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PriankMathur
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resources

Article
Regression Model to Predict the Higher Heating
Value of Poultry Waste from Proximate Analysis
Xuejun Qian 1,2 , Seong Lee 1,2, *, Ana-maria Soto 3 and Guangming Chen 1
1 Industrial and Systems Engineering Department, Morgan State University, 1700 East Cold Spring Lane,
Baltimore, MD 21251, USA; xuqia1@morgan.edu (X.Q.); guangming.chen@morgan.edu (G.C.)
2 Center for Advanced Energy Systems and Environmental Technologies, School of Engineering,
Morgan State University, 5200 Perring Parkway, Baltimore, MD 21239, USA
3 Department of Chemistry, Towson University, 8000 York Road, Towson, MD 21252, USA; asoto@towson.edu
* Correspondence: seong.lee@morgan.edu; Tel.: +1-443-885-3106

Received: 18 May 2018; Accepted: 23 June 2018; Published: 26 June 2018 

Abstract: Improper land application of excess poultry waste (PW) causes environmental issues and
other problems. Meanwhile there is an increasing trend of using PW as an alternative energy resource.
The Higher Heating Value (HHV) is critical for designing and analyzing the PW conversion process.
Several proximate-based mathematical models have been proposed to estimate the HHV of biomass,
coal, and other solid fuels. Nevertheless, only a small number of studies have focused on a subclass of
fuels, especially for PW. The aim of this study is to develop proximate-based regression models for an
HHV prediction of PW. Sample data of PW were collected from open literature to develop regression
models. The resulting models were then validated by additional PW samples and other published
models. Results indicate that the most accurate model contains linear (all proximate components),
polynomial terms (quadratic and cubic of volatile matter), and interaction effect (fixed carbon and
ash). Moreover, results show that best-fit regression model has a higher R2 (91.62%) and lower
estimation errors than the existing proximate-based models. Therefore, this new regression model
can be an excellent tool for predicting the HHV of PW and does not require any expensive equipment
that measures HHV or elemental compositions.

Keywords: poultry waste; energy resources; higher heating value; proximate analysis; regression
model; estimation errors

1. Introduction
The increasing demand for animal and protein products (e.g., egg, meat) has led to a high
number of animal feeding operations and massive quantities of poultry waste (PW) in confined
areas [1]. PW from poultry farming includes a mixture of poultry manure (excreta), bedding
materials (e.g., wood shavings, sawdust, straw, pine or rice husk), waste feed, dead birds, broken
eggs, and feathers removed from poultry houses [2,3]. Poultry manure (or chicken manure) is
an organic waste, mainly feces and urine of chicken, whereas poultry litter refers to a mixture of
poultry manure, bedding materials, spilled feed and feathers [1]. In 2009, with the assumption of
1.4 ton of litter per 1000 birds, a total of about 25 million tons of poultry litter were generated in the
USA and the EU [1]. Due to its rich nutrient contents, such as nitrogen, phosphorous, potassium,
and calcium, most PW has traditionally been utilized as an organic fertilizer on agricultural land [1,2].
However, excess application of PW can lead to an overabundance of nutrients in the watershed, with a
resulting eutrophication on water bodies and water pollutions (e.g., nitrate contamination). As a
result, excess application of PW can pose a risk to the health of humans, animals, and the aquatic
ecosystem [2,4]. Because of its energetic and superior fuel properties, PW is recognized as a biomass

Resources 2018, 7, 39; doi:10.3390/resources7030039 www.mdpi.com/journal/resources


Resources 2018, 7, 39 2 of 14

fuel and energy resource for alternative thermochemical conversion processes, namely composting,
anaerobic digestion, combustion, gasification, and pyrolysis [2,5]. Among these alternative conversion
technologies, combustion and co-combustion has been strongly suggested to be a cost-effective and
environmentally-friendly disposal route for PW while providing an energy source for both space
heating of poultry houses and large-scale power generation [2–4].
The design and operation of more efficient biomass combustion systems rely substantially
on several fuel characteristics, namely heating value, moisture, ash content, and elemental
composition [6,7]. The heating value (or calorific value) defines the energy content of fuel and is
one of the most important fuel properties for achieving energy balance, engineering analysis, design
calculations, and numerical simulations of thermal conversion systems [6–8]. The heating value is
usually measured by the higher heating value (HHV) or lower heating value (LHV). HHV, also known
as the gross calorific value or gross energy, refers to the heat released by the complete combustion
of fuel, assuming that the water originally present in the fuel and any generated water are present
in a condensed state [6,9]. LHV, also known as the net heating value, assumes that the water is
present in a vapor state at the end of combustion and is determined by subtracting the latent heat
of water vaporization from the HHV [10]. Experimentally, an adiabatic bomb calorimeter is used to
measure the enthalpy change between reactants and products [6,11]. In a previous study, the HHV
of PW samples from nine different farms was experimentally determined to vary between 12,052
and 13,882 kJ/kg [12]. An IKA C5003 bomb calorimeter was used in accordance with the Spanish
Association for Standardization, UNE standard 164001EX [12]. Cotana et al. [13] also measured
the HHV of two PW samples from different farming practices by using a LECO AC350 calorimeter,
in compliance with UNI9017 standard. However, bomb calorimeters may not always be accessible to
all laboratories. Additionally, experimental methods to measure the HHV are usually time consuming,
complicated, and have higher possibilities of experimental errors [7,14,15].
Therefore, numerous mathematical models have been developed to predict the HHV of energy
resources from results collected from ultimate analysis (or elemental analysis), proximate analysis,
chemical analysis, and structural analysis [10,16]. Ultimate and proximate analyses provide basic fuel
characterizations and are the most commonly used analyses to predict the HHV. Ultimate analysis
measures the major elemental composition of samples, such as carbon (C), hydrogen (H), oxygen
(O), nitrogen (N) and sulfur (S), in weight percentage (wt %) [7]. Sheng and Azevedo [6] found
that mathematical models based on ultimate analysis are more accurate than models derived from
proximate and chemical analyses because ultimate analysis quantifies elemental contents and provides
a more detailed chemical composition of fuels. Yin et al. [7] also suggested that ultimate analysis-based
models are more accurate than proximate analysis. But ultimate analysis requires expensive element
analyzers as well as special experimental arrangements with skillful analysts [17]. Proximate analysis
is used to determine the composition of moisture (M), fixed carbon (FC), volatile matter (VM) and
ash contents, also in weight percentage [7]. Hence, proximate-based models have developed into
an important tool for estimating the HHV of energy resources over time. Proximate analysis is
rapid, economical, easy, and can be run by any competent scientist, researcher, or engineer using
common laboratory equipment with standard test methods (e.g., American Society for Testing and
Materials (ASTM) or European Committee for Standardization (CEN) [10,17–19]. Common laboratory
equipment namely includes a balance, simple oven (for determination of M content), and furnace (for
determination of VM and ASH contents) [15,17,20].
Seventeen proximate-based models that have been proposed and applied for estimating the HHV
for a variety of solid fuels were collected from literature reviews and evaluated [6–8,11,15–17,19–28].
A summary of our findings can be found in Table 1. Unfortunately, most models used a wide range
of data points and fuel types, which is not very accurate and applicable for other fuel types [28].
Özyuğuran and Yaman (2017) also found that the values of the coefficient of determination, R2 were
not very close to one (about 81–83%) because several different biomass species were accounted for in
the samples [15]. In response to the need of more accurate HHV predictions, several researchers have
Resources 2018, 7, 39 3 of 14

