Energy Fuels 2010, 24, 4673–4680 Published on Web 03/11/2010
: DOI:10.1021/ef9012246
Multiscale Modeling of Hydrothermal Pretreatment: From Hemicellulose Hydrolysis to Biomass Size Optimization† Seyed Ali Hosseini,*,‡,§ Romain Lambert,‡ Sergei Kucherenko,‡ and Nilay Shah‡,§ ‡
Centre for Process Systems Engineering and §The Porter Alliance, Imperial College London, London SW7 2AZ, United Kingdom Received October 27, 2009. Revised Manuscript Received February 15, 2010
In the general process for lignocellulosic bioconversion to ethanol, pretreatment has been viewed as the main cause of low process yield. Consequently, it is believed that obtaining a better understanding of the hydrothermal pretreatment method would pave the way for overall process optimization. This work focuses on developing a model for a pretreatment process that considers both the chemical and physical natures of the process. The chemical aspect of the process mainly involves the hydrolysis of hemicellulose to monomeric sugars. This paper considers all xylooligomers, with a degree of polymerization up to 30 as soluble, and that the bond breakage is a function of the position in the hemicellulose chain. Also, all of the bonds with the same position undergo breakage at the same time. The physical aspect of the process involves reducing the size of the feedstock as well as heating the feedstock to a desired temperature. For this aspect, we have developed a model to estimate the energy requirements for size reduction and proposed a method to find the optimum chip size for pretreatment. Finally, we performed two sets of sensitivity analysis: first, to compare the dynamic importance of xylooligomer size evolution versus xylose decomposition and, second, to compare the relative importance of kinetic parameters versus the length of particle on the overall process yield. Sensitivity analysis revealed that, at the beginning of the process, the chemical reaction is more important than diffusion; however, as the reaction proceeds, diffusion becomes the determinant factor. It was also shown that the solidphase reaction rate, xylooligomer size evolution, and xylose decomposition are all determinant factors; therefore, any model for hemicellulose hydrolysis should take all three of these factors into account.
Bioethanol is now mainly produced from the fermentation of starch and sugar. Fermentation technologies for sugar and starch crops are very well-developed but have certain limits; these crops have a high food application value, and their sugar yield per hectare is very low compared to the most prevalent forms of sugar in nature (cellulose and hemicellulose).3 Furthermore, Farrell et al.4 suggested that only lignocellulosic ethanol offers considerable greenhouse gas emission reductions compared to fossil fuel. However, the conversion process for a lignocellulosic-based feedstock to ethanol is more complex than processes using sugar- or starchbased feedstocks.5-8 Although various bioconversion processes are employed for lignocellulosic conversion, a general process includes the main steps shown in Figure 1. Size reduction and pretreatment are required to make cellulose more accessible to enzymes, so that hydrolysis of the cellulose fraction to glucose can be achieved more rapidly
1. Introduction The world is facing the dangers of an energy crisis because of the depletion of traditional fuel sources, such as coal and petroleum. Over the past few years, there has been an increasing awareness and acceptance of biofuels as a viable potential substitute for petroleum. As a result, ethanol has become an essential product in the fuel market. Its global market grew from less than a billion liters in 1975 to more than 39 billion liters in 2006, and current predictions show that the market may reach more than 100 billion liters in 2015.1 In addition, the global economic downturn offers an opportunity to invest in green technology while costs are lower. Also, the authors believe that green growth is the only realistic future for growth and overcoming world poverty. However, to be viable, bioenergy should ultimately be economically competitive with fossil fuel. Developments in conversion technology have reduced the projected gate price of ethanol from about U.S. $0.95/liter (U.S. $3.60/gallon) in 1980 to only about U.S. $0.32/liter (U.S. $1.22/gallon) in 1994;2 however, for ethanol to be competitive with fossil fuel, further cost and energy reductions in conversion technologies are required.
(3) Hamelinck, C. N.; Hooijdonk, G.; Faaij, A. P. C. Ethanol from lignocellulosic biomass: Techno-economic performance in short-, middle- and long-term. Biomass Bioenergy 2005, 28 (4), 384–410. (4) Farrell, A. E.; Plevin, R. J.; Turner, B. T.; Jones, A. D.; O’Hare, M.; Kammen, D. M. Ethanol can contribute to energy and environmental goals. Science 2006, 311 (5760), 506–508. (5) Hahn-H€agerdal, B.; Galbe, M.; Gorwa-Grauslund, M. F.; Liden, G.; Zacchi, G. Bio-ethanol;The fuel of tomorrow from the residues of today. Trends Biotechnol. 2006, 24 (12), 549–556. (6) Zaldivar, J.; Nielsen, J.; Olsson, L. Fuel ethanol production from lignocellulose: A challenge for metabolic engineering and process integration. Appl. Microbiol. Biotechnol. 2001, 56 (1), 17–34. (7) Galbe, M.; Zacchi, G. Simulation of processes for conversion of lignocellulosics. In Bioconversion of Forest and Agricultural Plant Residues; Saddler, J. N., Ed.; CABI: Oxfordshire, U.K., 1993; p 291. (8) McMillan, J. D. Bioethanol production: Status and prospects. Renewable Energy 1997, 10 (2-3), 295–302.
