10818
Ind. Eng. Chem. Res. 2010, 49, 10818–10825
Mixing Effects in Cellulase-Mediated Hydrolysis of Cellulose for Bio-Ethanol Production Saikat Chakraborty,* Aniket, and Ashwin Gaikwad Department of Chemical Engineering Indian Institute of Technology, Kharagpur, Kharagpur 721302, India
Conversion of cellulose to glucose is the rate-limiting step in converting biomass into fuel. In this paper, we explore the effects of micro- and macro-mixing on the enzymatic hydrolysis of various cellulosic substrates to glucose by using a spatially averaged low-dimensional CSTR model. We quantify the effects of mixing on glucose yield, cellulose depolymerization rate and the synergy between the enzymes. We conclude that micromixing limitations provide an important mechanism to increase yield, reduce the dominance of synergy and guide optimum process design by offsetting inhibitory effects by preventing the inhibitors from coming in contact with the enzymes. On quantifying the effects of inhibition type (competitive vs noncompetitive) and mixing type (macro- vs micro-), we find that noncompetitive inhibition inhibits glucose yield more strongly than competitive inhibition, and that unlike micromixing limitations, macromixing limitations reduce glucose yield. On the basis of our analysis, we recommend 2 tank reactors in series with minimal local mixing in each tank and glucose removal at the exit of the first tank as the optimal reactor configuration for maximizing glucose yield from enzymatic hydrolysis of cellulose. Introduction
kCBH
Gi + CBH u CBH · Gi f CBH + Gi-2 + G2
The conversion of cellulose to glucose is the rate-limiting step in the conversion of biomass into cellulosic fuel. The detailed kinetics of the cellulase-catalyzed reactions follows modified Michaelis-Menten kinetics, and includes product inhibition of enzymes. The system comprises of a ternary mixture of Trichoderma reesei (T.reesei) cellulase, constituting of enzymes such as endoglucanase I (EGI), exoglucanse or cellobiohydrolase (CBH I and CBH II), and β-glucosidase. T. reesei consists of at least two cellobiohydrolases1 [Cel 7A (formerly CBH I) and Cel 6A (CBH II)], five endoglucanases [Cel 7B (EG I), Cel 5A (EG II), Cel 12A (EG III), Cel 61A (EG IV), and Cel 45A (EG V)], and two β-glucosidase. Endoglucanase randomly cuts the cellulose chains at a rapid rate to form two smaller chains; exoglucanase forms complexes with either reducing or the nonreducing end of the cellulose chain cleaving them end-wise into primarily cellobiose - the two carbon ring dimer, while β-glucosidase cleaves the cellobiose to form glucose. Both glucose and cellobiose inhibit the system either competitively or noncompetitively. While in our previous work2 we focused on simultaneous reaction and diffusion in a batch system, this work deals with the effect of (macro- and micro-) mixing on product yield and inhibition in a continuous stirred tank reactor (CSTR). The starting point for the kinetic model we have used is the one by Okazaki and Moo-Young3 and later revised by Zhang and Lynd.4 We modified these models to include a ternary mixture of enzymes acting on celluloses. Thus, the activity of endoglucanase is described as kEG1
Gi + EG1 u EG1 · Gi f EG1 + Gi-j + Gj
(1)
The exoglucanse (CBH) is the second kind of enzyme forming complexes with either reducing or the nonreducing end of the cellulose, the reaction for which is given by * Corresponding author. E-mail:
[email protected]. Phone: +91-32222-83930. Fax: +91-32222-82250.
