool to simulate phase change conditions especially when solid formation is involved. © 2019 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.

Contents 1. 2.

3.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 1.1. Concerns and considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 Design of blowdown system for pressure vessels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 2.1. DIERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 2.2. BLOWDOWN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 2.3. FRICRUP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 2.4. BLOWSIM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 2.5. PHAST . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 2.6. P. S. Cumber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 2.7. A. Fredenhagen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 2.8. H. Mahgerefteh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 2.9. SDM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 2.10. J. Zhang . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 2.11. VBsim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 2.12. A. Park . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 Design of blowdown system for pressure pipelines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 3.1. META . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 3.2. Fairuzov . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

∗ Corresponding author. E-mail address: [email protected] (A.M. Shariff). https://doi.org/10.1016/j.psep.2019.10.035 0957-5820/© 2019 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.

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4. 5. 6.

105

3.3. CNGS-MOC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 3.4. A. Oke . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 3.5. VPM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 3.6. OLGA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 3.7. S. Brown . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 3.8. S. Martynov . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 3.9. M. Drescher . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 Major findings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

Nomenclature BP CCS CFD EoS FBR FDM FEM HC HEM HRM ID MAD META MOC MSM PR PRV QRA SCWR SDM SRK TEM VBsim V-L VPM V-S VLE

British Petroleum Carbon Capture and Sequestration Computational Fluid Dynamics Equation of State Full Bore Rupture Finite Difference Method Finite Element Method Hydrocarbon Homogenous Equilibrium Model Homogenous Relaxation Model Inner Diameter Maximum Absolute Deviation Multi-Component Equilibrium Two-Phase Analyser Method of Characteristics Marginal Stability Two-Fluid Model Peng & Robinson Pressure Relief Valve Quantitative Risk Assessment Supercritical Water-Cooled Reactor Simplified Dynamic Model Soave-Redlich-Kwong Thermodynamic Equilibrium Model Vessel Blowdown Simulator Vapor-Liquid Vent Pipe Model Vapor-Solid Vapor Liquid Equilibrium

1. Introduction Air-tight pressurized vessels and pipelines are widely used to transport or hold gases and process liquids or fluids in petrochemical plants, refineries, and process industries. These vessels are generally subjected to high-pressure loading and unidentical external or internal pressures in comparison to the ambient pressure (Barma et al., 2017). Consequently, it becomes potentially hazardous and dangerous because of characteristic operational pressure of the vessel (Ladokun et al., 2010). The rupture of pipeline and subsequent eruption of fire broke down the platform into seabed resulting in a loss of 167 lives during the Piper Alpha incident (Cullen, 1990). Many other tragedies have been witnessed that caused a significant number of fatalities due to pipeline and vessel rupture (Bond, 2002; Fletcher, 2001). After the Piper Alpha tragedy, the offshore industry carried out a great deal of research work to understand the characteristics of hydrocarbon fires and explosions (Selby and Burgan, 1998; Tolloczko, 1992). The results indicate that a pressure above 4 bar developed in typical topsides of the vessels

Fig. 1. Common reasons for pressure vessel failures.

is enough to inflict the structural damage such as weld failure, local instability, or extensive inelasticity. The National Board of Boiler and Pressure Vessel Inspectors recorded a 24 % increase in the number of accidents involving pressure vessels during 1999–2000. Steam heating, power boilers, and unfired pressure vessels were the major sources of such accidents (Transporter B. Boiler, 2001). From 1992–2001, a total of 23,338 accidents related to pressure vessels were recorded (Transporter B. Boiler, 2001; The National Board of Boiler and Pressure Vessel Inspectors, 2002; AirConditioning, 2002). Similarly, according to Swedish Nuclear Power Inspectorate (Lydell, 2000), more than 66 % (2476) of the pipeline failure incidents recorded during 1994–1999 were triggered due to leakage or puncture. Common reasons for pressure vessel failures are illustrated in Fig. 1. In oil and gas platforms or offshore operations, overpressure of pressurized vessels also arises during emergency situations due to fire or valves’ malfunction. These industries usually work with CO2, natural gas, and fossil fuels (Talbi, 2017; Milano et al., 2016). Most of the accidents at offshore oil and gas industries, nuclear power plants, and chemical plants cause the outflow of radioactive, toxic, explosive, or flammable materials. Particularly in the oil and gas facilities, failure or rupture of pressurized vessels poses higher risk due to the possible escape of flammable gaseous mixture in a fire event. Therefore, process vessels are depressurized for the transportation of flammable or environmentally toxic gaseous mixture to a safer place (Mahgerefteh and Wong, 1999; Moss, 2004; Cui et al., 2010; Onyebuchi et al., 2017). Blowdown is a typical way of minimizing the failure hazard of vessels when an emergency arises in a process facilities. However, for the safe use of a pressure relief system, some of the parameters are crucial; for example, temperature, pressure, selection of construction material, and sizing of relief valves. Prediction of precise minimum vessel wall temperature during depressurization process can affect the selection of construction material, reduce over-design, and subsequently lower the project cost. Similarly, over-design can also be reduced by precise prediction of maximum flow rate during blowdown. Critical parameters for a safe blowdown process are portrayed in Fig. 2.

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sure vessels and pipelines, is presented in this paper to summarize existing work and set out most overlooked aspects. 2. Design of blowdown system for pressure vessels

Fig. 2. Important parameters for safe blowdown process.

In case of blowdown of vessels, a hazard may emerge due to very low temperature gained by the material inside the process vessel. This can potentially lead to rupture even with a small amount of force if temperature falls below the ductile-brittle transition temperature of vessel’s material of construction (Byrnes et al., 1964). If free water is present inside vessel, it can result in growth of hydrates or formation of liquid condensate that can get carried-over into the flare or vent system. If large droplets of liquid condensate or continuous liquid stream gets into the flare, they will start falling from the top covering entire flare into flames. This condition is extremely dangerous as this falling and burning liquid may cause a major fire incident in vicinity of the plant (Richardson and Saville, 1993). To date, several numerical models and simulation tools have been developed that can simulate different blowdown scenarios of vessels based on vessel sizing, blowdown conditions, and compositions etc. A timeline of these simulation tools or numerical models is illustrated in Fig. 4 followed by a brief description (Some of the authors didn’t name their simulation tools; therefore, we have mentioned the name of the authors instead of the simulation tool). 2.1. DIERS

1.1. Concerns and considerations In recent years, safety and process engineers have encountered several safety-related issues while dealing with high-pressure blowdown. The key principle of sustainable depressurization process design is to decrease the pressure and discharge the inventory safely in the minimum possible time (Gradle, 1984). The discharge rate of compressible fluids generally depends upon pressure, pressure drop, temperature, friction factor, Reynolds number, pipeline diameter, roughness, length, and gas properties (L-b and Aziz, 1996). However, the rapid expansion of gas and generation of vapors can expose the pressure vessel to pressurized thermal shock during an emergency blowdown process. This shock initiates due to integrated stress from rapid transitions in pressure and temperature that result in the non-uniform distribution of temperature in vessel walls and, therefore, lead to the differential contraction and expansion. Pressurized thermal shocks can also cause embrittlement of vessel walls and subsequent “failure by fatigue” due to very low temperature generated inside the vessel because of JouleThomson effect. Therefore, to predict the effects of vessel/pipeline rupture or leak, or to design a sustainable blowdown process, there is dire need of a technique to predict the mass efflux. Moreover, to calculate optimum blowdown time, a precise balance between maximum acceptable depressurization time (Api, 1990) and minimum fluid and wall temperature that may be safely considered, is required. Some of the important factors to be considered before designing the blowdown system are illustrated in Fig. 3. Conventionally, several numerical models and simulation tools are reported in literature for the prediction of maximum possible blowdown time and fluid and vessel conditions. The numerical models have been developed by commonly adopting the Homogenous Equilibrium Model (HEM) assumption such that each phase is considered to be at the phase equilibrium and thermal equilibrium. Some of the researchers also coded simulation tools based on their numerical models. However, the available mathematical models or simulation tools cover different aspects of blowdown or depressurization process. Therefore, a literature review of the existing correlations, numerical models, and computational tools that have capability to calculate optimum blowdown parameters for pres-

