Case Study. Modeling of SSF of Biomass in Batch and Continuous Regime

The importance of modeling SSF processes is invaluable considering the design of fuel ethanol production processes employing lignocellulosic materials as feedstocks. In a previous work (Sanchez et al., 2005), the analysis of SSF for conversion of cellulose into ethanol was performed in both batch and continu­ous regimes. The kinetic model of such a process was based on the mathemati­cal description developed by South et al. (1995). However, considering that this model will be employed in subsequent procedures and algorithms for process synthesis of ethanol production, the expressions were simplified to not add more complexity to the calculations to be performed during process synthesis and opti­mization procedures. This is justified because process synthesis tools deal with many alternative process flowsheets. These flowsheets involve all the processing steps for conversion of feedstocks into products. As pointed out by Grossmann et al. (2000), there exist different levels of detail for the mathematical description of each unit processes and operations involved in each flowsheet (see Chapter 2). In fact, for the task of process synthesis, it is not desirable to consider models with a higher degree of detail especially if equation-oriented simulators are used, or optimization-based process synthesis procedures are applied. The simplification of the kinetic model mentioned above wasn’t meant to consider its population and adsorption components, but to take into account the rigorous description of the kinetic processes involved.

For simulation of the batch SSF process, the rate equations were extracted from South et al. (1995). Equations (9.1) and (9.2) correspond to the enzymatic hydrolysis

of cellulose and cellobiose, respectively. Equations (9.3) through (9.5) represent cell biomass production, glucose uptake and formation, and ethanol biosynthesis, respectively:












The nomenclature of all the variables and kinetic parameters involved in the above equations are presented in Table 9.3. In Equation (9.1), the last two terms represent the inhibition by cellobiose and ethanol. These terms influence all the rate equation directly or indirectly. Similar expressions can be observed in Equation (9.2) for the inhibitory effect of glucose on the P-glucosidase activity. In Equation (9.3), the expression for biomass formation rate has a lowering term due to high ethanol concentrations present in the broth. For this case, a cellulose conversion (x) of 0.70 was preset. The general mass balance expression for each one of i components (cellulose S, cellobiuse C, cell biomass X, glucose G, and ethanol P) is:


d (Ci) = dt Г




In all cases, a lignocellulosic substrate with cellulose loading of 60 g/L and initial concentrations of cellobiose, biomass, glucose, and ethanol of 0, 1, 8.5, and 0 g/L, respectively, were considered. The selected kinetic model involved the use of T. reesei cellulases and fermentation by S. cerevisiae, according to South et al. (1995). The system of five nonlinear ordinary differential equations was solved by fourth-order Runge-Kutta method using Matlab™ (MathWorks, Inc., USA) with the initial values mentioned above and for a process time of 72 h. Ethanol pro­ductivity and product yield were calculated for this type of regime. The parameter values used for solving the kinetic model can be found in South et al. (1995).




Nomenclature of the Variables and Kinetic Parameters Involved in Equations Derived from the Model of south et al. (1995)






Input stream to the pervaporator, l/h


Exponent of the declining substrate reactivity, dimensionless


p-glucosidase concentration in solution, U/L


Ethanol concentration, g/L


Conversion independent component in rate function, 1/h


Initial ethanol concentration, g/L


Cellobiose concentration, g/L


Output stream for pervaporation (permeate), L/h


Concentration of the i-th component


Recirculation (retentate) stream from pervaporation unit to reactor, L/h


Initial cellobiose concentration, g/L


Rate of formation of compound i,

g/(L x h)


Concentration of cellulose-cellulase complex, U/L


Cellulose component of the biomass substrate remaining, g/L


Feed reactor stream, L/h


Initial cellulose component of the biomass substrate, g/L


Glucose concentration, g/L


Reaction volume, L


Initial glucose concentration, g/L


Residual flow, L/h


Hydrolysis rate constant, g/L


Fractional reactor cellulose conversion, dimensionless


Rate constant for hydrolysis of cellobiose to glucose, g/(Uxh)


Cell concentration, g/L


Monod constant, g/L


Initial cell concentration, g/L


Inhibition of cellobiose hydrolysis

by glucose, g/L


Cell yield per substrate consumed, dimensionless


Inhibition of cellulose hydrolysis by cellobiose, g/L


Ethanol yield per substrate consumed, dimensionless


Inhibition of cellulose hydrolysis by ethanol, g/L


Separation factor in pervaporation


Adsorption constant for cellulosic


Specific capacity of cellulosic

fraction of biomass, L/U

component for cellulose, U/g



Adsorption constant for p-glucosidase for cellobiose, g/L


Maximum cell growth rate, 1/h


Any of the substances involved in the fermentation



Initial concentration in batch processes or feed concentration in continuous processes Product (ethanol)

Source: Adapted from South, C. R., D. A.L. Hogsett, and L. R. Lynd. 1995. Enzyme and Microbial Technology 17:797-803.

FIGURE 9.5 Behavior of batch SSF process for ethanol production from cellulose.

The results for batch SSF process can be seen in Figure 9.5. The final cellu­lose concentration was 28.6 g/L and the ethanol concentration reached at the end of fermentation was 17.5 g/L. The amounts of cellobiose and glucose when the cultivation was finished were near zero, which shows the efficiency of the com­bined process and the neutralization of the inhibitory effects of glucose on cel — lulases. In the case of the SHF process, the accumulating glucose in the medium during cellulose saccharification leads to reduced conversion of cellulose and hydrolyzates with lower concentrations of fermentable sugars. In contrast, dur­ing the SSF process, the accumulation of ethanol in the medium can inhibit the growth rate and, therefore, the ethanol production rate according to the kinetic expressions on which the model was based. The productivity attained by the batch SSF process was 0.292 g/(L x h) and the ethanol yield was 0.454 g/g, cal­culated at 48 h of cultivation.

For solving the model of an SSF process in a CSTR, the mass balance for each of the i substances involved in the process (cellulose, cellobiose, biomass, glucose, and ethanol) was considered according to following equation:

Подпись: (9.7)


FCi0 — WCi + Vrt = 0

Taking into consideration that Equations (9.1) through (9.5) describe the forma­tion or consumption rate of each component, a system of five nonlinear algebraic equations with five unknowns was obtained by applying equation (9.7). For solving this system, the Newton-Raphson algorithm was used with the same initial con­centrations used for the SSF process in batch regime. Equation (9.1) includes a term for cellulose conversion (x) that in the original paper of South et al. (1995) is a func­tion of mean residence time of particulate matter of cellulose. In this case study, the conversion was set to a value of 0.70 with the use of a CSTR for carrying out both transformations (cellulose hydrolysis and ethanol fermentation) and, therefore, assuming an intensive mixing of the reaction volume.

The results obtained for continuous SSF process with a mean residence time of 72 h showed that the cellulose had a more complete conversion and that the ethanol was produced in higher amounts. The concentrations of cellulose and ethanol in the outlet stream were 10.7 and 24.9 g/L, respectively. The biomass concentration in the exiting stream was 5.6 g/L, which is comparable with that of the corresponding batch process. The concentrations of the other involved components in the effluent of the fermenter were near zero, demonstrating the good performance of the SSF process. In this case, the concentration of cellulose in the feed stream was 60 g/L. The productivity attained by the continuous SSF process was 0.345 g/(L x h) and the ethanol yield was 0.506 g/g showing favorable performance indexes related to the batch SSF process.

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