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Hydrothermal carbonization of waste biomass to fuel: A novel technique for analyzing experimental data
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Hydrothermal carbonization of waste biomass to fuel: A novel technique for analyzing experimental data Alberto Gallifuoco*, Luca Taglieri, Alessandro Antonio Papa University of L’Aquila, Department of Industrial and Information Engineering & Economics, Via G. Gronchi, 18, 67100, L’Aquila, Italy
a r t i c l e i n f o
a b s t r a c t
Article history: Received 19 March 2019 Received in revised form 28 June 2019 Accepted 20 October 2019 Available online xxx
This paper deals with a new stochastic approach to handling data from waste biomass hydrothermal carbonization. The dynamics of hydrochar properties are described using the concept of reaction time distributions. A set of cumulative frequency distribution functions is provided that could very well correlate the most disparate experimental data. The procedure for analyzing the results is detailed. The method is illustrated with experiments on batch runs with five different wastes from the agro-food industry. Isothermal reactions (200 C) were performed up to 120 min at a constant 7/1 water/biomass ratio. The regression analyses fully confirm the correctness of the method. The use of dynamical van Krevelen plots is proposed. The approach allows also obtaining from lab-scale runs fundamental information for the correct waste-to-fuel process development at the industrial scale. The mathematics is not demanding and, unlike other methods, the difficulties substantially do not increase with the complexity of the modeled kinetic scheme. © 2019 Elsevier Ltd. All rights reserved.
Keywords: Hydrothermal carbonization Agro-food wastes exploitation Hydrochar formation Stochastic modeling Van krevelen plot
1. Introduction Hydrothermal carbonization (HTC) could add energy value to waste biomass and improve the sustainability of the energy supply chain [1,2]. The numerous potential applications, the easiness of implementation, and the versatility as a waste-to-fuel process maintain the technical and scientific research on this topic lively and intense [3e5]. As a further convenience, the HTC energy balance, not particularly advantageous for lignocellulosic materials, becomes favorable in the case of wet materials [6]. During the progressive transformation of the native substrate to hydrochar, chemicals transfer between the solid phase and the hot compressed water. These phenomena improve the properties of the hydrochar as fuel. The solid densifies the energy content, releases impurities that could be harmful as a result of the combustion, and levels out its chemical-physical properties regardless of the heterogeneity of the native biomass [7,8]. A better understanding of these mechanisms would be fundamental for the correct technology transfer from research to industry. Researchers actively study the chemicalphysical evolution of the solid phase and propose techniques to monitor it [9e12]. The dynamics of the reacting system and the
* Corresponding author. E-mail address: [email protected] (A. Gallifuoco).
development of the hydrochar properties depend mainly on temperature and time, even for HTC of non-conventional, water-rich substrates [13]. Although the severity factor could lump satisfactory temperature and time, investigate the effect of time alone could give a broader view of the process [14]. The higher the retention time in the HTC reactor, the better the properties of the solid fuel obtained, but also the worse the energy balance of the process. Most likely, an optimum should be sought, especially if one keeps in mind to move from batch to continuous HTC, where the reactor retention time should be tuned accurately. To date, kinetic studies are a challenging topic potentially fruitful of valuable new information. Researchers agree that the mathematical modeling of the complex kinetics is not yet wholly satisfactory, whatever the adopted approach be [5]. The complexity of the network of chemical reactions, however not fully understood yet, makes the use of closed-form solutions cumbersome. Furthermore, the reaction patterns may vary depending on the type of biomass treated, and the exploitation of waste biomass is undoubtedly a case of variable raw materials. HTC deserves the international attention also for non-energy implementations, such as synthesis of performing nanomaterials [15] or removal of pollutants from both liquid and gaseous phases [16,17]. These second-generation HTC processes often require the addition to the reaction mixture of catalysts or substances which could establish new kinetic patterns [18]. Non-conventional
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substrates could undergo HTC through unusual kinetic patterns. This difficulty could occur when dealing with mixtures of plastic and biomass, a case of the waste-to-fuel chain rich in interesting developments. As an example of these hybrid materials, an improved PVC de-chlorination was observed during HTC in the presence of lignin [19]. Finally, multistep HTC processes are under study for the simultaneous upgrade of biomass to fuel and recover of platform chemicals from the liquid phase [20,21]. In the authors’ opinion, such a vast and differentiated scenario requires to collect a more significant number of kinetic data and to analyze them through several kinetic models. More in-depth information could result from approaching the problem with more than one method. Recent studies gave a satisfactory interpretation of lignocellulosic biomass HTC as a stochastic phenomenon and showed how to treat the experimental data accordingly [22]. One of the scopes of the present paper is to extend the analysis to other kinds of biomass. The study also illustrates some significant new practical effects and developments, made possible by the technique adopted here. Keeping in mind a plausible waste-to-fuel chain, the experiments here discussed concern typical scraps from the local agro-food industry: freezing industry of potatoes, peas, and carrots (potato, pea, and carrot), olive tree pruning (olive) and wheat bran (bran). The attention is focused on the evolution of the solid phase during the reaction, particularly on the dynamics of its properties as a fuel. An innovative method is also proposed to acquire information relevant to the development of industrial HTC through the use of the traditional van Krevelen plot. 2. Materials and methods The residual biomass has been collected directly in the district as a representative sample of the local agro-industrial activities. Potato, carrot, pea, and bran were dried in an oven at 60 C for 48 h and then milled to 0.5 mm mesh size. Olive was milled, then dried in an oven at 105 C for 24 h. The HTC apparatus is described in detail in a previous study [23]. The substrates and the demineralized water (pH ¼ 6.3 ÷ 6.5) were accurately weighed and loaded into the reactor, which was then sealed and evacuated. The reactor warmup lasted 20 min, and after that, the residence time was measured. At the end of each run, the reactor was cooled down within 4 min by quenching it first with air and then by immersion in a cold water bath. In all the experiments, the amount of gas produced was negligible. The condensed phase recovered by the reactor was filtered to separate liquid and solid products. The wet spent filter and the solid phase were dried (oven, 105 C, 24 h). The filter and the solid were weighed before and after drying, for measuring the yield respect to the dry biomass loadings. The hydrochar was stored in vials and analyzed for the CHNS (Perkin Elmer-2440 series II elemental analyzer). Elemental analyses followed the ASTM D3176e89 standard test method for coal and coke, calculating oxygen content by the difference. The pH of the process liquid was 2.5 ÷ 3.1, regardless of the biomass and almost constant with the residence time. All measurements were in triplicate. 3. Results and discussions In the present approach, the HTC batch reactor is modeled as a vast set of biomass particles. Each element, at a random time, could undergo a transformation releasing a chemical group into the liquid phase. The likelihood of a reaction occurring at a particular site depends only on the current state of the solid particle and not on its previous history. Accordingly, one could use a stochastic