A consortium of several companies founded DIERS program in 1976 to design pressure relief system for runaway reactions and develop the additionally required technology. DIERS research program performed several experimental studies, coded a comprehensive simulation tool, and designed a bench-scale prototype apparatus. The aim was to predict two-phase flow venting and analyze the possible applicability of various two-phase (vapor-liquid) flashing flow methods for sizing of relief systems. In this model, it is considered that boiling takes place through the entire volume of liquid rather than solely at the surface. Each bubble occupies volume and displaces the liquid surface upward. Individual bubbles are able to rise (slip) through the liquid with a velocity that depends on buoyancy and surface tension, whereas they are retarded by viscosity and foamy character of the fluid (Simon et al., 2008). DIERS program evolved over time; the initial phase included study of vapor-liquid phase dynamics, second phase involved the experimental investigations for small and large scale integral blowdown and vented runaway reaction, and the final phase included the development of a coded computational package along with a bench scale prototype experimental apparatus (Fisher et al., 2010). 2.2. BLOWDOWN A brief description of prediction and experimentation of fluid and vessel behavior during blowdown process was presented by Haque et al. in 1990 (Haque et al., 1990). Experiments were performed on blowdown of pressurized vessels containing pure N2, 70 % N2–30 % CO2, and natural gas/hydrocarbon mixture. Based on the experiments performed and assessment of available data, a computational tool called BLOWDOWN was coded to simulate rapid depressurization of vessels. The developed BLOWDOWN package has the ability to measure the temperature, pressure, and composition as a function of time. For the experimental investigation, a 6.325 mm orifice was used to blowdown the mixture from a 0.086 m3 vessel with 25 mm of wall thickness. Pure N2 took almost 100 s to reach the atmospheric pressure from 15 MPa. Whereas, the vessel containing 70 % N2–30 % CO2 binary mixture reached the atmospheric pressure in 60 s. The

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Fig. 3. Factors to be considered before designing a sustainable pressure relief system.

Fig. 4. Timeline for blowdown simulation tools and numerical models for vessels.

dynamic change in gas and wall temperature is depicted in Fig. 5. To analyze the predicted results, the coefficient of determination, R2 , and geometric mean bias of the model data are calculated. For this model, the R2 for temperature prediction is ≈ 0.977. A comparative illustration of R2 values and geometric mean bias of different models is presented in Figs. 33 and 34 respectively. Subsequently, an extension in the simulation tool was made that can also be used to simulate the blowdown of pipeline, particularly a long subsea pipeline. Extension of this work by Haque et al. in 1992 covers simulation study of free water (produced during depressurization) for the arbitrary combinations of vessels and pipelines (Haque et al., 1992a). This extended version of BLOWDOWN tool was validated again in 1992 by Haque et al. while supported by several case studies (Richardson and Saville, 1991; Haque et al., 1992b). In the first case study; 53,804 m long, 16.5 subsea gas line containing 51 MMSCF methane at 283 K was blown down from a pressure of 12 MPa. In the second case study, full-bore depressurization of 2000 m long pipeline containing 1975 tonnes of methane condensate was carried out. The initial pressure inside the pipeline was 20 MPa and initial temperature was around 313 K. Another comparison of BLOWDOWN predictions and experimental data was made during LPG test performed by British Petroleum (BP) and Shell on the Isle of Grain in 1985 (Richardson and Saville, 1996; Cowley and Tam, 1988; Tam and Higgins, 1990). Further experimental investigations on the prediction of blow-

Fig. 5. Dynamic temperature changes during blowdown for (a) 70 % N2–30 % CO2 mixture and (b) pure N2 (Haque et al., 1990).

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down parameters using BLOWDOWN package are also available in literature (Saville et al., 2004). In all the experimental studies, BLOWDOWN package provides a reasonable understanding of the physical processes occurring and an ability to make predictions with adequate certainty. However, use of extended corresponding states principle introduces uncertainties that make the simulation computationally difficult. Moreover, the limitations of a cubic equation of state (EoS) near or at the critical region are well documented but their effect on the accuracy of blowdown simulation is still unknown. Further improvement and simulation of practical problems imply the assumptions of homogeneity when the flow is two-phase and the quasi-steadiness could be neglected.

2.3. FRICRUP A simple mechanistic model named FRICRUP was coded by Norris et al. in FORTRAN program to predict single and multi-phase flow behavior during blowdown of vessels or pipelines (Norris and Puls, 1993). HEM and thermodynamic equilibrium model (TEM) assumptions along with no relative velocities between liquid and vapor phases were taken into account. Moreover, FRICRUP tool was validated with the available data for gaseous mixture of CO2, carbonated water, and air. The comparison shows that a reasonable mechanistic model has been developed that can predict single and multi-phase blowdown from the vessel as well as the pipe. Regardless of its complexities, the mechanistic model indicates disagreement with multi-phase flow possibly due to TEM assumptions. A year later, Norris et al. conducted another experimental study using HC gases (Norris, 1994). The results were similar to the ones achieved while using the non-HC gases because the basic mechanical model assumptions remained the same.

Fig. 6. Correlation between predicted and experimental pressure-time profiles (Mahgerefteh and Wong, 1999).

Fig. 7. Correlation between predicted and experimental vapor temperature profile (Mahgerefteh and Wong, 1999).

2.5. PHAST 2.4. BLOWSIM BLOWSIM model (Mahgerefteh and Wong, 1999; Wong, 1998), developed by Mahgerefteh and Wong is based on three cubicEoSs including Peng and Robinson (PR) (Peng and Robinson, 1976), Soave-Redlich-Kwong (SRK) (Soave, 1972), and newly developed TCC Cubic-EoS (Twu et al., 1992). BLOWSIM (BLOWdownSIMulation) requires a minimum number of input parameters. It is computationally efficient and can predict pressure, mass flow rate, and fluid and wall temperature, all as a function of time. BLOWSIM model considers the following: 1 Heat transfer between fluid phases and their corresponding sections of the vessel wall. 2 Non-equilibrium effect between phases. 3 The effect of sonic flow at the orifice. 4 Interphase fluxes because of condensation and evaporation. The performance of the featured model was assessed by the correlation of predicted data generated from BLOWDOWN and experimental results obtained from blowdown of condensable gas. Typical output results include dynamic temperature and pressure profiles for liquid and vapor phases as well as unwetted and wetted walls. The achieved results and their comparison with different EoSs as well as the experimental data are illustrated in Figs. 6 and 7. BLOWSIM’s predictions are quite insensitive to the Cubic-EoS used. In general, it can be inferred that choice of the Cubic-EoS has a negligible effect on predicted results. Moreover, both numerical models are capable of reasonably predicting the dynamic pressure variations. The R-square noted for TCC (TWU) model for temperature predictions is ≈ 0.992.

The Unified Dispersion Model (UDM) developed by Woodward and Cook in the early 90’s was later implemented into DNV software package, termed as PHAST in version 6.0 (Witlox and Holt, 1999; Woodward et al., 1995; Woodward and Papadourakis, 1995). PHAST is a helpful tool to study the initial release of mixture as well as the far-field dispersion. Previously, PHAST was limited only to vapor and liquid phase release of the chemicals. However, the upgraded version allows to study the occurrence of fluid to solid transition during release of CO2. PHAST was validated against several experimental studies for unpressurized release of CO2 (Witlox and Holt, 1999, 2001). Later, Witlox et al. performed some more experimental studies for the validation against pressurized release of CO2 (Witlox et al., 2014). An overview of the validation of different models including flammable effect, dispersion and pool spreading/evaporation, and discharge models was provided along with extensive experimental database for validation of the above models and scenarios (Witlox et al., 2018). 2.6. P. S. Cumber A numerical model was coded by Cumber for the prediction of vent sizing of pressurized vessel during blowdown batch process (Cumber, 2001). The pressure vessel containing gas mixture is considered as a single unit with thermodynamic equilibrium assumptions. This model has a vast range of venting models implemented for a two-phase system. However, selection of the most suitable model for a specific case study necessitates the user to have comprehensive information on the scope of application of the respective model. For this particular case, predicted blowdown data was plotted against the experimental data as shown in Figs. 8 and 9. The trend indicates that predicted gas temperature in the initial

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Fig. 8. Dynamic pressure profile during blowdown of LPG (Cumber, 2001).

