Synergistic Optimal Integration of Continuous and Fed-Batch Reactors

ARTICLE pubs.acs.org/IECR

Synergistic Optimal Integration of Continuous and Fed-Batch Reactors for Enhanced Productivity of Lignocellulosic Bioethanol Hyun-Seob Song, Seung Jin Kim, and Doraiswami Ramkrishna* School of Chemical Engineering, Purdue University, West Lafayette, Indiana 47907, United States ABSTRACT: With significant technological advances in metabolic engineering, there are currently available efficient recombinant yeast strains capable of fermenting lignocellulosic sugars (i.e., glucose and xylose) to bioethanol. Conventional batch fermentation, preferred in most bioprocesses, may not provide the most appropriate environments for those engineered strains to perform their best. In this article, we consider new reactor configurations integrating different types of reactors to examine their maximal productivity of lignocellulosic bioethanol. Among various possible scenarios, the highest performance was acquired from a synergistic operation of continuous and fed-batch reactors. In a chemostat, glucose is fermented alone by the hexose-only fermenting (wild-type) yeast, and unconverted xylose is fed to a batch reactor where mixed sugars are fermented by recombinant yeast. The optimization of the feed rate is a critical issue in order to maximize the productivity in a fed-batch reactor. It is shown that the proposed idea is able to increase the bioethanol productivity by up to 50% in comparison to a simple batch operation. Obviously, these considerations must be integrated with a more comprehensive cost
benefit analysis before a clear choice of reactor configuration can emerge.

1. INTRODUCTION We are pleased to contribute to the special issue in honor of Professor K. D. P. Nigam, who has made lasting contributions to Chemical Reaction Engineering. Our article addressing reactor configurations to improve bioethanol productivity is hopefully a fitting tribute to Professor Nigam with respect to his focus on process intensification. The production of bioethanol has an old history. It had been used, for example, as a transportation fuel in Germany and France, and as a fuel in Brazil and United States as well as in Europe, already during the late 19th and early 20th centuries.1 After the oil crisis in the 1970s, current interest in bioethanol is even greater due to not only depletion of the oil reserves but also the negative impact of fossil fuels on the environment such as high greenhouse gas emissions. Production of bioethanol as an alternative to petroleum-based liquid fuels has increased over the last several decades, in particular rapidly from 2000.2 The bulk of currently used bioethanol is produced from sucrose-containing feedstocks (e.g., sugar cane) or starch-based materials (e.g., corn, wheat and barley). The use of these first generation feedstocks is not considered sustainable because of several issues such as food-fuel conflict and their limited availability relying on geographic locations and seasons. The second generation feedstock, which can serve as a renewable resource for bioethanol production, is lignocellulosic biomass such as rice straw,3 wheat straw,2 corn stover,4 switchgrass,5 and various other agriculture and forest residues. Lignocelluose is mainly composed of cellulose, hemicelluloses, and lignin. Through the pretreatment and hydrolysis steps, they are broken down to release a wide spectrum of sugars with six (hexoses) and five carbons (pentoses). Bioethanol is finally obtained via fermention of those mixed sugars. The lignocellulosic bioethanol is, however, not at the stage of commercial production for which it is essential to reduce the production cost in all possible steps throughout r 2011 American Chemical Society

biomass-to-bioethanol processes. Our objective in this paper is to seek ways to increase the productivity of lignocelluosic ethanol at the fermentation step. Traditionally, the yeast Saccharomyces cerevisiae has been used for industrial bioethanol production from crop-based feedstocks. The same strain is not suitable, however, for fermenting cellulosic sugars containing pentoses (i.e., xylose) as well as hexoses (i.e., glucose). This is because the wild-type S. cerevisiae can ferment glucose but hardly xylose, the second most abundant sugar (next to glucose) in the spectrum of cellulosic sugars. Various metabolic engineering attempts have been made to push and pull xylose into the central metabolism of S. cerevisiae.6,7 Push strategies include introduction of xylose transport and its initial metabolic routes (e.g., by expressing heterologous genes encoding xylose reductase and xylitol dehydrogenase), while pull strategies include overexpression of xylulose kinase and/or other enzymes of pentose phosphate pathways. Consequently, a number of recombinant yeast strains cofermenting glucose and xylose are now available.6 The productivity of ethanol is affected by cultivation methods as well as fermenting organisms. Batch reactors are most commonly used in industry, although fed-batch and modified forms of continuous systems are also considered.8 The suitable choice of reactors should be made considering the substrate type and traits of fermenting organisms, as well as economic aspects. This is a practically important subject that has not been investigated in detail in regard to lignocellulosic bioethanol.

