Enzymatic Hydrolysis of Lignocellulosic Biomasses via CFD and

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Enzymatic Hydrolysis of Lignocellulosic Biomasses via CFD and Experiments Danilo Carvajal,†,‡ Daniele L. Marchisio,† Samir Bensaid,† and Debora Fino*,† † ‡

Department of Materials Science and Chemical Engineering, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy Escuela de Ingeniería Química, Pontificia Universidad Catolica de Valparaíso, Av. Brasil 2147, 2362804 Valparaíso, Chile ABSTRACT: The time evolution of the rheological properties of pretreated Arundo slurries has been estimated, during enzymatic hydrolysis for bioethanol production, by computational fluid dynamics simulations in conjunction with experimental tests on a laboratory scale anchor reactor with different solid concentrations (18.5 and 27.5% w/w) and stirring velocities (50200 rpm). The simulations were carried out with Fluent 6.2 using the moving reference frame approach and the HerschelBulkley rheological model. Great care was taken in the development of the computational grid and in the solution of the numerical issues. The identification of the rheological parameters was successful and the results are consistent with other works published in the literature on similar systems. The next steps of this work will involve the use of these results to design new continuous reactors for enzymatic hydrolysis and their scale up to a pilot and industrial level.

1. INTRODUCTION In recent years the possibility of producing biofuels, such as ethanol, from residual nonfood parts of current crops (i.e., second generation biofuels) has received more and more attention from the scientific community. One of the most promising approaches for the conversion of lignocellulosic biomasses to ethanol involves a steam explosion pretreatment, followed by an enzymatic hydrolysis of cellulose to glucose, which is fermented to ethanol. Finally, a distillation step separates the ethanol from the remaining residue. A general process flow diagram of the involved unit operations is shown in Figure 1. The main problem that arises is that the cellulose molecules are locked-in by the ligninhemicellulose network, and a very efficient enzymatic hydrolysis step is therefore needed. Moreover, in order to reduce the energy required for cooling and heating, and in order to reduce the operational costs of down-processing, notably for the final distillation step,1,2 enzymatic hydrolysis must be operated with very high solid contents: a concentration of 3040% by weight of lingocellulosic biomass in water, in the initial stages of enzymatic hydrolysis, is believed to be the target value to make the overall ethanol production process cost-competitive.3 However, the complex behavior of this multiphase system poses some serious mixing problems and innovative mixing technologies therefore need to be developed. One critical aspect, for example, is the contact between the enzyme and the substrate. In fact, under typical operating conditions the process performance could suffer from a certain decrease, due to the formation of stagnant zones and settling, which in turn reduces the opportunities for contact between the enzyme and substrate. Whereas, in order to avoid thermal inactivation of the enzyme, the heat dissipation from the moving parts has to be carefully managed. Furthermore, great attention should be paid to the shear stress distribution in the mixing device, since high levels of shear stress can inactivate the enzyme, due to damages to its molecular structure.4 The development of novel mixing solutions requires detailed knowledge of the rheological properties of the biomass slurries and of their evolution during the hydrolysis process. In the r 2011 American Chemical Society

literature, there is scarce information on pretreated lignocellulosic slurries. To our knowledge, the only available data are for pretreated corn stover with dilute sulfuric acid, at a solid concentration ranging from 5 to 30% solids by weight,5 from 10 to 40% insoluble solids by weight,6 and from 5 to 20% solids by weight.7 Experimental findings show that pretreated lignocellulosic materials generally exhibit a variety of different behaviors, which depend on the solid content; for solid concentrations higher than 10% by weight, the system can be described as a highly viscous slurry, constituted by a mixture of water, cellulose, hemicellulose, lignin, organic acids, and inorganic compounds, often (but not always) characterized by viscoplastic behavior of a shear-thinning type, with a significant yield stress. At concentrations higher than 30% by weight, the material behaves as a semisolid, in which a continuous liquid phase can no longer be distinguished. Under these very high concentrations, shearthickening behavior can also be observed. These systems are generally described with a pseudo-single-phase approach, with non-Newtonian models, such as the well-known Power Law expression or the HerschelBulkley model. However, the determination of the rheological parameters that appear in such models is complicated by the inherent multiphase nature of the system, notably the presence of large elongated fibers. For this reason, the use of standard rheometers, where a simple shear flow is used for the estimation of the rheological parameters through fundamental constitutive equations, is not applicable. As a consequence, for lignocellulosic slurries these rheological parameters are directly extracted from measurements conducted in real mixing devices (i.e., torque required to stir the slurry at different stirring rates) and then by Special Issue: Russo Issue Received: July 30, 2011 Accepted: October 12, 2011 Revised: October 11, 2011 Published: October 12, 2011 7518

