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Cooper, Kim, and MacDonald
Volume 49 April 1999 Journal of the Air & Waste Management Association 4 7 1
ISSN 1047-3289J. Air & Waste Manage. Assoc.49:471-476
C o p yr i g h t 1 9 9 9 A i r & W a s t e M a n a g e me n t A s s oc i a t io n
T E C HN I C A L PA P E R
Estimating the Lower Heating Values of Hazardous andSolid Wastes
C. David Cooper, Brian Kim, and John MacDonald
Civil & Environmental Engineering Department, University of Central Florida, Orlando, Florida
ABSTRACT
A new equation is proposed to predict the lower heating
value of hazardous and non-hazardous materials. The
equation was developed by a statistical correlation of heat-
ing value and composition data for a variety of materials
as reported in a number of sources. The model takes intoaccount the carbon, hydrogen, oxygen, chlorine, and sul-
fur content of the material being combusted.
INTRODUCTION
The incineration of hazardous and solid wastes is an im-
portant technique for destroying and disposing of these
materials. Effective incineration achieves very high de-
struction and removal efficiencies of principal organic haz-
ardous constituents and minimizes the formation of prod-
ucts of incomplete combustion. Such performance re-
quires a sufficiently high temperature, a long enough resi-dence time, an excess of oxygen, and good turbulence in
the gases to promote completion of the oxidation reac-
tions to produce stable end products. In the design of the
combustion chamber and the afterburner, a good estimate
of the lower heating value (LHV) of the waste to be incin-
erated is important. However, in most instances, only the
higher heating value (HHV) of the waste is reported.
IMPLICATIONS
Prediction of heating values of hazardous and solid wastes,
and other hazardous and non-hazardous combustiblematerials, is important for several reasons, including com-
bustion analysis and the design of combustion equipment.
For mixtures of wastes, heating values often must be de-
termined experimentally, which may introduce questions
as to the accuracy of the testing and whether the sample
being tested is representative. Existing prediction correla-
tions either do not consider all the atoms often found in
hazardous waste, or have been based on data sets that
are too sparse. This paper presents a generalized equa-
tion developed from a diverse group of materials, which
performs well statistically and depends only on the ulti-
mate analysis. It is proposed for use on a variety of solid
or liquid materials.
The LHV is a better measure than the HHV of the heat
released by the waste under actual operating conditions.
The HHV is the gross heat released when a small sample of
the material is burned in a test calorimeter at a reference
temperature (usually 25 oC) and all products are in their
standard states at that temperature. The HHV includes theheat of condensation of water vapor formed in the com-
bustion reaction, which is not realistic for industrial com-
bustion equipment. The LHV is related to the HHV through
the heat of vaporization of water, as shown for methane:
CH4
+ 2 O2 CO
2+ 2 H
2O (liq) (1)
whereHHV= 212,800 cal/gmole CH4,
CH4
+ 2 O2 CO
2+ 2 H
2O (gas) (2)
whereLHV= HHV - 2*(Hv
of water) = 212,800 - 2*
10,519 = 191,762 cal/gmole CH4.
If the material burned contains chlorine, then HCl is
formed as a principal product of combustion and, by anal-
ogy, the HHV and LHV are related by the heats of vapor-
ization of both water and HCl.
In calculating the initial heat balance on an incinerator
to determine the amount of supplemental fuel required, the
usable heat released from the waste must be calculated. Us-
able heat can be defined as the LHV less the heat required to
vaporize any free water in the waste and adjusting for the
dilution effect of any noncombustible ash in the waste. For
design, the percent carbon combustion also must be taken
into account because small amounts of unburned carbon
usually remain in the ash. Likewise, heat losses through the
walls of the furnace must be subtracted. The remaining heat
is the net usable energy that is available to heat the combus-
tion gases and excess air. Thus, the LHV is needed to predict
the expected final temperature of the combustion gases.