(2)
The third kind of enzyme in the cellulase mixture is β-glucosidase, which cleaves cellobiose to form glucose, cellobiose being a major enzyme inhibitor in the system. The kinetics of this cleavage reaction is given by Kβglulcosidase
G2
f
2G1
(3)
Different substrates are characterized by their number average degree of polymerization (DP). The values for the average initial DP (DPo) are estimated based on information for various substrates as tabulated elsewhere.4 We perform simulations by matching the relative concentration of each component in the ternary mixture to their values in T. reesei mixture and by using experimentally determined kcat (turnover number)4-8 and Km (Michaelis-Menten constant) values.3,4,9,10 We consider competitive as well as noncompetitive inhibition with different reported product inhibition constant (Ki) values for both glucose and cellobiose for the T. reesei cellulase system.1 Analysis of the hydrolysis data show that the Ki values for pure noncompetitive inhibition are only slightly than those for competitive inhibition.5 Although the reported values of Ki may vary from being very high11 to very low,12,13 the values reported in most literature are of the order of millimolar.5,14,15 Our model also incorporates some other features such as various forms of activities (rates), the degree of synergy,9 and enzyme deactivation.6 Mixing Model For this analysis, we use the reactive mixing model developed by Chakraborty and Balakotaiah model16,17 from the threedimensional convection-diffusion-reaction (CDR) equations using multiscale spatial averaging technique based on the Liapunov-Schmidt (LS) method of the classical bifurcation theory. The model, which accounts for mixing effects in a CSTR, is given by
10.1021/ie100466h 2010 American Chemical Society Published on Web 10/01/2010
Ind. Eng. Chem. Res., Vol. 49, No. 21, 2010
d〈Cj〉 1 ) (Cin - Cj,m) + νjRj(〈C〉) dt τ j,m Cj,m - 〈Cj〉 )
tmix in (Cj,m - Cj,m) τ
(4)
DP′′i such that DP′i + DP′′i ) DPi. The equation of continuity of species Gi from the above set of equations is given by
(5)
d [G ] ) -ks1(i - 1)[E]f[Gi] + ks-1[E1Gi] + dt i n
where 〈Cj〉 and Cj,m are the spatially averaged concentration and the mixing-cup concentration of the jth component of the substrate, respectively, νjRj(〈C〉)is the reaction rate for hydrolysis of the jth component of the substrate (please refer to the Appendix for detailed derivation of the reaction rates), τC is the total residence time in the reactor, and tmix is the overall characteristic mixing time of a premixed feed in the tank, which depends on local variables such as local velocity gradients, local diffusion length scale, diffusivity, etc., as well as reactor scale variables such as baffle position, stirrer type, circulation time or stirrer speed, feed pipe location etc. Thus, the mixing time tmix incorporates both micro- and macro-mixing effects through its dependence on both microscale and reactor-scale variables. Equations 4 and 5 could be combined and written as a single equation in terms of 〈Cj〉 as d〈Cj〉 Cin j,m - 〈Cj〉 ) + νjRj(〈C〉) dt tmix + τC
Our kinetic model uses Michaelis-Menten kinetics with some modifications, which is explained here. Let us start with endoglucanase (EGI), denoted here by E1 (for the simplicity of notation). In eq 7, Gj is a cellulose chain with j number of carbon atoms whose concentration is denoted by [Gj]. We assume noncompetitive inhibition. k1
ks-1
(7)
kC1
E1 + G2 a E1G2 kC-1
(8)
kG1
E1Gi + G1 a E1GiG1 kG-1
(9)
kG1
E1 + G1 a E1G1 kG-1
(10)
ks-1
(11)
kC1
E1Gi + G2 a E1GiG2 kC-1
ks-1
∞
∞
∞
∑ [E G ] + ∑ [E G G ] + ∑ [E G G ] 1
i
1
i)1
i
1
1
i)3
i
2
i)3
(15) Now, assuming quasi-steady state for the different intermediate species, we obtain d ([E G ]) ) ks1(i - 1)[E1]f[Gi] + (ks-1 + k1)[E1Gi] ) 0 dt 1 i (16) d ([E G ]) ) kG1[E1]f[G1] + kG-1[E1G1] ) 0 dt 1 1
(17)
d ([E G ]) ) kC1[E1]f[G2] + kC-1[E1G2] ) 0 dt 1 2
(18)
d ([E G G ]) ) kG1[E1Gi][G1] + kG-1[E1GiG1] dt 1 i 1 ) ks1(i - 1)[E1G1][Gi] - ks-1[E1GiG1] ) 0
(19)
d ([E G G ]) ) kG1[E1Gi][G2] + kC-1[E1GiG2] dt 1 i 2 ) ks1(i - 1)[E1G2][Gi] - ks-1[E1GiG2] ) 0
(20)
Now, rearranging eqs 14-20, we obtain
d ([G ]) ) dt i
k1[E1](2
(13)
Here, k1, ks1, k′s1, kG1, k′G1, kc1, and k′c1 are the rate constants for E1 (independent of the degree of polymerization i) in the seven reactions listed above; E1Gi, E1G1, E1G2, E1GiG1, E1GiG2 are the enzyme-substrate and end-product complexes. G′i and G″i are cellulose chains with degree of polymerization DP′i and
∑
[Gp] - (i - 1)[Gi])
p)i+1 ∞
(KM1 +
∑ {(i - 1)[G ]})(1 + i
i)3
(12)
ks1
E1G2 + Gi a E1GiG2
(14)
∞
ks1
E1G1 + Gi a E1GiG1
∑
Here, [E1]f is the concentration of free E1. The term 2/(p - 1) denotes the equal probability of a chain of length p to break into a particular smaller fraction i. Hence, it is assumed that the rate and the probability of breaking of a chain into a smaller chain of a particular size are equal with any other size. The factor two accounts for the two cases, when i is broken down into the same fractions j and (i-j) and correspondingly when (i - j) and j. The term (i - 1) represents the number of bonds that are available for breakage in cellulose chain of size i. These bonds are assumed to have equal probability for degradation by endoglucanase. The total concentration of E1 in the system of all cellulose molecules is given by [E1] ) [E1]f +
Derivation of the Reaction Kinetics for Cellulose Hydrolysis
E1 + Gi a E1Gi f E1 + Gj + Gi-j
[E1Gp] p-1 p)i+1 - ks1(i - 1)[E1G1][Gi] + ks-1[E1GiG1] - ks1(i - 1)[E1G2][Gi] + ks-1[E1GiG2] 2k1
(6)
where the expression for νjRj(〈C〉), the reaction rate for hydrolysis of the jth component of the substrate, are given by eqs 30-32, and νj is negative for reactants and positive for products.
