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Air quality

Last modified by Omid Abouali on 2026/08/26 10:23

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TABLE OF CONTENT

Air quality

Air quality

Eight measures of the air quality have been implemented in the program:

age of air (hours)
extinction coefficient (m^-1)
humidity fraction (m³ vapor/m³ air)
particle content (μg/m³)
CO₂-fraction (ppm (vol))
NO₂ content (μg/m³)
CO content (mg/ m³)
HC content (μg/m³).

Of these, three are available in IDA Road Tunnel, extinction coefficient, NO₂ content and CO content.

The CO₂ content is relative the standard level and is assumed to be produced by passengers at the platforms and in trains and by equipment in tunnel sections. The measures are described by differential equations in the tunnel section models and in the platform and plenum models. To make it possible to resolve fronts moving in the tunnel (e.g. smoke from a fire) the integration of the air quality measures can de done with a finer grid than the one defined by the segments and with smaller time steps. A subroutine called from the section models carries out this either by explicit or implicit time integration where the accuracy is determined by the parameters dx_nSub (maximal size of sub segments) and maxStep (maximal number of explicit steps per global step). Implicit time integration with no refinement of time step is always used in IDA RTV, and in IDA Tunnel in sections with fire or transverse ventilation. <<<A model for traffic induced diffusion is not yet included due to lack of measurement data.>>>

Age of air

Age of air is a measure of how long the air has been within the tunnel system. In the tunnel section models the equation reads

$\frac{\partial C}{\partial t}+v\frac{\partial C}{\partial x}=\frac{1}{3600}+q_{trans}(x)$

where

C		age of air (hours)
v		velocity (m/s)
q_trans(x)		$(u_{TrIn}(x)\cdot C_{TrIn}(x)-u_{TrOut}(x)\cdot C(x))/A(x)$ = source due to transverse ventilation (see 2.1.1) (hours/s)
u_TrIn		supplied air volume flow per length tunnel (m²/s)
u_TrOut		exhausted air volume flow per length tunnel (m²/s)
C_TrIn		age of air of supplied airflow (hours)
A		cross section area of tunnel (m²).

In the platform and plenum the following equation is used

$V\frac{d(\rho_{dry}C)}{dt}=\rho_{dry}(\sum_{j} C_{dot_j}+\frac{V}{3600})$

where

V		volume of platform/plenum (m³)
C_{dot_j}		inflow from tunnel/leak j = C_j ∙ A_j ∙ v_j
v_j		velocity in connected tunnel/leak j, positive into platform (m/s)
A_j		tunnel area of connected tunnel/leak j (m²)
C_j		age of air in connected tunnel/leak (hours)
ρ_dry		density of dry air (kg/m³).

CO₂ content

The CO₂ content computed is relative the standard level and is assumed to be produced by diesel trains, by passengers on platform and on train and by equipment (explicit sources) in rail tunnel sections. In the rail tunnel section models the equation for computing the carbon dioxide content reads

$\frac{\partial C}{\partial t}+v\frac{\partial C}{\partial x}=(q_{trn}(x)+q_{occ}(x)+\sum{q_i(x)})/(\frac{\rho_{CO_2}}{\rho_{dry}}m_{air}(x))+q_{trans}(x)$