Several methods have been used in the past to estimate
the HHV and LHV of wastes. Brunner1 cites DuLongs
approximation (which was developed for coal) as follows:
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Cooper, Kim, and MacDonald
4 7 2 Journal of the Air & Waste Management Association Volume 49 April 1999
HHV = 14,544 C + 62,028 (H - 0.125 O) + 4,050 S
(3)
whereHHVis in Btu/lb of waste, and C,H, O, and S are
the weight fractions in the waste of carbon, hydrogen,
oxygen and sulfur, respectively. Theodore and Reynolds2
report a modified form of DuLongs equation
LHV = 14,000 C + 45,000 (H - 0.125 O) -
760 Cl + 4,500 S (4)
whereLHVis in Btu/ lb of waste.
In eqs 3 and 4, the term (H - 0.125 O) reflects the
assumption that any oxygen in the waste will preferen-
tially combine with hydrogen in the waste in the mass
ratio of 8:1 to produce water and, thus, prevent that much
hydrogen from reacting with atmospheric oxygen. Pre-
sumably, this will avoid the exothermic effect (heat re-
leased by) that amount of hydrogen, if it had reacted withmolecular oxygen in the air.
Recently, Liu, Paode and Holsen3 reviewed several re-
lationships that have been applied to municipal solid wastes,
including ones based on physical composition, proximate
analysis, and ultimate analysis. They conducted a statisti-
cal step-wise multiple regression analysis to develop an equa-
tion for predicting the net calorific value of the municipal
solid waste from Kaohsiung City, Taiwan, and concluded
that their equation based on ultimate analysis was better
than previous models/methods. They included the ultimate
analysis parameters (C, H, O, N, S, and water) as possibleindependent variables to develop their final equation
Hn = 1,558.80 + 19.96 (%C) + 44.30 (%O) -
671.82 (%S) - 19.92 (%W) (5)
whereHn = net calorific value (kcal/kg of waste), and %C,
%O, %S, and %W= % by weight of carbon, oxygen, sul-
fur, and water, respectively.
One disadvantage of this result is that it is purely sta-
tistical and, therefore, may be appropriate only for the spe-
cific municipal waste studied. For example, it has no sepa-rate coefficient for hydrogen and a negative coefficient on
sulfur. The authors note that their finding of no significant
effect of hydrogen is in contrast to the results of DuLong
and others. Their waste was low in sulfur and, thus, the
negative sign did not affect the result significantly. How-
ever, the oxidation of sulfur is exothermic, so this runs
counter to expectations. Therefore, this equation cannot
be extended with confidence to other materials.
OBJECTIVES
This paper results from the interest and efforts of two stu-
dents in a graduate class at the University of Central
Florida (UCF) on hazardous waste incineration. After re-
viewing ways to estimate heating values of wastes as part
of the class, the conclusion was made that a better method
for predicting LHV of hazardous wastes was needed. Thus,
the authors set out to develop an equation based on ulti-
mate analysis that could be applied to a variety of hazard-
ous compounds. A secondary objective was to see if the
same equation could be made applicable to non-hazard-
ous materials as well, so the authors included a number
of non-hazardous materials in the database.
METHODOLOGY
Data Sources and Data Reduction
In conducting this work, data were gathered from several
sources on the reported heating values of two kinds of
materials. Twenty different hazardous compounds were
selected that contained various percentages of carbon,
hydrogen, chlorine, sulfur, oxygen, and nitrogen, as
shown in Table 1. Twenty different non-hazardous ma-terials were selected, again with an eye for diversity of
composition. Because data on non-hazardous solid
wastes were difficult to find, some data on coals and
other solid materials were included in the database, as
shown in Table 2.
The HHVs for the hazardous materials were re-
ported for pure compounds; the HHVs for the non-
hazardous materials were generally reported by the
original authors on an as-is basis, which includes
free water and ash. These HHVs first were adjusted from
an as-is basis to a dry, no-ash basis as follows:
HHVdna
= (HHVasis
)/(1- fw
- fash
) (6)
where fw
and fash
= mass fractions of free water and ash in
the waste, respectively. The LHVs were then calculated as
follows:
LHVdna
= HHVdna
- mwH
vw- m
HClH
vHCl(7)
where mw
= mass of water produced by combustion (lb
H2O/lb waste), mHCl = mass of HCl produced by combus-tion (lb HCl/lb waste), and H
v= heat of vaporization
[Btu/lb (1049 for water, 884 for HCl)].
