40 CFR 1065.655 - Chemical balances of fuel, intake air, and exhaust.

§ 1065.655 Chemical balances of fuel, intake air, and exhaust.
(a) General. Chemical balances of fuel, intake air, and exhaust 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, you may use chemical balances to determine the flows of the other two. For example, you may use chemical balances along with either intake air or fuel flow to determine raw exhaust flow.
(b) Procedures that require chemical balances. We require chemical balances when you determine the following:
(1) A value proportional to total work, W when you choose to determine brake-specific emissions as described in § 1065.650(f).
(2) The amount of water in a raw or diluted exhaust flow, x H2Oexh, when you do not measure the amount of water to correct for the amount of water removed by a sampling system. Correct for removed water according to § 1065.659.
(3) The calculated dilution air flow when you do not measure dilution air flow to correct for background emissions as described in § 1065.667(c) and (d).
(c) Chemical balance procedure. The calculations for a chemical balance involve a system of equations that require iteration. We recommend using a computer to solve this system of equations. You must guess the initial values of up to three quantities: The amount of water in the measured flow, x H2Oexh, fraction of dilution air in diluted exhaust, x dil/exh, and the amount of products on a C1 basis per dry mole of dry measured flow, x Ccombdry. You may use time-weighted mean values of combustion air humidity and dilution air humidity in the chemical balance; as long as your combustion air and dilution air humidities 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, you must determine their completely dry concentrations, x dry and x H2Oexhdry. You must also use your fuel's atomic hydrogen-to-carbon ratio, α, oxygen-to-carbon ratio, β, sulfur-to-carbon ratio, γ, and nitrogen-to-carbon ratio, δ. You may measure α, β, γ, and δ or you may use default values for a given fuel as described in § 1065.655(d). Use the following steps to complete a chemical balance:
(1) Convert your measured concentrations such as, x CO2meas, x NOmeas, and x H2Oint, 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 flow, x H2Oexh, iteratively solve for that value in the system of equations. If you measure only total NOX and not NO and NO2 separately, use good engineering judgment to estimate a split in your total NOX concentration between NO and NO2 for the chemical balances. For example, if you measure emissions from a stoichiometric spark-ignition engine, you may assume all NOX is NO. For a compression-ignition engine, you may assume that your molar concentration of NOX, x NOx, is 75% NO and 25% NO2. For NO2 storage aftertreatment systems, you may assume x NOx is 25% NO and 75% NO2. Note that for calculating the mass of NOX emissions, you must use the molar mass of NO2 for the effective molar mass of all NOX species, regardless of the actual NO2 fraction of NOX.
(2) Enter the equations in paragraph (c)(4) of this section into a computer program to iteratively solve for x H2Oexh, x Ccombdry, and x dil/exh. Use good engineering judgment to guess initial values for x H2Oexh, x C combdry, and x dil/exh. We recommend guessing an initial amount of water that is about twice the amount of water in your intake or dilution air. We recommend guessing an initial value of x Ccombdry as the sum of your measured CO2, CO, and THC values. We also recommend guessing an initial x dil/exh between 0.75 and 0.95, such as 0.8. Iterate values in the system of equations until the most recently updated guesses are all within ±1% of their respective most recently calculated values.
(3) Use the following symbols and subscripts in the equations for this paragraph (c):
x dil/exh = amount of dilution gas or excess air per mole of exhaust.
x H2Oexh = amount of water in exhaust per mole of exhaust.
x Ccombdry = amount of carbon from fuel in the exhaust per mole of dry exhaust.
x H2dry = amount of H2 in exhaust per amount of dry exhaust.
K H2Ogas = water-gas reaction equilibrium coefficient. You may use 3.5 or calculate your own value using good engineering judgment.
x H2Oexhdry = amount of water in exhaust per dry mole of dry exhaust.
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.
x int/exhdry = amount of intake air required to produce actual combustion products per mole of dry (raw or diluted) exhaust.
x raw/exhdry = amount of undiluted exhaust, without excess air, per mole of dry (raw or diluted) exhaust.
x O2int = amount of intake air O2 per mole of intake air.
x CO2intdry = amount of intake air CO2 per mole of dry intake air. You may use xCO2intdry = 375 µmol/mol, but we recommend measuring the actual concentration in the 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. If you use air as diluent, you may use xCO2dildry = 375 µmol/mol, but we recommend measuring the actual concentration in the intake air.
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. Measure or estimate these values according to § 1065.145(e)(2).
x H2Oint = amount of water in the intake air, based on a humidity measurement of intake air.
α = atomic hydrogen-to-carbon ratio of the mixture of fuel(s) being combusted, weighted by molar consumption.
β = atomic oxygen-to-carbon ratio of the mixture of fuel(s) being combusted, weighted by molar consumption.
γ = atomic sulfur-to-carbon ratio of the mixture of fuel(s) being combusted, weighted by molar consumption.
