Multiobjective Optimization Approach for Cellulosic Biomass

Article pubs.acs.org/IECR

Multiobjective Optimization Approach for Cellulosic Biomass Pretreatment Lorena Pedraza-Segura and Hector Toribio-Cuaya Departamento de Ingeniería y Ciencias Químicas, Universidad Iberoamericana, Prolongación Paseo de la Reforma 880, México, D.F. 01219, México

Antonio Flores-Tlacuahuac*,† Department of Chemical Engineering, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, Pennsylvania 15213, United States ABSTRACT: Ethanol manufactured from cellulosic residues has the potential to become one of the alternative energy sources in the portfolio of renewable energies. Before reaching that status some technological problems must be resolved. Among them are the availability of reliable mathematical models for simulation, design, optimization, and control purposes as one the major hurdles that remains to be tackled. Another challenge refers to process design and operation when several conflicting and/or contradictory goals must be met. In this work we use corn cob, a widely available cellulosic residue, for ethanol manufacturing. Among all the steps that must be carried out for ethanol manufacturing we concentrate on the pretreatment process. Hence, the corn cob thermo-chemical pretreatment step was studied in order to model plant cell wall degradation and the release of polymers and monomeric sugars. During the pretreatment step xylose, xylan and some unwanted products are attained. We are mostly interested in maximizing the concentration of xylose while simultaneously minimizing the amount of xylan and undesired side products. However, increasing the amount of xylose will also increase the amount of xylan and side products. Therefore, both goals cannot be achieved simultaneously, and a trade-off solution must be sought. In this work trade-off solutions are computed as the point on the Pareto front that features minimum distance to the Utopia region. To verify the goodness of the trade-off solutions such a theoretical trade-off solution was implemented on experimental facilities. The experimental results clearly demonstrate that maximum xylose yield, and a minimum amount of xylan and side products can be obtained by using multiobjective optimization techniques especially when compared against similar results obtained from linear design of experimental techniques.

1. INTRODUCTION

The process for ethanol manufacturing involves several steps: milling, pretreatment, fermentation, and separation. In this work we will address the determination of optimal experimental operating conditions for the pretreatment step by using advanced nonlinear optimization techniques. Biomass pretreatment is a bottleneck on a cellulosic ethanol process for several reasons: most of the pretreatment technologies are energy intensive (AFEX, steam explosion, liquid hot water) and produce inhibitors from carbohydrate degradation, which impacts directly on enzymatic hydrolysis and fermentation performance and must be removed in an extra step of detoxification. Several authors4−6 consider that research on pretreatment should also be focused on reducing the environmental impact of this step by reducing of use of utilities (energy, water, and chemicals), improvement of recovery of carbohydrates and byproducts, and reduction of furfural and 5HMF. Optimization techniques can be used to achieve this aim. Recent works regarding the use of

It has been forecasted that ethanol, one of the new sources of renewable energies, will have a relevant role in the portfolio of energies aimed to meet future energy demands taking into account sustainable development issues. However, traditionally ethanol has not been considered as a sustainable energy source because the first generations of ethanol manufacturing processes deployed sugar cane and corn as raw materials. These raw materials are intensively used for human consumption. Ethanol production will really feature sustainable characteristics when its manufacturing deploys waste materials (i.e., cellulosic residues) so it is not in competition against the human food chain. In fact, first generation ethanol is considered unsustainable from an energy life cycle point of view and for the huge consumption of feedstock that are part of human and animal food supplies. In the first case Patzek1 analyzed the impact of corn ethanol production from a thermodynamics approach and found unbalance between energy inputs and outputs. Others authors2 made emphasis in competence for a feedstock use, fuel or food, as an important aspect for sustainability of biofuels. For this reason research about second generation bioethanol processes, obtained from agricultural, municipal, and forest waste,3 has increased. © XXXX American Chemical Society

Received: November 20, 2012 Revised: February 26, 2013 Accepted: March 20, 2013

A

dx.doi.org/10.1021/ie3032058 | Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Industrial & Engineering Chemistry Research