The resulting LHVs of the hazardous and non-hazard-
ous compounds are shown in Tables 1 and 3, respectively.
In contrast to the non-hazardous materials (discussed in
the next two paragraphs), the data reduction for the haz-
ardous compounds was much simpler due to the fact that
each compound was essentially pure (without free water or
ash) and was represented by one chemical formula. In or-
der to provide for a more robust data set, 3 and 10 data
sources were used for the hazardous materials and non-haz-
ardous materials, respectively.
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Cooper, Kim, and MacDonald
Volume 49 April 1999 Journal of the Air & Waste Management Association 4 7 3
For the non-hazardous materials, assumptions some-
times were required when handling data from different
sources. In some cases, whether a reported heating valuewas the HHV or the LHV was not stated explicitly, but
from other comments in the text, the inference was that
the heating value was the HHV. When the authors were
unable to determine whether reported heating values
were for the as-received condition (including free water
and ash) or had been adjusted to a dry, no-ash basis, the
data were not used in this study.
The most difficult problem encountered in interpret-
ing the raw data was that many of the reported percent
compositions did not sum to 100%. (In the most severe
case, the constituents summed to 99.6%) How chlorine wasreported was a particular problem. Some sources listed chlo-
rine separately along with the major components (C, H, O,
N, and S). In other sources, the major constituents summed
to 100%, but percentages for certain trace elements (includ-
ing chlorine) were also reported. For the latter case, the
oxygen percentage was decreased by the reported chlorine
percentage. This was justified because oxygen content is
usually determined by difference. For those cases in which
chlorine was already listed as a major constituent, no ad-
justments could be made if the total did not add to 100%.
From these raw percentages, the percent water and ash were
subtracted to achieve raw dry, no-ash percentages for use
in determining the dry, no-ash HHV. However, for use in
the statistical modeling, the dry, no-ash composition was
normalized to 100%.
Statistical Treatment of Data
Numerous computer runs were made to try to correlate
the dry, no-ash LHVs of the materials to their composi-
tions. All statistical analyses were done using SAS.4 The
proposed models were formulated in two ways: as a no-
intercept model that included all the independent vari-
ables, or as intercept models leaving out nitrogen as an
independent variable. This reduced the potential infla-
tion of the variances due to collinearity. Collinearity ex-
ists because the independent variables are mass fractionsthat sum to 1.00.
The statistical modeling was conducted in several
ways. During the initial analysis, the hazardous com-
pounds were analyzed separately from the non-hazard-
ous materials data. Then the two data sets were combined
and analyzed as one data set. For each set of data, the
statistical treatment first produced a multiple regression
equation of the form:
LHVdna
= B1C + B
2H + B
3O + B
4S + B
5Cl + B
6N
(8)
or
Ta b le 1 . Hazardous compoundscomposition and heating values.
HHVa
% Wt. LHVa
Source
Compound Formula (Btu/lb) C H O N S Cl Total (Btu/lb) (Ref.)
Methylcyclohexane (l) C7H
1420,000 85.60 14.40 0.00 0.00 0.00 0.00 100.00 18,650 2
Benzene (l) C6H
617,990 92.24 7.76 0.00 0.00 0.00 0.00 100.00 17,270 2
DDT (l) C14H9Cl5 8,100 47.43 2.56 0.00 0.00 0.00 50.00 100.00 7,600 2Diallate (l) C
10H
17Cl
