Obtain accurate NOX values for strategies to reduce emissions from combustion

In the process of developing low-nitrogen-oxide-emissions (NO_X) combustion appliances, the request for the volume of NO_X emissions from the tail flame is given in milligrams/kilowatt hour (mg/kWh) in almost all national and regional standards and related certifications. However, the instrument that measures NO_X in the exhaust tail flame of the combustion reports only in ppm or mg/m³. This requires the calculation of the NO_X in mg/kWh, based on the measured NO_X in ppm or mg/m³ and related data for these specific combustion systems.

This article summarizes how the combustion industry presently converts ppm to mg/m³ and introduces a concept for measuring the emission rate of a combustion system. With this concept, a formula can be derived to calculate the NO_X produced by combustion in mg/kWh. The combustion of methane and propane are used as examples in a demonstration of the measured ppm or mg/m³ concentration of NO_X, along with the the CO₂ or O₂ concentration in the tail flame, to calculate the NO_X emissions in mg/kWh.

This discussion explains how, when applying various methods to reduce NO_X emissions from the combustion process, the traditional measurement results of NO₂ content (accounting for 5%–10% of NO_X) can give an estimated result. However, to obtain accurate NO_X values, it is necessary to precisely measure NO value, as well as NO₂ value. More accurate measurement of emissions values and amounts aids in emissions reductions for combustion, thereby helping control air pollution.

Incentives for accurate emissions measurement. Immense economic growth in China since the 1980s has resulted in significant air pollution in major cities, which poses a serious threat to public health. However, decades of hard work and investment by the municipal government have paid off, resulting in a dramatic reduction in air pollution.

The Beijing 2013–2017 Clean Air Action Plan¹ is the most comprehensive and systematic pollution control program put into practice in Beijing to date. From 2013–2017, emissions of SO₂, NO_X, volatile organic compounds (VOCs) and particulate matter (PM2.5) decreased by 83%, 43%, 42% and 55%, respectively (FIG. 1, left). However, during the same time period, changes in major air pollutant emissions in the areas surrounding Beijing (including Tianjin, Hebei, Henan, Shandong, Shanxi and Inner Mongolia) were not as desirable (FIG. 1, right). Other areas in the country face the same problem. To clean China’s air supply, numerous issues must still be addressed; this article was written with this task in mind.

FIG. 1. Changes in anthropogenic emissions of SO2, NOX, VOCs and PM2.5 in Beijing, 2013–2017 (left). Changes in major air pollutant emissions in the areas surrounding Beijing (including Tianjin, Hebei, Henan, Shandong, Shanxi and Inner Mongolia), 2013–20171 (right).

NO_X emissions caused by combustion are an important factor in the formation of air pollution and smog.^2–5 NO_X, which comprises mainly NO and NO₂, is the general term for a group of highly reactive gases. Most nitrogen oxides are colorless and tasteless; however, in many cities or densely populated areas, the pollutant NO₂ and other particles in the air often form a reddish-brown smog or haze.

When NO reacts with O₂ in the air under sunlight, ozone is produced near the ground. Ground-level ozone has an adverse effect on the respiratory system, causing lung cancer and affecting agricultural production. NO_X also reacts to form nitrate particles and acidic aerosols, which can cause respiratory problems. When NO_X reacts with water to form nitric acid, it causes acid rain and deterioration of water quality. Additionally, acid gases and airborne particles can cause reduced visibility and reduced air quality.

Many standards, both at home and abroad, restrict NO_X emissions and outline specific regulations—e.g., Beijing boiler air pollutant emissions standard DB11/139-2015,⁶ Chinese gas heater standard CJT113-2015,⁷ and European CE standard for infrared heaters BSEN 416-1.⁸ In all of these standards, the emissions reporting is given in mg/kWh. Many customers require manufacturers to provide NO_X emissions data in mg/kWh when purchasing combustion-related appliances. For example, in Beijing, the NO_X emissions from a newly built boiler cannot be greater than 100 mg/kWh.

However, almost all instruments that measure the tail flame of a burner offer a reading of NO_X only in ppm or mg/m³.⁹ Using the measured NO_X data (in ppm or mg/m³) to calculate the NO_X produced by the combustion system (in mg/kWh) is an important calculation, but many relevant documents and standards offer complicated conversions or, conversely, very simple tables^8,9 that do not explain the theoretical basis behind the conversions. Many standards simply do not mention the conversion method, causing confusion and difficulty for the engineering community. This article describes a simple, accurate calculation method that was derived in the process of developing low-NO_X heaters.

