A New Homogeneous Non-Equilibrium Model to Compute Vapor-Liquid Two-Phase Critical Pressure Ratios of Multicomponent Hydrocarbon Mixtures

The critical pressure ratio (η_c) is an essential parameter for computing the vapor-liquid two-phase critical pressure and mass flow rate of multicomponent hydrocarbon mixtures flowing through valves and leakage orifices. The Homogeneous Non-Equilibrium Diener-Schmidt (HNE-DS) model widely used to calculate η_c assumes that the fluid's volume linearly changes with the pressure (using the Clausius-Clapeyron equation), which is not suitable for multicomponent gas mixtures. In this paper, a new Homogeneous Non-Equilibrium (new-HNE) model is proposed to calculate η_c of gas mixtures. Firstly, a new critical flow compressibility factor (ω_c) is developed from its thermodynamic definition and the Peng-Robinson equation of state (EOS), overcoming the inherent limitations of the Clausius-Clapeyron equation. Then, η_c is correlated to the newly derived ω_c by fitting experimental data at various pressures and gas mass fractions of both single-component and multicomponent gas mixtures, yielding the new HNE-DS model. Results show that, for the water-steam and air-water two-phase flow, the average relative deviations (ARD) between the calculated critical pressure ratios and experimental values are equal to 2.8% and 4.93%, respectively, which represents a significant improvement in comparison with the original HNE-DS model. Moreover, this new model is extended to the applications of Liquefied natural gas (LNG)/liquefied petroleum gas (LPG) fluids, and will further contribute to the calculation of the leakage mass flow rate of fluid flowing through the orifices/valves.     

An experimental study of viscous flows in contractions

The need to improve the methods used when designing emergency, pressure-relief systems on polymerisation reactors, has made the flow of highly viscous fluids in pipeline fittings highly topical. This paper investigates the flow processes involved in single-phase, viscous flows in nozzles and orifice plates. These fittings were chosen because they would give an insight into the behaviour of highly viscous flows in other geometries, such as the flow upstream of the seat in a pressure relief valve. Experimental data are presented for a pipe, two conical nozzles and a sharp-edged orifice plate for laminar flows in the Reynolds number range 50–400 and for turbulent flows. The volume flow rate—pressure drop characteristics are presented for both nozzles and the orifice plate. The discharge momentum flow rate for the pipe, a nozzle and the orifice plate are also given. Analysis of the data shows that nozzles and orifice plates that are geometrically similar have a similar resistance to flow. It is also shown that the contraction coefficient for an orifice plate tends to unity at low Reynolds numbers.     

Experimental study on the characteristics of the strong boiling induced by pressure relief at the top of vertical vessels

In this study, the strong boiling process of a superheated liquid induced by pressure relief at the top of a vertical vessel was experimentally investigated. Through monitoring the response of the pressure at the top of the vessel and the full field morphology of the two-phase flow, the correlations between the pressure rise and the two-phase flow as well as the trend of the characteristic pressure values under different discharge areas and filling rates were analyzed. The results indicated that the expansion of the mist-like two-phase flow, which was generated due to the strong boiling and bubble collapse, was the direct reason for the two pressure rebounds at the top of the vessel. And under the effect of the intermittent expansion of the two-phase flow, the pressure rising rate in the second rebound stage fluctuated. When the discharge area changed, the characteristic pressure values presented different relativeness under different filling rates. In addition, the average pressure rising rate during the second pressure rebound process presented an exponential growth with the increase of the discharge area, and the exponent coefficient decreased with the increase of the liquid filling rate.     

Sizing of safety valves for multi-purpose plants according to ISO 4126-10

Multi-purpose plants are frequently protected with mechanical safety devices like safety valves or bursting disks. Due to many changes of recipes it must be checked regularly whether the safety devices are sufficiently sized. But the sizing procedure of individual safety devices can be very tedious. Therefore energy specific relief areas (effective relief area per kW of energy input) have been determined for approx. 60 typical solvents. They are indicated for reactors with safety devices which have a set pressure of 7 bar (abs) or 11 bar (abs). These values are independent of the size of the reactors for vaporizing systems and arbitrary safety valves. The energy specific relief areas allow the minimum required relief area quickly to recalculate if the energy input of the reactor is known. In addition, the application of solvents in multi-purpose plants can be evaluated from a safety point of few.The energy specific relief areas are calculated based on a relief of two-phase gas/liquid mixtures. The data have been determined with the non-equilibrium HNE-DS method, which takes into account the boiling delay of the liquid in the safety device and the slip between gases and liquids. The method is recommended in the international standard ISO 4126 part 10. In addition, practical advice and possible improvements are outlined. The method leads to significantly smaller relief areas than according to the API 520. For multi-purpose plants with available safety devices this method allows for a considerable expansion of the application range of reactors.     

