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SL are BS that are produced commonly by liquid fermentation (LF) using glucose as the hydrophilic carbon source and oleic acid (C18:1) as the hydrophobic source [95]. Glucose can be replaced by sugar cane or sugar beet juices, which have high contents of sugars and nitrogen and avoid the use of the expensive yeast extract and urea for the fermentation media [96]. Some potential hydrophobic sources are solid at fermentation temperature (e.g. stearic acid, m.p. = 69.3 °C), complicating their use as substrates in these liquid processes. In such a case, solid‐state fermentation (SSF) is a potentially useful alternative. Furthermore, the SSF avoids the problems that generally occur during the production of SL by liquid fermentation, such as foaming and viscosity increase [96].

BS production in liquid media is carried out with aeration and forced agitation. However, this causes problems when BS production starts because a large amount of foam is generated. Moreover, there is a tendency for microorganisms to accumulate within the foam, eliminating cells from the culture medium. Also, the presence of foam increases the risk of cross‐contamination and reduces the efficiency of oxygen transfer between the liquid and gas phase in the bioreactor [97]. The use of antifoams has disadvantages. These can be toxic to microorganisms, have high costs, and are extra‐components that must be separated from the BS during the purification processes [98].

Scientific literature about BS shows a clear tendency in the use of liquid fermentations over SSF, being batch processes at laboratory scale the most used methods. Nonetheless, recent studies, including our group in Mexico, point out that SSF is an advantageous alternative for BS production since oxygen transfers are efficient, and no foaming problems are seen during fermentations, especially when production yields are greater than 0.3 g_BS/kg_dr.

Our research group has some experience with the use of non‐pathogenic microorganisms for producing SL by SSF both at the laboratory and pilot level. Using glucose, vegetable oils, and solid supports of natural origin, production of BS in our hands has been monitored from respirometry studies using an analytical device patented by our group [99] without disturbing the culture. For example, Figure 2.6 shows the carbon dioxide production rate (CDPR) recorded in real‐time during BS production. This measurement is an invaluable tool for the process because it allows us to make decisions in real‐time. In this example, it is seen an imminent increase of CDPR (ca 1.2) followed by a rapid decrease (ca 0.8) that stabilizes in a plateau to drop off subsequently. This is the common behavior observed in many of our productive fermentation. In Figure 2.7, it is observed that O₂ consumption rate is similar to CO₂ production rate during the first days of incubation. After that, greater O₂ consumption is observed with respect to CO₂ production (Figure 2.7). This is reflected in a decrease in respiratory quotient (RQ, Figure 2.8).

Figure 2.6 CO₂ formation rate (empty symbols) and O₂ uptake rate (full symbols) during the production of SL in SSF.

Figure 2.7 Total CO₂ formation (empty symbols) and O₂ uptake (full symbols) during sophorolipid production in SSF.

The RQ (Figure 2.8) is less than 1.0 during the entire cultivation time, and the maximum value of the RQ (0.82 mol of CO₂/mol of O₂) is observed around 36 hours of incubation. These RQ values could be explained by the oxidation of glucose and suggest that, during the first days, fatty acids could be mainly used for synthesizing BS. Literature indicates that fatty acids are hydroxylated and incorporated directly into the synthesis of BS [100], whereas, after glucose depletion, fatty acids can be mainly used as energy source assimilated via β‐oxidation.

Figure 2.8 Respiratory quotient observed during SL production by SSF.

Figure 2.9 Evolution of pH during the production de sophorolipids.

Another parameter that can be easily measured to follow BS production is pH. The change of pH values over time is shown in Figure 2.9. pH values show a significant decrease during the first days of cultivation (from 6 to 3) and then remain. This behavior is similar in liquid fermentation [100]. The addition of alkali has been proposed to control the pH values around 3.5, which are optimal for sophorolipid production [101]. However, for SSF, it is not feasible due to the lack of homogeneity.

Figure 2.10 Kinetics for sophorolipid production (black) and substrates (○, □) uptake in SSF.