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Industrial & Engineering Chemistry Research

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2. GOVERNING EQUATIONS AND MODELING APPROACH

Figure 1. Block diagram of the cellulosic ethanol production process.

making use of empirical correlations. The most commonly used method consists in assuming that the power number is inversely proportional to the Reynolds number (under laminar flow conditions), and that the average shear rate in the vicinity of the impeller is proportional to its angular velocity (this assumption is known as the MetznerOtto correlation). Both relationships are defined by constants of proportionality that are only dependent on the geometry of the system. These proportionality constants are obtained by means of a reference fluid with known rheology.5 Some of the limitations of this approach can be overcome by resorting to computational fluid dynamics (CFD), for which knowledge of the geometry of the mixing device (e.g., the stirred tank) and of the torque values obtained experimentally at different stirring rates is sufficient to identify the rheological parameters. When using CFD, in fact, the rheological parameters can be identified directly by comparing the simulation predictions with the experiments. However, although CFD is nowadays used extensively and is considered quite reliable for these specific applications,811 a comparison of the numerical solution with an analytical result is always recommended, mainly to estimate the effect of numerical issues. In this work, this CFD approach is employed with the aim of estimating the time evolution of the rheological properties of Arundo slurries (pretreated with steam explosion) during enzymatic hydrolysis. Unlike empirical methods such as the Metzner and Otto approach, our method does not require a fluid with a known rheology to establish a relationship between the couples shear rate/shear stress and torque/stirring velocity. To validate this CFD approach, experiments have been conducted with a labscale anchor reactor with different operating conditions and solid concentrations. This shape of the blades was chosen in order to avoid slurry from sticking to the wall surface. The reactor showed very good mixing performance for a wide range of experimental conditions. A preliminary experimental validation, with a fluid with known rheological characteristics and high viscosity (glycerin), was carried out to check the accuracy of torque measurements. The CFD model prediction was refined by appropriate computational grid-refinement and boundary treatment. Then, to extract the parameters for the HerschelBulkley model for the pretreated Arundo, experimental data of torque at different stirring rates have been used together with CFD simulations. The computational grids were built with Gambit 2.2, whereas the CFD simulations were carried out with Fluent 6.2 in a laminar regime by means of the moving reference frame approach.

2.1. Governing Equations. A simple mathematical model, which considers the material as a continuous single-phase fluid, has been adopted. The interactions between particles at a microscopic level were not considered and the overall effect of these interactions was estimated through an empirical rheological model. The general assumptions for the mathematical models used are of a laminar, incompressible, and isothermal flow. A single rotating reference frame approach was applied to obtain a laminar steadystate flow, induced by the rotation of the blades in the geometry. Under these conditions, the governing equations are:

∇ 3 uB ¼ 0

ð1Þ

1 1 uB 3 ∇ð uBÞ ¼ ∇p þ ∇τ þ gB F F

ð2Þ

where F is the fluid density, u is the fluid velocity, g is the gravity acceleration, p is the fluid pressure, and τ is the stress tensor due to viscous forces. The rotational axis is about the y-axis, and the relative velocity is given by: ~ rÞ uBr ¼ uB ðΩ B

ð3Þ

where Ω B is the rotating speed of the blades and B r is the position vector in the rotating frame. The continuity equation becomes: ∇ 3 uBr ¼ 0

ð4Þ

In terms of the relative velocities, the momentum equation (eq 2) can be written as: ~ u þ Ω ~Ω ~ rÞ uBr 3 ∇ð uBr Þ þ ð2Ω Br B 1 1 ¼ ∇p þ ∇τ þ gB F F