developed models for each subclass of fuels, such as herbaceous, woody, and agriculture residues [15].
However, few researchers have centered their studies on subclass of fuels from poultry raising process,
e.g., PW samples. In addition, Lynch et al. [1] compared experimental results (18.0 GJ/t) of the HHV
with calculated results (15.7 GJ/t) from existing proximate-based model. The relatively high percentage
error indicates unsuitability of existing proximate-based models when utilizing a fuel such as PW [1].
The aim of this study is to develop proximate-based regression models for HHV predictions
of PW. The proposed regression models are based only on components (FC, VM and ash) from
proximate analysis in order to provide a rapid, easy, and cheap prediction of the HHV, such that the
new regression models are not dependent on more expensive facility and sophisticated personnel to
measure the HHV or elemental compositions. The resulting regression models were validated with
additional samples and compared with existing proximate-based models.

Table 1. Proximate analysis-based models for the HHV Prediction from the literature review.

Existing Models HHV (MJ/kg) * Raw Materials Ref.


E1 HHV = −10.81408 + 0.3133 (VM + FC) Lignocellulosic Residues [21]
E2 HHV = 76.56 − 1.3 (VM + A) + 7.3 × 10−3 (VM + A)2 Coal [17]
E3 HHV = 0.196 (FC) + 14.119 Biomass [22]
E4 HHV = 0.3543 FC + 0.1708 VM Lignocellulosics & Charcoals [11]
E5 HHV = −0.066 (FC)2 + 0.5866 (FC) + 8.752 Shell of biomass [23]
E6 HHV = 0.356047 VM − 0.118035 FC − 5.600613 Municipal solid waste [24]
E7 HHV = 19.914 − 0.2324 A Biomass fuels [6]
E8 HHV = 0.3536 (FC) + 0.1559 (VM) − 0.0078 A Solid fuels [20]
E9 HHV = 0.25575 VM + 0.28388 FC − 2.38638 Sewage sludge [25]
E10 HHV = 18.96016 − 0.22527 A Straw [16]
E11 HHV = −0.1882 (VM) + 32.94 Vegetable oil and tallow [19]
E12 HHV = 0.1905 VM + 0.2521 FC Biomass [7]
E13 HHV = −2.057 − 0.092 A + 0.279 VM Greenhouse crop residues [26]
HHV = 20.7999 − 0.3214 VM/FC + 0.0051 (VM/FC)2
E14 − 11.2277 A/VM + 4.4953 (A/VM)2 − 0.7223 Biomass [8]
(A/VM)3 + 0.038 (A/VM)4 + 0.0076 FC/A
E15 HHV = 1.83 × 104 − 3.98 A2 − 112.10 A Spanish biofuels [27]
E16 HHV = 0.1846 VM + 0.3525 FC Torrefied biomass [28]
E17 HHV = 10.982 + 0.1136 VM − 0.2848 A Biomass [15]
* HHV = Higher Heating Value; FC = Fixed Carbon; VM = Volatile Matter; A = Ash.