† This paper has been designated for the Bioenergy and Green Engineering special section. *To whom correspondence should be addressed. E-mail: s.hosseini07@ imperial.ac.uk. (1) FO Licht. World Ethanol and Biofuels Report 2006. FO Licht, Kent, U.K., 2006. (2) Wyman, C. E. Ethanol from lignocellulosic biomass: Technology, economics, and opportunities. Bioresour. Technol. 1994, 50 (1), 3–15.
r 2010 American Chemical Society
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Figure 1. General process for lignocellulosic-based ethanol production.
and with greater yield.9 Although numerous pretreatment methods, such as steam explosion, lime pretreatment, ammonia fiber explosion (AFEX), and organic solvent pretreatment, are extensively studied in the literature, acid pretreatment is still the choice of several model processes.10,11 Hydrothermal pretreatment usually involves exposure of lignocellulosic material to a chemical (e.g., acid) at elevated temperatures for a period of time depending upon the physiochemical structure of the biomass until most C5 sugars are solublized prior to enzymatic hydrolysis. The main drawback of pretreatment is that it leads to the formation, in addition to sugars, of unwanted compounds that are inhibitory to ethanol-producing microorganisms.12 To overcome the negative effect of inhibitors on subsequent process steps, it is common to detoxify the hydrolyzate; biological, physical, and chemical methods have been employed for this detoxification.13 Enzymatic hydrolysis includes processing steps that convert cellulose polymers into monomeric sugars using cellulase-based enzymes. During the fermentation processes, the monomeric sugars are converted to ethanol and then ethanol is recovered from the fermentation broth, usually by distillation.10,14 On the basis of the general process of lignocellulosic bioconversion, Hosseini and Shah15 showed that pretreatment is the main cause of low process yield. Consequently, it is believed that obtaining a better understanding of the hydrothermal pretreatment method would pave the way for overall process optimization. The remaining part of this work focuses on the development of a model for the pretreatment process that considers both the chemical and physical natures of the process. The chemical aspect of bioconversion involves the hydrolysis of hemicellulose to monomeric sugars. The model of the
chemical reaction presented in this study is an extended version of what was previously developed by Hosseini and Shah.15 They assumed that oligomers with a degree of polymerization (DP) up to 5 were soluble. However, in this work, the model was improved by oligomers with a DP up to 30 and assuming that they are soluble. The physical aspect of bioconversion involves reducing the size of the feedstock as well as heating the feedstock to the desired temperature. For this, we developed a model to estimate the energy requirement for size reduction and then found the optimum size for pretreatment based on the model that was previously developed by Hosseini and Shah.16 Although some models were developed in the literature for the physical or chemical aspect of the bioconversion process, it should be noted that, to obtain a good understanding of the bioconversion process, it is necessary to consider both the physical and chemical aspects of the bioconversion simultaneously. The chemical aspect of the process is mainly a reaction-diffusion system, and the most determinant factors for any reaction-diffusion system are the temperature and diffusion length of the system, which are both determined in the physical aspect of the process (heating and size reduction). 2. Simulation Tool To model the different process events as well as to estimate the parameters in the model, the software package generalized process modeling system (gPROMS) was used (www.psenterprise.com/gproms/). The gPROMS package is an equationoriented modeling tool for combined discrete and continuous processes. We chose gPROMS because, once a model has been developed in this software, it can be solved in many different ways to perform many different activities, for example, steady-state simulation, dynamic simulation, parameter estimation, and model-based experiment design.
(9) Weil, J.; Westgate, P.; Kohlmann, K.; Ladisch, M. R. Cellulose pretreatments of lignocellulosic substrates. Enzyme Microb. Technol. 1994, 16 (11), 1002–1004. (10) Mosier, N.; Wyman, C.; Dale, B.; Elander, R.; Lee, Y. Y.; Holtzapple, M.; Ladisch, M. Features of promising technologies for pretreatment of lignocellulosic biomass. Bioresour. Technol. 2005, 96 (6), 673–686. (11) Aden, A.; Ruth, M.; Ibsen, K.; Jechura, J.; Neeves, K.; Sheehan, J.; Wallace, B.; Montague, L.; Slayton, A. Lignocellulosic biomass to ethanol process design and economics utilizing co-current dilute acid prehydrolysis and enzymatic hydrolysis for corn stover. National Renewable Energy Laboratory, Golden, CO, 2002. (12) L opez, M. J.; Nichols, N. N.; Dien, B. S.; Moreno, J.; Bothast, R. J. Isolation of microorganisms for biological detoxification of lignocellulosic hydrolysates. Appl. Microbiol. Biotechnol. 2004, 64 (1), 125–131. (13) Palmqvist, E.; Hahn-H€agerdal, B. Fermentation of lignocellulosic hydrolysates. I: Inhibition and detoxification. Bioresour. Technol. 2000, 74 (1), 17–24. (14) Gulati, M.; Kohlmann, K.; Ladisch, M. R.; Hespell, R.; Bothast, R. J.; Agricultural Research Service-United States Department of Agriculture (ARS-USDA). Assessment of ethanol production options for corn products. ARS-USDA, Washington, D.C., 1996. (15) Hosseini, S. A.; Shah, N. Multiscale modelling of biomass pretreatment for biofuels production. Chem. Eng. Res. Des. 2009, 87 (9), 1251–1260.
