Model-Based Optimization of Cyclic Operation of Acetone-Butanol

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Model-Based Optimization of Cyclic Operation of AcetoneButanol-Ethanol (ABE) Fermentation Process with Ex-Situ Butanol Recovery (ESBR) for Continuous Biobutanol Production Boeun Kim, Hong Jang, Moon-Ho Eom, and Jay H. Lee Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.6b02670 • Publication Date (Web): 25 Jan 2017 Downloaded from http://pubs.acs.org on January 27, 2017

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Industrial & Engineering Chemistry Research

Model-Based Optimization of Cyclic Operation of Acetone-Butanol-Ethanol (ABE) Fermentation Process with Ex-Situ Butanol Recovery (ESBR) for Continuous Biobutanol Production Boeun Kim1, Hong Jang1, Moon-Ho Eom2, Jay H. Lee1* 1. Department of Chemical and Biomolecular Engineering, Korea Advanced Institute of Science and Technology (KAIST), 291 Daehak-ro, Yuseong-gu, Daejeon 305-701, Republic of Korea 2. R&D Center, GS Caltex Corporation, 359 Expo-ro, Yuseong-gu, Daejeon 305-380, Republic of Korea.

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ABSTRACT

This paper proposes a model-based optimization strategy for a fermentation process coupled with an ex-situ butanol recovery-by-adsorption (termed ‘ESBR-by-adsorption’ hereafter) process used for continuous biobutanol production. The ESBR-by-adsorption system exhibits cyclic dynamic behavior caused by the periodic switching of the adsorption column for its renewal. Since performance of such a system is largely determined by its dynamic behavior seen after converging to Cyclic Steady State (CSS), and hence the optimization strategy should search for the optimal operating condition leading the most profitable CSS. For the CSS optimization, we select key optimization variables and define the objective function and constraints. The resulting CSS optimization problem is strongly nonconvex largely due to the various nonlinearities in the objective function and constraints e.g., those in the kinetics of the ABE fermentation and adsorption. To alleviate the numerical convergence problem associated with nonconvex optimization problems, we adopt an initialization strategy of identifying a feasible solution region and a ‘good’ initial guess through a coarse grid search. With the initialization strategy, two CSS optimization approaches, ‘sequential’ and ‘simultaneous’, are examined for the system. With the model and simulation, performances of the two approaches are compared with respect to varying qualities of the initial guess to propose an effective practical CSS optimization strategy for the ESBR-by-adsorption system. The optimized continuous production by the ESBR-by-adsorption system showed significantly improved volumetric productivity of butanol, 5.5- and 3.7-fold increases respectively over the batch fermentation or semi-batch fermentation with in-situ product recovery.

KEYWORDS Biobutanol; Ex-Situ Butanol Recovery; Acetone-Butanol-Ethanol (ABE) fermentation; Adsorption; Cyclic Steady State; Model-based optimization


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1. INTRODUCTION Biobutanol has received much attention as a promising renewable energy source (e.g., a gasoline substitute) and also as a renewable feedstock for many chemicals. However, commercializing the traditional batch Acetone-Butanol-Ethanol (ABE) fermentation for this purpose has faced a major obstacle of low fermentation performance such as low butanol concentration and low productivity owing to the inhibitory effect of the produced butanol on cell growth and production

1, 2

. To overcome

this limitation for enhanced commercial viability of the ABE fermentation, several processes that combine the ABE fermentation with butanol recovery have been suggested. In these combined processes, the butanol concentration in the fermentation broth is maintained below the threshold of toxicity by recovering butanol during the fermentation via various separation technologies

3-5

. Liquid-

liquid extraction, pervaporation, gas stripping, and adsorption have been considered as promising methods for the butanol recovery owing to their low energy requirements

6, 7

. The detailed process

description and performance of these recovery technologies are well reviewed in several papers

5, 8-12

.

Their advantages and disadvantages are summarized as follows. The liquid-liquid extraction has a low energy consumption and high selectivity for butanol. However, it requires a large amount of extractant that is insoluble in water, nontoxic to the cells and immiscible with the fermentation broth, 13 leading to a high material cost. The pervaporation also has a high selectivity for butanol but fouling and clogging problems are common for the membranes. The gas stripping comes with the advantages of easy implementation, no requirement of membrane, and no harmful effect on the culture, but it has a low butanol selectivity and a relatively high energy requirement due to the co-removal of water. The adsorption is seen as a particularly attractive choice due to its simplicity and high energy efficiency but adsorbents screening and regeneration need further research. To compensate for the respective disadvantages of the individual technologies, several hybrid recovery processes have been suggested, such as the two-stage gas stripping process

14

stripping-vapor permeation (VSVP) process

, the gas stripping-pervaporation process

15, 16

17

18

and the extraction-distillation process

, the vapor

. In addition,


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(semi-)continuous fermentation processes are proposed to enhance the fermentation performance, for example, using ex-situ product recovery by extraction 19-21 and adsorption 22-25. Recently, Eom, Kim, Jang, Lee, Kim, Shin and Lee

22

has proposed a fermentation process

integrated with an ex-situ butanol recovery (ESBR) system composed of a fermenter and stirred-tanktype adsorption columns (Figure 1), and developed a dynamic model for it. In the ‘ESBR-by-adsorption’ system named hereafter, the adsorption column is filled with some butanol-selective adsorbents, and the fermentation broth is continuously circulated between the fermenter and the adsorption column. The major operation steps of the system

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are illustrated in Figure S1. In the start-up step, the ABE

fermentation is carried out in a batch manner without feeding and circulation (Figure S1A). When the butanol concentration reaches a preset control level determined based on the butanol toxicity and efficiency of the adsorbents, the cyclic operation begins involving the following three steps (comprising a cycle). 1) Filling of the adsorption column with the fermentation broth (Fc,r > 0 and Fc,ad = 0) 2) Fermentation broth circulation between the fermenter and the adsorption column (Fc,r = Fc,ad > 0) 3) Restoring the volume of the fermenter if Vr < Vr,0, Fc,r = 0 and Fc,ad > 0 if Vr > Vr,0, Fc,r > 0 and Fc,ad = 0 Obviously, almost the entire cycle time is spent by the second step. In the continuous mode, constant feeding into the fermenter continues to keep the glucose concentration within a proper range for cell growth and production, and circulation of the fermentation broth helps maintain the butanol concentration below the control level. When the capacity of the adsorbents is exceeded, and the butanol concentration in the adsorption column reaches a target level, which is about 7 g/L, the volume of broth in the fermenter is restored to the initial level (Vr,0) and the saturated column is replaced by a refreshed one. Then the whole cycle is repeated. In the meantime, the remaining broth in the saturated column is transferred to the harvest tank, and the saturated adsorbents are regenerated by steam for reuse in the next cycle. This cyclic operation enables continuous ACS Paragon Plus Environment