ks1
10819
[G1]
/KG1 +
[G2]
/KC1)
(21) for i > 2, where KM1 )
kS-1 + k1 kG-1 kC-1 , KG1 ) , and KC1 ) kS1 kG1 kC1
The process of deriving the rate equation is similar for exoglucanase or Cellobiohydrolase (CBH), and the final result for CBH (for i > 2) is given as
10820
Ind. Eng. Chem. Res., Vol. 49, No. 21, 2010
d ([G ]) ) dt i
k2[E2]([Gi+2] - [Gi])
cellulose fragments is the same, the rate of change of number average degree of polymerization is given by (d)/ j P)) (dt)(∑i)1[Gi])[Gi] ) (d)/(dt)(∑i)1{(i - 1)[Gi]}) ) No(d)/(dt)((1)/(D
∞
∑ [G ])(1 +
(KM1 +
/KG2 +
[G1]
i
i)3
[G2]
/KC2)
(22)
∞
where KM2 is the Michaelis constant of CBH, KG2, KC2 are the dissociation constants between CBH and glucose and cellobiose, respectively. So a substrate (with glucose chain length i and degree of polymerization DPi) reacting with a combination of the three enzymes can be written as d[Gi] d[Gi] d[Gi] d[Gi] ) Endo + CBH + dt dt dt dt βglucosidase
∑
∞
∑ {(i - 1)[G ]})(1 +
(KM1 +
/KC1)
3
i)3
+
(23)
∑ [G ]
∞
∑ [G ])(1 +
(KM1 +
/KG2 +
[G1]
i
[G2]
/KC2)
i)3
k3[E3][G2]
+
(KM3 + [G2])(1 + [G1]/KG3) k2[E2]SM k3[E3][G2] k1[E1]SW + + ) (KM1 + SW)Ih1 (KM2 + SM)Ih2 (KM3 + [C2])Ih3
[Gp] - (i - 1)[Gi])
(27)
∞
(KM1 +
∑ {(i - 1)[G ]})(1 +
/KG1 +
[G1]
i
k2[E2]([Gi+2] - [Gi])
+
∑ [G ])(1 +
[G1]
i
i)3
/KG2 +
[G2]
/KC1)
Here,
, for i > 2
∞
(KM1 +
[G2]
∞
/KC2)
∑ (i[G ]) i
(24)
i)1
DP )
∞
Here, there is no contribution from glucosidase because it only converts the cellobiose chains to glucose, and hence play no role when i > 2. EA1 and EA2 are the maximum enzyme activities given by EA1 ) k1[E1]. For cellobiose and glucose, the expressions are given in eqs 25 and 26, respectively, as
∞
∑ [G ]
∑ [G ]
∞
d ([G ]) ) dt 2
k1[E1](
Ih2 ) (1 +
[G1]
Ih3 ) (1 +
[G1]
∑ [G ], i
i)3
/KG1 +
[G2]
/KG2 +
[G2]
/KC1), /KC2),
/KG3)
∑ [G ])
(28)
i
i)3
Similarly, we obtain the expression for competitive inhibition. Thus
∞
(KM1 +
∑
{(i - 1)[Gi]})(1 +
[G1]
i)3
/KG1 +
[G2]
/KC1) d ( dt
∞
∑ [G ])(1 +
(KM1 +
∞
SM )
i
[G1]
i
i)1
∑ {(i - 1)[G ]},
Ih1 ) (1 +
∑ (i[G ]) ) constant, i)1
i)3
k2[E2]([G4] - [G2])
+
, NO )
i
i)1 ∞
SW )
∞
NO
)
i
/KG2 +
[G1]
i
i)3
[G2]
)
/KC2)
∑ [G ]) ) - dtd ( ∑ {(i - 1)[G ]}) ) N dtd ( DP1 ) i
i
1
O
1
k1[E1]SW k2[E2]SM k3[E3][G2] + + (KM1Ih1 + SW) (KM2Ih2 + SM) (KM3Ih3 + [G2])
(29)
k3[E3][G2] (KM3 + [G2])(1 +
[G1]
/KG3)
(25)