Special Issue: Nigam Issue Received: April 22, 2011 Accepted: June 30, 2011 Revised: June 29, 2011 Published: June 30, 2011 1690

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Table 1. Reactor Configurations Integrating Two Different Types of Reactors Operation 1 (O1)

Operation 2 (O2)

configuration reactor type yeast strain fermented sugars reactor type yeast strain fermented sugars

a

a

c

d

remarks

C1

batch

GM

GLC, XYL

batch

GM

GLC, XYL

O2 is identical to O1.

C2

batch

WTb

GLC

fed-batch

GM

GLC, XYL

Leftover sugars in O1 are fed to O2 at its startup.

C3

continuous

WT

GLC

fed-batch

GM

GLC, XYL

C4

batch

WT

GLC

fed-batch

GM

GLC, XYL

C5

continuous

WT

GLC

fed-batch

GM

GLC, XYL

Leftover sugars in O1 are fed to O2 in an optimal way.

GM = genetically modified strain. b WT = wild-type strain. c GLC = glucose. d XYL = xylose.

Most recombinant S. cerevisiae strains show a sequential consumption pattern in fermenting cellulosic sugars. Glucose is consumed initially alone, and xylose consumption starts when the preferred sugar is depleted or present at very low levels. Bioethanol productivity could increase, however, if simultaneous consumption is promoted. In an earlier study by Song and Ramkrishna,9 the possibility of improving the productivity in batch reactors was examined by increasing the initial concentration of xylose. Elevation of xylose concentration has both positive and negative effects, i.e., it facilitates simultaneous consumption initially but prolongs the fermentation time after glucose depletion. Overall, this trade-off resulted in the increase in ethanol productivity only at low sugar concentrations. They further showed that continuous operation produces significantly more ethanol than batch when only glucose is consumed but less when mixed sugars are consumed. These findings suggest the investigation of new reactor configurations that may outperform conventional batch fermentation. In this article, we explore reactor-level strategies toward enhanced productivity of lignocellulosic bioethanol. Various configurations combining batch, fed-batch, and continuous reactors are considered for the comparison with conventional batch fermentation. The maximum achievable productivity of different configurations is assessed. For this purpose, we employ the dynamic metabolic model developed by Song et al.10 with minor modification to its kinetics. The most significant increase in ethanol productivity is made by the optimal integration of continuous and fed-batch reactors. The basic idea is to ferment glucose alone in the continuous reactor and feed unconverted xylose to the batch reactor where mixed sugars are handled. The productivity of the fed-batch reactor is affected by the xylose feeding policy, which thus needs to be optimized. Detailed methodologies are provided below.

2. METHODS 2.1. Reactor Configurations. We consider the following five configurations (denoted by C1
C5), each of which combines two different reactor operations (O1 and O2) (Table 1). C1 represents a conventional batch operation where mixed sugars are fermented to ethanol by recombinant S. cerevisiae. The same is repeated at every batch (i.e., O1 is identical to O2). In C2, O1 is a batch reactor for the growth of the wild-type S. cerevisiae, which can ferment glucose alone. Sugars leftover in O1 are then fed to O2 (i.e., fed-batch operation) where mixed sugars are fermented using the recombinant strain. C3 is the same as C2, except that a chemostat is used for O1. C4 and C5 are respective counterparts of C2 and C3, and these two groups are differentiated only by the xylose feeding policy in O2. That is, in C2 and C3, all sugars

Figure 1. Dynamic simulation curves for primary metabolites in batch fermentation before (solid line) and after (dashed line) incorporating substrate inhibition terms into uptake kinetics. Panels (a
d) are differentiated by initial sugar concentrations.

leftover in O1 are fed into O2 at its startup (which implies that O2 is a batch system with elevated initial concentration of xylose). In C4 and C5, on the other hand, the xylose feeding rate is optimized such that the ethanol productivity in O2 is maximized. In all configurations, O1 and O2 are not necessarily connected. For convenience of analysis, it is assumed that leftover sugars to be fed to O2 are already available from prior operation of O1. We introduced a continuous reactor in C3 and C5. However, chemostats have been preferred less than batch reactors in practice. One of the primary reasons for this is the genetic instability of fermenting organisms as continuous operation will impose strong selective pressure of fast growing cells instead of efficient ethanol producers.8 This will pose a serious problem for recombinant yeast strains but may not for the wild-type. Thus, we consider C3 and C5 also as practically meaningful configurations. 2.2. Reactor Model. In order to evaluate the performance of different reactor configurations listed in Table 1, we carry out dynamic simulations using the metabolic model developed by Song et al.10 This high-fidelity model provides accurate descriptions of the growth of recombinant yeast on single or mixed sugars as verified from experimental data of Krishnan et al.11 The same model has been used previously for the study of continuous and batch production of lignocellulosic ethanol.9,12 In their 1691