Database-supported documentation and verification of pressure relief device design in chemical plants

In this paper the results of a multi-year analysis of the pressure relief devices located in several plants in major chemical sites are summarized. The analysis consisted of a systematic evaluation of existing safety valves and rupture discs including the identification of the service conditions and design cases as well as the sizing calculations of the individual device and associated piping. Furthermore, from the total amount and the hazardous potential of the effluents the necessity of retention systems is evaluated to ensure a safe disposal.Because the knowledge in the field of emergency pressure relief changed very rapidly in recent years, the design of some safety devices was not according to the state of the art. An essential part of the verification program was the recommendation of measures to find the most economical yet technically correct way to correct these deficiencies. Rather than by carrying out wholesale replacement of an incorrectly sized safety device or vent line, often a reduction of the mass flow rate to be discharged, for example, by an orifice in a supply line, is sufficient.Results of the analysis were recorded on a novel database to capture the sizing information and maintain correct pressure relief device sizing into the future. The systematic databased approach has been used for the evaluation of about 4000 safety devices so far. The procedure has been proven to enable an experienced design engineer to carry out the analysis of a great number of pressure relief devices in a time-saving, reliable and reviewable way.     

A new approach to determine relieving temperature and thermodynamic behavior of trapped single and multi-phase fluid exposed to fire

Process safety plays a key role in modern industries. This is more significant specifically in off-shore oil and gas platforms where releasing hydrocarbons could cause irreversible damages to both environment and personnel. An important instrument device which can provide safety for process equipment in oil and gas fields is safety relief valve. Correct sizing procedure of such devices depends strongly on physical properties of fluid and relieving condition. The present study revolved around applying thermodynamic concepts and modeling to throw some light on the behavior of trapped fluid exposed to fire in order to evaluate precise temperature and fluid properties at relieving condition. Peng–Robinson equation of state together with a three phase flash has been utilized to handle the calculation. Effect of different design parameters has been evaluated for three distinct categories of fluids namely natural gas, gas-condensate mixture, and gas-oil mixtures. These parameters encompass of operating temperature, operating pressure, Difference of Operating and Design Pressure, gas and oil specific gravities, gas-oil ratio, and water cut. The study depicted that American Petroleum Institute practice number 521 which suggests an ideal gas assumption fails to provide reliable predictions as it significantly overestimate the relieving temperature. Moreover, black oil correlations were also used for the relief temperature estimation of gas-oil-water mixtures. Comparison with HYSYS results as a prominent engineering software proved that black oil models are reliable tools to predict relief temperature.     

Thermodynamic investigation and hydrate inhibition of real gas flow through orifice during depressurization

A thermodynamic procedure has been proposed which can be used to predict the gas pressure, temperature and flow rate through orifice upon chock flow condition, using equation of state (EOS). The procedure applied for emergency depressurization operation incorporating the Peng-Robinson EOS and validated by comparing flow rates of a multi-component hydrocarbon gas mixture for thirteen experimental cases. The average absolute deviations of the predicted flow rates for orifice discharge coefficients of 0.85 and 0.9, are 7.36% and 2.03%, respectively. The corresponding error for API 520 (American Petroleum Institute Recommendation Practice 520) method is 6.91%. In this work, the hydrate formation temperature and hydrate inhibitor type and its required weight fraction for preventing the hydrate formation upon orifice and its upstream conditions are evaluated by the EZ-Thermo software using the Moshfeghian–Maddox method. The results qualitatively show that the hydrate prevention is essential for the safety of the operation due to low temperature condition.     