where

C	CO₂ volume fraction (m³/m³)
$\frac{\rho_{CO_2}}{\rho_{dry}}$	1.5194 = relation between densities of CO₂ and dry air
m_air(x)	ρ_dry(x)∙V(x) = air mass in segment containing position x (kg)
ρ_dry(x)	density of dry air in segment containing position x (kg/m³)
V(x)	volume of segment containing position x (m³)
q_trn(x)	Q_dieselSup ∙ 700/3600 = emission from trains in segment containing position x (kg/s)	emTrain
q_i(x)	s_i ∙ l_{equip_i} ∙ q_{nom_i} = emission from equipment i in segment containing position x (kg/s)
s_i	schedule (varies in interval [0:1] )
l_{equip_i}	length of equipment i (m)
q_{nom_i}	nominal emission of equipment i (kg/sm)
Q_dieselSup	heat emitted by diesel operation (see 2.2.7) (W)
q_trans(x)	$(u_{TrIn}(x)\cdot C_{TrIn}(x)-u_{TrOut}(x)\cdot C(x))/A(x)$ = source due to transverse ventilation (see 2.1.1) (1/s)
u_TrIn	supplied air volume flow per length tunnel (m²/s)
u_TrOut	exhausted air volume flow per length tunnel (m²/s)
C_TrIn	CO₂ volume fraction in supplied airflow (m³/m³)
A	cross section area of tunnel (m²)
q_occ(x)	s_occ ∙ N_occ ∙ 17.0 ∙ 1.8 ∙ MET / 3.6 = emission from persons on trains in segment containing position x (kg/s)
s_occ	schedule (varies in interval [0:1] )
N_occ	number of persons on train
MET	activity, 1 Met = 58 W/m2 (Met).

In the platform and plenum the following equation is used

$V\frac{d(\rho_{dry}C)}{dt}=\rho_{dry}(\sum_{j} C_{dot_j}+q_{occ}+(q_{trn}+\sum_{i} q_{equip_i})/\rho_{CO_2})$

where

q_occ	s_occ ∙ N_occ ∙ 17.0 ∙ MET / 3.6 / ρ_dry
s_occ	schedule (varies in interval [0:1] )
N_occ	number of persons on platform
MET	activity, 1 Met = 58 W/m² (Met)
ρ_dry	density of dry air (kg/m³)
q_trn	Q_dieselSup ∙ 700/3600 = emission from trains (kg/s)	emTrain
q_{equip_i}	s_{equip_i} ∙ q_{nom_i} = emission from equipment i (kg/s)
s_{equip_i}	schedule for equipment i (varies in interval [0:1] )
q_{nom_i}	nominal emission of equipment i (kg/s)
ρ_CO2	ρ_dry ∙ 1.5194 _ = density of CO₂ (kg/m³)
C_{dot_j}	inflow from tunnel/leak j = C_j ∙ A_j ∙ v_j
v_j	velocity in connected tunnel/leak j, positive into platform (m/s)
A_j	tunnel area of connected tunnel/leak j (m²)
C_j	CO₂ volume fraction in connected tunnel/leak (m³/m³).

Extinction coefficient

The extinction coefficient is a measure of the visibility in fire smoke. It describes the drop of light per meter. Tests have shown that smoke with extinction coefficients bigger than 0.3 has to be considered as dark smoke (orientation in tunnel with denser smoke impossible). Coefficient 0.3 corresponds to the case when only 5% of the emitted light is received 10 m away. In the tunnel section models the equation for computing the extinction coefficient reads

$\frac{\partial C}{\partial t}+\frac{\partial(vC)}{\partial x}=(\frac{Y_s\cdot K}{\chi_c\cdot H}\cdot q_{fire}\cdot\delta(x)+q_{trf}(x)+\sum{q_i(x)})/V(x)+q_{trans}(x)$

where

C	extinction coefficient (m^-1)
q_fire	fire power (see 2.2.6) (W)
Y_s	soot load (kg_soot/kg_fuel)
K	specific absorption area (m²/kg_soot)
χ_c	combustion efficiency
H	heat coefficient (J/kg_fuel)
δ(x)	1 in segment with fire, 0 otherwise
V(x)	volume of segment containing position x (m³)
q_trf(x)	emission from vehicles in segment containing position x (m²/s)	emTraff
q_i(x)	s_i ∙ l_{equip_i} ∙ q_{nom_i} = emission from equipment i in segment containing position x (m²/s)
s_{equip_i}	schedule for equipment i (varies in interval [0:1] )
l_{equip_i}	length of equipment i (m)
q_{nom_i}	nominal emission of equipment i (m²/sm)
q_trans(x)	$(u_{TrIn}(x)\cdot C_{TrIn}(x)-u_{TrOut}(x)\cdot C(x))/A(x)$ = source due to transverse ventilation (see 2.1.1) (1/sm)
u_TrIn	supplied air volume flow per length tunnel (m²/s)
u_TrOut	exhausted air volume flow per length tunnel (m²/s)
C_TrIn	extinction coefficient in supplied airflow (m^-1)
A	cross section area of tunnel (m²).