Hence, the expressions for reaction kinetics used in the model equations given by eqs 4, 5, and 6 are
∞
d ([G ]) ) dt 1
k1[E1](
∑ [G ])
∞
i
kendo[Eendo](2
i)3
(KM1 +
∑ {(i - 1)[G ]})(1 + i
[G1]
/KG1 +
[G2]
/KC1)
∑ [G ])(1 +
/KG2 +
[G1]
i
i)3
[G2]
/KC2)
+
∞
[G1]
i
/KG1 +
[G2]
/KC1)
kCBH2[ECBH2]([Gi+2] - [Gi]) ∞
(KM,CBH2 +
k3[E3][G2] (KM3 + [G2])(1 +
i
i)3
∞
(KM1 +
p
∑ {(i - 1)[G ]})(1 +
(KM,endo +
k2[E2][G3]
+
∑ [G ] - (i - 1)[G ])
p)i+1
Ri([Gi]) )
∞
i)3
+
[G2]
∞
k2[E2]
p)i+1
i)3
-
/KG1 +
[G1]
i
i)3
∞
k1[E1](2
i
i)3
)
The above equation can be substituted by the respective values of expressions (eqs 21 and 22) to obtain
d ([G ]) ) dt i
∑ (i - 1)[G ])
k1[E1](
∑ [G ])(1 +
/KG2 +
[G1]
i
[G2]
/KC2)
i)3
[G1]
/KG3)
(26) Here, the maximum enzyme activity of glucosidase is given by k3[E3]. Assuming that each association of cellulases with
+
kCBH1[ECBH1]([Gi+2] - [Gi])
for i g 3
∞
(KM,CBH1 +
∑ [G ])(1 + i
/KG2 +
[G1]
[G2]
/KC2)
i)3
(30)
Ind. Eng. Chem. Res., Vol. 49, No. 21, 2010
10821
Figure 1. Dynamics of glucose formation in a CSTR with different mixing limitations: (a) with inhibition, (b) no inhibition. Substrate, PASC (phosphoric acid swollen cellulose); substrate concentration ) 20 mg/mL; total enzyme conc. ) 25 mg/L; Endo:CBHI:CBHII ) 3:14:3; τ ) 1000 min; kinetic value of enzymes (Km in mg/mL and kcat in g min-1 L-1), Kmendo ) 46.3; Kmcbh1 ) 12; Kmcbh2 ) 44.1; for substrate, Kcatendo ) 0.5073; Kcatcbh1 ) 0.0027; Kcatcbh2 ) 0.0045. ∞
kendo[Eendo](
∑ [G ]) i
i)3
R2([Gi]) )
∞
(KM,endo +
∑ {(i - 1)[G ]})(1 +
/KG1 +
[G1]
i
[G2]
/KC1)
i)3
kCBH2[ECBH2]([G4] - [G2])
+
∞
(KM,CBH2 +
∑ [G ])(1 +
/KG2 +
[G1]
i
Results
[G2]
/KC2)
i)3
kCBH1[ECBH1]([G4] - [G2])
+
∞
(KM,CBH1 +
∑ [G ])(1 +
/KG2 +
[G1]
i
[G2]
/KC2)
i)3
-
kbetaG[EbetaG][G2] (KM,betaG + [G2])(1 +
for i ) 2 (i.e., cellobiose)
[G1]
/KG3)
(31) ∞
kendo[Eendo](
∑ [G ]) i
i)3
R1([Gi]) )
∞
(KM,endo +
∑ {(i - 1)[G ]})(1 + i
/KG1 +
[G1]
[G2]
/KC1)
i)3
kCBH2[ECBH2]([G3])
+
∞
(KM,CBH2 +
∑ [G ])(1 +
/KG2 +
[G1]
i
[G2]
/KC2)
i)3
kCBH1[ECBH1]([G3])
+
∞
(KM,CBH1 +
∑ [G ])(1 +
/KG2 +
[G1]
i
[G2]
/KC2)
i)3
+
total concentrations of enzymes in the cocktail. KG1 and KC1 are inhibition constants of glucose and cellobiose for endoglucanase; KG2 and KC2 are the inhibition constants of products glucose and cellobiose for inhibition of CBH I and CBH II enzymes while KG3 is the inhibition constant for inhibition of β-glucosidase by glucose.
