One of the approaches highlighted in Chapter 2 for accomplishing process synthe­sis consists of the application of the principles of topologic thermodynamics (see Section 2.2.6). In the work mentioned above (Sanchez et al., 2006), a preliminary short-cut method to analyze the extractive co-fermentation was developed. In par­ticular, the main components (substrate-water-product-solvent) can be represented in a quaternary diagram in order to locate initial conditions. For representation of the reaction trajectory and considering that the overall fermentation process is irreversible, a stoichiometric approach was used. Therefore, the fermentation is described as follows:

C6Hi2O6 г > 2C2H5OH + 2CO2

Glucose Ethanol

ЗС5Н10О5 Z mobi“s > 5C2H5OH + 5CO2

Xylose Ethanol

Having determined the proportion between substrate (expressed as the sum of both sugars) and ethanol, using a maximum stoichiometric yield from substrate of 0.511 g/g, the inlet conditions are located in the ternary diagram water-ethanol — я-dodecanol, where the liquid-liquid equilibrium is represented as well. Finally, the balance lines corresponding to the operating conditions for the steady-states were drawn in order to define the zone where the performance of extractive fer­mentation process is more stable and advantageous. The procedure for locating the steady-states in the concentration simplex using a short-cut approach is illustrated in Figure 9.17. The process is ideally divided into two steps: microbial conversion and liquid-liquid extraction. The initial sugar concentration is represented in the quaternary diagram by the point A (see Figure 9.17a). The transformation of sugars into ethanol is shown by the line AB, B being the state of the system where the total amount of produced ethanol is represented. This point is the starting mixture for

(a) (b)

the liquid-liquid equilibrium. The line BC represents the addition of я-dodecanol to the aqueous medium containing ethanol (Figure 9.17b). This line lies in the ternary diagram water-ethanol-«-dodecanol, where the zone of heterogeneous mixtures is also drawn. Vertical lines represent the geometric place of points that represent the operating conditions related to the solvent feed stream/aqueous feed stream (R). The intersection of these vertical lines with the line BC (point D) represents the the­oretical conditions corresponding to the mixtures before the separation in phases (the equivalent to the feed mixture in a liquid extractor). Through tie lines, the com­positions of the extract (E) and the raffinate (W) are obtained. These correspond to the compositions of solvent phase effluent and aqueous phase effluent, respectively. For identical inlet concentrations of sugars in the aqueous stream, the position of the starting point B changes when the inlet dilution rate varies. For example, if DAi increases, the new line B’C will lie below the original line BC, which it is explained by a major dilution of ethanol and, therefore, the line approaches the bottom edge of the ternary diagram.

Using this short-cut approach, the zone of feasible operating points can be easily determined. Let us analyze the extreme case when the feed aqueous stream has the maximum allowable concentration of sugars. From the fermentation stoichiometry, this condition corresponds to an inlet concentration in the feed aqueous stream of about 600 g/L of total sugars. Assuming a 95% yield, the total amount of etha­nol that could be produced is 0.486 g/g, which implies a theoretical starting etha­nol concentration of 291.6 g/L (approximately an ethanol mass fraction of 0.42). This value determines the position of the substrate solubility boundary (point H in Figure 9.18). Because the concentration of ethanol in the aqueous phase (raffinate) should not be above the ethanol inhibition boundary (approximately 10% w/w), the operation conditions represented by the line R3 should be such that the ethanol content in the raffinate corresponding to point D" be equal to the ethanol content of the point I to avoid product inhibition. In this way, the area delimited by the points R3D"EK is the zone of feasible steady-states for given conditions of the process

with the maximum concentrations of sugars in the culture broth. For a given inlet dilution rate of 0.1 h-1, an R ratio of 3.6 (line R2), and a working volume of 1 L, the location of the point D’ and the corresponding composition of the extract, can be found. In this case, the ethanol mass content of the extract and raffinate is of 7.5% and 9.0%, respectively, resulting in a total ethanol productivity of 26.4 g/(L x h). The productivity calculated by the rigorous model using ModELL-R is 28.86 g/(L x h). Hence, the developed short-cut method allows one to determine the feasibility of operating parameters and an estimation of the productivities.

The delimited zones can be taken into account for the development of a pre­liminary strategy of optimization. Since the region of feasible steady-states was determined in the ternary diagram (see Figure 9.18), the values range of such manipulating variables as inlet dilution rate, the R ratio, and the concentration of the sugars in the inlet aqueous stream is known and can be bounded for solving an optimization algorithm. The GAMS system was employed to find the optimal value of above-mentioned variables that maximize the total ethanol productivity using the nonlinear programming (NLP) solver CONOPT3. With this aim, liquid — liquid equilibrium relationships were simplified for generating a way to evaluate the ethanol concentration in both phases during extractive fermentation. For this, the distribution coefficient &EtOH was assumed to be linearly dependent of the total concentration of substrates. A good concordance with the data obtained from the ModELL-R was achieved, especially for high values of substrates concentration. The results of this optimization are presented in Table 9.11. From this table, it is evi­dent that calculated optimal variables are indeed in the zone predicted by the short­cut method, and the predicted increase in total productivity is effectively attained, as is shown by the rigorous model.

For a more accurate solution of the optimization problem, the rigorous descrip­tion of the equilibrium model should be coupled or embedded into the GAMS code. Further analysis of this extractive fermentation process could include the formula­tion of an objective function that considers, besides ethanol productivity, other per­formance indexes like the conversion of sugars (better utilization of the feedstock), or the amount of generated wastewater (evaluation of environmental impact). These issues are very significant considering process synthesis procedures. After obtain­ing a global picture of the space of operating conditions and their optimal values for the studied process, experimental runs should be performed in order to confirm the validity of the given theoretical approach. In this manner, the acquired insight of the process will make possible the reduction of expensive experimental work in the search of the optimal operation.