Background on conversion of ppm to mg/m³. The engineering and academic communities have held recent discussions on the conversion of ppm to mg/m³.¹⁰ A brief overview of the conversion history follows for those readers seeking background information.

Ppm is often used to express concentration, such as mass ppm concentration or volume ppm concentration (i.e., ppmv). Ppmv is a common way of expressing gas phase concentration. Gas is miscible and, generally speaking, once equilibrium is reached the gas is homogeneous, meaning its components are evenly mixed together. In SI units, the volume for this gas is cubic meters (m³). If the gas mixture is divided into components and the concentration of one component in the gas mixture is assumed to be 1 ppm, and if the mixture is 10⁶ m³, then the gas of this component should be 1 m³. This results in 1 m³ of a certain component, or 10⁶ m³ for a mixture = 1 ppm.

Eqs. 1 and 2 are derived from the ideal gas law (for gases at lower pressures):¹¹

      PV = nRT                   (1)
      PVi = n_iRT                  (2)

Here, P is the pressure (in pascal); V is the volume (m³); n is the number of moles (proportional to the number of molecules) of all components; R is a constant, called the universal gas constant, with a value of 8.3143 joules/K mole; T is the Kelvin (K) temperature; V_i is the partial volume of the gas component i; and n_i is the molar number of gas component i.

Eqs. 1 and 2 can be rewritten, as shown in Eqs. 3 and 4:

      V = nRT / P                           (3)
      V_i = n_iRT / P                          (4)

Next, a certain trace gas in the mixed gas can be considered. Assuming that V_i is the volume of the trace gas and V_T is the total volume of the mixed gas, both sides of the second equation are divided by V_T, which gives the concentration of the trace gas that can be expressed as a volume ratio (Eq. 5):

                (5)

Then, x_i can be used as the concentration of the trace gas component i in ppm (Eq. 6):

                 (6)

Using X_i as the mass concentration of component i in mg/m³ and assuming the molar weight of component i is M_i (g/mole) gives Eq. 7:

                      (7)

When the low index i in these equations is neglected, Eqs. 8 and 9 result:

      X = x(MP ÷ RT) × 10³ mg/m³                        (8)
      x = X(RT ÷ MP) × 10^–3 ppm                          (9)

Note that the concentration x is in ppm, the unit of concentration X is in mg/m³, and M is the molecular weight of the trace gas concerned (g/mole). Eqs. 8 and 9 have been generally accepted by the academic and engineering communities, and literature¹⁰ describes them at constant temperature.

Simple calculation procedures are also provided on relevant websites in America and Europe. For example, on some sites,^12,13 the only required inputs are the value of the concentration x or X of a certain gas at atmospheric pressure and 25°C, along with the molecular weight of the gas. The program will immediately give the value of X or x under the corresponding conditions. In addition to the calculation,^12,13 users can change the gas temperature and pressure inputs.¹⁴ The molecular weight of NO₂ is 46.01 g, and the molecular weight of NO is 30.01 g; therefore, at a temperature of 20°C (293.15 K) and 1 atm, 1 ppm NO₂ = 1.91 mg/m³, and 1 ppm NO = 1.25 mg/m³.

In the general combustion system, NO₂ in tail flame accounts for approximately 5%–10% of NO_X and NO accounts for about 90%–95%.^15–18 When NO₂ accounts for 10% of NO_X, the average molecular weight of NO_X can be calculated as M = 31.61. Under the same temperature and pressure conditions as the previous calculation, for NO_X, 1 ppm = 1.29 mg/m³.

Calculation of NO_X in mg/kWh for a combustion system.  For a combustion system, the NO_X concentration in the tail flame can be measured in ppm or mg/m³. However, the NO_X emission in mg/kWh dictates how many mg of NO_X are produced in a combustion system when it releases 1 kW in 1 hr. This means that NO_X in mg/kWh is not only related to the NO_X concentration in the tail flame, but also to the volume flowrate of the tail flame and the power produced by the combustion system.