2. Materials and Methods

2.1. Data Collection, Selection and Nomalization


To account for various geological locations and farming practices, a total of forty-eight samples of
PW were collected from different published open literature reviews to form a database for derivation,
evaluation, and validation of proximate-based HHV models. Complete datasets for the proximate
analysis, ultimate analysis, raw material type, and the HHV of PW samples along with the references
therein, are listed in Table S1 as a supplementary file. During sample selection for the proximate-based
HHV models, three samples (#43, 44, and 45) were deleted because only moisture (M) and ash
information was provided. Additionally, two samples (#46 and 47) with HHV of 14.587 J/g and
11.552 J/g were excluded due to extremely low HHV values in contrast to the rest of the samples.
In addition, sample (#48) was removed due to uncertainty over whether proximate analysis was
conducted under dry-basis or wet-basis conditions. In this study, the VM, FC, and ash contents are
normalized in dry-basis (moisture free) because sample characteristics become more meaningful in
and dry-basis have been used in most previous HHV prediction studies. The missing data of FC
contents are calculated by subtracting VM and ash contents from 100%. Table 2 summarizes the FC,
VM, ash content and the HHV results of PW samples, with sources. The HHV (e.g., Btu/lb, kJ/kg,
GJ/t, and kcal/kg) results are converted into MJ/kg on dry-basis. Composition of proximate analysis
components are presented in wt % on dry-basis. One PW sample (#49) from a local poultry farm
Resources 2018, 7, 39 4 of 14

(Bethel Farms, Salisbury, MD, USA) is experimentally analyzed by Mineral Labs Inc. (Salyersville, KY,
USA) and summarized in the Table 2 as well.

Table 2. Summary of FC, VM, and A Content (wt %) along with HHV results (MJ/kg) in dry-basis.

No. FC 1 VM 2 ASH 3 HHV 4 Ref.


1 2.98 68.25 28.77 10.62 [3]
2 6.88 65.16 27.96 11.8 [4]
3 9.07 61.2 29.73 12.02 [29]
4 11.02 60.77 28.21 12.33 [29]
5 5.31 55.61 39.09 9.96 [29]
6 2.08 38.46 59.46 6.78 [29]
7 13.36 71.26 15.49 18.02 [1]
8 14.4 47.93 37.79 13.52 [1]
9 14.4 47.82 37.79 14.9 [1]
10 11.05 68.63 20.33 12.52 [30]
11 12.4 53.6 33.9 12.38 [31]
12 15.4 62.7 21.9 14.84 [31]
13 15 66.3 18.7 14.05 [31]
14 17.2 71.9 10.9 17.48 [31]
15 14 62.2 23.9 14.07 [31]
16 13.49 65.1 21.61 14.87 [32]
17 2.91 68.28 28.81 10.62 [33]
18 12.74 71.11 16.16 17.11 [34]
19 13.36 61.49 25.15 14.69 [35]
20 22.77 66.39 11.54 18.3 [36]
21 24.4 60.2 15.4 16 [37]
22 23.2 75.3 1.6 20.9 [38]
23 19.42 63.97 16.61 16.8 [39]
24 9.63 69.13 21.25 14.87 [40]
25 27 42.3 30.7 19.03 [41]
26 35.5 18.3 46.2 14.75 [41]
27 16.56 68.83 14.61 16.8 [42]
28 5.5 67.9 26.6 13.3 [43]
29 9.6 65.7 24.7 14.7 [43]
30 12.8 65.56 21.65 13.15 [44]
31 14.45 47.42 37.83 14.24 [45]
32 14.17 60.99 26.42 10.79 [46]
33 13.88 62.55 23.39 12.8 [46]
34 25.9 14.3 59.8 11.71 [20]
35 3.37 71.54 26.09 10.62 [47]
36 55.6 26.7 17.7 27.9 [48]
37 4.7 75.1 20.2 12.8 [49]
38 14.3 58.64 27.06 12.77 [50]
39 11.7 63.1 25.2 11 [38]
40 9.08 43.57 47.35 10 [39]
41 8.8 74.3 16.9 15.11 [41]
42 4.53 57.93 37.54 10.33 [51]
43 - - 17.2 14.59 [52]
44 - - 25.1 13.67 [52]
45 - - 22.9 15.28 [53]
46 - 26.56 10.6 14.587 [13]
47 - 64.43 15.41 11.552 [13]
48 3.3 54.3 - 10.1 [54]
49 11.98 63.96 24.06 14.34
1 FC = Fixed Carbon; 2 VM = Volatile Matter; 3 A = Ash; 4 HHV = Higher Heating Value.
Resources 2018, 7, 39 5 of 14

2.2. Proposed Regression Models


Before the development of new regression models, the experimental HHV results from PW
samples are plotted against the different components of the proximate analysis to get a visual insight
into the relationship between proximate analysis components and the HHV. As shown in Table 3,
fifteen new regression models are proposed to establish the relationship between the HHV and
proximate analysis components from thirty-seven PW samples (#1–37). Equation (1) considers that all
components of the proximate analysis have linear relationships with the HHV. Equations (2)–(4) only
consider that two components of proximate analysis have linear relationships with HHV. Equations
(5)–(7) consider two components as linear and one component as a polynomial (quadratic) relationship
with HHV while Equations (8) and (9) consider one component as linear and two components as
quadratic for its relationship with the HHV. Equation (10) considers all components as quadratic
relationship with the HHV. Among Equations (1) through (10), the most suitable and simple multiple
linear regression model (Equation (1)) is used to further improve the accuracy of HHV prediction.
Equation (11) combines Equation (1) and polynomial terms (both quadratic and cubic) of VM contents.
Equations (12)–(14) are used to compare the different interaction effects between two components
on the accuracy of HHV prediction. Equation (15) combines Equation 1 plus polynomial terms of
VM and best interaction effect to get a best-fit proximate-based HHV model. The constant terms of
proposed regression models are calculated and determined according to the Least Squares Method.
Data for selected PW samples are inserted into Minitab to preform curve fitting, calculate constant
terms, and derive the proposed regression models.

Table 3. List of proposed regression models to predict the HHV of PW samples.

