Parameter values and references.
Abstract
Bioprocess optimization is important in order to make the bioproduction process more efficient and economic. The conventional optimization methods are costly and less efficient. On the other hand, modeling and computer simulation can reveal the mechanisms behind the phenomenon to some extent, to assist the deep analysis and efficient optimization of bioprocesses. In this chapter, modeling and computer simulation of microbial growth and metabolism kinetics, bioreactor dynamics, bioreactor feedback control will be made to show the application methods and the usefulness of modeling and computer simulation methods in optimization of the bioprocess technology.
Keywords
- modeling
- simulation
- bioprocess
- fermentation
- bioreactor
- control
1. Introduction
Bioindustry is important in utilization of reproducible resources, developments of environmental friendly production processes, and sustainable economy. In order to make the bioprocesses more efficient and economic, bioprocess optimization and automatic control are needed. The conventional optimization methods cost much labor, time, and money; on the other hand, modeling and computer simulation method can reveal the mechanisms behind the phenomenon to some extent, to assist the deep analysis and optimization of bioprocesses. The modeling and computer simulation method is much efficient and economic, and widely used in research and modern bioindustries.
Bioprocess efficiency depends on the cell capability, bioreactor performances, and the optimal control of the cultivation conditions. The metabolic network inside the cells involves thousands of enzymes, and the enzyme expression and activities are dynamically affected by the cultivation conditions. As a result, the cultivation condition affects the cell growth, metabolism, and product production in a sophisticated and nonlinear way. Control and maintain relatively optimal cultivation conditions through proper operation and control of the bioreactor are needed to improve the production efficiency of the bioprocess.
Bioprocess mathematical modeling involves the modeling of the dynamic changes of the metabolic rates and their distribution inside the cells with the changes of time and cultivation conditions, the modeling of the dynamic changes of the reaction rates and mass transfer rates as well as the cultivation conditions inside the bioreactor, and the modeling of the dynamics of the bioreactor control system etc., based on which optimizations of the bioreactor operation and control strategies can be made and the results can be predicted and evaluated by computer simulation. In this chapter, examples of modeling and computer simulation of microbial growth and metabolism kinetics, bioreactor dynamics, and the feedback control of the bioreactor are given to show the application methods and the usefulness of modeling and computer simulation methods in bioprocess technology.
2. Modeling of microbial cell growth and metabolism
2.1. Modeling of microbial cell growth
Cell growth is one of the most important variables to be investigated in bioprocess. The cell growth is usually described by the specific growth rate,
The specific growth rate is related with many process variables, like temperature (
In real applications, only the key process variable(s) are included in Eq. (2) for simplification. Monod equation [1] using the substrate concentration as the single independent variable is shown by Eq. (3), as
where
The typical cell growth curve is of “S” type, which has a lag growth phase and cannot be properly modeled by Monod equation as discussed later. At the initial cultivation stage, the cells need some time to adapt to the new environmental conditions for induction of some new enzymes needed for cell metabolism, etc., and the specific growth rate is zero or at a low value resulting in the lag growth phase. One way to model the lag growth phase is to separate the newly inoculated cells as active cells,
where
After the lag growth phase, the specific growth rate increases gradually and the cells go into the exponential growth phase, which is expressed by Eqs. (9) and (10)
where
From above analysis, it can be seen that the specific growth rate will start from zero or a low value in the lag growth phase, increases gradually and reaches the maximum value in the exponential growth phase, and then decreases gradually in the declined growth phase, which makes the time course of the specific growth rate the “bell” type curve and the time course of cell concentration the typical “S” type curve (Figure 1), which cannot be well fitted by the models discussed above. In order to simulate the “bell” type specific growth rate curve and the “S” type cell growth curve more accurately, the following model is developed shown by Eqs. (12) and (13) [5]
where
Even if Monod model has some limitations, it is still the widely used growth model in real applications for the major reasons of simplification and the single independent variable of substrate concentration, which is the key process variable to be investigated in many fermentation processes. In cases of high density fermentation, or substrate or product inhibition, modifications of Monod model are needed. Contois model shown by Eq. (16) is an example for high density fermentation, in which modeling the cell concentration is included in the denominator of the specific growth rate equation to show the limitation effect of high cell concentration on the growth, to make the specific growth rate to be reciprocal to the cell concentration (
In some cases, the substrates which have inhibitory effect on cell growth, like ethanol or acetate, etc., are used. One example of the growth model under noncompetitive substrate inhibition with
One example for modeling product inhibition, like ethanol or lactic acid fermentation, is shown by Eq. (18)
In case of dual substrates, the growth model in form of the sum or product of two Monod type terms is often used for the substitutable and nonsubstitutable substrates, respectively. For example, glucose and glycerol are substitutable substrates which can be modeled by Eq. (19), while glucose and oxygen are nonsubstitutable substrates which can be modeled by Eq. (20).