kbetaG[EbetaG][G2] (KM,betaG + [G2])(1 +
[G1]
/KG3)
for i ) 1 (i.e., glucose)
(32) Here, kendo, kCBH2, kCBH1, and kbetaG are the turnover numbers (also known as kcat values) for endoglucanase, cellobiohydrolase II, cellobiohydrolase I, and beta-glucosidase. Similarly, KM,endo,KM,CBH2,KM,CBH1, and KM,betaG are respective Michelis Menten kinetics. [Eendo], [ECBH2], [ECBH1], and [EbetaG] denote the respective
The main objective of this work is to quantify the relationship between inhibition and mixing by studying the dynamics of glucose formation under different extents of mixing. Effect of Micromixing. The extent of micromixing is quantified by the dimensionless mixing time η, where η ) tmix,j/ τC. Thus η)0 corresponds to complete mixing (or no mixing limitations) and ηf∞ corresponds to no mixing (or complete mixing limitations). These two asymptotes of complete mixing (η)0) and no mixing (ηf∞) have been illustrated in Figure 1. [It may be mentioned here that our mixing model is only qualitatively valid in the limit of very large η.17] As may be intuited from eq 6 and seen from Figure 1, higher mixing limitations increase the apparent residence time in the reactor leading to more glucose formation. Figure 2 shows the temporal variation of the degree of polymerization (DP) for different mixing times in the CSTR. As mixing limitations in the tank increase, the number average DP rapidly decreases, resulting in faster scission of cellulose chains by endo- and exoglucanases. Figure 3 shows that the amount of glucose formation for different cellulosic substrates decreases as the crystallinity and the average chain length increase. Or in other words, the higher the DP of the substrate, the more difficult it is to depolymerize it, and hence the lower the glucose yield. The degree of synergy (DS) is defined as the ratio of the combined activity of different enzymes in the hydrolysis process to the sum of their isolated activities under the same conditions. DS is used to determine the optimum enzyme ratio to be used for the process. Panels a and b in Figure 4 show the variation in DS for different endo- and exoglucanase ratios. Our model simulations show that different substrates give similar qualitative characteristics. Figure 4b shows a biphasic relation for different endo:exo ratios in case of finite mixing limitations (η > 0), whereas Figure 4a shows a monophasic response for complete
10822
Ind. Eng. Chem. Res., Vol. 49, No. 21, 2010
Figure 2. Variation in degree of polymerization (DP) with time for various mixing limitations for the cases of (a) inhibition and (b) no inhibition (substrate, Avicel; other conditions remain the same as in Figure 1).
From eq 27 for noncompetitive inhibition, we get
∑
∑
( )
d d 1 d ( [G ]) ) ( {(i - 1)[Gi]}) ) No ) dt i)1 i dt i)1 dt DP k1[E1]Sw k2[E2]SM k3[E3][G2] + + (KM1 + Sw)Ih1 (KM2 + SM)Ih2 (KM3 + [C2])Ih3
(33)
while from eq 29 for competitive inhibition, we get
∑
∑
( )
d d 1 d ( [G ]) ) ( {(i - 1)[Gi]}) ) No ) dt i)1 i dt i)1 dt DP k2[E2]SM k3[E3][G2] k1[E1]Sw + + (KM1Ih1 + Sw) (KM2Ih2 + SM) (KM3Ih3 + [C2])
Figure 3. Dynamics of glucose formation for different substrates for the same T. reesei cellulose, with other conditions being the same as in Figure 1.
mixing (η ) 0) scenario. It was observed from our simulations that the relative synergy effects for different substrates reverse their patterns for the cases of complete mixing (η ) 0) and finite mixing limitations (η > 0). For the complete mixing case, the low-molecular-weight substrates (PASC and Avicel) give higher synergy levels because less surface area is available for endoglucanase to act all by itself and lesser ends for CBH to act in isolation. Effect of Inhibition Type. In this subsection, we explore the effect of inhibition type on glucose yield in the presence of mixing limitations. We compare the effect of noncompetitive inhibition with that of competitive inhibition for various levels of mixing limitations, η ) 0 (perfectly mixed CSTR), η ) 1 (moderate mixing limitation), and η ) 10 (severe mixing limitations), and the results are presented in Figure 5a-c. As could be seen from Figure 5, the glucose yield for the case of competitive inhibition is 1 order of magnitude higher than that for noncompetitive inhibition. However, in both cases, the larger the value η, the higher the rate of glucose formation, or in other words, micromixing limitations help increase the glucose yield, the reasons for which are same as that discussed in the preceding subsection. Below, we use our kinetic model to illustrate why competitive inhibition leads to higher glucose formation than noncompetitive inhibition.
