Calculation of combustion gas ¯ow rate and residence time based on
Calculation of combustion gas ¯ow rate and residence time based on
stack gas data
stack gas data
Anth
Anthony R. Eic
ony R. Eicher
her *
*
Focus Environmental, Inc., 9050 Executive Park Drive, Suite A-202, Knoxville, Tennessee, USA Focus Environmental, Inc., 9050 Executive Park Drive, Suite A-202, Knoxville, Tennessee, USA
Accepted 6 December 1999 Accepted 6 December 1999
Abstract Abstract
In many situations, it is desired to estimate the combustion chamber gas residence time of operating combustion systems. This is In many situations, it is desired to estimate the combustion chamber gas residence time of operating combustion systems. This is typically accomplished by performing a mass and energy balance around the combustion chamber. Unfortunately, the detailed typically 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, euents, and combustion gases are often not physical, chemical, and thermodynamic data needed for each of the feed streams, euents, and combustion gases are often not readily available. Further, a rigorous mass and energy balance calculation can be time-consuming unless a computerized routine is readily available. Further, a rigorous mass and energy balance calculation can be time-consuming unless a computerized routine is available. It is possible, however, to calculate the combustion gas ¯ow rate and the gas phase residence time of a combustion available. It is possible, however, to calculate the combustion gas ¯ow rate and the gas phase residence time of a combustion chamber when only
chamber when only stack gas data stack gas data and the and the combustcombustion chamber temperaturion chamber temperature are e are availaavailable. The ble. The technitechnique presented is que presented is applicaapplicable toble to systems that incorporate adiabatic saturation cooling of the ¯ue gas using direct water evaporation in a quench chamber or similar systems that incorporate adiabatic saturation cooling of the ¯ue gas using direct water evaporation in a quench chamber or similar device. The technique can be extended to systems in which adiabatic saturation cooling is not achieved (i.e. partial quenching) or device. The technique can be extended to systems in which adiabatic saturation cooling is not achieved (i.e. partial quenching) or those systems incorporating external heat removal (i.e. boilers, indirect scrubber water cooling, etc.). The procedure for determining those systems incorporating external heat removal (i.e. boilers, indirect scrubber water cooling, etc.). The procedure for determining the combustion chamb
the combustion chamber ¯ow er ¯ow rate utilizerate utilizes the concept of s the concept of a mass and a mass and energy balancenergy balance (in a e (in a simpli®esimpli®ed form) to d form) to relate stacrelate stack gas k gas data todata to combustion chamber conditions. In the case of a system using adiabatic saturation cooling, the energy in the hot combustion gas is combustion chamber conditions. In the case of a system using adiabatic saturation cooling, the energy in the hot combustion gas is used to directly evaporate water sprayed into the combustion gas stream. The temperature of the combined combustion gas and used to directly evaporate water sprayed into the combustion gas stream. The temperature of the combined combustion gas and water vapor stream decrease
water vapor stream decreases as s as energy (expreenergy (expressed as ssed as sensiblsensible heat e heat and heat of and heat of vaporizvaporization) is transferred from the ation) is transferred from the combustcombustion gasion gas to the water. This temperature decrease reaches a practical limit when the combustion gas stream becomes saturated with water (the to the water. This temperature decrease reaches a practical limit when the combustion gas stream becomes saturated with water (the adiabatic saturation temperature). Therefore, assuming that there is negligible leakage of air into the system, the mass of stack gas adiabatic 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 combustion is equal to the mass of combustion gas plus the amount of water added for cooling. Further, since the water vapor and combustion gas are combined, no energy has left the system, thus the total enthalpy of the cooled stack gas stream is equal to the total enthalpy gas are combined, no energy has left the system, thus the total enthalpy of the cooled stack gas stream is equal to the total enthalpy of the
of the hot combustion gas stream. A simpli®ed mass hot combustion gas stream. A simpli®ed mass and energy balance is used and energy balance is used to determine the moisture added to the to determine the moisture added to the combustcombustionion gas stream for cooling, and then the mass ¯ow rate of combustion gas is determined by subtracting this amount of moisture from gas stream for cooling, and then the mass ¯ow rate of combustion gas is determined by subtracting this amount of moisture from the measured stack gas mass ¯ow rate. The paper describes the theory behind this calculation technique, presents the formulas the measured stack gas mass ¯ow rate. The paper describes the theory behind this calculation technique, presents the formulas needed to perform the calculations, discusses the sensitivity of the calculations to errors in the assumptions used and the data needed to perform the calculations, discusses the sensitivity of the calculations to errors in the assumptions used and the data measure
measurements, and describes how the ments, and describes how the technitechnique can que can be extended to systems which achieve cooling of be extended to systems which achieve cooling of the combustion gases throughthe combustion gases through means other
means other than adiabatic saturation.than adiabatic saturation.##2000 Elsevier Science Ltd. All rights reserved.2000 Elsevier Science Ltd. All rights reserved. Keywords:
Keywords:Combustion gas ¯ow rate; Adiabatic saturation; Calculations; Stack gasCombustion gas ¯ow rate; Adiabatic saturation; Calculations; Stack gas
1.
