Calculation of combustion gas ¯ow rate and residence time based onstack gas data

Anthony R. Eicher *

Focus Environmental, Inc., 9050 Executive Park Drive, Suite A-202, Knoxville, Tennessee, USA

Accepted 6 December 1999

Abstract

In many situations, it is desired to estimate the combustion chamber gas residence time of operating combustion systems. This istypically accomplished by performing a mass and energy balance around the combustion chamber. Unfortunately, the detailed

physical, chemical, and thermodynamic data needed for each of the feed streams, e�uents, and combustion gases are often notreadily available. Further, a rigorous mass and energy balance calculation can be time-consuming unless a computerized routine isavailable. It is possible, however, to calculate the combustion gas ¯ow rate and the gas phase residence time of a combustion

chamber when only stack gas data and the combustion chamber temperature are available. The technique presented is applicable tosystems that incorporate adiabatic saturation cooling of the ¯ue gas using direct water evaporation in a quench chamber or similardevice. The technique can be extended to systems in which adiabatic saturation cooling is not achieved (i.e. partial quenching) orthose systems incorporating external heat removal (i.e. boilers, indirect scrubber water cooling, etc.). The procedure for determining

the combustion chamber ¯ow rate utilizes the concept of a mass and energy balance (in a simpli®ed form) to relate stack gas data tocombustion chamber conditions. In the case of a system using adiabatic saturation cooling, the energy in the hot combustion gas isused to directly evaporate water sprayed into the combustion gas stream. The temperature of the combined combustion gas and

water vapor stream decreases as energy (expressed as sensible heat and heat of vaporization) is transferred from the combustion gasto the water. This temperature decrease reaches a practical limit when the combustion gas stream becomes saturated with water (theadiabatic saturation temperature). Therefore, assuming that there is negligible leakage of air into the system, the mass of stack gas

is equal to the mass of combustion gas plus the amount of water added for cooling. Further, since the water vapor and combustiongas are combined, no energy has left the system, thus the total enthalpy of the cooled stack gas stream is equal to the total enthalpyof the hot combustion gas stream. A simpli®ed mass and energy balance is used to determine the moisture added to the combustion

gas stream for cooling, and then the mass ¯ow rate of combustion gas is determined by subtracting this amount of moisture fromthe measured stack gas mass ¯ow rate. The paper describes the theory behind this calculation technique, presents the formulasneeded to perform the calculations, discusses the sensitivity of the calculations to errors in the assumptions used and the datameasurements, and describes how the technique can be extended to systems which achieve cooling of the combustion gases through

means other than adiabatic saturation. # 2000 Elsevier Science Ltd. All rights reserved.

Keywords: Combustion gas ¯ow rate; Adiabatic saturation; Calculations; Stack gas

1. Introduction

In many situations, it is desired to estimate the com-bustion chamber gas residence time of operating com-bustion systems. This is typically accomplished byperforming a mass and energy balance around thecombustion chamber. Unfortunately, the detailed phy-sical, chemical, and thermodynamic data needed foreach of the feed streams, e�uents, and combustion gasesare often not readily available. Further, a rigorous mass

and energy balance calculation can be time-consumingunless a computerized routine is available. It is possible,however, to calculate the combustion gas ¯ow rate andthe gas phase residence time of a combustion chamberwhen only stack gas data and the combustion chambertemperature are available.The procedure for determining the combustion

chamber ¯ow rate utilizes the concept of a mass andenergy balance (in a simpli®ed form) to relate stack gasdata to combustion chamber conditions. In the case of asystem using adiabatic saturation cooling, the energy inthe hot combustion gas is used to directly evaporatewater sprayed into the combustion gas stream. The

0956-053X/00/$ - see front matter # 2000 Elsevier Science Ltd. All rights reserved.

PI I : S0956-053X(99 )00342-6

Waste Management 20 (2000) 403±407

www.elsevier.nl/locate/wasman

* Tel.: +1-865-694-7517; fax: +1-865-531-8854.

