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Crater Model Theory

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SAFETI-NL INNOVATIVE MAINTENANCE Crater modelling for long pipelines RIVM Report No.: 984B0039, Rev. 2 Document No.: 1 Date: 20/09/2017 DNV GL – Report No. 984B0039, Rev. 2 – www.dnvgl.com Page i Project name: SAFETI-NL Innovative Maintenance DNV GL Software BSRGB984 3 Cathedral Street London [Office Post 3] SE1 9DE Tel: +44(0)20 357 6080 Report title: Crater modelling for long pipelines Customer: RIVM, P.O. Box 1, 3720BA Bilthoven Contact person: Paul Uijt de Haag Date of issue: 20/09/2017 Project No.: 984B0039 Organisation unit: DNV GL Software Report No.: 984B0039, Rev. 2 Document No.: 1 Prepared by: Verified by: Approved by: H.W.M. Witlox, DNV Software Senior Prinicpal Engineer [Name] [title] [Name] [title] [Name] [title] [Name] [title] [Name] [title] [Name] [title] ☐ Unrestricted distribution (internal and external) Keywords: [Keywords] ☐ Unrestricted distribution within DNV GL ☐ Limited distribution within DNV GL after 3 years ☐ No distribution (confidential) ☐ Secret Reference to part of this report which may lead to misinterpretation is not permissible. Rev. No. Date Reason for Issue Prepared by Verified by Approved by 1 2014-07-01 Preliminary Draft H.W.M. Witlox 2 2015-08-24 Added sensitivity analysis results M. Fernandez 3 2017-09-20 Phast/Safeti 8.0 (remove HAGAR details and add abstract) H.W,M. Witlox M. Fernandez DNV GL – Report No. 984B0039, Rev. 2 – www.dnvgl.com Page ii Table of contents 1 EXECUTIVE SUMMARY . 1 2 INTRODUCTION 2 2.1 Phast long pipeline models (GASPIPE, PIPEBREAK) 2 2.2 PIPESAFE crater model 2 2.3 COOLTRANS crater model 3 2.4 Implementation of COOLTRANS crater model in Phast 5 2.5 Plan of report 5 3 CRATER MODEL – THEORY . 6 3.1 Crater dimensions 8 3.2 UDM source-term input data at crater exit plane 9 4 CRATER MODEL – SENSITIVITY ANALYSIS 11 APPENDICES 0 Appendix A. Guidance on input and output data for CRATER model 0 5 REFERENCES . 3 List of figures Figure 2-1 Phast long pipeline model (GASPIPE or PIPEBREAK) . 2 Figure 2-2 PIPESAFE crater source model 3 Figure 2-3 COOLTRANS stages in defining effective source for ground-level cloud 4 Figure 3-1 Crater geometry (full-bore rupture) . 6 Figure 3-2 Crater geometry (punctures at top, middle or bottom of pipe) 7 Figure 3-3 Pollutant fraction and velocity ratio as a function of the path length 10 Figure 4-1 Base case (full bore rupture) - Velocity before and after crater versus time 12 Figure 4-2 Base case (full bore rupture) - Pollutant and air mass rate versus time 12 Figure 4-3 Velocity at crater exit plane versus time for various pipe depths . 13 Figure 4-4 Air entrainment mass rate at crater exit plane versus time for various pipe depths 14 Figure 4-5 Velocity before and after crater versus time for various fracture lengths 15 Figure 4-6 Pollutant and air mass rates at crater exit plane versus time for various fracture lengths 15 Figure 4-7 Velocity before and after crater versus time for various soil types . 16 Figure 4-8 Pollutant and air mass rates at crater exit plane versus time for various soil types . 17 Figure 4-9 Velocity at crater exit plane vs time for various aperture ratios for puncture in the middle and full bore rupture 18 Figure 4-10 Air mass rate at crater exit plane vs time for various aperture ratios for puncture in the middle and full bore rupture 18 Figure 4-11 Velocity before and after crater versus time for various puncture locations . 19 Figure 4-12 Pollutant and air mass rate at crater exit plane versus time for various puncture locations 20 DNV GL – Report No. 984B0039, Rev. 2 – www.dnvgl.com Page 1 1 EXECUTIVE SUMMARY The hazard assessment software package Phast and the QRA software package Safeti include the models Gaspipe and Pipebreak for modelling of discharge of vapour or two-phase flashing liquids from long pipelines. For buried pipelines, Gaspipe and Pipebreak invoke a crater model to calculate the effect of the crater on the initial momentum (initial velocity) and the initial dilution at the crater exit plane. The thus calculated data at the crater exit plane are the source term data for the Phast dispersion model UDM and jet fire model. This report first provides a review of available models in the literature for crater modelling, corresponding to crater models developed as part of the DNV GL Loughborough JIP projects Pipesafe and Cooltrans. Subsequently it describes the implementation of the Cooltrans crater model into Gaspipe and Pipebreak, including full details of the adopted crater theory. Finally, a sensitivity analysis is carried out to demonstrate the effect of input data on the initial velocity and initial dilution at the crater exit plane. DNV GL – Report No. 984B0039, Rev. 2 – www.dnvgl.com Page 2 2 INTRODUCTION 2.1 Phast long pipeline models (GASPIPE, PIPEBREAK) The hazard assessment software package Phast and the QRA software package Safeti include the models GASPIPE and PIPEBREAK for modelling