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Fig. 10. Calculated and measured pressure transients for 17 mm2 orifice (Fredenhagen and Eggers, 2001).

Fig. 9. Dynamic temperature profile during blowdown of LPG (Cumber, 2001).

phases of depressurization is in agreement with the experimental data. However, ultimately it poorly predicts temperature with an R-square ≈ 0.445 because of the adiabatic vessel wall assumption as shown in Fig. 9. The significant difference is with respect to the phase temperature measurement that shows that thermodynamic equilibrium assumption is not effective for this case. However, the measured pressure of vessel was precisely predicted. For the vessel depressurizing over long time-scale, the temperature of the vessel was under-predicted after first few minutes as a consequence of assuming no heat transfer through the vessel walls. This did not have a substantial effect on the simulated mass flow rate though. Another discrepancy with the application of this model is the robustness that needs to be addressed (Skouloudis, 1992). 2.7. A. Fredenhagen Previously accomplished research work on depressurization of pure CO2 leads towards successful modeling of the pressure transitions and axial void profile during the expansion process (Eggers and Green, 1990; Gebbeken and Eggers, 1995, 1996; Gebbeken and Eggers, 1997). However, an experimental investigation on blowdown of the top vented pressurized vessel containing CO2 with impurities (N2) was performed by Fredenhagen and Eggers in 2001 to study the effect of impurities (Fredenhagen and Eggers, 2001). In this study, the axial void profiles, axial temperature profiles, and pressure and mass were measured. Top vented cylindrical vessel with 0.05 m3 volume, 0.242 m ID, and a 4:5 height to diameter ratio was used. The venting line was linked to a quick opening ball valve with a cross-sectional area of 50 mm2 . PR EoS was used for the calculation of phase equilibrium. For the prediction of this process, a simulation tool was also coded based on the energy and mass balance and a drift flux model. The dynamic pressure and temperature profiles predicted by featured simulation tool and the experimental results are illustrated in Figs. 10 and 11. The computational model predicted reasonable results of pressure transition throughout the process. The overall R-square for temperature pre-

Fig. 11. Calculated and measured temperature transients (Fredenhagen and Eggers, 2001).

dictions is ≈ 0.955, however, the temperature predictions at low pressure were not much precise. Consequently, an improvement needs to be made for more precise modeling of thermodynamic behavior of the mixture. 2.8. H. Mahgerefteh Most comprehensive blowdown model reported in literature was BLOWDOWN, later on extended as BLOWSIM as discussed earlier. Although validated extensively with the experimental results, the prediction is still limited to depressurization under ambient temperature. This is a serious drawback since the blowdown situations may involve a fire case most of the time. To overcome this issue in 2002, Mahgerefteh et al. described the establishment of a numerical model for quantitative risk assessment (QRA) of rupture following the depressurization of vessel under fire (Mahgerefteh et al., 2002). The model is able to predict the tri-axial transient pressure and thermal stress produced in both unwetted and wetted wall sections of the vessel. The fluid/wall heat transfer was obtained using the following equation.



n 

’ Q = h Tw (a, t)



’ Tw (a, t) − TZ At

(1) 

Where h is the heat transfer coefficient, Tw (a, t) refers to the unknown wall temperature at time t, TZ is the liquid or vapor temperature, A is the heat transfer area and n stands for power index. A hypothetical case study for the depressurization of a vessel containing higher-HC was performed. The vessel was supposed to be at the initial pressure and temperature of 11.6 MPa and 293 K respectively. Two types of blowdown scenarios were simulated: (1) the vessel under ambient conditions and (2) the vessel under fire radiating a heat flux of 90 kW/m2 . The predicted pressure and temperature profiles for a vessel under ambient and fire conditions are illustrated in Fig. 12. The predicted results show that thermal radiation compensates the temperature drop to a large

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Fig. 12. Temperature and pressure histories under ambient and fire conditions (Mahgerefteh et al., 2002). Fig. 13. Comparison of experimental results and SDM (Song et al., 2013).

extent. A comprehensive analysis of pressure stress and triaxial thermal profiles indicates that rupture occurs in dry section of vessel because of the combined effect of resident total stress and thermally induced mechanical weakening of vessel walls. The featured numerical model serves as a powerful tool for the calculation of minimum required blowdown time to eradicate the risk of vessel puncture under fire. 2.9. SDM Over the years, the researchers’ primary focus has been on the performance of pressure relief valve (PRV) using dynamic modeling approach. Unfortunately, most of the processes were simulated for dynamic properties of PRV at the fixed inlet scenarios and not during the reclosing process (API, 1993). To predict the dynamic properties of PRV during reclosing process, a simplified dynamic model (SDM) was presented by Song et al. (Song et al., 2013). When the disc moves, PRV behaves as one degree-of-freedom system and motion of the moving part (stem and disc) was resolved based on force balance when open. The motion of value was simulated based on second-order differential equation deduced from Newton’s second law (Eq. 2). mx¨ + c x˙ + Fs = Ff − Fg + fc

(2)

Where m, x¨ , and x˙ represent the mass of the moving parts, acceleration, and velocity of the disc part in the moving direction respectively. c represents the damping coefficient and Fs stands for the spring force acting on the disc that was calculated using k(x0 + x (t)). Ff , Fg , and fc are the flow force acting on the disc part, the gravity of disc, and the coulomb friction parameters respectively. One degree-of-freedom system based on the equation of motion was calculated using Eq. 3. ¨ mx/

˙ + c x/

+ k(x0 + x)/

= (/4).Cf .

(3)

Where k is the spring stiffness. and  are the reference force and pressure difference ratio. The dynamic numerical model was based on the major principles of the steady computational fluid dynamics (CFD) analysis and rigid-body motion of the PRV. Afterwards, the results from a case study revealed that SDM predicted the blowdown of conventional PRV reliably as shown in Fig. 13. In addition, the effect of reclosing/opening process and spring stiffness can also be easily studied using this dynamic numerical model. 2.10. J. Zhang To Simulate the blowdown process for the supercritical water-cooled reactor (SCWR), a transient analysis code using a comprehensive numerical model was developed by Zhang et al. in 2013 (Zhang et al., 2014). Three different phase separation models were implemented for the calculation of stagnation enthalpy of two-phase fluid. Firstly, a homogenous mixture model was used to

Fig. 14. Dynamic pressure comparison of different models (Zhang et al., 2014).

calculate subcooled, supercritical, and overheated fluid by neglecting phase separation effect. Secondly, assuming that bubble rising and blowdown periods are comparable and ignoring neither discharge rate nor the bubble rising velocity, bubble rising model describes this process properly. Thirdly, a complete separation model is considered suitable for conditions when bubble rising velocity is faster as compared to the discharge speed and when the droplets falling velocity is higher than discharge speed for condensation because there is enough time for vapor dome development in both the cases. Supercritical CO2 and H2O were blown down initially from 313 K temperature and 25 MPa pressure for experimental investigation and verification of the developed code. The experiments were performed on a cylindrical vessel with a 4 m height, 2 m diameter and a 17 mm2 orifice for depressurization. The experimental study and predicted pressure drop results with different models as shown in Fig. 14. The R-square for pressure predictions is ≈ 0.377 by complete separation model. The consequence of the initial condition on pressure drop was considered for different regions divided by the relationship between corresponding pseudo-critical and initial temperature. Furthermore, it was concluded that both void fraction and blowdown speed increase with the decrease in initial pressure and an increase of initial temperature, yet vice versa for the fluid inventory. 2.11. VBsim To predict the depressurization behavior of vessel containing two-phase (V-L) HC mixture with non-ideal behavior, Alessandro et al. described the modeling and experimental validation of the new unsteady model, VBsim (Vessel Blowdown Simulator) (D’Alessandro et al., 2015). The featured model accounts for non-equilibrium effects between constituent fluid phases such as temperature difference between phases. The numerical model evaluates dynamic fluid temperature, pressure, and composition

