Quantification of Uncertainty in CFD Simulation of Accidental Gas Release for O & G Quantitative Risk Assessment
Abstract
:1. Introduction
- Ratio between flammable volume and total volume (σDamage):
- External perimeter of the platform reached by the flammable cloud () can be seen as a measure of possible damage to specific targets (e.g., escape routes) that in the offshore platform are commonly located on the external perimeter:
- Flammable volume developed under 1.5 m () can be considered an important measure of the damage because the main electrical and mechanical components are placed on the floor; these can generate friction triggers and electrical triggers, which may ignite the flammable gas cloud, whereas, at higher elevation, the probability of having ignition sources is quite low:
2. CFD Tools
2.1. SBAM
2.2. FLACS and KFX
3. CFD Validation
3.1. Free Jet Validation
3.1.1. Benchmark Description
- Hole diameter: de = 0.5 m;
- Upstream pressure and temperature: prel = 11 bar Trel = 293 K;
- Environmental pressure and temperature: pamb = 1 bar Tamb = 293 K;
- Dimension of the simulated domain: 120 m (X-direction), 40 m (Y-direction), 8 m (Z-direction).
- -
- FLACS
- ○
- A mass flow is imposed on all the boundaries
- ○
- Semi-empirical Birch model is used for the release phase
- -
- KFX
- ○
- A static pressure (atmospheric) is imposed on all the boundaries
- ○
- Semi-empirical Birch model is used for the release phase
- -
- Fluent
- ○
- A static pressure (atmospheric) is imposed on all the boundaries
- ○
- CH4 concentration equal to 1, and pressure equal to 11 bars are imposed on the release hole.
3.1.2. Results
3.2. Jet Impinging on a Cylinder
3.2.1. Benchmark Description
- Hole diameter: 0.0107 m;
- Mass flow rate from the hole: m = 0.011 kg/s;
- Obstacle diameter: dcyl = 0.150 m;
- Distance, along the axis of symmetry, between the release point and the obstacle: l = 683 mm or 157 mm;
- Dimensions of the simulated domain: 26 m (X-direction), 4 m (Y-direction), 24 m (Z-direction).
- -
- FLACS
- ○
- A mass flow is imposed on all the boundaries
- -
- KFX
- ○
- A static pressure (atmospheric) is imposed on all the boundaries
- -
- Fluent
- ○
- A static pressure (atmospheric) is imposed on all the boundaries
- ○
- CH4 concentration equal to 1 and mass flow rate of 0.0107 kg/s are imposed on the release hole.
3.2.2. Results
4. The Realistic Case Study
- Release pressure: prel = 50 bar;
- Release hole diameter: de = 3 cm;
- Domain dimensions: 5 m height (Z), 30 m lengths (X), 20 m width (Y);
- Release point and direction: X = 3 m, Y = 2 m, Z = 1.5 m along the X direction;
- Wind direction: 0.5 X + 0.5 Y;
- Wind intensity: u = 6 m/s.
4.1. Simulation Setup
- CH4 concentration equal to 1 and a pressure of 50 bar are imposed on the release hole;
- The cylindrical nearby obstacle is modeled as a wall with no-slip conditions;
- Ambient pressure is imposed on the external faces of the source box (SB).
- Wind velocity with a magnitude of u = 6 m/s with a direction of 0.5 X + 0.5 Y is imposed on S and E sides;
- Atmospheric pressure is imposed on N and W faces;
- All the interactions with obstacle surfaces are modeled with walls with no-slip conditions.
- Uniform wind profile is imposed on S and E sides (analogous to SBAM);
- Ambient pressure is imposed in KFX on W and N sides (analogous to SBAM);
- Mass flow outlet is used in FLACS, as suggested in [36], to obtain a convergent solution.