distribution of reaction times for modeling the time course of the process. Previous evidence endorsed the validity of the method, highlighted the mechanistic foundations, and demonstrated some preliminary practical results obtained with lignocellulosic biomasses [22]. Data available in the literature for several materials show that, although the major part of the batch HTC process occurs within the first hour of retention, an appreciable part of the biomass reacts in a longer time. The rate of transformation reaches a peak and then progressively declines: this implies that the probability density time distribution should be right-skewed. In this sense, a convincing and fruitful analogy exists between this HTC model and survival and failure analyses, if one replaces the lifetime duration with the reaction time. The Burr equations are a set of 12 cumulative distribution functions which yield the proper density shape [24]. This family of distributions, easy to handle mathematically, gives satisfactory fittings when applied to the survival analysis [25]. The most used function is the so-called Burr type XII distribution, already introduced by the authors into HTC studies. In the following, the method is enlarged and expressed formulaically, testing its validity with data of HTC of a broader range of residual biomasses. The proposed technique could be used to model the solid yield, the CHNS composition, the higher heating value (HHV), the atomic ratios on the van Krevelen plot and many other properties. Each of these properties, say y(t), is time depending and vary from an initial (y0) and a final (y∞) value. The extent of transformation is given by:
XðqÞ ¼
yðqÞ y0 y∞ y0
(1)
In equation (1), the time is scaled by a characteristic reaction time, i.e., q ¼ t/th. If one considers the portion of the particle population which has already reacted within the time q, a cumulative frequency distribution (CFD) describes the function X. Table 1 lists the only 5 out of the 12 Burr CFDs that have a trend conform to the observed HTC dynamics. The second column reports the CFDs, while the third column displays the corresponding functions y calculated according to the definition (1). Each of these latter functions could correlate experimental data concerning any time-depending property of the solid phase measured during HTC. As an example, Fig. 1 concerns the carbon percentage (C%) measured in the hydrochar at fixed reaction time (0, 10, 15, 30, 60, and 120 min) with the five different biomasses tested. The estimated values obtained fitting the data with the five y of Table 1 are reported as a function of the corresponding measured values. A total of 150 points, all of them very well aligned along the bisector (R2 ¼ 0.99989), testifies to the goodness of the correlations. It is noteworthy that this satisfactory result is valid regardless of the type of biomass. Starchy substances (potato), lignocellulosic biomass (olive), high-protein content materials (pea) equally well arranged on the bisector. This finding supports the hypothesis that a general mechanism rules the phenomenon, by which a method for testing kinetic patterns have been proposed in another paper submitted elsewhere. On the contrary, the present paper slants toward getting practical information not necessarily deepening the kinetic analysis. In this sense, a first result shown by Fig. 1 is the possibility to model the dynamics of an industrial reactor fed with a variable mixture of agro-food scrapes. The time-scale parameter th measures the characteristic time of the phenomenon and furnishes valuable information on the rapidity of the transformation for the different biomasses, thus helping in designing the optimal process time. The five proposed CFDs also depend on one or two shape parameters. The first of
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Table 1 Cumulative distribution functions and corresponding y functions. Type
XðqÞ
yðqÞ ¼ y0 þ ðy∞ y0 Þ XðqÞ
VII
1 ½1 þ tanhðqÞp 2p p 2 tan1 ðeq Þ
1 ½1 þ tanhðqÞp y0 þ ðy∞ y0 Þ 2p p 2 y0 þ ðy∞ y0 Þ tan1 ðeq Þ
VIII
p
IX X XII
k ½ð1 þ eq Þp 1 k ½ð1 þ eq Þp 1 þ 2 ð1 eq Þp 2
p
y0 þ ðy∞ y0 Þ
y0 þ ðy∞ y0 Þ ð1 eq Þp 2
p k
ð1 þ q Þ 1 ð1 þ qp Þk
them, p, rules the steepness of the system dynamics and is the most important. The second one, k, could to the best of our knowledge set constant to the unity, as this value give the best fitting for all the experiments performed so far. It is appropriate to maintain the presence of the parameter in the equation, as in the Burr’s original XII distribution, for the sake of flexibility. Reaction conditions very different from those studied here could give k values significantly different from the unit. Fig. 2 is an example of the quality of the fittings obtainable.
Fig. 1. Comparison between measured carbon contents and values estimated with the five functions.
Fig. 2. Solid yield as a function of process time for the five biomasses. The regressions are reported as full (XII) and dashed (VII) lines.
k ½ð1 þ eq Þp 1 k ½ð1 þ eq Þp 1 þ 2 p k
y0 þ ðy∞ y0 Þ
ð1 þ q Þ 1 ð1 þ qp Þk
The hydrochar yields measured with all the biomasses are reported as a function of the reaction time. The solid lines are the regressions obtained with the type XII, the dotted ones those obtained using the type VII. These last lines are traced only for potato and olive for the sake of clarity since they differ slightly to the others, but similar results repeat whatever the biomass and the CFD. The regression parameters are reported in Table 2. The estimates y0 and y∞ are obtained by regression via the cumulative frequency distribution functions. y (0) and y (120) are the experimental measures, respectively, at zero and 120 min of reaction. It appears that model predictions almost coincide with the measures. This substantial identity allows two essential comments. First, at the adopted operational conditions, the conversion process occurs almost entirely within 2 h of retention into the reactor, so that this reaction time could be considered the endpoint. Second, y0 and y∞ could be deleted from the list of parameters to be estimated, and replaced by the respective measured values. Table 2 also shows that the parameter th varies in a broad range for different biomass and CFD, from 10 to 30 min th has the physical meaning of the characteristic time of the process, i.e., the reaction time is scaled by it. This critical finding ensures that the model could apply to several different HTC processes, from those treating biomasses easy to convert, to those employed for recalcitrant materials. Another significant result appears by inspection of Fig. 2. The yield decreases with time for the lignocellulosic olive, while increases more or less markedly for the other materials, and neatly for potato. This evidence agrees with the widely accepted hypothesis, which considers two reactions for the formation of hydrochar. The first one, relatively fast, is the direct, solid-phase transformation of the biomass. The second one, slower, occurs between liquid and solid phase and is due to the recombination of dissolved chemicals. According to this scenario, the trend observed with potato should be attributed to the predominance of the second step, since hot water dissolves almost entirely the starchy materials during the reactor warmup time. A more in-depth study of the dynamics of the liquid phase composition could support the hypothesis. For this study, it is remarkable that the proposed regression functions could model both trends as well. Furthermore, CFD functions can correlate the time course of the hydrochar HHV equally well. The HHV calculation went according to the equations universally used in the literature, and the results are not reported here for the sake of brevity. Some recent calorimetric measurements are confirming this result. The method of using CFDs allows not only to have available a set of functions which ensures good correlations in general. One could also infer valuable information on the relative rate of the phenomena occurring during HTC. The procedure could be as follows. The second column of Table 3 lists the time derivative of each CFD, i.e., the corresponding probability density functions (PDF). These functions f(q) have the dimension of a frequency and could be regarded as a time variable pseudo-first-order kinetic
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Table 2 Regression parameters for data of Fig. 2. Substrates
p
y0 ½C%
t h ½min
y∞ ½C%
yð0Þ½C%
R2
Estimated
yð120Þ½C%
Measured
Type XII Olive Pea Bran Carrot Potato
2.52 3.39 3.61 1.06 2.09
10.63 18.86 24.09 22.55 25.89
0.945 0.404 0.297 0.293 0.162
0.752 0.435 0.428 0.395 0.388
0.871 0.987 0.938 0.993 0.995
2.89 3.63
13.84 30.18
0.975 0.141
0.803 0.279
0.902 0.999
0.947 0.404 0.307 0.293 0.161
0.766 0.436 0.434 0.379 0.376
Type VII Olive Potato
Table 3 Probability density functions and rates of property change. Type
f ðqÞ
VII
2q p1 e 2p e2q þ 1 th eq þ eq p 2 p eq tan1 ðeq Þp1 p th e2q þ 1
VIII
IX
2kp th
X
2p th
XII
kp th
dy ¼ ðy∞ y0 Þ f ðqÞ dq
eq ðeq þ 1Þp1
½kðeq þ 1Þp k þ 22 ð1 e2q Þp ðe2q 1Þ
ðy∞
2p y0 Þ t h p 2
ðy∞ y0 Þ ðy∞ y0 Þ ðy∞
q
dy ¼ ðy∞ y0 Þf ðqÞ dq
(2)
Table 3 also reports the five derivatives calculated according to Equation (2). Fig. 3 illustrates the trend of the five f(q) functions, which Equation (2) shows to be proportional to the rate of change. The plot is drawn adjusting the parameter k, where present, to the unity, while p and th to the mean of the estimated values of
Fig. 3. The five CFDs dynamics as a function of dimensionless time.