1. IntrodIntroductionuction
In many situations, it is desired to estimate the In many situations, it is desired to estimate the bustion chamber gas residence time of operating bustion chamber gas residence time of operating com-bu
buststioion n sysyststemems. s. ThThis is is is tytypipicacalllly y acaccocompmplilishshed ed byby pe
perfrformormining g a a mamass ss anand d enenerergy gy babalalancnce e ararouound nd ththee combustion chamber. Unfortunately, the detailed combustion chamber. Unfortunately, the detailed phy-sic
sical, al, chechemicmical, al, and and thethermormodyndynamiamic c datdata a neeneeded ded forfor each of the feed streams, euents, and combustion gases each of the feed streams, euents, and combustion gases are often not readily available. Further, a rigorous mass are often not readily available. Further, a rigorous mass
and
and energenergy y balanbalance ce calcucalculatiolation n can can be be timetime-consu-consumingming unless a computerized routine is available. It is possible, unless a computerized routine is available. It is possible, however, to calculate the combustion gas ¯ow rate and however, to calculate the combustion gas ¯ow rate and the gas phase residence time of a combustion chamber the gas phase residence time of a combustion chamber when only stack gas data and the combustion chamber when only stack gas data and the combustion chamber temperature are available.
temperature are available. Th
The e prproceocedudure re fofor r dedetetermrmininining g ththe e cocombmbusustitionon chamber ¯ow rate utilizes the concept of a mass and chamber ¯ow rate utilizes the concept of a mass and energy balance (in a simpli®ed form) to relate stack gas energy balance (in a simpli®ed form) to relate stack gas data to combustion chamber conditions. In the case of a data to combustion chamber conditions. In the case of a system using adiabatic saturatio
system using adiabatic saturation n coolicooling, the ng, the energenergy y inin the hot
the hot comcombusbustiotion n gas is gas is useused d to to dirdirectlectly y evaevaporporateate wat
water er sprsprayeayed d intinto o the the comcombusbustiotion n gas gas strstreameam. . TheThe
0956-053X/00/$ - see front matter
0956-053X/00/$ - see front matter##2000 Elsevier Science Ltd. All rights reserved.2000 Elsevier Science Ltd. All rights reserved. P I I : S 0 9 5 6 - 0 5 3 X ( 9 9 ) 0 0 3 4 2 - 6
P I I : S 0 9 5 6 - 0 5 3 X ( 9 9 ) 0 0 3 4 2 - 6
www.elsevier.nl/locate/wasman www.elsevier.nl/locate/wasman
*
* Tel.: +1-865-694Tel.: +1-865-694-7517; fax: +1-865-531-8-7517; fax: +1-865-531-8854.854. E-mail address:
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 gas to the water. This temperature decrease reaches a practical limit when the combustion gas stream becomes saturated with water (the adiabatic 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 combustion gas are combined, no energy has left the system, thus the total enthalpy of the cooled stack gas stream is equal to the total enthalpy of 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 com-bustion gas is determined by subtracting this amount of moisture from the measured stack gas mass ¯ow rate.
