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The variation of thermal expansion coefficient av of subliming solid and saturated liquid CO2 with temperature. Curve A: Calculated based on the PR EoS. Curve B: Calculated based on the extended PR EoS.
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The Peng-Robinson equation of state (PR EoS) for liquid-vapor equilibrium is extended to model the solid-vapor (sublimation) and solid-liquid (melting) phase equilibria for carbon dioxide (CO2). The sublimation behavior is modeled through the re-formulations of the empirically based analytical expressions for the two temperature dependent parameter...
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... V of saturated liquid and subliming solid CO 2 as functions of temperature. Unfortunately no experimental data is available in the temperature range of interest (100 K to T tr ) to enable the evaluation of the performance of the two EoS. Nevertheless, it is interesting to note that in the case of (c P -c V )/R (Curve B, Fig. 7) and α V (curve B, Fig. 9) for the subliming solid, both equa- tions of state produce similar predictions. In the case of the adiabatic speed of sound for the solid however (cf. Curves A and B, Fig. 8) the diff erences between the two prediction is more marked (ca. 40-65 %). As would be expected, the solid phase adiabatic speed of sound predicted using the ...
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... be expected, the solid phase adiabatic speed of sound predicted using the extended PR EoS is larger than that predicted using the PR EoS (cf. Curves B and A in Fig. 8). Similarly, the thermal expansion coeffi cient of solid phase predicted using the extended PR EoS is smaller than that obtained using the original PR EoS (cf. Curves B and A in Fig. 9). Nota- bly, unlike the other derivative properties examined above, in the case of α V (Fig. 9) no discontinuity in its value may be observed at T tr ...
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... is larger than that predicted using the PR EoS (cf. Curves B and A in Fig. 8). Similarly, the thermal expansion coeffi cient of solid phase predicted using the extended PR EoS is smaller than that obtained using the original PR EoS (cf. Curves B and A in Fig. 9). Nota- bly, unlike the other derivative properties examined above, in the case of α V (Fig. 9) no discontinuity in its value may be observed at T tr ...
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... There are many equations to calculate the state of a gas, but the equation of state of the cubic type is still commonly used. 31 The Peng-Robinson (PR) equation, 32 which can calculate the phase equilibrium and volumetric properties of the mixed system, is chosen, and its equation is as follows: ...
The gas lift in the offshore M field will be performed with high CO2‐content associated gas, but the change of wellbore temperature and pressure during the injection process will lead to the change of phase and physical parameters of associated gas, which has a great impact on the design of gas lift. To ensure the smooth implementation of gas lift in the offshore M field, this paper conducts a study on the physical parameters of associated gas considering the change of CO2 phase state. We obtained the density, viscosity, compression factor, constant pressure specific heat capacity, thermal conductivity, and Joule Thomson coefficient at each temperature and pressure by Hysys calculation, and regression analysis to obtain the regression model of the physical parameters; finally, the regression model was compared with the flash experiment and Hysys calculation results. The results show that the CO2 phase change has a large influence on the physical parameters; R² > 0.8, which indicates that the regression model has sufficient reliability; the results of the comparison show that the empirical formulas of all physical properties have sufficient accuracy and superiority except Joule–Thomson coefficients. In addition, the empirical formula of the Joule–Thomson coefficient also has good accuracy and superiority at the pressure not exceeding 22 MPa. The study of phase changes and physical parameters of associated gas with high CO2 content provides a basis for subsequent gas lift design in the offshore M field and multiphase flow calculations in the wellbore during the gas lift. Although this study is only applicable to this sample, it also provides a feasible research method for other samples.
... In the diffusion of CO 2 , it was found that the P-R equation is expected to all fit the supercritical CO 2 property, so the P-R equation was adopted for the state equation (Martynov et al., 2013). The P-R equation is as follows: ...