3. Model Development Because large amounts of cellulose in most untreated lignocellulosics are not accessible to enzymes, it is necessary to alter the structure of a biomass prior to enzymatic hydrolysis. Consequently, most of the developed bioconversion processes for lignocellulosics start with size reduction and pretreatment. Pretreatment can be physical, chemical, or even biological; nevertheless, the goal of any method is to alter or remove any structural or compositional impediments to enzymatic hydrolysis to improve its rate and increase the yield of fermentation.17 (16) Hosseini, S. A.; Shah, N. Multiscale modelling of biomass pretreatment for biofuels production. Chem. Eng. Res. Des. 2009, 87 (9), 1251–1260. (17) Zhang, Y. H. P.; Lynd, L. R. Toward an aggregated understanding of enzymatic hydrolysis of cellulose: Noncomplexed cellulase systems. Biotechnol. Bioeng. 2004, 88 (7), 797–824.
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process and, ultimately, the economics of the process.10 Studies have shown that pretreatment is the most important determinant of success in cellulosic bioethanol technology because it defines the extent to and cost at which the carbohydrates of cellulose and hemicellulose can be converted to bioethanol.16,21 Although numerous pretreatment methods, such as steam explosion, lime pretreatment, AFEX, and organic solvent pretreatment, have been extensively reported in the literature, acid pretreatment is still the choice of several model processes.21 Dilute acid pretreatments at moderate temperatures have been widely studied for converting lignocellulosic biomass, including the hemicellulose fraction to soluble sugars, followed by cellulase-catalyzed hydrolysis of the cellulosic fraction to glucose.7,10,11 In general, a higher pretreatment temperature (T), shorter residence time, and smaller biomass chip size result in higher soluble xylose recovery yields and enzymatic cellulose digestibility; the modified severity factor represents the interrelationship of these factors.16,22 residence time T -100 exp 10-pH R ¼ ð2Þ diffusion time 14:7
Figure 2. Energy consumption for grinding wheat straw (moisture content = 8.3%), barley straw (moisture content = 6.9%), corn stover (moisture content = 6.2%), and switchgrass (moisture content = 8.0%).
3.1. Size Reduction. With regard to energy consumption, size reduction is a very inefficient process. Only between 0.1 and 2.0% of the energy supplied to a machine appears as increased surface energy in the solids. The energy required to effect size reduction is related to the internal structure of the material and consists of two parts: (1) opening any small fissures that are already present and (2) forming new surfaces.18 Although it is impossible to accurately estimate the amount of energy required to effect a size reduction of a given material, a number of empirical laws have been proposed. The following three are the most popular:18,19 (1) Rittinger’s law, which assumes that the energy required for size reduction is directly proportional to the increase in surface area, (2) Kick’s law, which assumes that the energy required for size reduction is directly proportional to the size reduction ratio, and (3) Bond’s law, which is an intermediate between Rittinger’s and Kick’s laws. Mani et al.20 reported the specific energy to grind different feedstocks as a function of the monitor size with two different moisture contents. Using the constant variance parameter estimation method in the gPROMS modeling package, we attempted to fit the above-mentioned three models with the data reported by Mani et al.20 The only model that showed a good correlation with experimental data was Kick’s model. Figure 2 shows a summary of the results. It can be concluded that the net energy required for size reduction can be calculated from Kick’s law by knowing the initial size of the feedstock as well as the required size after grinding. Consequently, the energy consumption per unit mass of feedstock is as follows: L1K E ¼ CK ln ð1Þ L2K
It is suggested that, after size reduction, dilute acid pretreatment can be divided into the following subprocesses:15 (1) The chips are heated to reach the desired temperature. (2) In dilute acid treatments, protons diffuse into the chips. (3) Water or steam diffuses into the chips. (4) Hydrolysis of hemicellulose takes place. (5) Solublized sugar diffuses out of the chips. 3.2.1. Heating and Diffusion. In the process design proposed by the National Renewable Energy Laboratory (NREL), the washed, shredded feedstock is sent to pretreatment, where it is first steamed with low-pressure steam and then brought to the desired temperature (190 °C) and pressure (12.1 atm) by the direct injection of high-pressure steam.11 With regard to the time needed for the chips to reach the desired temperature, Simpson23 proposed a model to calculate the heating time of wood with round or square cross-sections and saturated steam. Using Simpson’s model to estimate the heating time for wood chips in the size range of 1-10 mm implies that the time for heating is at least 3 orders of magnitude smaller than the pretreatment time (data not shown), which is usually in the order of minutes.24,25 However, using direct steam injection into the pretreatment reactor will dramatically increase the water and energy consumption of the process. Consequently, an alternative design to minimize water and energy consumption will be part of our future plan. The time needed for the diffusion of hydrogen ions into the biomass is assumed to be negligible in comparison to the time needed for the diffusion of water because of the higher mobility of ions and their smaller size. In addition, protons act as a catalyst for the hydrolysis reaction; consequently, prior to the diffusion of water, the reaction cannot take place. This all implies that neglecting the ion diffusion time is acceptable. As a result of neglecting the time needed for heating and ion diffusion, the five subprocesses discussed above can be reduced to three, namely, (1) diffusion of water into the chips, (2) reaction, and (3) diffusion of soluble sugars out of the chips.