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Fig. 15. VBsim and BLOWDOWN predictions vs experimental data (S9) (D’Alessandro et al., 2015).

using EoS for non-ideal gas. SRK and PR EoS with Van der Waals mixing rules have been implemented. Vapor phase discharge ( G, out ) was estimated using equations of motion for compressible fluid through the orifice (Eqs. 4 and 5). G, out

= CDG

G is /MW

⎧  (+1)/2(−1) ⎨ SG, or √pG 2/( + 1) is = ⎩ SG, or 1/ 2/( − 1)pG 1 − (−1)/ 

(4)



/(−1)



/(−1) (5)

p/pext ≥ 2/( + 1)

p/pext < 2/( + 1)

G is the vapor phase molar weight and C G is fixed to Where MW D a default value of 0.84. G is the vapor density, SG, or is the orifice area, p is the vessel pressure, pext is the atmospheric pressure, is the ratio of p & pext , and  is the isentropic coefficient of the real gas. The equation for an incompressible fluid through an orifice was used for the calculation of liquid phase discharge rate (Eqs. 6 and 7). L, out L

= CDL

= SL, or L

L

L /MW



2 (p − pext )/L + gHL

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Fig. 16. Vessel wall temperature histories and comparison with other simulation tools and numerical models (Park et al., 2018).

nucleate boiling using PR EoS (Park et al., 2018). Mass and energy conservations for the fluid were calculated using equations presented by Speranza and Terenzi Speranza and Terenzi (2005). The model consists of sub-algorithms of flash calculation, discharge rate calculation, and heat transfer rate calculation in order to estimate the realistic expansion path. The predicted results were compared with the measured and simulated data from literature including renowned simulation tools such as BLOWDOWN, BLOWSIM, VBsim, BLOW, and commercial tools such as VessFire 1.2 and Aspen HYSYS v9. The model reasonably predicted the vapor temperature within the experimental range while BLOWDOWN, VBsim, and HYSYS predicted 2–10 K higher temperature. Similarly, the model also precisely predicted the wall temperature within the experimental range while VessFire v1.2 and BLOW predicted almost 2–8 K higher wall temperature in contact with vapor, and VBsim predicted 10 K higher wall temperature in contact with liquid as shown in Fig. 16).

(6)



3. Design of blowdown system for pressure pipelines (7)

Where SL, or , L and HL are the orifice area, liquid density, and liqL stands for liquid phase molar uid static head respectively. The MW weight. The liquid discharge coefficient, CDL , is fixed to a default value of 0.61. The liquid and the vapor daughter phase compositions were calculated by xi and yi respectively. xi = zi /(1 − ˇ + ˇKi ’ )

(8)

yi = Ki zi /(1 − ˇ + ˇKi )

(9)

Where Ki is the initial equilibrium coefficient and the overall vapor fraction, ˇ, is calculated by solving the Rachford–Rice equation. For experimental validation of the developed model, the predicted results were plotted against the experimental data from Haque et al. (PR and SRK) and HSE (SRK) (Haque et al., 1992a, b; Roberts et al., 2000). A comparison with the previously defined blowdown model (BLOWDOWN) prediction was also made as shown in Fig. 15. Considering the overall performance, VBsim produced reasonable results with R-square ≈ 0.682 for temperature predictions and less CPU time requirements. However, the impact of the model could be significantly improved if compared with further experimental data. 2.12. A. Park Previously, Haque et al. and Mahgerefteh et al. developed models to study heat transfer between the mixture and the vessel walls. However, the correlation used and the value of the heat transfer coefficient were unclear. Therefore, Park et al. (2018) presented an elaborated heat transfer model including combined convection (forced and natural), multi-layer transient conduction, and the

The blowdown of a pipeline and a vessel differs from each other due to a considerable pressure difference within the vessel but not within the pipeline. For blowdown of a vessel, pressure drop is across the orifice, whereas for a pipeline blowdown, pressure drop is along the line and across the orifice if it is small enough. In case of blowdown of pipelines, the hazard emerges not only following the low temperature generated in the pipeline walls but also due to the high efflux rates and large total efflux that arise when a massive inventory in a typical line is depressurized (Richardson and Saville, 1993; Jarrah, 2016). To avoid accidents caused by these issues, several numerical models have been developed. Later, some of them have also been coded as computerised program usually known as simulation tools. A timeline for the available simulation tools and numerical models capable to simulate the depressurization process is illustrated in Fig. 17 followed by a brief description (Some of the authors didn’t name their simulation tools; therefore, we have mentioned the names of those authors instead of the simulation tool). 3.1. META Marginal stability two-fluid model (MSM) based on extended Geurst’s variational principle to generalize multi-component twophase dispersion was presented by Chen et al. in 1995 (Geurst, 1985a, b; Geurst, 1986; Chen et al., 1995a). Thermodynamic equilibrium assumptions were made to develop the equations of motion and energy conversion for compressible single or multi-component vapor-liquid (V-L) mixture. To make the mathematical simulation of physical process possible and profound, the flow was considered to be marginally stable to achieve hyperbolicity of the equations.

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Fig. 17. Timeline for blowdown numerical models.

Fig. 18. Dynamic pressure changes’ histories at the closed end (Chen et al., 1993).

In the later volume of publication, the simplified numerical method developed by Chen et al. in 1993 (Chen et al., 1993) was modified and applied to the MSM for multi-component mixtures (Chen et al., 1995b). Subsequently, MSM and HEM were incorporated on the basis of simplified numerical method, and a computational package termed as META (Multi-component Equilibrium Two-phase Analyser) was coded. A comparison of different case studies was made between HEM and the MSM with experimental data for single or binary component two-phase blowdown. A 100 m long horizontal commercial steel pipeline with 0.15 m inner diameter (ID) containing LPG (95 mol % propane and 5 mol % butane) was blown down. The testing temperature and pressure were kept between 288–293 K (ambient temperature) and 800–2100 kPa respectively. The bore size was varied from 0.05 m to full-bore in diameter and controlled with the circular orifice plate. Figs. 18 and 19 show the history of the pressure and temperature variations with respect to time at the closed ends. An R-square ≈ 0.957 was found in case of META-MSM CS for the temperature predictions. The comparison of HEM predictions and the measured data has been exceptionally reasonable. All the predicted temperature, pressure, inventory, and void fraction transitions correspond with the measured data. The only peculiarity was in case of the void fraction that was over-predicted after 7 s at the closed end. The most significant findings are presented as follows. 1 The simplified numerical method predicted reasonable results for blowdown through experimental validations as shown in Figs. 18 and 19. 2 In case of a full-bore short pipeline blowdown (< 10 m), both mechanical and thermal non-equilibriums are significant. How-

Fig. 19. Dynamic temperature changes’ histories at the closed end (Chen et al., 1993).

ever, for a long pipeline blowdown, thermal non-equilibrium is found to be insignificant. 3 Precise predictions of the phase equilibrium and thermodynamic behavior are important for the transient flow calculations. 3.2. Fairuzov Previously, most of the work encompassed the modeling of depressurization from vessels or relatively short pipelines (Lahey and Moody, 1977; Reibold et al., 1981; Jackson et al., 1981). Therefore, a numerical simulation model for the depressurization of relatively large pipeline transporting multi-component flashing mixtures was coded by Fairuzov in 1998 (Fairuzov, 1998). The effect of heat transfer between fluid flow and pipeline wall during blowdown phenomenon was also described. Heat transfer model, the hydrodynamic model, and break-flow model were the building blocks of the featured model. No experimental study was conducted, however, the simulation tool was validated against the already available experimental data from BP and Shell on the Isle of Grain (Cowley and Tam, 1988). The calculations were carried out on an HP Apollo Series 700 working station using a double-precision FORTRAN 77 code. Fairuzov proposed a higher amount of heat transfer amongst fluid and pipe walls during the depressurization process, hence, the adiabatic assumption for simulation became invalid. Therefore, effect of thermal capacitance was integrated into the model using a different method in the development of energy conversion equation. The study unveiled considerable effect of thermal capacitance of pipeline on the behavior of two-phase fluid flow. Consequently, thermal capacitance should not be ignored especially in case of the

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Fig. 20. Dynamic pressure transitions at the open and closed ends of the line (Fairuzov, 1998).

