Pressure relief valve sizing: a review of the impact of thermodynamic property method selection and numerical algorithms applied in industrial process design

Abstract

Pressure relief devices (PRDs) are essential to ensure safe design and operation of most chemical processes ranging from chemical facilities, refineries and pharmaceutical facilities. PRDs are used as overpressure protection devices to avoid vessel or equipment rupture and subsequent uncontrolled loss of containment of process material. The most common type of PRD is the pressure relief valve (PRV). The design of PRVs’ is governed (industrial practice) by guidelines set out by several professional bodies that include the American Society of Mechanical Engineers (ASME), American Petroleum Institute (API) and National Boiler Code (NBI). The study explored the impact of two factors that typically influence the calculation of an appropriate size of a PRV. The factors include the selection of a property method (equation of state) to predict the system physical properties, and the algorithms that are applied to calculate the PRV orifice size. Three cubic equations of state (Peng-Robinson, Redlich-Kwong and Soave Redlich Kwong) were compared, relative to the ideal gas equation of state The predicted physical properties were applied to two different methods of calculating the mass flux (and subsequently the rated flow capacity) through the pressure relief valve orifice. The methods included a rigorous numerical method (direct integration method) and an empirical formula (API simplified method) to calculate the pressure relief valve orifice size to satisfy the required relief rate. The study was based on a vapor discharge stream from an ethylene oxide synthesis reactor. The following observations were noted form the results of the study

The relative deviation of mass flux prediction (and subsequently pressure relief valve orifice size) ranges between 1% and 7% for all cubic equations of state, relative to the ideal gas equation. The largest relative deviation from ideal gas conditions was demonstrated by the Peng-Robinson equations of state. The trend was consistent for both relief valve sizing methods. The relative difference between the mass flux predicted using the simplified API method and the direct integration method ranged between 54% and 39%. The largest relative deviation was noted for the ideal gas equation of state, whilst the lowest relative difference was noted for the Peng-Robinson equation of state. The relative difference between the mass flux for each of the cubic equations of state is within a range of 0.95% and 0.07%. The largest difference is between Peng-Robinson and Redlich-Kwong equation of state, whilst the smallest difference is between the Redlich-Kwong and Soave-Redlich-Kwong equations of state. The application of the cubic equations of state with either of the PRV orifice sizing algorithms yields a narrow range of orifice sizes. The range is sufficiently small such that one commercial size of orifice is sufficient for all cases (orifice size G). The application of the ideal gas equation of state and the API simplified method, demonstrated significant deviation (relative to the cubic equations of state) for the prediction of the required PRV orifice size. The calculated PRV size is one commercial size smaller that the size predicted using the cubic equations of state. This error is significant because relative orifice area difference for the adjacent commercial sizes is in excess of 35%.

The results suggest that the pressure relief valve sizing algorithm has a significant impact on the selection of a pressure relief valve, and this effect is magnified when ideal gas assumptions are applied for a non-ideal gas. This practice may lead to the selection of a relief valve with an orifice size that is significantly smaller than the required size. The risk of an inappropriately sized relief valve is significant, as it could lead to valve spring oscillation due to an imbalance in forces at the orifice. This phenomenon is defined as cycling or chattering in industry. This behavior has been synonymous with valve spring failure which could either wedge the relief valve permanently open or closed and lead to a prolonged loss of containment or excessive pressure accumulation respectively. However, if the correct relief valve sizing algorithm is selected, the cubic equations of state predict pressure relief valve orifice sizes that are virtually identical. The Peng-Robinson equation of state demonstrated the highest relative deviation from ideal gas conditions amongst all the cubic equations of state that were evaluated. This observation is consistent for both mass flux prediction algorithms that were applied. Furthermore, the Peng-Robinson cubic equation of state includes the most non-zero parameters that are applied to the general form of all cubic equations of state. In the absence of pressure volume and temperature (P, V, T) experimental data for the selected ethylene oxide system, the absolute accuracy of each cubic equation of state could not be determined. However, similar comparisons of cubic equations of state have been conducted with similar compounds (polar, non-polar and associative) in comparison to experimental (P,V,T) data. The results of such assessments for similar compounds highlight a consistent pattern, whereby polar compounds reflect a generally lower error in the average relative deviation (%) for predicting the saturated vapor volume and vapor pressure when applying the Peng-Robinson predicted thermodynamic properties. This observation suggests a correlation between the extent of deviation from ideal gas assumptions for real gases under high pressure non ideal conditions and the relatively higher accuracy of the Peng-Robinson cubic equation of state for compounds of similar molecular structure. This is primarily because the Peng-Robinson equation of state demonstrates two attributes that include; the highest relative deviation from ideal gas equations of state and the lowest deviation from real P, V, T data for similar polar compounds. However, in order to definitively distinguish the cubic equations of state based on accuracy, system specific P, V, T data would be required because the system parameters for each cubic equation of state are dependent on the species and the thermodynamic conditions of the system. The study has however provided some insight on the validity of the general limitations that arise due to the polarity of the molecules (molecular structure) and the algorithms that are applied to appropriately select a pressure relief device size (direct integration method vs the API simplified method). Such correlations are generally applied in the process design of pressure relief devices. For the ethylene oxide system selected, the results demonstrate a relatively small variance between the PRV size estimation based on the cubic equations of state. However, the most significant factor is the relief size estimation algorithm. The API simplified method demonstrates significant limitation when applied to real gas systems, due to the inherent compressibility factor range limitation that it is known to be applicable.