No. Proposed New Models * Note


1 HHV = a + bFC + cVM + dA Linear (FC, VM, A)
2 HHV = a + bFC + cVM Linear (FC, VM)
3 HHV = a + bFC + cASH Linear (FC, A)
4 HHV = a + bVM + cASH Linear (VM, A)
5 HHV = a + bFC2 + cVM + dA Quadratic (FC), Linear (VM, A)
6 HHV = a + bFC + cVM2 + dA Quadratic (VM), Linear (FC, A)
7 HHV = a + bFC + cVM + dA2 Quadratic (A), Linear (FC, VM)
8 HHV = a + bFC2 + cVM2 + dA Quadratic (FC, VM), Linear (A)
9 HHV = a + bFC2 + cVM + dA2 Quadratic (FC, A), Linear (VM)
10 HHV = a + bFC2 + cVM2 + dA2 Quadratic (FC, VM, A)
11 HHV = a + bFC + cVM + dA + eVM2 + fVM3 Linear (FC, VM, A), Quadratic & Cubic (VM)
12 HHV = a + bFC + cVM + dA + eFC × VM Linear (FC, VM, A), Interaction (FC&VM)
13 HHV = a + bFC + cVM + dA + eFC × A Linear (FC, VM, A), Interaction (FC&A)
14 HHV = a + bFC + cVM + dA + eVM × A Linear (FC, VM, A), Interaction (VM&A)
HHV = a + bFC + cVM + dA + eVM2 + fVM3 Linear (FC, VM, A), Quadratic & Cubic (VM),
15
+ gFC × A Interaction (FC&A)
* HHV = Higher Heating Value; FC = Fixed Carbon; VM = Volatile Matter; A = Ash; a, b, c, d, e, f and g are the
constant terms for the proposed regression models.

2.3. Evalation and Validation of New Regression Models


Three statistical parameters, average absolute error (AAE), average biased error (ABE),
and coefficient of determination (R2 ), are employed to evaluate the accuracy and suitability of the
new regression models. Estimation errors such as ABE calculate the degree of overestimation and
underestimation of models while AAE measures the degree of closeness between the predicted and
measured results. R2 value is used widely in statistical and regression analyses to determine the degree
of goodness and accuracy of models. All the estimation errors and R2 are derived from equations
listed below:  
|P −M |
∑ni=1 iMi i
AAE = × 100%, (1)
n
Resources 2018, 7, 39 6 of 14

 
(Pi −Mi )
∑ni=1 Mi
ABE = × 100%, (2)
n
2
∑ni=1 (Pi − Mi )
R2 = 1 − 2 , (3)
∑ni=1 Mi − M
where P, M, M, i and n represent predicted results, measured results, average of measured results,
specific sample number, and total number of samples, respectively. In this study, R2 values are
calculated along with the derivation of regression models while the AAE and ABE of regression
models are calculated separately with Microsoft Excel. The developed model is considered to be
the best fit if the estimation errors, AAE and ABE, tended to be zero and the R2 value was close
to 1 [6,8,28]. The accuracy of the new regression models is tested by comparing the experimental
results with predicted results from the new regression models. To further confirm the validity of these
new regression models, proximate analysis results of additional five PW samples (#38–42) and one
experimentally tested sample (#49) in Table 2 were used to calculate estimation errors. In addition, the
estimation errors of the simple multiple linear regression model (N1) and best-fit regression model
(N15) were compared with other published seventeen proximate-based models (for biomass and solid
fuels as shown in Table 1) by using the same PW samples data points (#1–37) to further determine the
accuracy and necessity of new proximate-based models for PW samples.

3. Results and Discussion

3.1. Effects of Proximate Analysis Composition on HHV


As shown in Figure 1, the HHV of PW samples are plotted as a function of FC, VM, and ash
components (in wt %, dry-basis) by using scatter plots to show how HHV results vary with different
composition of proximate analysis data. For the instance of PW samples, HHV results were found to
increase with the FC contents. In contrast, there is a clear trend in HHV results decreasing with the
increase of ash contents. Previous studies have drawn similar conclusions in that FC content has a
positive effect whereas ash content has a negative effect on the HHV of raw biomass materials and
torreffied biomass materials [28]. For the case of coal, Majumder et al. [14] also found the same trend.
This may be possible due to ash having an inert effect on the heating value. Some detrimental effect on
the apparent heat obtained during the biomass combustion process because the energy of ash forming
inorganics for thermal breakdown and phase transition is taken from biomass combustion process [15].
These results further confirm that ash content is one of the most important fuel properties directly
affecting the HHV, with high amounts may making PW less desirable as energy resource during the
conversion processes. But the effect of VM composition on the HHV of PW is less obvious. Previous
studies also found that the effect of VM content on HHV is much more complicated and inconclusive.
High VM does not guarantee a high calorific value since some of the ingredients in VM are formed
from non-combustible gases, such as CO2 and H2 O [15,27]. Therefore, the results infer that linear
regression models for VM may not represent the most appropriate solution to accurately estimate the
HHV of PW samples. As such, the polynomial terms, such as quadratic, cubic, and interaction effect
are proposed in this study to predict the precise HHV of PW samples.
Correlation is evaluated to measure the strength of the association between the factors (e.g., FC,
VM, ash) and response variables (e.g., HHV). As shown in Figure 1, there is a relatively strong linear
correlation between the HHV and FC (R2 = 0.6167) while only a moderate correlation exists between
the HHV and ash (R2 = 0.3593) with the current PW database. However, Sheng and Azevedo [6]
found a different phenomenon for biomass, in that there exists a significant correlation between HHV
and ash (R2 = 0.625) while only a trend exists between the HHV and VM (R2 = 0.307). In addition,
Akkaya et al. [55] observed a linear relationship between the HHV and two components (VM and
FC), as well as a stronger non-linear dependence for percentages of other two components (M and
ash) with coal samples. Compared with biomass and coal samples, the correlation between proximate
correlation between the HHV and FC (R2 = 0.6167) while only a moderate correlation exists between
the HHV and ash (R2 = 0.3593) with the current PW database. However, Sheng and Azevedo [6] found
a different phenomenon for biomass, in that there exists a significant correlation between HHV and
ash (R2 = 0.625) while only a trend exists between the HHV and VM (R2 = 0.307). In addition, Akkaya
et al. [55]
Resources observed
2018, 7, 39 a linear relationship between the HHV and two components (VM and FC), as well 7 of 14
as a stronger non-linear dependence for percentages of other two components (M and ash) with coal
samples. Compared with biomass and coal samples, the correlation between proximate analysis
analysis
componentscomponents and for
and HHV HHV PWforsamples
PW samples is significantly
is significantly different.
different. ThisThis suggests
suggests that
that theexisting
the existing
correlation of proximate-based models for solid fuels, such as biomass and coal, are not
correlation of proximate-based models for solid fuels, such as biomass and coal, are not appropriate appropriate
for
forestimating
estimatingthe theHHV
HHV ofof PW
PW samples. Thus, fifteen
samples. Thus, fifteen new
newregression
regressionmodels
modelsareareproposed
proposedtotocorrelate
correlate
the HHV and proximate analysis components of
the HHV and proximate analysis components of PW samples.PW samples.