Numerical investigation of flow erosion and flow induced displacement of gas well relief line

High-pressure particle-laden gas flow should be discharged through relief line of gas well timely to ensure safe test and exploitation. Erosion and vibration usually take place on the bend in relief lines, bringing a potential safety hazard to field operation. The majority of this paper investigates the factors affecting the erosion of bend and displacement of relief line in the downstream of bend using the computational fluid dynamics (CFD) methodology. A three-dimensional elbow pipe is selected as computational domain in this investigation. The kinematics and trajectory of discrete solid particles and liquid droplets are described by discrete phase model (DPM) while the hydrodynamic characteristics of continuous phase are obtained based on Reynolds-Averaged-Navier-Stokes (RANS) equations. An empirical erosion model is employed to predict the erosion rate of bend, and a fluid–structure interaction (FSI) model is adopted to calculate the displacement of relief line. The effects of types of multiphase flow (such as gas–solid two-phase flow and gas–liquid–solid three-phase flow), inlet flow rate and pipe diameter on erosion and displacement are discussed. The results show that large displacement and severe erosion present with large inlet flow rate in minor diameter pipe. The increase in liquid droplet content has less effect on flow erosion than that by the same increase in sand particle content.     

Safety valve sizing according to EN ISO 4126-4 and industrial practice in case of highly viscous liquid duty

The calculation of the minimum relief area on the basis of the iterative procedure, as reported in EN ISO 4126-4 and by adopting an explicit method as carried out in the industrial practice, leads to the same valve size. This applies to valves with a high and low value of the related lift, respectively, with a valve nozzle orifice according to API RP 526. However, under extraordinary conditions it may be possible that the discharge areas differ due to the graduation of the valve sizes within a suppliers' production program. Indeed, neither method gives systematically larger relief areas than the other, the procedures are equivalent.     

Predictive accuracy of simplified vent area sizing methods for the case of thermal runaway reactions

A systematic comparison of the predictive accuracy of simplified design methods with respect to the relief diameter and the discharged mass flow on the basis of experimental results obtained in reactors with volumina ranging between 0.01 and 10 m³ allow for the conclusion that empirical design rules are not suited for an extrapolation. The preliminary recommended method in case of vapour systems is this of J.C. Leung and for use with gassy or hybrid systems the method by H.K. Fauske and J.C. Leung is promoted. Indeed, partly non acceptable overpredictions are evident. By using SAFIRE/VENT reasonable predictions are possible though still an oversizing can not be cut off.     

Steady-state critical two-phase flashing flow with possible multiple choking phenomenon: Part 1: Physical modelling and numerical procedure

In this paper, the modelling of pure fluid steady-state adiabatic flashing flow through a pipe involving an abrupt enlargement is presented. The thermal non-equilibrium two-phase flow model DEM has been adjusted for subcooled inlet conditions close to saturation and/or for inlet two-phase mixture state. The multichoking flow phenomenon occurs when two basic criteria are simultaneously fulfilled. A general procedure taking into account this possible occurrence is developed on the basis of two iterative algorithms. The first algorithm is applied to the mass flow rate upstream from the enlargement and the second algorithm is based on the length of the pipe downstream from the enlargement. The proposed methodology involves the improved physical one-dimensional two-phase flow model DEM and the global non-equilibrium model through the abrupt enlargement.     

Small scale experiments on boiling liquid expanding vapor explosions: Vessel over-pressure

The boiling liquid expanding vapor explosion (BLEVE) is a type of physical explosion that has caused massive damage in the petrochemical industry. In this paper, a study has been made of the conditions that could lead to a BLEVE. A device was built to simulate the occurrence of suddenly initiated release through a top orifice. As there is some danger in using liquefied petroleum gas (LPG) in the experiments, water was used as the test fluid. The change of pressure and temperature was measured during the experiment. It was determined that two pressure peaks result after the pressure is released: the first pressure peak seems to occur because of the vapor pressure caused by the swelled two-phase layer after the initial venting, the second pressure peak is possibly due to a dynamic impact or ‘liquid hammer’ and is maintained by bubbles collapse or something like cavitation at the surface of the inner wall of the head space that occurs with the ejection of two-phase flow.Liquid heights, orifice size, and the degree of liquid superheating all have differing influence on the magnitude of the measured over-pressure; the greater the degree of liquid superheat, the stronger the over-pressure; smaller opening areas delay and reduce the magnitude of the first over-pressure; at fill levels between 60% and 80%, the impact pressure appears more violent than with other fills.     