ð5Þ

The second term in eq 5 is the Coriolis force. 2.2. Rheological Model. Pretreated lignocellulosic slurries are generally non-Newtonian, where the non-Newtonian viscosity η _ In the present study, is a nonlinear function of the shear rate γ. the HerschelBulkley model was used, based on its capacity to describe the rheological behavior of biomass slurries. Conversely, the power law model was not considered to be appropriate since it does not foresee the presence of a yield stress component, which was always observed in our experiments on pretreated lignocellulosic slurries. In the case of Newtonian behavior, the stress tensor is written as follows: ! ∂uj ∂ui τ ¼μ þ ð6Þ ∂xj ∂xi

where μ is the viscosity for Newtonian fluids and ui (and uj) is the fluid velocity in tensor form. In the case of non-Newtonian behavior, the following model is employed: ! ∂uj ∂ui τ ¼η þ ð7Þ ∂xj ∂xi 7519

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where η is non-Newtonian viscosity, which is considered to be a function of the shear rate only. For the HerschelBulkley model, in order to avoid numerical problems when the non-Newtonian viscosity becomes unbounded at a small shear rate, FLUENT utilizes a biviscosity model of the following form: :n τ0HB þ kHB ½γ HB ðτ0 =μyield ÞnHB τ0 : : η¼ η ¼ μyieldγ < μyield γ : τ0 γg ð8Þ μyield i.e., for low shear rates the material acts as a very viscous liquid with a viscosity equal to “yielding viscosity” μyield. After solving these equations using a commercial CFD code, and once the geometry has been defined, the torque T, applied to the moving parts of the reactor, can be easily calculated. The torque on the rotating parts is defined as follows: T ¼ð

Z

S

ðB r ðτ 3 ^nÞÞdSÞ 3 â

Figure 2. Geometry of the laboratory scale anchor reactor.

ð9Þ

where S represents the surfaces comprising all rotating parts, ^n is a unit vector normal to the surface and â is a unit vector parallel to the axis of rotation. The knowledge of T is sufficient to calculate the power number, Np, which for a stirred tank is defined as follows: Np ¼

P FN 3 Di 5

ð10Þ

where P = 2πNT is the overall power consumption, N is the stirring rate, and Di is the characteristic diameter of the impeller. The power number is often plotted versus the Reynolds numbers, Re, which quantifies the ratio of the inertial to the viscous forces, and which for a Newtonian fluid is simply written as follows: Re ¼

FNDi μ

ð11Þ

3. MATERIALS AND METHODS The enzymatic hydrolysis experiments and glycerin tests for model validation were carried out using a conventional anchor reactor with two blades of 5 mm and a clearance of about 2.5 mm. The volume of the reactor is about 5 L. A sketch of the reactor is reported in Figure 2. The reference fluid for the model validation was glycerin (99.9%). A Heidolph RZR 2102 motor control was used in the experiments. The temperature was controlled by a water jacket heater with a temperature of 36 °C for glycerin and 45 °C for the hydrolysis tests. The stirring rate was varied between 50 and 200 rpm for all the materials under study, whereas the duration of the tests for hydrolysis was between 3.5 and 5 h. The viscosity of glycerin was measured independently using a Rheolab DC Anton Paar rheometer, with a torque in the 0.2575 mN m range and equipped with cylindrical bane geometry with a Pioli impeller. The experiments were carried out with Arundo donax harvested in 2008 (Italy) and pretreated with steam explosion (200 °C for 8 min). Before being used, the material was conserved at 4 °C in order to prevent any microbial contamination and physicalchemical degradation. The tests were

Figure 3. Anchor impeller reactor: meridian section of the threedimensional computational mesh where the cell type arrangement and the basic reactor dimensions are provided.

performed by adding water to the biomass samples reaching a final solid concentration of 18.5 and 27.5% (by weight), and a given amount of the enzyme (cellulase Cellic CTec and hemicellulase Cellic HTec, both from Novozymes). The pretreated Arundo can be described as a heterogeneous mix of particles and fibers varying in terms of size and aspect ratio. From a physical characterization, it showed an average fiber length of less than 1 mm and an average density of 1100 kg/m3. A chemical characterization of the material (dry based, percentages by weight) resulted in 44.9% of glucan, 29.3% of lignin, 6.4% of xyloolygomers, 4.1% of xylan, 3.9% of xylose, 1.9% of acetic acid, 1.03% of formic acid, and the rest consisted of acetyl compounds, hydroxymethylfurfural (HMF) and others. The slurry appeared to be homogeneous during the tests, without any stratification or other strong deviation from fluid continuity: hence, the latter is a very important condition for the application of such a CFD model for this purpose.