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framework called the hybrid cybernetic modeling,13,14 elementary modes (EMs)15,16 are taken as metabolic options. Cellular regulation is viewed to occur among EMs such that the carbon uptake flux is maximized under dynamically changing environmental conditions. A hybrid cybernetic model for a continuous reactor is given as below dx Fin ¼ Sx ZrM c þ ðx in
xÞ dt V dV ¼ Fin
Fout dt

With Z normalized with respect to a reference substrate, rM implies uptake fluxes through EMs. Fluxes through EMs are given as follows kin rM, j ¼ vM, j ðeM, j =emax M, j ÞrM, j

where the subscript j denotes the index of EM, vM,j is the cybermax are the netic variable controlling enzyme activity, eM,j and eM,j kin is the kinetic term. enzyme level and its maximum value, and rM,j Enzyme level eM,j is obtained from the following dynamic equation

ð1Þ

deM, j kin ¼ RM, j þ uM, j rME
βM, j eM, j
μeM, j dt

kin rM, j

¼

KGLC

> max > : kj K

XYL

xGLC 1 0 2 þ xGLC þ xGLC =K I;GLC 1 þ xETH =KI;GLC xXYL 1 þ xXYL þ xXYL 2 =K 0I;XYL 1 þ xETH =KI;XYL

where kmax is the maximum reaction rate constant, xGLC and xXYL j are concentrations of glucose and xylose, respectively, KGLC and KXYL are Michaelis constants, KI,GLC and KI,XYL are ethanol inhibition constants, and K0 I,GLC and K0 I,XYL are substrate inhibition constants which are newly introduced in this work. The values of K0 I,GLC and K0 I,XYL are taken from Krishnan et al.11 as 27167 and 542 [mM2], respectively, and the other parameters are the same as those of the original model. Uptake kinetics for EMs consuming mixed sugars are simply obtained by combining those for individual sugars given in eq 4. For more immediate interpretations, metabolite concentrations are presented in the unit of [g/L] throughout this article. Figure 1 shows the difference in predicted concentrations of various species before and after incorporating the substrate inhibition term into uptake kinetics. The effect of xylose inhibition is shown to be significant, while that of glucose is not pronounced. Panels (a) and (b) of Figure 1 represent normal batch fermentation when the ratio of glucose and xylose is 2:1 in their mass concentration. Batch reactors with elevated concentration of xylose are simulated in panels (c) and (d) of Figure 1. Understandably, the fermentation time is significantly prolonged because of the elevated xylose concentration, which is suitably captured by the modified model accounting for substrate inhibition. It is thus important to establish optimal feeding policies for a minimum level of substrate inhibition. 2.3. Optimization methods. Assuming that sugars leftover in O1 include glucose as well as xylose, we formulate an optimization problem to determine the optimal feeding policy in O2 as follows: max PETH ðtf Þ

Fin ðtÞ, tf

ð5Þ

ð3Þ

where the first and second terms of the right-hand side denote constitutive and inducible rates of enzyme synthesis, and the last two terms represent the decrease of enzyme levels by degradation and dilution, respectively. In the second term of the righthand side, uM,j is the cybernetic variable regulating the induction kin is the kinetic part of inducible of enzyme synthesis, and rME,j kin . enzyme synthesis rate, which is often set similar to rM,j 10 While missing in the original model of Song et al., incorporation of substrate inhibition is necessary for more realistic simulations, in particular of fed-batch systems. Thus, kinetic equations including substrate inhibition are formulated as follows

where x is the vector of nx concentrations of extracellular components in the reactor (such as substrates [mM], products [mM], and biomass [g/L]), SX is the (nx  nr) stoichiometric matrix, and Z is the (nr  nz) EM matrix; rM is the vector of nz fluxes through EMs [mM/gDW/h], Fin and Fout are volume feed rates [L/h] at the inlet and outlet, V is the culture volume [L], xin is the vector of nx concentrations of extracellular components in the feed [mM]. Equation 1 can also represent batch by setting Fin = Fout = 0, and fed-batch systems by setting Fout = 0. In chemostat operations, Fin = Fout = F, and F/V is often given as dilution rate D [1/h]. 8 > max > < kj

