Using CFD to Estimate Mass Flow Rate to Classify PSE According to API 754

Leakages have been the main cause of major accidents like Flixborough, Seveso, and Bhopal. In the Flixborough disaster, a crack in a pipe led to the release of cyclohexane, causing an explosion and fire. In Seveso, Italy, a pressure relief valve failed, leading to the release of dioxin, a highly toxic chemical. In Bhopal, India, a gas leakage occurred due to the failure of a safety valve, releasing methyl isocyanate and resulting in the deaths of thousands of people.

These accidents highlight the importance of preventing leaks in process plants to avoid catastrophic consequences. In the wake of them, numerous regions worldwide have implemented Process Safety regulations to safeguard process plants against loss of primary containment (LOPC). However, despite the broad implementation of process safety practices, significant leakage incidents persist (Paul Baybutt, 2016; MARSH, 2023). In this sense, the technical report of MARSH (Global Leader in Insurance Broking and Risk Management) states that between 2018 and 2019 have seen several major losses from refineries and petrochemical assets, particularly those of at least 50 years in age (MARSH, 2020).

To revert this scenario and preventing this type of events, the American Petroleum Institute (API) has created the ANSI/API Recommended Practice 754. This standard identifies leading and lagging process safety indicators useful for driving performance improvement. Regarding LOPC, the indicators are classed in three levels (Tier 1, Tier 2 and Tier 3).

To comply with API 754 requirements, it is necessary to classify each industry leakage. In this context, an accurate prediction of leakage amounts constitutes a key information.

Type of fluid released, leak hole diameter, and the process conditions, mainly pressure and temperature, are the required input parameters for the calculation of the leakage flow rate. While pressure and temperature are quantities monitored in the production process and, therefore, known, the geometry of the leak and density require a more detailed study. For example, Market et al. (2014) show that the ideal gas equation predicts an unrealistically high hydrogen density and thus overestimates the total amount of hydrogen released. In contrast, Xiu et al. (2014) shows that when using the ideal gas equation, the discharge mass rate was considerably under-predicted.

In industry, software such as ALOHA and Phast® or analytical equations are commonly used to calculate leak flow rate. These tools require input such as fluid properties, velocity, and hole geometry. However, they have limitations. For example, while ALOHA allows the user to select between circular and rectangular geometry, it does not provide the option to choose between real or ideal gas behavior. On the other hand, Phast® allows the user to select between ideal and real gas behavior but only offers a circular orifice geometry. On the other hand, using an analytical equation requires knowledge of the fluid velocity at the orifice, which is often unknown.

Furthermore, these tools require as input the discharge coefficient (Cd), a parameter that considers the effect of fluid friction and contraction during the leakage through the orifice (Yellow Book, 1997). The values of this coefficient are generally obtained empirically because of difficulty in accurately predicting the effects of geometrical complicacy and flow separation from the wall. (A. Erdal and H. I. Andersson (1997) and. M. S. Shah et al. (2012))

Alternatively, numerical modeling via Computational Fluid Dynamics (CFD) appears as an alternative approach to estimate a mass flow rate during a leakage, since it allows the analysis of a wide range of accidental scenarios in complex geometries at low cost. (Fiates and Vianna, 2016). Due to its potential for the analysis of more complex scenarios, the use of CFD tools to simulate dispersion has increased significantly. Xiu et al. (2014) performed a CFD analysis of an accidental CO2 leakage through an orifice of 11.9 mm using real and ideal gas models, obtaining satisfactory estimations when comparing predicted and measured total mass release (less than -3% deviation).

Market et al. (2014) used CFD to simulate accidental hydrogen releases from high pressure storage at low temperatures, comparing ideal and real gas behavior and discussing their limitations to estimate the mass flow rate. CFD has also proven to be an excellent alternative for working with geometric factors such as the discharge coefficient. According to Shah et al. (2012), CFD can be used as an alternative and cost-effective tool towards replacement of experiments required for empirical estimation of the discharge coefficient.

The studies on the CFD simulation of leakage bring relevant information on this type of event and show the adequacy of CFD as a powerful tool for leakage analysis. However, there are still important aspects in the CFD simulation of leakage that should be addressed, mainly regarding its application in processes that operate under severe conditions, such as in petrochemical plants.

It is observed in practice that most leaks are caused by failures in pipelines such as ruptures and problems related to corrosion or flange failures. In these cases, the geometry of the leak orifice is usually non-circular. However, more detailed data on this aspect are required since the hole geometry is a factor that significantly affects the leakage mass flow rate.

Based on the previous considerations, the purpose of this study is to estimate leakage mass flow rate through both circular and rectangular orifices in a wide range of pressures and temperatures. Leaks of methane, the main component of natural gas, and ethylene, the main gas processed in petrochemical plants, are considered as basis of analysis. A pressure range from 4 to 1961.3 bar and a temperature range of 200 to 583.2 K were considered. The CFD results are compared with those of Phast® and of the analytical equations proposed in Yellow Book (1997).