Commission Delegated Regulation (EU) 2017/654 of 19 December 2016 supplementing Regulation (EU) 2016/1628 of the European Parliament and of the Council with regard to technical and general requirements relating to emission limits and type-approval for internal combustion engines for non-road mobile machinery

Calculation of emissions shall be performed according to either section 2 (mass based calculations) or section 3 (molar based calculations). Mixture between the two methods is not permitted. It shall not be required to perform the calculations according to both section 2 and section 3.

The specific requirements for particle number (PN) measurement, where applicable, are laid down in Appendix 5.

Section 2	Section 3	Unit	Quantity
	A	m2	Area
	At	m2	Venturi throat cross-sectional area
b, D 0	a 0	t.b.d. (3)	y intercept of the regression line
A/F st		—	Stoichiometric air to fuel ratio
	C	—	Coefficient
C d	C d	—	Discharge coefficient
	C f	—	Flow coefficient
c	x	ppm, % vol	Concentration/mole fraction (μmol/mol = ppm)
c d	(1)	ppm, % vol	Concentration on dry basis
c w	(1)	ppm, % vol	Concentration on wet basis
cb	(1)	ppm, % vol	Background concentration
D	x dil	—	Dilution factor (2)
D 0		m3/rev	PDP calibration intercept
d	d	m	Diameter
d V		m	Throat diameter of venturi
e	e	g/kWh	Brake specific basis
e gas	e gas	g/kWh	Specific emission of gaseous components
e PM	e PM	g/kWh	Specific emission of particulates
E	1 – PF	%	Conversion efficiency (PF = Penetration fraction)
F s		—	Stoichiometric factor
	f	Hz	Frequency
f c		—	Carbon factor
	γ	—	Ratio of specific heats
H		g/kg	Absolute humidity
	K	—	Correction factor
K V			CFV calibration function
k f		m3/kg fuel	Fuel specific factor
k h		—	Humidity correction factor for NOx, diesel engines
k Dr	k Dr	—	Downward adjustment factor
k r	k r	—	Multiplicative regeneration factor
k Ur	k Ur	—	Upward adjustment factor
k w,a		—	Dry to wet correction factor for the intake air
k w,d		—	Dry to wet correction factor for the dilution air
k w,e		—	Dry to wet correction factor for the diluted exhaust gas
k w,r		—	Dry to wet correction factor for the raw exhaust gas
μ	μ	kg/(m·s)	Dynamic viscosity
M	M	g/mol	Molar mass (3)
M a	(1)	g/mol	Molar mass of the intake air
M e	v	g/mol	Molar mass of the exhaust gas
M gas	M gas	g/mol	Molar mass of gaseous components
m	m	kg	Mass
m	a 1	t.b.d. (3)	Slope of the regression line
	ν	m2/s	Kinematic viscosity
m d	v	kg	Mass of the dilution air sample passed through the particulate sampling filters
m ed	(1)	kg	Total diluted exhaust gas mass over the cycle
m edf	(1)	kg	Mass of equivalent diluted exhaust gas over the test cycle
m ew	(1)	kg	Total exhaust gas mass over the cycle
m f	(1)	mg	Particulate sample mass collected
m f,d	(1)	mg	Particulate sample mass of the dilution air collected
m gas	m gas	g	Mass of gaseous emissions over the test cycle
m PM	m PM	g	Mass of particulate emissions over the test cycle
m se	(1)	kg	Exhaust gas sample mass over the test cycle
m sed	(1)	kg	Mass of diluted exhaust gas passing the dilution tunnel
m sep	(1)	kg	Mass of diluted exhaust gas passing the particulate collection filters
m ssd		kg	Mass of secondary dilution air
	N	—	Total number of a series
	n	mol	Amount of substance
	ṅ	mol/s	Amount of substance rate
n	f n	min– 1	Engine rotational speed
n p		r/s	PDP pump speed
P	P	kW	Power
p	p	kPa	Pressure
p a		kPa	Dry atmospheric pressure
p b		kPa	Total atmospheric pressure
p d		kPa	Saturation vapour pressure of the dilution air
p p	p abs	kPa	Absolute pressure
p r	p H2O	kPa	Water vapour pressure
p s		kPa	Dry atmospheric pressure
1 — E	PF	%	Penetration fraction
qm	ṁ	kg/s	Mass rate
qm ad	ṁ (1)	kg/s	Intake air mass flow rate on dry basis
qm aw	(1)	kg/s	Intake air mass flow rate on wet basis
qm Ce	(1)	kg/s	Carbon mass flow rate in the raw exhaust gas
qm Cf	(1)	kg/s	Carbon mass flow rate into the engine
qm Cp	(1)	kg/s	Carbon mass flow rate in the partial flow dilution system
qm dew	(1)	kg/s	Diluted exhaust gas mass flow rate on wet basis
qm dw	(1)	kg/s	Dilution air mass flow rate on wet basis
qm edf	(1)	kg/s	Equivalent diluted exhaust gas mass flow rate on wet basis
qm ew	(1)	kg/s	Exhaust gas mass flow rate on wet basis
qm ex	(1)	kg/s	Sample mass flow rate extracted from dilution tunnel
qm f	(1)	kg/s	Fuel mass flow rate
qm p	(1)	kg/s	Sample flow of exhaust gas into partial flow dilution system
qV	V̇	m3/s	Volume flow rate
qV CVS	(1)	m3/s	CVS volume rate
qV s	(1)	dm3/min	System flow rate of exhaust gas analyzer system
qV t	(1)	cm3/min	Tracer gas flow rate
ρ	ρ	kg/m3	Mass density
ρ e		kg/m3	Exhaust gas density
	r	—	Ratio of pressures
r d	DR	—	Dilution ratio (2)
	Ra	μm	Average surface roughness
RH		%	Relative humidity
r D	β	m/m	Ratio of diameters (CVS systems)
r p		—	Pressure ratio of SSV
Re	Re#	—	Reynolds number
	S	K	Sutherland constant
σ	σ	—	Standard deviation
T	T	°C	Temperature
	T	Nm	Engine torque
T a		K	Absolute temperature
t	t	s	Time
Δt	Δt	s	Time interval
u		—	Ratio between densities of gas component and exhaust gas
V	V	m3	Volume
qV	V̇	m3/s	Volume rate
V 0		m3/r	PDP gas volume pumped per revolution
W	W	kWh	Work
W act	W act	kWh	Actual cycle work of the test cycle
WF	WF	—	Weighting factor
w	w	g/g	Mass fraction
		mol/mol	Flow-weighted mean concentration
X 0	K s	s/rev	PDP calibration function
	y	—	Generic variable
			Arithmetic mean
	Z	—	Compressibility factor
(1) See subscripts; e.g.: ṁ air for mass rate of dry air, ṁ fuel for fuel mass rate, etc. (2) Dilution ratio r d in section 2 and DR in section 3: different symbols but same meaning and same equations. Dilution factor D in section 2 and x dil in section 3: different symbols but same physical meaning; equation (7-124) shows the relationship between x dil and DR. (3) t.b.d.= to be defined.
Section 2 (1)	Section 3	Quantity
---	---	---
act	act	Actual quantity
i		Instantaneous measurement (e.g.: 1 Hz)
	i	An individual of a series
(1) In section 2 the meaning of subscript is determined by the associated quantity; for example, the subscript ‘d’ can indicate a dry basis as in ‘c d = concentration on dry basis’, dilution air as in ‘p d = saturation vapour pressure of the dilution air’ or ‘k w,d = dry to wet correction factor for the dilution air’, dilution ratio as in ‘r d’.
Section 2	Section 3	Quantity
---	---	---
Ar	Ar	Argon
C1	C1	Carbon 1 equivalent hydrocarbon
CH4	CH4	Methane
C2H6	C2H6	Ethane
C3H8	C3H8	Propane
CO	CO	Carbon monoxide
CO2	CO2	Carbon dioxide
	H	Atomic hydrogen
	H2	Molecular hydrogen
HC	HC	Hydrocarbon
H2O	H2O	Water
	He	Helium
	N	Atomic nitrogen
	N2	Molecular nitrogen
NOx	NOx	Oxides of nitrogen
NO	NO	Nitric oxide
NO2	NO2	Nitrogen dioxide
	O	Atomic oxygen
PM	PM	Particulate matter
S	S	Sulphur
Section 2 (1)	Section 3 (2)	Quantity
---	---	---
w C (4)	w C (4)	Carbon content of fuel, mass fraction [g/g] or [% mass]
w H	w H	Hydrogen content of fuel, mass fraction [g/g] or [% mass]
w N	w N	Nitrogen content of fuel, mass fraction [g/g] or [% mass]
w O	w O	Oxygen content of fuel, mass fraction [g/g] or [% mass]
w S	w S	Sulphur content of fuel, mass fraction [g/g] or [% mass]
α	α	Atomic hydrogen-to-carbon ratio (H/C)
ε	β	Atomic oxygen-to-carbon ratio (O/C) (3)
γ	γ	Atomic sulphur-to-carbon ratio (S/C)
δ	δ	Atomic nitrogen-to-carbon ratio (N/C)
(1) Referred to a fuel with chemical formula CHαOεNδSγ. (2) Referred to a fuel with chemical formula CHαOβSγNδ. (3) Attention should be paid to the different meaning of symbol β in the two emissions calculation sections: in section 2 it refers to a fuel having the chemical formula CHαSγNδOε (i.e. the formula CβHαSγNδOε where β = 1, assuming one carbon atom per molecule), while in section 3 it refers to the oxygen-to-carbon ratio with CHαOβSγNδ. Then β of section 3 corresponds to ε of section 2. (4) Mass fraction w accompanied by the symbol of the chemical component as a subscript.