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Fig. 22. Dynamic pressure histories at the open end for the P42 test LPG (Mahgerefteh et al., 1999).

poor. The CNGS-MOC predicted the physical process with R-square ≈ 0.850 for pressure predictions. 3.4. A. Oke

Fig. 21. Dynamic temperature transitions at the open and closed ends of the line (Fairuzov, 1998).

flashing fluids. The dynamic pressure and temperature profiles are reported in Figs. 20 and 21 respectively. Fig. 20 illustrates that the model slightly over-predicted depressurization rate at the closed end of pipe. However, when the fluid flow was considered to be adiabatic, the temperature at the open end was significantly predicted with R-square ≈ 0.914. 3.3. CNGS-MOC An efficient mathematical model (CNGS-MOC) for the simulation of full-bore rupture (FBR), based on the method of characteristics (MOC) was developed by Mahgerefteh et al. in 1999 (Mahgerefteh et al., 1999). The MOC was implemented to simulate FBR or depressurization of a long pipe containing two-phase or condensable HC mixtures. This method was used to develop a more suitable method than the Finite Difference Method (FDM) and Finite Element Method (FEM) because both had troubles in handling the choking scenarios at the ruptured end. Moreover, the MOC is more precise than FDM and FEM because it can resolve the blocked flow intrinsically using Mach line characteristics. The MOC significantly reduces number of iterations involved while solving the system of simultaneous equations. The use of curved characteristics in conjunction with fast-mathematical algorithm and compound nested grid system leads to a dramatic reduction in CPU time in addition to improved accuracy. The model was extensively validated using field data obtained during Isle of Grain (Richardson and Saville, 1996) as well as Piper Alpha tragedy (Chen, 1993). The simulation studies were performed on the basis of HEM assumptions. In Fig. 22, the predicted data with CNGS-MOC and field data are correlated with those based on other simulation tools including BLOWDOWN (Haque et al., 1990), META-HEM (Chen et al., 1995a, b; Chen, 1993), MSM-CS (Chen et al., 1995a, b; Chen, 1993) as well as PLAC (Hall et al., 1993). Both META-HEM and CNGS-MOC produced reasonably precise predictions while other models’ predictions were relatively

Regardless of the fact that most common pipeline tragedies include rupture, majority of the reported models so far are based on 1-D axial flow. Others just treat the pipeline as a vessel discharging through an orifice. Therefore, Oke et al. developed a model that can predict the transient release rate through the punctured plane based on MOC (Oke et al., 2003). The model accounts for axial and radial flow and real fluid behavior as well as the rupture locality with respect to pipeline length. The PR EoS was employed to get suitable phase and thermodynamic equilibrium data that is particularly appropriate for high-pressure HC mixtures (DeReuck et al., 1996; Assael et al., 1996). In case of 1-D unsteady flow, assuming phase and thermodynamic equilibrium among phases, the energy, momentum, and continuity conservation equations for a fluid in a rigidly clamped pipeline were taken from literature (Veersteg and Malalasekera, 1995). The continuity equation was reformulated as follows. [T + ϕ] dP/dt − ϕ*dh/dt + 2 a2 T *∂u/∂x = 0

(10)

Where h and ϕ represent enthalpy and thermodynamic function respectively.  and u are density and velocity as a function of time (t) and distance (x) respectively. Using MOC, the conservation of continuity, energy, and momentum equations can be substituted with three compatibility equations along with their corresponding characteristic lines. The isolated flow was modeled based on termination of the inlet feed upon rupture. In case of non-isolated flow, inlet feed is supposed to be stopped after a prescribed period of time. Fig. 23 is schematic illustration of the fluid flow analysis following rupture and emergency isolation with various boundary conditions from B1 -B6 . In Fig. 23, C stands for match line, C0 stands for path line, and J represents solution joints. The simulation of pressure and velocity profiles specifies three separate fluid flow regimes predominant within the pipe that manage the dynamic transitions of the release rate. For validation of the numerical model, the simulated outcomes were plotted against the data from experiments performed by BP and Shell on the Isle of Grain (Cowley and Tam, 1988). Pressure and temperature transitions at closed and opened end are shown in Figs. 24 and 25 respectively. The results ended up with a reasonable prediction of the physical process with R-square ≈ 0.942 for temperature at the closed end as shown in Fig. 25. 3.5. VPM Until 2011, no numerical model was developed to analyze the blowdown conditions for a vent pipeline. Therefore, Rajiwate

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Fig. 23. Rupture plane and fluid flow study following line puncture (Oke et al., 2003).

Fig. 24. Pressure transitions at closed and opened end of P40 (LPG) test (Oke et al., 2003).

Fig. 26. Measured upstream pressure and temperature (Clausen et al., 2012).

geometry, and assumed friction factor, Eq. 11 and 12 define the flow (Parker, 1985). The predicted results were then validated with the experimental study performed on a 12 m long stainless-steel pipeline. A total of 9 experimental studies were conducted with an initial pressure and temperature of 200–400 kPa and ≈ 19 ◦ C respectively. The experimental data were plotted only for a steady-state period that showed a good agreement with the predicted values. 3.6. OLGA

Fig. 25. Temperature transitions at closed and opened end of P40 (LPG) test (Oke et al., 2003).

developed a vent pipe model (VPM) to investigate the behavior of compressible gas in a vent pipeline using thermodynamic and fluid dynamic approach (Rajiwate, 2011). Integrated with the GERG EoS, the use of REFPROP makes a highly adequate prediction with the VPM (Lemmon et al., 2009; Kunz et al., 2007). Temperature, pressure, and density relations in terms of stagnation properties were defined previously (Bansal, 2005; Saad, 1993; Shapiro, 1954). Mass efflux prediction for pipe is the central step for the development of blowdown model for vent system in terms of static pressure and static temperature that is expressed as: G = PM



/ZRT

(11)

The above equation for mass flux in terms of stagnation properties was represented as:



G = Po /



To *



/ZRM/ 1 + ( − 1)/2 *M 2

(+1)/2(−1)

(12)

Where To , Po are the stagnation temperature and pressure respectively,  is the specific heat ratio, and Z, R and M are the compressibility factor, universal gas constant and match number respectively. For a given downstream and stagnation pressure,

Most of the reported data on experimental study of CO2 blowdown (Gebbeken and Eggers, 1996; de Koeijer et al., 2009; Clausen and Munkejord, 2012; de Koeijer et al., 2011; Cho et al., 2013) describes findings from small-scale laboratory setups of flow loops and vessels. Thus, it is of great interest for carbon capture and sequestration (CCS) community to collect field data from existing large-scale CO2 facilities. Therefore, a large-scale CO2 pipeline blowdown was carried out by Clausen et al. in 2012 while pointing the possible limitations of existing dynamic multi-phase flow simulator (OLGA) (Clausen et al., 2012). An onshore buried 50 km long 24 ID pipeline containing 93,000 tonnes of CO2 (>99 % Pure) was initially depressurized from supercritical conditions. The initially reported temperature and pressure were 304 K and 8.1 MPa respectively. The blowdown process was modeled using OLGA V5.3.2, a multi-phase thermo-hydraulic simulation tool developed by SPT Group (Bendiksen et al., 1991). The new coded module of OLGA for CO2 single component was used that utilizes Span-Wagner EoS for pure CO2 (Span and Wagner, 1996; Aursand et al., 2013). The total blowdown time was noted to be nearly 10.50 h while OLGA predicted duration of 10 h and 25 min. Both simulation and experimental data showed that the blowdown stayed well above the CO2 triple point, and no traces of solidification were found as shown in Fig. 26. However, the minimum simulated temperature was almost 17 K lower than the minimum measured temperature. The deviation between simulated and measured blowdown path reveals inability of the simulation tool to handle CO2 along with

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115

Table 1 Predominant conditions and pipeline characteristics for the COOLTRANS shock tube test. Pipeline characteristics Pipeline length Internal diameter Pipeline wall roughness

Initial conditions 144 m 150 mm 0.05 mm

Fluid temperature Fluid pressure Ambient pressure

278.35 K 15.335 MPa 0.101 MPa

Fig. 27. Pressure transition of simulated and measured data for 92 % CO2–8 % N2 blowdown (Huh et al., 2014).