Carbon emission reductions is gaining increasing attention in various countries, and the risk of leakage is inevitable in the transport of captured CO2 to storage. In view of how to accurately explain the diffusion law after leakage occurred from the high-pressure CO2 pipeline, this paper describes experimental studies on the diffusion of atmospheric CO2 in full-size burst discharge tests of pipelines containing high-pressure supercritical phase CO2, combined with computational fluid dynamics (CFD)simulation technique, based on the heterogeneous assumption and the diffusive source assumption, the whole leakage process is divided into a jet segment and a diffusion segment, the leakage continues by means of the de inheritance method with the release data acquired from the jet segment as a new diffusion source, and a numerical model of the high-pressure CO2 leakage jet and diffusion process is constructed segmentally to analyze the leakage characteristics after the rupture of the high-pressure CO2 pipeline. The CFD models were validated against the experimental data. Based on the analysis of the data, a prediction model for the leakage hazard area of different caliber pipes is proposed, and the relationship between the caliber of the supercritical CO2 leakage and the dangerous distance is quantitatively analyzed, which provides a feasible method for the specific determination of the leakage hazard of supercritical CO2 transportation.
... The specific heat at constant volume for the nitrogen vapor as a real gas is calculated by Eq. (A.7) [73]: ...
Low temperatures and high pressure at the nozzle inlet of the thrusters can cause liquid droplets to form downstream. During this event, the outlet pressure of the nozzle increases, and depending on the location of the condensation shock region, the velocity of the flow may decrease or increase. However, because of the significant increase in the flow temperature, the Mach number of the flow in the condensation region decreases intensively. In this study, using a 1D semi-analytical approach in Eulerian-Lagrangian viewpoint, the effect of the condensation phenomenon on the propulsion performance of a cold gas thruster is studied for various expansion ratios and inlet pressures of the nozzle. The available non-equilibrium models are used for nucleation and droplet growth. For increasing the accuracy of the model, the real gas behavior is included by using a Peng-Robinson equation of state. Meanwhile, the multi-diameter growth model is considered for applying droplet distribution at each nozzle section. The presented model has the ability to study the nozzle performance parametrically at different conditions. The results of this study, unlike some previous studies, show that the condensation occurrence improves the propulsion performance of the thrusters so that the specific impulse and thrust coefficient of the cold gas thruster increase up to 5% relative to the dry flow assumption.
... 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 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. ...
... 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. ...
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.
... It should be noted that f S CO 2 represents pure CO 2 alone, and can be calculated with an appropriate equation of state. Here, the extended Peng-Robinson equation of state developed by Martynov [69] is used, which gives ...
Hydrogen (H2) plays a vital role both as a reactant in petrochemical processes and as an energy carrier and storage medium. When produced from carbon-containing feed stocks, such as fossil fuels and biomass, hydrogen is typically produced as a mixture with carbon dioxide (CO2), and must be subsequently separated by the associated energy, with an invertible energy penalty. In this study, the process for the removal of carbon dioxide from CO2 - H2 mixtures by de-sublimation was analysed. This process is particularly relevant to the production of liquid hydrogen (LH2) at cryogenic temperatures, for which cooling of the H2 stream is already necessary. The solid – gas equilibrium of CO2 - H2 was studied using the Peng-Robinson equation of state which provided a wide range of operating conditions for process simulation. The de-sublimation process was compared with selected conventional separation processes, including amine-based absorption, pressure swing adsorption and membrane separation. In the scenario in which the resulting products, carbon dioxide and hydrogen, were subsequently liquefied for transportation and storage at 10 bar and −46 °C, and 1 bar and −251.8 °C, respectively. The overall energy consumption per kg of CO2 separated (MJ/kgCO2), was found to follow the order: 8.19–11.21 for monoethanolamine (MEA) absorption; 1.81–8.93 for membrane separation; 1.53–5.69 for pressure swing adsorption; and 0.81–3.35 de-sublimation process. Each process was evaluated and compared on the bases of electricity demand, cooling water usage, high-pressure steam usage, and refrigeration energy requirements. Finally, the advantages and disadvantages were discussed and the feasibility and sustainability of the processes for application in the production of liquid hydrogen were assessed.
... The Peng−Robinson EOS was taken from a previous experimental study. 59 The inset shows the potential energy of CO 2 as a function of pressure. where τ r represents the residence time, n is the number of adsorbed molecules, and ⟨n⟩ is the average number of molecules adsorbed on the surface. ...