of discharge of vapour or two-phase flashing liquids from long pipelines. The model allows for the presence of a possible pump at the upstream of the pipe (prescribed fixed flow rate) and a number of valves (shutdown valves, excess valves or non-return valves) along the pipe. The breach can occur at any location of the pipe and the breach could be a full-bore rupture or a partial leak (defined by relative aperture). The GASPIPE and PIPEBREAK models call the atmospheric expansion model ATEX to calculate the depressurisation from the exit pressure to the atmospheric pressure. The GASPIPE and PIPEBREAK model consists of the following successive stages (see Figure 2-1): 1. Calculate time-varying data for branch A upstream of the breach and branch B downstream of the branch. For both branches this includes data at the breach location both before expansion (immediately upstream of the breach) and after ATEX expansion to atmospheric pressure: a. flow rate b. (before and after ATEX expansion) velocity, pressure, temperature, liquid mass fraction c. (after expansion for superheated liquid) droplet size (Sauter Mean Diameter – SMD) 2. Combine the two plumes arising from branches A and B into one combined plume (T) ignoring crater and impingement effects and presuming both jets point in the same direction (colliding into one single plume). The data for the total plume T [flow rate, velocity, temperature (GASPIPE) or liquid fraction (PIPEBREAK), droplet size] are derived by imposing conservation of mass, momentum, energy or liquid mass and by evaluating an overall Sauter Mean Diameter. See the GASPIPE theory manual/1/ and PIPEBREAK theory manual/2/ for further details of the above calculations. The data for the total plume T are used in Phast to define the initial conditions (‘source term’) for the Unified Dispersion Model (UDM). Figure 2-1 Phast long pipeline model (GASPIPE or PIPEBREAK) 2.2 PIPESAFE crater model DNV GL Lougborough developed the model PIPESAFE (Cleaver et al.2001)/3/, which includes the effects of crater formation for natural gas long pipelines. This includes calculations for upstream and downstream branches as indicated above for branches A and B (pre-ATEX GASPIPE and PIPEBREAK calculations). Pump at upstream end downstream endBreach – orificeValve A B T (total) DNV GL – Report No. 984B0039, Rev. 2 – www.dnvgl.com Page 3 Subsequently a crater source model is used to calculate the post-expansion data for the combined plume T; see Figure 2-2. This model includes (a) air entrainment before both jets impact on each other or the crater wall, (b) air entrainment due to jets interacting with each other and the crater wall, and (c) momentum loss for the jets to the crater wall during jet interaction. The approach taken has been to extend the pseudo-diameter model by Birch (1987) /5/for sonic free jets for combining the jets and accounting for air entrainment and crater effects, while assuming ambient pressure and ambient temperature at the crater exit plane. This includes four equations [conservation of mass and momentum, two equations of state] for four unknown variables [density, velocity, area, mass fraction of pollutant in pollutant/air mixture]. In these equations, empirical correlations are presumed for the air entrainment in the crater and the momentum loss in the crater. The model has been validated against large-scale natural gas pipeline rupture experiments. The PIPESAFE crater model is specific to natural gas and is quoted not to be applicable to other chemicals. Figure 2-2 PIPESAFE0 crater source model [Schematic presentation of crater source; Figure taken from reference /3/] 2.3 COOLTRANS crater model As part of the COOLTRANS JIP Cleaver/4/,/7/ developed a crater source model which was validated against CO2 pipeline releases. Unlike the above PIPESAFE crater model specific for natural gas, Cleaver quotes this to be a generic model applicable for any chemical and not specific to CO2. As illustrated by Figure 2-3 it consists of the following main steps using models in DNV GL Loughborough package FROST (Warhurst and Cleaver, 2010)/6/: 1. Carry out outflow calculations for both upstream and downstream branches. This includes expansion to atmospheric pressure using the pseudo-diameter model by Birch (1987) /5/,1. 2. Combining plume into total plume presuming vertically upwards flow 1 The Birch model assumes that the final post-expansion temperature is equal to the ambient temperature, and this is not always realistic (e.g. for CO2 releases significant cooling would be expected). Thus the Phast ATEX logic would be preferred. DNV GL – Report No. 984B0039, Rev. 2 – www.dnvgl.com Page 4 3. Evaluation of size and shape of crater; and calculate data at exit plane of crater. The COOLTRANS crater source model accounts for air entrainment by introducing an empirical correlation for the initial pollutant mass fraction at the crater exit plane (with air being added presuming isenthalpic mixing), and it accounts for momentum loss by introducing a correlation for the velocity at the crater exit plane. Furthermore it assumes there is no significant re- entrainment of pollutant material into the crater as a result of the plume stalling and returning to the ground level around the crater. 