NUMERICAL ANALYSIS OF METHANE-AIR
POLLUTION
Skiteva I., Seleznev V.
Computation Mechanics Technology Center, RussiaAbstract: The method described in the paper is meant for enhancing fire safety of gas industry and proposes to
use numerical simulation for analysis of methane-air mixture combustible clouds propagation and for prevention of fires and explosions. Method is based on numerical solution of Reynolds equations. The particular examples are presented for safety analysis of natural gas distribution stations.
1. Introduction
Gas industry includes fire and explosive risk industrial facilities. Deterioration of pipelines and violation of the standard modes of gas pipeline equipment operation lead to increase in number of failures entailing emission of transmitted gases and being the cause of the intense fires. The method described in the paper is meant for enhancing fire safety of gas industry and proposes to use numerical simulation for analysis of methane-air mixture combustible clouds propagation and for prevention of fires and explosions. Method is based on numerical solution of Reynolds equations. Solution is carried out by grid methods. Material presentation is executed by Russian and Slovak Gas-Distributing Stations (GDS). The paper presents the particular examples of safety analysis for GDS.
2. Mathematical Models
Numerical simulation problem concerned with natural gas emission from failure gas transmission pipeline and methane-air clouds propagation inside the buildings and at the territory of GDS proposes defining the relative mass fraction fields of methane in the area of jet emission as a result of numerical analysis of Reynolds’ fluid dynamics equations completed by
k
or
k
turbulence model and corresponding to boundary conditions. These boundary conditions describe [1]: atmospheric state, terrain, structure of buildings, geometry of the emission source. The geometry of the emission source is determined basing on the results of numerical simulation of pipeline rupture.Multicomponent gas mixture flow is simulated in diffusion approximation providing necessary (from the view of industrial problem solution) accuracy. Mathematical model of this flow has the following view in Cartesian coordinate system:
0; D Dt
V (1) 1 1 0, 1, 1; 1 N ; m T m N m m DY Y m N Y Y Dt Sc
(2)
2
; 3 T atm D P K Dt
V gτ (3)
v 1 2 3 ; atm T T N T m m m D H P Q Dt t t T K C T Y Sc
g V τ V V (4)
; Pr Pr T T K T DK K G Dt
g (5)
2 3 1 Pr Pr T T T D C G C C Dt K
g ;
(6)
0 3 3,0 1 v 1 ; ; 2 , , where , , , ; m atm p m m N s m m p m Y P R T g x x H C T M f Y C C
V V(7) 3 2 0 273,15 , 273,15 S S C T T C
2 ; T C K
T ; Pr p T T C
; Sc D
(8) 2 ; 3 j i k i j i j j i k u u u x x x
(9) 2 2 1 2 2 2 3 3 j i k k T j i k k u u u u G K x x x x
,
(10)
where – mixture density; P – piezometric pressure; T – temperature; V – velocity with the components u u u1, 2, 3; Dm – molecular diffusivity;
1 1 N m m D D N
; Sc – Schmidt number; m mY
– relative mass fraction of m-component (m – density of m-component of mixture); N number of components in gas mixture (in our case-2
N (air and methane)); g – gravitational acceleration; t – time; - nabla operator;
D D t t V - substantial derivative from scalar function; notation of substantial derivative from vector function means substantial derivation of vector function components;
2
H h V V
– total enthalpy, where h C T p - enthalpy for ideal gas, p
C – specific heat capacity at constant pressure; Cv– specific heat capacity at constant volume; - thermal conductivity; T - turbulent conductivity; - dynamic viscosity;
S
C – Sutherland constant; 0 - dynamic viscosity under the normal conditions; T -turbulent viscosity; Q
t
– heat generation rate; R – gas constant; x x x1, ,2 3 - Cartesian
coordinates of the point (x3 - coordinate being on the vertical axis, directed from the
center of the Earth); x3,0 - fixed coordinate corresponding to the sea level; τ - viscous
stress tensor; i j - Kronecker delta; - turbulence dissipation rate; K - kinetic turbulence energy; Ci, i1,4 - empirical constants; Pr - Prandtl number; inferior index T means “turbulent”; inferior index “atm” means “atmosphere”; R0 - universal
gas constant; f
- known semi-empirical functions. It is proposed to use the following constants’ values in (6): C 0,09; C11, 44; C21,44; C31,92;PrK 1,0; Pr 1,219. If gas flows are simulated close to impermeable surfaces, so the
system of equations (6) is added by well known near the wall layer logarithmic functions. The following boundary conditions are used to complete the above mentioned system of equations:
on the boundaries of the computational domain where gas is emitted from the pipeline into the atmosphere: kinetic turbulence energy; its dissipation rate and conjugation conditions that connect mass flow rate, pressure, temperature and relative mass fractions (these parameters of the failure pipelines are defined at each time step as a result of CFD-simulator of GDS piping operation [1]);
on the terrain and crater surfaces: conditions corresponding to impermeable adiabatic stationary wall;
on the “inlet” side boundary: the field of the wind; relative mass fractions; temperature; kinetic turbulence energy and its dissipation rate;
on the “outlet” side boundary: piezometric pressure; diffusion fluxes of temperature, relative mass fractions, kinetic turbulence energy and its dissipation rate;
on the upper boundary and on the “passive” side boundaries: piezometric pressure; temperature and relative mass fractions, kinetic turbulence energy and its dissipation rate (if gas flows into the computational domain through this boundary); if gas outflows, so there are the outlet boundary conditions.