2NOS 10,120 44.44 6.35 5.92 5.18 11.86 26.24 100.00 9,357 5
Dimethyl carbamoyl chloride (l) C3H
6ClNO 9,140 33.50 5.63 14.88 13.03 0.00 32.96 100.00 8,400 5
3-Chloropropionitrile (l) C3H
4ClN 8,100 40.24 4.51 0.00 15.65 0.00 39.60 100.00 7,420 5
Endosulfan (s) C9H
6Cl
6O
3S 4,190 26.56 1.49 11.80 0.00 7.88 52.27 100.00 3,720 5
1-Acetyl-2-thiourea (s) C3H
6N
2OS 8,190 30.49 5.13 13.54 23.71 27.13 0.00 100.00 7,710 6
Benzidine (s) C12
H12
N2
16,500 78.22 6.58 0.00 15.21 0.00 0.00 100.00 15,900 6
Chloroacetaldehyde (l) C2H
3ClO 5,260 30.60 3.86 20.38 0.00 0.00 45.16 100.00 4,600 6
p-Chloroaniline (s) C6H
6ClN 11,100 56.48 4.75 0.00 10.98 0.00 27.79 100.00 10,400 6
1-(o-Chlorophenyl) thiourea (l) C7H
7ClN
2S 9,540 45.04 3.79 0.00 15.01 17.17 18.99 100.00 9,060 6
Dinitrobenzene (s) C6H
4N
2O
47,470 42.86 2.40 38.07 16.67 0.00 0.00 100.00 7,250 6
2,4-Dithiobiuret (s) C2H
5N
3S
23,820 17.76 3.73 0.00 31.08 47.42 0.00 100.00 3,470 6
1-Naphthyl-2-thiourea ( s) C11
H10
N2S 13,500 65.31 4.99 0.00 13.85 15.85 0.00 100.00 13,000 6
p-Nitroaniline (s) C6H
6N
2O
29,900 52.16 4.39 23.16 20.28 0.00 0.00 100.00 9,490 6
Propylthiouracil (s) C7H
10N
2OS 11,300 49.38 5.93 9.40 16.46 18.83 0.00 100.00 10,700 6
TCDD (s) C12
H4Cl
4O
26,170 44.76 1.25 9.94 0.00 0.00 44.04 100.00 5,770 6
Toluene (l) C7H
818,250 91.23 8.77 0.00 0.00 0.00 0.00 100.00 17,400 6
2,4,6-Trichlorophenol (s) C6H
3Cl
3O 5,180 36.50 1.53 8.10 0.00 0.00 53.86 100.00 4,690 6
aRaw data were reported in different units and required conversion to Btu/lb. All values derived from the raw data were rounded to indicate significant figures of the original data.
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Cooper, Kim, and MacDonald
4 7 4 Journal of the Air & Waste Management Association Volume 49 April 1999
LHVdna
= Int. + B1C + B
2H + B
3O + B
4S + B
5Cl
(9)
where Bi= best-fit coefficient, and C,H, etc. = mass frac-
tion of that element in the material, on a dry, no-ash ba-
sis. Furthermore, some correlations with models of other
forms were attempted, such as
LHVdna = Int. + B1C + B2(H - O/8) + B3 S + B4Cl(10)
LHVdna
= Int. + B1C + B
2(H - Cl/35.5) + B
3O + B
4S
(11)
and
LHVdna
= Int. + B1C + B
2(H - O/8 - Cl/35.5) + B
3S
(12)
During the statistical work, F tests were performed on the
models developed from each of the two individual data
sets and from the combined data set. The model based on
the combined 40-point data set was as good as either of
the models based on individual data sets, and was not
being driven by one or the other data set.
Regression diagnostics were performed to check for
non-constant variance of the residuals, bias among the vari-
ables, tolerances, and outliers. Partial residual plots showed
no bias or non-linearity occurring among the variables.
There were some fan-shaped variance plots, which were
corrected by using weights equal to the squares of the fit-
ted values. Collinearity was minimized by using the formof the model equation shown in eq 9 or 12. Tolerances were
checked and found to be greater than 0.08, indicating that
collinearity was not a problem. Externally studentized
residuals were evaluated to determine if any of the points
were outliers. One possible outlier was identified (sewage
sludge), but that datum was retained in the modeling.
RESULTS
Eqs 9 through 12 were modeled using each of the 20-
point data sets (hazardous and non-hazardous materials),
in addition to the combined data set. For all equations
and for all data sets, very similar values were obtained for
T ab le 2 . Non-hazardous materialsreported values.
Reported % Wt.b
(Reported) Source
Fuel HHVa
(Btu/lb) C H O N S Cl H2O Ash (Ref.)