ð2Þ

ðfor EMs consuming glucoseÞ ð4Þ

ðfor EMs consuming xyloseÞ such that y_ ¼ gðy, Fin Þ

ð6Þ

xGLC ð0Þ ¼ xGLC, 0 , xGLC, in ¼ 1000

FGLC , MGLC

ðwGLC, O1 FGLC þ wXYL, O1 FXYL Þ mGLC ðtf Þ þ mXYL ðtf Þ ¼ mR, O2 Z

tf

FXYL MXYL

ð8Þ

Fin ðtÞdt ¼ mR, O1

ð9Þ

xXYL, in ¼ 1000 Z

V ð0Þ þ

ð7Þ

xXYL ð0Þ ¼ xXYL, 0

tf

0

ð10Þ

Fin ðtÞdt e V 

ð11Þ

0 e Fin ðtÞ

ð12Þ

0

0 e yðtÞ,

where the objective function PETH(tf) [g/L/h] is the volumetric productivity of bioethanol at the final time tf, eq 6 is an abstract representation of eqs 1 and 3 (here, y denotes the vector composed of x, V, and eM, and Fout = 0), and eqs 7 and 8 are initial and feed sugar concentrations, respectively. Symbols FGLC and FXYL denote densities of glucose and xylose [g/L], respectively, and MGLC and MXYL their molecular weights [g/mol]. In eq 9, the amount of total sugars fed into O2 (i.e., left-hand side) [g] is equated with the amount of sugars unconverted in O1 (i.e., mR,O1). 1692

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Industrial & Engineering Chemistry Research wGLC,O1 and wXYL,O1 are mass fractions of glucose and xylose of the leftover sugars in O1. Equation 10 represents that the total sugars remaining unconverted at tf in a fed-batch reactor should satisfy the previously given quantity (i.e., mR,O2). Inequality constraint, eq 11, limits the culture volume to not exceeding a certain limit (V*) to prevent flooding. Equations 5
12 form a free-end-time optimization with differential algebraic equations (DAEs) as constraints. Such DAE optimization problems have been solved using indirect17
19 and direct20
24 methods, respectively. Indirect (or variational) methods obtain the optimal control profile by solving a two-pointboundary-value problem formulated from the first order necessary condition for optimality on the basis of Pontryagin’s Minimum Principle.25 With indirect methods, however, it is difficult to handle path constraints in the presence of singular arcs.21 Direct methods convert an infinite dimensional problem to one of finite dimension by discretizing continuous variables and solve it by nonlinear programming (NLP). Direct methods are classified into sequential (or single-shooting),20 simultaneous,21 and multishooting22,23 approaches. Sequential approaches parametrize the control variable only, and dynamic equations are solved by DAE or ordinary differential equation solvers. In simultaneous methods, on the other hand, all variables including control and state variables are fully discretized. Thus, continuous differential equations are converted into a set of algebraic equations. A multishooting idea combines both, i.e., discretizes controls piecewise on a coarse grid, and solves differential equations on each interval. Multishooting and simultaneous methods are suitable for highly unstable systems, while single-shooting methods are also useful for mildly unstable systems. In this article, we employ direct sequential methods to determine the optimal feeding policy in O2 of C4 and C5. Singleshooting methods can use the state-of-the-art dynamic equation solvers as well as NLP algorithms. Sequential methods offer a small size of NLP as they discretize the control variable only. They are currently adopted in optimization packages such as gOPT (Process Systems Enterprise Ltd.) and DyOS.26 The continuous sugar feeding rate Fm(t) is discretized into N piecewise constant values, i.e., Fin,1, Fin,2, 3 3 3 ,Fin,N, on equidistant time grid 0 < t1 < t2 < 3 3 3 < tf. Given N, xGLC,0, xXYL,0, and mR,O2, the variables Fin,1, Fin,2, 3 3 3 ,Fin,N, and tf are optimized such that the bioethanol productivity at the final time, PETH(tf), is maximized under the constraints given in eqs 6
12. This constrained NLP is solved using a MATLAB function fmincon. At each iteration, ODEs are solved using the fourth-order Runge
Kutta method. In several test examples (e.g., lysine fermentation considered in Modak and Lim18 and tutorial examples considered by Wang at http://www4.ncsu.edu/∼xwang10/), we confirmed that the developed numerical algorithm based on the direct single-shooting method could successfully compute the optimal control vector (results not shown).

3. RESULTS AND DISCUSSION To evaluate the performance of reactor configurations C1
C5, dynamic simulations are carried out under the following typical conditions for bioethanol fermentation experiments: • The operating culture volume of O1 and O2 is 1 L. The culture volume in O2 with the additional sugar feed is not allowed to exceed 1.5 L (=V*). This constraint is accounted for in eq 11, which is, however, inactive as the volume increment by the additional sugars in O2 is not appreciable.

