A Simple Prediction Model for Higher Heat Value of Biomass

Nov 15, 2016 - mass which is leveraged to predict higher heating value (HHV), was ... mathematical models for predicting the heating value of biomass...
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A Simple Prediction Model for Higher Heat Value of Biomass Hongliang Qian,†,‡,# Xiaojing Guo,§,# Sudong Fan,⊥ Kiros Hagos,† Xiaohua Lu,† Chang Liu,*,† and Dechun Huang*,‡ †

State Key Laboratory of Materials-Oriented Chemical Engineering, Nanjing Tech University, Nanjing, 210009, China School of Engineering, China Pharmaceutical University, Nanjing, 210009, China § Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai, 201800, China ⊥ NANTEX Industry Co., Ltd, Zhenjiang, 212006, China ‡

ABSTRACT: A simple prediction model, based on ultimate analysis of biomass which is leveraged to predict higher heating value (HHV), was proposed in this paper. In the literature there are two facts offering some bases for the study. One is that oxygen (O) content is not an accurate value in the calculation of the reductance degree as well as the heat of combustion per unit of oxygen consumed of the biomass, and as a result, the determination of HHV turns out to be inaccurate, too. The other is that the O variable does not contribute to the overall physical interpretation of the HHV from the perspective of mathematics (the p-value), and therefore, a modified reductance degree of biomass was presented, whereas O content was neglected. According to the modified reductance degree, HHV per gram of oxygen consumed of one biomass was identified to be nearly a constant. Thus, two theoretical prediction models for the bio mass with and without sulfate (HHV′ = 873.52(C/3 + H + S/8), HHV″ = 874.08(C/3 + H)) were established. The comparison between mean absolute error (MAE) of Thornton’s method and 15 recently established empirical correlations shows that the MAE of the two prediction models is the least, which serves as strong evidence for the good HHV predictive capability of the two models, and their easy-to-operate quality as well. Furthermore, the coefficients of the two models are almost the same value, which indicates that the S content also has negligible effect on HHV. The final model that we proposed is model 2 (HHV″ = 874.08(C/3 + H)).

1. INTRODUCTION In a broad sense, the term “biomass” means organic material generated via a spontaneous or induced biological process. As an energy source, biomass includes certain types of wood, energy crops, marine algae, agricultural and silviculture residues, and certain animal, industrial, and human wastes.1,2 The theory of material and energy balances is widely cited in analyzing the processes associated with solar energy. The utilization of biomass is frequently required for engineering analysis and design. One of the most important properties in material and energy balances is the heating value.3 The heating value of a biomass fuel can be figured out experimentally by employing an adiabatic bomb calorimeter which measures the enthalpy change between reactants and products.4 The use of bomb calorimeter, though relatively simple in operation and accurate in calculation, may not always be accessible to researchers. To circumvent this problem, researchers together with their respective elemental analyzer, usually make proximate or ultimate analysis that will provide data, and thereafter work out the heating value via established empirical correlations.5 Many of the previous attempts were made to correlate the HHV with data from proximate and ultimate analysis. One of the earliest and most popular correlations is the Dulong correlation6 which was first introduced in the late 1800s and based on the data from the ultimate analysis of coal. Vargas-Moreno7 reviewed the © XXXX American Chemical Society

mathematical models for predicting the heating value of biomass materials, and among these models many have relied on the results of proximate and ultimate analysis and those of structural analysis or chemical or physical determinations. In biochemical engineering, the carbon weight fraction in a dry microbial biomass, the number of equivalents of available electrons per gram atom carbon (reductance degree) in biomass, and the heat of reaction per equivalent of available electrons transferred to oxygen, are all relatively constant.3 Erickson et al.8 have capitalized on the average values of these regularities with considerable success in his analysis of microbial growth and product formation, which states that the heat of combustion is directly proportional to the quantity of oxygen consumed in the combustion process. With Thornton’s method as a groundwork, Patel3 presented a method which utilizes the weight fraction carbon on a dry basis and employs the reductance degree so as to predict the heat of combustion of renewable resources. In the field of fires, the heat of combustion per unit of oxygen consumed is measured for evaluating the rate of heat release of fuel. Huggett9 designed a method on the basis of the generalized idea Special Issue: Proceedings of PPEPPD 2016 Received: June 28, 2016 Accepted: November 3, 2016