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biobutanol production without the inhibitory effect of the produced butanol resulting in increased volumetric productivity. Although the ESBR-by-adsorption fermentation system gives the advantage of continuous operation, there are significant challenges in designing and operating the system at a commercial scale for biobutanol production. The kinetics of the fermentation and adsorption are typically described by nonlinear models. And several constraints on the components’ concentration for maintaining fermentation performance should be considered. In addition to this, the adsorption column is periodically switched in the ESBR-by-adsorption system, resulting in a specific cyclic dynamic pattern called Cyclic Steady State (CSS), rather than a steady state in the usual sense. Given the complexity of the system, model-based optimization and control of the combined system can enhance its chance for economic viability. On the other hand, according to a recent review 26, studies on the optimization of biobutanol fermentation processes integrated with gas stripping, pervaporation, and vacuum separation have been sparse 27-29. Moreover, the particular system of ESBRby-adsorption has not been studied from this perspective. The optimization problem of the ESBR-byadsorption system is nonconvex and the quality of a numerical solution can be dependent on the initial guesses of decision variables. In addition, the CSS is an inherent characteristic of the system so that optimal operation condition should be determined based on the CSS (rather than a static steady state) behavior of the system. This paper aims to provide insights into the CSS behavior of the ESBR-by-adsorption system through dynamic simulation and also propose a strategy for optimizing the CSS condition as a basis for determining the operating conditions and controlling it around them. For this, we use the dynamic model developed in our previous study

22

. After key operating variables are identified, dynamic

simulation is performed to analyze the CSS behavior with respect to these variables. For optimizing the operating condition, we select an objective function defined in terms of productivity and loss, and state the constraints of the operation. To solve the resulting nonconvex CSS optimization problem, which can be quite sensitive to the initial guesses for the decision variables, we first identify a feasible solution ACS Paragon Plus Environment

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region within which the system indeed converges to a CSS while all the constraints are satisfied. Initial guess for the decision variables are then chosen, e.g., by coarsely gridding the feasible region and evaluating the objective function values. The two CSS optimization strategies of the ‘sequential’ and ‘simultaneous’ approaches are compared for two cases: 1) starting with a ‘good’ initial guess obtained from a grid search; 2) starting with a poorer initial guess. Performances are evaluated in terms of the accuracy of CSS convergence, calculation time, and sensitivity to the choice of initial guess. This work represents the first study that addresses optimization of a biobutanol fermentation process coupled with a recovery system at a cyclic steady state rather than a steady state. The proposed two-step procedure for the CSS optimization of the ESBR-by-adsorption system should yield a solution despite the strong non-convexity of the optimization problem. In addition, the effect of the quality of the initial guess on performance of the two CSS optimization approaches (the sequential and simultaneous approaches) is studied to ensure a proper choice of the optimization approach given an initial guess. The proposed CSS optimization strategy should be applicable to other repeated batch/fed-batch bioprocess, leading to an optimal operating condition for cyclic steady state operation. The rest of the paper is organized as follows. In Section 2, the overall process of the ESBR-byadsorption system is described, and the dynamic model equations for the system are presented. Section 3 presents the approaches to dynamic simulation and optimization of the CSS of the ESBR-byadsorption system. The results of the optimization are discussed in Section 4. Section 5 gives a summary and conclusion of this work.


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2. THEORY 2.1 Dynamic model of the system In the ESBR-by-adsorption system, the ABE fermentation occurs in both the fermenter and the adsorption column, while the product adsorption occurs only in the adsorption column. Based on this, mass balance equations of the cell, glucose, and products in the fermenter and the adsorption column were constructed separately with the assumptions and equations used in our previous work

22

. The

kinetic model of the ABE fermentation was established based on the Monod/Luedeking-Piret model, and the production rates were developed only for the butanol and ethanol because only very small amounts of acetone, acetic acid, and butyric acid are produced. Although the ratio of butanol, acetone and ethanol in the product is 6:3:1 for wild-type Clostridia, a recombinant microbe30 was used in our study, which showed a remarkably low level of acetone concentration; therefore acetone was excluded from the modeling 22. The kinetic model of the adsorption was developed based on the external masstransfer equation, and the adsorption equilibrium of the multi-component solution based on the extended Langmuir model 31. The model parameters are reported in Table 1. The specific cell growth rate is described by modifying the Monod equation to reflect three inhibitory effects by i) high substrate concentration, ii) high butanol concentration and, iii) high cell concentration and is expressed as follows.

iB

iX

 C   X µg = × 1− B  × 1−  2 Ks + S + S / KI  PB   PX 

(1)

µnet = µ g − kd

(2)

µmS

The kinetic models for glucose consumption rate and production rates of the butanol and ethanol are formulated based on the Luedeking-Piret model 32, as shown below:


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iB'

rs = −

 C  1 dS × = αGlu × µg + βGlu × 1 − B'  X dt  PB 

(3)

rB =

1 dCB = α B µg + β B X dt

(4)

rE =

1 dCE = α E µg + βE X dt

(5)

The overall dynamic model of the ESBR-by-adsorption system can be expressed by eqs 6 – 11. Subscripts r and ad in the equations indicate the concentration or property of components in the fermenter and the adsorption column, respectively. Eqs 6 – 8 below represent the mass balance equations of the cell (Xr), glucose (Sr), butanol (Cr,B), and ethanol (Cr,E) in the fermenter including the effect of dilution and circulation:

dX r 1 = ( µnet ,r − Dr ) X r + ( Fc ,ad X ad − Fc,r X r ) dt Vr

(6)

dSr 1 = ( FS f + Fc,ad Sad − Fc,r Sr ) + rr , S X r − Sr Dr dt Vr

(7)

dCr , j dt

= ( Fc,ad Cad , j − Fc,r Cr , j )