4. NUMERICAL DETAILS The Fluent 6.2 CFD software was used for all the simulations; this software uses a finite-volume method to discretize the governing equations. Both the geometry and the computational mesh were created in Gambit 2.2. Different three-dimensional grids were tested and a final hybrid mesh of 590 000 hexahedral/ tetrahedral cells was used (see Figure 3). The effect on the predicted torque of further grid refinement, in the proximity of the clearance between the impeller and the vessel, was found to 7520



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A multivariate function f is used to relate the torque with the stirring velocity and the rheological parameters. The general expression for this function is T ¼ f ðN, R, jÞ

ð12Þ

where R represents the rheological parameters (τ0HB, kHB, nHB) for the HerschelBulkley model, and j represents the parameters that define the function f. It is worth mentioning that the function f has a purely numerical use, which is to give approximations of the rheological parameters for each iteration of our proposed algorithm. We proposed the following expression for f: T ¼ Aτ0HB þ BkHB N CnHB Figure 4. Flow diagram of the algorithm for identification of the rheological parameters.

be negligible. To reduce the numerical diffusion, the number of tetrahedral cells was kept at about 37%, with respect to the total number of cells. The single rotating reference frame approach, which solves the momentum equations for the entire domain in a rotating frame, was used to model the moving parts (impeller); the Coriolis force must be included in the process. The reactor wall was defined as stationary, whereas the impeller moves with the fluid domain, with an angular velocity ranging from 50 to 200 rpm as in the experiments. The upper surface of the liquid (free surface) was defined as free of shear stress. A non-slip wall condition was used for both the walls and the surface of the impeller. The formation of a vortex-induced surface modification was not observed experimentally (the surface remained flat at the investigated stirring velocities), so it was not necessary to include a physical model which predicts such a phenomenon. The segregated solver was used for all simulations, whereas the standard firstorder up-wind discretization scheme was employed for pressure and momentum. The pressurevelocity coupling was solved utilizing the SIMPLE approach. Convergence was achieved when all normalized residuals reached values smaller than 104 and the torque applied by the impeller about the z-axis reached a stationary value with a maximum deviation of 1%. The convergence of the average velocity magnitude was also monitored over the entire computational domain, obtaining a similar trend with respect to the torque convergence evolution. Simulations were performed on an HP XW8600 Workstation with 8 Intel Xeon 3.0 GHz cores and 16 GB RAM. The average CPU time was between 16 and 90 min per simulation.

5. IDENTIFICATION OF THE RHEOLOGICAL PARAMETERS To estimate the rheological parameters of the test fluids using our method, it was necessary to carry out torque measurements at different stirring velocities with the test fluid in the laboratory scale reactor. The rheological parameters were estimated by means of an iterative method using the obtained data along with CFD simulations. A general block diagram of the algorithm is shown in Figure 4 to indentify the rheological parameters. The calculation procedure is described below.

ð13Þ

where A, B, and C are model parameters (j) which define f for the rheological model. The iterative procedure is described as follows: Step 1 Simulations of the anchor reactor are carried out at different stirring velocities (50200 rpm), using the same rheological parameters for each simulation. Rheological parameters from the literature are used for the first approximation,5 with fluids having characteristics similar to the test fluid. Step 2 The torque series obtained from the previous step are used to calculate j through the least-squares method using the f function defined by the R values used in the previous step. Step 3 The resulting expression for f previously obtained is used to recalculate R through the least-squares method, this time using the torque series from the experimental data. Step 4 With the new R values, return to Step 1 and repeat the procedure until the convergence of R is reached. We considered the system converged when the rheological parameters resulted in a maximum deviation of 1% from the previous iteration. After several tests, we concluded that the proposed expression for f (eq 13) was satisfactory, since a very fast convergence, which usually required less than six iterations, was obtained. The obtained values for A ranged from 0.002022 to 0.007245 m3 and for B they ranged from 0.000854 to 0.009880 m3, whereas in the case of C, the obtained values were very close to unity with no more than 1% of deviation. The model parameters (j) showed a considerable dependence on the rheological parameters and very little dependence on the stirring velocity.