where CK is Kick’s constant and L1K and L2K are the initial and final sizes of the feedstock, respectively. In this study, the shape of the reduced-size biomass is assumed to be spherical; however, it should be noted that, having the data for spherical biomass, it is possible to estimate these values for other shapes using the hydraulic diameter. 3.2. Pretreatment. Pretreatments can have significant implications on the configuration and efficiency of the rest of the
€ C. Progress in bioethanol processing. (21) Balat, M.; Balat, H.; Oz, Prog. Energy Combust. Sci. 2008, 34 (5), 551–573. (22) Garrote, G.; Dominguez, H.; Paraj o, J. C. Mild autohydrolysis: An environmentally friendly technology for xylooligosaccharide production from wood. J. Chem. Technol. Biotechnol. 1999, 74 (11), 1101– 1109. (23) Simpson, W. T. Estimating heating times of wood boards, square timbers, and logs in saturated steam by multiple regression. For. Prod. J. 2006, 56 (7/8), 26. (24) Galbe, M.; Zacchi, G. A review of the production of ethanol from softwood. Appl. Microbiol. Biotechnol. 2002, 59 (6), 618–628. (25) Sassner, P.; Galbe, M.; Zacchi, G. Steam pretreatment of Salix with and without SO2 impregnation for production of bioethanol. Appl. Biochem. Biotechnol. 2005, 124 (1), 1101–1117.
(18) Sinnott, R. K.; Coulson, J. M.; Richardson, J. F. Coulson and Richardson’s Chemical Engineering; Butterworth-Heinemann: Oxford, U.K., 2005. (19) Perry, R. H.; Green D. W. Perry’s Chemical Engineers’ Handbook; McGraw-Hill Professional: New York, 2007. (20) Mani, S.; Tabil, L. G.; Sokhansanj, S. Grinding performance and physical properties of wheat and barley straws, corn stover and switchgrass. Biomass Bioenergy 2004, 27 (4), 339–352.
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8.86 kg of sulphuric acid 41.14 kg of water 386.2 kg of water 1000 kg of biomass grinding of 1000 kg of biomass
T1
T2
energy required
20 70 100 100 20
T2 T2 T2 T2 20
mCpΔT = 8.86 1420(T2 - 20) (mCpΔT)water þ (mCpΔT)steam þ L = 41.4(4190 30 þ 3475.5(T2 - 20) þ 334000) (mCpΔT)steam = 386.2 3475.5(T2 - 20) mCpΔT = 1000 1463.6(T2 - 20) E = 2946621 þ 8.43 3600 1000 ln(1.5/L2)
It is assumed here that the biomass enters the plant with a characteristic size of around 4 in. (10 cm). On the basis of all of the above considerations, the overall energy required for size reduction and pretreatment would be as follows: 00 1 " #1 2 1:5 A -20A E ¼ 8:86 1420@@190 -14:7 ln L2 0 00 1 " #1 2 1:5 A -20A þ 41:4@4190 30 þ 3475:5@@190 -14:7 ln L2 00
!
"
þ 334000 þ 386:23475:5@@190 -14:7 ln Figure 3. Energy consumption as a function of the compression ratio.
