Modelling three-phase releases of carbon dioxide from high-pressure pipelines

This paper describes the development and experimental validation of a three-phase flow model for predicting the transient outflow following the failure of pressurised CO₂ pipelines and vessels. The choked flow parameters at the rupture plane, spanning the dense-phase and saturated conditions to below the triple point, are modelled by maximisation of the mass flowrate with respect to pressure and solids mass fraction at the triple point. The pertinent solid/vapour/liquid phase equilibrium data are predicted using an extended Peng–Robinson equation of state.The proposed outflow model is successfully validated against experimental data obtained from high-pressure CO₂ releases performed as part of the FP7 CO2PipeHaz project (www.co2pipehaz.eu).The formation of solid phase CO₂ at the triple point is marked by a stabilisation in pressure as confirmed by both theory and experimental observation. For a fixed diameter hypothetical pipeline at 100 bar and 20 °C, the flow model is used to determine the impact of the pipeline length on the time taken to commence solid CO₂ discharge following its rupture.     

Non-equilibrium phenomena in carbon dioxide expansion

Release of liquid and supercritical carbon dioxide is a fundamental research topic in CCS. Traditional approach is largely based on HEM and, in general, assumes equilibrium from the outlet to the Mach disc. Experimental results have shown that this approach is not always effective in describing the expansion phenomenon; therefore a significant lack of knowledge exists about CO₂ properties at the under-expanded jet zone boundary, which is a main focus in process safety. Here, solid formation, vapour quality, sonic velocity and final temperature are generally calculated according to equilibrium saturation condition, and this is generally incorrect. This article deals with non-equilibrium thermodynamics of liquid and supercritical CO₂ expansion, illustrating relaxation dynamics through the HRM models, and discussing the very specific singularities of CO₂ phase transitions, vapour to liquid and liquid to solid, that result away from the equilibrium condition, due to the rapid phase changes and to the specific properties of CO₂ multi phase thermodynamics, including nucleation and particle growth. Statistical rate theory has been applied with the aim at identifying the phase transition energy barrier, resulting in a significant entropy increase. A case study based on HEM conservation equations integrated with the statistical rate approach has been presented, which covers the gap of the equilibrium hypothesis. The objective of the article is to provide a more accurate method to predict the properties of carbon dioxide following an expansion.     

Numerical study of choked two-phase flow of hydrocarbons fluids through orifices

Valves and orifices are the most widely devices of flow control used in oil and gas industry. In particular, they are installed in relief piping system in order to control the discharge flow during potential plant overpressuring scenarios, thus ensuring plant safety. It is a common practice to flow liquid and gas mixtures through such restriction devices.Rigorous models are available to precisely size pressure relief devices operating in single phase flow; however for two-phase flow, no models are considered sufficiently reliable for predicting the relevant flow conditions.In the present paper, two-phase flow of hydrocarbons fluids through an orifice under critical conditions has been numerically investigated.The existing literature has been analyzed and data on two-phase flow of highly volatile mixtures of hydrocarbons through openings have been collected. A comparison has been carried out with numerical simulations carried out by the multiphase flow simulation tool OLGA by SPT.The Henry–Fauske model has been used as orifice choke model and the orifice discharge flow coefficient, required as input by OLGA, has been calculated by Chisholm's model.Comparison between OLGA's results and experimental data shows that Henry–Fauske model markedly underestimates the mass flow rate through the orifice, if Chisholm's model is used to calculate discharge coefficient. It was found that the error of the model could be minimized using different values of orifice discharge coefficient (C_d).A new discharge flow coefficient model, suitable for choked two-phase flow across orifices, is proposed in this study and it has been determined to match the above mentioned experimental measurements.     