Fig. 29. Pressure-time profile at 0.1 m from release end of the CO2PipeHaz FBR test (Brown et al., 2013).

∂E/∂t + ∂u(E + P)/∂z = −u(fw u2 /Dp )(Energy Balance)

Fig. 28. Temperature changes of simulated and measured data for 92 % CO2–8 % N2 blowdown (Huh et al., 2014).

impurities. Even a very small amount of impurities will disturb the blowdown path. To further study the effect of impurities on CO2 blowdown and reliability of the OLGA tool, Huh et al. conducted experimentation in 2014 with 2–8 % N2 addition by mass fraction (Huh et al., 2014). The experimental apparatus comprises of the pressurization part, liquefying part, mixing zone, and the test section. Total length of the testing apparatus was 51.96 m with 3.86 mm ID. The temperature and pressure measurements were observed at four different positions as illustrated in Figs. 27 and 28. However, the simulation tool did not predict temperature drop precisely. The results show that the numerical simulator predicted better pressure drop at higher concentration of impurities. Furthermore, the R-square value at initial portion (7.93 m) of pipeline is ≈ 0.697. While, at last portion (51.85 m), the temperature predictions are much precise with R-square ≈ 0.859. It can be inferred that the numerical simulator requires further improvements in phase change model. 3.7. S. Brown The commonly reported vessel/pipeline outflow numerical models were based on HEM assumptions where the fluid phase was considered to be at the mechanical and thermal equilibrium. Consequently, there was no-equilibrium V-L transition and phase-slip phenomena, that is, delayed bubble formation was ignored. In 2013, Brown et al. extended the prior work by establishing and validating homogeneous relaxation model (HRM) for depressurization of dense phase CO2 pipeline (Brown et al., 2013). Initially, the phases were assumed to be at mechanical and thermal equilibrium, hence, the mass, momentum, and energy conservation were presented by Eqs. 13–15 respectively.

∂/∂t + ∂u/∂z = 0(Conservation of Mass)

(13)

∂u/∂t + (∂u2 + P)/∂z = −fw u2 /Dp

(14)

(15)

Where , Dp , P, u, and fw are the mixture density, pipeline diameter, pressure, velocity, and fanning friction factor respectively. All of these factors were evaluated using Chen’s correlation (1979) (Chen, 1979) as function of space (z) and time (t). E stands for the energy of the mixture. For the non-equilibrium V-L transition, HRM was used with the mechanical equilibrium assumption such that no phase slip was maintained. The non-equilibrium V-L transition equation with thermodynamic equilibrium for the vapor mass fraction is presented in Eq. 16.

∂x/∂t + u(∂x/∂z) = (xeq − x)/

(16)

Where x represents the dynamic vapor quality and stands for relaxation time accounting for the phase change transition delay. Angielczyk et al. proposed an empirically determined correlation for the relaxation time as given in Eq. 17 (Angielczyk et al., 2010).



= 2.15 × 10−7 x(/sv

−0.54 

(Ps (Tin ) − P)/(Pc − Ps (Tin ))

−1.76

(17)

Where Pc , sv and Ps are critical pressure, saturated vapour density at given pressure, and saturation pressure at given temperature respectively. To validate numerical flow model’s reliability, the hypothetical shock tube test was conducted initially for both single (Liquid) and two-phase CO2. Table 1 presents the initial conditions and pipeline characteristics for the COOLTRANS FBR dense-phase CO2 shock tube test. Moreover, CO2PipeHaz CO2 pipeline rupture experiment conditions were used as an experimental study (Mahgerefteh et al., 2011). A 37 m long with 40 mm ID instrumented pipeline carrying pure CO2 was blown out using an explosive charge. Pipeline’s initial conditions were 7 MPa pressure and 298.35 K temperature. In general, HRM produced plausibly good estimations of the experimental data especially during the initial period of blowdown as shown in Fig. 29. R-square for pressure predictions is ≈ 0.924 that indicates reliability of the model. It was observed that FBR clearly indicates fully dispersed flow and, hence, the phase-slip can’t be ignored. 3.8. S. Martynov Since most of the prior reported blowdown simulation models have been developed for V-L phase depressurization, they were not appropriate for simulating solid CO2 release. Martynov et al. in 2013

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Table 2 Initial experimental conditions of the release. Initial fluid condition

Test 1

Test 2

Test 3

Pressure/MPa Temperature/K Inventory/tonne

8.0 307 6.5

8.6 312 4

5.3 290 6.5

Fig. 31. Comparison of numerical and experimental (PT-40, TT-40) dynamic temperature changes for different compositions at 50 m (Drescher et al., 2014).

Fig. 30. Time variation of the pressure measured in test 3 (Martynov et al., 2014).

extended HEM for the development of outflow model accounting for CO2 solidification during blowdown (Martynov et al., 2014). A set of equations describing the HEM flow including mass conversion, and momentum and energy balance equations were used. For mass conservation, Eq. 13 was used. Eqs. 14 and 15 were modified to Eqs. 18 and 19 to calculate the momentum and energy balance respectively.

∂u/∂t + (∂u2 + P)/∂z = −2f w u2 /D(Momentum Balance) (18)

Fig. 32. Comparison of numerical and experimental (PT-40, TT-40) dynamic pressure changes for different compositions at 50 m (Drescher et al., 2014).

∂E/∂t + ∂u(E + p)/∂z = 4qw /D − 2f w u3 /D(Energy Balance) (19) To calculate the properties of vapor-solid (V-S) and vapor-liquid (V-L) equilibrium mixtures formed during the depressurization of vessel/pipeline containing CO2, previously developed PR EoS by Martynov et al. (Martynov et al., 2013) was extended and applied. p = RT/(v − b) − a/(v (v + b) + (b (v − b))

(20)

Where R, T , p, and v are the universal gas constant, temperature, pressure, and specific volume respectively. a and b are the empirical parameters accounting for the intermolecular attraction forces and molecular volume respectively. The instantaneous heat flux at the pipe wall was calculated based on pipeline wall temperature transitions with time using Eq. 21. average

qw

average

= w Cp,w ıw *((dTw

)/dt)

(21)

average Tw

Where represents the average pipeline wall temperature. w , Cp,w , and ıw stand for density, pipeline heat capacity, and wall thickness of pipeline respectively. The featured numerical model was validated against experiments conducted by Dalian University of Technology (DUT) under CO2PipeHaz project. The model precisely predicts the pressure transitions in the pipeline for initially supercritical fluid (Test 1 and 2). The initial experimental conditions for all the case studies are presented in Table 2. In case of an initially two-phase fluid (Test 3), the given HEM model is not much reliable because of R-square ≈ 0.661 for pressure predictions as shown in Fig. 30. Moreover, the release model also predicted the dry ice formation and explained the transition phenomena from V-L to V-S equilibrium at a triple point of CO2. 3.9. M. Drescher HEM was validated mostly against the experimental data from CO2 pressure release. However, Dresher et al. (2014) executed

experiments with different CO2–N2 compositions to study the potency of the modified HEM for a multi-component system (Drescher et al., 2014). For simulation study, PR EoS was used and experiments were performed on a 140 m long horizontal tube with 10 mm ID. Initially, the binary mixture in the supercritical region was at 12 MPa pressure and a temperature of approximately 293 K. The numerical results for all three fluid compositions regarding the relative and absolute value match the experimental results very well as illustrated in Figs. 31 and 32. With the increase in composition, the model predictions become more precise as maximum R-square ≈ 0.919 for temperature prediction is noted in case of 90 % composition. Despite few complexities in the HEM employed, it still contains several simplifications in view of the comparatively reasonable results. Further work could involve the advanced heattransfer models considering the effect of flow regimes or boiling. 4. Major findings Table 3 presents a matrix of modeling outlooks presented in literature that could aid in a holistic simulation of blowdown use in the industrial sector. Based on the literature reviewed, Table 3 illustrates the followings: • Commonly, the models focused on pressure and mixture temperature transitions with time to understand the blowdown process. • Limited studies on vessel wall temperature and void fraction are also available, however, further research is required when applied to multi-phase processes. • HEM is extensively used to solve the blowdown process with thermodynamic assumptions. • Mostly, the models were validated against previously published experimental data, especially for pure or impure CO2.