A

DOI: 10.1021/acs.jced.6b00537 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41

alder-fir sawdust balsam bark beech bark birch bark Christmas trees elm bark eucalyptus bark fir mill residue forest residue hemlock bark maple bark oak sawdust oak wood olive wood pine bark pine chips pine pruning pine sawdust poplar poplar bark sawdust spruce bark spruce wood tamarack bark willow wood wood residue arundo grass bamboo whole bana grass buffalo gourd grass kenaf grass miscanthus grass reed canary grass sorghastrum grass sweet sorghum grass switchgrass alfalfa straw barley straw corn straw mint straw

biomass

76.6 77.4 73.7 78.5 74.2 73.1 78 82 79.9 72 76.6 86.3 78.1 79.6 73.7 72.4 82.2 83.1 85.6 80.3 84.6 73.4 81.2 69.5 82.5 84.1 78 80.2 81.6 73.6 81.6 79.4 81.2 73.4 81.6 77.2 80.4 78.9 76.2 73.1 69.7

VMa 19.2 20 18.5 19.4 20.7 18.8 17.2 17.5 16.9 25.5 19.4 13.4 21.4 17.2 24.4 21.6 15.1 16.8 12.3 17.5 14.3 23.4 18.3 26.3 15.9 15.7 16.6 16.4 17.5 16.6 13.7 17 15.8 17.7 14.2 18.1 14.5 15.8 18.5 19.2 19.5

FCa 4.2 2.6 7.8 2.1 5.1 8.1 4.8 0.5 3.2 2.5 4 0.3 0.5 3.2 1.9 6 2.7 0.1 2.1 2.2 1.1 3.2 0.5 4.2 1.6 0.2 5.4 3.4 0.9 9.8 4.7 3.6 3 8.9 4.2 4.7 5.1 5.3 5.3 7.7 10.8

A

proximate analysis (wt %) 50.9 52.6 47.4 55.8 51.7 46.8 46.3 51.1 51 53.6 49.9 49.9 50.3 47.4 52.8 49.6 50.5 50.9 50.5 52.4 49.2 51.9 52 54.6 49 49.5 48.6 47 51.5 45.2 43.9 46.6 47.7 45 47.3 47.4 47.2 47.3 46.8 45 45.1

C 5.84 6.04 5.53 6.56 5.6 5.33 5.42 5.97 5.23 5.75 5.95 5.88 6.07 5.23 5.79 5.73 6.13 5.99 5.97 6.55 5.93 6 6.07 9.77 6 6.09 5.77 5.89 5.05 5.41 6.2 5.78 5.82 5.74 6.03 5.81 5.79 5.97 5.87 5.91 5.53

H 38.5 38.5 38.5 35 36.7 39.1 43.1 42.3 39.8 37.8 39.6 43.8 42.7 43.5 39.2 38.1 40.2 42.9 40.8 38.4 43.2 38.7 41 30.7 42.7 44 39.6 43 42.1 38.7 42.4 42.9 42.9 38.9 42.1 41.7 41.2 38.6 41.3 40.7 35.8

O 0.5 0.2 0.6 0.5 0.5 0.6 0.3 0.1 0.7 0.2 0.4 0.1 0.3 0.7 0.3 0.5 0.5 0.1 0.6 0.3 0.5 0.1 0.3 0.7 0.6 0.1 0.5 0.6 0.4 0.8 2.5 1 0.4 1.4 0.3 0.4 0.7 2.7 0.7 0.6 2.5