1 + rr , j X r − Cr , j Dr Vr

(8)

where F is the feed flow rate, and Fc,r and Fc,ad are the circulation flow rates from the fermenter to the adsorption column and vice versa. In the circulation step, Fc,ad equals to Fc,r, and the dilution rate in the fermenter is derived from Dr = F/Vr. In the adsorption column, there is no dilution effect, and the concentrations of the cell, glucose, butanol and ethanol are changed by the adsorption as well as the circulation. Eqs 9 – 11 below show the mass balance equations of the components in the adsorption column: ACS Paragon Plus Environment

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dX ad 1 = µnet ,ad X ad + ( Fc ,r X r − Fr ,ad X ad ) dt Vad

(9)

dSad 1 = ( Fc,r Sr − Fc,ad Sad ) + rad ,S X ad dt Vad

(10)

dCad , j dt

= ( Fc,r Cr , j − Fc,ad Cad , j )

dA 1 + rad , j X ad + j Vad dt

(11)

where dAj/dt is the rate of change in the concentration of component j by adsorption in the adsorption column. This was derived in our previous study 31 as below:

dAi m dqi m =− = − × ki ( qi ,eq − qi ) dt Vr dt Vr qi , eq =

qi , m Bi C r ,i

(12)

(13)

n

1 + ∑ Bi C r ,i i =1

Since the stirred-tank-type adsorption column is used for product adsorption in the ESBR-by-adsorption system, the axial variations in the column are ignored and the effect of pressure drop in the column can be neglected.


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2.2 Cyclic steady state (CSS) As explained before, the ESBR-by-adsorption system shows cyclic concentration trajectories due to the periodic switching of the adsorption column. Typically, after a few start-up cycles, the concentration patterns approach a cyclic steady state (CSS), in which the state at the end of a cycle returns to what it was in the beginning of the cycle. In contrast to a conventional steady state, system states are varying over time at a CSS, resulting in a heightened complexity for its determination and optimization. Successive substitution is the most straightforward way to determine the CSS condition; the dynamic simulation of the dynamic model is executed with the terminal state of the previous cycle set as the initial state of the current cycle 33.

x k (t f ) = H ( x k (0))

(14)

x k +1 (0) = x k (t f )

(15)

In the above, x represents the vector of system states containing the concentrations of the cell, glucose, and products. H is the mapping (defined by the dynamic model introduced in Section 2) between the initial state xk(0) and the end state xk(tf) of the kth cycle. Hence k is the cycle index, and tf is the time length of a cycle. To find the CSS, this substitution is continued until the difference between the entire state trajectories of two successive cycles in the fermenter becomes smaller than a tolerance (εCSS).

xik (t) − xik +1 (t) ≤ ε CSS ∀t ∈[0, t f ] xik (t)

(16)


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xki(t) indicates the simulated concentration of the ith component at time t of the kth cycle.

2.3 Objective function and constraints To determine operating condition leading to an optimal CSS condition, firstly, the CSS should be expressed as a function of the operating variables (i.e., degrees-of-freedom). In the ESBR-byadsorption system, there are two main operational degrees-of-freedom: the feeding rate into the fermenter, and the circulation rate between the fermenter and the adsorption column. The feed rate directly affects glucose concentration and fermentation performance; a proper glucose concentration manifested by a suitable feeding rate has a favourable effect on the cell growth and productivity. Too large a feed rate leads to an excessive dilution effect and high glucose concentration in the broth leading to large waste or high recovery cost. In addition, since the adsorption occurs more quickly as the circulation increases, the circulation rate has a strong influence on the butanol concentration level in the fermenter. Besides the two variables chosen as the main degrees-of-freedom, there are other important operating variables. Switching time is one such variable. During operation, the first and third steps are completed when the volumes of the adsorption column and the fermenter reach their desired levels, respectively (See Introduction), and time required for the two steps are directly affected by the circulation rate. However, the duration of the circulation step is such that it totally dominates the other steps, and this is determined based on the level of butanol concentration in the fermentation broth. Therefore, the cycle time is assumed to be set to keep the butanol concentration below a tolerance value (7 g/L) to minimize the inhibition effect (See Introduction). Another candidate variable for the optimization is feed concentration. In this study, it is assumed to be fixed to keep the complexity of the optimization low. Nevertheless, several discrete choices of the feed concentration within the range of possible operation specified by our industrial partner will be examined in order to see the effect of its ACS Paragon Plus Environment

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choice and select a good value. Note that a strong negative correlation exists between the optimal values of the feed concentration and the feed rate. In order to maintain an optimal balance between productivity and loss of the undigested substrate, the feed rate needs be reduced as the feed concentration increases. In this study, only the fermentation process is optimized as the ABE fermentation process is the main bottleneck of biobutanol production. Since the duration of the desorption step for the saturated column after each cycle can be adjusted by the controlling the flow rate of steam used for the regeneration 31, the desorption step does not govern the cycle time in general. Thus, the optimization of the ESBR-by-adsorption system in this study does not take into account the desorption step. For optimizing the operating variables at CSS of the ESBR-by-adsorption system, the objective function should be determined with respect to butanol productivity and glucose loss over one cycle. In continuous mode, profit can be expressed as a weighted sum of the butanol productivity per hour and the glucose loss per hour. Therefore, the objective function (J) of the system to be maximized is defined as below:

 qB (t f ) × m Cad , B (t f ) ×Vad (t f )   Sad (t f ) ×Vad (t f )  J = w1  + − w2       t t t f f f    

(17)

The first term in eq 17 represents the butanol productivity over one cycle composed of the adsorbed butanol on the adsorbents and the remaining butanol in the broth which is not adsorbed but discharged from the adsorption column at switching time (tf) (Figure 2). The amount of adsorbed butanol is derived from multiplying the amount of adsorbed butanol per unit mass of adsorbent (qB) per cycle by the mass of adsorbent (m). The quantity of remaining butanol in the discharged broth equals to the butanol concentration in the adsorption column (Cad,B) mutiplied by the liquid volume of the column (Vad) at the switching time. The glucose loss refers to the remaining glucose in the discharged broth at the end of a cycle (Figure 2). This can be calculated in a similar way to the quantity of the remianing