E-mail address: areicher@focusenv.com (A.R. Eicher).

temperature of the combined combustion gas and watervapor stream decreases as energy (expressed as sensibleheat and heat of vaporization) is transferred from thecombustion gas to the water. This temperature decreasereaches a practical limit when the combustion gasstream becomes saturated with water (the adiabaticsaturation temperature). Therefore, assuming that thereis negligible leakage of air into the system, the mass ofstack gas is equal to the mass of combustion gas plusthe amount of water added for cooling. Further, sincethe water vapor and combustion gas are combined, noenergy has left the system, thus the total enthalpy of thecooled stack gas stream is equal to the total enthalpy ofthe hot combustion gas stream.A simpli®ed mass and energy balance is used to

determine the moisture added to the combustion gasstream for cooling, and then the mass ¯ow rate of com-bustion gas is determined by subtracting this amount ofmoisture from the measured stack gas mass ¯ow rate.

2. Basis and assumptions

The following data requirements and assumptions areneeded to use the technique presented.

1. The following stack gas data must be available(typically determined in any measurement pro-gram where stack gas particulate matter is col-lected isokinetically):� Stack gas ¯ow rate (dry, standard conditions).� Stack gas temperature.� Stack gas moisture content.� Stack gas dry molecular weight.

2. Combustion gas temperature is known.3. Stack gas is saturated with moisture at the mea-

sured stack gas temperature.4. In®ltration of air between the combustion cham-

ber temperature measurement point and the stackgas sampling point is su�ciently small that it canbe ignored.

5. Heat losses from devices between the combustionchamber temperature measurement point and thestack gas sampling point are su�ciently small thatthey can be ignored.

6. The volume of gaseous contaminants removed in theair pollution control system is not signi®cant in rela-tion to the total volume of gas entering the system.

7. The stack gas enthalpy can be determined from hightemperature psychrometric data, assuming that stackgas behaves like air. This is a typical assumptionmade in EPA stack sampling methods where themeasured stack gas moisture content is compared tothe theoretical saturation moisture content.

8. Standard conditions are 0�C (32�F), and 101.325kPa (1 standard atmosphere) pressure. These speci®c

conditions are commonly referred to as ``normalconditions'' and are designated by the pre®x letter``N'' (e.g. Nm3 is normal cubic meters). (Constantsused in the equations can be changed for otherstandard conditions.)

3. Calculation method

If any air in®ltration between the combustion cham-ber temperature measurement point and the stack gassampling point can be ignored, then the dry stack gasmass ¯ow rate is equal to the dry combustion gas mass¯ow rate.Determine the dry stack gas mass ¯ow rate:

m:

sd � Qsd �Md

22:4�1�

where:

m:

sd = Stack gas dry mass ¯ow rate (kg/h).Qsd = Stack gas dry volumetric ¯ow rate (Nm3/h, dry).Md = Stack gas dry molecular weight (kg/kgmol).

The factor 22.4 is used to convert mass to volume,and is in units of (Nm3/kgmole).Determine the total stack gas enthalpy:

Hst � m:

sd � hs �2�

where:

Hst = Enthalpy of wet stack gas (J/h) (total enthalpy).m:

sd = Stack gas dry mass ¯ow rate (kg/h).hs = Unit enthalpy of saturated stack gas (J/kg dry

gas) from psychrometric data.

Determine the dry stack gas enthalpy:

Hsd � m:

sd � ha �3�

where:

Hsd = Enthalpy of dry stack gas (J/h).m:

sd = Stack gas dry mass ¯ow rate (kg/h).ha = Unit enthalpy of dry stack gas (J/kg dry gas)

from psychrometric data.

Since the mass of dry stack gas is equal to the mass ofdry combustion gas, the enthalpy of the dry combustiongas can be determined from the ¯ow rate of dry stackgas and the temperature di�erence between the com-bustion gas and the stack gas, as follows:

Hcd � Hsd � bm: sd � Cpc � Tc ÿ Ts� �c �4�

404 A.R. Eicher /Waste Management 20 (2000) 403±407

where:

Hcd = Enthalpy of dry combustion gas (J/h).Hsd = Enthalpy of dry stack gas (J/h).m:

sd = Stack gas dry mass ¯ow rate (kg/h).Cpc = Combustion gas heat capacity (J/kg-�C).Tc = Combustion gas temperature (�C).Ts = Stack gas temperature (�C).