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Figure 2. Relation between the fractional glucose conversion and dilution rate in a chemostat. [GLC]/[XYL] denotes the ratio of mass concentrations of glucose and xylose in the culture medium.

• The culture medium contains no metabolites other than sugars. Considering typical compositions of cellulosic sugars,27,28 we set the ratio of the mass concentrations of glucose and xylose in the medium (i.e., [GLC]/[XYL]) to be 2:1.9 Thus, culture composition can be identified by specifying glucose (or xylose) concentration only. The range of glucose concentration is set as from 20 to 120 g/L. • In each reactor configuration, the fractional mass conversion of the total sugars (denoted by ξ) is 0.95. Such high conversion of sugars is necessary to fulfill the industrial requirement that bioethanol yield should be more than 90% of its theoretical maximum.1 • Material properties and other basic operating conditions are specified as follows: FXYL = 1525[g/L], FGLC = 1540[g/L], initial biomass concentration = 0.1 g/L, and initial relative enzyme levels for EMs consuming glucose and xylose = 0.091 and 0.51, respectively.9 With the 2:1 ratio of mass concentrations of glucose and xylose in the culture medium, the total amount of the leftover sugars in every reactor configuration is 6(1
ξ)mXYL,0 [g], where mXYL,0 is the initial amount of xylose. Consequently, the content of unconverted sugars in O2 (i.e., mR,O2 in eq 10) is represented as 6(1
ξ)mXYL,0
mR,O1. As the performance measure for comparing C1 to C5, the overall ethanol productivity (PETH) is calculated as follows PETH ¼

mETH, O1 þ mETH, O2 1 V tO1 þ tO2

ð13Þ

where mETH,O1 and mETH,O2 [g] are the amount of ethanol obtained from O1 and O2, respectively, V is the culture volume of individual reactors (i.e., 1 L), and tO1 and tO2 are the total processing times taken in O1 and O2 that are obtained by tO1 ðor tO2 Þ ( tf , O1 þ ts ðor tf , O2 þ ts Þ ðfor a batch or fed-batch reactorÞ ¼ 1=D ðfor a chemostatÞ

ð14Þ Here, tf,O1 and tf,O2 are the fermentation times of O1 and O2, respectively, and ts is the extra time taken for harvesting and preparation for the next batch. The normal range of ts is from 3 to 10 h,8 and we set ts to be 6 h. Fermentation time of continuous 1693

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Figure 3. Total ethanol productivities of C1, C2, and C3 in the range of 20/10 to 120/60 of [GLC]/[XYL]. The productivity of C3 is calculated by setting the fractional conversion of glucose in O1 to be 0.95. Figure 5. Optimal feed profiles (left column) and resulting dynamic curves for primary metabolites (right column): (a) [GLC]/[XYL] = 20/10, (b) 70/35, and (c) 120/60.

Figure 4. Dependence of the ethanol productivity on the number of discretization intervals: (a) [GLC]/[XYL] = 20/10, (b) 70/35, and (c) 120/60.

operation is given as 1/D. The concept of the overall bioethanol productivity presented in eq 13 can readily be generalized for a case with any number of reactor operations. 3.1. Comparison of C1, C2 and C3. We begin with examining the performance of C1
C3. The roles of O1 and O2 are identical in C1 but differentiated in C2. That is, in C2, O1 converts glucose alone using the wild-type strain and O2 ferments mixed sugars using the recombinant strain. Unconverted xylose in O1 is added to O2. C3 is basically the same as C2, but a chemostat is used for O1 instead of a batch reactor. In a chemostat, D is adjusted to meet the target conversion of glucose. According to the relationship between the conversion and D given in Figure 2, D should go to almost zero to achieve a complete fermentation of glucose, meaning that fermentation time becomes infinite. To avoid this inefficiency, we strategically set the target conversion of glucose in a chemostat as 95% as denoted by dashed line in Figure 2. Unconverted glucose and xylose in a chemostat are then added to O2.

Figure 6. Total bioethanol productivities of C1 to C5 (left column) and relative increase (or decrease) in productivities of C2
C4 in comparison to C1 (right column): (a) [GLC]/[XYL] = 20/10, (b) 70/35, and (c) 120/60.