00 þ 1000 1463:6@@190 -14:7 ln
16
We previously developed a model for water diffusion into woodchips (assuming that woodchips have a porous structure) and found that the time needed for water diffusion into the woodchips is as follows: 1 2 Fr 1 - ln Φ 2 ð3Þ tw ¼ 2MΦDΔC
"
1:5 L2
1 1 # 1:5 2 A -20A L2
2 #
þ 2946621 þ 8:43 3600 1000 ln
1
1
A -20A
1:5 L2
Figure 3 shows the amount of energy required for grinding and heating as well as the overall energy requirement of the units. Figure 3 shows that reducing the size of the feedstock decreases the energy demand on the system. This is due to the low energy requirement for grinding corn stover, which can also be seen even in the grinding data that shows that corn stover has the lowest Kick’s constant. These all imply that pretreatment of corn stover should be performed at the lowest possible temperature. This minimum temperature is the temperature at which the hydrolysis reaction starts to take place. Consequently, performing the pretreatment at 140 °C, for example, and a 5 times smaller chip will reduce the overall energy requirement of the system by 1.3 times. Finding the exact minimum temperature at which the reaction takes place at an appreciable rate would result in being able to operate the pretreatment at the exact optimum point, but it can be seen from Figure 3 that the overall energy curve starts to flattened at a compression ratio of around 5. No substantial energy savings can be made after this point. 3.2.3. Kinetics of Hemicellulose Hydrolysis. In general, hemicellulose hydrolysis models are based on the acid-catalyzed breakdown of long chains of hemicellulose to form shorter oligomers that continue to break down to monomeric sugars. Those monomeric sugars may undergo a degradation reaction under certain conditions.26 In many kinetic models, it is assumed that the rate of the oligomer-monomer reaction is so much faster than the rate of oligomer production that the latter reaction step can be omitted; however, few physical data support this hypothesis. We have previously proposed a new mechanism for the hydrolysis of hemicellulose, in which the bond breakage is a function of the position in the hemicellulose chain and all of the bonds with the same position undergo the breakage at the same rate. Although the proposed model showed a good correlation with experimental data, it was developed for a mixture of five xylooligomers. We have extended that model in this study, assuming that xylooligomers with a DP up to 30 are
where F is the density, r is the particle radius, Φ is the porosity, D is the diffusion coefficient, M is the molecular weight, and ΔC is the concentration gradient. 3.2.2. Optimum Chip Size. With the aid of the model developed by the authors earlier, it is possible to evaluate the energy requirement for different chip sizes.16 It is clear that increasing the size of the biomass requires a more severe pretreatment to result in the same yield. With a better understanding of the amount of energy required for a given increase in biomass size, it is assumed that only a temperature increase would compensate for the size increase, assuming that all factors except size and temperature remain constant, which results in the following equations: T1 -100 e 14:75 R2 r1 2 ¼ ð4Þ T2 -100 R1 r2 e 14:75 " # R2 r1 2 ð5Þ T2 ¼ T1 -14:7 ln R1 r2 To show the practicality of our proposed model, we employed our model to find the optimum size of corn stover in a design proposed by NREL. From the theoretical view, the amount of biomass entering the pretreatment unit should not have any effect on the optimum size; however, to show a quantitative result in all calculations, it was assumed that, in each batch cycle, 1 ton of biomass enters the pretreatment unit. In the NREL design, the temperature is 190 °C for a biomass size of 1.5 in., which requires around 9 kg of acid in addition to around 420 kg of water in the reactor.11 To achieve the same severity, changing the size of the biomass requires a different temperature. Consequently, the amount of energy needed for any chip size would be as indicated in Table 1.
(26) Jacobsen, S. E; Wyman, C. E. Cellulose and hemicellulose hydrolysis models for application to current and novel pretreatment processes. Appl. Biochem. Biotechnol. 2000, 84 (1), 81–96.
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by assuming that the concentration is the only driving force for diffusion; diffusion happens only in a longitudinal direction, and there is no external resistance for water adsorption to the surface of the wood. For diffusion of soluble sugars out of the wood in an aqueous solution, a model has been developed on the basis of Fick’s law by replacing the diffusion coefficient with an effective diffusion coefficient for porous media. Integrating the kinetic and diffusion models would result in the following model: dCW d dCW D ¼ ð7Þ dl dt dl dCH ¼ -KH CH CW dt For 5 < y < 31, dCy ¼ -ky Cy CW þ KH CH CW -K5 þ 2k2y C2y CW dt DCy D Dl=W þ 2k2y þ 1 C2y þ 1 CW Dy Dl
Figure 4. Mechanism of hemicellulose hydrolysis.
ð10Þ
dC4 D DC4 ¼ KH CH CW -K4 C4 CW - D4=W Dl dt Dl
ð11Þ
dC2 ¼ KH CH CW þ 2R5 K5 C5 CW þ 2R4 K4 C4 CW dt D DC2 þ ð1 -R4 ÞK4 C4 CW -K2 C2 CW - D2=W Dl Dl
ð13Þ
dCx ¼ KH CH CW þ R5 K5 C5 CW þ 2ð1 -R5 ÞK5 C5 CW dt þ 2ð1 -R4 ÞK4 C4 CW þ 3K3 C3 CW þ 2K2 C2 CW D DCx ð14Þ -Kd Cx CW - Dx=W Dl Dl dCd D DCd Dd=W ¼ Kd Cx CW Dl dt Dl
ð15Þ
The above equations are based on the mass balance for a given point inside the wood particle, in which accumulation terms have been shown as a partial derivative of the concentration with respect to time. We have previously estimated the kinetic parameters for xylooligomers with a DP ranging from 1 to 5 based on experimental results; however, we could not find any study in the literature reporting a concentration of xylooligomers with a DP up to 30. Because the degree of polymerization has an important effect on the overall behavior of the system, we are working on a method in which it is possible to calculate the DP based on a measurement of cellulose viscosity by a nitration method. Even without such a method, it is possible to examine the trend of model solutions with the aid of some typical data (temperature of 160 °C and a pH of 4.75 with extrapolation of kinetic parameters) as follows. Although the xylose formation rate increases when considering xylooligomers with a higher DP soluble, the exact impact can be determined just by having a method to measure the dynamic DP of the cellulose, which again highlights the importance of the nitration method to measure the DP of cellulose.