2kp th
eq tan1 ðeq Þp1 e2q þ 1
eq ðeq þ 1Þp1
½kðeq þ 1Þp k þ 22 ð1 e2q Þp ðe2q 1Þ
kp th
ðqp þ 1Þkþ1
ðy∞ y0 Þ
constant. Making use of Equation (1) and of the relationship which holds by definition between any CFD and its PDF, one can get the rate of variation of any property during HTC, viz:
th
p
2p y0 Þ th
p
ðqp þ 1Þkþ1
p
p1 e2q e2q þ 1 eq þ eq
qp
Table 2, respectively 2.74 and 21 min. The use of average values does not invalidate the general qualitative trend of the curves in Fig. 3. The features of the different curves steer the proper choice for modeling experimental data. Type VII exhibits the higher frequencies, type IX the lower ones. Types X and XII are more suitable for describing HTC processes whose initial velocity is slow, while the initial value of the remaining types is non-zero and depends on the combination of the parameter values. Finally, type IX is the only one monotonically decreasing. Although the mathematical analysis ensures that all the curves are right-skewed, for particular combinations of parameter values, the left part of the curve IX rests on the second quarter of the plot. One could take advantage of the feature of type IX for analyzing data where, at the adopted operational conditions, a significant part of the process occurs during the reactor warmup. In other words, instead of dealing with a complicated analysis of the heating transient, it could be assumed that the initial condition of the reactor is the state at the instant when the temperature reaches the set-point d the faster the heating phase, the better the validity of this approach. Fig. 4 is the starting point for implementing a new procedure for analyzing experimental data by use of Equation (2), without necessarily hypothesize a specific kinetic mechanism. The plot reports the time course of the atomic ratios, O/C (full symbols) and H/C (open symbols) as measured for the five biomasses. H/C and O/C ratios are critical parameters for monitoring the quality of the hydrochar as a fuel, in comparison to fossil materials. Carbon-oxygen and carbon-hydrogen bonds contain less energy than the carbon-carbon bond. As a consequence, the higher the proportions of oxygen and hydrogen to that of carbon, the lower the energy value. The fittings of experimental data to type XII
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speculate that the solid evolution could depend on a linear combination of elimination reactions (dehydration, decarboxylation) which transfer chemicals to the liquid phase at a constant rate. So was demonstrated to be the case for purely wooden biomasses [11]. This behavior not necessarily could be that of non-lignocellulosic biomass. A more in-depth analysis could start by calculating the rate of variation for each of the ten series of data in Fig. 4. One can compute the instantaneous slope of a van Krevelen trajectory according to Equation (2):
3 2 H C H H d H C C C 7 fHC ðtÞ 6 d ∞ 07 ¼ dt ¼ 6 5 fO ðtÞ ¼ ½sðfÞ 4 O O C O d O C C C C ∞ 0 d dt Fig. 4. Atomic ratios as a function of time for the five biomasses (open symbols, H/C; closed symbols, O/C). The regressions are reported as full (H/C) and dashed (O/C) lines.
are reported as solid lines for H/C and dashed lines for O/C. The regression parameters, not reported for the sake of brevity, are satisfactory as usual. Fig. 4 illustrates the possibility of using the y functions for fitting disparate data. Further confirmations come from other, preliminary experiments (not reported here) which show that the method of CFD functions also holds for higher temperature hydrothermal conversions, included supercritical water conditions, and for more prolonged reactions. The proposed technique is not only a new procedure for effectively correlating experimental data, but is also a harbinger of practical applications. The use of the proposed distribution functions for modeling the kinetic constants also has a further practical advantage. This novel method is less sensitive to the complexity of the reaction mechanism hypothesized than the traditional ones, based upon the solution of coupled differential equations, and the subsequent correlation of experimental data. Besides, the stochastic approach could easily lead to introduce into the HTC studies techniques such as Monte Carlo methods, already employed by some authors for modeling in the field of biomass pyrolysis. The ongoing research is moving on this way, and the first results are encouraging. The success of CFDs in predicting the dynamics of hydrochar properties also makes them useful for the correct development of the process on an industrial scale. The choice of the correct residence time is fundamental for the optimization of continuous reactors, seeking for both the quality of the solid biofuel and the productivity of the industrial plant. Small-scale, batch HTC reactor processes could also tune the retention time to the proper value exploiting the features of the distribution functions here introduced. Since the method applies to the atomic ratios satisfactorily, a further analysis is possible that has significant repercussions on the van Krevelen plot. This kind of diagram, long ago introduced, is still universally employed for illustrating HTC data, in particular, the evolution of raw biomass toward solid fuel with the increasing process temperature. The dynamics of biomass conversion reflects on the plot in a time-depending trajectory, and this kind of representation appears in the literature more seldom, although, in the authors’ opinion, this approach would be fruitful. The closer a point of the line is to the lower left corner, the better is the quality of the solid as fuel. Should the slope of the trajectory be constant with time, the rate of H/C diminishing would be proportional to that of O/C during the whole process. Under that condition, one could
(3)
In this last expression, the quantity inside the square brackets represents the slope of the segment between the initial and final reaction point on the van Krevelen (s). Should the ratio of the f function of H/C to that of O/C (f), keep constant during the time, the trajectory would be a straight line. In particular, if the ratio is equal to the unit, then the trajectory coincides with the segment. However, should f depend on time, the trajectory would result in a curve. Fig. 5 shows the dynamics featured by the five substrates studied. The function f is computed using the values of the parameters values estimated from data of Fig. 4 for each of the substrates. The horizontal dashed line is the critical value, i.e., unity. The parts of curves below the critical line indicate that the solid is releasing oxygen groups faster than hydrogen groups (instantaneous slope of the trajectory lower than s). Above the critical limit, the reaction proceeds more quickly for hydrogen than for oxygen (instantaneous slope higher than s). All the curves present a similar behavior, starting from zero, passing through a maximum, and asymptotically tending to zero for long reaction time. Considering this common behavior at the extremities of the time interval, one could say that the HTC process starts and ends releasing at a relatively small rate the hydrogen groups in the hot compressed water. Fig. 5 also shows that for all the tested biomasses, a range of reaction time exists within which the curves exceed the critical value. The amplitude of this time interval and the height of the peak value, however, depend on the biomass. As an example, most of the curve of pea lies below the critical line, while potato features the highest
Fig. 5. Dimensionless group f vs. process time for the five biomasses.