2. Basis and assumptions
The following data requirements and assumptions are needed 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 stack gas sampling point is suciently small that it can be ignored.
5. Heat losses from devices between the combustion chamber temperature measurement point and the stack gas sampling point are suciently small that they can be ignored.
6. The volume of gaseous contaminants removed in the air 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 high
temperature psychrometric data, assuming that stack gas behaves like air. This is a typical assumption made in EPA stack sampling methods where the measured stack gas moisture content is compared to the theoretical saturation moisture content.
8. Standard conditions are 0C (32F), and 101.325 kPa (1 standard atmosphere) pressure. These speci®c
conditions are commonly referred to as ``normal conditions'' and are designated by the pre®x letter ``N'' (e.g. Nm3
is normal cubic meters). (Constants used in the equations can be changed for other standard conditions.)
3. Calculation method
If any air in®ltration between the combustion cham-ber temperature measurement point and the stack gas sampling point can be ignored, then the dry stack gas mass ¯ow rate is equal to the dry combustion gas mass ¯ow rate.
Determine the dry stack gas mass ¯ow rate:
mXsd
Qsd M d
22X4 I
where:
mXsd = Stack gas dry mass ¯ow rate (kg/h).
Qsd = Stack gas dry volumetric ¯ow rate (Nm3/h, dry).
M d = Stack gas dry molecular weight (kg/kg mol).
The factor 22.4 is used to convert mass to volume, and is in units of (Nm3
/kg mole).
Determine the total stack gas enthalpy:
H st mXsd  hs P
where:
H st = Enthalpy of wet stack gas (J/h) (total enthalpy).
mXsd = 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:
H sd mXsd h Q
where:
H sd = Enthalpy of dry stack gas (J/h).
mXsd = Stack gas dry mass ¯ow rate (kg/h).
h = 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 of dry combustion gas, the enthalpy of the dry combustion gas can be determined from the ¯ow rate of dry stack gas and the temperature dierence between the com-bustion gas and the stack gas, as follows:
where:
H d = Enthalpy of dry combustion gas (J/h).
H sd = Enthalpy of dry stack gas (J/h).
mXsd = Stack gas dry mass ¯ow rate (kg/h).
C p = Combustion gas heat capacity (J/kg-C).
T = Combustion gas temperature (C).
T s = Stack gas temperature (C).
Since the total enthalpy of the combustion gas is equal to the total enthalpy of the stack gas, the dier-ence between the calculated dry combustion gas enthalpy (from Eq. 4) and the calculated total stack gas enthalpy (from Eq. 2) must be attributed to water vapor in the combustion gas. Thus, the amount of water vapor in the combustion gas can be determined as follows: H w H st À H d S
where:
H w = Enthalpy of water vapor in the combustion gas
(J/h).
H st = Enthalpy of wet stack gas (J/h) (total enthalpy).
H d = Enthalpy of dry combustion gas (J/h).
mXw
H w
hw
T
where:
mXw=Mass ¯ow rate of water vapor in combustion gas
(kg/h).
H w=Enthalpy of water vapor in the combustion gas
(J/h).
hw=Unit enthalpy of water vapor (superheated steam)
at combustion gas temperature (J/kg).
As stated earlier, the mass ¯ow rate of dry stack gas is equal to the mass ¯ow rate of dry combustion gas. Thus, the total combustion gas mass ¯ow rate is equal to the sum of the dry gas mass ¯ow rate plus the mass ¯ow rate of water vapor in the combustion gas:
mX mXsd mXw U
where:
mX = Total combustion gas mass ¯ow rate (kg/h).
mXsd= Stack gas dry mass ¯ow rate (kg/h).
mXw = 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:
Q std Qsd mXwÂ22X4 M w
!
