A significant number of papers and works related to cellulose hydrolysis have been published. For instance, the reader can consult the reviews of Lynd et al. (2002) and Zhang and Lynd (2004) on this theme. The description of cellulose degradation, in particular, the kinetics of cellulose hydrolysis, is difficult due to the influence of factors such as (Bernardez et al., 1993; Kadam et al., 2004; Meunier-Goddik and Penner, 1999; Philippidis and Hatzis, 1997; Philippidis et al., 1993; Zhang and Lynd, 2004):

• Adsorption of the enzymes to the substrate particles.

• Presence of interactions between the lignin and enzymes that do not lead to sugars formation.

• Decrease of cellulose hydrolysis as substrate conversion progresses.

• Enzyme dosage.

• Synergistic action of endoglucanases and cellobiohydrolases.

• Need of supplementing the cellulases with P-glucosidase to diminish cellulase inhibition by cellobiose formed.

• P-glucosidase inhibition by the glucose formed.

• Solids load to the reactor, among others.

The importance of cellulose hydrolysis description is recognized considering that the mathematical modeling of this process allows for developing appropriate simulation tools to be used during process synthesis procedures. Such institutions as the NREL have funded projects regarding the modeling of cellulose break­down, sugar formation, and ethanolic fermentation in order to assess several alter­native technological configurations of the biomass-to-ethanol process. This was the case of the work of South et al. (1995) dealing with the hydrolysis of cellulose contained in pretreated wood that, in turn, used the experimental data obtained in a previous work by these same authors using commercial fungal cellulase (South et al., 1993). In this study, a kinetic model, considering the cellulose conversion and the formation and disappearance of cellobiose and glucose, was developed. In addition, a Langmuir-type model taking into account the adsorption of cel — lulases on the solid particles of cellulose and lignin and expressions describing the dependence of cellulose conversion on the residence time of nonsoluble solid particles of biomass were considered.

The adsorption of cellulases to the particles present in the solid fraction of pretreated lignocellulosic biomass should be modeled in a suitable way to obtain results useful during the design of cellulosic ethanol production. This is not the case for starch saccharification considering that the amylases attack their substrate in a soluble form after starch cooking. In contrast, during the first steps of ligno — cellulosic hydrolysis, the cellulases are added to a suspension of cellulose and lignin particles. The Langmuir model is widely used for description of adsorption processes involving cellulases taking into account the good adjustment to experi­mental data in most cases (Cardona and Sanchez, 2007). In addition, it represents a simple mechanistic model that can be used to compare kinetic properties of various cellulase-cellulose systems. Kadam et al. (2004) employed a Langmuir — type isotherm to describe the enzymatic hydrolysis of cellulose for the case of dilute-acid pretreated corn stover. In this model, the inhibition effect on cellulases of other sugars present in the biomass hydrolyzate as xylose was considered as well as the effect of temperature (through the Arrhenius equation) and the dosage of P-glucosidase. In an early work, Bernardez et al. (1993) studied the adsorption process of complexed cellulase systems (cellulosomes) released by the anaerobic thermophilic bacterium Clostridium thermocellum onto crystalline cellulose, pretreated wood, and lignin employing the Langmuir description. Nevertheless, some experimental data indicate that the negative effect of lignin content in the hydrolyzate is not principally due to the enzyme partitioning between cellulose and lignin, suggesting that lignin hinders saccharification by physically limiting the enzyme accessibility of the cellulose (Meunier-Goddik and Penner, 1999). Hence, more structure-oriented modeling is required to gain insight on biomass hydrolyzate’s hydrolysis and its optimal operating conditions. Other models have been proposed since the union of the cellulases to the cellulose does not meet all the assumptions inherent to the Langmuir model. To this end, two-site adsorption models, Freundlich isotherms, and combined Langmuir-Freundlich isotherms have been proposed (Zhang and Lynd, 2004). Lynd et al. (2002) present in their wide review about the microbial cellulose utilization, a compilation of values of adsorption parameters for cellulases isolated from different microorganism and for diverse substrates. In that work, the kinetic constants for cellulose utilization by different microorganisms are reported as well. On the other hand, it has been shown that the intensity of the agitation in batch reactors has little effect over cel­lulose hydrolysis when cellulose particles are suspended. Based on the analysis of the kinetic constants and on experimental data, it was concluded that the external mass transfer is not a limiting factor of the global process of hydrolysis. However, when the internal area is much greater than the external one, as in the case of most cellulosic substrates, it is probable that cellulases can remain entrapped in the pores provoking lower hydrolysis rates (Zhang and Lynd, 2004). These con­siderations are essential when mathematical representations of cellulose saccha­rification are developed. On the other hand, some kinetic studies for cellulose hydrolysis highlight the significant effect the enzyme dosage has on glucose yield. In particular, Schell et al. (1999) accomplished the saccharification of dilute-acid pretreated Douglas fir and obtained data from which was derived a useful empiri­cal model to calculate the glucose yield as well as to formulate a kinetic cellulose hydrolysis model.

Zhang and Lynd (2004) reviewed in detail the works concerning the model­ing of cellulose hydrolysis and point out that most of proposed models for the

design of industrial systems fall in the category of semimechanistic models, i. e., models taking into account the substrate concentration or one of the enzymatic activities as a state variable. These models meet the requirement of including the minimum of necessary information for the description of the process (Cardona and Sanchez, 2007). These authors emphasize that most kinetic models do not consider the changes in the hydrolysis rate during the course of the reaction, and that those models that do this, are based mainly on empirically adjusted param­eters and not on a mechanistic approach. For instance, the model of a simultane­ous saccharification and fermentation (SSF, to be analyzed in Chapter 9) process developed for the case of nonpretreated wastepaper using commercial cellulases and S. cerevisiae for both batch and two-stage continuous regimes (Philippidis and Hatzis, 1997) made use of an exponential decay term to describe the time — dependent decline in the rate of cellulose hydrolysis. With the help of an exhaus­tive sensitivity analysis, the model showed that further improvements in the fermentation stage do not have great influence on ethanol yield. In contrast, the digestibility of substrate (as a result of pretreatment), cellulase dosage, specific activity, and composition have a great effect on ethanol yield. This confirms that major research efforts should be oriented to the development of more effective pretreatment methods and the production of cellulases with higher specific activ­ity (Cardona and Sanchez, 2007).

Half of the mechanistic models cited by Zhang and Lynd (2004) are based on the Michaelis-Menten model, which is valid when the limiting substrate is in excess relative to the enzyme. In addition, competitive inhibition is the mecha­nism most found in the literature, although a combination of both noncompeti­tive and competitive mechanisms for different inhibition effects can be found, as are analyzed in the work of Philippidis et al. (1993). Due to the importance of modeling, these authors highlight the need for developing functional models that include the adsorption process, several state variables for substrate besides the concentration (e. g., polymerization degree or amount of amorphous cellulose), and multiple enzymatic activities.