In the platform and plenum the following equation is used

$V\frac{dC}{dt}=\sum_{j} C_{dot_j}+\frac{Y_s\cdot K}{\chi_c\cdot H}\cdot q_{fire}$

where

C_{dot_j}		inflow from tunnel/leak j = C_j ∙ A_j ∙ v_j
v_j		velocity in connected tunnel/leak j, positive into platform/plenum (m/s)
A_j		tunnel area of connected tunnel/leak j (m²)
C_j		extinction coefficient in connected tunnel/leak (m^-1).

The relation between soot content C_s (kg/m³) and extinction coefficient C is given by C_s = C/K.

Humidity fraction

The humidity is omitted in IDA RTV but in IDA Tunnel the equations described below are used. For tunnel sections the equation reads

$\frac{\partial C}{\partial t}+v\frac{\partial C}{\partial x}=\alpha_{surf}(C_{surf}-C)+\alpha_{sat}min{(}0,C_{sat}-C)+q_{vapTrn}+\sum_{i}{(q_i(x)}+q_{wat_i}(x))+q_{trans}(x)$

where

C	=	humidity fraction (m³/m³)
C_surf	=	humidity fraction on wall (m³/m³)
C_sat	=	saturated humidity fraction in air (m³/m³)
α_surf	=	U_conv ∙ p_act /(c_pAir ∙∙ ∙ A) (s^-1)
U_conv	=	convective heat transfer coefficient (W/ m²˚C)
c_pAir	=	specific heat of air (J/kg˚C)
ρ	=	density of air (kg/ m³)
A	=	cross section area (m²)
p_act	=	actual wet perimeter (see 2.4) (m)
α_sat	=	c_cond /ρ (s^-1)
c_cond	=	coefficient for moisture condensation (kg/sm³)
q_vapTrn	=	q_occVapE + Q_dieselSup ∙ 0.72 / 3600 = emission from trains (= 0 in road sections) (kg/s)
q_occVapE	=	vapour emission ventilated from trains (see 2.2.8) (kg/s)
Q_dieselSup		heat emitted by diesel operation (see 2.2.7) (W)
q_i(x)	=	emission from equipment i, proportional to s_i ∙ l_{equip_i} ∙ q_{nom_i}
q_{wat_i}(x)	=	water emission from equipment i, proportional to s_i ∙ l_{equip_i} ∙ q_{watNom_i} where
s_i	=	schedule for equipment i (varies in interval [0:1] )
l_{equip_i}	=	length of equipment i (m)
q_{nom_i}	=	nominal emission of equipment i (kg/sm)
q_{watNom_i}	=	nominal water emission of equipment i (kg/sm)
q_trans(x)		$(u_{TrIn}(x)\cdot C_{TrIn}(x)-u_{TrOut}(x)\cdot C(x))/A(x)$ = source due to transverse ventilation (see 2.1.1) (1/s)
u_TrIn		supplied air volume flow per length tunnel (m²/s)
u_TrOut		exhausted air volume flow per length tunnel (m²/s)
C_TrIn		humidity fraction in supplied airflow (m³/m³)
A		cross section area of tunnel (m²).

In the platform and plenum the following equation is used

$V\frac{d(\rho_{dry}C)}{dt}=\rho_{dry}(\sum_{j} C_{dot_j}+V(\alpha_{surf}(C_{surf}-C)+\alpha_{sat}min{(}0,C_{sat}-C)))+(q_{vapTrn}+\sum_{i}{(q_i+q_{wat_i}})+q_{occ})/f_{mol}$