The ethanol productivities of C1, C2, and C3 are presented in a wide range of sugar concentrations in Figure 3. Compared with C1, the ethanol productivity of C2 is higher when sugar concentration is low, while lower when sugar concentration is high. Substrate inhibition caused by extra xylose added to O2 is responsible for the drop of productivity at high sugar concentrations. The impact of introducing a chemostat for O1 is shown to be dramatic. The ethanol productivity of C3 is substantially higher than that of C1, i.e., by 52, 23, and 8% when the ratios of mass concentrations between glucose and xylose (i.e., [GLC]/[XYL]) are 20/10, 70/35, and 120/60, respectively. 1694

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Industrial & Engineering Chemistry Research 3.2. Evaluation of C4 and C5. The productivity of C2 and C3 can further be improved by optimizing the feed rate of additional xylose into O2. The optimal feed rate was obtained using direct single-shooting methods. The feed profile was equally discretized into N piecewise constant values Fin,1, Fin,2, 3 3 3 ,Fin,N over the time domain [0,tf]. The fermentation time tf is optimized together with the vector of Fin,i’s (i = 1,2, 3 3 3 N). Computational time exponentially increases with the increasing number of discretization intervals N. For its reasonable choice, we examined the dependence of the ethanol productivity in O2 (of C4) on N. As shown in Figure 4, the effect of N immediately disappears for N g 2. In this article, we set N to be 10 over, for which no appreciable improvement of the productivity is achieved. The resulting optimal feed policies strongly depend on sugar concentration of the culture medium (Figure 5). At low sugar concentration (e.g., [GLC]/[XYL] = 20/10), it is desirable to add extra sugars at the initial stage of fermentation because it will promote simultaneous consumption of mixed sugars (Figure 5a). On the other hand, when sugar concentration in the culture is high ([GLC]/[XYL] = 120/60), it is required to feed sugars at later times (Figure 5c). Otherwise, fermentation time would be prolonged seriously because of strong substrate inhibition. It is interesting to find that the optimal feed profile at the medium sugar concentration ([GLC]/[XYL] = 70/35) is determined as in-between of these two extreme policies (Figure 5b). In Figure 6, an overall comparison is made for C1
C5 at three different sugar concentrations. The left and right columns show the actual productivity and its relative change, respectively. Relative change of the productivity is defined as (PETH
PETH,C1)/ PETH,C1 where PETH,C1 is the productivity of C1, which is the reference for comparison. From the comparison of the C2
C3 group and the C4
C5 group, it is clear that the effect of optimizing the feed rate is most significant at high sugar concentration (Figure 6c) and appreciable at medium concentration (Figure 6b) but least at low concentration(Figure 6a). Strangely, at [GLC]/[XYL] = 20/10, the productivities of C4 and C5 with optimal feeding policies are lower than those of C2 and C3, respectively, where all extra sugars are dumped into reactors at their startup without optimization. This is because the initial feeding of C2 and C3 is closer to the “true” optimal than the feed profiles of C4 and C5 obtained with N = 10 (e.g., the one shown in Figure 5a). Other than this exception, C5 exhibits the highest productivity among all other configurations. In comparison to C1, C5 achieves a substantial increase of the bioethanol productivity, i.e., by 48, 29, and 23% when [GLC]/[XYL] = 20/10, 70/35, and 120/60, respectively.

4. CONCLUSIONS We have shown that the productivity of lignocellulosic bioethanol can significantly be enhanced by combining different types of reactors and optimizing their operating conditions. While experimental verification should follow, our model-based study provides solid proof-of-concept support for the success of the proposed methods. As new reactor configurations basically require separation of unconverted sugars from the culture medium, it will raise the process operating cost. Perhaps, the use of less stringent separation levels will alleviate this increase in cost, but nevertheless, the actual choice of the best reactor configuration must be based on a comprehensive cost
benefit analysis.

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’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]. Phone: (765) 494-4066. Fax: (765) 494-0805.

’ ACKNOWLEDGMENT The authors are pleased to acknowledge a special grant from the Dean’s Research Office at Purdue University for support of the current work. ’ NOMENCLATURE Acronyms

C1
C5 = reactor configurations 1
5 CDW = cell dry weight EM = elementary mode ETH = ethanol GLC = glucose O1 and O2 = operations 1 and 2 XYL = xylose [GLC] = mass concentration of glucose in the culture medium [g/L] [XYL] = mass concentration of xylose in the culture medium [g/L] Symbols