正态分布式弧形板除雾器压降的模拟研究

为提高除雾器对瓦斯气体中细水雾的分离效率,同时确保气雾两相流流经除雾器后的压降符合要求。以气雾两相流动的均相流动模型为前提,根据稳定一维流动的基本方程推导出气雾两相流动的压降计算式;通过对瓦斯细水雾在除雾器中的流动进行数值模拟、分析,结果表明除雾器板间距、叶片长度、转折角和气流速度对压降都有影响,其中气流速度的变化对除雾器压降的影响较大,压降随气流速度的增大而增大;转折角的变化对除雾器压降的影响最大,压降随着转折角的增大而减小。这对正态分布式弧形板除雾器的优化设计有一定的指导意义。     

Numerical analysis of phase behavior during rapid decompression of rich natural gases

The effect of the condensation process on the gas and liquid phase behavior during rapid decompression of rich natural gases is studied in the paper numerically. A one-dimensional mathematical model of transient thermal two-phase flow of compressible multi-component natural gas mixture and liquid phase in a shock tube is developed. The set of mass, momentum and enthalpy conservation equations are solved for the gas and liquid phases. The approach to model a liquid condensation process during rapid decompression of rich natural gas mixture is proposed. The mass transfer between the gas and the liquid is taken into account by introducing the appropriate terms into the governing equations. Thermo-physical properties of multi-component natural gas mixture are calculated by solving the Equation of State (EOS) in the form of the Soave–Redlich–Kwong (SRK-EOS) model. The proposed liquid condensation model is integrated into the GDP model. A simple case of GDP model, where the liquid was not considered, was extensively validated on base and dry natural gases. The proposed two-phase model is validated against the experiments where the decompression wave speed was measured in rich natural gases at low temperature. It shows a good agreement with the experimental data.     

超临界CO2气爆致裂规律实验研究

针对我国低渗透性煤层增透困难的现状,研发了可控超临界二氧化碳气爆发生装 置,对不同强度的模拟煤体进行了不同温压条件下的超临界CO2气爆实验,结合孔内窥 镜观测和外观测量手段,对爆后宏观裂隙数目和长度等爆破响应信息进行统计分析。结 果表明:气爆裂纹起裂所需的最小爆破压力与介质的抗拉强度呈指数式增长的关系,主 要是固体材料在动力载荷作用下强度增大引起的;超临界二氧化碳气爆后产生宏观裂隙 的数目和累计长度与爆破压力满足Logistic函数关系,是裂隙面积超线性增加所消耗能 量也超线性增加的结果;超临界CO2对温压条件敏感,爆破有降温作用,是良好的物理 爆破原料,使用超临界二氧化碳作为爆破原料的爆破效果优于空气爆破效果。     

Assessment of the maximum possible liquid superheat during flashing leak flow

During the discharge of flashing liquids through leaks due to abrupt depressurization a transient thermodynamic non-equilibrium in the form of a boiling delay in the superheated liquid flow can occur. As a consequence the actual mass flow quality is smaller than calculated under the assumption of an immediate adjustment of the thermodynamic equilibrium between the phases. For the prediction of the leak mass flow for a given pressure difference the magnitude of this self-adjusting mass flow quality is needed.

Most of the models cited in the literature include only the equilibrium mass quality as limiting quantity and ignore further effects as that of the depressurization velocity or the mean nucleus distance. For the assessment of the maximum possible liquid superheat during flashing only the conduction heat transfer from a stagnant liquid to the bubble surface is used to describe the bubble growth.

The sub-model for the bubble growth due to expansion and mass transfer necessary for the global prediction of the transient thermodynamic non-equilibrium in flashing liquids was validated using bubble radii measured by Hooper et al. [Bubble growth and pressure relationship in the flashing of superheated water. Technical publication 6904, Mechanical Engineering Department, University of Toronto, 1969] for the case of a sudden depressurization of initially saturated water. On this basis the calculated time-dependent temperature field, the actual mass quality, the mean liquid temperature and, in comparison to the corresponding values based on the assumption of immediate thermodynamic equilibrium, the maximum possible liquid superheat are predicted.     

Modelling of discharge and atmospheric dispersion for carbon dioxide releases

This paper discusses the modelling of the discharge and subsequent atmospheric dispersion for carbon dioxide releases using extensions of models in the consequence modelling package Phast. Phast examines the progress of a potential incident from the initial release to the far-field dispersion including the modelling of rainout and subsequent vaporisation. The original Phast discharge and dispersion models allow the released chemical to occur only in the vapour and liquid phases. As part of the current work these models have been extended to also allow for the occurrence of liquid to solid transition or vapour to solid transition. This applies both for the post-expansion state in the discharge model, as well as for the thermodynamic calculations by the dispersion model. Solid property calculations have been added where necessary. The above extensions are generally valid for fluid releases including CO₂. Using the extended dispersion formulation, a sensitivity study has been carried out for mixing of solid CO₂ with air, and it is demonstrated that solid effects may significantly affect the predicted concentrations.     