The emission rate, E, of pollutants like NO_X from a combustion system must first be defined. A combustion system is used to generate certain power or heat, thereby producing pollutants. The higher the power is generated by the system, the more pollutants are produced. Since all pollutants are discharged to air through the tail flame, the total mass flowrates of the pollutants can be calculated from the volume mass concentration of pollutants, mg/m³, and the volume flowrate of the tail flame.

E can be defined for a certain pollutant as the total mass flowrate for this pollutant in the tail flame, divided by the power generated by the combustion system. This E is listed in mg/kWh. In this article, E is used for emission of NO_X, but it also can be used for emission of other pollutants, such as CO, SO₂, SO₃, etc.

Now the volume flowrate of the tail flame of a combustion system can be calculated. For the sake of simplicity, it is assumed that the concentrations of CO, NO, NO₂, SO₂, etc. in the combustion products are negligible compared to the concentrations of O₂, CO₂, H₂O and N₂. At the same time, it is assumed that there is no water vapor condensation, at least at the measurement point in the tail flame generated by the combustion system. Based on the authors’ many years of experience in the research and development of various types of heaters in the U.S. and China, these two assumptions should be valid for general combustion systems, such as infrared heaters, unitary heaters, home heaters, etc.

In air, the composition of O₂ is 20.95%, while N₂, Ar and other elements make up 79.05% in volume.¹⁶ If the volume flowrate of O₂ is 1 for a combustion system, then the ratio of the volume flowrate of N₂, Ar, etc. to the volume flowrate of O₂ is 79.05 ÷ 20.95 = 3.77. Since gas components like Ar do not participate in the reaction, for the sake of brevity, only N₂ is used to represent these components.

Consider the combustion of methane (Eq. 10):

      CH₄ + 2O₂ = CO₂ + 2H₂O                                                        (10)

If the reaction or combustion occurs in air, then Eq. 11 can be used:

      CH₄ + 2(O₂ + 3.77 N₂) = CO₂ + 2H₂O + 7.54 N₂                       (11)

If V_a represents the volume rate of CH₄ consumption, then when the reaction product is cooled to normal temperature (assuming that the water vapor is not condensed at this time), the volume rate of the tail flame generated will be V_a + 2V_a + 7.54V_a = 10.54V_a. According to combustion theory,¹⁸ to avoid significant production of CO and carbon, there should be a certain excess of O₂ in combustion systems. Considering this, the reaction formula in Eq. 11 can be written as shown in Eq. 12:

      CH₄ + (2 + y)(O₂ + 3.77N₂) = CO₂ + 2H₂O + 7.54N₂ + y(O₂ + 3.77N₂)             (12)

It is assumed that y(O₂ + 3.77N₂) is O₂ and corresponding N₂ in the excess air. If V_a is the rate at which the volume of fuel gas CH₄ is consumed, then the volume rate at which the reactants disappear and the volume rate of the products generated in the tail flame (when cooled to room temperature) can be calculated as shown in Eq. 13:

      V_a + 2(V_a + 3.77V_a) + y(V_a + 3.77V_a) and
      V_a + 2V_a + 7.54V_a + y(V_a + 3.77V_a)                                      (13)

Therefore, the total flow of the tail flame produced by the combustion system will be (10.54 + 4.77y)V_a.

The y in Eqs. 12 and 13 can be obtained from the concentration of CO₂ measured in the tail flame or the concentration of O₂ measured. First, the measured CO₂ concentration is measured, as shown in Eq. 14:

                  (14)

The result is applied to Eq. 15:

                                               (15)

In this way, the volumetric flow of the tail flame can be represented as shown in Eq. 16:

Volume flowrate of the tail flame = 10.54V_a + 4.77yV_a = (1 / CO_2measured)V_a            (16)

The power of the combustion system is generated by the consumption of CH₄ at a specified flowrate (V_a) and heat of combustion (HV), with the power of combustion = HV × V_a. Since the mass emission rate of NO_X is X, Eq. 17 is used to calculate E:

      E = (Volume mass concentration of emission
      of NO_X × Volume flow of tail flame) /
      Power of combustion system                                                        (17)

Substituting Eq. 16 and the power of combustion (HV × V_a) into the formula results in Eq. 18:

      E = X / (CO_2measured × HV)                                                        (18)

Using the same procedure, from the measured O₂ concentration (O_2measured), E can be found, as shown in Eq. 19:

                                (19)

In Eq. 19, HV can be the low-combustion value (LHV) of CH₄ or the high combustion value (HHV) of CH₄, which is determined by the condensation of water vapor in the tail flame. The authors suggest using the LHV because it is assumed that the measurement is conducted before the water condensation,¹⁹ resulting in Eq. 20:

                                  (20)

It is known that 1 hr = 3,600 sec, and 1 joule/sec = 1 W. If pressure is assumed at 1 atm and temperature is assumed at 20°C (293K), and if X = 1.25 qx mg/m³ is used, then Eqs. 21 and 22 can be calculated:

E = (0.125x)q ÷ CO_2measured mg/kWh                                                    (21)

                                                  (22)

Here, q = M_NOx ÷ M_NO.