(34)
As could be noticed from the above two equations, the numerators of the three terms for competitive inhibition are same as that of the numerators of the respective terms for the noncomepetitive inhibition, while the denominators are different. The denominator of the first term on the right-hand side of eq 33 is given by Dncl ) (Kml+Sw)Ih1 whereas the denominator of the first term on the right-hand side of eq 34 is given by Dc1 ) (Km1Ih1+Sw) On subtracting the denominator for the competitive inhibition case from that of the noncompetitive case, we get Dncl - Dcl ) SwIh1 - Sw ) Sw(Ih1 - 1) ) Sw([G1]/KG1 + [G2]/KC1) > 0 In a similar way, Dnc2 - Dc2 ) SMIh2 - Sw ) Sw(Ih2 - 1) ) SM([G1]/KG2 + [G2]/KC2) > 0, and Dnc3 - Dc3 ) C2(Ih3 - 1) ) C2([G1]/KG3) > 0 Therefore, the denominators in all the three terms in the noncompetitive inhibition are higher than their respective
Ind. Eng. Chem. Res., Vol. 49, No. 21, 2010
10823
Figure 4. Degree of synergy (DS) with endo:exo ratio for systems with (a) complete mixing and (b) finite mixing limitations for different substrates but without significant product inhibition (all other conditions remain the same as in Figure 1). Substrate, Avicel (PH 101); substrate concentration ) 20 mg/mL; total enzyme conc. ) 25 mg/L; endo:CBHI:CBHII ) 3:14:3; τ )1000 min; kinetic value of enzymes (Km in mg/mL and kcat in g min-1 L-1), Kmendo ) 46.3; Kmcbh1 ) 12; Kmcbh2 ) 44.1; for substrate, Kcatendo ) 0.005268; Kcatcbh1 ) 0.00076; Kcatcbh2 ) 0.0024.
Figure 5. Effect of inhibition type on glucose yield for competitive inhibition (solid line) and noncompetitive inhibition (dashed lines) for different mixing limitaions (η ) 0 [ideal CSTR], η ) 1, η ) 10).
counterparts in competitive inhibition. So, the rate of glucose formation for noncompetitive inhibition is lower than that of competitive inhibition, as has been quantified by our numerical simulations shown in Figure 5. Effect of Macromixing. Macromixing or large scale mixing effects in CSTRs are accounted for by using the tanks-in-series model, where the number of tanks N is used to quantify the macromixing limitations in the system. Macromixing in tubular reactors is captured by the Axial Dispersion model, where the axial Pecle´t number Pe quantifies the extent of macromixing in the reactor. These two macromixing parameters, N and Pe, in tank and tubular reactors, respectively, are related through the correlation Pe ) 2(N - 1). We know that for the axial dispersion model for a tubular reactor, larger macromixing limitations imply that the axial Pecle´t number Pe is large. Similarly, for the tanks-in-series model, the greater the number of tanks in series, the larger the macromixing limitations in the system. Figure 6 illustrates the effect of macromixing on glucose yield by using the tanks-in-series model for different micromixing limitations. For example, Figure 6 a shows the effect of
macromixing in the complete absence of micromixing limitations (η ) 0). As may be observed from this figure, increasing macromixing limitations to the system (i.e., increasing the number of CSTRs from 1 through 2 to 3, while maintaining the total residence time of the system constant) decreases the glucose yield. This is contrary to the case of micromixing, where we had earlier seen how increasing micromixing limitations improves glucose yield. This contrary behavior may be attributed to the fact that both micromixing and enzyme inhibition are molecular scale phenomena, while macromixing is a reactor scale phenomenon. Thus, it is hardly surprising that a reactor scale phenomenon such as macromixing is incapable of influencing a molecular scale phenomenon such as the kinetics of enzyme inhibition. Figures 6a-c show the effect of increasing the micromixing limitations in the reactor in the presence of macromixing limitations. Although the generic trend that micromixing helps but macromixing hurts glucose yield from cellulose is consistent, a comparison of Figure 6a with panels b and c in Figure 6 shows that the negative effect of macromixing limitations on yield is minimal in the absence of micromixing limitations (i.e., η ) 0) and increases as micromixing limitations (or η) increase. Discussion This present study shows that mixing limitations provides an important mechanism to offset inhibition, increase glucose yield as well as the rate of rate of formation of glucose. This reduction in reaction inhibition is achieved through the fact that mixing limitations prevent the two enzyme inhibitors, namely, cellobiose (dimer) and glucose (monomer), both of which are reaction products, from coming in contact with the enzymes. While mixing limitations can be attributed to both micro- and macro-mixing effects, the role of micromixing is predominant as indicated by the reduced inhibition, which is a microscale phenomenon. Our analysis also shows that introducing mixing limitations reduce the quantitative dominance of synergy on yield while retaining the qualitative features such as the biphasic nature of synergistic effects of the kinetic model resulting from product inhibition. This may be attributed to the inability of different enzymes to attack the same chain sites in presence of mixing
10824
Ind. Eng. Chem. Res., Vol. 49, No. 21, 2010
Figure 6. Effect of macromixing on glucose yield from Avicel obtained by using tanks-in-series model for different amounts of micromixing limitations.