Emergency venting into redundant pipelines

The evolution of pressure, temperature, and gas inventory during containment of blowdown from two high pressure gas networks into a third lower pressure relatively large redundant pipeline is followed through a simple lumped parameter model. Numerical solution of the non-linear model equations enabled to study the effects of relevant operating conditions on the system's dynamics. The effects of initial pressure difference between the supply and receiving networks, ratio of discharge orifice to pipe diameters in the supply networks, and heat transfer from the surroundings are investigated. A set of computer generated results are presented to demonstrate vividly the effect of the above variables on the percent of gas recovered in the lower pressure pipeline, the blowdown time, and the minimum temperatures reached in the networks.     

Experimental measurement and numerical analysis of binary hydrocarbon mixture flammability limits

The flammability limits of binary hydrocarbon mixtures in air were measured in a combustion apparatus using an innovative method developed for this apparatus. The experimental results were obtained at standard conditions (room temperature and ambient atmospheric pressure) with upward flame propagation. The experimentally determined flammability limits for pure hydrocarbons (methane and ethylene) were compared with existing data reported in the literature. Le Chatelier's Law was fit to all experimental data to obtain LFLs and UFLs for various two-component combinations of saturated and unsaturated hydrocarbons (methane, ethylene, acetylene, propane, propylene, and n-butane). A modification of this law was used if experimental observations showed large deviations from Le Chatelier's predictions. Also, experimentally measured flammability limit data of the binary hydrocarbon mixtures were analytically related to the stoichiometric concentrations.     

A CFD-based empirical model for hazardous area extent prediction including wind effects

Hazardous extent predictions that ensure process safety while avoiding overestimation have been a challenge for hazardous area classification. Specific leak scenarios can be addressed to build rapid empirical models to accurately determine hazardous extent considering several factors that are not included in general approaches. In view of that, this work aims to propose a novel CFD-based empirical model for gas emissions in open and unobstructed areas. It considers a wide range of variables such as storage temperature and pressure, orifice diameter, molecular weight, gas concentration, and wind velocity. A sensitivity analysis was performed to evaluate each variable's contribution to the gas cloud extent. The linear regression model resulting from the combination of all variables contribution was coupled with Ewan and Moddie's model to minimize the prediction errors due to the non-monotonic wind effects. The suggested algorithm accurately calculates the hazardous extent with a coefficient of determination equals to 0.9842 and a RMSE of 0.0151 for a dataset of 600 cases of generic gases release. The proposed model was also validated for 60 cases of hydrogen releases under different storage conditions, giving a coefficient of determination equal to 0.9829 and a RMSE of 0.0680, indicating a good agreement with the data.     

The effects of phosphorus-free inhibitors on the ignition of lycopodium dust

The minimum ignition temperature of dust suspension (MIT) and the hot surface ignition temperature of the dust layer (LIT) are essential safety parameters for the process industry. However, the knowledge of the ignition behavior when solid mixtures of flammable fuels and phosphorous-free inhibitors are considered is still scarce and further experimental and theoretical analyses are requested. In this work, the ignition temperature of phosphorous-free inhibitors (coal fly ash and calcium carbonate) mixed with lycopodium dust have been studied in terms of LIT analysis (hot plate thickness: 5 mm, 12.5 mm and 15 mm), and by the Godbert-Greenwald test for the MIT. Both coal fly ash and calcium carbonate have been tested at different concentrations and particle sizes.Results show that the effects of the inhibitor can be counter-productive when layer ignition temperature is considered even if the minimum ignition temperature of the dust suspension shows a positive effect from the safety point of view. This behavior has been analyzed in the terms of thermal conductivity and diffusivity of the mixture, by using Maxwell's equation for two-phase solid mixtures. Standard empirical correlations for the ignition temperature of solid mixtures have been also tested, showing their weakness in reproducing mixture behavior.     