N

ultimate analysis (wt %) 0.04 0.1 0.1 0.1 0.4 0.1 0.05 0.03 0.1 0.1 0.11 0.01 0.1 0.03 0.07 0.08 0.01 0.01 0.02 0.1 0.02 0.1 0.1 0.11 0.06 0.06 0.08 0.13 0.04 0.12 0.26 0.14 0.15 0.14 0.05 0.09 0.1 0.2 0.12 0.07 0.25

S 19949 20597 18624 21865 19973 18306 18352 20203 19589 20699 19738 19818 20051 18574 20508 19451 20062 20181 19978 20904 19629 20353 20527 23608 19599 19841 19213 18904 19685 17856 18198 18712 19073 18048 19050 18906 18818 18955 18755 18195 17896

expt HHV kJ·kg−1 20376 21244 18704 23536 20661 18166 17513 20061 19539 21392 19967 19293 19815 17656 20937 19817 20313 19923 20046 21760 19171 20906 20698 27327 19245 19352 19273 18323 19198 17709 17589 18062 18523 17979 18723 18568 18540 19150 18466 17917 18218

calc HHV kJ·kg−1 2.14 3.141 0.43 7.642 3.445 −0.765 −4.572 −0.703 −0.255 3.348 1.16 −2.649 −1.177 −4.942 2.092 1.882 1.251 −1.278 0.34 4.095 −2.333 2.717 0.833 15.753 −1.806 −2.465 0.312 −3.073 −2.474 −0.823 −3.347 −3.474 −2.884 −0.382 −1.717 −1.788 −1.477 1.029 −1.541 −1.528 1.799

RE%

Thornton’s method 19926 20603 18643 21989 19989 18294 18221 20097 19429 20641 19739 19667 19959 18373 20439 19456 20060 20054 19921 20990 19508 20364 20454 24444 19515 19739 19200 18844 19411 17900 18227 18633 18989 18132 19045 18887 18812 19009 18768 18273 17990

calc HHV′ kJ·kg−1

model 1

Table 1. Experimental (expt) HHVs of Biomass Samples as Well as Proximate and Ultimate Analysis Calculated (calc) from the literature

19936 20606 18645 21993 19959 18295 18228 20108 19432 20644 19741 19680 19962 18383 20446 19461 20073 20067 19933 20994 19519 20367 20458 24449 19522 19747 19205 18843 19420 17899 18211 18631 18986 18129 19053 18890 18814 19001 18768 18278 17975

−0.115 0.029 0.102 0.567 0.08 −0.066 −0.714 −0.525 −0.817 −0.28 0.005 −0.762 −0.459 −1.082 −0.336 0.026 −0.01 −0.629 −0.285 0.411 −0.616 0.054 −0.356 3.541 −0.429 −0.514 −0.068 −0.317 −1.392 0.246 0.159 −0.422 −0.44 0.465 −0.026 −0.1 −0.032 0.285 0.069 0.429 0.525

model 2 calc HHV″ kJ·kg−1

RE%

RE% −0.065 0.044 0.113 0.585 −0.07 −0.06 −0.676 −0.47 −0.801 −0.266 0.015 −0.696 −0.444 −1.028 −0.302 0.051 0.055 −0.565 −0.225 0.431 −0.56 0.069 −0.336 3.562 −0.393 −0.474 −0.042 −0.323 −1.346 0.241 0.071 −0.433 −0.456 0.449 0.016 −0.085 −0.021 0.243 0.069 0.456 0.441

Journal of Chemical & Engineering Data Article

B

DOI: 10.1021/acs.jced.6b00537 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

a

C

oat straw rape straw rice straw straw wheat straw almond hulls almond shells coconut shells coffee husks cotton husks grape marc groundnut shells hazelnut shells mustard husks olive husks olive pits olive residue palm fibres-husks palm kernels pepper plant pepper residue pistachio shells plum pits rice husks soya husks sugar cane bagasse sunflower husks walnut blows walnut hulls and blows walnut shells wood-agricultural residue wood-almond residue wood-straw residue currency shredded demolition wood furniture waste mixed waste paper MAE%