The emission rate of a gaseous emission qm gas, i [g/h] for each mode i of the steady state test shall be calculated by multiplying the concentration of the gaseous emission with its respective flow, as follows:

	(7-1)

where:

The total mass per test of a gaseous emission m gas [g/test] shall be calculated by multiplication of the time aligned instantaneous concentrations and exhaust gas flows and integration over the test cycle by means of equation (7-2):

	(7-2)

where:

If the emissions are measured on a dry basis, the measured concentration c d on dry basis shall be converted to the concentration c w on a wet basis by means of equation (7-3):

	(7-3)

where:

For complete combustion, the dry-to-wet conversion factor for raw exhaust gas is written as k w,a [-] and shall be calculated by means of equation (7-4):

	(7-4)

where:

with:

	(7-5)

where:

In equation (7-4), the ratio p r/p b may be assumed:

	(7-6)

For incomplete combustion (rich fuel air mixtures) and also for emission tests without direct air flow measurements, a second method of k w,a calculation is preferred:

	(7-7)

where:

	(7-8)

As the NOx emission depends on ambient air conditions, the NOx concentration shall be corrected for ambient air temperature and humidity with the factors kh,D or kh,G [-] given in equations (7-9) and (7-10). These factors are valid for a humidity range between 0 and 25 g H2O/kg dry air.

(a) for compression-ignition engines (7-9)

(b) for spark ignition engines kh.G = 0,6272 + 44,030 × 10^{– 3} × Ha – 0,862 × 10^{– 3} × Ha ² (7-10)

where:

Two calculation procedures are described in points 2.1.5.1 and 2.1.5.2. The procedure set out in point 2.1.5.1 is more straightforward, since it uses tabulated u values for the ratio between component and exhaust gas density. The procedure set out in point 2.1.5.2 is more accurate for fuel qualities that deviate from the specifications in Annex VIII, but requires elementary analysis of the fuel composition.

Applying some simplifications (assumption on the λ value and on intake air conditions as shown in Table 7.1) to the equations set out in point 2.1.5.2, the resulting values for u gas are given in Table 7.1.

Fuel	ρe			Gas
NOx	CO	HC	CO2	O2	CH4
		ρgas [kg/m3]
2,053	1,250	()	1,9636	1,4277	0,716
		ugas ()
Diesel (non-road gas-oil)	1,2943	0,001586	0,000966	0,000482	0,001517	0,001103	0,000553
Ethanol for dedicated compression ignition engines (ED95)	1,2768	0,001609	0,000980	0,000780	0,001539	0,001119	0,000561
Natural gas / bio-methane ()	1,2661	0,001621	0,000987	0,000528 ()	0,001551	0,001128	0,000565
Propane	1,2805	0,001603	0,000976	0,000512	0,001533	0,001115	0,000559
Butane	1,2832	0,001600	0,000974	0,000505	0,001530	0,001113	0,000558
LPG ()	1,2811	0,001602	0,000976	0,000510	0,001533	0,001115	0,000559
Petrol (E10)	1,2931	0,001587	0,000966	0,000499	0,001518	0,001104	0,000553
Ethanol (E85)	1,2797	0,001604	0,000977	0,000730	0,001534	0,001116	0,000559
(1) Depending on fuel (2) At λ = 2, dry air, 273 K, 101,3 kPa (3) u accurate within 0,2 % for mass composition of: C = 66 – 76 %; H = 22 – 25 %; N = 0 – 12 %. (4) NMHC on the basis of CH2,93 (for total HC the u gas coefficient of CH4 shall be used). (5) u accurate within 0,2 % for mass composition of: C3 = 70 – 90 %; C4 = 10 – 30 %.

The component specific factor, u gas,i, may be calculated by the density ratio of the component and the exhaust gas or alternatively by the corresponding ratio of molar masses [equations (7-11) or (7-12)]:

	(7-11)

or

	(7-12)

where:

The molar mass of the exhaust gas, M e,i shall be derived for a general fuel composition CHαOεNδSγ under the assumption of complete combustion, and shall be calculated by means of equation (7-13):

(7-13)

Where:

The instantaneous raw exhaust gas density ρ e, i [kg/m³] shall be calculated by means of equation (7-14):

	(7-14)

where:

The method involves measurement of the air flow and the fuel flow with suitable flowmeters. The instantaneous exhaust gas flow qm ew, i [kg/s] shall be calculated by means of equation (7-15):

qm ew, i = qm aw, i + qm f, i	(7-15)

where:

This involves measurement of the concentration of a tracer gas in the exhaust gas. The instantaneous exhaust gas flow q mew,i [kg/s] shall be calculated by means of equation (7-16):

	(7-16)

where:

The background concentration of the tracer gas c b may be determined by averaging the background concentration measured immediately before the test run and after the test run. When the background concentration is less than 1 % of the concentration of the tracer gas after mixing c mix, i at maximum exhaust gas flow, the background concentration may be neglected.

This involves exhaust gas mass calculation from the air flow and the air to fuel ratio. The instantaneous exhaust gas mass flow q mew, i [kg/s] shall be calculated by means of equation (7-17):

	(7-17)

with:

	(7-18)
	(7-19)

where:

The following 1-step formula set out in equation (7-20) can be used for the calculation of the wet exhaust gas mass flow rate qm ew, i [kg/s]:

	(7-20)

with the carbon factor f c [-] given by:

	(7-21)

Where:

and factor k fd [m³/kg fuel] that is calculated by means of equation (7-22) on a dry basis by subtracting the water formed by combustion from k f:

k fd = k f – 0,11118 · w H	(7-22)

where:

The exhaust gas mass flow rate shall be measured with a constant volume sampling (CVS) system, which may use a positive displacement pump (PDP), a critical flow venturi (CFV) or a subsonic venturi (SSV).

For systems with constant mass flow (i.e. with heat exchanger), the mass of the pollutants m gas [g/test] shall be determined by means of equation (7-23):

m gas = k h · k · u gas · c gas · m ed	(7-23)

where:

For systems with flow compensation (without heat exchanger), the mass of the pollutants m gas [g/test] shall be determined by calculation of the instantaneous mass emissions, by integration and by background correction by means of equation (7-24):

	(7-24)

Where:

The concentrations c gas, c e and c d can be either values measured in a batch sample (bag, but not allowed for NOx and HC) or be averaged by integration from continuous measurements. Also m ed, i has to be averaged by integration over the test cycle.

The following equations show how the needed quantities (c e, u gas and m ed) shall be calculated.

All concentrations set out in point 2.2.1 measured dry shall be converted to a wet basis by means of equation (7-3).

Dry concentrations shall be converted to wet concentrations by means of one of the following two equations [(7-25) or (7-26)] applied to equation:

	(7-25)

or

	(7-26)

where:

The dry to wet correction factor k w2 takes into consideration the water content of both intake air and dilution air and shall be calculated by means of equation (7-27):

	(7-27)

where:

The dilution factor D [-] (which is necessary for the background correction and the k w2 calculation) shall be calculated by means of equation (7-28):

	(7-28)

where:

The stoichiometric factor shall be calculated by means of equation (7-29):

	(7-29)

Where:

Alternatively, if the fuel composition is not known, the following stoichiometric factors may be used:

If a direct measurement is made of the exhaust gas flow, the dilution factor D [-] may be calculated by means of equation (7-30):

	(7-30)

Where:

k w,d = (1 – k w3) · 1,008	(7-31)

with

	(7-32)

where:

The average background concentration of the gaseous pollutants in the dilution air shall be subtracted from measured concentrations to get the net concentrations of the pollutants. The average values of the background concentrations can be determined by the sample bag method or by continuous measurement with integration. Equation (7-33) shall be used:

	(7-33)

Where:

The component specific factor u gas of diluted gas can either be calculated by means of equation (7-34) or be taken from Table 7.2; in Table 7.2 the density of the diluted exhaust gas has been assumed equal to air density.