Figure 7. Effect of product removal on glucose yield from Avicel obtained using tanks-in-series model.
limitations in the solution. Also, the relative synergy effects for different substrates reverse their patterns for the cases of
complete mixing and finite mixing. For the complete mixing case, the low-molecular-weight substrate gives the highest
Ind. Eng. Chem. Res., Vol. 49, No. 21, 2010
synergy levels because in this case, less surface area is available for endoglucanase to act all by itself and lesser ends for CBH to act in isolation. Therefore, both act in tandem increasing synergy as compared to a substrate with high-molecular-weight crystalline structure. However, for systems with high mixing limitations, the synergy effects are less pronounced (Figure 4b). Introducing mixing limitations by reducing the stirring speed in the reactor, though seemingly advantageous, may offer challenges while using immobilized enzymes or when the sterilized conditions inside the reactor need to be monitored. Although mixing limitations do lead to better conversion and a continuous decrease in number average DP even after the freezing time (16-21 h), the glucose formation reaches saturation. Hence, although there is more conversion of large chainlength cellulose to relatively smaller fractions, formation of glucose and other soluble sugar saturates close to the reactor residence time. This problem can be partially offset by further reducing product inhibition by introducing mixing limitations along with the simultaneous addition of β-glucosidase for converting cellobiose to glucose. Novel Reactor Design. On the basis of the above analysis, we intuit that stage-wise cascaded CSTRs with membrane separation-based product removal and purification at each step could turn out to be an optimal design for this system. We perform model simulations for two and three CSTRs in series, where the product (glucose) is removed at the exit of each CSTR by using membrane separation techniques. The results of this simulation study are summarized in Figure 7 for the case Avicel as the cellulosic substrate hydrolyzed in three CSTRs in series (Figure 7a) and two CSTRs in series (Figure 7b), respectively. As is obvious from Figure 7, introducing product separation at the exit of each CSTR significantly improves glucose yield. It can also be observed by comparing the curves for substantial micromixing limitations (η ) 10) with that for perfectly micromixed CSTRs (η ) 0) that the glucose yield as well as its percentage improvement resulting from product separation are enhanced in the presence of micromixing limitations in the CSTR. A comparison of panels a and b in Figure 7 reiterates what we had discussed in the previous section: macromixing hurts while micromixing helps glucose yield. Thus, increasing the number of tanks from two to three increases macromixing limitations in the system and slightly reduces glucose yield. On the basis of our above analysis, we recommend two tank reactors in series with minimal local mixing in each tank and membrane-separation based glucose removal at the exit of the first tank as the optimal reactor configuration for maximizing glucose yield from enzymatic hydrolysis of cellulose. Conclusions We find that increasing micromixing limitations turns out to be an important strategy to increase reactor yield, reduce the dominance of synergy, and guide optimum process design in the production of glucose through enzymatic hydrolysis of cellulose. We show that increasing micromixing limitations in CSTRs offset inhibitory effects by preventing the inhibitors from coming in contact with the enzymes. Our model simulations of the effects of inhibition type (competitive vs noncompetitive) and mixing type (macro- vs micro-) allow us to conclude that