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.     

碳粒填充床燃烧及着火熄火特性的数值分析

本文提出了碳粒填充床在驻上流场中燃烧的一个轴对称二维数学模型，此模型由床内的气固两相流和床表面上驻点边界层流动两个子模型耦合而成，利用自编程序借助ＰＩＳＯ方法求解两组方程。分别计算了冻结流，平衡流和有限气相反应速率流这三种情况。通过计算确定了不同工况下碳粒床的质量燃烧率及燃烧过程中各参数的分布和变化规律，并对碳粒床的着火与熄持性进行了分析和探讨。计算结果合理，表明本模型可应用于阴燃及其转变为明火过     

三氟甲烷灭火剂在管网中流动状态分析

通过对三氟甲烷灭火剂在管网中的流动状态、管网中灭火剂流动的压力～时间(p～t)曲线分析,进一步阐明三氟甲烷灭火剂气液两相流动状态下管道压力损失,利用推导的压力损失计算公式对具体的系统进行实际计算,并通过实际的系统喷放所测得的数据对计算结果进行验证,进一步证明推导的压力损失计算公式的可用性和对三氟甲烷灭火剂在管网中的流动状态分析的正确性。     

Validation of discharge and atmospheric dispersion for unpressurised and pressurised carbon dioxide releases

This paper discusses the validation of discharge and subsequent atmospheric dispersion for both unpressurised and pressurised carbon dioxide releases using the consequence modelling package Phast.The paper first summarises the validation of the Phast dispersion model (UDM) for unpressurised releases. This includes heavy gas dispersion from either a ground-level line source (McQuaid wind-tunnel experiments) or an area source (Kit-Fox field experiments). For the McQuaid experiments minor modifications of the UDM were made to support line sources. For the Kit Fox experiments steady-state and 20-s finite-duration releases were simulated for both neutral and stable conditions. Most accurate predictions of the concentrations for finite duration releases were obtained using the UDM Finite Duration Correction method.Using experiments funded by BP and Shell and made available via DNV's CO2PIPETRANS JIP, the paper secondly summarises the validation of the Phast discharge and dispersion models for pressurised CO₂ releases. This modelling accounted for the possible presence of the solid CO₂ phase following expansion to atmospheric pressure. These experiments included both high-pressure steady-state and time-varying cold releases (liquid storage) and high-pressure time-varying supercritical hot releases. Both the flow rate and the concentrations were found to be predicted accurately.The above validation was carried out with no fitting whatsoever of the Phast extended discharge and dispersion models.     

Phast validation of discharge and atmospheric dispersion for pressurised carbon dioxide releases

The consequence modelling package Phast examines the progress of a potential incident from the initial release to the far-field dispersion including the modelling of rainout and subsequent vaporisation. The original Phast discharge and dispersion models allow the released substance to occur only in the vapour and liquid phases. The latest versions of Phast include extended models which also allow for the occurrence of fluid to solid transition for carbon dioxide (CO₂) releases.As part of two projects funded by BP and Shell (made publicly available via CO2PIPETRANS JIP), experimental work on CO₂ releases was carried out at the Spadeadam site (UK) by GL Noble Denton. These experiments included both high-pressure steady-state and time-varying cold releases (liquid storage) and high-pressure time-varying supercritical hot releases (vapour storage). The CO₂ was stored in a vessel with attached pipework. At the end of the pipework a nozzle was attached, where the nozzle diameter was varied.This paper discusses the validation of Phast against the above experiments. The flow rate was predicted accurately by the Phast discharge models (within 10%; considered within the accuracy at which the BP experimental data were measured), and the concentrations were found to be predicted accurately (well within a factor of two) by the Phast dispersion model (UDM). This validation was carried out with no fitting whatsoever of the Phast extended discharge and dispersion models.     