	(7-34)

Where:

Fuel	ρe			Gas
NOx	CO	HC	CO2	O2	CH4
		ρgas [kg/m3]
2,053	1,250	(1)	1,9636	1,4277	0,716
		ugas (2)
Diesel (non-road gas-oil)	1,2943	0,001586	0,000966	0,000482	0,001517	0,001103	0,000553
Ethanol for dedicated compression ignition engines (ED95)	1,2768	0,001609	0,000980	0,000780	0,001539	0,001119	0,000561
Natural gas / bio-methane (3)	1,2661	0,001621	0,000987	0,000528 (4)	0,001551	0,001128	0,000565
Propane	1,2805	0,001603	0,000976	0,000512	0,001533	0,001115	0,000559
Butane	1,2832	0,001600	0,000974	0,000505	0,001530	0,001113	0,000558
LPG (5)	1,2811	0,001602	0,000976	0,000510	0,001533	0,001115	0,000559
Petrol (E10)	1,2931	0,001587	0,000966	0,000499	0,001518	0,001104	0,000553
Ethanol (E85)	1,2797	0,001604	0,000977	0,000730	0,001534	0,001116	0,000559
(1) Depending on fuel. (2) At λ = 2, dry air, 273 K, 101,3 kPa. (3) u accurate within 0,2 % for mass composition of: C = 66 – 76 %; H = 22 – 25 %; N = 0 – 12 %. (4) NMHC on the basis of CH2,93 (for total HC the u gas coefficient of CH4 shall be used). (5) u accurate within 0,2 % for mass composition of: C3 = 70 – 90 %; C4 = 10 – 30 %.

The mass of the diluted exhaust gas [kg/test] over the cycle shall be calculated by means of equation (7-35), if the temperature of the diluted exhaust gas m ed is kept within ± 6 K over the cycle by using a heat exchanger:

	(7-35)

where:

If a system with flow compensation is used (i.e. without heat exchanger), the mass of the diluted exhaust gas m ed, i [kg] during the time interval shall be calculated by means of equation (7-36):

	(7-36)

where:

The mass flow over the cycle m ed [g/test] shall be calculated by means of equation (7-37), if the temperature of the diluted exhaust gas is kept within ± 11 K over the cycle by using a heat exchanger:

	(7-37)

Where:

If a system with flow compensation is used (i.e. without heat exchanger), the mass of the diluted exhaust gas m ed, i [kg] during the time interval shall be calculated by means of equation (7-38):

	(7-38)

where:

The diluted exhaust gas mass over the cycle m ed [kg/test] shall be calculated by means of equation (7-39), if the temperature of the diluted exhaust gas is kept within ± 11 K over the cycle by using a heat exchanger:

m ed = 1,293 · qV SSV · Δt	(7-39)

Where:

with

	(7-40)

Where:

If a system with flow compensation is used (i.e. without heat exchanger), the mass of the diluted exhaust gas m ed, i [kg] during the time interval shall be calculated by means of equation (7-41):

m ed, i = 1,293 · qV SSV · Δt i	(7-41)

Where:

The particulate mass shall be calculated after buoyancy correction of the particulate sample mass in accordance with point 8.1.13.2.5 of Annex VI.

The particulate emission over the cycle m PM [g] shall be calculated by means of equation (7-42):

	(7-42)

where:

with:

	(7-43)

Where:

In case of the total sampling type system, m sep and m sed are identical.

The particulate emission over the cycle m PM [g] shall be calculated by means of equation (7-44):

	(7-44)

Where:

The total mass of equivalent diluted exhaust gas mass over the cycle m edf [kg] shall be determined by means of equation (7-45):

	(7-45)

With:

	(7-46)
	(7-47)

Where:

The mass emission shall be calculated by means of equation (7-48):

	(7-48)

where:

with

m sep = m set – m ssd	(7-49)

Where:

The particulate mass m PM,c [g] may be background corrected by means of equation (7-50):

	(7-50)

Where:

All calculations shall be based upon the average values of the individual modes i during the sampling period.

(a) For partial-flow dilution, the equivalent mass flow of diluted exhaust gas shall be determined by means of equation (7-51) and the system with flow measurement shown in Figure 9.2: (7-51) (7-52) Where: qm edf = equivalent diluted exhaust gas mass flow rate [kg/s] qm ew = exhaust gas mass flow rate on a wet basis [kg/s] r d = dilution ratio [-] qm dew = diluted exhaust gas mass flow rate on a wet basis [kg/s] qm dw = dilution air mass flow rate [kg/s]

(b) For full-flow dilution systems qm dew is used as qm edf.

The particulate emission flow rate over the cycle q mPM [g/h] shall be calculated by means of equations (7-53), (7-56), (7-57) or (7-58):

(a) For the single-filter method (7-53) (7-54) (7-55) Where: qm PM = particulate mass flow rate [g/h] m f = particulate mass sampled over the cycle [mg] = average equivalent diluted exhaust gas mass flow rate on wet basis [kg/s] qm edf i = equivalent diluted exhaust gas mass flow rate on wet basis at mode i [kg/s] WFi = weighting factor for the mode i [-] m sep = mass of diluted exhaust gas passing the particulate collection filters [kg] m sep i = mass of diluted exhaust gas sample passed through the particulate sampling filter at mode i [kg] N = number of measurements [-]

(b) For the multiple-filter method (7-56) Where: qm PM i = particulate mass flow rate for the mode i [g/h] m f i = particulate sample mass collected at mode i [mg] qm edf i = equivalent diluted exhaust gas mass flow rate on wet basis at mode i [kg/s] m sep i = mass of diluted exhaust gas sample passed through the particulate sampling filter at mode i [kg] The PM mass is determined over the test cycle by summation of the average values of the individual modes i during the sampling period. The particulate mass flow rate qm PM [g/h] or qm PM i [g/h] may be background corrected as follows:

(c) For the single-filter method (7-57) Where: qm PM = particulate mass flow rate [g/h] m f = particulate sample mass collected [mg] m sep = mass of diluted exhaust gas sample passed through the particulate sampling filter [kg] m f,d = particulate sample mass of the dilution air collected [mg] m d = mass of the dilution air sample passed through the particulate sampling filters [kg] Di = dilution factor at mode i [see equation (7-28) of point 2.2.2.2] [-] WFi = weighting factor for the mode i [-] = average equivalent diluted exhaust gas mass flow rate on wet basis [kg/s]

(d) For the multiple-filter method (7-58) Where: qm PM i = particulate mass flow rate at mode i [g/h] m f i = particulate sample mass collected at mode i [mg] m sep i = mass of diluted exhaust gas sample passed through the particulate sampling filter at mode i [kg] m f,d = particulate sample mass of the dilution air collected [mg] m d = mass of the dilution air sample passed through the particulate sampling filters [kg] D = dilution factor [see equation (7-28) of point 2.2.2.2] [-] q medf i = equivalent diluted exhaust gas mass flow rate on wet basis at mode i [kg/s] If more than one measurement is made, m f,d/m d shall be replaced with

.

Reference is made to points 2.1 and 2.2 for raw and diluted exhaust gas respectively. The resulting values for power P [kW] shall be integrated over a test interval. The total work W act [kWh] is calculated by means of equation (7-59):

	(7-59)

Where:

Where auxiliaries were fitted in accordance with Appendix 2 of Annex VI there shall be no adjustment to the instantaneous engine torque in equation (7-59). Where, according to points 6.3.2 or 6.3.3 of Annex VI to this regulation necessary auxiliaries that should have been fitted for the test are not installed, or auxiliaries that should have been removed for the test are installed, the value of Ti used in equation (7-59) shall be adjusted by means of equation (7-60):

T i = T i ,meas + T i, AUX	(7-60)

Where:

The specific emissions e gas [g/kWh] shall be calculated in the following ways depending on the type of test cycle.