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peak value (in fact, for the sake of readability of the diagram the values reported in Fig. 5 are halved). These findings show that the dynamics of HTC strongly depends on the nature of the biomass and should warn the researchers not to adopt a unique kinetic model whatever the biomass is, but to consider the peculiarity which a specific class of materials has. In other words, a kinetic model describing the HTC kinetics of both starchy materials (as potato in the present study) and lignocellulosic biomass is likely to be not satisfactory. Fig. 6 strengthens this hypothesis, showing the data obtained with all the five substrates in a dynamical van Krevelen plot. The solid lines connect the initial and final points (closed symbols). The corresponding slopes s are reported in Table 4. The slope of straight lines on the van Krevelen indicates the relative extent of the main reactions occurring during HTC (dehydration, decarboxylation, and other reactions). The wide range of values displayed in Table 4, from 0.90 to 3.21 shows that the dominant elimination reactions depend on the type of raw material processed. A closer look at Fig. 6 also shows that the time sequences of the experimental points (open symbols) do not arrange on the lines but twist more or less markedly around them. To the best of Author’s knowledge, the argumentations of this paper constitute the first explanation of the presence of curved trajectories on dynamical van Krevelen diagrams. It is likely to suppose that a significant portion of the data presented in the literature exhibit similar behavior. An odd choice of the scales on the axes could mask this tendency, and consequently, one could consider correct to fit data linearly, even obtaining acceptable regression coefficients. The magnification of the diagram should make observable the correct patterns, which unquestionably demonstrate that the nature of the chemical reactions between the solid and the liquid phases changes during HTC. This information could result valuable for optimizing the process, e.g., to set the correct residence time in a continuous reactor to recover platform chemicals from the liquid. Out of the five biomasses, the only olive gives rise to a nearly straight line in Fig. 6, and this result confirms the behavior already observed for wooden materials. To support the argumentation stated here, a clear example of a van Krevelen plot with curved time-trajectories appears in the recent literature [26]. Those Authors presented data on the HTC of pure cellulose, straw, and poplar, performed in the range 200 ÷ 260 C and from 0 to 480 min. The similarity of the experimental conditions with that here adopted confirms the validity of the approach discussed here.
Fig. 6. Dynamical van Krevelen plot. Initial and end point reaction time are signaled by full symbols. The solid lines show the different slopes s.
Table 4 Regression parameters of Fig. 4 and corresponding s values. Substrates
Olive Pea Bran Carrot Potato
O/C
H/C
s
p
th
p
th
2.03 2.93 1.20 1.61 1.81
93.90 6.95 11.60 2.39 13.08
1.53 3.74 2.29 2.27 2.40
24.49 10.11 13.01 9.94 13.27
0.90 3.21 1.94 1.04 1.76
Trusting in the potential greater flexibility of the CFD method compared to more traditional approaches, research is in progress testing more waste biomass, performing detailed analyses of the liquid phases, and sampling the reacting system at shorter time intervals. 4. Conclusions The proposed set of statistical functions fit satisfactory data of batch HTC of different residual biomasses of the agro-food industry, spanning from wooden to starchy materials. The functions are not empirical, but base on a statistical interpretation of the reactions occurring during HTC. The dynamics of the actual solid/liquid reacting system is well described by the model equations. The procedure for analyzing the HTC experiments is detailed, proved by practical examples, and assessed for possible extensions. Novel use of van Krevelen plots is discussed, which could furnish valuable information for steering the industrial development of the HTC process. The flexibility of the proposed method and the relatively simple mathematics required portend future developments, especially in the modeling of HTC complex reaction mechanisms. The research is pursuing these objectives by testing other biomasses and performing experiments at a higher temperature. This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.renene.2019.10.121. References [1] P. Zhao, Y. Shen, S. Ge, Z. Chen, Clean solid biofuel production from high moisture content waste biomass employing hydrothermal treatment, Appl. Energy 131 (2014) 345e367. [2] M. Heidari, A. Dutta, B. Acharya, S. Mahmud, A review of the current knowledge and challenges of hydrothermal carbonization for biomass conversion, J. Energy Inst. (2018), https://doi.org/10.1016/j.joei.2018.12.003. [3] M.T. Munir, M.M. Mansouri, I.A. Udugama, S. Barautian, K.V. Gernaey, B.R. Young, Resource recovery from organic solid waste using hydrothermal processing: opportunities and challenges, Renew. Sustain. Energy Rev. 96 (2018) 64e75. [4] C. He, C. Tang, C. Li, J. Yuan, K.-Q. Tran, Q.-V. Bach, R. Qiu, Y. Yang, Wet torrefaction of biomass for high quality solid fuel production: a review, Renew. Sustain. Energy Rev. 91 (2018) 259e271. [5] S. Roman, J. Libra, N. Berge, E. Sabio, K. Ro, L. Li, B. Ledesma, A. Alvarez, S. Bae, Hydrothermal carbonization: modeling, final properties Design and Applications: a Review, Energies 11 (2018) 216, https://doi.org/10.3390/en11010216. [6] J.A. Libra, K.S. Ro, K. Kammann, A. Funke, N. Berge, Y. Neubauer, M.-M. Titirici, C. Fühner, O. Bens, J. Kern, K.-H. Emmerich, Hydrothermal carbonization of biomass residuals: a comparative review of the chemistry, processes and applications of wet and dry pyrolysis, Biofuels 2 (1) (2011) 89e124. [7] S. Nizamuddin, N.M. Mubarak, M. Tiripathi, N.S. Jayakumar, J.N. Sahu, P. Ganesan, Chemical, dielectric and structural characterization of optimized hydrochar produced from hydrothermal carbonization of palm shell, Fuel 163 (2016) 88e97. [8] A.Y. Krylova, V.M. Zaitchenko, Hydrothermal carbonization of biomass: a review, Solid Fuel Chem. 52 (2) (2018) 47e59. [9] X. Zhuang, H. Zhan, Y. Song, C. He, Y. Huang, X. Yin, Insights into the evolution
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Renewable Energy journal homepage: www.elsevier.com/locate/renene
Hydrothermal carbonization of waste biomass to fuel: A novel technique for analyzing experimental data Alberto Gallifuoco*, Luca Taglieri, Alessandro Antonio Papa University of L’Aquila, Department of Industrial and Information Engineering & Economics, Via G. Gronchi, 18, 67100, L’Aquila, Italy
a r t i c l e i n f o
a b s t r a c t
Article history: Received 19 March 2019 Received in revised form 28 June 2019 Accepted 20 October 2019 Available online xxx
This paper deals with a new stochastic approach to handling data from waste biomass hydrothermal carbonization. The dynamics of hydrochar properties are described using the concept of reaction time distributions. A set of cumulative frequency distribution functions is provided that could very well correlate the most disparate experimental data. The procedure for analyzing the results is detailed. The method is illustrated with experiments on batch runs with five different wastes from the agro-food industry. Isothermal reactions (200 C) were performed up to 120 min at a constant 7/1 water/biomass ratio. The regression analyses fully confirm the correctness of the method. The use of dynamical van Krevelen plots is proposed. The approach allows also obtaining from lab-scale runs fundamental information for the correct waste-to-fuel process development at the industrial scale. The mathematics is not demanding and, unlike other methods, the difficulties substantially do not increase with the complexity of the modeled kinetic scheme. © 2019 Elsevier Ltd. All rights reserved.
