Microsoft Word - 35fakandu.docx CHEMICAL ENGINEERING TRANSACTIONS VOL. 53, 2016 A publication of The Italian Association of Chemical Engineering Online at www.aidic.it/cet Guest Editors: Valerio Cozzani, Eddy De Rademaeker, Davide Manca Copyright © 2016, AIDIC Servizi S.r.l., ISBN 978-88-95608-44-0; ISSN 2283-9216 An Analytical Model of Carbon Dioxide Jet from Pressurized Systems for Safety Distance Evaluation Emilio Palazzi*, Fabio Currò, Erika Lunghi, Bruno Fabiano DICCA Civil, Chemical and Environmental Engineering Department - Polytechnic School, University of Genoa, via Opera Pia 15, 16145 Genoa, Italy emilio.palazzi@unige.it Normative legislations relating to standards and international guidelines within the framework of carbon capture sequestration (CCS) and the transport of carbon dioxide in the actual operating conditions are still under development. The focus of the present study is the cold jet modelling, including the orientation factor, representing a scenario still partially unexplored. The framework provides by simple analytical formulae the boundaries of the jet region and air entrainment behaviour, as well as the resulting ground level hazardous concentrations to humans. The model relies on a first experimental validation of the jet phase, evidencing that the model can be applied, at least as a first cautious screening tool, for safety distance evaluation. 1. Introduction As amply reported, CCS is developed into three stages, namely carbon dioxide capture, transport by pipelines and sequestration, e.g. by by CO2 injection into geological underground formation. High-pressure pipeline transport is required as economics are not favourable for transporting large amounts of CO2 over considerable distances in the gas phase due to its elevated molar volume. The properties and the behaviour of carbon dioxide in the supercritical phase are not completely known and still under investigation, requiring time consuming modelling approaches. For example, the description by Span and Wagner equation of state allows attaining reliable predictions, once evaluated 42 terms, 8 of which being complex exponentials, thus representing a hard computational burden (Kim, 2007). The definition of the source term in CO2 releases of carbon dioxide from pressurized pipelines is currently an up-to-date research topic, as demonstrated by several research papers. Carbon dioxide transport by pipeline in USA recorded an accident frequency corresponding to 0.32 events per year per 1,000 km (Gale and Davidson, 2004), i.e. a statistical figure nearly double than natural gas pipeline one. Pipeline within congested areas may represent a significant hazard also in view of possible fragment impact resulting from domino effect (Lisi et al., 2015). Additionally, the evaluation of the rate of air mixing, with a sudden release, deriving from loss of containment of pressurized vessels, is an essential tool in studies of hazard assessment and risk evaluation, both under confined (Palazzi et al., 2013) and unconfined conditions (Palazzi et al., 2014). A general analytical model providing a correlation between the capacity expressed in mass terms of CO2 piping and the extension of the surrounding critical area (characterized by the maximum distance of release, r*, into which the exposition to CO2 can provoke serious effects), is identified and proposed as a function of the operative modes and of the ambient conditions: r* = r* (m, o.c. , a.c.) (1.a) m*=m*(r*, o.c., a.c.) (1.b) Table 1: Carbon dioxide levels of toxicity Concentration y* Exposure Time τ* (s) Effects Source Dose D* (s) 0.25 60 Death (Mazzoldi et al, 2012) 15 0.10 600 (1) Death (Mazzoldi et al, 2012)) 60 0.04 1,800 IDLH NIOSH 72 (1) Precautionary assumption, within the given range: 600 – 750 s (Mazzoldi et al., 2012). DOI: 10.3303/CET1653051 Please cite this article as: Palazzi E., Curro F., Lunghi E., Fabiano B., 2016, An analytical model of carbon dioxide jet from pressurized systems for safety distance evaluation, Chemical Engineering Transactions, 53, 301-306 DOI: 10.3303/CET1653051 301 The correlations (1.a) and (1.b) can be used, respectively, in order to address verification issues or to face design problems. The study has been divided into two phases: the former concerns data collection and analysis referred to CO2 levels of toxicity, relevant dose effect and release peculiarities, the latter regards the modelling, including a thorough discussion on simplifying assumptions, the calculations aimed at identifying the most critical situations and the presentation of preliminary results. Clearly a more complete modelling approach covering the dispersion phase, would require accurately calculating the values of the meteorological parameters in the boundary-layer, starting from on-site meteorological data, e.g. Vairo et al., 2015. 2. Carbon dioxide: inherent properties and release peculiarities In the following, we discuss toxicological, operative and ambient parameters by which the degree of risk associated with accidental CO2 releases depends on, highlighting the situations of main interest for this study. Table 1 reports benchmarks related to toxic effects for humans resulting from inhalation of carbon dioxide (Mazzoldi et al., 2012), namely critical concentration in the atmosphere, expressed as molar (or volumetric) fraction, y*; critical exposition time, τ*, at y* and the corresponding effects; critical dose according to Eq (2): D*=y*τ* (2) For the purposes of risk assessment, the critical concentration y* can be used in order to find out, by means of a suitable atmospheric dispersion model, the distance r* from the release, beyond which yTc. • After the violent expansion from pi until ambient pressure pa, the spilled CO2 partially sublimates, forming a biphasic mixture (S + V) at (pa , Ts). • After the rapid mixing and air entrainment following situation are sorted: - dry air: all the CO2 at solid state sublimates (S  V), forming a gaseous solution A, at (pa , Ts); - wet air: as above, furthermore all the water vapour sublimates (vw  sw), settling down (snow, ice). The previous hypotheses represent a cautious approach: in fact, they neglect the possibility that part of CO2, settling down into solid form, may reduce the quantitative of pollutant subjected to atmospheric diffusion in a short time, as well as the residual moisture in the mixture CO2 – air (with further reduction of carbon dioxide). Because of the overall high-pressure difference, the fluid (L, F) velocity in the outflow section will be rather high (≈ 100 ms-1). We consider a semi-continuous jet release (generally, decreasing flow rate over time), with duration of not less than one minute, following a non-catastrophic loss of containment. 3. Modelling Starting from similar studies (e.g., Mazzoldi et al., 2012; Webber, 2011), it is assumed that pressure and temperature in CO2 transport activities, vary in the following ranges: 100 ≤ pi ≤ 200 [bar], 273 ≤ Ti ≤ 323 [K]. Ambient conditions that can more significantly determine the dispersion mode of the release and the reference range are summarized in Table 2. 302 Table 2: Reference ambient/environmental conditions. Characteristics / Properties Assumptions Orography / Topography Flat ground, no obstacles Temperature 273 – 323 K Moisture 0 – yw,sat Wind speed (10 m above the ground) 0 – 10 ms-1 As already remarked, the focus of the current study is the attainment of an analytical correlation between extensive release properties (dimension, m, critical area, r), as a function of intensive properties characterizing the state of a system (CO2) and of the external environment. Concerning these issues, 48 different situations, corresponding to the combinations among 4 operative conditions and 12 different environmental situations, were thoroughly examined, as summarized in Table 3. 