where

Q_vapTrn	emission from trains (= 0 in plenums) (see above) (kg/s)
q_occ	$s_{occ}\cdot N_{occ}\cdot1.8\cdot(3.05\cdot(5733-6.99\cdot MET\cdot58-p_{vap})+1.7\cdot10^{-5}\cdot MET\cdot58\cdot(5867-p_{vap}))$ = vapor emission from occupants (= 0 in plenums) (kg/s)
N_occ	maximum number of persons on platform	nOcc
s_occ	occupancy coefficient (schedule)	schedOcc
MET	activity, 1 Met = 58 W/m² (Met)
p_vap	p_amb· w/( f_mol + w) = partial vapour pressure (Pa)	PVap
w	humidity ratio of air
f_mol	0.62198 = ratio of molecular masses of water and air
ρ_dry	density of dry air (kg/m³)
q_i	s_i ∙ q_{nom_i} = emission from equipment i (kg/s)
q_{wat_i}	s_i ∙ q_{watNom_i} = water emission from equipment i (kg/s)
s_i	schedule for equipment i (varies in interval [0:1] )
q_{nom_i}	nominal emission of equipment i (kg/s)
q_{watNom_i}	nominal water emission of equipment i (kg/s)
C_{dot_j}	C_j ∙ A_j ∙ v_j = inflow from tunnel/leak j
v_j	velocity in connected tunnel/leak j, positive into platform (m/s)
A_j	tunnel area of connected tunnel/leak j (m²)
C_j	humidity fraction in connected tunnel/leak (m³/m³).

Particle content

The emission and transport of particles from brakes and wheels of trains and rail due to friction is in sections modelled by

$\frac{\partial C}{\partial t}+\frac{\partial(vC)}{\partial x}=(q_{trn}(x)+\sum{q_i(x)})/V(x)-\varepsilon_{rem}\cdot\varepsilon_{filt}\cdot V_{filt}/V_{sub}(x)\cdot C+q_{trans}(x)$

where

C	particle content (μg/m³)
q_trn(x)	((k_b · F_brake · (1- f_regen) + k_r · F_roll + k_loc · \|F_loc \|)· v_veh + Q_dieselSup · q_PMx) · 10⁶ /3600 = emission of particles in segment containing position x (= 0 in road sections) (μg/s)	particleFlow, emPart
q_i(x)	s_i ∙ l_{equip_i} ∙ q_{nom_i} · 10⁶ = emission from equipment i in segment containing position x (μg/s)
V(x)	volume of segment containing position x (m³)
k_b	coefficient (g/ kWh)	k_b
k_r	coefficient (g/ kWh)	k_r
k_loc	coefficient (g/ kWh)	k_loc
F_brake	F_tract - F_loc = braking force (N)	BrakeF [kN]
f_regen	quotient regenerative braking power to actual braking power	RegenRat
F_tract	max(0, F_loc) = tractive force (N)	TractF [kN]
F_loc	F_drag+ F_roll + M_veh· g · sin(f_slope) + km_veh· M_veh · a_veh = locomotive force (see 2.2.7) (N)	LocF [kN]
F_roll	(A_veh+ B_veh· v_veh) · M_veh = rolling resistance force (N)	RollF [kN]
v_veh	velocity of vehicle (m/s)	x_dot
Q_dieselSup	heat emitted by diesel operation (see 2.2.7) (W)
q_PMx	emission of particles from diesel trains (g/ kWh)	emPMx
ε_rem	contaminant removal effectiveness	removeEff
ε_filt	filter efficiency	filterEff
V_filt	filter airflow (m³/s)	VFFilter
V_sub(x)	volume of sub-segment containing position x (m³)
q_trans(x)	$(u_{TrIn}(x)\cdot C_{TrIn}(x)-u_{TrOut}(x)\cdot C(x))/A(x)$ = source due to transverse ventilation (see 2.1.1) (μg/m³s)
u_TrIn	supplied air volume flow per length tunnel (m²/s)
u_TrOut	exhausted air volume flow per length tunnel (m²/s)
C_TrIn	particle content in supplied airflow (μg/m³)
A	cross section area of tunnel (m²).