Figure 2.10 shows the consumption of hydrophilic and lipophilic substrates over time. Glucose consumption is recorded around the fifth day of cultivation; at this point, the consumption of the lipophilic substrate is around 65%. However, the lipophilic substrate is still consumed until the end of incubation, where consumption of around 90% was observed. It seems that lipophilic substrate remains as the only carbon source available and is used to obtain energy, which is reflected in the low increase in BS production registered from fifth day of incubation.

It is important to mention that the decrease in the production of BS could be correlated with the decrease in CDPR observed by respirometry (Figure 2.10). In this case, CDPR is a variable of the process determining the time of the maximum production of BS according to the physiological state of the yeasts in the SSF.

From the analysis of the experimental data, three balance equations for the substrate’s consumption are proposed based on modified first‐order decay kinetics. These three equations are coupled to the formation of BS through the conversion yields, corresponding consumption of glucose, and oil in the formation of BS. The set of ordinary differential equations (ODE) corresponds to initial value problems and are shown below:

(2.1)

(2.2)

(2.3)

Where Gluc and Gluc₀ are the glucose concentration at any time, and the initial glucose concentration expressed in g/kg _{dry mass}; Oil and Oil₀ are the oil concentration at any time and the initial oil concentration expressed in g/kg_{dry mass}; SL and SL₀ are the sophorolipid concentrations at any time and the initial sophorolipid concentration expressed in g/kg_{dry mass}, respectively. The first‐order reaction constants correspond to k₁ and k₂ (h⁻¹) for the consumption of glucose and oil, respectively. The constants B and C correspond to the residual concentrations of glucose and oil, respectively. The parameters Y₁ and Y₂ correspond to the yield coefficients of glucose and oil in BS, respectively. The ODE was solved with the Berkeley – Madonna program, integrating with the Runge–Kutta method to solve the ODE, and also comparing the experimental values with those calculated by the model. Parameter estimation was carried out using the deepest descent methodology proposed by Marquardt in 1963 [102]; this technique minimizes the difference of the sum of squares between the experimental data and those calculated by the model. Table 2.4 shows the parameters estimated by the program. The estimation of the initial and final values of the three variables are similar to experimental data. However, the conversion yield estimation (Y₁ and Y₂) does not reflect the global yield of raw materials.

Figure 2.10 presents the results of the model simulation (lines) compared to the experimental data. Calculated values for substrate consumption fit well to those obtained experimentally. Glucose and oil consumption have a classic descending behavior of first‐order kinetics. However, the pattern of the BS formation, the most important variable of the process, does not fit correctly to experimental data, particularly during the first 3 days of culture. The curve calculated by the model is not sigmoidal; this latter is a typical pattern for microbial fermentations. Levenspiel [103] pointed out that the kinetics of the formation of the product of interest (sophorolipid in this case) is the basis for obtaining the design equations of ideal reactors. This is done by plotting the inverse of the product formation rate against the sophorolipid concentration (Figure 2.11).

Using this plot, the size of the batch reactor will be proportional to the area under the curve of the inverse of the reaction rate, evaluated between the limits of product formation (0–100 g/kg_{dry mass}). On the other hand, in the case of continuous culture of SSF, the size of the bioreactor will be proportional to a rectangle whose base is the increase in product formation (0–100 g/kg_{dry mass}) and the height of the rectangle is the value of the inverse of the reaction rate (1/r_SL) evaluated at the point of discharge (~ 100 g/kg_{dry mass}). A comparison of these two types of bioreactor systems indicates that the batch reactor is much smaller than the continuous culture reactor; therefore, up to this level of analysis, the batch reactor is the most suitable type of reactor to produce the sophorolipid by SSF. However, it is necessary to deepen the analysis of the concavity of the sophorolipid production curve to have a model that better represents the behavior of the production of BS in SSF.

Table 2.4 Estimated parameters to characterize the kinetics of the production of sophorolipids by SSF. The Runge–Kutta method of 4 order was used, in a time interval of 0–360 hours with an increase in time step of 0.05 hours.