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Table 1. Pretreatments Methods for Lignocellulosic Biomass classification

pretreatment

chemicals

physical

milling (hammer and ball milling) uncatalyzed steam explosion steam explosion alkaline alkaline peroxide ammonia fiber expansion (AFEX) ammonia recycled percolation (ARP) dilute acid fungi, actinomyces

no no yes yes yes yes yes Yes No

chemical

biological

hemicellulose removal

lignin removal

cellulose decrystallization

increase of surface area

* * * * *

* * * * *

*

* * *

* * * * * * *

*

there is not a single optimal solution that suits to all the design goals so a trade-off solution must be picked up by the designer based on considering all the trade-off solutions in the form of a Pareto front. In this work we propose a multiobjective optimization methodology for maximizing the concentration of xylose and minimizing the concentration of xylan, the design goals, and using as decision variable the initial amount of solids. After the Pareto front is obtained we selected one of the best trade-off optimal solutions and carried out the experimental pretreatment process. The Pareto optimal results are compared against similar results obtained from experimental conditions set by traditional linear design of experiments. The results clearly demonstrate that for the underlying system larger ratios of xylose/xylan concentration set by the Pareto optimal design outperform those obtained from design of experiments techniques. We are not implying that linear design of experimental techniques should not be used. Instead, what we propose is the use of advanced nonlinear optimization techniques when the designer suspects nonlinear effects and interactions will be worth taking care of and mainly when meeting several conflicting and/or contradictory goals becomes a key issue. We would like to point out that one of the disadvantages of the proposed approach has to do with the availability of a good mathematical model which means a model free of modeling errors. However, this issue is not perceived as a real disadvantage since either stochastic or robust optimization techniques can be used to fill this gap. The paper outline goes as follows. First we discuss the materials and methods used for running the experimental work. Next a dynamic mathematical model of the pretreatment process is identified. Following, we discuss the numerical optimization procedure used for the generation of the Pareto front. Next, the experimental results are recorded for experimental conditions set by linear design of experiments and those obtained from the Pareto front. Finally, the results of the two experimental sets are discussed and some conclusions regarding the results achieved in this work are formulated.

optimization tools for ethanol production from biomass can be found elsewhere.7−11 Agricultural activities in Mexico generate about 4 million MG/year of lignocellulosic residues, mainly derived from corn, sugar cane, and cereals. As a result each year 450 000 Mg of corn cob are produced and, unlike corn stover, has reduced value as animal food, in spite of the high potential sugar content of this material.12 Corn cob like other lignocellulosic biomass must be fractioned into structural polymers: cellulose, hemicellulose, and lignin. Corn cob has an approximate composition of 39% cellulose, 31.2% hemicellulose, 22% lignin, 4.94% extractives, and 2.2% ash. Like other lignocellulosic biomasses it must be fractioned in order to obtain monomeric sugars (mainly glucose and xylose) from polysaccharides by using acid or enzymatic hydrolysis.13 Biomass can be pretreated by different methods, in order to remove hemicellulose and/or lignin besides partially modifying the structure of the cellulose, allowing enzyme−substrate interaction. Pretreatment methods are classified according to the phenomena on which they are based: physical, chemical, or biological. Each one of these has different effects over biomass. Table 1 shows a summary of pretreatment methods; details of these experimental methods can be found elsewhere.14−19 In this work thermo-chemical pretreatment was selected, because it can remove hemicellulose and modify plant cell wall structure, leaving the cellulose exposed for the enzyme attack. This method differs from steam explosion in operating conditions; temperature is lower (120− 150 °C) and so is system pressure. Residence time, solid−water ratio, and catalyst concentration (acid medium) are other parameters that can be modified in order to reduce byproducts such as acetic acid, furfural, and 5-hydroxymethyl furfural that can inhibit yeast metabolism.20 However, if temperature and pressure conditions are too moderate, the structure of the biomass will remain unaltered and the enzymatic hydrolysis efficiency will vanish. It is desirable to identify experimental conditions where hemicellulose removal is maximum and inhibitors production is minimal, to ensure high cellulose conversion onto glucose. It turns out that some of the best experimental conditions can be difficult to identify, especially when common design of experimental techniques are used. This is so because traditional design of experiments methodologies rely on the assumption of linear system behavior that can be hard to justify. Taking into account system interactions in the form of nonlinear behavior actually may lead to experimental conditions under which better optimal designs can be found. The situation turns out to be more complicated when in addition several conflicting and often contradictory design objectives are pursued. Under this situation two or more experimental objectives must be simultaneously met in the best possible manner. Normally,