Sewage sludge 1,700 13.0 2.0 6.0 2.3 0.3 0.01 67.0 9.0 7
RDF 5,590 33.0 6.0 22.5 1.0 0.2 0.2 22.5 14.5 7
Tire-derived fuel 16,250 83.87 7.09 2.17
c
0.24 1.23 0.16
d
0.62 4.78 8Black liquor 5,880 34.9 3.05 35.1
c0.11 2.9 0.67 0
e0
e9
Auto fluff 7,810 39.72 4.58 11.76c
0.92 0.25 0.77 0f
42.77 10
Byker densified RDF 6,914 36.0 5.1 31.82c
0.5 0.12 0.32 11.4 14.8 11
Castle Bromwich densified RDF 8,685 46.5 6.7 32.3c
0.8 0.18 1.09 2.3 11.0 11
Coal 12,890 70.3 4.72 6.43c
1.56 1.59 0.37d
7.6 7.8 11
Average RDF 4,020 23.48 3.17 17.84 0.64 0.21 0.46d
37.79 16.87 12
RDF 7,313 42.73 6.37 26.53 0.79 0.47 0.27 0f
22.83 13
RDF 7,398 42.49 5.46 25.46 0.56 0.14 0.35 0f
25.54 13
Slurry (Upper Freeport coal) 13,500 73.73 4.89 6.30c
1.34 1.29 0.17 0f
12.28 14
West Virginia bituminous coal 10,100 63.27 4.40 4.73 1.25 3.38 0.04 8.00 14.93 15
Texas lignite coal 6,900 40.60 3.10 13.10 0.70 1.00 0.04 32.20 9.26 15
Illinois bituminous coal 10,100 57.50 3.70 5.80 0.90 4.00 0.10 12.00 16.00 15
Wyoming subbituminous coal 8,020 47.87 3.40 10.83 0.62 0.48 0.03 30.40 6.37 15
Absaloka, MT, coal 8,810 65.6 4.5 15.1 0.8 0.8 0.02 0f
13.2 16
Navajo, NM, coal 8,745 56.6 4.3 12.5 1.1 0.8 0.03 0f
24.6 16
River-King, IL, coal 8,900 54.5 4.0 8.2 0.9 4.2 0.05 0f
28.2 16
Pyro, KY, coal 12,200 68.5 5.9 5.7 1.4 4.3 0.25 0f
15.2 16
aRaw data were reported in different units and required conversion to Btu/lb. All values were rounded to indicate significant figures of the original data.
bPercent compositions may not sum to 100% due to rounding and the inclusion of other elements (sodium, potassium, etc.) in the overall composition.
cOxygen content determined by difference.
dValue represents a trace percentage for an oxide compound. This percentage was incorporated into the overall composition by reducing the oxygen percentage by an equivalent
amount.eComposition reported for dry, no-ash basis.
fComposition reported for dry basis.
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Cooper, Kim, and MacDonald
Volume 49 April 1999 Journal of the Air & Waste Management Association 4 7 5
F i gu re 1 . P r e di c t e d v e r s u s a c t u a l L H V s, u s i ng m o de l s o f t h e fo r m of
e q 1 2 o n t h re e d at a s et s .
Table 3. Non-hazardous materialsdry, no-ash basis.
HHVa
(Btu/lb) % Wt.a, b
LHVa
(Btu/lb) Source
Fuel Dry & No ash C H O N S Cl Dry & No Ash (Ref.)
Sewage sludge 7,300 55.1 8.5 25.4 9.7 1.3 0.04 6,500 7
RDF 8,880 52.5 9.5 35.8 1.6 0.3 0.3 7,980 7
Tire-derived fuel 17,180 88.66 7.49 2.14 0.25 1.30 0.16 16,480 8Black liquor 5,880 45.5 3.97 45.7 0.14 3.8 0.87 5,500 9
Auto fluff 13,650 69.40 8.00 19.20 1.61 0.44 1.35 13,560 10
Byker densified RDF 9,616 48.7 6.8 43.11 0.7 0.16 0.43 9,559 10
Castle Bromwich densified RDF 9,780 53.1 7.7 36.9 0.9 0.20 1.25 9,701 11
Coal 15,240 83.1 5.58 7.16 1.84 1.88 0.44 15,190 11
Average RDF 8,860 51.50 6.95 38.67 1.40 0.46 1.01 8,790 12
RDF 9,477 55.38 8.26 34.38 1.02 0.61 0.35 9,409 13
RDF 9,936 57.06 7.33 34.19 0.75 0.19 0.47 9,881 13
Slurry (Upper Freeport coal) 15,400 84.05 5.57 7.18 1.53 1.47 0.19 15,300 14
West Virginia bituminous coal 14,930 82.09 5.71 6.14 1.62 4.39 0.05 14,890 14
Texas lignite coal 11,800 69.35 5.30 22.38 1.20 1.71 0.07 11,700 15
Illinois bituminous coal 14,030c
79.86 5.14 8.06 1.25 5.56 0.14 13,990c
15
Wyoming subbituminous coal 12,700 75.71 5.38 17.13 0.98 0.76 0.05 12,600 15
Absaloka, MT, coal 13,400 75.6 5.2 17.4 0.9 0.9 0.02 13,360c
15
Navajo, NM, coal 13,380 75.2 5.7 16.6 1.5 1.1 0.04 13,330 16
River-King, IL, coal 13,800 75.9 5.6 11.4 1.3 5.9 0.07 13,700 16
Pyro, KY, coal 14,810 79.6 6.9 6.6 1.6 5.0 0.29 14,750 16
aAll values were rounded to indicate significant figures.