Keywords: Hydrothermal carbonization Agro-food wastes exploitation Hydrochar formation Stochastic modeling Van krevelen plot
1. Introduction Hydrothermal carbonization (HTC) could add energy value to waste biomass and improve the sustainability of the energy supply chain [1,2]. The numerous potential applications, the easiness of implementation, and the versatility as a waste-to-fuel process maintain the technical and scientific research on this topic lively and intense [3e5]. As a further convenience, the HTC energy balance, not particularly advantageous for lignocellulosic materials, becomes favorable in the case of wet materials [6]. During the progressive transformation of the native substrate to hydrochar, chemicals transfer between the solid phase and the hot compressed water. These phenomena improve the properties of the hydrochar as fuel. The solid densifies the energy content, releases impurities that could be harmful as a result of the combustion, and levels out its chemical-physical properties regardless of the heterogeneity of the native biomass [7,8]. A better understanding of these mechanisms would be fundamental for the correct technology transfer from research to industry. Researchers actively study the chemicalphysical evolution of the solid phase and propose techniques to monitor it [9e12]. The dynamics of the reacting system and the
* Corresponding author. E-mail address: [email protected] (A. Gallifuoco).
development of the hydrochar properties depend mainly on temperature and time, even for HTC of non-conventional, water-rich substrates [13]. Although the severity factor could lump satisfactory temperature and time, investigate the effect of time alone could give a broader view of the process [14]. The higher the retention time in the HTC reactor, the better the properties of the solid fuel obtained, but also the worse the energy balance of the process. Most likely, an optimum should be sought, especially if one keeps in mind to move from batch to continuous HTC, where the reactor retention time should be tuned accurately. To date, kinetic studies are a challenging topic potentially fruitful of valuable new information. Researchers agree that the mathematical modeling of the complex kinetics is not yet wholly satisfactory, whatever the adopted approach be [5]. The complexity of the network of chemical reactions, however not fully understood yet, makes the use of closed-form solutions cumbersome. Furthermore, the reaction patterns may vary depending on the type of biomass treated, and the exploitation of waste biomass is undoubtedly a case of variable raw materials. HTC deserves the international attention also for non-energy implementations, such as synthesis of performing nanomaterials [15] or removal of pollutants from both liquid and gaseous phases [16,17]. These second-generation HTC processes often require the addition to the reaction mixture of catalysts or substances which could establish new kinetic patterns [18]. Non-conventional
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substrates could undergo HTC through unusual kinetic patterns. This difficulty could occur when dealing with mixtures of plastic and biomass, a case of the waste-to-fuel chain rich in interesting developments. As an example of these hybrid materials, an improved PVC de-chlorination was observed during HTC in the presence of lignin [19]. Finally, multistep HTC processes are under study for the simultaneous upgrade of biomass to fuel and recover of platform chemicals from the liquid phase [20,21]. In the authors’ opinion, such a vast and differentiated scenario requires to collect a more significant number of kinetic data and to analyze them through several kinetic models. More in-depth information could result from approaching the problem with more than one method. Recent studies gave a satisfactory interpretation of lignocellulosic biomass HTC as a stochastic phenomenon and showed how to treat the experimental data accordingly [22]. One of the scopes of the present paper is to extend the analysis to other kinds of biomass. The study also illustrates some significant new practical effects and developments, made possible by the technique adopted here. Keeping in mind a plausible waste-to-fuel chain, the experiments here discussed concern typical scraps from the local agro-food industry: freezing industry of potatoes, peas, and carrots (potato, pea, and carrot), olive tree pruning (olive) and wheat bran (bran). The attention is focused on the evolution of the solid phase during the reaction, particularly on the dynamics of its properties as a fuel. An innovative method is also proposed to acquire information relevant to the development of industrial HTC through the use of the traditional van Krevelen plot. 2. Materials and methods The residual biomass has been collected directly in the district as a representative sample of the local agro-industrial activities. Potato, carrot, pea, and bran were dried in an oven at 60 C for 48 h and then milled to 0.5 mm mesh size. Olive was milled, then dried in an oven at 105 C for 24 h. The HTC apparatus is described in detail in a previous study [23]. The substrates and the demineralized water (pH ¼ 6.3 ÷ 6.5) were accurately weighed and loaded into the reactor, which was then sealed and evacuated. The reactor warmup lasted 20 min, and after that, the residence time was measured. At the end of each run, the reactor was cooled down within 4 min by quenching it first with air and then by immersion in a cold water bath. In all the experiments, the amount of gas produced was negligible. The condensed phase recovered by the reactor was filtered to separate liquid and solid products. The wet spent filter and the solid phase were dried (oven, 105 C, 24 h). The filter and the solid were weighed before and after drying, for measuring the yield respect to the dry biomass loadings. The hydrochar was stored in vials and analyzed for the CHNS (Perkin Elmer-2440 series II elemental analyzer). Elemental analyses followed the ASTM D3176e89 standard test method for coal and coke, calculating oxygen content by the difference. The pH of the process liquid was 2.5 ÷ 3.1, regardless of the biomass and almost constant with the residence time. All measurements were in triplicate. 3. Results and discussions In the present approach, the HTC batch reactor is modeled as a vast set of biomass particles. Each element, at a random time, could undergo a transformation releasing a chemical group into the liquid phase. The likelihood of a reaction occurring at a particular site depends only on the current state of the solid particle and not on its previous history. Accordingly, one could use a stochastic
distribution of reaction times for modeling the time course of the process. Previous evidence endorsed the validity of the method, highlighted the mechanistic foundations, and demonstrated some preliminary practical results obtained with lignocellulosic biomasses [22]. Data available in the literature for several materials show that, although the major part of the batch HTC process occurs within the first hour of retention, an appreciable part of the biomass reacts in a longer time. The rate of transformation reaches a peak and then progressively declines: this implies that the probability density time distribution should be right-skewed. In this sense, a convincing and fruitful analogy exists between this HTC model and survival and failure analyses, if one replaces the lifetime duration with the reaction time. The Burr equations are a set of 12 cumulative distribution functions which yield the proper density shape [24]. This family of distributions, easy to handle mathematically, gives satisfactory fittings when applied to the survival analysis [25]. The most used function is the so-called Burr type XII distribution, already introduced by the authors into HTC studies. In the following, the method is enlarged and expressed formulaically, testing its validity with data of HTC of a broader range of residual biomasses. The proposed technique could be used to model the solid yield, the CHNS composition, the higher heating value (HHV), the atomic ratios on the van Krevelen plot and many other properties. Each of these properties, say y(t), is time depending and vary from an initial (y0) and a final (y∞) value. The extent of transformation is given by:
XðqÞ ¼
yðqÞ y0 y∞ y0
(1)
In equation (1), the time is scaled by a characteristic reaction time, i.e., q ¼ t/th. If one considers the portion of the particle population which has already reacted within the time q, a cumulative frequency distribution (CFD) describes the function X. Table 1 lists the only 5 out of the 12 Burr CFDs that have a trend conform to the observed HTC dynamics. The second column reports the CFDs, while the third column displays the corresponding functions y calculated according to the definition (1). Each of these latter functions could correlate experimental data concerning any time-depending property of the solid phase measured during HTC. As an example, Fig. 1 concerns the carbon percentage (C%) measured in the hydrochar at fixed reaction time (0, 10, 15, 30, 60, and 120 min) with the five different biomasses tested. The estimated values obtained fitting the data with the five y of Table 1 are reported as a function of the corresponding measured values. A total of 150 points, all of them very well aligned along the bisector (R2 ¼ 0.99989), testifies to the goodness of the correlations. It is noteworthy that this satisfactory result is valid regardless of the type of biomass. Starchy substances (potato), lignocellulosic biomass (olive), high-protein content materials (pea) equally well arranged on the bisector. This finding supports the hypothesis that a general mechanism rules the phenomenon, by which a method for testing kinetic patterns have been proposed in another paper submitted elsewhere. On the contrary, the present paper slants toward getting practical information not necessarily deepening the kinetic analysis. In this sense, a first result shown by Fig. 1 is the possibility to model the dynamics of an industrial reactor fed with a variable mixture of agro-food scrapes. The time-scale parameter th measures the characteristic time of the phenomenon and furnishes valuable information on the rapidity of the transformation for the different biomasses, thus helping in designing the optimal process time. The five proposed CFDs also depend on one or two shape parameters. The first of
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Table 1 Cumulative distribution functions and corresponding y functions. Type
XðqÞ
yðqÞ ¼ y0 þ ðy∞ y0 Þ XðqÞ
VII
1 ½1 þ tanhðqÞp 2p p 2 tan1 ðeq Þ
1 ½1 þ tanhðqÞp y0 þ ðy∞ y0 Þ 2p p 2 y0 þ ðy∞ y0 Þ tan1 ðeq Þ
VIII
p
IX X XII
k ½ð1 þ eq Þp 1 k ½ð1 þ eq Þp 1 þ 2 ð1 eq Þp 2
p
y0 þ ðy∞ y0 Þ
y0 þ ðy∞ y0 Þ ð1 eq Þp 2
p k
ð1 þ q Þ 1 ð1 þ qp Þk
them, p, rules the steepness of the system dynamics and is the most important. The second one, k, could to the best of our knowledge set constant to the unity, as this value give the best fitting for all the experiments performed so far. It is appropriate to maintain the presence of the parameter in the equation, as in the Burr’s original XII distribution, for the sake of flexibility. Reaction conditions very different from those studied here could give k values significantly different from the unit. Fig. 2 is an example of the quality of the fittings obtainable.
Fig. 1. Comparison between measured carbon contents and values estimated with the five functions.
Fig. 2. Solid yield as a function of process time for the five biomasses. The regressions are reported as full (XII) and dashed (VII) lines.
k ½ð1 þ eq Þp 1 k ½ð1 þ eq Þp 1 þ 2 p k
y0 þ ðy∞ y0 Þ
ð1 þ q Þ 1 ð1 þ qp Þk
The hydrochar yields measured with all the biomasses are reported as a function of the reaction time. The solid lines are the regressions obtained with the type XII, the dotted ones those obtained using the type VII. These last lines are traced only for potato and olive for the sake of clarity since they differ slightly to the others, but similar results repeat whatever the biomass and the CFD. The regression parameters are reported in Table 2. The estimates y0 and y∞ are obtained by regression via the cumulative frequency distribution functions. y (0) and y (120) are the experimental measures, respectively, at zero and 120 min of reaction. It appears that model predictions almost coincide with the measures. This substantial identity allows two essential comments. First, at the adopted operational conditions, the conversion process occurs almost entirely within 2 h of retention into the reactor, so that this reaction time could be considered the endpoint. Second, y0 and y∞ could be deleted from the list of parameters to be estimated, and replaced by the respective measured values. Table 2 also shows that the parameter th varies in a broad range for different biomass and CFD, from 10 to 30 min th has the physical meaning of the characteristic time of the process, i.e., the reaction time is scaled by it. This critical finding ensures that the model could apply to several different HTC processes, from those treating biomasses easy to convert, to those employed for recalcitrant materials. Another significant result appears by inspection of Fig. 2. The yield decreases with time for the lignocellulosic olive, while increases more or less markedly for the other materials, and neatly for potato. This evidence agrees with the widely accepted hypothesis, which considers two reactions for the formation of hydrochar. The first one, relatively fast, is the direct, solid-phase transformation of the biomass. The second one, slower, occurs between liquid and solid phase and is due to the recombination of dissolved chemicals. According to this scenario, the trend observed with potato should be attributed to the predominance of the second step, since hot water dissolves almost entirely the starchy materials during the reactor warmup time. A more in-depth study of the dynamics of the liquid phase composition could support the hypothesis. For this study, it is remarkable that the proposed regression functions could model both trends as well. Furthermore, CFD functions can correlate the time course of the hydrochar HHV equally well. The HHV calculation went according to the equations universally used in the literature, and the results are not reported here for the sake of brevity. Some recent calorimetric measurements are confirming this result. The method of using CFDs allows not only to have available a set of functions which ensures good correlations in general. One could also infer valuable information on the relative rate of the phenomena occurring during HTC. The procedure could be as follows. The second column of Table 3 lists the time derivative of each CFD, i.e., the corresponding probability density functions (PDF). These functions f(q) have the dimension of a frequency and could be regarded as a time variable pseudo-first-order kinetic
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Table 2 Regression parameters for data of Fig. 2. Substrates
p
y0 ½C%
t h ½min
y∞ ½C%
yð0Þ½C%
R2
Estimated
yð120Þ½C%
Measured
Type XII Olive Pea Bran Carrot Potato
2.52 3.39 3.61 1.06 2.09
10.63 18.86 24.09 22.55 25.89
0.945 0.404 0.297 0.293 0.162
0.752 0.435 0.428 0.395 0.388
0.871 0.987 0.938 0.993 0.995
2.89 3.63
13.84 30.18
0.975 0.141
0.803 0.279
0.902 0.999
0.947 0.404 0.307 0.293 0.161
0.766 0.436 0.434 0.379 0.376
Type VII Olive Potato
Table 3 Probability density functions and rates of property change. Type
f ðqÞ
VII
2q p1 e 2p e2q þ 1 th eq þ eq p 2 p eq tan1 ðeq Þp1 p th e2q þ 1
VIII
IX
2kp th
X
2p th
XII
kp th
dy ¼ ðy∞ y0 Þ f ðqÞ dq
eq ðeq þ 1Þp1
½kðeq þ 1Þp k þ 22 ð1 e2q Þp ðe2q 1Þ
ðy∞
2p y0 Þ t h p 2
ðy∞ y0 Þ ðy∞ y0 Þ ðy∞
q
dy ¼ ðy∞ y0 Þf ðqÞ dq
(2)
Table 3 also reports the five derivatives calculated according to Equation (2). Fig. 3 illustrates the trend of the five f(q) functions, which Equation (2) shows to be proportional to the rate of change. The plot is drawn adjusting the parameter k, where present, to the unity, while p and th to the mean of the estimated values of
Fig. 3. The five CFDs dynamics as a function of dimensionless time.