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butanol in the discharged broth. Therefore, to maximize the profit at the CSS, the operating variables have to be optimized to balance between the two conflictring objectives of maximizing the butanol productivity and minimizing the glucose loss. At the end of a cycle, the remaining broth in the saturated column is discharged into a harvest tank. Although further ABE fermentation is performed in the harvest tank to convert the remaining glucose into products, the delay in the butanol production caused by the need to process the remaining glucose gives a loss of production time. In this respect, the weighting coefficients, w1 and w2, are chosen as 1 and 0.35 (corresponding to the glucose conversion yield of the ABE fermenteion), respectively. Note that the weighting factors can be changed by client decision, strain, market situation, condition of the downstream process, etc. The weighting coefficients, w1 and w2 are normalized to sum of 1 as follow:

w1 : w2 = 1: 0.35 = 0.74 : 0.26

To maintain the optimal fermentation condition, the concentrations of glucose, butanol, and ethanol in the broth have to be controlled within some proper ranges. Based on insights and experiences, constraints on the concentrations of glucose and products in the fermenter and the adsorption column are given as the following inequality constraints:

1 ≤ Sr ≤ 10

(18)

0 ≤ Cr , E ≤ 5

(19)

( C ( t ) − C ( t ) ) / C ( t ) ≤ 0.1 r ,B

f

ad , B

f

r ,B

f

(20)


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Eq 18 represents a proper range of glucose concentration in both the fermenter Sr (g/L); despite the positive influence of high glucose concentration on the cell growth and productivity, too high a glucose concentration can be a major cause of loss. The maximal allowable concentrations of ethanol in the fermenter Cr,E (g/L) is set as in eq 19. Since the swithcing condition of a cycle is set to keep the butanol concentration below a certain level and the model includes the inhibitory effect of butanol, a separate constraint on the butanol concentration is not needed. The last requirement, eq 20, means that the difference between the butanol concentrations of the fermenter Cr,B (g/L) and of the adsorption column Cad,B (g/L) at the swithcing time has to be smaller than ten percent of Cr,B. Note that Cr,B is always higher than Cad,B because of the adsorption occurring in the column. If the difference becomes larger than this, due to a high Cr,B, the fermenter would suffer from an inhibitory effect on the cell growth and production, whereas a low Cad,B(tf) could lead to a decreased efficiency of the desorption step caused by a reduction in the amount of adsorbed products.

2.4 Optimization method Since the ESBR-by-adsorption system trajectories converge to a CSS after some transience, the CSS condition is used as the basis for design and optimization of the system. Simulation and optimization of CSS have been widely studied for processes involving periodic switches, such as Pressure Swing Adsorption (PSA) and Simulated Moving Bed (SMB)

34-38

. However, optimization of

CSS for a fermentation process integrated with an adsorption system has not been looked at before. In this study, the optimization of CSS of the ESBR-by-adsorption system is conducted in the following two steps to address the problem of convergence and non-convexity. First, a coarse grid search is performed to identify a feasible solution region and a reasonable initial guess for the optimization. Based on this, a nonlinear optimization can be carried using two separate approaches: the sequential approach and the simultaneous approach (Figure 3). The former approach is conceptually simple and is less sensitive to the initial guess but convergence to CSS can requires the simulation of a large number


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of cycles thereby increasing the evaluation time for each iteration

36, 37

. The latter approach optimizes

the operating variables and the CSS condition simultaneously without the need for using successive substitution

35, 38

and therefore the system model is executed only once for each iteration. Thus,

computational requirement can be less but the performance can be more sensitive to the initial guess owing to an increased number of decision variables.

2.4.1 Grid search In the optimization of the ESBR-by-adsorption system, it is required that the system converges to CSS for the candidate operating variables as their optimal values are decided based on the objective function value calculated at CSS. The optimization problem is highly nonconvex because the system equations, the objective function and the constraints are all nonlinear. In particular, the dynamic model and one of the constraints contain the nonlinear rate expressions describing the ABE fermentation kinetics and the extended Langmuir isotherm. Therefore, the convergence of the optimization problem can be quite sensitive to the initial guess of the decision variables. In addition, for some choices, the system fails to converge to CSS. For this reason, a good initial guess within the feasible region of the decision variables is required for the optimization. As mentioned in Section 3.2, the only operating variables we consider for the ESBR-byadsorption system are the feed rate and the circulation rate. Given the low dimension of the search space, a coarse grid search is performed initially, on a uniform grid with spacing of 0.1 L/h for the feed rate and 10 L/h for the circulation rate, in order to identify a good initial guess over the space of operating variables. The search ranges of the feed rate and the circulation rate are chosen as 5 L/h ~ 15 L/h and 150 L/h ~ 250 L/h, respectively, based on the consideration of pump cost and other design constraints. The search domain is further reduced by discarding the regions corresponding to those grid points not converging to CSS or converging to CSS violating the constraints. The initial guess is selected as the point resulting in the maximum value of the objective function, and the identified feasible region is used


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to set boundaries of the operating variables for the CSS optimization. Note that the grid search is seldom practical beyond one or two dimensions since the number of grid points grows exponentially in the search dimension 39, 40.

2.4.2 Sequential optimization The sequential approach determines the optimal operating variables through two loops as represented in Figure 3A. In this approach, the decision variables are only the operating variables: the feed rate and the circulation rate for the ESBR-by-adsorption system. In the inner loop, given trial values of the decision variables from the outer loop, the system model is simulated via successive substitution until the CSS convergence criteria of eq 16 is satisfied. At the simulated CSS, the objective function value and the constraints are evaluated and returned to the optimizer in the outer loop. In the outer loop, the optimizer, which solves the constrained nonlinear optimization problem, gives next trial values of the decision variables to the inner loop. The operating variables are initialized as the best grid point obtained from the grid search. For solving the constrained nonlinear optimization problem in the outer loop, fmincon in MATLAB R2015b Optimization Toolbox based on the SQP (Sequential Quadratic Programming) algorithm is employed. The optimization algorithm using the sequential approach can be expressed as shown in Figure 4. Through dynamic simulation, CSS condition x* is determined for a current candidate operating condition. J is the objective function in eq 17 and its value is calculated from the terminal state of CSS x*(tf). D≤0 refers to the inequality constraints specified in Section 3.2, and its satisfaction is examined for the entire states of CSS. The vector of optimization variable u includes the feed rate (F) and the circulation rate (Frc/Fcr) with lower bounds ul and upper bounds uu decided based on the results of the grid search, to confine the search to those region resulting in CSS satisfying the constraints. G=0 stands for the nonlinear system model, and D≤0 refers to the inequality constraints specified in Section 3.2. Other design variables represented by q are fixed a priori based on insights and experiences obtained from the ACS Paragon Plus Environment

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laboratory and pilot experiments

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: the liquid volume of the fermenter (Vr) that of the adsorption

column (Vad), and the mass of adsorbent (m) are set as 200 L, 20 L, and 10 kg, respectively.