δ = atomic nitrogen-to-carbon ratio of the mixture of fuel(s) being combusted, weighted by molar consumption.
(4) Use the following equations to iteratively solve for x dil/exh, x H2Oexh, and x Ccombdry:
(5) The following example is a solution for x dil/exh,x, x H2Oexh, and x Ccombdry using the equations in paragraph (c)(4) of this section:
α = 1.8
β = 0.05
γ = 0.0003
δ = 0.0001
(d) Carbon mass fraction. Determine carbon mass fraction of fuel, w c, using one of the following methods:
(1) You may calculate w c as described in this paragraph (d)(1) based on measured fuel properties. To do so, you must determine values for α and β in all cases, but you may set γ and δ to zero if the default value listed in Table 1 of this section is zero. Calculate w c using the following equation:
Where:
w c = carbon mass fraction of fuel.
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 sulfur-to-carbon ratio of the mixture of fuel(s) being combusted, weighted by molar consumption.
M S = molar mass of sulfur.
δ = atomic nitrogen-to-carbon ratio of the mixture of fuel(s) being combusted, weighted by molar consumption.
M N = molar mass of nitrogen.
Example:
α = 1.8
β = 0.05
γ = 0.0003
δ = 0.0001
M C = 12.0107
M H = 1.01
M O = 15.9994
M S = 32.065
M N = 14.0067
w c = 0.8205
(2) You may use the default values in the following table to determine w c for a given fuel:
Table 1 of § 1065.655 —Default Values of α, β, γ, δ, and w c, for Various Fuels
Fuel Atomic hydrogen, oxygen, sulfur, and nitrogen-to-carbon ratiosCHαOβSγNδ Carbon mass fraction, w c g/g
Gasoline CH1.85O0S0N0 0.866
E10 Gasoline CH1.92O0.03S0N0 0.833
E15 Gasoline CH1.95O0.05S0N0 0.817
E85 Gasoline CH2.73O0.38S0N0 0.576
#1 Diesel CH1.93O0S0N0 0.861
#2 Diesel CH1.80O0S0N0 0.869
Liquefied Petroleum Gas CH2.64O0S0N0 0.819
Natural gas CH3.78 O0.016S0N0 0.747
E100 Ethanol CH3O0.5S0N0 0.521
M100 Methanol CH4O1S0N0 0.375
Residual fuel blends Must be determined by measured fuel properties as described in paragraph (d)(1) of this section.
(e) Calculated raw exhaust molar flow rate from measured intake air molar flow rate or fuel mass flow rate. You may calculate the raw exhaust molar flow rate from which you sampled emissions,n exh, based on the measured intake air molar flow rate, n int, or the measured fuel mass flow rate, m fuel, and the values calculated using the chemical balance in paragraph (c) of this section. Note that the chemical balance must be based on raw exhaust gas concentrations. Solve for the chemical balance in paragraph (c) of this section at the same frequency that you update and record n int orm fuel.
(1) Crankcase flow rate. If engines are not subject to crankcase controls under the standard-setting part, you may calculate raw exhaust flow based on n int orm fuel using one of the following:
(i) You may measure flow rate through the crankcase vent and subtract it from the calculated exhaust flow.
(ii) You may estimate flow rate through the crankcase vent by engineering analysis as long as the uncertainty in your calculation does not adversely affect your ability to show that your engines comply with applicable emission standards.
(iii) You may assume your crankcase vent flow rate is zero.
(2) Intake air molar flow rate calculation. Based onn int, calculaten exh as follows:
Where:
n exh = raw exhaust molar flow rate from which you measured emissions.
n int = intake air molar flow rate including humidity in intake air.
Example:
n int = 3.780 mol/s
x int/exhdry = 0.69021 mol/mol
x raw/exhdry = 1.10764 mol/mol
x H20exhdry = 107.64 mmol/mol = 0.10764 mol/mol
n exh = 6.066 mol/s
(3) Fuel mass flow rate calculation. Based on m fuel, calculate n exh as follows:
Where:
n exh = raw exhaust molar flow rate from which you measured emissions.
m fuel = fuel flow rate including humidity in intake air.
Example:
m fuel = 7.559 g/s
w c = 0.869 g/g
M C = 12.0107 g/mol
x Ccombdry = 99.87 mmol/mol = 0.09987 mol/mol
x H20exhdry = 107.64 mmol/mol = 0.10764 mol/mol
n exh = 6.066 mol/s
(f) Calculated raw exhaust molar flow rate from measured intake air molar flow rate, dilute exhaust molar flow rate, and dilute chemical balance. You may calculate the raw exhaust molar flow rate, n exh, based on the measured intake air molar flow rate, n int, the measured dilute exhaust molar flow rate, n dexh, and the values calculated using the chemical balance in paragraph (c) of this section. Note that the chemical balance must be based on dilute exhaust gas concentrations. For continuous-flow calculations, solve for the chemical balance in paragraph (c) of this section at the same frequency that you update and record n int and n dexh. This calculated n exh may be used for the PM dilution ratio verification in § 1065.546; the calculation of dilution air molar flow rate in the background correction in § 1065.667; and the calculation of mass of emissions in § 1065.650(c) for species that are measured in the raw exhaust.
(1) Crankcase flow rate. If engines are not subject to crankcase controls under the standard-setting part, calculate raw exhaust flow as described in paragraph (e)(1) of this section.
(2) Dilute exhaust and intake air molar flow rate calculation. Calculate n exh as follows:
Example:
n int = 7.930mol/s
x raw/exhdry = 0.1544 mol/mol
x int/exhdry = 0.1451 mol/mol
x H2Oexh = 32.46 mmol/mol - 0.03246 mol/mol
n dexh = 49.02 mol/s
n exh = (0.1544−0.145(· (1−0.03246) · 49.02 7.930 = 0.4411 7.930 = 8.371 mol/s
[73 FR 37331, June 30, 2008, as amended at 73 FR 59334, Oct. 8, 2008; 75 FR 23051, Apr. 30, 2010; 76 FR 57458, Sept. 15, 2011]