Hydrotalcites (HTlcs) or layered double hydroxides (LDHs) have been used in a wide range of applications such as catalysis, electrochemical sensors, wastewater treatment, and carbon dioxide (CO2) capture. In the current study, molecular dynamics simulation was employed to investigate carbon dioxide adsorption behavior on amorphous layered double oxides (LDOs) derived from LDHs at elevated temperatures. The thermal stability of LDHs was first examined by heating the sample up to T = 1700 K. Radial distribution functions confirmed the structural evolution upon heating and the obtained structures were in good agreement with experiments, where periclase was confirmed to be the stable phase in the recrystallized mixed oxides above T = 1200 K. Further, CO2 adsorption was studied as a function of amorphous HTlc-derived oxide composition, where static and dynamic atomistic measures have been employed to characterize the CO2 adsorption behavior. The simulation results showed that the CO2 dynamic residence time on LDH-derived LDOs was sensitive to the Mg/Al molar ratio and the average amount of residence time of CO2 on the surface of LDOs reached maximum when the Mg/Al molar ratio was equal to 3.0. Meanwhile, the activation energy for diffusion also showed local maximum when the Mg/Al molar ratio was 3.0, suggesting that this particular ratio of Mg/Al mixed oxides possessed the highest CO2 adsorption capacity. This is consistent with experimental results. Examination of the binding between CO2 and mixed oxides revealed that both magnesium and oxygen in amorphous LDOs contributed to CO2 adsorption. Further analysis suggested that the interaction between Mg–O and O(LDO)–C were the most important interactions for the physisorption of CO2 on amorphous surface and different CO2 adsorption behavior on different Mg/Al molar ratio surfaces was directly related to their amorphous local structure.
... Friction was assumed to be the only fluid/wall interaction modelled using Chen's correlation (Chen 1979). To account for solid CO2, the extended PR EoS (Martynov et al. 2013) previously developed by the authors was employed to determine the solid-vapour and solid-vapour-liquid phase equilibrium data. MoC (Zucrow & Hoffman 1976) was applied as the numerical solution technique. ...
... In this study, thermal properties of each fluid phase and phase equilibrium data are computed using extended PR EoS (Martynov et al. 2013) capable of handling the solid phase. ...
... both GERG 2008 Equation of State (EoS)(Kunz & Wagner 2012) and ePR ('e' stands for 'extended') EoS(Martynov et al. 2013) are employed. The former is applied for the predictions of CO2 above its triple point. ...
The internationally agreed global climate deal reached at the Paris Climate Conference (COP21) in December 2015 is intended to limit the increase in global average temperature to less than 2°C above pre-industrial levels by 2050. Achieving this goal requires a 50 – 80% reduction in CO2 emissions. Alongside renewable energy sources, CO2 Capture and Sequestration (CCS) is widely considered as a key technology for meeting this target, potentially reducing the cost of inaction by some $2 trillion over the next 40 years. It is estimated that transporting the predicted 2.3 - 9.2 Gt of captured CO2 to its point of storage will require the use of a global network of between 95000 - 550000 km pipelines by 2050. The economic pipeline transportation of such large amounts of CO2 will require operation in dense or supercritical phase. In Europe, this will likely mean pipelines at line pressures above 100 bar, some passing through or near populated areas. Given that CO2 is increasingly toxic at concentrations higher than 7%, the safe operation of CO2 pipelines is of great importance and indeed pivotal to the public acceptability of CCS as a viable means for tackling the impact of global warming. The accurate prediction of the discharge rate of the escaping inventory in the event of accidental pipeline rupture is central to the safety assessment of such pipelines. This information forms the basis for determining the minimum safe distances to populated areas, emergency response planning and the optimum spacing of isolation valves. In addition, in an emergency situation, the controlled depressurisation of CO2 pipeline is critically important given the unusually high Joule-Thomson cooling of CO2. Too rapid depressurisation poses the risk of embrittlement of the pipe wall causing pipeline running fracture, solid CO2 formation leading to blockage of pressure relief valves