Above growth models are relatively simple, which are unstructured and unsegregated models, and are useful for practical applications. Structured and segregated growth models, which involve the intracellular structure or the nonhomogeneity of the cells, respectively, are generally sophisticated and contain uneasily measurable model parameters, and are usually used for theoretical purposes.
2.2. Modeling of microbial substrate uptake and product production
In many cases, the ratio of cell mass produced per substrate utilized is a constant and defined as the cell yield from the substrate,
The minus sign in Eq. (21) is to ensure
Further, the total substrate consumed can be considered of two parts, with one part for real cell growth and the other part for life maintenance to develop Eq. (22) into Eq. (23)
where
From Eq. (24), it can be seen that in order to increase the cell yield,
The specific substrate consumption rate is defined by the consumption in grams of substrate (g) per gram dry cells (g) per hour (h), and can be modeled by Eq. (25)
From Eqs. (23) and (25), Eq. (26) can be obtained
Then, Eq. (22) or (23) can be expressed in a simple way by Eq. (27)
For the metabolism of facultative anaerobes grown in oxygen limited condition, the cell yield varies greatly depending on the degree of oxygen limitation. Catabolism of 1 mole of glucose can produce 36 (or 38) mole ATP under aerobic condition or produce 2 mole ATP under anaerobic condition. The ATP‐based cell yield,
In modeling of specific product production rate, Luedeking‐Piret equation is most often used for its simplification and usefulness, which relates the specific product production rate to the growth related and nongrowth related parts by using
3. Modeling of bioreactor with different operation methods
Continuous stirred tank reactor (CSTR) is the most popular type of bioreactor, which can be operated in batch, fed‐batch, and continuous modes. For batch culture, no substrate is fed into the bioreactor except air for aeration or acid or base for pH control, and no culture broth is taken out of the bioreactor during the fermentation process. For modeling of a typical batch culture, the specific rates of cell growth (
For fed‐batch culture, substrate is fed into the bioreactor but no culture broth is taken out during the fermentation process, so that the liquid volume is increasing. For modeling fed‐batch culture,
where
In fed‐batch culture,
Continuous culture is another kind of bioreactor operation method, with which method substrate is continuously fed into the bioreactor meanwhile the culture broth is continuously taken out of the bioreactor at the same rate so that the liquid volume remains unchanged. Continuous culture has the advantage of high production efficiency but the disadvantages of low substrate conversion yield, strain deterioration, and easy contamination, and is not often used in industry. As a result, examples of only batch and fed‐batch cultures are investigated in next section.
4. Modeling and simulation of control of fermentation processes
4.1. Effects of early pulse aeration on ethanol fermentation
4.1.1. Mathematical modeling
Bioethanol is produced by anaerobic fermentation using
Fermentation period, which can be roughly divided into growth phase and production phase, is one major factor affecting the production cost. Fermentation period will be shortened if the cell growth phase is shortened. By employing an aerobic condition during the cell growth phase to fasten the cell growth and an anaerobic condition during the ethanol production phase, the fermentation period should be shortened while the ethanol production remained. The growth phase aerobic pulse stimulated ethanol fermentation and the normal anaerobic ethanol fermentation operated in batch mode are investigated and compared by modeling and simulation [6].
The specific glucose consumption rate (
where
where OUR is oxygen uptake rate.