2. MATERIALS AND METHODS Raw Materials. Corn cobs were obtained from a cultivated field (Puebla, Mexico). They were air-dried and ground in a hammermill, in order to obtain particle sizes around 0.5 mm. Reagents and Equipment. All reagents were of analytical grade. Deionized water was obtained from a Milli-Q water purification system (Millipore, Billerica, MA). Corn cob composition analysis was determined according to the national renewable energy laboratory (NREL) methodology.21 Monosaccharides, furfural, 5-(hydroxymethyl)furfural (5HMF), and acetic acid concentrations were quantified by high performance liquid chromatography (HPLC), using an Agilent 1050 B



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dCg

Chromatograph, equipped with an ion exchange Aminex HPX87H column. Analysis was performed at 65 °C, with 5 mM H2SO4 as eluent, at flow rate of 0.6 mL/min. Pretreatment. Ground corn cob was incubated in a 1.5% sulphuric acid solution, using a solid load of 8% w/v. After an overnight incubation, the material was placed in a jacketed reactor and heated with steam until reaching 12 psi. After fifteen minutes at this condition the reactor was cooled to room temperature. Pretreated biomass was neutralized with 5 M NaOH, filtered with Whatman No. 1 filter paper; an aliquot of the resultant liquid was passed through a Millipore nitrocellulose membrane of 0.22 μm in order to prepare the sample for HPLC analysis. Solid samples were dried in an oven to constant weight at 105 °C. The pretreatment conditions were varied according the objective of the experiment, as indicated in section 5.

= (k1 − k 2)Cg

(2)

dC hmf = (k 2 − k 3)C hmf dt

(3)

dC hcl = −(k4 + k 7)C hcl dt

(4)

dCxo = k4C hcl − (k5 + k6)Cxo dt

(5)

dCac = k 7C hcl − k10Cac dt

(6)

dCxi = k6Cxo − k 9Cxi dt

(7)

dCar = k5Cxo − k 8Car dt

(8)

dCfur = k 9Cxi + k 8Car − k11Cfur dt

(9)

dt

3. MODELING AND PARAMETER FITTING A dynamic mathematical model was identified from experimental data and deployed for carrying out multiobjective optimization calculations. The set of reactions that take place reads as follows: k1

cel ⎯⎯→ g

dCplig

H+

dt

k2

g ⎯⎯→ hmf

dC lig

H+

k3

dt

H+

dCdp

hmf ⎯⎯→ dp

dt

k4

hcl ⎯⎯→ xo

(10)

= k12Cplig − k13C lig

(11)

= k 3C hmf + k11Cfur + k10Cac + k13C lig

(12)

where Ci, i = cel, g, hmf, hcl, xo, ac, xi, ar, fur, plig, lig, and dp, represent the composition of cellulose, glucose, 5-HMF, hemicellulose, xylan, acetic acid, xylose, arabinose, furfural, lignin products, lignin, and depolymerized products concentrations, respectively, whereas kj, j = 1, ..., 13, stands for the kinetic rate constants. The above model represents modifications of plant cell wall under thermo-chemical pretreatment conditions, changes in the concentrations of polymers and monomers, and the appearance of other compounds due to chemical reactions. Another way to model the phenomenon is the severity factor, which is a measure of the hardness of the process; this equation relates the time and temperature with measured responses, e.g., xylose, acetic acid, furfural concentration, etc. The model used in this work is based on first order reactions; in cases of certain compounds (furfural and 5-HMF) the initial concentration is so low that it cannot be measured, so the value is set to zero; however, there is a minimum amount from the previous stage. In this section we provide details of the thermochemical pretreatment process. Thermochemical pretreatment is a process based on a hydrolytic reaction; it takes place in the presence of a dilute acid solution and a quick depressurization of the system whereby the corn cob complex cellular wall is substantially modified. In the first instance, a hemicellulose fraction composed of (arabinan) glucuronoxylan oligomers22 and another composed of acid-soluble lignin are removed. The chemical bond attacks occur during the incubation process on the β-(1→4)-glycosidic, 4-O-Me-α-D-glucopyranose, and 2,3acetyl bonds; additionally it happens over the C(O)-3 and C(O)2 arabinose branches, all of them found in hemicellulose polymer.23 The chemical attack releases xylose, glucose,