bPercent compositions are normalized to 100%, but may not sum to 100% due to rounding.
cValues should be rounded to three significant figures, but were kept at four to indicate a difference between HHV and LHV values.
the correlation coefficients (R2) and variances. Therefore,
only the final results for the models depicted by eq 9 and
12 are presented here.
In the scatter plot shown in Figure 1, the predictions
using models of the form of eq 12 for both 20-point data
sets are plotted, along with the predictions from the 40-
point combined data set. All the data sets are modeled
well. The R2 values were all about 0.95 for all three data
sets (using all data points) and were about 0.97 when the
tests excluded the suspected outlier.
The models represented by eqs 9 and 12 were com-
pared using the combined data set. The results are
shown in Table 4 and Figure 2. As can be seen, both
models fit the data well. In fact, in Figure 2, the two
lines representing the least-squares fit of the predicted
versus actual data for each equation appear to lie al-
most on top of each other. However, eq 12 has fewer
coefficients (resulting in a slightly lower variance) and
has a positive coefficient on sulfur; therefore, it was
selected as the best model. In addition, with this equa-
tion, all coefficients were found to be statistically dif-
ferent from zero, except for the intercept.
CONCLUSIONS
The high R2 values and the good appearance of Figures
1 and 2 lead to the conclusion that the fitted equa-
tions provide accurate predictions of the LHVs for a
variety of materials. Based on the work done in this
study, the authors conclude that a good general for-
mula for predicting the LHV of a hazardous or non-
hazardous waste or other combustible material is
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4 7 6 Journal of the Air & Waste Management Association Volume 49 April 1999
F ig ur e 2 . P r ed i ct e d v e rs u s a c tu a l L H Vs , co m pa r in g e q 9 t o eq 1 2
u s i n g t h e c o mb i n e d d a t a s e t .
LHVdna
= -791 + 17,050 C +
32,030 (H - O/8 - Cl/35.5) + 4,591 S (13)
whereLHVdna
= lower heating value on a dry, no-ash basis
(Btu/lb); and C, H, O, Cl, and S = mass fraction of that
element in the material on a dry, no-ash basis. For any
given waste or other combustible material, once theLHVdna
is predicted using eq 13, eqs 6 and 7 can be solved to
estimate theHHVasis
if desired.
ACKNOWLEDGMENTS
The authors acknowledge the advice of Mortaza
Jamshidian, Department of Statistics, UCF, in the statisti-
cal testing.
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Ta b le 4 . Final model parameters for predicting lower heating values.
Parameter Estimates
Model Intercept B1
B2
B3
B4
B5
R2
Eq 9 3,918 12,650 24,340 -9,725 -3,240 -5,471 0.953
Eq 12 -791 17,050 32,030 4,591 NA NA 0.948
Note: NA = not applicable.
About the Authors
C. David Cooper, PE, QEP (corresponding author), is pro-
fessor of engineering in the Civil and Environmental Engi-
neering (CEE) Department at University of Central Florida,
Orlando, FL, 32816-2450. Brian Kim and John MacDonald
are Ph.D. students in the CEE Department.