4.1.2. Simulation results
Simulation was made using above mathematical model (Figure 3). The references for the parameter values used in the model or in calculation of the parameter values used in the model are shown in Table 1. In aerobic condition,
The simulation results of the conventional anaerobic ethanol fermentation and the early growth phase aerobic pulse stimulated ethanol fermentation processes are shown in Figure 3. In simulation of the early growth phase aerobic pulse stimulated ethanol fermentation process,
4.2. Fermentation with substrate feeding using DO stat control strategy
4.2.1. Mathematical modeling
In this section, glucose feeding control based on dissolved oxygen (DO) will be investigated by using a fed‐batch fermentation process using
The specific growth rate is modeled by Logistic equation shown by Eq. (50). The specific glucose consumption rate is modeled to include two parts, one for the net growth and the other for the maintenance shown by Eq. (51). The mole specific oxygen consumption rate is six times of the specific glucose consumption rate as shown by Eq. (52). The specific product production rate is modeled by Luedeking‐Piret [Eq. (53)]. OUR and OTR are shown by Eqs. (54) and (55), respectively.
where
The mass balance equations for fed‐batch culture can be made and transformed into Eqs. (56)–(60).
where
4.2.2. Simulation results
In the simulation, glucose pulse feeding was made when DO increased over 10% in order to avoid noise interruptions. In each pulse feeding, a dosage equivalent to 20 g/L increase in glucose concentration was fed. The initial glucose was depleted at about 75 h and the product concentration was a little over 6 g/L at that time. By glucose pulse feeding, the product concentration was more than doubled (Figure 4). Glucose and DO concentrations go up and down in turn and fluctuate during the control period. By using this control strategy, glucose concentration can be maintained in an averaged low concentration, which is desired and helps to overcome the glucose effects and increase the product yields. In addition, the DO stat control strategy does not need the extra sensor and is easily applied.
4.3. Fermentation with DO feedforward‐feedback control and substrate‐feedback control
4.3.1. Mathematical modeling
DO control is important in fermentation process. The level of DO can affect the metabolic flux distribution and the product yield and production efficiency. As oxygen has low solubility in water, DO control is a hard task for fermentation process. Compared with feedback control, DO feedforward‐feedback (FF‐FB) control has the advantage in dealing with the time‐varying characteristics resulted from the cell growth during the fermentation process. The oxygen consumption of the microbial cells is considered the disturbance to the control system and is estimated by using the mathematical model and compensated by the FF control action. The substrate is FB controlled by repeated pulse‐fed of carbon source. The schematic diagram for the control system is shown in Figure 5 [13].
The specific cell growth rate is modeled using double substrate Monod equation shown by Eq. (61). The equations for the specific glucose consumption rate, the specific oxygen consumption rate, OUR, and OTR are shown by Eqs. (62)–(65), which are the same as that of Section 4.2.1.
The mass balance equations for the repeated fed‐batch culture are described by Eqs. (66–69).
where
For FF control of DO, in order to compensate the DO disturbance resulted from the cell growth, OTR should be equal to OUR according to Eq. (68) if the dilution effect of the feeding is neglected so as to ensure
The value of
Between the two manipulated variables,
where the subscripts
As model predictions may not be very accurate, FB control is used to eliminate the control error and ensure the control accuracy. In the case of FB control, the error between DO set‐point and process variable is calculated by Eq. (74).
where
Then, the total DO control actions of
where
4.3.2. Simulation results
In this system, DO is FF‐FB controlled by agitation speed and aeration rate and the substrate concentration is FB controlled by repeated pulse‐fed of certain amount of the concentrated feeding solution to make the substrate concentration reach 30 g/L when the substrate concentration is lower than the set‐point of 5 g/L. In order to confirm the robustness of the control system under model prediction errors and noises, 5% randomized noises and 20% over estimate of the cell growth were added in the mathematical model predictions in FF control. Then, simulations were made with the above noises and prediction errors. The results indicated that even if the noises and relatively large model prediction errors existed, the control system still had good performance. The reason is that FB control finally compensated the inaccuracy of the FF control, as shown in Figure 6 [13].
5. Conclusion
Modeling and simulation are useful tools for understanding, analysis, and optimization of bioprocesses [14–17]. By using the modeling and computer simulation methods, the dynamics of cell growth and metabolism under different conditions and various fermenter operation modes can be evaluated and the information can be used for bioprocess optimization and bioreactor control.
Acknowledgments
This work was supported by grants from the Natural Science Foundation (Grant No. 31370138, 31570036), the National Basic Research Program (2010CB630902), the Natural Science Foundation (Grant No. 31400093, 31370084, 30800011), the Postdoctoral Science Foundation (Grant No. 2015M580585), and the State Key Laboratory of Microbial Technology Foundation (M2015‐03) of China.
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