80.5 77.4 64.3 73.4 74.8 73.8 74.9 73.8 76.5 78.4 65.8 73.9 77.1 72.6 79 77 67.3 72.8 77.3 64.7 64.8 81.6 80.8 62.8 74.3 85.5 76 80.7 79.6 59.3 78.5 77.2 75.1 82.9 75.8 83 84.2

VMa 13.6 17.9 15.6 15.8 18.1 20.1 21.8 23 20.7 18.2 26.4 22.7 21.4 23.3 18.7 19.9 25.5 18.9 17.5 20.9 27 17 17.8 19.2 20.3 12.4 20.9 16.9 17.5 37.9 18.2 15.9 16.7 11.6 17.3 13.4 7.5

FCa 5.9 4.7 20.1 10.8 7.1 6.1 3.3 3.2 2.8 3.4 7.8 3.4 1.5 4.1 2.3 3.1 7.2 8.3 5.2 14.4 8.2 1.4 1.4 18 5.4 2.1 3.1 2.4 2.9 2.8 3.3 6.9 8.2 5.5 6.9 3.6 8.3

A

proximate analysis (wt %)

Notation: VM, mean volatile matter; FC, fixed carbon.

42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78

biomass

Table 1. continued

45.9 46.2 40 43.5 45.9 47.5 48.6 49.5 44.1 48.7 49.8 49.2 50.7 43.9 48.9 51.2 54.2 47.2 48.4 36.1 42 50.2 49.2 40.4 42.9 48.8 48.8 53.6 53.5 48.5 50.7 47.4 47.4 42.9 48.1 49.9 48

C 5.65 6.1 4.56 4.99 5.67 6.01 5.99 5.42 4.76 8.11 5.62 7.24 5.42 8.82 6.06 6.4 5.38 6.05 6.16 4.28 2.94 6.31 6.61 5 6.34 5.88 5.33 6.54 6.5 6.03 5.8 5.49 5.78 5.95 5.96 5.88 6.6

H 42 42.4 34.4 39.7 40.5 39.2 41.1 41.7 46.9 38.4 34.5 39 41 42.6 41.2 38.2 31.7 36.8 37.5 42 43.2 41.2 41.8 35.8 44.4 43 41.7 36 35.4 41.2 39.8 39.6 38.1 43.6 37.9 40.3 36.9

O 0.5 0.5 0.8 0.9 0.7 1.1 1 0.1 1.1 1.4 2.2 1.2 1.4 0.4 1.6 1.1 1.3 1.4 2.6 2.7 3.1 0.7 0.9 0.7 0.9 0.2 1.1 1.4 1.6 1.4 0.4 0.6 0.4 1.8 1 0.3 0.2

N

ultimate analysis (wt %) 0.08 0.1 0.13 0.12 0.16 0.07 0.05 0.1 0.34 0.01 0.14 0.02 0.04 0.19 0.05 0.07 0.21 0.28 0.26 0.49 0.55 0.22 0.08 0.07 0.09 0.06 0.03 0.11 0.12 0.09 0.04 0.07 0.12 0.3 0.08 0.04 0.07

S 18351 18774 15511 17078 18321 19039 19422 19282 17342 20857 19354 20409 19683 19967 19572 20422 20457 18911 19405 14405 15344 20134 20062 15986 17989 19427 19042 21214 21152 19430 19867 18630 18795 17712 19150 19702 19489

expt HHV kJ·kg−1 17778 18344 15392 16450 18013 19186 19310 18919 15397 22130 20278 21249 19471 20528 19488 21166 22063 19458 19936 12528 13067 20262 20139 15844 17087 18991 18553 22541 22543 19303 20071 18503 19043 16759 19540 19789 20368

−3.122 −2.29 −0.767 −3.677 −1.681 0.772 −0.577 −1.883 −11.216 6.103 4.774 4.116 −1.077 2.81 −0.429 3.643 7.851 2.892 2.736 −13.03 −14.84 0.636 0.384 −0.888 −5.014 −2.244 −2.568 6.255 6.576 −0.654 1.027 −0.682 1.319 −5.381 2.037 0.442 4.51 2.971