10825
noncompetitive inhibition inhibits glucose yield more strongly than competitive inhibition, and that unlike micromixing limitations, macromixing limitations reduce glucose yield. On the basis of our analysis, we recommend two tank reactors in series with minimal local mixing in each tank and glucose removal at the exit of the first tank as the optimal reactor configuration for maximizing glucose yield from enzymatic hydrolysis of cellulose. Literature Cited (1) Henrissat, B.; Driguez, H.; Viet, C.; Shulein, M. Synergism of cellulases from Trichoderma reesei in the degradation of cellulose. BioTechnol 1985, 3, 722–726. (2) Aniket; Chakraborty, S.; Sen, R. K. Mathematical Modeling of Cellulase-mediated Hydrolysis of Cellulose for Bio-ethanol Production. Int. J. Anaerobic Digestion Renewable Energy 2010, 1 (1), 119–126. (3) Okazaki, M.; Moo-Young, M. Kinetic of Enzymatic Hydrolysis of Cellulose: Analytical Description of a Mechanistic Model. Biotechnol. Bioeng. 1978, 20, 637–663. (4) Lynd, L. R.; Zhang, Y. H. P. A functionally based model for Hydrolysis of Cellulose by Fungal Cellulase. Biotechnol. Bioeng. 2006, 94 (5), 888–898. (5) Gruno, M.; Valjamae, P.; Pettersson, G.; Johannson, G. Inhibition of Trichoderma reesei cellulases by cellobiose is strongly dependent on the nature of the substrate. Biotechnol. Bioeng. 2004, 86, 503–511. (6) Drissen, R. E. T.; Maas, R. H. W.; Van Der Maarel, M. J. E. C.; Kabel, M. A.; Schols, H. A.; Tramper, J.; Beeftink, H. H. A generic Model for glucose production from various cellulose sources by a commercial cellulase complex. Biocatal. Biotransform. 2007, 25 (6), 419–429. (7) Nidetzky, B.; Zachariae, W.; Gercken, G.; Hayn, M.; Steiner, W. Hydrolysis of cellooligosaccharides by Trichoderma reesei cellobiohydrolases: Experimental data and kinetic modeling. Enzyme Microb. Technol. 1994, 16, 43–52. (8) Valjamae, P.; Pettersson, G.; Johansson, G. Mechanism of substrate inhibition in cellulose synergistic degradation. Eur. J. Biochem. 2001, 268, 4520–4526. (9) Lynd, L. R.; Zhang, Y. H. P. Towards an Aggregated Understanding of Enzymatic Hydrolysis of Cellulose:Non Complexed Cellulase System. Biotechnol. Bioeng. 2004, 88, 797–824. (10) Beldman, G.; Voragen, A. G. J.; Rombouts, F. M.; Searle-ven Leeuwen, M. F.; Pilnik, W. Adsorption and Kinetic Behavior of Purified Endoglucanases and Exoglucanases from Trichoderma Viride. Biotechnol. Bioeng. 1987, XXX, 251–257. (11) Bothast, R. J.; Saha, B. Production, purification and characteriziation of highly glucose tolerant β glucosidase from Candida Peltata. Appl. EnViron. Microbiol. 1996, 62, 3165–3170. (12) Claeyssens, M.; van Tilbeurgh, H.; Tomme, P.; Wood, M. T.; McRae, I. S. Fungal cellulase systems. Comparison of the specificities of the cellobiohydrolases isolated from Penicillium pinophilum and Trichoderma reesei. Biochem. J. 1989, 261, 819–825. (13) van Tilbeurgh, H.; Claeyssens, M. Detection and differentiation of cellulase components using low molecular mass fluorogenic substrates. FEBS Lett. 1985, 187, 283–188. (14) Ryu, D. D. Y.; Lee, S. B. Enzymatic hydrolysis of cellulose: Determination of kinetic parameters. Chem. Eng. Commun. 1986, 45, 119– 134. (15) Lee, H. K.; Hong, S. I. Effect of inhibitor on enzymatic hydrolysis of cellulose. J. Korean Inst. Chem. Eng. 2004, 10, 9–114. (16) Chakraborty, S.; Balakotaiah, V. Low-dimensional models for describing mixing effects in laminar flow tubular reactors. Chem. Eng. Sci. 2002, 57, 2545. (17) Chakaraborty, S.; Balakotaiah, V. Spatially Averaged Multi-scale models for chemical reactors. AdV. Chem. Eng. 2005, 30, 205–297.
ReceiVed for reView March 2, 2010 ReVised manuscript receiVed August 28, 2010 Accepted September 1, 2010 IE100466H