	(7-61)

Where:

In case of the NRTC, for gaseous emissions other than CO2 the final test result e gas [g/kWh] shall be a weighted average from cold-start run and hot-start run by means of equation (7-62):

	(7-62)

Where:

In case of the NRTC, for CO2 the final test result e CO2 [g/kWh] shall be calculated from the hot-start NRTC by means of equation (7-63):

	(7-63)

Where:

The specific emissions e gas [g/kWh] are calculated by means of equation (7-64):

	(7-64)

where:

The particulate specific emissions shall be calculated with equation (7-61) where e gas [g/kWh] and m gas [g/test] are substituted by e PM [g/kWh] and m PM [g/test] respectively:

	(7-65)

where:

The emissions on the transient composite cycle (i.e. cold-start NRTC and hot-start NRTC) shall be calculated as shown in point 2.4.1.1.

The particulate specific emission e PM [g/kWh] shall be calculated by means of equations (7-66) or (7-67):

(a) For the single-filter method (7-66) where: Pi = engine power for the mode i [kW] calculated by adding to the measured power Pmeas [kW] the power required to drive auxiliaries PAUX [kW] determined in accordance with equation (6-8) of Annex VI (Pi = Pmeas + PAUX) WFi = weighting factor for the mode i [-] qm PM = particulate mass flow rate [g/h] Nmode = number of modes in applicable discrete-mode NRSC

(b) For the multiple-filter method (7-67) Where: Pi = engine power for the mode i [kW] calculated by adding to the measured power Pmeas [kW] the power required to drive auxiliaries PAUX [kW] determined in accordance with equation (6-8) of Annex VI (Pi = Pmeas + PAUX) WFi = weighting factor for the mode i [-] qm PM i = particulate mass flow rate at mode i [g/h] Nmode = number of modes in applicable discrete-mode NRSC

For the single-filter method, the effective weighting factor, WF e i, for each mode shall be calculated by means of equation (7-68):

	(7-68)

Where:

The value of the effective weighting factors shall be within 0,005 (absolute value) of the weighting factors listed in Appendix 1 of Annex XVII.

In case of engines, other than those of category RLL, equipped with exhaust after-treatment systems that are regenerated on an infrequent (periodic) basis (see point 6.6.2 of Annex VI), the specific emissions of gaseous and particulate pollutants calculated according to points 2.4.1 and 2.4.2 shall be corrected with either the applicable multiplicative adjustment factor or with the applicable additive adjustment factor. In the case that infrequent regeneration did not take place during the test the upward factor shall be applied (k ru,m or k ru,a). In the case that infrequent regeneration took place during the test the downward factor shall be applied (k rd,m or k rd,a). In the case of the discrete-mode NRSC, where the adjustment factors have been determined for each mode they shall be applied to each mode during the calculation of the weighted emission result.

The specific emissions of gaseous and particulate pollutants calculated according to points 2.4.1 and 2.4.2, where applicable inclusive of the infrequent regeneration adjustment factor according to point 2.4.3, shall also be adjusted by the applicable multiplicative or additive deterioration factor established according to the requirements of Annex III.

The CVS system shall be calibrated by using an accurate flowmeter and a restricting device. The flow through the system shall be measured at different restriction settings, and the control parameters of the system shall be measured and related to the flow.

Various types of flowmeters may be used, e.g. calibrated venturi, calibrated laminar flowmeter, calibrated turbine meter.

All the parameters related to the pump shall be simultaneously measured along with the parameters related to a calibration venturi which is connected in series with the pump. The calculated flow rate (in m³/s at pump inlet, absolute pressure and temperature) shall be plotted versus a correlation function which is the value of a specific combination of pump parameters. The linear equation which relates the pump flow and the correlation function shall be determined. If a CVS has a multiple speed drive, the calibration shall be performed for each range used.

Temperature stability shall be maintained during calibration.

Leaks in all the connections and ducting between the calibration venturi and the CVS pump shall be maintained lower than 0,3 % of the lowest flow point (highest restriction and lowest PDP speed point).

The airflow rate (qV CVS) at each restriction setting (minimum 6 settings) shall be calculated in standard m³/s from the flowmeter data using the manufacturer's prescribed method. The airflow rate shall then be converted to pump flow (V 0) in m³/rev at absolute pump inlet temperature and pressure by means of equation (7-69):

	(7-69)

where:

To account for the interaction of pressure variations at the pump and the pump slip rate, the correlation function (X 0) [s/rev] between pump speed, pressure differential from pump inlet to pump outlet and absolute pump outlet pressure shall be calculated by means of equation (7-70):

	(7-70)

Where:

A linear least-square fit shall be performed to generate the calibration by means of equation (7-71):

V 0 = D 0 –m · X 0	(7-71)

with D 0 [m³/rev] and m [m³/s], intercept and slope respectively, describing the regression line.

For a CVS system with multiple speeds, the calibration curves generated for the different pump flow ranges shall be approximately parallel, and the intercept values (D 0) shall increase as the pump flow range decreases.

The calculated values from the equation shall be within ± 0,5 % of the measured value of V

Calibration of the CFV is based upon the flow equation for a critical venturi. Gas flow is a function of venturi inlet pressure and temperature.

To determine the range of critical flow, K V shall be plotted as a function of venturi inlet pressure. For critical (choked) flow, K V will have a relatively constant value. As pressure decreases (vacuum increases), the venturi becomes unchoked and K V decreases, which indicates that the CFV is operated outside the permissible range.

The airflow rate (qV CVS) at each restriction setting (minimum 8 settings) shall be calculated in standard m³/s from the flowmeter data using the manufacturer's prescribed method. The calibration coefficient K V

shall be calculated from the calibration data for each setting by means of equation (7-72):

	(7-72)

Where:

The average K V and the standard deviation shall be calculated. The standard deviation shall not exceed ± 0,3 % of the average K V.

Calibration of the SSV is based upon the flow equation for a subsonic venturi. Gas flow is a function of inlet pressure and temperature, pressure drop between the SSV inlet and throat, as shown in equation (7-40).

The airflow rate (qV SSV) at each restriction setting (minimum 16 settings) shall be calculated in standard m³/s from the flowmeter data using the manufacturer's prescribed method. The discharge coefficient shall be calculated from the calibration data for each setting by means of equation (7-73):

	(7-73)

Where:

To determine the range of subsonic flow, C d shall be plotted as a function of Reynolds number Re, at the SSV throat. The Re at the SSV throat shall be calculated by means of equation (7-74):

	(7-74)

with

	(7-75)

Where:

Because qV SSV is an input to the Re equation, the calculations shall be started with an initial guess for qV SSV or C d of the calibration venturi, and repeated until qV SSV converges. The convergence method shall be accurate to 0,1 % of point or better.

For a minimum of sixteen points in the region of subsonic flow, the calculated values of C d from the resulting calibration curve fit equation shall be within ± 0,5 % of the measured C d for each calibration point.

The calculations in this section shall be performed to determine if gas analyzer drift invalidates the results of a test interval. If drift does not invalidate the results of a test interval, the test interval's gas analyzer responses shall be corrected for drift in accordance with point 2.6.2. The drift-corrected gas analyzer responses shall be used in all subsequent emission calculations. The acceptable threshold for gas analyzer drift over a test interval is specified in point 8.2.2.2 of Annex VI.

The general test procedure shall follow the provisions specified in Appendix 1 with concentrations xi or

being replaced by concentrations ci or

.

The drift correction shall be calculated by means of equation (7-76):

	(7-76)

Where:

	Quantity
abs	Absolute quantity
act	Actual quantity
air	Air, dry
atmos	Atmospheric
bkgnd	Background
C	Carbon
cal	Calibration quantity
CFV	Critical flow venturi
cor	Corrected quantity
dil	Dilution air
dexh	Diluted exhaust gas
dry	Dry quantity
exh	Raw exhaust gas
exp	Expected quantity
eq	Equivalent quantity
fuel	Fuel
	Instantaneous measurement (e.g.: 1 Hz)
i	An individual of a series
idle	Condition at idle
in	Quantity in
init	Initial quantity, typically before an emission test
max	Maximum (i.e. peak) value
meas	Measured quantity
min	Minimum value
mix	Molar mass of air
out	Quantity out
part	Partial quantity
PDP	Positive displacement pump
raw	Raw exhaust
ref	Reference quantity
rev	Revolution
sat	Saturated condition
slip	PDP slip
smpl	Sampling
span	Span quantity
SSV	Subsonic venturi
std	Standard quantity
test	Test quantity
total	Total quantity
uncor	Uncorrected quantity
vac	Vacuum quantity
weight	Calibration weight
wet	Wet quantity
zero	Zero quantity

x dil/exh = Amount of dilution gas or excess air per mole of exhaust gas

x H2Oexh = Amount of water in exhaust per mole of exhaust gas

x Ccombdry = Amount of carbon from fuel in the exhaust per mole of dry exhaust gas

x H2Oexhdry = Amount of water in exhaust per dry mole of dry exhaust gas

x prod/intdry = Amount of dry stoichiometric products per dry mole of intake air

x dil/exhdry = Amount of dilution gas and/or excess air per mole of dry exhaust gas

x int/exhdry = Amount of intake air required to produce actual combustion products per mole of dry (raw or diluted) exhaust gas

x raw/exhdry = Amount of undiluted exhaust gas, without excess air, per mole of dry (raw or diluted) exhaust gas

x O2intdry = Amount of intake air O2 per mole of dry intake air

x CO2intdry = Amount of intake air CO2 per mole of dry intake air

x H2Ointdry = Amount of intake air H2O per mole of dry intake air

x CO2int = Amount of intake air CO2 per mole of intake air

x CO2dil = Amount of dilution gas CO2 per mole of dilution gas

x CO2dildry = Amount of dilution gas CO2 per mole of dry dilution gas

x H2Odildry = Amount of dilution gas H2O per mole of dry dilution gas

x H2Odil = Amount of dilution gas H2O per mole of dilution gas

x [emission]meas = Amount of measured emission in the sample at the respective gas analyzer

x [emission]dry = Amount of emission per dry mole of dry sample

x H2O[emission]meas = Amount of water in sample at emission-detection location

x H2Oint = Amount of water in the intake air, based on a humidity measurement of intake air

This section uses the following values for dry air composition:

This section uses the following molar masses or effective molar masses of chemical species:

M air = 28,96559 g/mol (dry air)

M Ar = 39,948 g/mol (argon)

M C = 12,0107 g/mol (carbon)

M CO = 28,0101 g/mol (carbon monoxide)

M CO2 = 44,0095 g/mol (carbon dioxide)

M H = 1,00794 g/mol (atomic hydrogen)

M H2 = 2,01588 g/mol (molecular hydrogen)

M H2O = 18,01528 g/mol (water)

M He = 4,002602 g/mol (helium)

M N = 14,0067 g/mol (atomic nitrogen)

M N2 = 28,0134 g/mol (molecular nitrogen)

M NOx = 46,0055 g/mol (oxides of nitrogen (*))

M O = 15,9994 g/mol (atomic oxygen)

M O2 = 31,9988 g/mol (molecular oxygen)

M C3H8 = 44,09562 g/mol (propane)

M S = 32,065 g/mol (sulphur)

M HC = 13,875389 g/mol (total hydrocarbon (**))

(**)The effective molar mass of HC is defined by an atomic hydrogen-to-carbon ratio, α, of 1,85;

(*)The effective molar mass of NOx is defined by the molar mass of nitrogen dioxide, NO2.

This section uses the following molar gas constant R for ideal gases:

R = 8,314472J (mol · K)

This section uses the following ratios of specific heats γ [J/(kg · K)]/[J/(kg · K)] for dilution air and diluted exhaust:

γ air = 1,399 (ratio of specific heats for intake air or dilution air)

γ dil = 1,399 (ratio of specific heats for diluted exhaust gas)

γ exh = 1,385 (ratio of specific heats for raw exhaust gas)

This section describes how to determine the amount of water in an ideal gas:

The vapour pressure of water p H2O [kPa] for a given saturation temperature condition, T sat [K], shall be calculated by means of equations (7-77) or (7-78):

(a) For humidity measurements made at ambient temperatures from 0 to 100 °C or for humidity measurements made over super-cooled water at ambient temperatures from – 50 to 0 °C: (7-77) Where: p H2O = vapour pressure of water at saturation temperature condition [kPa] T sat = saturation temperature of water at measured condition [K]

(b) For humidity measurements made over ice at ambient temperatures from (– 100 to 0) °C: (7-78) Where: T sat = saturation temperature of water at measured condition [K]

If humidity is measured as a dew point, the amount of water in an ideal gas x H2O [mol/mol] shall be obtained by means of equation (7-79):

	(7-79)

Where:

x H2O = amount of water in an ideal gas [mol/mol]

p H2O = vapour pressure of water at the measured dew point, T sat=T dew [kPa]

p abs = wet static absolute pressure at the location of dew point measurement [kPa]

If humidity is measured as a relative humidity RH %, the amount of water of an ideal gas x H2O [mol/mol] is calculated by means of equation (7-80):

	(7-80)

Where:

RH % = relative humidity [%]

p H2O = water vapour pressure at 100 % relative humidity at the location of relative humidity measurement, T sat=T amb [kPa]

p abs = wet static absolute pressure at the location of relative humidity measurement [kPa]

If humidity is measured as a relative humidity, RH %, the dew point, T dew, shall be determined from RH % and dry bulb temperature by means of equation (7-81):

(7-81)

Where

p H2O = water vapor pressure scaled to the relative humidity at the location of relative humidity measurement, T sat = T amb

T dew = dew point as determined from relative humidity and dry bulb temperature measurements

The general chemical formula of fuel is CHαOβSγNδ with α atomic hydrogen-to-carbon ratio (H/C), β atomic oxygen-to-carbon ratio (O/C), γ atomic sulphur-to-carbon ratio (S/C) and δ atomic nitrogen-to-carbon ratio (N/C). Based on this formula the carbon mass fraction of fuel w C can be calculated. In case of diesel fuel the simple formula CHαOβ may be used. Default values for fuel composition may be derived from Table 7.3:

Fuel	Atomic hydrogen, oxygen, sulphur and nitrogen-to-carbon ratios CHαOβSγNδ	Carbon mass concentration, w C [g/g]
Diesel (non-road gas-oil)	CH1,80O0S0N0	0,869
Ethanol for dedicated compression ignition engines (ED95)	CH2,92O0,46S0N0	0,538
Petrol (E10)	CH1,92O0,03S0N0	0,833
Petrol (E0)	CH1,85O0S0N0	0,866
Ethanol (E85)	CH2,73O0,36S0N0	0,576
LPG	CH2,64O0S0N0	0,819
Natural Gas/Biomethane	CH3,78O0,016S0N0	0,747

As an alternative to the default values in Table 7.3, or where default values are not given for the reference fuel being used, the carbon mass concentration w C may be calculated from measured fuel properties by means of equation (7-82). Values for α and β shall be determined for the fuel and inserted into the equation in all cases, but γ and δ may optionally be set to zero if they are zero in the corresponding line of Table 7.3:

	(7-82)

where:

M C = molar mass of carbon.

α = atomic hydrogen-to-carbon ratio of the mixture of fuel(s) being combusted, weighted by molar consumption.

M H = molar mass of hydrogen.

β = atomic oxygen-to-carbon ratio of the mixture of fuel(s) being combusted, weighted by molar consumption.

M O = molar mass of oxygen.

γ = atomic sulphur-to-carbon ratio of the mixture of fuel(s) being combusted, weighted by molar consumption.

M S = molar mass of sulphur.

δ = atomic nitrogen-to-carbon ratio of the mixture of fuel(s) being combusted, weighted by molar consumption.

M N = molar mass of nitrogen.

For HC measurement, x THC[THC-FID] shall be calculated by using the initial THC contamination concentration x THC[THC-FID]init from point 7.3.1.3 of Annex VI by means of equation (7-83):

	(7-83)

Where:

x THC[THC-FID]cor = THC concentration corrected for contamination [mol/mol]

x THC[THC-FID]uncorr = THC uncorrected concentration [mol/mol]

x THC[THC-FID]init = initial THC contamination concentration [mol/mol]

In some points of this section, it may be necessary to calculate a flow-weighted mean concentration to determine the applicability of certain provisions. A flow-weighted mean is the mean of a quantity after it is weighted proportional to a corresponding flow rate. For example, if a gas concentration is measured continuously from the raw exhaust gas of an engine, its flow-weighted mean concentration is the sum of the products of each recorded concentration times its respective exhaust gas molar flow rate, divided by the sum of the recorded flow rate values. As another example, the bag concentration from a CVS system is the same as the flow-weighted mean concentration because the CVS system itself flow-weights the bag concentration.  A certain flow-weighted mean concentration of an emission at the emission limit value might be already expected based on previous testing with similar engines or testing with similar equipment and instruments.

Chemical balances of fuel, intake air and exhaust gas may be used to calculate flows, the amount of water in their flows, and the wet concentration of constituents in their flows. With one flow rate of either fuel, intake air or exhaust gas, chemical balances may be used to determine the flows of the other two. For example, chemical balances along with either intake air or fuel flow to determine raw exhaust gas flow may be used.