RE%

Thornton’s method calc HHV kJ·kg−1

model 1 18309 18792 15644 17038 18335 19088 19389 19158 17036 21265 19425 20652 19501 20508 19537 20506 20504 19059 19502 14304 14857 20153 20108 16139 18039 19352 18868 21332 21269 19399 19833 18605 18864 17722 19220 19670 19749

calc HHV′ kJ·kg−1 −0.229 0.096 0.857 −0.234 0.076 0.257 −0.17 −0.643 −1.765 1.956 0.367 1.191 −0.925 2.709 −0.179 0.411 0.23 0.783 0.5 −0.701 −3.174 0.094 0.229 0.957 0.278 −0.386 −0.914 0.556 0.553 −0.16 −0.171 −0.134 0.367 0.056 0.366 −0.162 1.334 0.538

RE%

model 2 18313 18794 15641 17037 18330 19094 19397 19161 17011 21279 19423 20664 19511 20501 19546 20513 20495 19041 19487 14260 14808 20143 20114 16142 18042 19359 18878 21335 21270 19403 19843 18610 18864 17701 19225 19680 19755

calc HHV″ kJ·kg−1

RE% −0.207 0.107 0.838 −0.24 0.049 0.289 −0.129 −0.628 −1.909 2.023 0.357 1.249 −0.874 2.674 −0.133 0.446 0.186 0.687 0.423 −1.007 −3.493 0.045 0.259 0.976 0.295 −0.35 −0.861 0.57 0.558 −0.139 −0.121 −0.107 0.367 −0.062 0.392 −0.112 1.365 0.533

Journal of Chemical & Engineering Data Article

DOI: 10.1021/acs.jced.6b00537 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Figure 1. hhvi, hhvi′ and hhvi″ of different biomass. Dashed lines indicate the 1% relative error

The combustion reaction on the basis of 0.1 kg of dry and ashfree (DAF) biomass entering the control volume is described by

that the heats of combustion per unit of oxygen consumed are approximately the same for most fuels commonly encountered in fires. A measurement of the rate of oxygen consumption can therefore be converted to that of the value of rate of heat release. The former provides a simple but versatile and powerful tool for estimating the rate of heat release in fire experiments and fire tests. But with a further examination about the previous views, a critical problem is found that the inaccurate value of O content leads to inexact determination of reductance degree and heats of combustion per unit of oxygen consumed, for the actual value of O, as a calculated value, cannot be obtained by experiment. In this paper, two new prediction models for the biomass with and without sulfate on the basis of ultimate analysis of biomass that is used for predicting HHV were presented, and in the two models O content was neglected. The accuracy of their models was compared with recent biomass-based HHV correlations. The two models offer easy-to-operate quality to predict HHV and are particularly beneficial to researchers without the comparatively more expensive and complicated equipment for determination of HHV by experiment. At last, the effect of S content on HHV of biomass was discussed through the two new prediction models for the biomass with and without sulfate and the optimum model was proposed.

⎛ ⎞ y z Cx HyOz NaSb + ⎜x + − + b⎟O2 (g) ⎝ ⎠ 4 2 y a → xCO2 (g ) + H 2O(l) + N2(g) + bSO2 (g) 2 2

Reductance degree is defined as follow. γb =

4x + y − 2z + 4b x

(1)

where x, y, z, b are the mole of C, H, O, S in 0.1 kg of dry and ash-free (DAF) biomass, respectively. Therefore, x = C/12, y = H, z = O/16, b = S/32. C, H, S are figured out by elemental analyzers (wt %), and the O content usually serves as an indicator to differentiate the sum of the percentages of C, H, N, S and that of the ash (O = 100 − C − H − N − S − ash. Some authors also take Cl content into consideration apart from the C, H, N, and S content10,11), with the unit of all elements as wt %. Therefore, O cannot represent the accurate value oxygen content in that it is the sum of the contents of oxygen and other elements in the organic material. This is why the amount of O content is not an accurate value. In the research of Yin,5 a significant phenomenon has been observed that the p-value for the coefficients of O variable is higher than 0.05, implying that the variable does not contribute to the overall physical interpretation of the HHV. This study proposes a modified definition of reductance degree because of inaccurate determination of O content in biomass, in which the O content is neglected and S content is considered.