In the platform and plenum the following equation is used

$V\frac{dC}{dt}=\sum_{j} C_{dot_j}+q_{trn}+\sum q_i-\varepsilon_{rem}\cdot\varepsilon_{filt}\cdot V_{filt}\cdot C$

where

C_{dot_j}	inflow from tunnel/leak j = C_j ∙ A_j ∙ v_j
q_trn	((k_b · F_brake · (1- f_regen) + k_r · F_roll + k_loc · \|F_loc \|)· v_veh + Q_dieselSup · q_PMx) · 10⁶ /3600 = emission of particles (= 0 in plenum) (μg/s)	particleFlow, emPart
q_i	s_i ∙ l_{equip_i} ∙ q_{nom_i} · 10⁶ = emission from equipment i (μg/s)
v_j	velocity in connected tunnel/leak j, positive into platform (m/s)
A_j	tunnel area of connected tunnel/leak j (m²)
C_j	particle content in connected tunnel/leak (μg/m³).

In the filter component the filtering is described by

$C_{dot_{out}}=(1-\varepsilon_{filt})\cdot C_{dot_{in}}=(1-\varepsilon_{filt})\cdot C_{in}\cdot m_{dot}/\rho$

where

C_{dot_out}	outflow from filter (μg/s)
C_{dot_in}	inflow to filter (μg/s)
C_in	particle content into filter (μg/m³)
ε_filt	filter efficiency	filterEff
m_dot	air mass flow (kg/s)	inlet.m_dot
ρ	air density (kg/m³).	Rho_tun1

The variable of xpar in Route>Outline>train provides the particle concentration on a sensor that moves with the train.

CO, NO₂ and HC contents

The contents of carbon oxide, nitrous oxide and hydrocarbon are produced by diesel trains and equipments. In road sections the car traffic contribute to the contents of carbon oxide and nitrous oxide. In the tunnel section models the equation for computing each content reads

$\frac{\partial C}{\partial t}+\frac{\partial(vC)}{\partial x}=(q_{traf}(x)+\sum{q_i(x)})/V(x)+q_{trans}(x)$

where

C		content: CO (mg/m³), NO₂ (μg/m³), HC (μg/m³)
q_traf(x)	= = =	emission in segment containing position x Q_dieselSup · q_C /3600 ·10⁶ from diesel trains in rail sections interpolated data from PIARC ECE tables (function of slope and speed) in road sections (μg/s)	emTrain, emTraff
q_i(x)		s_i ∙ l_{equip_i} ∙ q_{nom_i} · 10⁶ = emission from equipment i in segment containing position x (μg/s)
V(x)		volume of segment containing position x (m³)
Q_dieselSup		heat emitted by diesel operation (see 2.2.7) (W)
q_C		emission from diesel trains: CO (mg/ kWh), NO₂ (μg/kWh), HC (μg/ kWh)	emCO, emNOx, emHC
q_trans(x)		$(u_{TrIn}(x)\cdot C_{TrIn}(x)-u_{TrOut}(x)\cdot C(x))/A(x)$ = source due to transverse ventilation (see 2.1.1)
u_TrIn		supplied air volume flow per length tunnel (m²/s)
u_TrOut		exhausted air volume flow per length tunnel (m²/s)
C_TrIn		content in supplied airflow
A		cross section area of tunnel area (m²).

In the platform and plenum the following equation is used

$V\frac{dC}{dt}=\sum_{j} C_{dot_j}+q_{trn}+\sum q_i$

where

C_{dot_j}	inflow from tunnel/leak j = C_j ∙ A_j ∙ v_j
q_trn	Q_dieselSup · q_C /3600· 10⁶ = emission from diesel trains in platform (= 0 in plenum) (μg/s)	emTrain
q_i	s_i ∙ l_{equip_i} ∙ q_{nom_i} · 10⁶ = emission from equipment i (μg/s)
v_j	velocity in connected tunnel/leak j, positive into platform (m/s)
A_j	tunnel area of connected tunnel/leak j (m²)
C_j	particle content in connected tunnel/leak (μg/m³).

Air quality

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Air quality

Age of air

CO2 content

Extinction coefficient

Humidity fraction

Particle content

CO, NO2 and HC contents

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CO₂ content

CO, NO₂ and HC contents