H+

k7

hcl ⎯⎯→ ac H+ k5

xo ⎯⎯→ ar H+ k6

xo ⎯⎯→ xi H+ k8

ar ⎯⎯→ f H+

k9

xi ⎯⎯→ f H+ k10

ac ⎯⎯→ dp H+

k11

f ⎯⎯→ dp H+

k12

plig ⎯⎯→ lig H+

k13

lig ⎯⎯→ dp H+

The structure of the proposed dynamic mathematical model reads as follows:

dCcel = −k1Ccel dt

= −k12Cplig

(1) C



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Table 2. Experimental Dataa time

Ccel

Cg

Chmf

Chcl

Cxo

Cac

Cxi

Car

Cfur

Cplig

Clig

Cdp

0 2 4 7 10 15

49.971 49.864 49.864 49.682 49.643 49.489

1.992 2.222 1.661 1.909 1.868 1.879

0.000 0.000 0.000 0.000 0.000 0.066

24.378 21.861 20.691 21.685 15.163 12.289

2.032 4.864 6.799 6.626 6.776 6.236

0.340 0.830 2.240 1.299 3.071 3.778

1.875 1.629 2.378 2.324 3.751 6.767

0.000 0.899 1.463 1.432 2.352 3.016

0.000 0.032 0.036 0.037 0.050 0.068

14.599 12.150 13.121 9.152 6.694 4.574

3.040 6.634 7.841 12.436 13.969 15.239

0.000 0.368 1.230 2.475 2.369 2.271

a Time was measured in min and concentrations (C) are expressed in g/L. The meaning of the subindices is as follows: cel = cellulose, g = glucose, hmf = 5-HMF, hcl = hemicellulose, xo = xylan, acz = acetic acid, xi = xylose, ar = arabinose, fur = furfural, plig = lignin products, lig = lignin, and dp = depolymerized products.

mathematical model is linear, this fact can help to explain the observation that the dynamic behavior of the model can be represented using some few variables.

arabinose, and acetic acid in small quantities, while the major production is the one related to xylan. Besides, quantities of furfural and 5-hydroxy-methyl-furfural (5-HMF) are present as a consequence of xylose and glucose dehydration cycle.24 After the thermo-chemical treatment and the depressurization of the system, xylose, arabinose, glucose,and acetic acid concentrations increase due to the xylan fragmentation, while the ones of furfural and 5-HMF do not reach inhibitory levels (around 0.30 g/L, unpublished data). The lignin polymer is directly attack on the ether (β-O-4) and acid-labile bonds; the susceptible fraction of the polymer to react under the described conditions is well-known as acid-soluble lignin and it is capable of produce cinammyl alcohol byproducts such as vanillin, syringaldehyde, vanillic acid, syringic acid, etc.25 Cinammyl alcohol byproducts are produced during the incubation process and increase their concentration all trough the thermal treatment and the depressurization of the system. Using the above recorded experimental information (Table 2) the reactions rates kj, j = 1, ..., 13, were obtained by transforming the constant estimation problem in a dynamic optimization problem where the objective function is just the euclidian norm between the experimental and the theoretical results over the time horizon indicated by the experiment. The set of differential equations representing the dynamic model were fully discretized using collocation techniques.26 The estimated rate constants are shown in Table 3. It should be

4. MULTIOBJECTIVE OPTIMIZATION Frequently in science and engineering calculations design goals are contradictory. A common case involves the simultaneous maximization of revenues and minimization of environmental impact. However, both objectives are in conflict since normally increasing profit would also increase the environmental impact and vice versa. A similar situation occurs in the biomass pretreatment process where several operating objectives are contradictory too. For instance, commonly we would like to maximize the concentration of xylose and at the same time to minimize the concentration of xylan and inhibitors. It turns out that we cannot get high xylose concentration and at the same time low xylan concentration without generating furfural inhibitory concentrations as a result of side reactions. From an optimization point of view normally this kind of conflicting objectives calculations are approached by merging both operating objectives into a single objective function by using a weighting function to highlight the importance of a given objective and to make them consistent from a dimensional point of view when the objectives have different measurement units. However, the choice of the weighting functions is not systematic, and it depends completely on the user experience and can lead to suboptimal solutions.27 On the other hand, it has been stressed28 that optimization problems featuring multiple conflicting objectives should be approached using multiobjective optimization techniques to provide improved optimal solutions. Although several multiobjective optimization techniques have been proposed28−30 in this work we will deploy the ϵ-constraint technique31 to compute optimal solutions of multiobective optimization problems due to its simplicity. In the ϵ-constraint method the multiobjective optimization problem is formulated as a single objective optimization problem by keeping one goal (Φ1) as the objective function and moving the remaining goals (Φ 2...Φn ) as system constraints:

Table 3. Estimated Constant Rates [1/min] rate constant

value

k1 k2 k3 k4 k5 k6 k7 k8 k9 k10 k11 k12 k13

6.735319 × 10−4 0.007 1 0.040 0.028 0.057 0.007 0 0.048 0 1000 0.095 0

Min Φ1 s.t.

remarked that although some of concentrations were really small and hard to record we decided to pursue the fitting of all the reaction constants. As seen, some of the constant rates turned to be almost zero meaning the null influence of the concentration of certain compounds on given system states. Moreover, since the structure of the underlying dynamic

Φ2 ≥ ϵ2 · · Φn ≥ ϵn D



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Table 4. Operating Conditions for Running the Set of Experiments experiment

temperature [°C]

reaction time [min]

acid concentration % [v/v]

solid load % [w/v]

xylose concentration % recovery

1 2 3 4 5 6 7 8

132 132 132 118 132 118 118 118

12 12 18 18 18 12 18 12

1.5 0.5 1.5 0.5 0.5 1.5 1.5 0.5

12 12 8 12 8 8 12 8

64.61 44.33 56.60 14.19 50.08 60.08 40.56 18.77

where ϵ2, ..., ϵn are the bounds around which the Φ2, ..., Φn goals become feasible. Of course, additional problem constraints must be also incorporated. In low dimension systems the diagram of a given goal against another one is called the Pareto front. Using the Pareto front the trade-offs embedded in the optimal solutions become clear, and from here an optimal solution can be picked up by the designer based on process insight. There are some other numerical approaches suggested to estimate some of the better operating points along the Pareto front32 without using heuristics. They are based on locating the point on the Pareto front featuring minimum distance, using a given norm, to the Utopia region. Accordingly, after some trial and error calculations, we came to the conclusion that the maximization of xylose concentration (Cxi) and simultaneous minimization of xylan concentration (Cxo) represent a desirable operating target during the biomass pretreatment process. Therefore, we solved the following multiobjective optimization problem:

one aspect of the whole process. Other models can be developed for the production of sugar degradation compounds, like furfural and 5-hydroxy-methyl-furfural. Screening design of experiments, as Plackett−Burman matrix, allows knowing the significant factors of a process, rather than interactions effects. This design is useful for detecting major effects, assuming all interactions are negligible. Plackett−Burman design was performed testing the following parameters: temperature (118−132 °C), solid load (8−12%, w/ v), acid concentration (0.5−1.5%, v/v), and residence time (8− 12 min). Xylose concentration was the measured response (Table 4); data analysis of the linear model is represented by the following equation: xylose yield = 43.656 + 10.252A − 3.294B + 5.109E (13)

+ 11.810F − 2.730G

where A is the temperature (°C), B is the time (min), F is the acid concentration (v/v), G is the solid charge (w/v), and E is a dummy column. The linear model was developed by analyzing the experimental data through the Plackett Burman design matrix. From this matrix, the effects of each individual variable are obtained throughout the algebraic sum of the measured outputs. The effects are arranged into a regression model, which is a method similar to the two-route variance analysis. It is noticeable that experiment 1 presents the highest xylose production; unfortunately the tendency of it is to increase the level of inhibitory substances due to the temperature effect; therefore, experiment 6 is preferred. Once operating conditions were established (Experiment 6, Table 4), the kinetics of the xylose release and inhibitors production was obtained. In order to test new conditions, according to eq 13, new experiments were carried out at higher solid load (15%, w/v) and acid concentration (3.5%, v/v), maintaining the same temperature and sampling rate for a longer interval. Table 5 and Figure 1 show the recorded experimental results. Acid concentration has a positive coefficient (eq 13), and then this value was increased. However, decreasing solid load fermentable sugars, obtained

Min Cxi s.t. Cxo ≥ ϵ g ( x) ≤ 0

where g(x) stands for the set of constraints attained when using the full discretization orthogonal collocation method for dealing with dynamic optimization problems.26