2kp th
eq tan1 ðeq Þp1 e2q þ 1
eq ðeq þ 1Þp1
½kðeq þ 1Þp k þ 22 ð1 e2q Þp ðe2q 1Þ
kp th
ðqp þ 1Þkþ1
ðy∞ y0 Þ
constant. Making use of Equation (1) and of the relationship which holds by definition between any CFD and its PDF, one can get the rate of variation of any property during HTC, viz:
th
p
2p y0 Þ th
p
ðqp þ 1Þkþ1
p
p1 e2q e2q þ 1 eq þ eq
qp
Table 2, respectively 2.74 and 21 min. The use of average values does not invalidate the general qualitative trend of the curves in Fig. 3. The features of the different curves steer the proper choice for modeling experimental data. Type VII exhibits the higher frequencies, type IX the lower ones. Types X and XII are more suitable for describing HTC processes whose initial velocity is slow, while the initial value of the remaining types is non-zero and depends on the combination of the parameter values. Finally, type IX is the only one monotonically decreasing. Although the mathematical analysis ensures that all the curves are right-skewed, for particular combinations of parameter values, the left part of the curve IX rests on the second quarter of the plot. One could take advantage of the feature of type IX for analyzing data where, at the adopted operational conditions, a significant part of the process occurs during the reactor warmup. In other words, instead of dealing with a complicated analysis of the heating transient, it could be assumed that the initial condition of the reactor is the state at the instant when the temperature reaches the set-point d the faster the heating phase, the better the validity of this approach. Fig. 4 is the starting point for implementing a new procedure for analyzing experimental data by use of Equation (2), without necessarily hypothesize a specific kinetic mechanism. The plot reports the time course of the atomic ratios, O/C (full symbols) and H/C (open symbols) as measured for the five biomasses. H/C and O/C ratios are critical parameters for monitoring the quality of the hydrochar as a fuel, in comparison to fossil materials. Carbon-oxygen and carbon-hydrogen bonds contain less energy than the carbon-carbon bond. As a consequence, the higher the proportions of oxygen and hydrogen to that of carbon, the lower the energy value. The fittings of experimental data to type XII
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speculate that the solid evolution could depend on a linear combination of elimination reactions (dehydration, decarboxylation) which transfer chemicals to the liquid phase at a constant rate. So was demonstrated to be the case for purely wooden biomasses [11]. This behavior not necessarily could be that of non-lignocellulosic biomass. A more in-depth analysis could start by calculating the rate of variation for each of the ten series of data in Fig. 4. One can compute the instantaneous slope of a van Krevelen trajectory according to Equation (2):
3 2 H C H H d H C C C 7 fHC ðtÞ 6 d ∞ 07 ¼ dt ¼ 6 5 fO ðtÞ ¼ ½sðfÞ 4 O O C O d O C C C C ∞ 0 d dt Fig. 4. Atomic ratios as a function of time for the five biomasses (open symbols, H/C; closed symbols, O/C). The regressions are reported as full (H/C) and dashed (O/C) lines.
are reported as solid lines for H/C and dashed lines for O/C. The regression parameters, not reported for the sake of brevity, are satisfactory as usual. Fig. 4 illustrates the possibility of using the y functions for fitting disparate data. Further confirmations come from other, preliminary experiments (not reported here) which show that the method of CFD functions also holds for higher temperature hydrothermal conversions, included supercritical water conditions, and for more prolonged reactions. The proposed technique is not only a new procedure for effectively correlating experimental data, but is also a harbinger of practical applications. The use of the proposed distribution functions for modeling the kinetic constants also has a further practical advantage. This novel method is less sensitive to the complexity of the reaction mechanism hypothesized than the traditional ones, based upon the solution of coupled differential equations, and the subsequent correlation of experimental data. Besides, the stochastic approach could easily lead to introduce into the HTC studies techniques such as Monte Carlo methods, already employed by some authors for modeling in the field of biomass pyrolysis. The ongoing research is moving on this way, and the first results are encouraging. The success of CFDs in predicting the dynamics of hydrochar properties also makes them useful for the correct development of the process on an industrial scale. The choice of the correct residence time is fundamental for the optimization of continuous reactors, seeking for both the quality of the solid biofuel and the productivity of the industrial plant. Small-scale, batch HTC reactor processes could also tune the retention time to the proper value exploiting the features of the distribution functions here introduced. Since the method applies to the atomic ratios satisfactorily, a further analysis is possible that has significant repercussions on the van Krevelen plot. This kind of diagram, long ago introduced, is still universally employed for illustrating HTC data, in particular, the evolution of raw biomass toward solid fuel with the increasing process temperature. The dynamics of biomass conversion reflects on the plot in a time-depending trajectory, and this kind of representation appears in the literature more seldom, although, in the authors’ opinion, this approach would be fruitful. The closer a point of the line is to the lower left corner, the better is the quality of the solid as fuel. Should the slope of the trajectory be constant with time, the rate of H/C diminishing would be proportional to that of O/C during the whole process. Under that condition, one could
(3)
In this last expression, the quantity inside the square brackets represents the slope of the segment between the initial and final reaction point on the van Krevelen (s). Should the ratio of the f function of H/C to that of O/C (f), keep constant during the time, the trajectory would be a straight line. In particular, if the ratio is equal to the unit, then the trajectory coincides with the segment. However, should f depend on time, the trajectory would result in a curve. Fig. 5 shows the dynamics featured by the five substrates studied. The function f is computed using the values of the parameters values estimated from data of Fig. 4 for each of the substrates. The horizontal dashed line is the critical value, i.e., unity. The parts of curves below the critical line indicate that the solid is releasing oxygen groups faster than hydrogen groups (instantaneous slope of the trajectory lower than s). Above the critical limit, the reaction proceeds more quickly for hydrogen than for oxygen (instantaneous slope higher than s). All the curves present a similar behavior, starting from zero, passing through a maximum, and asymptotically tending to zero for long reaction time. Considering this common behavior at the extremities of the time interval, one could say that the HTC process starts and ends releasing at a relatively small rate the hydrogen groups in the hot compressed water. Fig. 5 also shows that for all the tested biomasses, a range of reaction time exists within which the curves exceed the critical value. The amplitude of this time interval and the height of the peak value, however, depend on the biomass. As an example, most of the curve of pea lies below the critical line, while potato features the highest
Fig. 5. Dimensionless group f vs. process time for the five biomasses.