Quasi-steady state distributions of fluid flow parameters are initial parameters if these distributions satisfying the boundary conditions, i.e. there is not outflow of gas from the failure pipeline.
k
turbulence model without near the wall layer function (as in
k
turbulence model), is proposed to be used for correct description of these processes and for enhancing adequacy of plume emission simulation. It is used whilecompleting Reynolds equations [2]. Method of finite volumes and fluid in cells method are used to solve the stated problem (1-10) and for enhancing reliability of the obtained computational estimations [1].
Numerical analysis of fire or explosion risk at GDS proposes investigating simulation of natural gas emission into the environment at different time steps. Formation of gas-air mixture clouds with dangerous concentration at the territory of GDS are considered as the criterion of fire risk at GDS. Fire and explosion risk zones (including asphyxiating effect of methane on people) and the ways for safe evacuation of personnel are marked on the topographic map of GDS.
Numerical analysis of the ways for fire or explosion prevention at GDS is applied for estimation of the following measures, namely: control for combustible gas accumulation at the territory of GDS, aeration of buildings, anticipatory retardation of fire risk and explosive medium. These measures are meant for fire or explosion risk reduction.
Fig.1. Relative mass fraction field of methane - 1,1s after the beginning of its emission from the failure pipeline
3. Results
Let us consider the application results of the stated earlier method for analysis of methane-air clouds propagation. We will consider these results by the example of failure methane emission at actual GDS belonging to SPP International Gas Transmission Company (Slovakia).
Fig. 1 presents the field of relative mass fraction of methane. It was obtained by numerical simulation of methane emission from the failure pipeline accounting the field of the wind and geometry of neighboring buildings situated in the considered GDS. The technology for structural analysis of pipelines developed by Dr. Vladimir Aleshin is used for analysis of emission source geometry [1].
(a) (b)
Fig.2. (a) dispatching point of GDS; (b) geometry of computational domain of the operators’ office (1 – store room, 2 – WC, 3 – lounge, 4 – control room, 5 – hall)
It was concluded that it is possible to neglect the buoyancy effect of gas cloud if the wind velocity in the earth surface area exceeds 10m/s. Let us consider the example of effective operation analysis of anticipatory retardation system in the GDS operators’ office which is filled with methane-air mixture through the windows caused by failure natural gas emission. Fig. 2 presents the general view of the operators’ office and its analytical model. Fig. 3 presents relative mass fraction field of the retarder (nitrogen) applied in the operators’ office.
Fig.3. Field of relative mass fractions of retarder while its supply into the building filled with fire risk and explosive methane-air mixture (time – 10s after beginning of the retarder supply)
(a) (b)
Fig.4 Mass fractions of methane and retarder in mixture in computational grid nodes. Time – 70 sec (a) and 254 sec (b) after the beginning of mixture dilution with nitrogen
Fig. 4 presents mass fractions of the mixture components for all nodes of the computational grid of the operators’ office. Mass fractions are presented in the following coordinates: “methane content in the mixture with air and nitrogen” and “nitrogen content in the mixture with air”. Diagrams are presented for time 70s after the beginning of retarder feeding into the building. The area of composition mass fraction and restricted by the retardation curve and axis of ordinates is combustible area, but the area beyond the retardation curve is noncombustible one. Simulation results have shown that mixture becomes noncombustible in 254s after the beginning of dilution of mixture with nitrogen (see Fig.4,b).
4. Concluding Remarks
The paper describes effective method for numerical analysis of methane-air clouds’ formation and propagation at the territory of GDS while technological gas pipeline ruptures. Application results of this method are used to create the scenarios of failures at GDS, to estimate their consequences, and to develop scientifically justified methods for avoiding similar failures and their consequences including ignition of gas-air mixtures or their explosion.
References
1. Seleznev V.E., Aleshin V.V. et al.: Numerical simulation of gas pipeline networks: theory, computational implementation, and industrial applications. Ed. by V.E. Seleznev. – Moscow: KomKniga, p.720, 2005.
2. Seleznev V., Aleshin V.: Computation technology for safety and risk assessment of gas pipline systems. Proceedings of the Asian International Workshop on Advanced Reliability Modeling (AIWARM’2004), (August 2004, Hiroshima City, Japan). – World Scientific Publishing Co. Pte. Ltd., London, p.443-450, 2004.