5. EXPERIMENTAL RESULTS In this section two kinds of experimental results are presented. First, we run some experiments using experimental conditions obtained from traditional linear design of experiments techniques. Second, new experimental results were recorded using as experimental conditions those attained from the point number 3 in the Pareto front (see Figure 2). The aim in carrying out these two sets of experiments was to demonstrate that by taking into account conflicting experimental goals and deploying nonlinear optimization techniques, better experimental results can be obtained. Experimental Conditions Set by Design of Experiments. The operating conditions used in the steam thermochemical process of the biomass pretreatment step differ according to the employed feedstock. As a result the temperature varies between 140 and 220 °C. The residence time, solid−water ratio, and acid concentration are other variables that can be also modified. In this work we used a Plackett−Burman design for 8 factors,33 to determine the influence of operating variables on hemicellulose removal (measured as free xylose) and subsequent cellulose hydrolysis. By this way a linear model was obtained which represents only

Table 5. Experimental Data Measured for the Conditions Indicated by Traditional Linear Design of Experiments (T = 118 °C, t = 12 min, 1.5% acid concentration, 8% (w/v) solid load)a

a

E

time

Cxi

Cxo

Car

Chmf

Cfur

0 10 20 40

0.43 12.43 17.43 19.65

6.21 10.53 6.36 2.49

0.25 2.17 2.37 2.25

0.03 0.06 0.14 0.19

0 0.06 0.08 0.13

Time was measured in min and concentrations are expressed in g/L. dx.doi.org/10.1021/ie3032058 | Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX


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Figure 1. Experimental results using experimentation conditions from linear design of experiments.

Figure 3. Dynamic optimization results for the third point on the Pareto front.

after hydrolysis, will result in a diluted solution for fermentation purposes. Experimental Conditions Set by the Pareto Front. In this part we used the ϵ-constraint method described in Section 4 to get a set of optimal experimental conditions that represent the best trade-off between the conflicting goals: maximization of the concentration of xylose and minimization of the concentration of xylan. The degree of freedom was taken as the initial amount of solids from which the initial conditions of all the state variables of the underlying mathematical model can be obtained. The results of the calculations are displayed in the Pareto front depicted in Figure 2. The Pareto front clearly

of initial conditions required by the dynamic model described by eqs 1−12 can be obtained. Experimental results are depicted in Figure 4 and summarized in Table 6.

Figure 4. Experimental results obtained from running point no. 3 of the Pareto front of the xylose vs xylan concentration [g/L].

Table 6. Experimental Data Measured for the Conditions Indicated by Point No. 3 of the Pareto Fronta time

Cxi

Cxo

Car

Chmf

Cfur

0 5 10 15 20 25

0.10 1.56 3.02 9.47 12.47 15.29

3.08 7.91 8.01 4.79 2.41 0.33

0.09 1.69 1.81 1.81 1.90 1.79

0.02 0.32 0.48 0.37 0.28 0.12

0 0 0 0.05 0.05 0.08

Figure 2. Pareto front of the xylose vs xylan concentration [g/L].

a

indicates that there is no way to get high xylose concentration while simultaneously obtaining low xylan concentration values. The physical explanation of this result has to do with the behavior of the reaction system. Using the information gathered in the Pareto front we selected the point number 3 as the best trade-off operating point. In Figure 3 the theoretical dynamic optimization results give an approximated idea about the performance of the reaction system around point number 3. To assess the advantage of operating at this trade-on solution experimental results were recorded for the optimal initial conditions embedded in point 3 of the Pareto front. For point 3 at Figure 2, the initial amount of solids was 90.808 from which all the sets

6. DISCUSSION The assessment of the influence of exogenous variables on the behavior of an experimental system is a rather complex task that has been addressed by traditional design of experiments that normally relies on the use of linear mathematical and optimization techniques.33 Normally experimental conditions perceived as target conditions are picked up in this manner. Of course, a clear disadvantage of this way of selecting experimental conditions has to do with the fact that system nonlinearities are completely neglected. The issue here is that due to the model and system mismatch the experimental F

Time was measured in min and concentrations are expressed in g/L.