2. COMPUTIONAL METHODS According to Patel’s work3 that takes Thornton’s method as a guideline, reductance degree of the biomass (γb) is defined as the number of equivalents of available electrons in the biomass, and it is transferred to oxygen per quantity of biomass containing 1 g of atom carbon for oxidation of biomass to CO2, H2O, N2, and SO2. The values of reductance degree, C = 4, H = 1, O = −2, N = 0, and S = 4, are used below; thus, CO2, H2O, N2, and SO2 have reductance degrees of zero.

γb′ = D

4x + y + 4b x

(2) DOI: 10.1021/acs.jced.6b00537 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 2. Summary of Recent and Established Correlations Used for Predicting the HHV of Biomass no.

year

correlations

equation (1) equation (2) equation (3) equation (4) equation (5) equation (6) equation (7) equation (8) equation (9) equation (10) equation (11) equation (12)

2002 2005 2005 2005 2005 2011 2011 2011 2011 2011 2012 2012

equation (13) equation (14)

2013 2014

equation (15)

2014

HHV = 0.3491C + 1.1783H + 0.1005S − 0.1034O − 0.0151 N − 0.0211ash HHV = 19.914 − 0.2324ash HHV = −3.0368 + 0.2218VM + 0.2601 FC HHV = 0.3259C + 3.4597 HHV = 3.55C2 − 232C − 2230H + 51.2C × H + 131 N + 20600 HHV = −2.057 − 0.092A + 0.279VM HHV = −3.393 + 0.507C − 0.341H + 0.067N HHV = −3.440 + 0.517(C + N) − 0.433(H+N) HHV = 0.1905VM + 0.2521FC HHV = 0.2949C + 0.8250H HHV = 19.2880 − 0.2135 VM/FC + 0.0234 × FC/ASH − 1.9584 × ASH/VM HHV = 20.7999 − 0.3214 × VM/FC + 0.0051 × (VM/FC)2 − 11.2277 × ASH/VM + 4.4953 × (ASH/VM)2 − 0.7223(ASH/VM)3 + 0.0383 × (ASH/VM)4 + 0.0076 × FC/ASH HHV = 157.34(VM + FC) + 4243.97 HHV = 0.367C + 53.883O/(2.131C2 − 3.299) + (C*H − 115.971)/(10.472*H + 0.129C*O) − 91.531/(35.299+N) + 232.698/(77.545 + S) HHV = 0.365 × FC + 0.131 × VM + 1.397/FC + 328.568 × VM/(10283.138 + 0.531 × FC3 × ash − 6.863 × FC2 × ash)

HHV per gram of oxygen consumed of one biomass i (hhvi′) is defined as follows. hhv′i = HHVexp per O2 =

0.1HHVexp

(

32 x +

y 4

)

=

+b

MAE% =

0.1HHVexp

Where 0.1 means the mass of biomass is 0.1 kg, 32 represents y the relative molecular mass of O2, x + 4 + b represents mole of oxygen consumed of one biomass, 8 is the relative atomic mass of O, HHVexp denotes the experimental value of HHV. Thereafter, the average HHV per gram of oxygen consumed of n different biomasses in Table 1 (hhv′) can be obtained.

1 n

(4)

i=1

Therefore, the calculated HHV′ (model 1) can be obtained through the following equation: HHV′ = hhv′ × 80 × xγb′

(5)

In this case, S is also ignored for the negligible concentration of S in biomass, and the second modified definition of reductance degree (without sulfate) is written as follows.