V where:Q std = Total combustion gas volumetric ¯ow rate at
normal conditions (Nm3
/h).
M w = Molecular weight of water (18 kg/kg mol).
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:
Q Q std  T 273 T std273
!
 Pstd P
!
W where:Q = Total combustion gas volumetric ¯ow rate at
combustion chamber conditions (m3
/h). Q std = Total combustion gas volumetric ¯ow rate at
normal conditions (Nm3
/h).
T = Combustion gas temperature (C).
T std = Standard temperature (C).
Pstd = Standard pressure (absolute).
P = Combustion gas pressure (absolute).
Finally, the combustion chamber gas residence time can be determined as follows:
V Â3600
Q
IH
where:
= Combustion chamber gas residence time (s). V = Combustion chamber useful volume (m3).
Q = 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 several assumptions. The impact of these assumptions on the calculations is discussed below:
4.1. Ignoring air in®ltration
The most important assumption is that the in®ltration of air between the combustion chamber temperature measurement point and the stack gas sampling point is small enough that it can be ignored. The calculations
are based on the assumption that the mass of dry gas exiting the stack is equal to the mass of dry gas exiting the combustion chamber. If air were to leak into the system 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 of combustion 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 the actual combustion gas ¯ow rate, and under-predict the combustion chamber residence time. The magnitude of the error is equal to the ratio of the air in®ltration rate to the total stack gas ¯ow rate. Most systems are expected to be operated under negative pressure and will experience some air in®ltration, therefore, the cal-culations will be likely to yield conservative results in most 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 valid since it is virtually impossible for air to leak into a sys-tem under positive pressure. However, if there are areas where gases can leak out of the positive pressure system, the calculations will under-predict the combustion gas ¯ow and will over-predict the combustion chamber residence time. Normally, leakage from positive pres-sure systems can be readily seen and corrected, thus ignoring any change in the mass of dry gas between the combustion 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 an energy balance. Thus, ignoring the heat loss may have an impact on the energy balance portions of the calcu-lation, just as ignoring air in®ltration may have an impact on the mass balance portions of the calculation. The assumption of adiabatic cooling is commonly used for wet gas quenching and wet scrubbing systems. As long as the combustion gas enters the adiabatic cooling device relatively quickly after leaving the combustion chamber (i.e. there are no long runs of hot gas ducting between the combustion chamber and the quench chamber) then ignoring heat losses should be reason-able. Heat loss from the devices carrying the cooled gases will be very low. The impact of heat losses between the combustion chamber and the stack is to under-predict the combustion gas ¯ow rate and over-predict the combustion chamber residence time. This occurs since the calculations use the dierence between the total enthalpy of the stack gas and the dry gas enthalpy of the combustion gas to determine the amount 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 combustion gas. The magnitude of possible eects resulting from ignoring heat losses is proportional to the true moisture content of the combustion gas, with higher moisture content combustion gases showing greater potential impact. In an eort to quantify the magnitude of error potentially introduced by ignoring heat losses, calcula-tions were performed for a combustion gas with no heat loss, and for the same combustion gas experiencing a 20% heat loss between the combustion chamber exit and the stack (this is an extremely high heat loss for a cooled gas at 80±85C). In this case, the loss of 20% of the total enthalpy of the gas between the combustion chamber and the stack resulted in an approximately 10% decrease in the calculated combustion gas ¯ow rate.
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 the heat loss or heat removal can be quanti®ed. For exam-ple, the enthalpy of the steam produced in a boiler represents the heat removal from the combustion gas. If the heat loss or heat removal can be quanti®ed, then the calculations presented earlier can be used if that heat is added back to the dry combustion gas enthalpy prior to the calculation of the combustion gas moisture content. This approach is valid as long as the heat loss or heat removal experienced in the system does not result in the condensation of moisture from the combustion gas.