Since the total enthalpy of the combustion gas isequal to the total enthalpy of the stack gas, the di�er-ence between the calculated dry combustion gasenthalpy (from Eq. 4) and the calculated total stack gasenthalpy (from Eq. 2) must be attributed to water vaporin the combustion gas. Thus, the amount of water vaporin the combustion gas can be determined as follows:

Hw � Hst ÿHcd �5�

where:

Hw = Enthalpy of water vapor in the combustion gas(J/h).

Hst = Enthalpy of wet stack gas (J/h) (total enthalpy).Hcd = Enthalpy of dry combustion gas (J/h).

m:

w � Hw

hwc�6�

where:

m:

w=Mass ¯ow rate of water vapor in combustion gas(kg/h).

Hw=Enthalpy of water vapor in the combustion gas(J/h).

hwc=Unit enthalpy of water vapor (superheated steam)at combustion gas temperature (J/kg).

As stated earlier, the mass ¯ow rate of dry stack gas isequal to the mass ¯ow rate of dry combustion gas.Thus, the total combustion gas mass ¯ow rate is equalto the sum of the dry gas mass ¯ow rate plus the mass¯ow rate of water vapor in the combustion gas:

m:

c � m:

sd �m:

w �7�

where:

m:

c =Total combustion gas mass ¯ow rate (kg/h).m:

sd =Stack gas dry mass ¯ow rate (kg/h).m:

w =Mass ¯ow rate of water vapor in combustion gas(kg/h).

The total volumetric ¯ow rate of the combustion gas,at normal conditions, is determined as:

Qc std� � � Qsd � m:

w � 22:4

Mw

� ��8�

where:

Qc std� � = Total combustion gas volumetric ¯ow rate atnormal conditions (Nm3/h).

Mw = Molecular weight of water (18 kg/kgmol).

The factor 22.4 is used to convert mass to volume,and is in units of (Nm3/kg-mol).The total volumetric ¯ow rate of combustion gas, at

combustion chamber conditions, is determined as:

Qc � Qc std� � � Tc � 273� �Tstd � 273� �

� �� Pstd

Pc

� ��9�

where:

Qc = Total combustion gas volumetric ¯ow rate atcombustion chamber conditions (m3/h).

Qc std� � = Total combustion gas volumetric ¯ow rate atnormal conditions (Nm3/h).

Tc = Combustion gas temperature (�C).Tstd = Standard temperature (�C).Pstd = Standard pressure (absolute).Pc = Combustion gas pressure (absolute).

Finally, the combustion chamber gas residence timecan be determined as follows:

�c � Vc � 3600

Qc�10�

where:

�c = Combustion chamber gas residence time (s).Vc = Combustion chamber useful volume (m3).Qc = Total combustion gas volumetric ¯ow rate at

combustion chamber conditions (m3/h).

The value of 3600 is the number of seconds per hour.

4. Discussion of assumptions

As noted earlier, the calculations are based on severalassumptions. The impact of these assumptions on thecalculations is discussed below:

4.1. Ignoring air in®ltration

The most important assumption is that the in®ltrationof air between the combustion chamber temperaturemeasurement point and the stack gas sampling point issmall enough that it can be ignored. The calculations

A.R. Eicher /Waste Management 20 (2000) 403±407 405

are based on the assumption that the mass of dry gasexiting the stack is equal to the mass of dry gas exitingthe combustion chamber. If air were to leak into thesystem between the combustion chamber and the stack,this air would be measured as part of the total stack gas¯ow and would then be included in the calculation ofcombustion gas ¯ow.For negative draft systems, where any leakage would

be into the system, the assumption of ignoring air in®l-tration is conservative, and tends to over-predict theactual combustion gas ¯ow rate, and under-predict thecombustion chamber residence time. The magnitude ofthe error is equal to the ratio of the air in®ltration rateto the total stack gas ¯ow rate. Most systems areexpected to be operated under negative pressure andwill experience some air in®ltration, therefore, the cal-culations will be likely to yield conservative results inmost cases. If air in®ltration is expected to be sig-ni®cant, appropriate corrections should be made.For systems under positive pressure, the assumption