6. RESULTS AND DISCUSSION As already stated in the Introduction, great attention should be paid to the numerical aspects especially for laminar simulations. In particular, the grid should be fine and regular in order to reduce numerical diffusion, which is artificially introduced by the finite-volume discretization, and in order to achieve a grid independent solution. By trading off computational time and numerical accuracy, the final grid for the anchor reactor is a hybrid in which almost 70% of the volume is occupied by a hexahedral mesh and the remaining 30% by a tetrahedral mesh which covers the most complex part of the reactor (close to the bottom) since this cell type is easier to adapt to complex geometries Different grids constituted by 80 103, 300 103, 600 103, 900 103, 1600 103, and 2000 103 cells were tested in this 7521



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Figure 6. Torque versus stirring velocity for glycerin at 36 °C for the experiments (triangles) and the CFD predictions (squares).

Figure 5. Comparison of the torque predicted by the CFD model with different cell numbers for a Newtonian Fluid (glycerin, with model parameters μ = 0.37 Pa 3 s and F = 1260 kg/m3) and for a non-Newtonian fluid (HerschelBulkley model with parameters τ0HB = 484.14 Pa, kHB = 0.00113 Pa 3 sn, and nHB = 2.3) for a stirring rate of 70 rpm.

work. Figure 5 shows the torque predicted by the CFD model for a Newtonian fluid (glycerin, with model parameters μ = 0.37 Pa 3 s and F = 1260 kg/m3) and for a non-Newtonian fluid (HerschelBulkley model with parameters τ0HB = 484.14 Pa, kHB = 0.00113 Pa 3 sn, and nHB = 2.3) with a stirring rate of 70 rpm and different numbers of cells. As can be seen in Figure 5, refining of the grid beyond 500 103 cells does not produce any significant improvement in the solution. It is worth mentioning that, for the tested grids, no significant difference was detected by resorting to higher-order discretization schemes (i.e., second order up-wind or QUICK), and therefore, for the sake of numerical stability, only the first order up-wind scheme was used. As previously mentioned, the CFD model was initially validated by employing a fluid with known rheological characteristics; to this end, glycerin was used at 36 °C (μ = 0.37 Pa 3 s). The experimentally measured torque and CFD predictions are reported in Figure 6. The agreement between the experimental data and the CFD calculations for the torque is satisfactory, although there are margins for improvement. To assess the source of this difference, the experimental and modeling data were plotted as a function of the power and the Reynolds numbers. It is well-known that for a Newtonian fluid in laminar flow, the logarithm of the power number is inversely proportional to the logarithm of the Reynolds number. Figure 7 reports the power number versus the Reynolds number for the experiments and simulations. The CFD predictions are close to the experimental results and both show a linear trend, as could be expected, and the differences may be due to problems in measuring the torque (problems of vibration or accuracy of the sensor) and in the temperature control system.

Figure 7. Power number versus Reynolds number for glycerin at 36 °C for the experiments (triangles) and the CFD predictions (squares).

Moving on to the identification of the parameters for the two investigated rheological models and for the pretreated Arundo, with initial concentrations of 18.5% and 27.5%, Figures 8 and 9 report the comparison between the experimental data and the CFD predictions with the best fitting rheological parameters obtained from the previously reported identification procedure. The CFD predictions are reported for the pretreated Arundo, with initial concentrations of 18.5% by weight (Figure 8) and 27.5% by weight (Figure 9). To determine the flow regime for the pretreated Arundo tests, the relationship between the Reynolds number and the Power number was analyzed using the methodology depicted by Prajapati et al.11 for non-Newtonian fluids, obtaining laminar regime for all tests. The estimated Reynolds number varied from about 2.2 to 551. As a general comment, the experimental data highlight a strong shear-thickening behavior, especially in the early stages of hydrolysis, which subsequently decreases in the last stages for both initial concentrations. The comparison of the CFD predictions and the experimental data of the initial concentration of pretreated Arundo of 18.5% by weight, reported in Figure 8, shows a very good agreement for the 7522



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Figure 8. Comparison between the experiments and CFD predictions (with best fitting parameters) for the torque versus the stirring rate for the pretreated Arundo at 18.5% by weight at different instants (experimental results: circles; HerschelBulkley model: continuous line).