30 30

HHV(MJ/kg,dry-basis)
HHV (MJ/kg, dry-basis)

25 y = 0.2909x + 9.9646 25
R² = 0.6167
20 20 y = -0.0079x + 14.543
R² = 0.001
15 15
10 10
5 5
0 0
0 20 40 60 0 50 100
FC (wt %, dry-basis) VM (wt %, dry-basis)
Resources 2018, 7, x FOR PEER REVIEW 7 of 13
(a) (b)

30
HHV(MJ/kg, dry-basis)

25
y = -0.1794x + 18.869
20 R² = 0.3593
15
10
5
0
0 20 40 60 80
A (wt %, dry-basis)
(c)
Figure 1. Relationships between HHV and composition of individual proximate analysis components:
Figure 1. Relationships between HHV and composition of individual proximate analysis components:
(a) Scatter Plot of fixed carbon (FC) along with HHV results; (b) Scatter plot of volatile matter (VM)
(a) Scatter Plot of fixed carbon (FC) along with HHV results; (b) Scatter plot of volatile matter (VM)
along with HHV results; (c) Scatter plot of Ash (A) along with HHV results.
along with HHV results; (c) Scatter plot of Ash (A) along with HHV results.

3.2. Derivation of the New Regression Models


3.2. Derivation of the New Regression Models
As shown in Table 4, fifteen new regression models are developed by using proximate analysis
As shown in Table 4, fifteen new regression models are developed by using proximate analysis
data of thirty-seven PW samples. R22 value, adjusted R22 value, along with AAE and ABE, are also
data of thirty-seven PW samples. R value, adjusted R value, along with AAE and ABE, are also
calculated and summarized. Results indicate that new proximate-based regression models can
calculated and summarized. Results indicate that new proximate-based regression models can predict
predict the HHV of PW with R2 values ranging between 78.14% and 91.62%. The estimation errors
2 values ranging between 78.14% and 91.62%. The estimation errors are found
the HHV of PW with R
are found to be in the range of 5.98% to 10.36% for AAE, and −0.35% to 1.53% for ABE. In the following
tosection,
be in the range
letter “N”ofindicates
5.98% tothe
10.36%
new for AAE, and
regression −0.35%
models to 1.53%
derived fromforthisABE.
studyInand
the “E”
following section,
indicates the
letter “N”models
existing indicates the were
that new regression
developedmodels
by otherderived from this
researchers. study
For and “E”
instance, N1indicates
indicatesthethe
existing
new
models that model
regression were developed by other
1. Excluding researchers.
N9 and N10, theFor
restinstance,
of the newN1 indicates
regression themodels
new regression
have bettermodel
R2
1.values
Excluding N9than
andthe
N10, the restmodels.
of the new 2
(>0.85) previous Oneregression models
possible reason forhave better high
relatively R values (>0.85)
R2 value than
is that the
only
previous models. One possible reason for relatively high R 2 value is that only one subclass of fuel (PW
one subclass of fuel (PW samples) is being used. Sheng and Azevedo [6] had a similar explanation
samples) is being
for why their used.was
R2 value Sheng
veryand
lowAzevedo [6] had
(<0.85). They a similarthat
postulated explanation for why
the low value was their R2evaluating
due to value was
very lowrange
a wide (<0.85).
of They postulated
biomass that compromised
species that the low value was due to evaluating
the accuracy a wide
of estimation [6].range of biomass
This infers that
considering only PW samples could improve the accuracy of HHV prediction.
According to previous studies, Cordero et al. [11] identified a simple equation based on
proximate analysis (VM and FC) that could predict the HHV of lignocellulosic materials as well as
char coals. Yin [7] also found that a simple empirical equation based on proximate analysis (VM and
FC) is sufficient for estimating the HHV of biomass. However, consideration of only two components
(VM and FC) of proximate analysis in N2 has lower R2 value and higher estimation errors than N1,
Resources 2018, 7, 39 8 of 14

species that compromised the accuracy of estimation [6]. This infers that considering only PW samples
could improve the accuracy of HHV prediction.

Table 4. Summary of new regression models for PW samples.