抽出式通风煤巷掘进过程中粉尘浓度分布规律的数值模拟

根据气固两相流理论，针对矿井掘进工作面的特点，采用计算流体力学的离散相模型（DPM）对掘进工作面通风过程中粉尘浓度进行数值模拟，总结抽出式通风掘进巷道中粉尘浓度的沿程分布及变化规律。     

基于FLACS的CH4/CO2/air混合气爆炸参数分析

利用FLACS软件分析初始压力、初始温度对CH4/CO2/air混合气的爆炸温度、最大爆炸压力的影响;并与计算值对比。结果表明:①初始压力对爆炸温度、爆炸前后压力比影响可以忽略。常温变压条件下二氧化碳浓度增加,爆炸温度与爆炸前后压力比基本呈线性降低。常压变温条件较复杂,二氧化碳浓度升高爆炸温度降低;初始温度对低浓度（<15%）二氧化碳混合气爆炸温度几乎没有影响,而高浓度（>15%）二氧化碳混合气爆炸温度随初始温度增加而升高;最大爆炸压力随二氧化碳浓度以及温度升高而降低。②在设定条件下,低浓度（5%~10%）二氧化碳混合气爆炸温度计算值与模拟值相对误差小于5.5%,吻合较好;最大爆炸压力计算值与模拟值相对误差在6.5%～10.5%之间。     

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.     

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.     

Experimental study on CO2/CF3I suppression of methane-air explosion and flame propagation

To explore the inhibitory effects of CF₃I and CO₂ gas on the explosion pressure and flame propagation characteristics of 9.5% methane, a spherical 20 L experimental explosion device was used to study the effect of the gas explosion suppressants on the maximum explosion pressure, maximum explosion pressure rise rate and flame propagation speed of methane. The results indicated that with a gradual increase in the volume fraction of the gas explosion suppressant, the maximum explosion pressure of methane and maximum explosion pressure rise rate gradually decreased, and the time taken to reach the maximum explosion pressure and maximum explosion pressure rise rate was gradually delayed. At the same time, the flame propagation speed gradually decreased. Additionally, the time taken for the flame to reach the edge of the window and the time taken for a crack as well as a cellular structure to appear on the flame surface was gradually delayed. The fluid dynamics uncertainty was suppressed. The explosion pressure and flame propagation processes were markedly suppressed, but the flame buoyancy instability was gradually enhanced. By comparing the effects of the two gas explosion suppressants on the pressure and flame propagation characteristics, it was found that at the same volume fraction, trifluoroiodomethane was significantly better than carbon dioxide in suppressing the explosion of methane. By comparing the reduction rates of the characteristic methane explosion parameters at a volume fraction of 9.5%, it was observed that the inhibitory effect of 4% trifluoroiodomethane on the maximum explosion pressure was approximately 4.6 times that of the same amount of carbon dioxide, and the inhibitory effect of 4% trifluoroiodomethane on the maximum explosion pressure rise rate and flame propagation speed was approximately 2.7 times that of the same amount of carbon dioxide. The addition of 0.5%–1.5% trifluoromethane to 4% and 8% carbon dioxide can improve the explosion suppression efficiency of carbon dioxide. This enhancing phenomenon is a comprehensive manifestation of the oxygen-decreasing effect of carbon dioxide and the trifluoroiodomethane-related endothermic effect and reduction in key free radicals.     

随钻压力波在用于早期气侵检测时的扰动传播特性研究*

为了研究随钻测量装置（Measurement While Drilling,MWD）压力波信号在用于早期气侵检测时的扰动传播特性,基于油气井多相流流动理论,建立随钻压力波在环空气液两相流中的扰动传播模型,对多参数影响下的压力波传播与衰减特性进行模拟,并对压力波检测技术的现场应用效果进行分析。结果表明:含气率、角频率、系统压力、虚拟质量力、拖曳力和壁面剪切力的变化都会对压力波在环空气液两相流中的传播与衰减特性造成不同程度的影响;相比于常规的全烃量检测技术,压力波检测技术可以更早地检测到气侵的发生,可进一步提高油气井建井的安全性。