5 < x : odd < 30 x -1 -mer þ xylose 2
dCx ¼ -kx Cx þ 2k2x C2x þ 2k2x þ 1 C2x þ 1 dt
dC5 D DC5 ¼ KH CH CW -K5 C5 CW - D5=W Dl dt Dl
ð12Þ
depolymerization x x-mer s -mer f2 2
depolymerization
ð9Þ
dC3 D DC3 ¼ KH CH CW þ ð1 -R5 ÞK5 C5 CW -K3 C3 CW - D3=W dt Dl Dl
soluble in water, which is in accordance with most studies in the literature.26-28 It was previously shown that the bond breakage in xylooligomers is function of the bond position in the hemicellulose chain, so that all of the bonds with the same position undergo breakage at the same rate. Moreover, it was found that the probability of xylooligomer breakage from the middle of the chain is higher than the probability of breakage from the sides. In the case of xylotetrose, 93% of bonds break from the middle, and for larger oligomers, almost all break from the middle. On the basis of the above discussion, a schematic representation of the reaction mechanism in the liquid phase (xylooligomers with DP up to 30) is shown in Figure 4. On the basis of the reaction mechanism proposed, the general kinetic equation for depolymerization describing the evolution of the distribution of sizes for xylooligomers with a DP ranging from 6 to 30 can have the following form: 5 < x : even < 30
x-mer s f2
ð8Þ
ð6Þ
3.2.4. Diffusion. During pretreatment, two diffusion processes occur: the diffusion of water into wood and the diffusion of soluble sugars out of the wood particles in an aqueous solution. In the former case, we previously developed a model (27) Maloney, M. T.; Chapman, T. W.; Baker, A. J. Dilute acid hydrolysis of paper birch: Kinetics studies of xylan and acetyl-group hydrolysis. Biotechnol. Bioeng. 1985, 27 (3), 355–361. (28) Bhandari, N.; Macdonald, D. G.; Bakhshi, N. N. Kinetic studies of corn stover saccharification using sulphuric acid. Biotechnol. Bioeng. 1984, 26 (4), 320–327.
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Figure 5. Xylose concentration profile for 1 cm wood.
Figure 5 shows the concentration of xylose at any point inside the particle during the course of hydrolysis. As mentioned earlier, reactions start immediately after water reaches the hemicelluloses inside a particle. As can be seen in Figure 5, between any two points inside a particle, three factors account for the xylose concentration: (1) the diffusion of xylose entering the first point, (2) the diffusion of xylose exiting the second point toward the bulk of the liquid, and (3) the reaction at the points to generate or consume xylose, i.e., positioned between 1 and 2. Consequently, as the reaction and diffusion proceed simultaneously, the peak of the xylose concentration moves toward the center. It is worth highlighting that, as seen in Figure 5, after around 8 h, almost all of the hemicellulose in the first half of the particle (close to the outer surface) has been consumed, while the reaction close to the center of the particle is just starting. This shows the importance of diffusion as a determining factor on the overall yield of any hydrothermal pretreatment method, because a long residence time for sugars inside the particles can result in their degradation to furfural. Figure 6 shows the relationship between the xylose and furfural concentrations at a position 0.5 cm inside a particle. Furfural is a product of xylose decomposition. As a result, as the concentration of xylose increases, the concentration of furfural increases as well. However, as can be seen in Figure 6, after a given period of time, the xylose concentration decreases, while the furfural concentration increases. This may imply that part of the xylose that is generated deeper inside the particle is decomposed to furfural during the diffusion process out of the wood particle. On the basis of these considerations, it can be concluded that the size of biomass is an important determinant in the yield of sugar recovery. Consequently, we performed a sensitivity analysis on the developed model to quantify the importance of each factor on the overall process yield.
Figure 6. Furfural concentration versus xylose concentration in the middle of the biomass.
processes whose experimental analysis is costly or impossible. The quality of models depends upon assumptions used for their derivations and accuracy of model parameter values. Modern complex models are nonlinear and can be very expensive to run. With respect to these aspects, GSA offers a comprehensive approach to model analysis.29 Unlike local sensitivity analysis, GSA methods evaluate the effect of a factor, while all other factors are varied as well, and thus, they account for interactions between variables and do not depend upon the stipulation of a nominal point. GSA enables the identification of key parameters whose uncertainty most strongly affects the output. It can be used to rank variables, fix unessential variables, and reduce model complexity. GSA can be applied in the model evaluation process to assess and increase the reliability of models.