Benchmarking of two-phase flow through safety relief valves and pipes

This paper compares calculated results for two-phase flows through safety relief valves and pipes using the TPHEM, CCFLOW and RRERSP computer programs. These studies were conducted to locate errors in the programs as well as to further our understanding of how each program worked. For most low-to-moderate viscosity flow examples, and for the frozen flow examples, the program results agreed despite differences in the calculation methods. Current thinking is that the TPHEM computer program gets better results for high viscosity flows through safety relief valves (nozzles) and for pipe down flows. This is because this program successively iterates nozzle flows to achieve results consistent with the choke pressure, temperature and quality and successively iterates pipe flows to achieve results consistent with the pipe length. Safety relief valve flows from the RRERSP computer program are reduced by the inlet pipe non-recoverable pressure loss. This effect is significant for several cases.     

API Standard 521 new alternative method to evaluate fire relief for pressure relief device sizing and depressuring system design

Since the 1950's, API Standards have provided guidance on determining relief loads for equipment exposed to pool fires. The API method is empirical based on tests performed in the 1940's. There is increasingly widespread interest in analytical methods based on heat transfer principles to model fire heat input. The API committee agreed to include an analytical method in the 6th edition of API Standard 521 to establish relief loads for pressure relief devices and to design depressuring systems for the fire scenario. The analytical method provides more flexibility than the empirical method but has limitations (e.g., too many permutations are possible leading to potential under-sizing of the pressure relief device).This paper discusses the basis for the empirical method in API Standard 521 and provides comparisons of the empirical and analytical method with two more recent large-scale pool fire tests. This pool fire test data indicates that the empirical method will provide a conservative estimate of pool fire heat input for most applications and is still the method of choice when designing pressure relief systems. However, these recent tests indicate the empirical method needs to be modified when a vessel or equipment is partially confined by adjacent embankments or walls equal or greater than the vessel height. In such cases, the wetted area exponent should be 1.0 instead of 0.82.The analytical method is useful in determining time-versus-temperature profiles for heating unwetted vessels of varying wall thicknesses and materials of construction. These profiles, which depend upon the type of fire (e.g., unconfined pool fire, jet fire, etc.), can be combined with tensile strength and stress-rupture data to specify a depressuring system's pressure-versus-time profile. This will minimize failure and/or mitigate the effects of failure due to overheating from fire exposure.     

Theoretical evaluation of lower explosion limit of hybrid mixtures

Lower explosion limits of hybrid fuel mixtures are usually determined through time consuming and expensive experiments. Although, mathematical expressions like Le-Chatelier's Law and Bartknecht curve have been used by many researchers to predict the LEL of hybrid mixtures, significant deviations remain unexplained. This research work, presents a more sophisticated and general approach for the determination of LEL of hybrid mixtures.Assuming that the combustion kinetics of pure species are independent and unchanged by the presence of other combustible species, complete conversion of the reactants and no heat losses, a simple mathematical model has been derived from the enthalpy balance of the whole system. For the experimental validation of the modelled values, modified version of 20L sphere has been employed, following the European standard (EN 14034-3: 2011) as experimental protocol. Hybrid mixtures of three dusts with two gases were selected for the scope of this publication. By analyzing the modelled as well as the experimental values, it can be concluded that the LEL values of the individual components in the hybrid mixture set the upper and lower limit for the LEL of the hybrid mixture provided the total amount of fuel in the system is considered as the concentration of the hybrid mixture. Moreover, the amount of dust or gas required to render the hybrid mixture flammable mainly depends on the energy contribution upon combustion of the individual species to raise the temperature of the whole system from ambient to the flame temperature.Le-Chatelier's Law and Bartknecht curve are empirical relations, which might hold true for a first-order approximation of LEL of hybrid mixtures, but do not represent the most conservative values of LEL reported in literature. This implies that there is a non-zero probability of occurrence of an explosible mixture in the non-explosible concentrations ranges defined by these relations. Considering these arguments, the authors suggest to employ the model presented in this paper – which presents reasonably conservative values of LEL of hybrid mixtures – for theoretical calculation of LEL of hybrid mixtures, when no precise experimental data is available.     

基于模糊规则的社会力模型改进研究

针对社会力模型人员作用范围系数进行优化,基于模糊规则改进模型中人员作用范围,使其成为受到疏散速度、疏散人员间距共同影响的动态参数,使模型中人员可通过自身模糊经验判断实际速度、人员交互距离状态来确定心理期望作用范围。仿真结果符合真实疏散特性,证明了人员作用范围系数受人员运动状态的动态影响,并提供参考模糊规则制定原则。