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 equationoriented simulators are used, or optimizationbased 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



















Nomenclature of the Variables and Kinetic Parameters Involved in Equations Derived from the Model of south et al. (1995)
symbol 
Remark 
symbol 
Remark 
B 
Input stream to the pervaporator, l/h 
n 
Exponent of the declining substrate reactivity, dimensionless 
Bg 
pglucosidase concentration in solution, U/L 
P 
Ethanol concentration, g/L 
c 
Conversion independent component in rate function, 1/h 
Po 
Initial ethanol concentration, g/L 
C 
Cellobiose concentration, g/L 
Q 
Output stream for pervaporation (permeate), L/h 
Ci 
Concentration of the ith component 
R 
Recirculation (retentate) stream from pervaporation unit to reactor, L/h 
Co 
Initial cellobiose concentration, g/L 
ri 
Rate of formation of compound i, g/(L x h) 
ES 
Concentration of cellulosecellulase complex, U/L 
S 
Cellulose component of the biomass substrate remaining, g/L 
F 
Feed reactor stream, L/h 
So 
Initial cellulose component of the biomass substrate, g/L 
G 
Glucose concentration, g/L 
V 
Reaction volume, L 
Go 
Initial glucose concentration, g/L 
W 
Residual flow, L/h 
k 
Hydrolysis rate constant, g/L 
x 
Fractional reactor cellulose conversion, dimensionless 
kc 
Rate constant for hydrolysis of cellobiose to glucose, g/(Uxh) 
X 
Cell concentration, g/L 
kG 
Monod constant, g/L 
Xo 
Initial cell concentration, g/L 
kC/G 
Inhibition of cellobiose hydrolysis by glucose, g/L 
Yx/g 
Cell yield per substrate consumed, dimensionless 
kS/C 
Inhibition of cellulose hydrolysis by cellobiose, g/L 
yp/g 
Ethanol yield per substrate consumed, dimensionless 
kS/P 
Inhibition of cellulose hydrolysis by ethanol, g/L 
a 
Separation factor in pervaporation 
Ks 
Adsorption constant for cellulosic 
4s 
Specific capacity of cellulosic 
fraction of biomass, L/U 
component for cellulose, U/g 

Km subindex 
Adsorption constant for pglucosidase for cellobiose, g/L 
Emax 
Maximum cell growth rate, 1/h 
i 
Any of the substances involved in the fermentation 

0 P 
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 17:797803.
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:
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 NewtonRaphson 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.