4.2. Results
4.2.1. Simulation Results
4.2.2. Uncertainty Quantification for Risk-Informed Decision-Making
- Assume a discrete solution f as a function of the characteristic size of the grid h
- According to the method of order p, the Equation (5) becomes:
- Linearly combining and , the general Richardson’s extrapolation is defined:
- If order p is unknown (i.e., the order of the solution is influenced by numerical schemes, boundary conditions…), three solutions with constant grid refinement ratio and can be used to estimate:
- FLACS: GCI = 7.8%, = 163 m3
- KFX: GCI = 10.6%, = 199 m3
- SBAM: GCI = 1.2%, = 83 m3
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Acknowledgments
Conflicts of Interest
References
- Ogwu, A.; Badamasuiy, S.; Joseph, C. Environmental Risk Assessment of Petroleum Industry in Nigeria Friday. Int. J. Sci. Res. Innov. Technol. 2015, 2, 4. [Google Scholar]
- Vinnem, J.E. Offshore Risk Assessment Vol 2—Chapter 14, 4th ed.; Springer: Berlin/Heidelberg, Germany, 2019. [Google Scholar]
- Casal, J. Evaluation of the Effects and Consequences of Major Accidents in Industrial Plants—Chapter 11; Elsevier: Amsterdam, The Netherlands, 2007. [Google Scholar]
- Carpignano, A.; Corti, T.; Uggenti, A.C.; Gerboni, R. Modelling of a supersonic accidental release in Oil&Gas offshore: Characterisation of a source box. GEAM Geoing. Ambient. 2017, 152, 58–64. [Google Scholar]
- Davis, S.; Gavelli, F.; Hansena, O.; Middhac, P. Onshore Explosion Studies—Benefits of CFD Modelling. Chem. Eng. Trans. 2013, 13, 205–273. [Google Scholar]
- Hanna, B.N.H.B.; Dinh, N.T.; Youngblood, R.W.; Bolotnov, I.A. Coarse-Grid Computational Fluid Dynamics (CG-CFD) Error Prediction using Machine Learning. Ph.D. Thesis, North Carolina State University, Raleigh, NC, USA, 2018. [Google Scholar]
- Gorle, C.; Zeoli, S.; Emory, M.; Larsson, J.; Iaccarino, G. Epistemic uncertainty quantification for Reynolds-averaged Navier-Stokes modeling of separated flows over streamlined surfaces. Phys. Fluids 2019, 31, 035101. [Google Scholar] [CrossRef]
- Gorle, C.; Iaccarino, G. A framework for epistemic uncertainty quantification of turbulent scalar flux models for Reynolds-averaged Navier-Stokes simulations. Phys. Fluids 2013, 25, 055105. [Google Scholar] [CrossRef]
- Xiao, H.; Cinnella, P. Quantification of Model Uncertainty in RANS Simulations. Prog. Aerosp. Sci. 2018, 108, 1–31. [Google Scholar] [CrossRef] [Green Version]
- Ke, W.C.; Chen, H.; Lin, H.W.W. A note of techniques that mitigate floating-point errors in PIN estimation. Financ. Res. Lett. 2019, 31. [Google Scholar] [CrossRef]
- Fraysse, F.; de Vicente, J.; Valero, E. Numerical Error Prediction and Its Applications in CFD Using τ-Estimation; BCAM: Bilbao, Spain, 2018. [Google Scholar]
- Colombo, E.; Inzoli, F.; Mereu, R. A methodology for qualifying industrial CFD: The Q3 approach and the role of a protocol. Comput. Fluids 2012, 54, 56–66. [Google Scholar] [CrossRef]
- Cutrono, A.; Visser, D.C.; Komen, E.M.J. Uncertainty Quantification method for CFD applied to the turbulent mixing of two water layers. Nucl. Eng. Des. 2018, 333, 1–15. [Google Scholar]
- Karniadakis, G.E. “Quantifying Uncertainty in CFD”. ASME J. Fluids Eng. 2002, 124, 2–3. [Google Scholar] [CrossRef] [Green Version]
- Richardson, L.F. The approximate arithmetical solution by finite differences of physical problems involving differential equations, with an application to the stresses in amasonry dam. J. Philos. Trans. R. Soc. Lond. Ser. A 1911, 210, 307–357. [Google Scholar]
- Roache, P.J. Verification and Validation in Computational Science and Engineering; Hermosa: Albuquerque, NM, USA, 1998. [Google Scholar]
- Stern, F.; Wilson, R.V.; Coleman, H.W.; Paterson, E.G. Verification and Validation of CFD Simulations; Report No. 407; Iowa Institute of Hydraulic Research: Iowa City, IA, USA, 1999. [Google Scholar]
- Lloyd’s Register. Comparative Study on Gas Dispersion; Lloyd’s Register: London, UK, 2012. [Google Scholar]
- Pappalardo, F.; Moscatello, A.; Uggenti, A.C.; Gerboni, R.; Carpignano, A.; Di Maio, F.; Mereu, R.; Zio, E. Comparison of CFD numerical ap-proaches for the simulation of accidental gas release in energy applications. In Proceedings of the ESREL2020 PSAM15 Conference, Venice, Italy, 2–5 November 2020; pp. 4067–4074. [Google Scholar]
- Franquet, E.; Perrier, V.; Gibout, S.; Bruel, P. Free under expanded jets in a quiescent medium: A review. Prog. Aerosp. Sci. 2015, 77, 25–53. [Google Scholar] [CrossRef]