2.4.3 Simultaneous optimization In the simuiltaneous apporach, the decision vbariables satisfying the CSS condition are found through optimization rather than through simulation. Therefore, the feed rate, the circulation rate, and the initial states in the fermenter are determined simultaneously as decision variables within a single optimization loop (Figure 3B). The initial values of the operating variables are set as those from the grid search (the same values used in sequential approach), and the initial states in the fermenter are set as the corresponding CSS which is derived from the dynamic simulation using the obtained operating variables. The same MATLAB function based on the SQP algorithm in Section 3.3.2 is adopted for solving the constrained nonlinear optimization problem in this approach. The optimization problem in eq 21 is modified as follows:

Max J ( u, q, x(t f ) ) − M ε u , x0

s.t. G( x&, x, u, q, t ) =0 D ( x(t) ) ≤ 0 ∀t ∈[0, t f ] ul ≤ u ≤ uu

εi =

xi (0) − xi (t f ) xi (0)

(21)

, i = 1,K, n

ε i ≤ ε CSS

where x0 is the vector of the initial states in the fermenter. xi is the ith component of the state vector and here xi(0) corresponds to the ith element of x0. xi(tf) is the ith element of the state vector at the end of a cycle initialized with x0. The objective function J, constraints on operating variables and component’s concentration (D≤0), and design variables q are the same as in the sequential approach. The operating ACS Paragon Plus Environment

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variables u and the initial state of the CSS x0 are decided by both maximizing the profit J and minimizing the error of CSS convergence ε multiplied by large penalty constant M. ε indicates the sum of the absolute relative error of ith component (εi) between the beginning state and end state of a cycle. εi has the upper bound εCSS (corresponding to the tolerance in dynamic simulation by using the successive substitution method) to guarantee the minimum accuracy.


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3. RESULTS AND DISCUSSION 3.1 Dynamic simulation of cyclic steady state (CSS) To analyze the CSS behavior of the ESBR-by-adsorption system, dynamic simulation following the cyclic operation steps presented in Section 2.1 is carried out. The initial concentrations of cell, glucose, butanol, and ethanol in the fermenter for the successive substitution approach are set as Xr,0 = 8.5 g/L, Sr,0 = 10 g/L, Cr,B,0 = 7 g/L, and Cr,E,0 = 2 g/L, respectively, which are based on the experimental setting and design requirements. ode45 in MATLAB is employed for integrating the ordinary differential equations (ODEs) describing the mass balance equations for the fermenter (eqs 6 – 8) and the adsorption column (eqs 9 – 11). Figure 5 shows the concentration profiles in the fermenter at the CSS after 51 cycles with the feed concentration of 200 g/L, the feed rate of 11 L/h, and the circulation rate of 200 L/h. In this dynamic simulation, the CSS convergence criterion of (eq 16) is examined for the difference between the concentrations of the various components in the fermenter for two successive cycles. The relative tolerance for the CSS convergence criterion (eq 16) is set as 10-4. At the CSS, the cell concentration is approximately constant over the whole period, while the concentrations of glucose, butanol and ethanol exhibit clear cyclic patterns. At the beginning of the circulation step, the concentrations of butanol and ethanol decrease immediately in both the fermenter and the adsorption column due to the adsorption by the fresh adsorbents in the column. After exceeding the capacity of adsorbents, these concentrations begin to creep up to their initial levels. Since the adsorbent has higher selectivity for butanol than for ethanol, the range of variation for the concentration of the former is wider than that of the latter. In addition, the amount of glucose consumed in the adsorption column is increased at this point due to significantly lowered butanol concentration which alleviates the butanol inhibition effect. During the circulation step, the broth with lowered glucose concentration is recirculated from the column to the fermenter. For this reason, the glucose concentration in the fermenter decreases as seen in the cyclic pattern of Figure 5. ACS Paragon Plus Environment

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3.2 CSS Optimization of the ESBR-by-adsorption system 3.2.1 Coarse grid search and CSS optimization with the initial guess obtained from the grid search We conducted optimization of CSS of the ESBR-by-adsorption system for three different feed concentration levels: 150, 200, and 250 g/L. The initial state values and the CSS convergence criterion for the dynamic simulation in the grid search and in the sequential approach were the same as in Section 4.1. The penalty constant M in the simultaneous approach was set as 104. The weighting coefficients for the objective function were fixed as discussed in Section 3.2. The results of the coarse grid search for the three different feed concentration values are summarized in Table 2. The feed rate decreases as the feed concentration increases due to the negative correlation between the feed concentration and the feed rate. Meanwhile, no distinct correlation is observed between the feed concentration and the circulation rate. Note that, the operation with the feed concentration of 150 g/L leads to a high feed rate and increased broth volume in the fermenter at the switching time from its initial level of 200 L. The best values and the feasible region of the operating variables determined through the grid search were selected as the initial guess and the boundaries of the operating variables for the optimization, respectively. (See Table 2) To analyze the effects of the operating variables on the process performance, we plotted the local trend of the objective function value, butanol productivity, and glucose loss around the chosen operating variables for the feed concentration of 200 g/L in Figure 6. For the constant circulation rate of 250 L/h, a higher feed rate leads to higher concentrations of cell and glucose in the fermenter and then increases the productivity and glucose loss (Figure 6B). The objective function value rises as the feed rate is increased from 11 L/h to 11.4 L/h as shown in Figure 6A, since the gain from the increased butanol productivity is larger than that the loss from the increased glucose loss. However, the amount of glucose loss grows exponentially with further increase in the feed rate as shown in Figure 6B. This is caused by the fact that the excess amount of glucose becomes larger when the feed rate increases from the optimal ACS Paragon Plus Environment

