The use of mathematical modeling and computer simulation has become prevalent throughout the petrochemical process industries. Models that are based on scientifi- cally demonstrated chemical and physical mechanisms, that is, “mechanistic models,”
allow engineers to design and test unit operations and their integrationin silicowith only limited supporting laboratory and pilot-scale experimentation. This has not yet been possible for biomass conversion processes, excepting techno-economic analyses that rely on empirical relationships. Mechanistic modeling of biochemical conver- sion of biomass to chemicals and fuels generally, including enzymatic hydrolysis specifically, is challenging for several reasons: the presence of multiple phases, non- Newtonian rheology, multiple reacting species, and phenomena occurring on multiple length and time scales. Over the last few years, progress has been made to address some of these challenges for enzymatic hydrolysis.
There has been a substantial effort to model the kinetics of enzymatic hydrolysis of cellulose and (pretreated) lignocellulosic substrates. Bansal et al. (2009) provide a comprehensive review of many of the models that have been developed. Most of these models are strictly empirical or based on highly simplified Michaelis–Menten concepts. Unfortunately, the assumptions commonly used with Michaelis–Menten kinetics models, namely, that reaction takes place in solution and there is a single
substrate species that is completely accessible, are not valid for insoluble, polymeric cellulose. Hence, these models are limited to the parameter space from which they were developed and provide few insights into the underlying mechanisms of the reaction. A couple of models treat cellulose as polymers with a distribution of chain lengths (Okazaki and Mooyoung, 1978; Zhang and Lynd, 2006), but do not address the insoluble structure of crystalline cellulose.
Recently, a few groups have independently developed mechanistic models for the enzymatic hydrolysis of cellulose that account for the distribution of cellulose degree of polymerization (DP), the changing morphology and accessibility of insoluble cel- lulose, and the differing functionality of the component cellulase enzymes (Zhou et al., 2009a,b; Levine et al., 2010; Zhou et al., 2010; Levine et al., 2011; Griggs et al., 2012a,b). The inhibition of enzymes by their products have also been included in some of the models (Griggs et al., 2012b). Although the specific features and math- ematical implementation for these three models are different, all predict that surface accessibility to enzymes is the rate-limiting phenomenon. These mechanistic mod- els are also able to predict synergism between endo- and exo-acting cellulases and show that the synergism changes with the DP of the cellulose substrate. Figure 4.3
BMCC Cotton linter
Relative amount of polymer Relative amount of polymer
Degree of polymerization Degree of polymerization
Control Control
FIGURE 4.3 Qualitative comparison of mechanistic model predictions (top row, from Griggs et al. (2012b)) with experimental results (bottom row, from Srisodsuk et al. (1998)) for the changing DP distribution of cellulose during enzymatic hydrolysis by EGIand CBHI. The left column compares results for bacterial microcrystalline cellulose (BMCC) with a relatively low initial DP, and the right column compares results for cotton linter with a relatively high initial DP. (For a color version, see the color plate section.)
shows simulated and experimentally measured DP distributions during enzymatic hydrolysis for two different substrates. For an initially low DP substrate (bacterial microcrystalline cellulose), there is little-to-no right-to-left shift in the DP distribu- tion. However, for an initially high DP substrate (cotton linter), there is a shift in the DP distribution to lower DP at early times. The mechanistic model predictions quali- tatively match the experimental results. Griggs et al. (2012b) suggest that for high DP substrates, endoglucanases (EGI) hydrolyzeβ-(1,4)-glycosidic bonds in the middle of the cellulose polymers, making chain ends available to exoglucanases (CBHI).
Once the DP of the cellulose is sufficiently reduced, the activity of exoglucanases dominates the digestion, and the total mass of the cellulose population is reduced.
Although these kinetic mechanistic models represent a significant step forward in our ability to predict transient behavior and process yields for the enzymatic hydrolysis of cellulose, they still fall short in several ways. Further model devel- opment will be needed to account for the presence of lignin and hemicellulose in lignocellulosic substrates. Furthermore, pretreated lignocellulosic biomass can vary considerably depending on the feedstock and pretreatment conditions. It may prove difficult to develop a universal mechanistic model that applies for all industrially rele- vant biomass substrates, but some progress can be made by incorporating measurable chemical and physical properties of the substrates, such as chemical composition and particle morphology. Recently, Luterbacher et al. (2012) developed a kinetic model that accounts for the pore-size distribution of biomass particles. Some experimental studies have suggested that processive enzymes such as cellobiohydrolase may get
“stuck” (Jalak and Valjamae, 2010), and others have suggested that cellulases may be spatially confined on the cellulose surface (Xu and Ding, 2007). Further work is needed to verify these phenomena and effectively incorporate them into mechanistic models, if necessary. As discussed in section 4.2, there exist many different cellulase, hemicellulase, and accessory enzymes with varying modes of action. As commercial enzyme preparations include more of these enzymes in appreciable concentrations, it may be necessary to explicitly include their action in mechanistic models. How- ever, as additional features are added to the mechanistic models, their complexity increases proportionally. Model developers and users should consider carefully the need to balance the level of detail needed to describe the phenomena of interest and the mathematical complexity and computational time needed for performing simulations.
In addition to models for the kinetics of enzymatic hydrolysis reactions, models for the transport of biomass slurries within reactors are needed. Computational fluid dynamics (CFD) can be used simulate convective and diffusive transport in process vessels, but only a few researchers have applied CFD to the enzymatic hydrolysis of lignocellulosic biomass (Um and Hanley, 2008; Shao et al., 2010; Carvajal et al., 2012), perhaps because it has been challenging to determine appropriate constitutive equations for use in CFD software. The CFD modeling approach may differ depend- ing on the concentration of biomass solids. For low solids concentrations, settling suspension models with a Newtonian suspending liquid may be used. The rheology will be non-Newtonian at higher solids concentrations, and simple yield stress and power law models, for example, the Herschel–Bulkley model, may be used.
In order to conduct comprehensive computer simulations of enzymatic hydrolysis for the purposes of performing reactor design and evaluating scale-up, it will be necessary to couple a mechanistic kinetics model with an appropriate CFD model.
To the authors’ knowledge, this has not yet been accomplished, and it could prove to be quite challenging. The number of independent equations in a CFD model for a reasonably complex vessel can be on the order of 106. If the mechanistic kinetics model has roughly 103equations, then the total system size will be on the order of 109. Solving such a system will require a high performance computer utilizing a parallel architecture. In addition, reaction and mixing may occur at different timescales, further complicating the implementation. Despite these challenges, the potential benefits that can be obtained from coupled transport and kinetics simulations, namely, accelerated technology development and reduced commercialization risk, should motivate further R&D in this area.