Title 40 published on 2014-07-01

no entries appear in the Federal Register after this date.

This is a list of United States Code sections, Statutes at Large, Public Laws, and Presidential Documents, which provide rulemaking authority for this CFR Part.

This list is taken from the Parallel Table of Authorities and Rules provided by GPO [Government Printing Office].

It is not guaranteed to be accurate or up-to-date, though we do refresh the database weekly. More limitations on accuracy are described at the GPO site.


United States Code
U.S. Code: Title 42 - THE PUBLIC HEALTH AND WELFARE

§ 7401 - Congressional findings and declaration of purpose

§ 7402 - Cooperative activities

§ 7403 - Research, investigation, training, and other activities

§ 7404 - Research relating to fuels and vehicles

§ 7405 - Grants for support of air pollution planning and control programs

§ 7406 - Interstate air quality agencies; program cost limitations

§ 7407 - Air quality control regions

§ 7408 - Air quality criteria and control techniques

§ 7409 - National primary and secondary ambient air quality standards

§ 7410 - State implementation plans for national primary and secondary ambient air quality standards

§ 7411 - Standards of performance for new stationary sources

§ 7412 - Hazardous air pollutants

§ 7413 - Federal enforcement

§ 7414 - Recordkeeping, inspections, monitoring, and entry

§ 7415 - International air pollution

§ 7416 - Retention of State authority

§ 7417 - Advisory committees

§ 7418 - Control of pollution from Federal facilities

§ 7419 - Primary nonferrous smelter orders

§ 7420 - Noncompliance penalty

§ 7421 - Consultation

§ 7422 - Listing of certain unregulated pollutants

§ 7423 - Stack heights

§ 7424 - Assurance of adequacy of State plans

§ 7425 - Measures to prevent economic disruption or unemployment

§ 7426 - Interstate pollution abatement

§ 7427 - Public notification

§ 7428 - State boards

§ 7429 - Solid waste combustion

§ 7430 - Emission factors

§ 7431 - Land use authority

§ 7450 to 7459 - Repealed.

§ 7470 - Congressional declaration of purpose

§ 7471 - Plan requirements

§ 7472 - Initial classifications

§ 7473 - Increments and ceilings

§ 7474 - Area redesignation

§ 7475 - Preconstruction requirements

§ 7476 - Other pollutants

§ 7477 - Enforcement

§ 7478 - Period before plan approval

§ 7479 - Definitions

§ 7491 - Visibility protection for Federal class I areas

§ 7492 - Visibility

§ 7501 - Definitions

§ 7502 - Nonattainment plan provisions in general

§ 7503 - Permit requirements

§ 7504 - Planning procedures

§ 7505 - Environmental Protection Agency grants

§ 7505a - Maintenance plans

§ 7506 - Limitations on certain Federal assistance

§ 7506a - Interstate transport commissions

§ 7507 - New motor vehicle emission standards in nonattainment areas

§ 7508 - Guidance documents

§ 7509 - Sanctions and consequences of failure to attain

§ 7509a - International border areas

§ 7511 - Classifications and attainment dates

§ 7511a - Plan submissions and requirements

§ 7511b - Federal ozone measures

§ 7511c - Control of interstate ozone air pollution

§ 7511d - Enforcement for Severe and Extreme ozone nonattainment areas for failure to attain