Percentage (%)
No. Developed New Regression Model *
R2 R2 (adj) AAE ABE
N1 HHV = 174.3 − 1.335 FC − 1.596 VM − 1.749 A 88.15 87.08 7.02 0.68
N2 HHV = −0.33 + 0.4109 FC + 0.1461 VM 85.72 84.88 7.50 0.70
N3 HHV = 14.355 + 0.2642 FC − 0.1480 A 86.11 85.29 7.42 0.69
N4 HHV = 40.89 − 0.2651 VM − 0.4138 A 86.73 85.95 7.25 0.61
N5 HHV = 36.27 + 0.00104 FC2 − 0.2140 VM − 0.3651 A 87.03 85.85 7.23 0.75
N6 HHV = 20.60 + 0.1900 FC − 0.000823 VM2 − 0.2281 A 86.43 85.20 7.28 0.66
N7 HHV = −0.02 + 0.4077 FC + 0.1426 VM − 0.00006 A2 85.72 84.42 7.53 0.73
N8 HHV = 28.46 + 0.002104 FC2 − 0.001712 VM2 − 0.3205 A 86.38 85.14 7.73 0.90
N9 HHV = 18.16 + 0.00425 FC2 − 0.0463 VM − 0.00288 A2 78.37 76.40 10.36 1.47
N10 HHV = 15.41 + 0.004800 FC2 − 0.000145 VM2 − 0.002430 A2 78.14 76.15 10.31 1.53
HHV = 143.7 − 1.161 FC − 0.364 VM − 1.562 A − 0.02458 VM2 +
N11 91.54 90.18 6.05 0.47
0.000173 VM3
N12 HHV = 174.3 − 1.331 FC − 1.595 VM − 1.751 A − 0.00012 FC × VM 88.16 86.68 7.01 0.46
N13 HHV = 172.2 − 1.262 FC − 1.587 VM − 1.698 A − 0.00237 FC × A 88.91 87.53 6.74 0.57
N14 HHV = 175.2 − 1.332 FC − 1.615 VM − 1.780 A + 0.000652 VM × A 88.32 86.86 7.05 0.20
HHV = 140.2 − 1.167 FC − 0.210 VM − 1.558 A − 0.02739 VM2 +
N15 91.62 89.94 5.98 −0.35
0.000191 VM3 + 0.00104 FC × A
* HHV = Higher Heating Value; FC = Fixed Carbon; VM = Volatile Matter.

According to previous studies, Cordero et al. [11] identified a simple equation based on proximate
analysis (VM and FC) that could predict the HHV of lignocellulosic materials as well as char coals.
Yin [7] also found that a simple empirical equation based on proximate analysis (VM and FC) is
sufficient for estimating the HHV of biomass. However, consideration of only two components
(VM and FC) of proximate analysis in N2 has lower R2 value and higher estimation errors than N1,
where all three proximate analysis components are included for PW samples. This indicates that a
proximate-based regression model in HHV predictions of PW samples should consider FC, VM and
ash content. Parikh et al. [20] and Nhuchhen [8] used a similar approach and concluded that developed
models with all three components of proximate analysis are required to lower estimation errors. AAE
in N1 to N8 is also observed to be lower than AAE in N9 and N10 (about 3%). Since both FC and ash
content are applied as quadratic in both N9 and N10, while at least one linear correlation (either FC or
ash) are included in models N1 to N8, we can conclude that the multiple linear regression model of all
three components of proximate analysis (N1) is the most accurate regression model among N1 to N10.
In further refining the steps (derivation of N11), polynomial relationships (quadratic and cubic)
with VM are added to the simple multiple linear regression model (N1) because the observation from
Figure 1b identified as the linear model for VM may not represent the most appropriate solution
to accurately estimating the HHV of PW samples. This addition shows a further increment of R2
and a reduction of estimation errors. In addition, N12, N13 and N14 are proposed to compare the
interaction effect between two proximate components. Even though the interaction effect provides
a small contribution in reducing the estimation errors, a significant interaction effect of FC and ash
has been identified. Therefore, N15 is developed by combining the simple multiple linear regression
model (N1), the polynomial terms of VM (quadratic, cubic), and the best interaction effect (FC and
ash). The best-fit regression model (N15) has the highest R2 in 91.62%, lowest AAE in 5.98%, and the
lowest ABE in −0.35%. This suggests that consideration of a polynomial dependence of VM as well as
interaction effects of FC and ash can improve the accuracy of predicting the HHV of PW samples.
small contribution in reducing the estimation errors, a significant interaction effect of FC and ash has
been identified. Therefore, N15 is developed by combining the simple multiple linear regression
model (N1), the polynomial terms of VM (quadratic, cubic), and the best interaction effect (FC and
ash). The best-fit regression model (N15) has the highest R2 in 91.62%, lowest AAE in 5.98%, and the
lowest ABE
Resources in39−0.35%. This suggests that consideration of a polynomial dependence of VM as9well
2018, 7, of 14
as interaction effects of FC and ash can improve the accuracy of predicting the HHV of PW samples.

3.3. Validation and


3.3. Validation and Comparative
Comparative Studies
Studies
As shown in Figure 2, the comparison
comparison between experimental and predicted HHV results from
new regression models (N1, N10 and N15) as well as three existing proximate-based models (E7, E14
and E17) are plotted by using the sample data
data points
points from
from Table
Table22(Sample
(Sample#1–37).
#1–37).