Parameters		Units	Parameter value
First‐order constant rate	k 1	h−1	0.01784
First‐order constant rate	k 2	h−1	0.00771
Yield of glucose to sophorolipids	Y 1	g SL/g Glucose	3.99 × 10−5
Yield of oil to sophorolipids	Y 2	g SL/g oil	0.69998
Residual glucose constant	B	g/kg dry mass	0.06616
Residual oil	C	g/kg dry mass	0.15279
Initial glucose	G 0	g/kg dry mass	251.20
Initial oil	Oil 0	g/kg dry mass	153.20
Initial sophorolipid	SL 0	g/kg dry mass	5.92 × 10−14

Figure 2.11 Plot of the equation design of ideal bioreactors for the production of sophorolipids using a first‐order reaction rate.

To analyze the change in the concavity of the sophorolipid production curve already indicated, the Gompertz model was used. This model is a sigmoidal equation that has the characteristic of not being symmetric at the inflexion point; as is the case with the logistic equation, it is a very flexible model to simulate behavior such as that described for the production of BS in SSF. Equations (2.4) and (2.5) show the differential and integral form of the model. Equation (2.6) shows the solution of Equation (2.5) for the initial conditions of the fermentation:

(2.4)

(2.5)

(2.6)

Where P is the product concentration (sophorolipid), P_max and P₀, are the maximum (88.9) and initial (1.61) concentrations of BS in g/kg_{dry mass}; k is a specific first‐order constant (0.032 h⁻¹), and b (8.898) is a parameter associated with the initial concentration of BS. The mentioned parameters were estimated using Excel’s Solver subroutine. Figure 2.12 shows the result of the simulation of the experimental data by the Gompertz model. It is worth noticing the use of the Gompertz model, allows predicting the change in the concavity of the production rate of BS in SSF. The correlation coefficient between experimental and calculated data was 0.98.

Figure 2.12 Simulation of sophorolipid production using the Gompertz model during the SSF. Symbols are the experimental and data solid line is the data calculated by the model.

Figure 2.13 The plot of the equation design of ideal bioreactors for the production of sophorolipids using the Gompertz model.

In a similar way to the methodology applied in Figure 2.11, the analysis of Figure 2.13 was carried out. Thus, in the same way, Levenspiel [103] indicates that from the kinetics of the formation of the product of interest (sophorolipid), it can be obtained. The design equations of the ideal reactors are obtained plotting the inverse of the product formation rate against the sophorolipid concentration (Figure 2.13. From this graph, the size of the reactor per batch will be proportional to the area under the curve of the inverse of the reaction rate, evaluated between the limits of the formation of product (~ 0–100 g/kg_{dry mass}). Compared to Figure 2.11, in this case, the size of the intermittent reactor increases when the level of BS is less than 40 (g/kg dry mass), this is due to the change in concavity modeled by the Gompertz equation, which simulates more precisely the production of BS.

On the other hand, in the case of continuous culture in SSF, the size of the mixed flow bioreactor will be proportional to a rectangle whose base is the increase in product formation (0–100 g/Kg_{dry mass}) and its height is the value of the inverse of the reaction rate (1/r_SL) evaluated at the point of discharge (~ 100 g/kg dry mass). In this case, there is no significant change in reactor size, either using the first‐order model or the Gompertz model. The comparison of these two types of bioreactor systems indicates that the batch reactor is smaller than the continuous culture reactor. Therefore, up to this point, the batch bioreactor is the most suitable to produce BS by SSF. The analysis of the areas indicates that the continuous reactor is almost 40 times larger than the batch reactor to obtain the same sophorolipid concentration (~ 100 g/kg dry mass). On the other hand, continuous reactors are very attractive due to their high productivity; however, these have the risk of contamination, especially in a relatively long‐time process. This possibility should not be ruled out for the future. To make it possible, it is essential to go deeper into the study of SSF bioreactors.