4. A correlation in terms of a “Richardson source number” is used to define whether flow from crater falls back on itself to form a gas blanket or behaves like a free plume. Figure 2-3 COOLTRANS stages in defining effective source for ground-level cloud [Figure taken from reference /4/; diagram above shows a rupture producing a ‘source blanket’ around the crater; same four stages are present if blanket not forms and/or if the release is a puncture] 5. In order to enable a link with the ground-level dispersion model HAGAR, data are defined at a cross-wind box of uniform height, width and concentration that moved downwind with the wind speed at a representative height. o This includes a correlation for the mass correlation at level. o Furthermore to avoid discontinuities between ‘gas blanket’ and ‘free plume formulations, interpolation between both models are carried out in the section describing borderline flow. o Empirical correlations are applied for the initial aspect ratio (ratio of half width to height), upwind spread and downwind offset of the dispersion source. 6. Ground-level dispersion using FROST heavy gas dispersion model HAGAR DNV GL – Report No. 984B0039, Rev. 2 – www.dnvgl.com Page 5 2.4 Implementation of COOLTRANS crater model in Phast The COOLTRANS crater model can be applied to any pollutant (although validated so far for CO2 only) and furthermore the above steps 1,2 are analogous to steps 1,2 applied for the GASPIPE/PIPEBREAK models in Phast. Thus GASPIPE/PIPEBREAK output for the total plume (after expansion to atmospheric pressure) can be directly used as input to the COOLTRANS crater source model (above step 3). Output from the Phast implementation of the COOLTRANS source model and input to the Phast dispersion model UDM are the data at the crater exit plane, i.e. the dimensions of the crater exit plane (non-spherical in general), the initial velocity and the initial pollutant mass fraction. The initial values of the temperature and/or liquid fraction of the pollutant (prior to any mixing of air) would correspond to total plume T prior to any crater and/or air entrainment effects (as directly output by GASPIPE/PIPEBREAK), while the initially added air is added at the ambient temperature assuming isenthalpic mixing with the pollutant. Above steps 4, 5, 6 are specific to the HAGAR model and are not applied. Instead UDM calculations are carried out as usual without adding further additional correlations. Thus, Phast was found not to require the logic for linking to ‘HAGAR’ crosswind box [formulas for initial aspect ratio, upwind spread and downwind offset of dispersion source]. Instead the jet assumption is always used, i.e. the UDM calculations are started directly from the crater exit plane based on momentum loss and initial air dilution as proposed by Appendix B of COOLTRANS report. Thus, there was no need to implement a ‘breakpoint’ to a crosswind box, if the plume release would come back to itself, and no Richardson number source term is required. As a consequence, the COOLTRANS crater model has been selected for Phast implementation rather than the above PIPESAFE model. 2.5 Plan of report Chapter 3 outlines the theory of the COOLTRANS crater model alongside its integration with existing Phast models. Chapter 4 summarises the validation of this model against experimental data. DNV GL – Report No. 984B0039, Rev. 2 – www.dnvgl.com Page 6 3 CRATER MODEL – THEORY The description of the COOLTRANS model as described in the current section has been directly derived from Cleaver/4/,/8/, while reformulating it as necessary to fit with the Phast methodology and notation conventions. The dimensions of the crater are given by the crater width Wcrater, the crater length Lcrater in the direction of the release, and the crater depth Hcrater; see Figure 3-1 for a schematic figure of the crater in the case of a full-bore rupture and see Figure 3-2 for the case of a puncture at the top of the pipe, middle of the pipe or the top of the pipe. Figure 3-1 Crater geometry (full-bore rupture) PIPE Lcrater Wcrater Hcrater Hrelease CRATER SOIL Pipe crater exit plane (initial dilution, momentum loss) DNV GL – Report No. 984B0039, Rev. 2 – www.dnvgl.com Page 7 (a) Puncture at top (b) Puncture at middle (c) Puncture at bottom Figure 3-2 Crater geometry (punctures at top, middle or bottom of pipe) PIPE puncture Lcrater Wcrater Hrelease=Hcrater CRATER SOIL PIPE puncture Lcrater Wcrater Hcrater Hrelease CRATER SOIL PIPE puncture Lcrater Wcrater Hcrater Hrelease CRATER SOIL DNV GL – Report No. 984B0039, Rev. 2 – www.dnvgl.com Page 8 3.1 Crater dimensions Crater width The crater width is defined by the following correlation: ( ) ( ) ( ) soilsandyDLDMaxDDMinH soilmixedDLDMa
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