4.3. Assuming stack gas is saturated
The calculations, as presented, assume that the stack gas is saturated with moisture at the measured stack gas temperature. This is a valid assumption for many sys-tems utilizing adiabatic quenching and wet scrubbers. In fact, EPA stack sampling methods utilize this same assumption for high moisture content stack gases. In the case where the measured stack gas moisture content is not at the theoretical saturation value, the calculations can be modi®ed by using psychrometric data for an unsaturated gas rather than the saturated gas data, or by using absolute humidity relationships.
Since the basic set of equations presented earlier in the paper assume saturated stack gas conditions, they will over-predict the total stack gas enthalpy if the stack gas actually contains less moisture than would be present at saturation. This, in turn, will over-predict the amount of moisture present in the combustion chamber, and sub-sequently will also over-predict the volumetric ¯ow rate in 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 true if the stack gas contains more moisture than would be
present at saturation. The calculations can be modi®ed, as described in the next several paragraphs, to account for non-saturation using absolute humidity relation-ships.
Part of the isokinetic stack sampling eort is to determine the stack gas moisture content, which is typi-cally reported in terms of volume percent moisture. This value can be expressed in terms of stack gas moisture ¯ow rate as follows:
mXws Qsd 1 ÀBws 100 À Qsd
H
f
d
I
g
e
 1 kgÁmol 22X4 xm3 M w II where:mXws= 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 %).
M w = Molecular weight of water (18 kg/kg mol).
The measured moisture content of the stack gas can then be compared to the theoretical moisture present at saturation using additional psychrometric data as fol-lows: t m X wsamXsd hum IP where:
t =Fraction of saturation moisture in actual stack gas (dimensionless).
mXws =Mass ¯ow rate of water vapor in stack gas (kg/h).
mXsd =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 gas due to non-saturated conditions can then be determined as:
Áh h sÀ h  1 À t IQ
where:
Áh=Error in unit enthalpy of wet stack gas due to non-saturation (J/kg dry gas).
hs =Unit enthalpy of saturated stack gas (J/kg dry gas)
from psychrometric data.
h =Unit enthalpy of dry stack gas (J/kg dry gas) from
psychometric data.
t=Fraction of saturation moisture in actual stack gas (dimensionless).
The error is then corrected in the calculation of total stack gas enthalpy by modifying Eq. 2 as follows:
H st mXsd  h sÀ Áh IR
Where:
H st = Enthalpy of wet stack gas (J/h) (total enthalpy).
mXsd = Stack gas dry mass ¯ow rate (kg/h).
hs = Unit enthalpy of saturated stack gas (J/kg dry
gas) from psychometric data.
Áh = Error in unit enthalpy of wet stack gas due to non-saturation (J/kg dry gas).
All remaining calculations are performed as discussed earlier in the paper using the total enthalpy value determined using the adjusted unit wet gas enthalpy as shown in Eq. 14.
4.4. Assuming gaseous component removal is not signi®cant
Since the calculations use a mass balance which is based on the assumption that the mass of dry gas exit-ing the stack is equal to the mass of dry gas exitexit-ing the combustion chamber, the removal of gaseous compo-nents from the combustion gas stream will reduce the measured stack gas volume, and thus the calculated combustion gas volume. For example, an incinerator burning an extremely high chlorine content liquid waste as 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 scrubbing system, the volume of gas decreases in proportion to the number of moles of hydrogen chloride removed. For most systems, this issue is not of concern, but if the situation arises, corrections must be made.
5. Conclusions
This paper has presented a technique to calculate the combustion gas ¯ow rate and the combustion chamber gas residence time when only stack gas data and the combus-tion chamber temperature are available. The technique presented is applicable to systems that incorporate adiabatic saturation cooling of the ¯ue gas using direct water evaporation in a quench chamber or similar device. The technique can be extended to systems in which adiabatic saturation cooling is not achieved (i.e. partial quenching) or those systems incorporating external heat removal (i.e. boilers, indirect scrubber water cooling, etc.). A discussion of assumptions has been presented which shows that under the most likely conditions, this technique is reason-able and is likely to yield conservative results (generally over-prediction of combustion gas ¯ow rate and under-prediction of combustion chamber gas residence time).