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value: the rate of increase in glucose concentration with the feed rate changing from 11.4 L/h to 11.8 L/h is 77 % higher than that from 11 L/h to 11.4 L/h. Thus, the objective function value is reduced as the feed rate goes from 11.4 L/h to 11.8 L/h (Figure 6B). The feed rate can directly affect the concentrations of glucose and cell resulting in the changes in butanol productivity, glucose loss, and objective function value. On the other hand, the circulation rate hardly influences the concentrations of glucose and cell but the concentrations of the products in the beginning phase of the circulation step. There is a monotonic relationship between the circulation rate and the objective function value at the constant feed rate of 11.4 L/h as shown in Figure 6C. Since a high circulation rate speeds up the adsorption occurring in the column and widens the range of butanol concentration in the initial stage of the circulation, it enhances the rate of production and then reduces the cycle time. For this reason, the values of butanol productivity and glucose loss increase as the circulation rate increases (Figure 6D). However, the increase in butanol productivity dominates over the increase in glucose loss in this case, and the maximum circulation rate is optimal. Table 3 summarizes the optimization results from the two approaches using the initial guess from the grid search for the three feed concentration values tried. The two optimization approaches give almost the same results for the optimal operating variables and objective function values for all feed concentration values. However, the averaged errors of CSS convergence for the sequential approach and the simultaneous approach are 2.77×10-5 and 3.42×10-8, respectively (Table S1). In addition, the averaged computational time of the sequential approach (106.5 sec) is about 4.5 times larger than that of the simultaneous approach (24.10 sec) as shown in Table 3. Therefore, in the case of optimization starting with good initial guesses like the ones we used here, the simultaneous approach achieves more accurate CSS for all the components in less calculation time than the sequential approach. In Figure 7, the results from the two approaches show same trends of butanol productivity and glucose loss. As the feed concentration increases, the optimal feed rate decreases and the returned broth from the adsorption column to the fermenter at the switching time increases. As a result, Vad(tf) in eq 17 becomes smaller, resulting in decreased butanol productivity and glucose loss. In comparison of the ACS Paragon Plus Environment

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values of butanol productivity and glucose loss at the feed concentrations of 250 g/L with those at 200 g/L, the amount of reduction in butanol productivity is much larger than that in glucose loss (Figure 7). Hence, the objective function value in overall shows a decrease when the feed concentration increases from 200 g/L to 250 g/L. On the other hand, with the feed concentration of 150 g/L, the optimal feed rate increases. A large drop in butanol productivity occurs as a result of the increased dilution effect on the cell concentration in the fermenter and the optimal objective function value at the feed concentration of 150 g/L is smaller than that at 200 g/L. Therefore, the feed concentration of 200 g/L gives the highest objective function value under the CSS condition (Table 3). As a result, the optimal CSS of the ESBR-by-adsorption system with the feed concentration of 200 g/L gives the butanol productivity of 3.03 g/L/h, representing 5.5- and 3.7-fold improvements over that of the batch fermentation process (0.55 g/L/h) and that of the fed-batch fermentation process with in-situ butanol recovery by adsorption (ISBR-by-adsorption) (0.81 g/L/h) when the same strain is used as in the previous study 22. Through the simultaneous butanol recovery in the ISBR-by-adsorption and ESBR-by-adsorption systems, the inhibitory effect of butanol is alleviated during the fermentation, resulting in the increased butanol productivity. However, in the ISBR-by-adsorption system, the fermentation has to be stopped once the adsorbents become saturated, and the time for the metabolic transition from acidogenesis to solventogenesis is needed during the initial phase of each fed-batch fermentation. On the other hand, since the ESBR-by-adsorption system enables continuous biobutanol fermentation, the cell concentration can be maintained at a high level (above 8 g/L) without the need to stop the fermentation, and this gives a significant enhancement in the productivity. In addition, the optimal CSS condition resulting from the optimization in this study shows a remarkably short cycle time (1.7 hr) and high volumetric productivity of butanol (3.03 g/L/h) in comparison with the results of the experimental studies in the ESBR-by-adsorption system41, 42 where the cycle time and the volumetric productivity of butanol were reported as 10 – 20 hr and 1 – 2.11 g/L/h, respectively. Therefore, there is the potential that the process performance of the ESBR-by-adsorption can be significantly improved


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through optimization of the major operating variables at the cyclic steady state and the optimization result needs experimental validation.

3.2.2 Sensitivity of the two CSS optimization approaches to initial guess Due to the nature of the fermentation process, model parameters can vary over time, especially after scale-ups, changes in the operating condition or restarts with new seeds. Thus, during the start-up or other upset periods, parameters in the dynamic model need to be readjusted, and recipe optimization should be repeated with the updated model. However, a new grid search after each updating of the model may be impractical. In this regard, optimization method for the fermentation process should be robust with respect to the quality of initial guess. We saw earlier that starting the initial guess from the grid search, the simultaneous approach finds the CSS and the optimal operating condition more quickly and accurately. To compare the sensitivity of two optimization approaches to the initial guess, CSS optimizations are performed again with poorer initial guesses: the feed rate of 11 L/h and 11.8 L/h for the feed concentration of 200 g/L. In this case, the circulation rate is fixed as 250 L/h and εCSS and M have the same values in Section 4.2.1. The optimization results with the two initial guesses of the feed rate are summarized in Table S2 and Table 4. As reported in Table S2, in spite of using the poor initial guesses, the sequential approach gives the identical values of the optimal operating variables as before, and the errors of CSS convergence, and the objective function values remain close to those reported in Table 3. However, it takes longer time to find solutions: the calculation time for the two initial guesses are 161.89 sec and 147.94 sec, respectively (Table S2). On the other hand, with the poor initial guesses, the solution quality of the simultaneous approach is highly sensitive to the initial guess; the resulting values of the feed rate stay close to each initial state leading to poorer CSS condition and objective function value (Table 4). As a way to overcome this problem of the simultaneous approach, we tried to adjust the penalty constant M for the error term of CSS convergence in the objective function (eq 21). The penalty