U. Shafiq, A.M. Shariff, M. Babar et al. / Process Safety and Environmental Protection 133 (2020) 104–123

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Table 3 Summary of modeling approaches. Title BLOWDOWN BLOWSIM P. S. Cumber A. Fredenhagen SDM J. Zhang VBsim A. Park META Fairuzov CNGS-MOC A. Oke OLGA S. Brown S. Martynov M. Drescher

Pressure √ √ √ √ √ √ √ √ √ √ √ √ √ √ √ √

Temperature Mixture √ √ √ √ × √ √ √ √ √ √ √ √ √ √ √

Wall √ √ × × × × √ √ × × × √ × √ √ ×

Flowrate

Void Fraction

√ √ √ √

√

× √ √ √ √ √ √ √ √ √ √ √

× √

× √ √

× × √ √ × × × × × ×

Fig. 33. Comparative illustration of R2 values for different models.

Fig. 34. MG bias values for different models.

Some of the numerical models or simulation tools produced incredibly precise predictions of the physical phenomenon occurring during the blowdown process. The BLOWSIM produced most precise results with R-square ≈ 0.9925 followed by BLOWDOWN with R-square ≈ 0.977. BLOWSIM, META, OLGA etc. also produced the accurate results before the process, however, they lack the ability to simulate some of the significant parameters. On the other hand, BLOWDOWN has the ability to predict most of the important parameters accurately. Cumber and J. Zhang produced poor results with R-square lower than 0.4. A bar chart (Fig. 33) illustrates R-square value for most of the reviewed simulation tools or numerical models. For the quantitative comparison of reviewed models, the geometric mean bias is taken into account (Fig. 34). A

perfect model is said to have a geometric mean bias equal to 1.0. A geometric mean bias less than 1.0 refers to underprediction and above 1.0 refers to overprediction (Hanna et al., 1993).

5. Summary Different simulation tools and numerical models for the calculation of optimum parameters during blowdown process are reviewed. Table 4 summarizes the operating conditions, vessel dimensions, characteristics, and key challenges. Several novel emerging blowdown models have been reviewed and a comparative study has been presented.

118

Table 4 Comparative analysis of different simulation tools and numerical models. Name/Title Models + Tools BLOWDOWN (1990)

Composition

Condition

Vessel/Pipeline Volume

Orifice Size (mm)

1990

N2, 70 % N2 – 30 % CO2, NG/C3 & HC

150 bar & 20 ◦ C

1.5 m long vessel with 10.6 diameter

6.325

117 bar & 10 ◦ C

40 km long pipeline

0.4191

200 bar & 40 ◦ C

20000 m long pipeline

0.4064

1991

Case 1: C1 –C6 + 4.03 % N2 Case 2: C1 –C5, C1 O, C2O + 3 % H2O

1996

LPG (95 % C3 – 5 % C4)

11.3-22.5 bar & 13.3-20 ◦ C

100 m long pipeline with 2-6 diameter

35-154

META (1994) Model + Tool

1995

LPG (95 % propane & 5 % butane

8 to 21 bar & 15 to 20 ◦ C

100 m in length, 0.15 m

0.05 m

FRICRUP (1993-94) Model + Tool

1993 1994

Air, CO2, carbonated water, CH4 and HHC

69-138 bar & 37.8 ◦ C (Vessel) and 40 bar & 15.5 ◦ C (pipeline).

25.5 km long pipeline with 7.992 diameter

1.5 to 12.7 for a bottle & 84 for Pipeline

Characteristics

Key Challenges

Ref

- Good understanding of the physical processes occurring - Ability to make predictions with an acceptable uncertainty - Based on a three fluids model (vapor, liquid and free water)

- No work in cryogenic conditions or emergency - Use of the extended principle of corresponding states for generating the pertinent fluid thermophysical properties - A simulation study is restricted to depressurization under ambient conditions only - Not fully documented

(Haque et al., 1990; Haque et al., 1992a, b)

- Good understanding of the physical processes occurring - Ability to make predictions with an acceptable uncertainty - Suitable for planned blowdown

- Homogeneity assumption when the flow is two-phase - Quasi-steadiness assumption - No work on cryogenic conditions

(Richardson and Saville, 1991)

- Predictions have been shown to be in at least adequate, and often good, agreement with the Isle of Grain measurements

- No work on Natural gas - No work in cryogenic conditions or emergency situation

(Richardson and Saville, 1996)

- Well prediction of experimental data

- More efficient thermodynamic measurement methods needed - Did not predict very well for multi-phase flow - Can predict Vessel/Pipeline Conditions - No work on Natural gas

- Predict P, T, time and mass flowrate. - For single and multi-phase - For multi-component

(Chen et al., 1995a, b)

(Norris and Puls, 1993; Norris, 1994)

U. Shafiq, A.M. Shariff, M. Babar et al. / Process Safety and Environmental Protection 133 (2020) 104–123

Model + Tool

Year

Table 4 (Continued) Year

Composition

Condition

Vessel/Pipeline Volume

Orifice Size (mm)

Characteristics

Key Challenges

Ref

Fairuzov (Model + Tool)

1998

LPG (95 % propane & 5 % butane

11.25 bar & 19.9 ◦ C

100 m long pipeline with 150 mm internal diameter

Full-bore rupture

- Multi-component, two-phase pipe flow model - Effect of heat transfer is discussed - For non-adiabatic fluid flow - Well prediction of experimental data

- Thermal equilibrium between the fluid and pipe wall was not reached - Rigorous conjugated heat transfer model should be used for transient heat transfer description

(Fairuzov, 1998)

BLOWSIM (Model + Tool)

1999

64 % C1 , 6 % C2, 28 % n-C3 & 2 % n-C4

116 atm & 293 K

N/A

10 mm

- Multi-component, the multi-phase pipe flow model - BLOWSIM performs better than BLOWDOWN - The cubic equation of state has positive effects on data

- Limited data on experimental validation - No work on Natural gas - Thermal and mechanical equilibrium assumption (Brown et al., 2013) - No work in cryogenic conditions or emergency situation

(Mahgerefteh and Wong, 1999)

CNGS-MOC (Model + Tool)

1999

LPG (95 % propane & 5 % butane

11.25 bar & 19.9 ◦ C

100 m long pipeline with 150 mm internal diameter

FBR

- Reasonably accurate predictions - Less CPU time - improving accuracy

- No Experimental Work - Less data on experimental validation

(Mahgerefteh et al., 1999)

P. S. Cumber (Model + Tool)

2001

LPG (C1 66.5 %, C2 3.5 % & C3 30 %

120 bar & 25 ◦ C

3.24 m height with 0.54 m ID

10 mm

- Precise prediction of pressure and mass flow rate - Less computational time

- No experimental study conducted - Imprecise temperature prediction - No heat transfer through vessel wall assumption

(Cumber, 2001)