Chemical balances are required to determine the following:

(a) The amount of water in a raw or diluted exhaust gas flow, x H2Oexh, when the amount of water to correct for the amount of water removed by a sampling system is not measured;

(b) The flow-weighted mean fraction of dilution air in diluted exhaust gas, x dil/exh, when dilution air flow is not measured to correct for background emissions. It has to be noted that if chemical balances are used for this purpose, the exhaust gas is assumed to be stoichiometric, even if it is not.

The calculations for a chemical balance involve a system of equations that require iteration. The initial values of up to three quantities shall be guessed: the amount of water in the measured flow, x H2Oexh, fraction of dilution air in diluted exhaust gas (or excess air in the raw exhaust gas), x dil/exh, and the amount of products on a C1 basis per dry mole of dry measured flow, x Ccombdry. Time-weighted mean values of combustion air humidity and dilution air humidity in the chemical balance may be used; as long as combustion air and dilution air humidity remain within tolerances of ± 0,0025 mol/mol of their respective mean values over the test interval. For each emission concentration, x, and amount of water x H2Oexh, their completely dry concentrations, x dry and x H2Oexhdry shall be determined. The fuel atomic hydrogen-to-carbon ratio, α, oxygen-to-carbon ratio, β and carbon mass fraction of fuel, w C shall also be used. For the test fuel, α and β or the default values in Table 7.3 may be used.

Use the following steps to complete a chemical balance:

(a) Measured concentrations such as, x CO2meas, x NOmeas, and x H2Oint, shall be converted to dry concentrations by dividing them by one minus the amount of water present during their respective measurements; for example: x H2OxCO2meas, x H2OxNOmeas, and x H2Oint. If the amount of water present during a ‘wet’ measurement is the same as the unknown amount of water in the exhaust gas flow, x H2Oexh, it has to be iteratively solved for that value in the system of equations. If only total NOx are measured and not NO and NO2 separately, good engineering judgement shall be used to estimate a split in the total NOx concentration between NO and NO2 for the chemical balances. The molar concentration of NOx, x NOx, may be assumed to be 75 % NO and 25 % NO2. For NO2 storage after-treatment systems, x NOx may be assumed to be 25 % NO and 75 % NO2. For calculating the mass of NOx emissions, the molar mass of NO2 for the effective molar mass of all NOx species, regardless of the actual NO2 fraction of NOx, shall be used;

(b) Equations (7-82) to (7-99) in paragraph (d) of this point have to be entered into a computer program to iteratively solve for x H2Oexh, x Ccombdry and x dil/exh. Good engineering judgment shall be used to guess initial values for x H2Oexh, x Ccombdry, and x dil/exh. Guessing an initial amount of water that is about twice the amount of water in the intake or dilution air is recommended. Guessing an initial value of x Ccombdry as the sum of the measured CO2, CO, and THC values is recommended. Guessing an initial x dil between 0,75 and 0,95, such as 0,8 is also recommended. Values in the system of equations shall be iterated until the most recently updated guesses are all within ± 1 % of their respective most recently calculated values;

(c) The following symbols and subscripts are used in the equation system of paragraph (d) of this point where x unit is mol/mol: Symbol Description x dil/exh Amount of dilution gas or excess air per mole of exhaust gas x H2Oexh Amount of H2O in exhaust per mole of exhaust gas x Ccombdry Amount of carbon from fuel in the exhaust per mole of dry exhaust gas x H2Oexhdry Amount of water in exhaust per dry mole of dry exhaust gas x prod/intdry Amount of dry stoichiometric products per dry mole of intake air x dil/exhdry Amount of dilution gas and/or excess air per mole of dry exhaust gas x int/exhdry Amount of intake air required to produce actual combustion products per mole of dry (raw or diluted) exhaust gas x raw/exhdry Amount of undiluted exhaust, without excess air, per mole of dry (raw or diluted) exhaust gas x O2intdry Amount of intake air O2 per mole of dry intake air; x O2intdry = 0,209445 mol/mol may be assumed x CO2intdry Amount of intake air CO2 per mole of dry intake air. x CO2intdry = 375 μmol/mol may be used, but measuring the actual concentration in the intake air is recommended x H2Ointdry Amount of the intake air H2O per mole of dry intake air x CO2int Amount of intake air CO2 per mole of intake air x CO2dil Amount of dilution gas CO2 per mole of dilution gas x CO2dildry Amount of dilution gas CO2 per mole of dry dilution gas. If air is used as diluent, x CO2dildry = 375 μmol/mol may be used, but measuring the actual concentration in the intake air is recommended x H2Odildry Amount of dilution gas H2O per mole of dry dilution gas x H2Odil Amount of dilution gas H2O per mole of dilution gas x [emission]meas Amount of measured emission in the sample at the respective gas analyzer x [emission]dry Amount of emission per dry mole of dry sample x H2O[emission]meas Amount of water in sample at emission-detection location. These values shall be measured or estimated according to point 9.3.2.3.1. x H2Oint Amount of water in the intake air, based on a humidity measurement of intake air K H2Ogas Water-gas reaction equilibrium coefficient. 3,5 or a different value might be calculated using good engineering judgement. α Atomic hydrogen-to-carbon ratio of the mixture of fuel(s) (CHαOβ) being combusted, weighted by molar consumption β Atomic oxygen-to-carbon ratio of the mixture of fuel(s) (CHαOβ) being combusted, weighted by molar consumption

(d) The following equations [(7-84) to (7-101)] shall be used to iteratively solve for x dil/exh, x H2Oexh and x Ccombdry: (7-84) (7-85) (7-86) (7-87) (7-88) (7-89) (7-90) (7-91) (7-92) (7-93) (7-94) (7-95) (7-96) (7-97) (7-98) (7-99) (7-100) (7-101)

At the end of the chemical balance, the molar flow rate is calculated as specified in points 3.5.3 and 3.6.3.

All the NOx concentrations, including dilution air background concentrations, shall be corrected for intake-air humidity using equation (7-102) or (7-103):

(a) For compression-ignition engines x NOxcor = x NOxuncor · (9,953 · x H2O + 0,832) (7-102)

(b) For spark-ignition engines x NOxcor = x NOxuncor · (18,840 · x H2O + 0,68094) (7-103) Where: x NOxuncor = uncorrected NOx molar concentration in the exhaust gas [μmol/mol] x H2O = amount of water in the intake air [mol/mol]

To calculate the total mass per test of gaseous emission m gas [g/test], its molar concentration shall be multiplied by its respective molar flow and by exhaust gas molar mass; then integration over test cycle shall be performed [equation (7-104)]:

	(7-104)

Where:

Since equation (7-104) has to be solved by numerical integration, it is transformed in equation (7-105):

⇒	(7-105)

Where:

General equation may be modified according to which measurement system is used, batch or continuous sampling, and if a varying rather than a constant flow rate is sampled.

(a) For continuous sampling, in the general case of varying flow rate, the mass of the gaseous emission m gas [g/test] shall be calculated by means of equation (7-106): (7-106) Where: M gas = generic emission molar mass [g/mol] ṅ exh i = instantaneous exhaust gas molar flow rate on a wet basis [mol/s] x gas i = instantaneous gaseous emission molar fraction on a wet basis [mol/mol] ƒ = data sampling rate [Hz] N = number of measurements [-]

(b) Still for continuous sampling but in the particular case of constant flow rate the mass of the gaseous emission m gas [g/test] shall be calculated by means of equation (7-107): (7-107) Where: M gas = generic emission molar mass [g/mol] ṅ exh = exhaust gas molar flow rate on a wet basis [mol/s] = mean gaseous emission molar fraction on a wet basis [mol/mol] Δt = time duration of test interval

(c) For the batch sampling, regardless the flow rate is varying or constant, equation (7-104) can be simplified by means of equation (7-108): (7-108) Where: M gas = generic emission molar mass [g/mol] ṅ exh i = instantaneous exhaust gas molar flow rate on a wet basis [mol/s] = mean gaseous emission molar fraction on a wet basis [mol/mol] ƒ = data sampling rate [Hz] N = number of measurements [-]

Parameters of this point are obtained from the results of the chemical balance calculated in point 3.4.3. The following relation exists between gas molar concentrations in the measured flow x gasdry and x gas [mol/mol] expressed on a dry and wet basis respectively [equations (7-109) and (7-110)]:

	(7-109)
	(7-110)

where:

For gaseous emissions a removed water correction shall be performed for the generic concentration x [mol/mol] by means of equation (7-111):

	(7-111)

Where:

The flow rate of the raw exhaust gas can be directly measured or can be calculated based on the chemical balance of point 3.4.3. Calculation of raw exhaust gas molar flow rate is performed from measured intake air molar flow rate or fuel mass flow rate. The raw exhaust gas molar flow rate can be calculated from the sampled emissions, ṅexh, based on the measured intake air molar flow rate, ṅint, or the measured fuel mass flow rate, ṁfuel, and the values calculated using the chemical balance in point 3.4.3. It shall be solved for the chemical balance in point 3.4.3 at the same frequency that ṅint or ṁfuel is updated and recorded.