§ 7511e - Transitional areas

§ 7511f - NO

§ 7512 - Classification and attainment dates

§ 7512a - Plan submissions and requirements

§ 7513 - Classifications and attainment dates

§ 7513a - Plan provisions and schedules for plan submissions

§ 7513b - Issuance of RACM and BACM guidance

§ 7514 - Plan submission deadlines

§ 7514a - Attainment dates

§ 7515 - General savings clause

§ 7521 - Emission standards for new motor vehicles or new motor vehicle engines

§ 7522 - Prohibited acts

§ 7523 - Actions to restrain violations

§ 7524 - Civil penalties

§ 7525 - Motor vehicle and motor vehicle engine compliance testing and certification

§ 7541 - Compliance by vehicles and engines in actual use

§ 7542 - Information collection

§ 7543 - State standards

§ 7544 - State grants

§ 7545 - Regulation of fuels

§ 7546 - Renewable fuel

§ 7547 - Nonroad engines and vehicles

§ 7548 - Study of particulate emissions from motor vehicles

§ 7549 - High altitude performance adjustments

§ 7550 - Definitions

§ 7551 - Omitted

§ 7552 - Motor vehicle compliance program fees

§ 7553 - Prohibition on production of engines requiring leaded gasoline

§ 7554 - Urban bus standards

§ 7571 - Establishment of standards

§ 7572 - Enforcement of standards

§ 7573 - State standards and controls

§ 7574 - Definitions

§ 7581 - Definitions

§ 7582 - Requirements applicable to clean-fuel vehicles

§ 7583 - Standards for light-duty clean-fuel vehicles

§ 7584 - Administration and enforcement as per California standards

§ 7585 - Standards for heavy-duty clean-fuel vehicles (GVWR above 8,500 up to 26,000 lbs.)

§ 7586 - Centrally fueled fleets

§ 7587 - Vehicle conversions

§ 7588 - Federal agency fleets

§ 7589 - California pilot test program

§ 7590 - General provisions

§ 7601 - Administration

§ 7602 - Definitions

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§ 7604 - Citizen suits

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§ 7607 - Administrative proceedings and judicial review

§ 7608 - Mandatory licensing

§ 7609 - Policy review

§ 7610 - Other authority

§ 7611 - Records and audit

§ 7612 - Economic impact analyses

§ 7613 - Repealed.

§ 7614 - Labor standards

§ 7615 - Separability

§ 7616 - Sewage treatment grants

§ 7617 - Economic impact assessment

§ 7618 - Repealed.

§ 7619 - Air quality monitoring

§ 7620 - Standardized air quality modeling

§ 7621 - Employment effects

§ 7622 - Employee protection

§ 7623 - Repealed.

§ 7624 - Cost of vapor recovery equipment

§ 7625 - Vapor recovery for small business marketers of petroleum products

42 U.S. Code § 7450 to 7459 - Repealed.

§ 7625a - Statutory construction

§ 7626 - Authorization of appropriations

§ 7627 - Air pollution from Outer Continental Shelf activities

§ 7628 - Demonstration grant program for local governments

§ 7641 - Noise abatement

§ 7642 - Authorization of appropriations

§ 7651 - Findings and purposes

§ 7651a - Definitions

§ 7651b - Sulfur dioxide allowance program for existing and new units

§ 7651c - Phase I sulfur dioxide requirements

§ 7651d - Phase II sulfur dioxide requirements

§ 7651e - Allowances for States with emissions rates at or below 0.80 lbs/mmBtu

§ 7651f - Nitrogen oxides emission reduction program

§ 7651g - Permits and compliance plans

§ 7651h - Repowered sources

§ 7651i - Election for additional sources

§ 7651j - Excess emissions penalty

§ 7651k - Monitoring, reporting, and recordkeeping requirements

42 U.S. Code § -

§ 7651m - Enforcement

§ 7651n - Clean coal technology regulatory incentives

42 U.S. Code § -

§ 7661 - Definitions

§ 7661a - Permit programs

§ 7661b - Permit applications

§ 7661c - Permit requirements and conditions

§ 7661d - Notification to Administrator and contiguous States

§ 7661e - Other authorities

§ 7661f - Small business stationary source technical and environmental compliance assistance program

§ 7671 - Definitions

§ 7671a - Listing of class I and class II substances

§ 7671b - Monitoring and reporting requirements

§ 7671c - Phase-out of production and consumption of class I substances

§ 7671d - Phase-out of production and consumption of class II substances

§ 7671e - Accelerated schedule

§ 7671f - Exchange authority

§ 7671g - National recycling and emission reduction program

§ 7671h - Servicing of motor vehicle air conditioners

§ 7671i - Nonessential products containing chlorofluorocarbons

§ 7671j - Labeling

§ 7671k - Safe alternatives policy

42 U.S. Code § -

§ 7671m - Relationship to other laws

§ 7671n - Authority of Administrator

42 U.S. Code § -

§ 7671p - International cooperation

§ 7671q - Miscellaneous provisions