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peak value (in fact, for the sake of readability of the diagram the values reported in Fig. 5 are halved). These findings show that the dynamics of HTC strongly depends on the nature of the biomass and should warn the researchers not to adopt a unique kinetic model whatever the biomass is, but to consider the peculiarity which a specific class of materials has. In other words, a kinetic model describing the HTC kinetics of both starchy materials (as potato in the present study) and lignocellulosic biomass is likely to be not satisfactory. Fig. 6 strengthens this hypothesis, showing the data obtained with all the five substrates in a dynamical van Krevelen plot. The solid lines connect the initial and final points (closed symbols). The corresponding slopes s are reported in Table 4. The slope of straight lines on the van Krevelen indicates the relative extent of the main reactions occurring during HTC (dehydration, decarboxylation, and other reactions). The wide range of values displayed in Table 4, from 0.90 to 3.21 shows that the dominant elimination reactions depend on the type of raw material processed. A closer look at Fig. 6 also shows that the time sequences of the experimental points (open symbols) do not arrange on the lines but twist more or less markedly around them. To the best of Author’s knowledge, the argumentations of this paper constitute the first explanation of the presence of curved trajectories on dynamical van Krevelen diagrams. It is likely to suppose that a significant portion of the data presented in the literature exhibit similar behavior. An odd choice of the scales on the axes could mask this tendency, and consequently, one could consider correct to fit data linearly, even obtaining acceptable regression coefficients. The magnification of the diagram should make observable the correct patterns, which unquestionably demonstrate that the nature of the chemical reactions between the solid and the liquid phases changes during HTC. This information could result valuable for optimizing the process, e.g., to set the correct residence time in a continuous reactor to recover platform chemicals from the liquid. Out of the five biomasses, the only olive gives rise to a nearly straight line in Fig. 6, and this result confirms the behavior already observed for wooden materials. To support the argumentation stated here, a clear example of a van Krevelen plot with curved time-trajectories appears in the recent literature [26]. Those Authors presented data on the HTC of pure cellulose, straw, and poplar, performed in the range 200 ÷ 260 C and from 0 to 480 min. The similarity of the experimental conditions with that here adopted confirms the validity of the approach discussed here.
Fig. 6. Dynamical van Krevelen plot. Initial and end point reaction time are signaled by full symbols. The solid lines show the different slopes s.
Table 4 Regression parameters of Fig. 4 and corresponding s values. Substrates
Olive Pea Bran Carrot Potato
O/C
H/C
s
p
th
p
th
2.03 2.93 1.20 1.61 1.81
93.90 6.95 11.60 2.39 13.08
1.53 3.74 2.29 2.27 2.40
24.49 10.11 13.01 9.94 13.27
0.90 3.21 1.94 1.04 1.76
Trusting in the potential greater flexibility of the CFD method compared to more traditional approaches, research is in progress testing more waste biomass, performing detailed analyses of the liquid phases, and sampling the reacting system at shorter time intervals. 4. Conclusions The proposed set of statistical functions fit satisfactory data of batch HTC of different residual biomasses of the agro-food industry, spanning from wooden to starchy materials. The functions are not empirical, but base on a statistical interpretation of the reactions occurring during HTC. The dynamics of the actual solid/liquid reacting system is well described by the model equations. The procedure for analyzing the HTC experiments is detailed, proved by practical examples, and assessed for possible extensions. Novel use of van Krevelen plots is discussed, which could furnish valuable information for steering the industrial development of the HTC process. The flexibility of the proposed method and the relatively simple mathematics required portend future developments, especially in the modeling of HTC complex reaction mechanisms. The research is pursuing these objectives by testing other biomasses and performing experiments at a higher temperature. This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.renene.2019.10.121. References [1] P. Zhao, Y. Shen, S. Ge, Z. Chen, Clean solid biofuel production from high moisture content waste biomass employing hydrothermal treatment, Appl. Energy 131 (2014) 345e367. [2] M. Heidari, A. Dutta, B. Acharya, S. Mahmud, A review of the current knowledge and challenges of hydrothermal carbonization for biomass conversion, J. Energy Inst. (2018), https://doi.org/10.1016/j.joei.2018.12.003. [3] M.T. Munir, M.M. Mansouri, I.A. Udugama, S. Barautian, K.V. Gernaey, B.R. Young, Resource recovery from organic solid waste using hydrothermal processing: opportunities and challenges, Renew. Sustain. Energy Rev. 96 (2018) 64e75. [4] C. He, C. Tang, C. Li, J. Yuan, K.-Q. Tran, Q.-V. Bach, R. Qiu, Y. Yang, Wet torrefaction of biomass for high quality solid fuel production: a review, Renew. Sustain. Energy Rev. 91 (2018) 259e271. [5] S. Roman, J. Libra, N. Berge, E. Sabio, K. Ro, L. Li, B. Ledesma, A. Alvarez, S. Bae, Hydrothermal carbonization: modeling, final properties Design and Applications: a Review, Energies 11 (2018) 216, https://doi.org/10.3390/en11010216. [6] J.A. Libra, K.S. Ro, K. Kammann, A. Funke, N. Berge, Y. Neubauer, M.-M. Titirici, C. Fühner, O. Bens, J. Kern, K.-H. Emmerich, Hydrothermal carbonization of biomass residuals: a comparative review of the chemistry, processes and applications of wet and dry pyrolysis, Biofuels 2 (1) (2011) 89e124. [7] S. Nizamuddin, N.M. Mubarak, M. Tiripathi, N.S. Jayakumar, J.N. Sahu, P. Ganesan, Chemical, dielectric and structural characterization of optimized hydrochar produced from hydrothermal carbonization of palm shell, Fuel 163 (2016) 88e97. [8] A.Y. Krylova, V.M. Zaitchenko, Hydrothermal carbonization of biomass: a review, Solid Fuel Chem. 52 (2) (2018) 47e59. [9] X. Zhuang, H. Zhan, Y. Song, C. He, Y. Huang, X. Yin, Insights into the evolution
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