A. Fredenhagen (Model + Tool)

2001

N2 – CO2

25-15 bar & 298 K

0.05 m3 vessel with 0.242 m diameter

29-17 mm2

- A good prediction of the process - Applicable for Multi-component process

- Tool commercially not available - Unable to predict equipment conditions - Limited data on experimental validation - No data on multi-phase process

(Fredenhagen and Eggers, 2001)

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Name/Title

119

120

Table 4 (Continued) Year

Composition

Condition

Vessel/Pipeline Volume

Orifice Size (mm)

Characteristics

Key Challenges

Ref

H. Mahgerefteh (Model)

2002

64 % C1 , 6 % C2, 28 % n–C3 & 2 % n–C4

116 bar & 293 K

3.24 m vessel with 1.13 m diameter and 59 mm wall thickness

10 mm

- Prediction of thermodynamic properties under fire and ambient conditions - For multi-component and multi-phase process - Vessel conditions calculations

- No experimentation validation - No simulation tools developed

(Mahgerefteh et al., 2002)

A. Oke (Model)

2004

LPG

21.6 bar & 20 ◦ C

100 m long with 0.154 m ID

150

- The model accounts for axial and radial flow, real fluid behavior as well as the locality of puncture with respect to the length of pipe

- No experimental study performed - No validation for natural gas mixture and cryogenic conditions

VPM (Model)

2011

78.12 % N2, 20.96 % O2 & 0.92 % Ar

200-400 kPa and ≈ 19 ◦ C

120 m long pipeline

N/A

- For multi-component process - Ability to calculate pipe wall temperature

- It can only predict steady state conditions - It is not suitable for the multi-phase process

2012

CO2

81 bar & 31 ◦ C

50 km long, 24 pipeline

8

- Experimental data from large-scale CO2 unit - Initially supercritical conditions - Multi-phase process

2014

CO2, 2–8 % N2

85b bar & 20 ◦ C

51.96 m tube with 3.86 mm ID

N/A

- Studied Effect of impurities on CO2 blowdown - Good predictions of initial pressure drop

- Non-reliable predications of experimental data - No work on multi-component & multi-phase process - No study on the effect of initial conditions

2013

CO2 & Water

25 MPa & 380 ◦ C

4 m height & 2 m diameter

0.008 m2

- A good prediction of the process - Supercritical conditions - Multi-component and multi-phase process

OLGA (1991)

Tool

J. Zhang

- Limited data on experimental validation - No work on natural gas - Only work on supercritical conditions

(Rajiwate, 2011)

(Clausen et al., 2012)

(Huh et al., 2014)

(Zhang et al., 2014)

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Name/Title

Table 4 (Continued) Name/Title S. Brown (Model)

Year 2013

Composition CO2

Vessel/Pipeline Volume

15.335 MPa & 278.35 K

144 m long pipeline with 150 mm diameter

7 MPa & 298.35 K

37 m long pipeline with 40 mm ID 256 m long pipeline with 233 mm diameter

Orifice Size (mm) FBR

Characteristics

Key Challenges

- Model predictions produced a reasonable agreement - Multi-phase process - Delayed phase transition has an insignificant effect on the depressurization rate of pipe - Good prediction for initially supercritical fluid - Prediction of dry ice formation

- Lack of sufficient and reliable experimental data - No work on the multi-component process - No work on natural gas and cryogenic conditions or emergency situation

Ref

- Unable to predict initially two-phase fluid - No work on cryogenic or emergency conditions - Experimental study performed only for single component

(Martynov et al., 2014)

(Brown et al., 2013)

S. Martynov (Model)

2013

CO2

53-86 bar & 34-39 ◦ C

M. Drescher

2014

CO2 + 10–30 % N2

120 bar & 20

140 m long pipeline with 10 mm ID

9.5 mm

- Good predication of experimental results - Experimental validation of HEM with binary components

- Require advancement of heat-transfer models - Temperature prediction was less accurate

(Drescher et al., 2014)

VBsim

2015

N2 CO2–HC (up to C1 O) & HC (up to C3)

290-323 K & 118.5-22 bar

8.429 m length with 1.97 m diameter

0.635-1.4 cm

- Good predication of experimental results - For multi-component and multi-phase process - Consider non-equilibrium effects between constituent fluid phases

- No experimental study performed. - No study in the cryogenic region.

(D’Alessandro et al., 2015)

A. Park

2017

HC Mixture

293-303 K & 117.5-120 bar

3.24 m length with 1.13 m ID

- Two-phase multi-component system prediction. - Can predict wall temperature contracting liquid and vapor. - More precise predictions than previously available models

- No experimental work performed No study in the cryogenic region.

50 mm

10 mm

(Park et al., 2018)

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Condition

121

122

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6. Conclusion In this paper, the available models for the optimum blowdown parameters’ calculation are discussed. The challenges for depressurization in process industry through a review of existing literature are also highlighted. The available models are capable of solving the blowdown scenarios, however, there are still some limitations listed as follows. • Only a few lab-scale experimental studies are reported for the validation of models. The reliability of models will be improved if also validated against the large scale experimental facilities. • More extensive experimental studies on natural gas and other gaseous mixtures could help to improve the validity of models. • Limited studies are reported for the blowdown of pressure vessels under fire conditions. • Experimental studies for blowdown from the cryogenic conditions could also be considered. It would help to study the blowdown process under worst case scenarios especially when a phase change is involved that can lead to the formation of solids. • A new numerical model can also be developed to overcome the problems related to dry ice formation during the blowdown process. • Studies on blowdown of vessels/pipelines through multiple chokes needs to be considered. • To avoid solidification during blowdown, the effect of additives can be studied. In addressing these research areas, industry should be empowered to make effective and sustainable retrofit decisions while simultaneously reducing hazards and improving the safety. This paper has focused on solutions for industrial hazards related to depressurization. However, the outcome of the identified research areas has wide-ranging applications with techniques that could be applied to solve many other system simulation challenges. Acknowledgements The authors would like to extend their most profound gratitude to the CO2 Research Centre (CO2RES), Universiti Teknologi PETRONAS (UTP), Malaysia, for the accomplishment of this Review article. References Hanna, S., Chang, J., Strimaitis, D., 1993. Hazardous gas model evaluation with field observations. Atmos. Environ. Part A Gen. Top. 27, 2265–2285. AirConditioning, H., 2002. Refridgeration-The News. Boiler Accident Report : To Err Is Human, November 8th. Angielczyk, W., Bartosiewicz, Y., Butrymowicz, D., Seynhaeve, J.-M., 2010. 1-D Modeling of Supersonic Carbon Dioxide Two-Phase Flow through Ejector Motive Nozzle. Api, R., 1990. Recommended Practice., pp. 521. API, 1993. Recommended Practice 520 Part 1—Sizing and Selction, sixth ed. Assael, M.J., Trusler, J.M., Tsolakis, T.F., 1996. Thermophysical Properties of Fluids: An Introduction to Their Prediction. World Scientific. Aursand, P., Hammer, M., Munkejord, S.T., Wilhelmsen, Ø., 2013. Pipeline transport of CO2 mixtures: models for transient simulation. Int. J. Greenh. Gases Control 15, 174–185. Bansal, R.K., 2005. Fluid Mechanics and Hydraulic Machines, 9 ed. Laxmi Publications (P) Ltd, New Delhi, ed. Barma, M., Saidur, R., Rahman, S., Allouhi, A., Akash, B., Sait, S.M., 2017. A review on boilers energy use, energy savings, and emissions reductions. Renew. Sustain. Energy Rev. 79, 970–983. Bendiksen, K.H., Maines, D., Moe, R., Nuland, S., 1991. The dynamic two-fluid model OLGA: theory and application. SPE Prod Eng. 6, 171–180. Bond, J., 2002. Institute of Chemical Engineers Accidents Database. Institute of Chemical Engineers., Rugby. UK. Brown, S., Martynov, S., Mahgerefteh, H., Proust, C., 2013. A homogeneous relaxation flow model for the full bore rupture of dense phase CO2 pipelines. Int. J. Greenh. Gases Control 17, 349–356.

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