γb″ =

4x + y x

HHVexperimental

proximate ultimate

kJ/kg MJ/kg

Phichai et al.15 Ghugare et al.16

proximate

MJ/kg

Ghugare et al.16

n

∑ |RE| × 100 (8)

i=1

= 10.919 × 80xγb′

With the help of eqs 3−5, the calculated HHV(Thornton’s method) and HHV″(model 2, without sulfate) can be obtained via representing γ′b by γb and γ″b , respectively. HHVs per gram of oxygen consumed of one biomass i are defined as hhvi (Thornton’s method) and hhvi″ (model 2), respectively. And the average HHVs per gram of oxygen consumed of n different biomasses in Table 1 are defined as hhv (Thornton’s method) hhv″ (model 2), respectively. Relative error (RE) and mean absolute error (MAE) were applied to estimate the developed models. RE% =

Channiwala and Parikh6 Shene and Azevedo4 Shene and Azevedo4 Shene and Azevedo4 Friedl et. al 13 Callejon-Ferre et al.10,11 Callejon-Ferre et al.10,11 Callejon-Ferre et al.10,11 Yin5 Yin5 Nhuchhen and Salam14 Nhuchhen and Salam14

HHV′ = hhv′ × 80 × xγb′

(6)

HHVcalculated − HHVexperimental

ref

MJ/kg MJ/kg MJ/kg MJ/kg kJ/kg MJ/kg MJ/kg MJ/kg MJ/kg MJ/kg MJ/kg MJ/kg

3. RESULTS AND DISCUSSION A database of experimental HHVs of biomass samples as well as proximate and ultimate analysis was created from the literatures12 and presented in Table 1. VM and FC in Table 1 mean volatile matter and fixed carbon in a biomass, which are determined by proximate analysis. Figure 1 panels a, b, and c display hhvi, hhv′i and hhv″i of different biomasses. It can be seen from Figure 1a that a large number of hhvi values of biomass appear beyond the ±1% relative error range. That is to say, most of hhvi values are more or less far from the average value hhv (14.194). According to Figure1b,c, it can be concluded that hhv′i and hhv″i values of different biomass remain respectively close to the average value hhv′ (10.919) and hhv″ (10.926), and most of hhv′i and hhv″i values are within the ±1% relative error range, indicating that it is tenable to consider hhvi′ and hhvi″ as a constant. The calculated formulas of HHV′ and HHV″ can be rewritten as follows.

n

∑ hhvi′

unit

ultimate proximate proximate ultimate ultimate proximate ultimate ultimate proximate ultimate proximate proximate

With the help of MAE, (based on the average of the filtered data in Table 1) the closeness of the predicted HHVs to the experimental values can be basically quantified, and lower MAE indicates higher accuracy of a particular model.

8xγb′ (3)

hhv′ =

1 n

analysis basis

= 873.52(4x + y + 4b) ⎛1 1 ⎞ = 873.52⎜ C + H + S⎟ ⎝3 8 ⎠

(9)

HHV″ = hhv″ × 80xγb″ = 10.926 × 80xγb″ = 874.08(4x + y) ⎛1 ⎞ = 874.08⎜ C + H⎟ ⎝3 ⎠

× 100 (7) E

(10) DOI: 10.1021/acs.jced.6b00537 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

4. CONCLUSIONS Two simple prediction models for prediction of HHV, based on ultimate analysis of biomass, have been developed via modifying reductance degree of the biomass. These models are easily applicable for they require only C, H or C, H, S contents (both on wt.% dry biomass basis). The conclusions are as follows. (1) The two prediction models are based on a modified reductance degree, the theoretical significance of which distinguishes them from other correlations based on regression in mathematics, and more importantly, their MAE is the least. (2) After neglecting O content, the heat of combustion per unit of oxygen consumed is proven to be nearly a constant as most of the values are within the ± 1% relative error range. (3) S content exerts a negligible influence on MAE when applying the two prediction models to calculate the HHV of biomass, therefore, model 2 (HHV″ = 874.08(C/3 + H)) is proposed finally. (4) Correlations developed from ultimate analysis exhibit lower MAE values than those developed from proximate analysis.