30 30 R² = 0.7814
R² = 0.8815 N10

Predicted HHV (MJ/kg)


Predicted HHV (MJ/kg)

N1

20 20

10 10

0 0
0 10 20 30 0 10 20 30
Measured HHV (MJ/kg) Measured HHV (MJ/kg)
Resources 2018, 7, x FOR PEER REVIEW 9 of 13
(a) (b)
30 30
E7 (Sheng and Azevedo, 2005)
Predicted HHV (MJ/kg)

N15
Predicted HHV (MJ/kg)

R² = 0.9161

20 20 R² = 0.3357

10 10

0 0
0 10 20 30 0 10 20 30
Measured HHV (MJ/kg) Measured HHV (MJ/kg)
(c) (d)
30 35
E14 (Nhuchhen and Salam, 2012) E17 (Özyuğuran and Yaman,
Predicted HHV (MJ/kg)

Predicted HHV (MJ/kg)

2017)
20 R² = 0.3613 25

R² = 0.1516
15
10

5
0
0 10 20 30 -5 0 10 20 30
Measured HHV (MJ/kg) Measured HHV (MJ/kg)
(e) (f)
Figure 2. Comparison between predicted and experimental HHV results for new regression models
Figure 2. Comparison between predicted and experimental HHV results for new regression models
and existing proximate-based models: (a) Simple multiple linear regression model (N1); (b) new
and existing proximate-based models: (a) Simple multiple linear regression model (N1); (b) new lowest
lowest
R2 value value regression
R2regression model model (N10);
(N10); (c) (c) best-fit
best-fit regression
regression model (d)
model (N15); (N15); (d) and
Sheng Sheng and Azevedo’s
Azevedo’s model
model (E7); (e) Nhuchhen and Salam’s model (E14); (f) Özyuğuran and Yaman’s
(E7); (e) Nhuchhen and Salam’s model (E14); (f) Özyuğuran and Yaman’s model (E17). The model (E17). The
orange
orange lines represent
lines represent thewhere
the points pointsHHV
where HHVpredicted
= HHV = HHVexperimental
. .
predicted experimental

Figure 2d–f indicate that the predicted HHV from existing proximate-based models are far away
from the line of HHVpredicted = HHVexperimental (orange lines in Figure 2) and therefore not applicable in
predicting the HHV of PW samples. On the other hand, the results show most of the estimated HHV
results from new regression models (N1, N10 and N15) are close to the line of HHVpredicted =
HHVexperimental, indicating good accuracy for HHV predictions of PW samples. The results further
confirm that the new regression models have better accuracy than existing proximate-based models
in predicting the HHV of PW samples. It is especially apparent that the predicated points from the
Resources 2018, 7, 39 10 of 14

Figure 2d–f indicate that the predicted HHV from existing proximate-based models are far away
from the line of HHVpredicted = HHVexperimental (orange lines in Figure 2) and therefore not applicable
in predicting the HHV of PW samples. On the other hand, the results show most of the estimated
HHV results from new regression models (N1, N10 and N15) are close to the line of HHVpredicted =
HHVexperimental , indicating good accuracy for HHV predictions of PW samples. The results further
confirm that the new regression models have better accuracy than existing proximate-based models
in predicting the HHV of PW samples. It is especially apparent that the predicated points from the
best-fit regression model (N15) are close to the measured values while slightly over-predicting or
under-predicting the HHV at different points in the curve.
The validations are carried out for the 15 new regression models to ensure the compatibility with
other PW samples with different characteristics. As shown in Figure 3, the AAE and ABE of 15 new
regression models are calculated by using additional six samples (#38–42, #49) and presented by the
bar chart. Results indicate new regression models have an AAE of 7.81 to 9.57% and ABE of 3.37 to
7.21%. Relatively low AAE and ABE infer that new regression models can be used to estimate the
HHV of2018,
Resources PW 7,samples from
x FOR PEER proximate analysis data with high accuracy.
REVIEW 10 of 13

10 9.57
AAE ABE
7.81
Error Percentage (%)

8 7.21

4 3.37

0
N1 N2 N3 N4 N5 N6 N7 N8 N9 N10 N11 N12 N13 N14 N15
Developed Equations

Figure 3.
Figure 3. Summary
Summary of of calculated
calculated error percentages, including
error percentages, including averaged
averaged absolute
absolute error (AAE) and
error (AAE) and
averaged based error (ABE) of new developed models by using additional PW samples.
averaged based error (ABE) of new developed models by using additional PW samples.