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conditions can be either infeasible or nonrepresentative when applied to the experimental system. Actually with the advance in optimization algorithms34,35 and computer hardware it may be difficult to justify the reason to keep deploying mainly linear optimization techniques when addressing the determination of optimal experimental conditions. Perhaps with the exception of large scale systems (on the order of thousands of equations), the solution of convex and nonconvex nonlinear optimization problems turns out to be a task that can be accomplished using optimizers embedded in standard algebraic modeling languages such as Gams36 and AMPL.37 Therefore, modern design of experiments should be approached deploying nonlinear modeling and optimization techniques, and there is no need to deploy only linear design of experiments techniques assuming problem size is not an issue. Following this approach natural interactions and nonlinearities can be completely taken into account leading to the computation of better experimental processing conditions. Specifically, as shown in this work, when considering several conflicting experimental goals the determination of the full Pareto front is a roadmap which can be used by the experimentalist to pick up those experimental conditions that better suit all the design goals in the sense that the selected experimental conditions represent the best trade-off among all the objective functions. It should be highlighted that the same kind of results can be difficult to attain using traditional design of experiments because nonlinear behavior has been neglected and because only a single goal is considered when deploying these techniques. Having said that, we must recognize that the quality of the results presented in this work is related to the multiobjective nature of the optimization problem rather than to take into account system nonlinearities since the underlying dynamic model features linear behavior. However, the optimization approach can perfectly deal with system nonlinear behavior. In fact, using the proposed multiobjective optimization approach to identify optimal experimental conditions, we have the potential to take into account system nonlinearities and to compute not only a single optimal experimental point but all the set of optimal experimental conditions that are the best trade-off solutions among all the experimental goals. In summary, even with all its disadvantages, linear experiment design techniques can provide an initial assessment of the impact of given variables on system response, and certainly, advanced nonlinear optimization strategies for determining better experimental points can also benefit from the knowledge gained trough the use of those techniques. From Figures 1 and 4 we notice that the experimental results based on the conditions set by the point number 3 at the Pareto front are much better than the corresponding ones attained from running the experiment but using traditional linear design of experiments (DOE) techniques. In fact, from Figure 4 we estimate that at 25 min the xylose/xylan ratio is about 32, whereas, from Figure 1, the same ratio is around 4, a remarkable improvement of almost 1 order of magnitude. Actually the experimental conditions set by the DOE approach lead to larger amounts of xylose, but this can be explained for a higher solid load. Table 7 shows differences between results from both approaches. However, it turns out that the amount of xylan also increases, which underlies the conflicting nature of both design goals. In summary, the experimental results indicate that using the initial conditions set by the point number 3 on the Pareto front lead to obtaining the maximum amount of xylose and minimum amount of xylan, which was the main objective of performing optimal Pareto calculations such

Table 7. Experimental Results Expressed as Percent of Chemical Species Released from Initial Material %

exp 6 (basis)

linear design approach

point 3 Pareto

Xi Xo Ar

33.83 31.18 15.08

46.48 16.96 6.32

41.76 21.12 7.98

that a trade-off between the two design goals can be established. Moreover, we would like to highlight that the improved experimental results were obtained by neither running an excessive number of experiments nor deploying huge amounts of computer power. The approach relies in having a good representative mathematical model of the addressed system and just using well-known and proven nonlinear optimization techniques38 for getting the Pareto frontier.

7. CONCLUSIONS In this work we have demonstrated that better experimental results can be obtained if advanced optimization techniques are used for determining some of best experimental conditions leading to meet some desired experimental design goals. Assuming that a representative system model is available, meaning negligible modeling errors, optimization techniques can take care of existing nonlinear interactions embedded into the model that represents the behavior of the real system. It is not completely necessary to use linear optimization design techniques (i.e., traditional design of experiments) to get a set of proper experimental conditions. Although in the present work the underlying model was linear, the proposed optimization approach can be easily applied to nonlinear systems. When faced with multiple design goals that must be met simultaneously, getting optimal experimental conditions from traditional design of experimental techniques can be cumbersome. On the other hand, advanced optimization techniques are in principle easy to apply for the generation of the Pareto front such that several trade-off solutions are attained from which the designer can pick up the one that best suits her/his experimental goals. Of course, the assumption of a model almost free of modeling errors can be a major drawback of the proposed experimental methodology. However, stochastic39 and robust optimization techniques can be helpful to get rid of this disadvantage. In summary, by using the proposed combination of multiobjective optimization techniques to help to get better experimental techniques during the biomass pretreatment process allows an increase in the amount of xylose and reductions in the amounts of undesired products.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: antonio.fl[email protected]; afl[email protected]. Notes

The authors declare no competing financial interest. † A.F.-T.: On leave from Universidad Iberoamericana.

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REFERENCES

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Multiobjective Optimization Approach for Cellulosic Biomass

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