3.1 Jet physical model In order to study the jet dispersion, we start from the one – dimensional model by Li et al., (2016), that allows considering the jet dispersion, with or without wind. It is possible demonstrating that, in order to avoid the effects resulting from the ground interference (i.e. impact and solid CO2 deposition, friction induced distortion of the flow field due, reduction of the contact surface with the free atmosphere and consequent air entrainment reduction, reflection of CO2 to the ground) it’s enough that the jet is inclined nearly 9° with respect to the horizontal line. For the sake of simplicity and conservatism, the jet dispersion model is referred to a horizontal jet parallel to the ground, perpendicular to the pipeline with the same wind direction. Under these conditions, the relative speed between the jet and the air is minimal, so that air entrainment into the jet is minimal too. The corresponding conservative results implies the overestimation of the critical distance, r*, by nearly 10% excess. A schematic diagram of the horizontally – directed jet and of the phenomena concurrent to its development, is reported in Figure 1. After a qualitative characterization of the different jet behaviours, in the following paragraphs we provide the analytical descriptions of the three regions describing the carbon dioxide evolving scenario following the LOC. I Internal region. Internal flux from the section of stagnation i, to the outflow section e. SE Expansion – Sublimation region. CO2 partial expansion and sublimation ((  S). Localized between section e and section s, where the sublimation from fluid to solid S ends. Status at s: Ts, CO2 (v), CO2 (s). SM Mixing – Sublimation region. Localized between s section and o section, where jet phase begins. Status at o: Ts, CO2 (v), air. -Mixing with dry air and complete CO2 sublimation (S  V). -Mixing with wet air and sublimation: CO2 (S  V); H2O (V  S). J Jet region, between section o and section *, where CO2 reaches y* concentration: -Mixing with dry air. -Mixing with wet air and H2O sublimation (V  S) followed by deposition to the ground Table 3: Chemical-physical properties of the fluids involved in the release and into atmospheric dispersion. CO2 Air H2O Status P [bar] T [K] ρ [kg m-3] p° [bar] h [kg kJ-1] H [kg kJ-1] ρ [kg m-3] H [kg kJ-1] Y [-] h [kg kJ-1] H [kg kJ-1] i (Initial) 100 273 975 34.8 499 200 273 1021 34.8 497 100 323 390 34.8 684 200 323 784 34.8 603 s (Sublimati on) 1.013 194.65 2.81 724 1.75 195 -476 a (Ambient) 1.013 273 1.29 273 0.0060 2,502 1.013 298 1.19 298 0.0313 2,546 1.013 323 1.09 323 0.1216 2,591 303 Figure 1: Schematization of the horizontal jet physical model according to three ideal region evolution. 3.2 Internal region I The most important parameter to be determined in this region is the outflow speed, vr,. As a cautious estimate neglecting frictions and overrating the value, we consider the fluid as a perfect one. According to scientific literature (Witlox et al., 2009; Martynov et al., 2014), two different cases can be sorted, as discussed in the following. If Ti ≤ Tc, the fluid is considered as an incompressible supercooled liquid, so that: vr = [2 (pi – pi°) / ρi] 1/2 (6) and the specific flow rate of the release is calculated as: mr = [2 (pi – pi°) ρi] 1/2 (7) If Ti > Tc, carbon dioxide is considered a compressible supercritical fluid, so that the outflow is sonic: = (8) where γ = 1.3 is the Poisson coefficient relating to carbon dioxide. Then: = 2+ 1 2+ 1 (9) In both situations, for a release of a given flow rate, mr, outflow section area, Ae, and its equivalent diameter, de, are calculated as follows: Ae = mr / ρr vr (10) = (11) 3.3 Jet expansion region S For the purposes of the study, it is not essential to analyze into details the transformations taking place within the sub-regions SE and SM. Since the status of incoming and outcoming fluids is known, in region S just the proper application of basic conservation principles is required. Considering the energy balance: Mrhr,i + masHa,a + mwsHw,a = masHa,s + mrHr,s + mwshw,s (12) where: mas = ms (1 – yw) (13) mws = msyw (14) Combining Eq (12)-(14), one can write: ms = η mr (15) η = , ,, , , , (16) 304 Considering the mass balance: m0 = mr [1 + η (1 – yw)] (17) the composition and density, ρ0, of the fluid referred to the outcoming section, o, are calculated: w0 = = [1 + η (1 – yw)] -1 (18) y0 = = [1 +μ η (1 – yw)] -1 = , + , (19) (20) Analogously, starting from the momentum balance, by proper calculations, one can easily obtain: v0 = (21) = 4 = 4 1 ++ (22) Since r0 is lower by about two orders of magnitude compared to r*, the problem of assessing it with accuracy presents no particular interest and it is possible assuming cautiously r0 = d0. 