4. Global Sensitivity Analysis (GSA) (29) Saltelli, A.; Tarantola, S.; Campolongo, F.; Ratto, M.; Andres, T. Global Sensitivity Analysis; John Wiley and Sons: New York, 2008; ISBN: 0470059974.
A model-based simulation of complex processes is an efficient, commonly used approach of exploring and studying 4678
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4.1. Sobol’s Method for GSA. The method of global sensitivity indices developed by Sobol30,31 is based on an analysis of variation (ANOVA) type of a high-dimensional model representation (HDMR). It is a variance-based method that enables the calculation of not only the individual contribution of each input parameter to the output variance but also captures the interaction effects. It can also treat “sets” of factors as one single factor. When the factors are grouped, the computational costs can be significantly reduced. It allows for the calculation of the total sensitivity indices, which measure the total contribution of a single input factor.32 The main drawback of Sobol’s method31 is its computational cost, because it requires a number of model evaluations equal to N(k þ 2), where k is the number of input variables and N is the number of samples used in the Monte Carlo integration. Monte Carlo or quasi-Monte Carlo integration is required for computing global sensitivity indices.33 Therefore, the method can become computationally prohibitive when the number of input variables is high. 4.2. GSA Based on Random Sampling (RS)-HDMRs. For many practical problems, only low-order correlations of the input variables are important. By exploiting this feature, an efficient set of techniques called HDMR was developed by Alıs and Rabitz.34 HDMR was introduced as a set of quantitative tools for efficiently mapping the input-output behavior of a model function involving high-dimensional inputs. It is based on a truncation of the ANOVA decomposition to low-order terms (in practice, to the second or third order). A practical form of HDMR, RS-HDMR has recently become a popular tool for building metamodels. A great advantage of the RS-HDMR technique is that the computation cost no longer depends upon the dimensionality of the function and the complexity becomes a linear function of the number of samples.35 RS-HDMR can also be used for computing global sensitivity indices, and it requires much lower computational efforts than Sobol’s method. The principal limitation of RS-HDMR is the truncation of ANOVA decomposition terms to the second or third order.34 This is, however, not always the case. Kucherenko et al.36 have established a classification of different function types and cases in which assumptions of HDMR are violated. An improvement of RS-HDMR based on quasirandom sampling (QRS) called QRS-HDMR was introduced by Kucherenko et al.36 4.3. Extension of HDMR for Metamodelling: Fast Equivalent Operational Models. In the computation of chemistry
transport models, the chemical rate equations involving many species require advanced numerical integration schemes [i.e., stiff ordinary differential equation (ODE) or partial differential equation (PDE) solvers] and can be extremely expensive to solve numerically. Furthermore, often there is a need to repeatedly solve them for different sets of initial conditions. Consider the following system of ODEs, where p is the vector of parameters and y is the vector of state variables: dy ¼ Fðy, p, tÞ ð16Þ dx yðt ¼ 0Þ ¼ y0 ðpÞ
ð17Þ
A fast equivalent operational model (FEOM) can be build by approximating y at specific times with RS-HDMR or QRS-HDMR metamodels. Practically, the algorithm consists of sampling a vector of parameters {pj} for all points pj, 35,36 solving the ODE for a specific set of time points {t*}. i
yðti , pj Þ, i ¼ 1, :::, n; j ¼ 1, :::, N
ð18Þ
Then, using these data, we can build the RS-HDMR or QRS-HDMR models for a set of time points {t*}. i
hðti , pg, i ¼ 1, :::, n
ð19Þ
The obtained set of HDMR models represents FEOM. Approximating the original model at chosen time points with the FEOM will only require the computation of algebraic functions. In this work, we use FEOM to account for the evolution of the global sensitivity indices with time. We performed two sets of sensitivity analyses. First, we compared dynamic xylooligomer size evolution versus xylose decomposition to furfural to see which one is the most influential factor in the overall yield of the process. In the second analysis, we compared kinetic parameters versus the particle length to determine the relative importance of diffusion versus reaction to see if one of the factors is ratelimiting or if both factors should be considered simultaneously. 4.3. Methodology. To analyze the bulk concentration of xylose as the target output of the system, we used the kinetic parameters and the length of the particle of wood as the input factors. The first-order global sensitivity indices with respect to the target output were computed for each factor, using QRS-HDMR. The factors are related to a particular phenomenon in the process, and the importance of the phenomena is linked to the global sensitivity indices. For example, in Figure 8, diffusion is associated with the length of the wood particle. Therefore, the evolution of the global sensitivity indices along time shows the relative importance of each physical phenomenon in the process. 4.4. Analysis of Results. Figure 7 shows the dynamics of global sensitivity indices of the solid-phase reaction, xylooligomer hydrolysis, and xylose decomposition to furfural. The dynamics shows that three main steps may be identified: (1) At the beginning of the process, the solid-phase reaction is the most important phenomena. Indeed, the sensitivity analysis has shown that the related kinetic parameter kh is the most influential factor, being close to 1. This is obvious because, at this stage of the process, only the solid phase exists. (2) Later on, after approximately 5 h, both xylose decomposition and liquid-phase reactions are progressively gaining importance. (3) After 7 h, the xylose decomposition is still gaining importance, while the liquid-phase reaction