c = cell dry weight per unit volume of the culture [g/L] D = dilution rate [1/h] eM,j = enzyme level for the jth EM max = maximal enzyme level for the jth EM eM,j Fin = volumetric flow rate at the inlet [L/h] Fin,i = volumetric flow rate at the inlet during ti
1 e t < ti [L/h] Fout = volumetric flow rate at the outlet [L/h] = uptake rate constant for the jth EM [mmol/gDW/h] kmax j KGLC = Michaelis constant for the EM group consuming glucose [mM] KXYL = Michaelis constant for the EM group consuming xylose [mM] KI,GLC = ethanol inhibition constant for the EM group consuming glucose [mM] KI,XYL = ethanol inhibition constant for the EM group consuming xylose [mM] K0 I,GLC = substrate inhibition constant for the EM group consuming glucose [mM2] 0 K I,XYL = substrate inhibition constant for the EM group consuming xylose [mM2] mETH,O1 = amount of ethanol produced in O1 [g] mETH,O2 = amount of ethanol produced in O2 [g] MGLC = molecular weight of glucose [g/mol] MXYL = molecular weight of xylose [g/mol] nr = number of individual reactions nx = number of extracellular metabolites nz = number of EMs N = number of discretization intervals for control vector PETH = volumetric ethanol productivity [g/L/h] PETH,C1 = volumetric ethanol productivity of C1 [g/L/h] rM = vector of uptake fluxes through EMs [mmol/gDW/h] rM,j = uptake flux through the jth EM [mmol/gDW/h] kin = kinetic part for uptake flux through the jth EM [mmol/ rM,j gDW/h] 1695

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Industrial & Engineering Chemistry Research kin rME,j = kinetic part for inducible enzyme synthesis rate for the jth EM [1/h] SX = stoichiometric coefficient matrix t = time [h] ti = end time of the ith interval [h] tf = batch fermentation time [h] tf,O1 = batch fermentation time in O1 [h] tf,O2 = batch fermentation time in O2 [h] tO1 = total processing time of O1 [h] tO2 = total processing time of O2 [h] ts = additional time for startup and shutdown of batch systems [h] uM,j = cybernetic variable controlling enzyme synthesis vM,j = cybernetic variable controlling enzyme activity V = culture volume [L] V* = maximal allowed culture volume [L] wGLC,O1 = mass fraction of glucose among the sugars leftover in O1 wXYL,O1 = mass fraction of xylose among the sugars leftover in O1 xGLC = molar concentration of glucose [mM] xXYL = molar concentration of xylose [mM] xGLC,0 = initial molar concentration of glucose [mM] xXYL,0 = initial molar concentration of xylose [mM] x = vector of extracellular metabolite concentrations [mM] xin = vector of extracellular metabolite concentrations in the feed [mM] y = vector of state variables Z = EM matrix

Greek Letters

aM,j = constitutive rate of enzyme synthesis for the jth EM [1/h] βM,j = rate of enzyme degradation for the jth EM [1/h] μ = specific cell growth rate [1/h] FGLC = density of glucose [g/L] FXYL = density of glucose [g/L] ξ = fractional mass conversion of the total sugars

’ REFERENCES (1) Balat, M. Production of bioethanol from lignocellulosic materials via the biochemical pathway: A review. Energy Convers. Manage. 2011, 52 (2), 858–875. (2) Talebnia, F.; Karakashev, D.; Angelidaki, I. Production of bioethanol from wheat straw: An overview on pretreatment, hydrolysis and fermentation. Bioresour. Technol. 2010, 101 (13), 4744–4753. (3) Binod, P.; Sindhu, R.; Singhania, R. R.; Vikram, S.; Devi, L.; Nagalakshmi, S.; Kurien, N.; Sukumaran, R. K.; Pandey, A. Bioethanol production from rice straw: An overview. Bioresour. Technol. 2010, 101 (13), 4767–4774. (4) Kadam, K. L.; McMillan, J. D. Availability of corn stover as a sustainable feedstock for bioethanol production. Bioresour. Technol. 2003, 88 (1), 17–25. (5) Keshwani, D. R.; Cheng, J. J. Switchgrass for bioethanol and other value-added applications: A review. Bioresour. Technol. 2009, 100 (4), 1515–1523. (6) Matsushika, A.; Inoue, H.; Kodaki, T.; Sawayama, S. Ethanol production from xylose in engineered Saccharomyces cerevisiae strains: Current state and perspectives. Appl. Microbiol. Biotechnol. 2009, 84 (1), 37–53. (7) Hahn-Hagerdal, B.; Karhumaa, K.; Fonseca, C.; SpencerMartins, I.; Gorwa-Grauslund, M. F. Towards industrial pentose-fermenting yeast strains. Appl. Microbiol. Biotechnol. 2007, 74 (5), 937–953. (8) Shuler, M. L.; Kargi, F. Bioprocess Engineering. Basic Concepts; Prentice-Hall, Inc.: Upper Saddle River, NJ, 2002.