With the help of the two models mentioned above, HHV′ and HHV″ of various biomasses are thus calculated. While the MAE% of the Thornton’s method is 2.971, that of model 1 and model 2 are respectively 0.538 and 0.533. These results indicate the good accuracy of model 1 and model 2 as well as the inaccurate determination of O content in biomass that exerts a profound influence on the HHV of biomass. The MAE% of model 1 and that of model 2 are nearly the same, which demonstrates that the S element content has an insignificant effect on the higher heat value and the assumption about the negligibility of S element is correct. For the convenience of comparing the accuracy of model 1 and model 2 with that of the exiting models in the literatures, 15 recent correlations (published after 2002) applied for predicting the HHV of biomass are listed in Table 2, among which eight of the correlations are derived from proximate analysis while the other seven from ultimate analysis. With the help of the data from Table 1, HHVs of biomass have been calculated through all the 15 equations. Figure 2 shows the

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AUTHOR INFORMATION

Corresponding Authors

*Tel.: +86 25 83587205. E-mail: [email protected]. *Tel.: +86 25 83244816. E-mail: [email protected]. ORCID

Kiros Hagos: 0000-0002-8834-1533 Author Contributions #

H.Q. and X.G. contributed equally to this work and should be considered cofirst authors. Funding

This work was financially supported by Chinese MOST 973 project (2013CB733501), Natural Science Foundation of China (21406272, 21136004, 21476106, 21306220, 21676291), the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD), Jiangsu Natural Science Foundation (BK20130062), and Jiangsu Planned Projects for Postdoctoral Research Funds(1402060B).

Figure 2. MAE (comparing with experimental HHV) of the 17 correlations. White columns represent correlations developed from proximate analysis while gray columns mean correlations derived from ultimate analysis.

Notes

The authors declare no competing financial interest.

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NOMENCLATURE HHV per gram of oxygen consumed of one biomass i (Thornton’s method), kJ.kg−1 hhvi′ HHV per gram of oxygen consumed of one biomass i (model 1), kJ·kg−1 hhv″i HHV per gram of oxygen consumed of one biomass i (model 2), kJ·kg−1 average HHV per gram of oxygen consumed of different hhv biomasses (Thornton’s method), kJ.kg−1 average HHV per gram of oxygen consumed of different hhv′ biomasses (model 1), kJ·kg−1 average HHV per gram of oxygen consumed of different hhv″ biomasses (model 2), kJ·kg−1 HHV HHV calculated by Thornton’s method, kJ·kg−1 HHV′ HHV calculated by model 1, kJ·kg−1 HHV″ HHV calculated by model 2, kJ·kg−1 HHVexp Experimental HHV, kJ·kg−1 γb reductance degree (Thornton’s method) γb′ Modified reductance degree (Model 1) γb″ Modified reductance degree (Model 2)

MAE of the developed correlations (model 1 and model 2) (as compared to experimental values of HHV) and their comparison with the recent empirical correlations in Table 2 (correlations 1−15). The 17 correlations are able to predict HHVs of biomass with MAE less than 7%, which proves their good applicability. From the 17 correlations, it can be seen that correlations derived from ultimate analysis exhibit lower MAE values than those developed from proximate analysis. This indicates that correlations derived from ultimate analysis can provide a higher accuracy of HHV predictions. This observation is in accordance with the work researched by Sheng and Azevedo.4 The reason is maybe VM and FC provide an oversimplification to the actual energy content of biomass. Another obvious observation is that MAE of the two prediction models (model 1 and model 2) in this paper is less than that of all the 15 correlations in the literatures, which effectively reflects the former’s good HHV predictive capabilities. Moreover, compared to most of the recent correlations, the two prediction models are simpler in both calculation and operation.

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DOI: 10.1021/acs.jced.6b00537 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

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DOI: 10.1021/acs.jced.6b00537 J. Chem. Eng. Data XXXX, XXX, XXX−XXX