3.4 Fully developed jet region J Starting from the approach of Li et al., (2016), carbon dioxide concentration on the jet axis, ya, is twice the average one. Assuming, precautionary, that y* = ya, it is obtained that the jet must be diluted until an average concentration equal to y*/2. The corresponding critical mass fraction of carbon dioxide is: w* = [1 + ( ∗ - 1)]-1 (23) From the mass balance referred to region J, remembering that m*= mr/w*, it follows : = ∗ − = ∗ − = 1 − = 1 − 1∗ − 1 (24) (25) According to the model, air entrainment into the jet is described by following equations: = (26) = 1 − (27) By integrating Eq (26), with some straightforward calculations it is possible obtaining the distance rj travelled by the fluid to drag the mass mj and, at last, the critical distance r*, as follows: = 11 − ∗ − 1 1 4 1 ++ (28) r*= rj + r0 (29) 3. Results and discussion As an illustrative example of the short-cut model, Table 4 shows the maximum and the minimum values of the critical distances, r*, depending on the explored environmental conditions and reference concentrations y. It must be noticed that the maximum critical distance, rmax*, corresponds constantly to ambient temperature Ta=323 K, saturated moist air and wind velocity u=10 ms -1, while the minimum one, rmin*, is always connected to Ta=273 K, dry air, u=10 ms -1. It is noteworthy observing that the maximum percentage difference between the two estimates, over the wide range of explored conditions, is rather limited: ∆%,max = 25.6%. Table 4: Short-cut model calculation of the maximum and minimum critical distances under different environmental and transport conditions considering a continuous CO2 release rate mr=10 3 kg s-1. y* 0.25 0.25 0.25 0.25 0.10 0.10 0.10 0.10 0.04 0.04 0.04 0.04 p [bar] 100 100 200 200 100 100 200 200 100 100 200 200 T [K] 273 323 273 323 273 323 273 323 273 323 273 323 r*max [m] 70 57 55 57 167 136 131 137 410 335 321 333 r*min [m] 57 44 46 47 128 106 103 106 305 253 245 252 305 Coeteris paribus, it can be inferred that, mainly due to lower air entrainment in the jet region, the releases characterized by lower energy result more critical than the other ones, in connection with a lower effective dilution. Referring to the most critical conditions identified, (Ta=323 K; saturated moist air; u=10 ms -1) we obtain in the given range: yw=0.122 ; η=2.16 ; wo=0.634 ; ρa=0.96 kg m -3. For a practical application in the design problem, Table 5 summarizes the main model parameters of interest, depending on the assumed hazardous carbon dioxide concentration. Starting from Eq(29), by calculating the release velocity vr corresponding to the explored CO2 conditions and ranging from 116-180 ms -1, a simple analytical expression described by Eq(30) can be obtained for the hazardous effect distance r* [m]. According to the dose approach, the values of φ parameter summarized in Table 6 are calculated for the limiting concentrations corresponding to the different CO2 hazardous effects. r* = φ mr 1/2 (30) Table 5: Values of the model parameters depending on the reference hazardous CO2 concentration y* y* w* ⁄ ∗⁄ 0.25 0.178 0.043 1.043 0.10 0.074 0.018 1.018 0.04 0.030 0.007 1.007 Table 6: Values of the parameter φ for the considered operative conditions and hazardous CO2 concentration y* p=100 bar T=273 K p=200 bar T=273 K p=100 bar T=323 K p=200 bar T=323 K 0.25 2.22 1.74 1.30 1.80 0.10 5.29 4.14 4.31 4.32 0.04 12.97 10.15 10.59 10.54 4. Conclusions The short-cut approach here developed allows obtaining, by means of explicit formulae, the safety distances from the carbon dioxide release following a loss of containment from a pressurized system. Starting from different limit CO2 concentrations, it is possible identifying the corresponding critical dose. 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