(a) Crankcase flow rate. The raw exhaust gas flow can be calculated based on ṅint or ṁfuel only if at least one of the following is true about crankcase emission flow rate: (i) The test engine has a production emission-control system with a closed crankcase that routes crankcase flow back to the intake air, downstream of intake air flow meter; (ii) During emission testing open crankcase flow shall be routed to the exhaust gas according to point 6.10 of Annex VI; (iii) Open crankcase emissions and flow are measured and added brake-specific emission calculations; (iv) Using emission data or an engineering analysis, it can be demonstrated that neglecting the flow rate of open crankcase emissions does not adversely affect compliance with the applicable standards;

(b) Molar flow rate calculation based on intake air. Based on ṅint, exhaust gas molar flow rate ṅexh [mol/s] shall be calculated by means of equation (7-112): (7-112) Where: ṅ exh = raw exhaust gas molar flow rate from which emissions are measured [mol/s] ṅ ind = intake air molar flow rate including humidity in intake air [mol/s] x int/exhdry = amount of intake air required to produce actual combustion products per mole of dry (raw or diluted) exhaust gas [mol/mol] x raw/exhdry = amount of undiluted exhaust gas, without excess air, per mole of dry (raw or diluted) exhaust gas [mol/mol] x H2Oexhdry = amount of water in exhaust gas per mole of dry exhaust gas [mol/mol]

(c) Molar flow rate calculation based on fuel mass flow rate Based on ṁfuel, ṅexh [mol/s] shall be calculated as follows: When conducting laboratory testing this calculation may only be used for discrete-mode NRSC and RMC [equation (7-113)]: (7-113) Where: ṅ exh = raw exhaust gas molar flow rate from which emissions are measured ṁ fuel = fuel flow rate including humidity in intake air [g/s] w C = carbon mass fraction for the given fuel [g/g] x H2Oexhdry = amount of H2O per dry mole of measured flow [mol/mol] M C = molecular mass of carbon 12,0107 g/mol x Ccombdry = amount of carbon from fuel in the exhaust gas per mole of dry exhaust gas [mol/mol]

(d) Exhaust gas molar flow rate calculation based on measured intake air molar flow rate, diluted exhaust gas molar flow rate, and dilute chemical balance Exhaust gas molar flow rate ṅ exh [mol/s] may be calculated based on the measured intake air molar flow rate, ṅ int, the measured diluted exhaust gas molar flow rate, ṅ dexh, and the values calculated using the chemical balance in point 3.4.3. Note that the chemical balance must be based on diluted exhaust gas concentrations. For continuous-flow calculations, solve for the chemical balance in point 3.4.3 at the same frequency that ṅ int and ṅ dexh are updated and recorded. This calculated ṅ dexh may be used for the PM dilution ratio verification, the calculation of dilution air molar flow rate in the background correction in point 3.6.1 and the calculation of mass of emissions in point 3.5.1 for species that are measured in the raw exhaust gas. Based on diluted exhaust gas and intake air molar flow rate, exhaust gas molar flow rate, ṅ exh [mol/s] shall be calculated as follows: (7-114) where ṅ exh = raw exhaust gas molar flow rate from which emissions are measured [mol/s]; x int/exhdry = amount of intake air required to produce actual combustion products per mole of dry (raw or diluted) exhaust gas [mol/mol]; x raw/exhdry = amount of undiluted exhaust gas, without excess air, per mole of dry (raw or diluted) exhaust gas [mol/mol]; x H2Oexh = amount of water in exhaust gas per mole of exhaust gas [mol/mol]; ṅ dexh = diluted exhaust gas molar flow rate from which emissions are measured [mol/s]; ṅ int = intake air molar flow rate including humidity in intake air [mol/s].

The calculation of gaseous emissions mass m gas [g/test] as a function of molar emissions flow rates shall be calculated as follows:

(a) Continuous sampling, varying flow rate, shall be calculated by means of equation (7-106): [see equation (7-106)] Where: M gas = generic emission molar mass [g/mol] ṅexhi = instantaneous exhaust gas molar flow rate on a wet basis [mol/s] xgasi = instantaneous generic gas molar concentration on a wet basis [mol/mol] f = data sampling rate [Hz] N = number of measurements [-]

(b) Continuous sampling, constant flow rate, shall be calculated by means of equation (7-107): [see equation (7-107)] Where: M gas = generic emission molar mass [g/mol] ṅexh = exhaust gas molar flow rate on a wet basis [mol/s] = mean gaseous emission molar fraction on a wet basis [mol/mol] Δt = time duration of test interval

(c) Batch sampling, regardless the flow rate is varying or constant, shall be calculated by means of equation (7-108): [see equation (7-108)] Where: M gas = generic emission molar mass [g/mol] ṅexhi = instantaneous exhaust gas molar flow rate on a wet basis [mol/s] = mean gaseous emission molar fraction on a wet basis [mol/mol] f = data sampling rate [Hz] N = number of measurements [-]

(d) In case of diluted exhaust gas calculated values for mass of the pollutants shall be corrected by subtracting the mass of background emissions, due to dilution air: (i) Firstly, the molar flow rate of dilution air nairdil [mol/s] shall be determined over the test interval. This may be a measured quantity or a quantity calculated from the diluted exhaust gas flow and the flow-weighted mean fraction of dilution air in diluted exhaust gas,

; (ii) The total flow of dilution air n airdil [mol] shall be multiplied by the mean concentration of background emission. This may be a time-weighted mean or a flow-weighted mean (e.g., a proportionally sampled background). The product of n airdil and the mean concentration of a background emission is the total amount of a background emission; (iii) If the result is a molar quantity, it shall be converted to a mass of the background emission m bkgnd [g] by multiplying it by emission molar mass, M gas [g/mol]; (iv) Total background mass shall be subtracted from total mass to correct for background emissions; (v) The total flow of dilution air may be determined by a direct flow measurement. In this case, the total mass of background shall be calculated, using the dilution air flow, n airdil. The background mass shall be subtracted from the total mass. The result shall be used in brake-specific emission calculations; (vi) The total flow of dilution air may be determined from the total flow of diluted exhaust gas and a chemical balance of the fuel, intake air, and exhaust gas as described in point 3.4. In this case, the total mass of background shall be calculated, using the total flow of diluted exhaust gas, n dexh. Then this result shall be multiplied by the flow-weighted mean fraction of dilution air in diluted exhaust gas,

. Considering the two cases (v) and (vi), equations (7-115) and (7-116) shall be used: or (7-115) m gascor = m gas – m bkgnd (7-116) where: m gas = total mass of the gaseous emission [g] m bkgnd = total background masses [g] m gascor = mass of gas corrected for background emissions [g] M gas = molecular mass of generic gaseous emission [g/mol] x gasdil = gaseous emission concentration in dilution air [mol/mol] n airdil = dilution air molar flow [mol] = flow-weighted mean fraction of dilution air in diluted exhaust gas [mol/mol] = gas fraction of background [mol/mol] n dexh = total flow of diluted exhaust gas [mol]

The same relations for raw gases (point 3.5.2) shall be used for dry-to-wet conversion on diluted samples. For dilution air a humidity measurement shall be performed with the aim to calculate its water vapour fraction x H2Odildry [mol/mol] by means of equation (7-96):

	[(see equation (7-96)]

Where:

(a) Calculation via chemical balance; The molar flow rate ṅ exh [mol/s] can be calculated based on fuel mass flow rate ṁ fuel by means of equation (7-113): (see equation 7-113) Where: ṅ exh = raw exhaust gas molar flow rate from which emissions are measured ṁ fuel = fuel flow rate including humidity in intake air [g/s] w C = carbon mass fraction for the given fuel [g/g] x H2Oexhdry = amount of H2O per dry mole of measured flow [mol/mol] M C = molecular mass of carbon 12,0107 g/mol x Ccombdry = amount of carbon from fuel in the exhaust gas per mole of dry exhaust gas [mol/mol]