Figure 9. Comparison between the experiments and CFD predictions (with best fitting parameters) for the torque versus the stirring rate for the pretreated Arundo at 27.5% by weight at different instants (experimental results: circles; HerschelBulkley model: continuous line).

HerschelBulkley model for all the investigated hydrolysis times. This model seems to be able to describe the transition from shear-thickening to Newtonian behavior very well, as soon

as enzymatic hydrolysis of the cellulose fibers takes place. A similar conclusion can be drawn from a comparison of the initial concentration of 27.5% reported in Figure 9. 7523



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expected ranges. However, in most cases, the values of the flow behavior index are far from those obtained for other types of material. In fact, values over unity indicate a shear-thickening behavior, which is opposite to that found for corn stover, which shows a shear-thinning behavior. Flow behavior index values smaller than, or very close to, the unity at the end of hydrolysis tests do not necessarily reflect a further transition to a shearthinning behavior, which should be verified with longer duration tests. The estimated average shear stresses for the pretreated Arundo tests were obtained from the CFD simulations, and varied from 11.6 to 213.5 Pa, falling within the range of progressive inactivation of the enzyme cellulase reported by Reese et al.4 These computed values should be taken into consideration in industrial practice.

Figure 10. HerschelBulkley model: time evolution of the consistency index, kHB, the flow behavior index, nHB, and yield stress, τ0HB, for an initial concentration of 18.5% by weight (triangles) and 27.5% by weight (squares) resulting from the best fitting procedure.

Figure 10 shows the time evolution of the HerschelBulkley parameters during the enzymatic hydrolysis. In all the tests, the yield stress, τ0HB, shows an overall decrease from values of between 174 and 213 Pa, in the first hour, to about zero at the end of the hydrolysis process; this is a direct consequence of the reduction in solids. As far as the consistency index is concerned, there is an overall increase from about zero to 0.258 Pa 3 s for an initial concentration of pretreated Arundo of 18.5% by weight, whereas for 27.5% solids, there is an increase from about zero to 1.16 Pa 3 s during the first 2 hours, and then they decrease until a final value of 0.0242 Pa 3 s is reached. For both materials, the decrease in the flow behavior index with time, beginning with values greater than 2 and reaching values close to or smaller than unity after 4 hours, is a consequence of a decrease in the shearthickening nature, moving to a Newtonian behavior. As no references have been found in the literature about rheological data of pretreated Arundo, it was only possible to compare our results with the experimental ones obtained by other authors for different materials, such as pretreated corn stover with dilute sulphuric acid.57 The yield stress values and consistency indices obtained through CFD are within the

7. CONCLUSIONS The present paper shows the time evolution of the rheological parameters of pretreated Arundo with steam explosion during enzymatic hydrolysis, estimated from experimental data, in conjunction with CFD simulations using HerschelBulkley as the rheological model. Although the used experimental data are characterized by a limited range of stirring rates (50200 rpm), the obtained parameter estimates were successful and the results are consistent with other works published in the literature on similar systems. The three-parameter HerschelBulkley model was found to be able to describe the nonlinear rheological behavior of pretreated Arundo slurries during enzymatic hydrolysis and in particular the transition from shear-thickening to a Newtonian behavior. The estimation of the HerschelBulkley parameters shows that the yield stress decreases with time, as a consequence of the reduction in the solid content, whereas, the consistency index increases in time, reflecting a change in the physicochemical characteristics of the slurry. The decrease of the flow behavior index with time, reaching values close to or smaller than unity, is a consequence of the transition from a shear-thickening behavior to a Newtonian one. Future steps of this work will involve the validation of our method using biomass reactors and testing materials different from those used in this study. ’ AUTHOR INFORMATION Corresponding Author

*Tel.: +39-011.090.4710; fax: +39-011-090.4699; e-mail: debora. fi[email protected].