(30) Sobol, I. M.; Tarantola, S.; Gatelli, D.; Kucherenko, S.; Mauntz, W. Estimating the approximation error when fixing unessential factors in global sensitivity analysis. Reliab. Eng. Syst. Saf. 2007, 92, 957–960. (31) Sobol, I. M. Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Math. Comput. Simul. 2001, 55, 271–280. (32) Homma, T.; Saltelli, A. Importance measures in global sensitivity analysis of model output. Reliab. Eng. Syst. Saf. 1996, 52 (1), 1–17. (33) Feil, B.; Kucherenko, S.; Shah, N. N. Comparison of Monte Carlo and quasi-Monte Carlo sampling methods in high dimensional model representation. The First International Conference on Advances in System Simulation, SIMUL 2009, Porto, Portugal, 2009. € F.; Rabitz, H. Efficient implementation of high dimen(34) Alıs, O. sional model representations. J. Math. Chem. 2001, 29, 127–142. (35) Li, G.; Hu, J.; Wang, S. W.; Georgopoulos, P. G.; Schoendorf, J.; Rabitz, H. Random sampling-high dimensional model representation (RS-HDMR) and orthogonality of its different order component functions. J. Phys. Chem. 2006, 110, 2474–2485. (36) Kucherenko, S.; Feil, B.; Shah, N.; Mauntz, W. The identification of model effective dimensions using global sensitivity analysis. J. Complexity 2009, manuscript submitted.
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: DOI:10.1021/ef9012246
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5. Conclusion In this work, we developed a model for a hydrothermal pretreatment process that considers both the chemical and physical natures of the process. The chemical aspect of the process mainly involves the hydrolysis of hemicellulose to monomeric sugars. We considered that all xylooligomers with a degree of polymerization up to 30 are soluble. Also, we considered that bond breakage is a function of the position in the hemicellulose chain and that all of the bonds with the same position undergo breakage at the same rate. It was found that, for the system studied, after around 8 h almost all of the hemicellulose in the first half of the particle (close to the outer surface) had been consumed, while the reaction close to the center of the particle had just started. This shows the importance of diffusion as a determinant factor on the overall yield of any hydrothermal pretreatment method, because a long residence time for sugars inside particles can result in their degradation to furfural. The physical aspect of the hydrothermal pretreatment process involves reducing the size of feedstock as well as heating the feedstock to a desired temperature. A model involving the diffusion of liquid into the biomass was developed, taking into account the inter-relationship between chip size and processing condition. With the aid of the developed model, a method to find the chip size that minimizes the energy requirement of grinding and pretreatment processes in the NREL design was proposed. Finally, we performed two sets of sensitivity analyses: first, to compare the dynamic importance of xylooligomer size evolution versus xylose decomposition and, then, to compare the relative importance of kinetic parameters versus the particle length on the overall process yield. Sensitivity analysis revealed that, at the beginning of the process, the chemical reaction is more important than diffusion; however, as the reaction proceeds, diffusion becomes the determinant factor. This could be due to the fact that a long residence time for sugars inside the particle can result in their degradation to furfural. It was also shown that the solid-phase reaction rate, xylooligomer size evolution, and xylose decomposition are all determinant factors; therefore, any model for hemicellulose hydrolysis should take all three of these factors into account.
Figure 7. Dynamic model sensitivity on the solid-phase reaction, xylooligomer hydrolysis, and xylose decomposition.
Nomenclature CK = Kick’s constant L1K = initial size of the feedstock in Kick’s law L2K = final size of the feedstock in Kick’s law R = modified severity factor tw = time needed for water diffusion into the woodchips F = density r = particle radius Φ = porosity D = diffusion coefficient M = molecular weight ΔC = concentration gradient T2 or T1 = temperature needed for chip size of r2 or r1 to obtain the same result, respectively Cp = heat capacity Cx = concentration of x-mer kx = reaction constant for x-mer Cd = furfural concentration Dx/W = diffusion coefficient of x-mer in water
Figure 8. Dynamic model sensitivity on the reaction and diffusion.
phenomenon becomes less significant. Obtained results are in direct correspondence with those presented in Figure 8. We showed that not only kinetic parameters but also and especially the size of the particle of wood and the processing time have a determining influence on the bulk concentration. Also, the FEOM approaches, when dynamic sensitivity indices are used, enabled us to account for the dynamic input-output behavior of the system. From a complexity reduction standpoint, it is probable that even the dimension of the problem (in the superposition sense) may be different at different times. It was possible to account for the evolution of the sensitivity indices considered in the system and to reduce the system to one that accounts for the decomposition of hemicelluloses and xylose into furfural. Finally, it should be noted that the HDMR approach offers an extremely fast alternative to Sobol’s method. 4680