in the event of crossing the triple point temperature (216.7 K) or a Boiling Liquid Expanding Vapour Explosion (BLEVE) due to the superheating of liquid phase CO2. This thesis presents the development, testing and validation of various transient flow models taking account of the above phenomena. These include a Homogeneous Equilibrium Mixture (HEM) pipe flow model, a Homogeneous Relaxation Mixture (HRM) pipe flow model, a Two-Fluid Mixture (TFM) pipe flow model, and an integral jet expansion model. The HEM model employing Computational Fluid Dynamics (CFD) techniques is developed for predicting solid CO2 formation during pipeline decompression. The pertinent vapour-liquid or vapour-liquid-solid multi-phase flow is modelled by assuming homogeneous equilibrium. The flow model is validated against pressure and temperature data recorded during the Full Bore Rupture (FBR) decompression of an extensively instrumented 144 m long, 150 mm i.d. CO2 pipe initially at 5.25 °C and 153.3 bar. For the conditions tested, the simulated results indicate CO2 solid mass fractions as high as 35% at the release end, whose magnitude gradually decreases with distance towards the pipe intact end. Turning to the HRM model, in its development, thermodynamic non-equilibrium between the constituent fluid phases during pipeline decompression is considered for both pure fluids and multi-component mixtures. The validation of the HRM model is carried out by comparing its predictions of a number of CO2-rich mixtures pipeline FBR decompression experiments against the corresponding measurements. For reference, the HEM model predictions (where thermodynamic non-equilibrium is ignored) for the same tests are also included in the comparison. The results show that improved agreement with the measured data can be obtained by the present model as compared to the HEM model. The last pipeline decompression model presented in this thesis is the TFM model, where the conservation equations are solved separately for each constituent fluid phases during decompression, unlike in the case of the HEM and HRM models. Fluid/fluid interface interactions are accounted for and modelled using appropriate closure relations. Furthermore, a new puncture outflow boundary condition is presented. For the numerical solution of the conservation equations, modifications towards previous schemes are introduced for improved accuracy and numerical stability. Model validation is carried out by comparing its predictions of two CO2 pipeline puncture decompression tests against the corresponding measurements, showing excellent agreement. The experimentally observed heterogeneous flow behaviour, that is, the significant temperature difference between the vapour and liquid phases, is captured by the present model. The final part of this thesis deals with the accurate prediction of the conditions of a pressurised jet upon its expansion to atmospheric pressure, where the simulated outflow data from the decompression flow models is used as the input conditions. Such prediction is of fundamental importance in assessing the consequences associated with accidental releases of hazardous fluids from pressurised vessels and pipes. An integral jet expansion model which for the first accounts for turbulence generation is presented. By the use of accidental release of two-phase CO2 from a pressurised vessel as an example, the proposed model is shown to provide far better predictions of the fully expanded jet momentum flux as compared to the existing integral model where the impact of turbulence generation is ignored.
... 22 The use of vessel blowdown model was justified given that in the case of puncture failure of a relatively short pipeline (233 mm internal diameter and 256 m long) the fluid inertia plays an insignificant role in the decompression process. 23 In a further study 24 to enable the simulation of the CO 2 decompression to pressures below the triple point, we applied an extended Peng−Robinson equation of state to deal with solid phase CO 2 . However, due to the underlying zero-dimensional approximation employed in this model, it could not resolve the spatial distribution of CO 2 solid formed along the decompressing pipe. ...
... The thermodynamic properties of the liquid and vapor phases are calculated using the GERG 2004 equation of state (EoS), 38 while the solid and vapor properties along the sublimation line are predicted using the extended PR EoS. 24 An isentropic speed of sound of the fluid required for the numerical solver (see next section) is defined as ...