that air in®ltration can be ignored is completely validsince it is virtually impossible for air to leak into a sys-tem under positive pressure. However, if there are areaswhere gases can leak out of the positive pressure system,the calculations will under-predict the combustion gas¯ow and will over-predict the combustion chamberresidence time. Normally, leakage from positive pres-sure systems can be readily seen and corrected, thusignoring any change in the mass of dry gas between thecombustion chamber and the stack is probably reason-able for most well maintained systems.

4.2. Ignoring heat losses

The calculations utilize both a mass balance and anenergy balance. Thus, ignoring the heat loss may havean impact on the energy balance portions of the calcu-lation, just as ignoring air in®ltration may have animpact on the mass balance portions of the calculation.The assumption of adiabatic cooling is commonly usedfor wet gas quenching and wet scrubbing systems. Aslong as the combustion gas enters the adiabatic coolingdevice relatively quickly after leaving the combustionchamber (i.e. there are no long runs of hot gas ductingbetween the combustion chamber and the quenchchamber) then ignoring heat losses should be reason-able. Heat loss from the devices carrying the cooledgases will be very low. The impact of heat lossesbetween the combustion chamber and the stack is tounder-predict the combustion gas ¯ow rate and over-predict the combustion chamber residence time. Thisoccurs since the calculations use the di�erence betweenthe total enthalpy of the stack gas and the dry gasenthalpy of the combustion gas to determine theamount of water vapor contained in the actual com-bustion gas. If the total stack gas enthalpy is lowered

through heat losses, then the calculations will under-predict the water vapor mass in the combustion gas,thus under-predicting the total ¯ow rate of combustiongas. The magnitude of possible e�ects resulting fromignoring heat losses is proportional to the true moisturecontent of the combustion gas, with higher moisturecontent combustion gases showing greater potentialimpact. In an e�ort to quantify the magnitude of errorpotentially introduced by ignoring heat losses, calcula-tions were performed for a combustion gas with no heatloss, and for the same combustion gas experiencing a20% heat loss between the combustion chamber exitand the stack (this is an extremely high heat loss for acooled gas at 80±85�C). In this case, the loss of 20% ofthe total enthalpy of the gas between the combustionchamber and the stack resulted in an approximately10% decrease in the calculated combustion gas ¯owrate.For systems with high heat losses, or those incorpor-

ating boilers or heat exchangers, the calculation techni-que presented can be extended to those systems if theheat loss or heat removal can be quanti®ed. For exam-ple, the enthalpy of the steam produced in a boilerrepresents the heat removal from the combustion gas. Ifthe heat loss or heat removal can be quanti®ed, then thecalculations presented earlier can be used if that heat isadded back to the dry combustion gas enthalpy prior tothe calculation of the combustion gas moisture content.This approach is valid as long as the heat loss or heatremoval experienced in the system does not result in thecondensation of moisture from the combustion gas.

4.3. Assuming stack gas is saturated

The calculations, as presented, assume that the stackgas is saturated with moisture at the measured stack gastemperature. This is a valid assumption for many sys-tems utilizing adiabatic quenching and wet scrubbers. Infact, EPA stack sampling methods utilize this sameassumption for high moisture content stack gases. In thecase where the measured stack gas moisture content isnot at the theoretical saturation value, the calculationscan be modi®ed by using psychrometric data for anunsaturated gas rather than the saturated gas data, orby using absolute humidity relationships.Since the basic set of equations presented earlier in the

paper assume saturated stack gas conditions, they willover-predict the total stack gas enthalpy if the stack gasactually contains less moisture than would be present atsaturation. This, in turn, will over-predict the amount ofmoisture present in the combustion chamber, and sub-sequently will also over-predict the volumetric ¯ow ratein the combustion chamber. The end result is to calcu-late a lower residence time than was actually experi-enced in the combustion chamber. The converse is trueif the stack gas contains more moisture than would be