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constant is usually set as a large value to ensure the constraint satisfaction. However, in the case of nonlinear optimization problem with many decision variables, it makes the problem ill-conditioned and the solution highly sensitive to the initial guess. As the penalty constant decreases, the optimization results with the poor initial guesses improve and become less sensitive to the initial guess (Table 4). With M of 102, the simultaneous approach can find the solution similar to the results from the sequential approach. Although the penalty for the error term is relaxed from 104 to 102, the average error of CSS convergence 5.00 ×10-5 remains at a similar error level as the sequential approach due to the constraint on the error term (εCSS) in eq 21. Table S3 gives the CSS convergence errors in the concentrations resulting from the optimization by using the simultaneous approach with poor initial guesses of the feed concentration of 200 g/L. In addition, the computational time with M = 102 has the smallest value of 25.22 sec in comparison with all other cases. Therefore, the simultaneous optimization algorithm with a well-adjusted M value can be an effective CSS optimization strategy for the ESBR-by-adsorption system, even with poor initial guess. However, it is not always clear what value of M should be used so several values must be tried.

4. CONCLUSIONS Simulation results showed that the concentration profiles of glucose, butanol and ethanol in the ESBR-by-adsorption followed cyclic pattern, and the system reached Cyclic Steady State (CSS) after a number of cycles. The CSS optimization problem for the ESBR-by-adsorption is formulated to maximize butanol productivity and minimize glucose loss over an operation cycle while satisfying some a priori chosen operational constraints. The feed rate and the circulation rate were optimized leading to the most profitable CSS condition for several feed concentration values. To ensure the convergence to a high quality solution (e.g. global maxima) of the nonconvex optimization problem, a feasible region and a ‘good’ initial guess for the decision variables were identified through a coarse grid search. Two CSS optimization approaches, the sequential and simultaneous approaches, were applied to the optimization


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for the ESBR-by-adsorption, and their performances were tested with ‘good’ initial guesses (e.g., those obtained through grid search) as well as poorer initial guesses. CSS optimization using the simultaneous approach with a well-chosen penalty constant was the most effective in terms of the accuracy of CSS convergence, calculation time, and sensitivity to initial guesses. Since the ESBR-by-adsorption system operates in continuous mode through simultaneous recovery of products which keeps the cell concentration in the fermenter at a high level, the productivity is significantly enhanced compared to the batch fermentation and the fed-batch fermentation process with in-situ butanol recovery by adsorption. In addition, through the model-based CSS optimization in this study, the operating condition of the system is optimized leading to a considerable improvement in cycle time and volumetric productivity. This work provides insights and a systematic basis for determining the basic operating condition for the ESBR-by-adsorption. A control strategy to reject disturbances and ensure fast convergence after a start-up or upset should be designed next.

7. AUTHOR INFORMATION * Corresponding authors Prof. Jay H. Lee: E-mail address: [email protected] ; Tel.: 82-42-350-3926

; Fax: 82-42-350-3910

8. ACKNONOWLEDGEMENTS This work was supported by the Energy Efficiency & Resources of the Korea Institute of Energy Technology Evaluation and Planning (KETEP) grant funded by the Korea government Ministry of Knowledge Economy (2010201010094C), and the Advanced Biomass R&D Center (ABC) of Global Frontier Project funded by the Ministry of Science, ICT and Future Planning (ABC-2011-0031354). SUPPORTING INFORMATION


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Supporting tables of the error of CSS convergence resulting from the CSS optimization Supporting table of optimization results by using the sequential approach with initial guesses for the feed concentration of 200 g/L Supporting figure of operation steps of the ESBR-by-adsorption system This information is available free of charge via the Internet at http://pubs.acs.org/.


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NOMENCLATURE Ai: rate of change in concentration of component i by adsorption [g/L] Bi: adsorption-equilibrium constant for component i [L/g] Ci: concentration of component i [g/L] Ci,eq: concentration of component i at equilibrium [g/L] Cad,i: concentration of component i in adsorption column [g/L] Cr,i: concentration of component i in fermenter [g/L] Dr: dilution rate [h-1] F: flow rate of feed media [L/h] Fc,ad: flow rate of circulation from adsorption column to fermenter [L/h] Fc,r: flow rate of circulation from fermenter to adsorption column [L/h] iB: product inhibition constant to cell growth i’B: product inhibition constant to glucose consumption iX: cell concentration inhibition constant to cell growth kd: specific death rate of cell [h-1] ki: adsorption kinetic parameter for component i [/min] KI: substrate inhibition constant [g/L] KS: substrate saturation constant [g/L] m: mass of adsorbent [kg]

PB: butanol concentration at which cell growth stops [g/L] ACS Paragon Plus Environment

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P’B: butanol concentration at which glucose consumption stops [g/L] PX: cell concentration at which cell growth stops [g/L] qi: amount of adsorbed component i per unit mass of adsorbent [g/kgadsorbent] qi,eq: amount of adsorbed component i per unit mass of adsorbent at equilibrium [g/kgadsorbent] qi,m: maximum adsorption capacity for component i per unit mass of adsorbent [g/kgadsorbent] rB: specific rate of butanol formation [h-1] rE: specific rate of ethanol formation [h-1] rS: specific rate of glucose consumption [h-1] S: concentration of substrate [g/L] Sr: concentration of substrate in fermenter [g/L] Sad: concentration of substrate in adsorption column [g/L] Sf: concentration of substrate in feed media [g/L] tf : final time of a cycle [h] V: volume [L] Vad: volume of adsorption column [L] Vr: volume of fermenter [L] X: concentration of cell mass [g/L] Xr: concentration of cell mass in fermenter [g/L] Xad: concentration of cell mass in adsorption column [g/L]

Greek letter ACS Paragon Plus Environment

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αi: yield coefficient for the substrate consumption or the production of component i βi: non-growth related effect of the cell mass on the substrate consumption or the production of component i [h-1] µg: specific growth rate of cell [h-1] µg,r: specific growth rate of cell in fermenter [h-1] µg,ad: specific growth rate of cell in adsorption column [h-1] µm: maximum growth rate of cell [h-1] µnet: net growth rate of cell [h-1] µnet,r: net growth rate of cell in fermenter [h-1] µnet,ad: net growth rate of cell in adsorption column [h-1]


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39. Neumaier, A., Complete search in continuous global optimization and constraint satisfaction. Acta numerica 2004, 13, 271-369. 40. Strongin, R. G.; Sergeyev, Y. D., Global optimization with non-convex constraints: Sequential and parallel algorithms. Springer: 2000; Vol. 45. 41. Lee, S.-H.; Eom, M.-H.; Kim, S.; Kwon, M.-A.; Kim, J.; Shin, Y.-A.; Kim, K. H., Ex situ product recovery and strain engineering of Clostridium acetobutylicum for enhanced production of butanol. Process Biochemistry 2015, 50, (11), 1683-1691. 42. Lee, S.-H.; Eom, M.-H.; Kim, S.; Kim, J.; Shin, Y.-A.; Kim, K. H., Ex situ product recovery for enhanced butanol production by Clostridium beijerinckii. Bioprocess and biosystems engineering 2016, 39, (5), 695-702.