- Moscatello, A.; Uggenti, A.C.; Gerboni, R.; Carpignano, A. A novel approach to high-pressure gas releases simulations. J. Loss Prev. Process. Ind. 2021, 72, 104531. [Google Scholar] [CrossRef]
- ANSYS. ANSYS Fluent 18.2 User’s Guide; ANSYS Inc.: Canonsburg, PA, USA, 2018. [Google Scholar]
- Birch, A.D.; Brown, D.R.; Dodson, M.G.; Swaffield, F. The Structure and Concentration Decay of High- Pressure Jets of Natural Gas. Combust. Sci. Technol. 1984, 36, 249–261. [Google Scholar] [CrossRef]
- Patankar, S.V.; Spalding, D.B. A calculation procedure for the transient and steady-state behaviour of shell-and-tube heat exchangers. In Heat Exchangers: Design and Theory Sourcebook; Afgan, N.H., Schundler, E.V., Eds.; McGraw-Hill: New York, NY, USA, 1974; pp. 155–176. [Google Scholar]
- Miguel, A.F.; Van de Braak, N.J.; Silva, A.M.; Bot GP, A. Wind-induced airflow through permeable materials. J. Wind. Eng. Ind. Aerodyn. 2001, 89, 59–72. [Google Scholar] [CrossRef]
- Launder, B.E.; Spalding, D.B. The numerical computation of turbulent flows. Comput. Methods Appl. Mech. Eng. 1974, 3, 269–289. [Google Scholar] [CrossRef]
- Eggins, P.L.; Jackson, D.A. Laser-Doppler velocity measurements in an under-expanded free jet. J. Phys. D Appl. Phys. 1974, 7, 14. [Google Scholar] [CrossRef]
- Cleaver, R.P.; Cooper, M.G.; Piper, D. Gas dispersion and build-up within offshore modules. In Proceedings of the SARSS’91: Safety and Reliability Society Symposium, Sutton Coldfield, UK, 18–19 September 1991. [Google Scholar]
- Novembre, N.; Podenzani, F.; Colombo, E. Numerical study for accidental gas releases from high-pressure pipelines. In Proceedings of the European Conference on Computational Fluid Dynamics ECCOMAS CFD, Egmond aan Zee, The Netherlands, 5–8 September 2006. [Google Scholar]
- Abramowitz, M.; Stegun, I.A. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th Printing; Dover: New York, NY, USA, 1992. [Google Scholar]
- DNV-GL. KFX-EXISM V.3.4 User Manual, Technical Manual; DNV-GL: Bærum, Norway, 2019. [Google Scholar]
- European Union. Directive 2013/30EU of the European Parliament and of the Council of 12 June 2013; European Union: Brussels, Luxembourg, 2013. [Google Scholar]
- Vivalda, C.; Gerboni, R.; Carpignano, A. A practical approach to risk-based gas monitoring system design for oil and gas offshore platforms. In Proceedings of the 14th Probabilistic Safety Assessment and Management Conference, London, UK, 22–26 June 2018. [Google Scholar]
- Wilcox, D.C. Basic Fluid Mechanics Fift 96-508; DCW Industries, Inc.: La Cañada Flintridge, CA, USA, 2013. [Google Scholar]
- Li, X.J.; Zhou, R.P.; Konovessis, D. CFD analysis of natural gas dispersion in engine room space based on multi-factor coupling. Ocean. Eng. 2016, 111, 524–532. [Google Scholar] [CrossRef]
- Gexcon, A.S. FLACS v10.4r2 User’s Manual; Technical Report. Available online: https://www3.gexcon.com/files/manual/flacs/html/index.html (accessed on 1 December 2021).
- Roache, P.J. Perspective: A Method for Uniform Reporting of GridRefiniment Studies. J. Fluids Eng. 1994, 116, 405–413. [Google Scholar] [CrossRef]
FLACS | KFX | Fluent | |
---|---|---|---|
Err | 5.0% | 12.2% | 1.46% |
Case 157 mm | FLACS | KFX | Fluent (Standard k-ε) | Fluent (SST k-ω) |
---|---|---|---|---|
Err | 223% | 230% | 55.9% | 42.3% |
Case 683 mm | FLACS | KFX | Fluent (Standard k-ε) | Fluent (SST k-ω) |
---|---|---|---|---|
Err | 42.8% | 98.2% | 22.4% | 18.2% |
FLACS | KFX | SBAM | |
---|---|---|---|
(5.43 ± 0.45)% | (6.63 ± 0.7)% | (2.7 ± 0.01)% | |
σtarget | 0% | 0% | 0% |
(39 ± 4.82)% | (41 ± 5.6)% | (29 ± 0.5)% |
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Pappalardo, F.; Moscatello, A.; Ledda, G.; Uggenti, A.C.; Gerboni, R.; Carpignano, A.; Di Maio, F.; Mereu, R.; Zio, E. Quantification of Uncertainty in CFD Simulation of Accidental Gas Release for O & G Quantitative Risk Assessment. Energies 2021, 14, 8117. https://doi.org/10.3390/en14238117
Pappalardo F, Moscatello A, Ledda G, Uggenti AC, Gerboni R, Carpignano A, Di Maio F, Mereu R, Zio E. Quantification of Uncertainty in CFD Simulation of Accidental Gas Release for O & G Quantitative Risk Assessment. Energies. 2021; 14(23):8117. https://doi.org/10.3390/en14238117
Chicago/Turabian StylePappalardo, Fabrizio, Alberto Moscatello, Gianmario Ledda, Anna Chiara Uggenti, Raffaella Gerboni, Andrea Carpignano, Francesco Di Maio, Riccardo Mereu, and Enrico Zio. 2021. "Quantification of Uncertainty in CFD Simulation of Accidental Gas Release for O & G Quantitative Risk Assessment" Energies 14, no. 23: 8117. https://doi.org/10.3390/en14238117