For propane (C₃H₈) combustion, the reaction shown in Eq. 23 occurs:

      C₃H₈ + 5O₂ = 3CO₂ + 4H₂O                                                            (23)

If the reaction or combustion occurs in air, then the reaction shown in Eq. 24 occurs:

      C₃H₈ + 5(O₂ + 3.77N₂) = 3CO₂ + 4H₂O + 18.85N₂                                  (24)

Using the same procedure as that for methane and taking the LHV of propane,¹⁹ LHV = 25.9kWh, Eqs. 25 and 26 are calculated as follows:

                                                         (25)

   

      E = 1.25xq[1 + 4.77O_2measured / (1 – 4.77O_2measured)]                           (26)

Here, q = M_NOx ÷ M_NO.

In recent years, to eliminate emissions of NO_X to the environment, countries around the world have been developing low-NO_X combustion technologies.^4,5,20,21,22 NO_X emissions reduction is important for decreasing the level of NO_X released into the atmosphere by combustion activities. When NO_X reduction strategies are used, the ratio of NO to NO₂ may change, and so the traditional calculation of NO₂ content accounting for 5% of NO_X can no longer be used.

At present, the value of NO₂ can be even greater than 50% of the total NO_X emission. In this scenario, it is important not only to accurately measure the value of NO, but also to accurately measure the amount of NO₂. Additionally, since NO₂ is very soluble in water, if condensation of water vapor occurs in the exhaust smoke, as much as 50% of NO₂ will be dissolved into the condensed water from the gas phase, which greatly affects the reading. Therefore, it is necessary to ensure that water vapor does not condense during the measurement.

Takeaway. This article summarizes the conversion method between ppm and mg/m³ presently used in the engineering world. It also explains the development of a method to calculate NO_X in mg/kWh from combustion systems that use methane or propane as fuel. This method can be used to calculate emissions of other pollutants, such as CO and SO₂. GP

LITERATURE CITED

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7. Ministry of Housing and Urban-Rural Development (MOHURD), Urban Construction Industry Standard of People’s Republic of China, “Gas bred space heaters,” CJ/T113-2015, January 2015.
8.  UK Standard, “Single burner gas-fired overhead radiant tube heaters for nondomestic use, Part 1: Safety,” BSEN 416-1:2009, April 2009; Updated version: BSEN 416:2019, “Gas-fired overhead radiant tube heaters and radiant tube heater systems for non-domestic use: Safety and energy efficiency,” November 2019.
9. Testo, “Flue gas analysis in industry: Practical guide for emission and process measurements,” 2nd Ed., August 2004, online: http://dl.icdst.org/pdfs/files3/d3633ea5fcec7d6010dd38a8e5ef91fa.pdf
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LING LIU has 7 yr of working experience in combustion and mechanical design. She has participated in the research and development of negative-pressure gas infrared radiant heaters, positive-pressure gas infrared radiant heaters, indirect-fired gas heaters and direct-fired gas heaters at Sunree Technology Development Co. Ltd. in Dalian, China. She holds a BS degree in building environment and equipment engineering from Southwest Jiaotong University in China.

 

 

 

MAO-SONG LI has 11 yr of working experience in thermodynamics, combustion and mechanical design. He formerly supervised the laboratory of Dalian Jinsanwei Technology Co. Ltd. and managed the R&D department of Sunree Technology Development Co. Ltd. During his 7 yr at Sunree, he participated in the design and testing of negative-pressure gas infrared radiant heaters, positive-pressure gas infrared radiant heaters, indirect-fired gas heaters, and direct-fired gas heaters. Mr. Li holds a BS degree from Zhengzhou Institute of Light Industry in China and an MS degree in power engineering and engineering thermophysics from Xi’an Jiaotong University in China.