Decompression of CO2 pipelines is studied both experimentally and numerically to provide a partially validated model as the basis for the prediction of the hazards associated with CO2 solid formation. The pipeline decompression experiments, performed using a fully instrumented 36.7 m long and 50 mm internal diameter test pipe up to a maximum pressure of 45 bar, incorporating discharge orifice diameters of 4 and 6 mm, reveal the stabilisation of pressure and temperature near the CO2 triple point. Also, video recordings of the decompression flow in the reinforced transparent section of the steel pipe show that initial stratification of the constituent liquid and vapour phases is followed by rapid CO2 solid formation and accumulation in the pipe. To aid the prediction of hazards associated with solids formation in pipelines, a homogeneous equilibrium pipeline decompression model is developed accounting for the pertinent physical properties of CO2 in the liquid, vapour and solid states. The model is validated against the experimental data, showing ability to accurately predict the measured pressure and temperature variations with time along the pipe, as well as the time and amount of the solid CO2 formed upon decompression across the triple point.
... for which R = 8.3145 J/(mol•K) and ω = 0.228 [62,83] of CO2 are used during the specification. In addition, the equation set (31) can also be rewritten as ...
Hydrodynamic shrinkage of liquid CO2 drops in water under a Taylor flow regime is studied using a straight microchannel (length/width ~ 100). A general form of a mathematical model of the solvent-side mass transfer coefficient (ks) is developed first. Based on formulations of the surface area (A) and the volume (V) of a general Taylor drop in a rectangular microchannel, a specific form of ks is derived. Drop length and speed are experimentally measured at three specified positions of the straight channel, namely, immediately after drop generation (position 1), the midpoint of the channel (position 2) and the end of the channel (position 3). The reductions of drop length (Lx, x = 1, 2, 3) from position 1 to 2 and down to 3 are used to quantify the drop shrinkage. Using the specific model, ks is calculated mainly based on Lx and drop flowing time (t). Results show that smaller CO2 drops produced by lower flow rate ratios (QLCO2/QH2O) are generally characterized by higher (nearly three times) ks and Sherwood numbers than those produced by higher QLCO2/QH2O, which is essentially attributed to the larger effective portion of the smaller drop contributing in the mass transfer under same levels of the flowing time and the surface-to-volume ratio (~ 104 m-1) of all drops. Based on calculated pressure drops of the segmented flow in microchannel, the Peng-Robinson equation of state (EOS) and initial pressures of drops at the T-junction in experiments, overall pressure drop (ΔPt) in the straight channel as well as the resulted drop volume change are quantified. ΔPt from position 1 to 3 is by average 3.175 kPa with a ~1.6% standard error, which only leads to relative drop volume changes of 0.3‰ to 0.52‰.
... In a recent study, 15 as part of the CO 2 PipeHaz project, 2 we developed a vessel blowdown model based on the homogeneous equilibrium mixture (HEM) assumption accounting for CO 2 liquid, vapor, and solid phases. Incorporating the extended Peng−Robinson Equation of State (ePR EoS) 16 to deal with solid phase CO 2 , we successfully simulated the depressurization trajectory of 256 m long, 233 mm i.d. ...
... Hammer et al. 17 also presented simulation data relating to a hypothetical full-bore pipeline rupture decompression scenario using their CFD model. Much the same as Martynov et al., 15 a pressure plateau at the triple point was reported. In their later publication, 19 a comparison between the model predictions and the measured pressure and temperature data during a CO 2 pipeline decompression test was presented. ...
The formation of significant quantities of solid CO 2 as a result of surpassing its triple point during rapid decompression of CO 2 pipelines employed as part of the Carbon Capture and Sequestration (CCS) chain can present serious operational and safety challenges. In this paper, the development, testing and validation of a rigorous Computational Fluid Dynamics (CFD) flow model for predicting solid CO 2 formation during decompression is presented. Multiphase flow is modelled by assuming homogeneous equilibrium, and the pertinent thermodynamic data are computed using real-fluid equations of state. The flow model is validated against pressure and temperature data recorded during the decompression of an extensively instrumented 144 m long, 150 mm i.d. CO 2 pipe initially at 5.25 o C and 153.3 bar. For the conditions tested, the simulated results indicate CO 2 solid mass fractions as high as 35% at the rupture plane, whose magnitude gradually decreases with distance towards the pipe's intact end.