(b) Measurement The exhaust gas molar flow rate may be measured by means of three systems: (i) PDP molar flow rate. Based upon the speed at which the Positive Displacement Pump (PDP) operates for a test interval, the corresponding slope a 1, and intercept, a 0 [-], as calculated with the calibration procedure set out in point 3.9.2, shall be used to calculate molar flow rate ṅ [mol/s] by means of equation (7-117): (7-117) with: (7-118) where: a 1 = calibration coefficient [m³/s] a 0 = calibration coefficient [m³/rev] p in, p out = inlet/outlet pressure [Pa] R = molar gas constant [J/(mol · K)] T in = inlet temperature [K] V rev = PDP pumped volume [m³/rev] f n.,PDP = PDP speed [rev/s] (ii) SSV molar flow rate. Based on the C d versus R e ^# equation determined in accordance with point 3.9.4, the Sub-Sonic Venturi (SSV) molar flow rate during an emission test ṅ [mol/s] shall be calculated by means of equation (7-119): (7-119) Where: p in = inlet pressure [Pa] A t = Venturi throat cross-sectional area [m²] R = molar gas constant [J/(mol · K)] T in = inlet temperature [K] Z = compressibility factor M mix = molar mass of diluted exhaust gas [kg/mol] C d = discharge coefficient of the SSV [-] C f = flow coefficient of the SSV [-] (iii) CFV molar flow rate. To calculate the molar flow rate through one venturi or one combination of venturis, its respective mean C d and other constants, determined in accordance with point 3.9.5, shall be used. The calculation of its molar flow rate ṅ [mol/s] during an emission test shall be calculated by means of equation (7-120): (7-120) Where: p in = inlet pressure [Pa] A t = Venturi throat cross-sectional area [m²] R = molar gas constant [J/(mol · K)] T in = inlet temperature [K] Z = compressibility factor M mix = molar mass of diluted exhaust gas [kg/mol] C d = discharge coefficient of the CFV [-] C f = flow coefficient of the CFV [-]

(a) Sampling from a varying flow rate: If a batch sample from a changing exhaust gas flow rate is collected, a sample proportional to the changing exhaust gas flow rate shall be extracted. The flow rate shall be integrated over a test interval to determine the total flow. The mean PM concentration

(which is already in units of mass per mole of sample) shall be multiplied by the total flow to obtain the total mass of PM m PM [g] by means of equation (7-121): (7-121) Where: ṅi = instantaneous exhaust gas molar flow rate [mol/s] = mean PM concentration [g/mol] Δti = sampling interval [s]

(b) Sampling from a constant flow rate If a batch sample from a constant exhaust gas flow rate is collected, the mean molar flow rate from which the sample is extracted shall be determined. The mean PM concentration shall be multiplied by the total flow to obtain the total mass of PM m PM[g] by means of equation (7-122): (7-122) where: ṅ = exhaust gas molar flow rate [mol/s] = mean PM concentration [g/mol] Δt = time duration of test interval [s] For sampling with a constant dilution ratio (DR), m PM [g] shall be calculated by means of equation (7-123): (7-123) where: m PMdil = PM mass in dilution air [g] DR = dilution ratio [-] defined as the ratio between the mass of the emission m and the mass of diluted exhaust gas m dil/exh (DR = m/m dil/exh). The dilution ratio DR can be expressed as a function of x dil/exh [equation (7-124)]: (7-124)

The same approach as that of point 3.6.1 shall be applied to correct the mass of PM for the background. Multiplying

by the total flow of dilution air, the total background mass of PM (m PMbkgnd [g]) is obtained. Subtraction of total background mass from total mass gives background corrected mass of particulates m PMcor [g] [equation (7-125)]:

	(7-125)

where:

Reference is made to points 3.5.1 and 3.6.1 for raw and diluted exhaust gas respectively. The resulting values for power Pi [kW] shall be integrated over a test interval. The total work W act [kWh] shall be calculated by means of equation (7-126):

	(7-126)

Where:

Where auxiliaries were fitted in accordance with Appendix 2 of Annex VI there shall be no adjustment to the instantaneous engine torque in equation (7-126). Where, according to points 6.3.2 or 6.3.3 of Annex VI to this regulation necessary auxiliaries that should have been fitted for the test are not installed, or auxiliaries that should have been removed for the test are installed, the value of Ti used in equation (7-126) shall be adjusted by means of equation (7-127):

Ti = Ti ,meas + Ti ,AUX	(7-127)

Where:

T i,meas is the measured value of instantaneous engine torque

T i,AUX is the corresponding value of torque required to drive auxiliaries determined in accordance with point 7.7.2.3(b) of Annex VI.

The specific emissions e gas [g/kWh] shall be calculated in the following ways depending on the type of test cycle.

	(7-128)

where:

In case of the NRTC, for gaseous emissions other than CO2 the final test result e gas [g/kWh] shall be a weighted average from cold-start run and hot-start run calculated by means of equation (7-129):

	(7-129)

Where:

In case of the NRTC, for CO2 the final test result e CO2 [g/kWh] shall be calculated from the hot-start NRTC calculated by means of equation (7-130):

	(7-130)

Where:

The specific emissions e gas [g/kWh] shall be calculated by means of equation (7-131):

	(7-131)

where:

The particulate specific emissions shall be calculated by transforming equation (7-128) into equation (7-132) where e gas [g/kWh] and m gas [g/test] are substituted by e PM [g/kWh] and m PM [g/test] respectively:

	(7-132)

Where:

The emissions on the transient composite cycle (i.e. cold-start NRTC and hot-start NRTC) shall be calculated as shown in point 3.8.1.1.

The particulate specific emission e PM [g/kWh] shall be calculated in the following way:

3.8.2.2.1.	For the single-filter method by means of equation (7-133): (7-133) Where: Pi = engine power for the mode i [kW] calculated by adding to the measured power Pmeas [kW] the power required to drive auxiliaries PAUX [kW] determined in accordance with equation (6-8) of Annex VI (Pi = Pmeas + PAUX). WFi = weighting factor for the mode i [-] ṁ PM = particulate mass flow rate [g/h] Nmode = number of modes in applicable discrete-mode NRSC
	(7-133)
Pi	=	engine power for the mode i [kW] calculated by adding to the measured power Pmeas [kW] the power required to drive auxiliaries PAUX [kW] determined in accordance with equation (6-8) of Annex VI (Pi = Pmeas + PAUX).
WFi	=	weighting factor for the mode i [-]
ṁ PM	=	particulate mass flow rate [g/h]
Nmode	=	number of modes in applicable discrete-mode NRSC
3.8.2.2.2.	For the multiple-filter method by means of equation (7-134): (7-134) Where: Pi = engine power for the mode i [kW] calculated by adding to the measured power Pmeas [kW] the power required to drive auxiliaries PAUX [kW] determined in accordance with equation (6-8) of Annex VI (Pi = Pmeas + PAUX). WFi = weighting factor for the mode i [-] ṁ PM i = particulate mass flow rate at mode i [g/h] Nmode = number of modes in applicable discrete-mode NRSC For the single-filter method, the effective weighting factor, WF eff i, for each mode shall be calculated by means of equation (7-135): (7-135) Where: m smpldexh i = mass of the diluted exhaust gas sample passed through the particulate sampling filters at mode i [kg] m smpldexh = mass of the diluted exhaust gas sample passed through the particulate sampling filters [kg] ṁ eqdexhwet i = equivalent diluted exhaust gas mass flow rate at mode i [kg/s] = average equivalent diluted exhaust gas mass flow rate [kg/s] The value of the effective weighting factors shall be within 0,005 (absolute value) of the weighting factors listed in Appendix 1 of Annex XVII.
---	---	---
	(7-134)
Pi	=	engine power for the mode i [kW] calculated by adding to the measured power Pmeas [kW] the power required to drive auxiliaries PAUX [kW] determined in accordance with equation (6-8) of Annex VI (Pi = Pmeas + PAUX).
WFi	=	weighting factor for the mode i [-]
ṁ PM i	=	particulate mass flow rate at mode i [g/h]
Nmode	=	number of modes in applicable discrete-mode NRSC
	(7-135)
m smpldexh i	=	mass of the diluted exhaust gas sample passed through the particulate sampling filters at mode i [kg]
m smpldexh	=	mass of the diluted exhaust gas sample passed through the particulate sampling filters [kg]
ṁ eqdexhwet i	=	equivalent diluted exhaust gas mass flow rate at mode i [kg/s]
	=	average equivalent diluted exhaust gas mass flow rate [kg/s]