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List of Table

Table 1. Model parameters of the kinetic models of ABE fermentation and adsorption Table 2. The best operating variables and the feasible region obtained from the grid search for three different feed concentrations Table 3. The optimization results by using the two approaches with good initial guesses from the grid search for three different feed concentration values Table 4. The optimization results by using the simultaneous approach with poor initial guesses for the feed concentration of 200 g/L

List of Figures

Figure 1. ESBR-by-adsorption system composed of a fermenter and stirred-tank-type adsorption columns filled with adsorbents Figure 2. Butanol recovery and discharge from the saturated adsorption column at the switching time Figure 3. Optimization of the cyclic operation by using (A) sequential approach, and (B) simultaneous approach Figure 4. CSS optimization algorithm by the sequential approach Figure 5. Concentration profiles in the fermenter at the cyclic steady state for a given operating condition: 200 g/L of the feed concentration, 11 L/h of the feed rate, and 200 L/h of the circulation rate Figure 6. The local behavior of the objective function, butanol productivity and glucose loss around the best operating condition determined from the grid search for the feed concentration of 200 g/L: (A) and (B) indicate changes in their values with respect to the feed rate (the circulation rate is fixed as 250 L/h), and (C) and (D) show changes in their values with respect to the circulation rate (the feed rate is fixed as 11.4 L/h)


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Figure 7. (A) Optimal butanol productivity and (B) optimal glucose loss for the three different feed concentration values resulting from the optimization using the sequential approach (solid filled symbols) and the simultaneous approach (not filled symbols)


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Table 1. Model parameters of the kinetic models of ABE fermentation 22 and adsorption 31

Parameters

Unit

Estimated value

µm

h-1

0.238

KS

g/L

0.357

KI

g/L

272.3

kd

h-1

0.0902

PB

g/L

12.57 0.0159

iB PX

g/L

iX P’B

9.499 0.2095

g/L

20

i’B

6.636

αGlu

9.103

βGlu

h-1

αB βB

0 2.59

h-1

αE

0 0

βE

h-1

0.0176

qm,B

g/kgadsorbent

132.95

qm,E

g/kgadsorbent

97.16

BB

L/g

0.359

BE

L/g

0.043

kB

min-1

0.404

kE

min-1

4.619


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Table 2. The best operating variables and the feasible region obtained from the grid search for three different feed concentrations

Feed concentration (g/L)

The feed rate (L/h) (the feasible region)

The circulation rate (L/h) (the feasible region)

150

13.8 (11.7-14.3)

250 (150-250)

200

11.4 (10.3-11.8)

250 (160-250)

250

7.8 (7.6-7.9)

250 (150-250)


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Table 3. The optimization results by using the two approaches with good initial guesses from the grid search for three different feed concentration values

Sequential approach

Simultaneous approach

10-4

10-4

Tolerance for CSS convergence, εCSS

104

Penalty constant, M Feed concentration (g/L)

150

200

250

150

200

250

Optimal feed rate (L/h)

13.7715

11.4387

7.7807

13.7959

11.4063

7.7999

Optimal circulation rate (L/h)

250

250

250

250

250

250

Execution time of the optimization solver in MATLAB (sec)

140.38

86.32

92.84

26.50

23.27

22.54

Objective function value

391.96

436.08

386.60

391.95

436.05

386.63


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Table 4. The optimization results by using the simultaneous approach with poor initial guesses for the feed concentration of 200 g/L

Simultaneous approach Initial guess of feed rate (L/h)

11

11.8

Tolerance for CSS convergence, εCSS

10-4

10-4

Penalty constant, M

104

Feed concentration (g/L)

103

102

104

200

103

102

200

Optimal feed rate (L/h)

11.0421

11.2409

11.4403

11.7113

11.4912

11.4404

Optimal circulation rate (L/h)

250

250

250

250

250

250

Execution time of the optimization solver in MATLAB (sec)

41.87

41.31

30.31

40.35

38.89

20.12

Objective function value

431.78

434.97

436.19

433.58

436

436.19


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Figure 1. ESBR-by-adsorption system composed of a fermenter and stirred-tank-type adsorption columns filled with adsorbents


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Figure 2. Butanol recovery and discharge from the saturated adsorption column at the switching time


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Figure 3. Optimization of the cyclic operation by using (A) sequential approach, and (B) simultaneous approach


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Figure 4. CSS optimization algorithm by the sequential approach


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12

Concentration in the fermenter (g/L)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Cell concentration Glucose concentration Butanol concentration Ehtanol concentration

10

8

6

4

2

0 0

2

4

6

8

10

Time (hr)

Figure 5. Concentration profiles in the fermenter at the cyclic steady state for a given operating condition: 200 g/L of the feed concentration, 11 L/h of the feed rate, and 200 L/h of the circulation rate


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Figure 6. The local behavior of the objective function, butanol productivity and glucose loss around the best operating condition determined from the grid search for the feed concentration of 200 g/L: (A) and (B) indicate changes in their values with respect to the feed rate (the circulation rate is fixed as 250 L/h), and (C) and (D) show changes in their values with respect to the circulation rate (the feed rate is fixed as 11.4 L/h)


44

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Figure 7. (A) Optimal butanol productivity and (B) optimal glucose loss for three different feed concentration values resulting from the optimization using the sequential approach (solid filled symbols) and the simultaneous approach (not filled symbols)


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TABLE OF CONTENTS


46

Model-Based Optimization of Cyclic Operation of Acetone-Butanol

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