’ ACKNOWLEDGMENT This work has been carried out in collaboration with Chemtex Italia S.r.l., in the framework of the PRO.E.SA project, funded by the Regione Piemonte, which is gratefully acknowledged for the support. ’ DEFINITIONS A = model parameter for the f function, m3 B = model parameter for the f function, dimensionless C = model parameter for the f function, m3 D = model parameter for the f function, m3 E = model parameter for the f function, dimensionless 7524



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Di = stirrer diameter, m g = gravitational acceleration, m/s2 kHB = HerschelBulkley model, consistency index, Pa 3 sn N = stirring rate, 1/s nHB = HerschelBulkley model, flow behavior index, dimensionless Np = Power number, dimensionless P = power consumption, W Re = Reynolds number, dimensionless u = fluid velocity, m/s ur = relative fluid velocity, m/s

’ GREEK SYMBOLS μ = Newtonian viscosity, Pa 3 s η = non-Newtonian viscosity, Pa 3 s F = density, kg/m3 τ = shear stress, Pa τ0HB = HerschelBulkley model, yield stress, Pa γ_ = shear rate, 1/s ’ SUBSCRIPTS i, j = tensor form x = coordinate ’ REFERENCES (1) Hodge, D. B.; Karim, M. N.; Schell, D. J.; McMillan, J. D. ModelBased fed-batch for high-solids enzymatic cellulose hydrolysis. Appl. Biochem. Biotechnol. 2008, 152 (1), 88–107. (2) Jorgensen, H.; Vibe-Pedersen, J.; Larsen, J.; Felby, C. Liquefaction of lignocellulose at high-solids concentrations. Biotechnol. Bioeng. 2006, 96 (5), 862–870. (3) Zimbardi, F.; Viola, E.; Gallifuoco, A.; de Bari, I.; Cantarella, M.; Barisano, D.; Braccio, G. Overview of the ethanol production, Report ENEA and University of L’Aquila. 2002. (4) Reese, E. T.; Ryu, D. Y. Shear inactivation of cellulase of Trichoderma reesei. Enzyme Microb. Technol. 1980, 2 (3), 239–240. (5) Pimenova, N. V.; Hanley, T. R. Effect of corn stover concentration on rheological characteristics. Appl. Biochem. Biotechnol. 2004, 114 (13), 347–360. (6) Viamajala, S.; McMillan, J. D.; Schell, D. J.; Elander, R. T. Rheology of corn stover slurries at high solids concentrations - Effects of saccharification and particle size. Bioresour. Technol. 2009, 100 (2), 925–934. (7) Roche, C. M.; Dibble, C. J.; Knutsen, J. S.; Stickel, J. J.; Iberatore, M. W. Particle concentration and yield stress of biomass slurries during enzymatic hydrolysis at high-solids loadings. Biotechnol. Bioeng. 2009, 104 (2), 290–300. (8) Savreux, F.; Jai, P.; Magnin, A. Viscoplastic fluid mixing in a rotating tank. Chem. Eng. Sci. 2007, 62 (8), 2290–2301. (9) Kelly, W.; Gigas, B. Using CFD to predict the behaviour of power law fluids near axial-flow impellers operating in the transitional flow regime. Chem. Eng. Sci. 2003, 58, 2141–2152. (10) Zhang, M.; Zhang, L.; Jiang, B.; Yin, Y.; Li, X. Calculation of Metzner Constant for Double Helical Ribbon Impeller by Computational Fluid Dynamic Method. Chinese J. Chem. Eng. 2008, 16 (5), 686–692. (11) Dular, M.; Bajcar, T.; Slemenik-Perse, L.; Zumer, M.; Sirok, B. Numerical simulation and experimental study of non-Newtonian mixing flow with a free surface. Braz. J. Chem. Eng. 2006, 23 (4), 473–486. (12) Prajapati, P.; Ein-Mozaffari, F. CFD Investigation of the mixing of yield-Pseudoplastic fluids with anchor impellers. Chem. Eng. Technol. 2009, 32 (8), 1211–1218. 7525


Enzymatic Hydrolysis of Lignocellulosic Biomasses via CFD and

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