406 A.R. Eicher /Waste Management 20 (2000) 403±407

present at saturation. The calculations can be modi®ed,as described in the next several paragraphs, to accountfor non-saturation using absolute humidity relation-ships.Part of the isokinetic stack sampling e�ort is to

determine the stack gas moisture content, which is typi-cally reported in terms of volume percent moisture. Thisvalue can be expressed in terms of stack gas moisture¯ow rate as follows:

m:

ws � Qsd

1ÿ Bws

100

ÿQsd

0B@1CA� 1 kg�mol

22:4 Nm3�Mw �11�

where:

m:

ws =Mass ¯ow rate of water in stack gas (kg/h).Qsd =Stack gas dry volumetric ¯ow rate (Nm3/h, dry).Bws =Stack gas moisture content (volume %).Mw =Molecular weight of water (18 kg/kgmol).

The measured moisture content of the stack gas canthen be compared to the theoretical moisture present atsaturation using additional psychrometric data as fol-lows:

Sat � m:

ws=m:

sd

hum�12�

where:

Sat =Fraction of saturation moisture in actual stackgas (dimensionless).

m:

ws =Mass ¯ow rate of water vapor in stack gas (kg/h).m:

sd =Stack gas dry mass ¯ow rate (kg/h).hum=Absolute humidity of saturated stack gas at

measured stack temperature (kg H2O/kg dry gas)from psychrometric data.

The error in unit enthalpy of the saturated stack gasdue to non-saturated conditions can then be determinedas:

�h � hs ÿ ha� � � 1ÿ Sat� � �13�

where:

�h=Error in unit enthalpy of wet stack gas due tonon-saturation (J/kg dry gas).

hs =Unit enthalpy of saturated stack gas (J/kg dry gas)from psychrometric data.

ha =Unit enthalpy of dry stack gas (J/kg dry gas) frompsychometric data.

Sat=Fraction of saturation moisture in actual stack gas(dimensionless).

The error is then corrected in the calculation of totalstack gas enthalpy by modifying Eq. 2 as follows:

Hst � m:

sd � hs ÿ�h� � �14�

Where:

Hst = Enthalpy of wet stack gas (J/h) (total enthalpy).m:

sd = Stack gas dry mass ¯ow rate (kg/h).hs = Unit enthalpy of saturated stack gas (J/kg dry

gas) from psychometric data.�h = Error in unit enthalpy of wet stack gas due to

non-saturation (J/kg dry gas).

All remaining calculations are performed as discussedearlier in the paper using the total enthalpy valuedetermined using the adjusted unit wet gas enthalpy asshown in Eq. 14.

4.4. Assuming gaseous component removal is not signi®cant

Since the calculations use a mass balance which isbased on the assumption that the mass of dry gas exit-ing the stack is equal to the mass of dry gas exiting thecombustion chamber, the removal of gaseous compo-nents from the combustion gas stream will reduce themeasured stack gas volume, and thus the calculatedcombustion gas volume. For example, an incineratorburning an extremely high chlorine content liquid wasteas the sole fuel, may produce a combustion gas con-taining a very high concentration of hydrogen chloride.When this hydrogen chloride is removed in a scrubbingsystem, the volume of gas decreases in proportion to thenumber of moles of hydrogen chloride removed. Formost systems, this issue is not of concern, but if thesituation arises, corrections must be made.

5. Conclusions

This paper has presented a technique to calculate thecombustion gas ¯ow rate and the combustion chamber gasresidence time when only stack gas data and the combus-tion chamber temperature are available. The techniquepresented is applicable to systems that incorporate adiabaticsaturation cooling of the ¯ue gas using direct waterevaporation in a quench chamber or similar device. Thetechnique can be extended to systems in which adiabaticsaturation cooling is not achieved (i.e. partial quenching)or those systems incorporating external heat removal (i.e.boilers, indirect scrubber water cooling, etc.). A discussionof assumptions has been presented which shows thatunder the most likely conditions, this technique is reason-able and is likely to yield conservative results (generallyover-prediction of combustion gas ¯ow rate and under-prediction of combustion chamber gas residence time).

A.R. Eicher /Waste Management 20 (2000) 403±407 407