ARTICLE

(9) Song, H. S.; Ramkrishna, D. Issues with increasing bioethanol productivity: A model directed study. Korean J. Chem. Eng. 2010, 27 (2), 576–586. (10) Song, H. S.; Morgan, J. A.; Ramkrishna, D. Systematic development of hybrid cybernetic models: Application to recombinant yeast co-consuming glucose and xylose. Biotechnol. Bioeng. 2009, 103 (5), 984–1002. (11) Krishnan, M. S.; Xia, Y.; Ho, N. W. Y.; Tsao, G. T. Fuel Ethanol Production from Lignocellulosic Sugars: Studies Using a Genetically Engineered Saccharomyces Yeast. In Fuels Chemicals from Biomass; Saha, B. C., Woodward, J., Eds.; ACS Symposium Series 666; American Chemical Society: Washington, DC, 1997, pp 74
92. (12) Wong, W. C.; Song, H. S.; Lee, J. H.; Ramkrishna, D. Hybrid cybernetic model-based simulation of continuous production of lignocellulosic ethanol: Rejecting abruptly changing feed conditions. Control Eng. Practice 2010, 18 (2), 177–189. (13) Kim, J. I.; Varner, J. D.; Ramkrishna, D. A hybrid model of anaerobic E. coli GJT001: Combination of elementary flux modes and cybernetic variables. Biotechnol. Prog. 2008, 24 (5), 993–1006. (14) Song, H. S.; Ramkrishna, D. Reduction of a set of elementary modes using yield analysis. Biotechnol. Bioeng. 2009, 102 (2), 554–568. (15) Schuster, S.; Fell, D. A.; Dandekar, T. A general definition of metabolic pathways useful for systematic organization and analysis of complex metabolic networks. Nat. Biotechnol. 2000, 18 (3), 326–332. (16) Schuster, S.; Hilgetag, C.; Woods, J. H.; Fell, D. A. Reaction routes in biochemical reaction systems: Algebraic properties, validated calculation procedure and example from nucleotide metabolism. J. Math. Biol. 2002, 45 (2), 153–181. (17) Song, H. S.; Park, Y. D.; Hyun, J. C. Optimization for the minimum reaction time of PET esterification. Korean J. Chem. Eng. 1996, 13 (4), 369–378. (18) Modak, J. M.; Lim, H. C. Feedback optimization of fed-batch fermentation. Biotechnol. Bioeng. 1987, 30 (4), 528–540. (19) Cazzador, L. On the optimal-control of fed-batch reactors with substrate-inhibited kinetics. Biotechnol. Bioeng. 1988, 31 (7), 670–674. (20) Vassiliadis, V. S.; Sargent, R. W. H.; Pantelides, C. C. Solution of a class of multistage dynamic optimization problems 0.1. Problems without path constraints. Ind. Eng. Chem. Res. 1994, 33 (9), 2111–2122. (21) Kameswaran, S.; Biegler, L. T. Simultaneous dynamic optimization strategies: Recent advances and challenges. Comput. Chem. Eng. 2006, 30 (10
12), 1560–1575. (22) Bock, H. G. Numerical Treatment of state-bounded control problems with multiple shooting method and homotopy method. Z. Angew. Math. Mech. 1977, 57 (5), T266–T268. (23) Bock, H. G.; Diehl, M. M.; Leineweber, D. B.; Schloder, J. P. A Direct Multiple Shooting Method for Real-Time Optimization of Nonlinear DAE Processes. In Nonlinear Model Predictive Control; Birkhauser Verlag: Berlin, 2000; Volume 26, pp 245
267. (24) Leineweber, D. B.; Bauer, I.; Bock, H. G.; Schloder, J. P. An efficient multiple shooting based reduced SQP strategy for large-scale dynamic process optimization. Part 1: Theoretical aspects. Comput. Chem. Eng. 2003, 27 (2), 157–166. (25) Pontryagin, L. S.; Boltyanskii, V. G.; Gamkrelidze, R. V.; Mishchenko, E. F. The Mathematical Theory of Optimal Processes; Interscience Publishers, Inc.: New York, 1962. (26) Schlegel, M.; Stockmann, K.; Binder, T.; Marquardt, W. Dynamic optimization using adaptive control vector parameterization. Comput. Chem. Eng. 2005, 29 (8), 1731–1751. (27) Lee, J. Biological conversion of lignocellulosic biomass to ethanol. J. Biotechnol. 1997, 56 (1), 1–24. (28) Sedlak, M.; Ho, N. W. Y. Production of ethanol from cellulosic biomass hydrolysates using genetically engineered Saccharomyces yeast capable of cofermenting glucose and xylose. Appl. Biochem. Biotechnol. 2004, 113
16, 403–416.

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