Detailed ABE and AAE results of new regression models (N1, N15) and existing proximate-
Detailed ABE and AAE results of new regression models (N1, N15) and existing proximate-based
based models (E1 to E17) are calculated using the same data points (#1–37) from Table 2. The results
models (E1 to E17) are calculated using the same data points (#1–37) from Table 2. The results are
are presented in Figure 4. Overall, the results indicate that the new regression models have lower
presented in Figure 4. Overall, the results indicate that the new regression models have lower
estimation errors than existing proximate-based models. It is not surprising that the resulting
estimation errors than existing proximate-based models. It is not surprising that the resulting
estimation errors from existing proximate-based are very different because the coefficients of the
estimation errors from existing proximate-based are very different because the coefficients of the
formula and constituent of proximate analysis are considerably different for each case. Three existing
formula and constituent of proximate analysis are considerably different for each case. Three existing
proximate-based models, E5, E11 and E15, are excluded due to extremely large estimation errors
proximate-based models, E5, E11 and E15, are excluded due to extremely large estimation errors
compared to the other models. AAE of existing models, E2 (coal), E3 (biomass) and E17 (biomass) is
compared to the other models. AAE of existing models, E2 (coal), E3 (biomass) and E17 (biomass) is
overestimated compared to the measured HHV (AAE > 20%) because they were developed for coal
overestimated compared to the measured HHV (AAE > 20%) because they were developed for coal
and biomass samples. Raw materials of biomass and coal were selected from a wide range of species
and biomass samples. Raw materials of biomass and coal were selected from a wide range of species
and are expected to cause large variations. In addition, the existing proximate-based model for
and are expected to cause large variations. In addition, the existing proximate-based model for subclass
subclass of fuels, E6 (municipal solid waste) and E9 (sewage sludge), also have larger AAE values
of fuels, E6 (municipal solid waste) and E9 (sewage sludge), also have larger AAE values (>25%) due
(>25%) due to existing proximate-based models for one specific subclass fuel (e.g., municipal solid
to existing proximate-based models for one specific subclass fuel (e.g., municipal solid waste, sewage
waste, sewage sludge) that are not appropriate for the other subclass of fuel (e.g., PW). However,
sludge) that are not appropriate for the other subclass of fuel (e.g., PW). However, relatively low AAE
relatively low AAE and ABE prove that the new regression models can generally have higher
and ABE prove that the new regression models can generally have higher accuracy than the existing
accuracy than the existing proximate-based models in HHV predictions of PW samples. Among the
proximate-based models in HHV predictions of PW samples. Among the 15 new regression models,
15 new regression models, the simple multiple linear regression model (N1) has a R2 value of 88.15%
the simple multiple linear regression model (N1) has a R2 value of 88.15% for predicting HHV of PW
for predicting HHV of PW samples. The best-fit regression model (N15) has the lowest AAE at 5.98%
and provides a marginal lower estimation at just 0.35%, further validating the model’s capability in
predicting the HHV of PW samples.

34 28.52 33.48 AAE ABE 33.9


27.04
25.97
and are expected to cause large variations. In addition, the existing proximate-based model for
subclass of fuels, E6 (municipal solid waste) and E9 (sewage sludge), also have larger AAE values
(>25%) due to existing proximate-based models for one specific subclass fuel (e.g., municipal solid
waste, sewage sludge) that are not appropriate for the other subclass of fuel (e.g., PW). However,
relatively
Resources low
2018, 7, 39AAE and ABE prove that the new regression models can generally have higher 11 of 14
accuracy than the existing proximate-based models in HHV predictions of PW samples. Among the
15 new regression models, the simple multiple linear regression model (N1) has a R2 value of 88.15%
samples.
for The best-fit
predicting HHV ofregression
PW samples.model
The(N15) has
best-fit the lowest
regression AAE(N15)
model at 5.98%
has and provides
the lowest AAEa marginal
at 5.98%
lower estimation at just 0.35%, further validating the model’s capability in predicting the
and provides a marginal lower estimation at just 0.35%, further validating the model’s capability HHV of in
PW samples.
predicting the HHV of PW samples.

34 28.52 33.48 AAE ABE 33.9


27.04
24.74 25.97
Error Percentages (%)

24 23.06 20.85

14
7.02 5.98
4 1.83 0.68

-6 E1 E2 E3 E4 E6 E7 E8 E9 E10 E12 E13 E14 E16 E17 N1 N15


-0.35
-16 -15.09

Figure 4. Comparison
Figure 4. Comparison of error percentages
of error percentages (both
(both AAE
AAE and
and ABE)
ABE) between
between existing
existing proximate-based
proximate-based
models (E1–E17) and
models (E1–E17) and new
new regression
regression models
models (N1,
(N1, N15).
N15).

4. Conclusions
The HHV (or the energy content) of PW samples is an important attribute when using PW as
an energy resource for various thermal conversion processes. In this study, a simple multiple linear
regression model and a best -fit regression model are developed to predict HHV of PW samples from
proximate analysis data. Results show that the simple multiple linear regression model (N1) can
compromise all three components of proximate analysis. Results also show that the polynomial terms
for VM, as well as interaction effects of FC and ash, are necessary for the best-fit regression model
(N15) to further lower estimation errors. The estimated HHV using the new regression models are
closer to experimental results. In addition, these new regression models provide better prediction
power than the existing proximate-based models (E1 to E17) when predicting the HHV from proximate
data for PW samples. Therefore, these new regression models can be used to predict the HHV of PW
samples from proximate analysis data, where sophisticated equipment for experimental determination
of the HHV are not available. In future study, additional PW samples will be collected from poultry
farms to study effect of proximate analysis compositions on the HHV. In addition, more powerful tools
(e.g., data mining, neural networks, machine learning) will be adopted to reduce errors and provide
much more robust results.

Supplementary Materials: The following are available online at http://www.mdpi.com/2079-9276/7/3/39/s1.


Table S1: Proximate analyses, ultimate analyses, and HHV of poultry waste samples.
Author Contributions: X.Q. reviewed published literature reviews and collected properties data of poultry waste
samples. X.Q. and S.L. conceived and designed approach to construct the regression models. X.Q. analyzed
data points and developed new regression models which presented in this study. X.Q. and S.L. wrote the draft
manuscript. A.-m.S., G.C. and S.L. reviewed this manuscript and provided their constructive comments and
suggestions to improve the quality of article.
Acknowledgments: The authors received funds from Graduate Student Association at Morgan State University for
covering the costs to publish in open access. The author (Xuejun Qian) would like to acknowledge the Graduate
Student Association, School of Graduate Studies at Morgan State University and The Abell Foundation for
providing a partial financial support for this study. In addition, author (Xuejun Qian) would like to appreciate kind
support of research facilities from Center for Advanced Energy Systems and Environmental Control Technologies
(CAESECT).
Conflicts of Interest: The authors declare no conflict of interest.
Resources 2018, 7, 39 12 of 14

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