Fermentation reactor modeling

Fermentation systems obey the same fundamental mass and energy balance relationships as do chemical reaction systems, but special difficulties arise in biological reactor modelling, owing to uncertainties in the kinetic rate expression and the reaction stoichiometry. In what follows, material balance equations are derived for the total mass, the mass of substrate and the cell mass for the case of the stirred tank bioreactor system (Dunn et ah, 2003). 

As in the steady-state simulation of continuous processes, it is convenient to convert from a process flowsheet to a simulation flowsheet. To accomplish this, it is helpful to be familiar with the library of models (or procedures) and operations provided by the simulator. For example, when using SUPERPRO DESIGNER to simulate two fermentation reactors in series, the process flowsheet in Figure 4.25a is replaced by the simulation flowsheet in Figure 4.25b. In BATCH PLUS, however, this conversion is accomplished without drawing the simulation flowsheet, since the latter is generated automatically on the basis of the recipe specifications for each equipment item. 

In this section, we develop a simplistic model of beer fermentation. This model is based upon the work of Engasser (1981) and Gee and Ramirez (1987). The fermentation medium is assumed to contain three major sugars. These are glucose, maltose, and maltotriose and are the limiting nutrients. The fermentation is carried out in a batch reactor which can be considered to be ideally mixed. The material balance relations for each sugar are... 

Gonzalez-Figueredo, C., De La Torre, L.M., and Sanchez, A. (2010) Dynamic modeling and experimental validation of a solid-state fermentation reactor. lEAC Proc. Vol, 11, 221-226. 

In this chapter the dynamics of fermentation reactors for the production of penicillin will be discussed. Since these reactors are usually operated in a fed-batch mode, this mode will be discussed in addition to a continuous operation mode. For the continuous reactor, the nonlinear dynamic model will be linearized to explain the dynamic responses of the reactor concentrations to a change in feed rate. 

So far, chemical processes have been discussed as well as fermentation reactors. These systems can be characterized by the fact that there are usually no discontinuities in the model equations. In physiological systems, however, there is often a threshold value that has to be succeeded before certain phenomena take place. This causes a threshold non-linearity in the model and therefore these systems can be analyzed well through simulation but theoretically they are difficult to analyze. It is not the purpose of this chapter to discuss different physiological models the two systems that will be selected for illustration of system dynamics are the modeling of glucose-insulin dynamics and cardiovascular modeling approaches. 

A feed concentration of 15 g glucose and 15 g xylose per litre was used over a feed rate of 20-200 ml/hr. Samples were taken at successive points along the reactor length, and the usual analysis for glucose and xylose consumption, organic acid production and cell density were done. A kinetic model for the growth and fermentation of P. acidipropionici was obtained from these data. 

There is an interior optimum. For this particular numerical example, it occurs when 40% of the reactor volume is in the initial CSTR and 60% is in the downstream PFR. The model reaction is chemically unrealistic but illustrates behavior that can arise with real reactions. An excellent process for the bulk polymerization of styrene consists of a CSTR followed by a tubular post-reactor. The model reaction also demonstrates a phenomenon known as washout which is important in continuous cell culture. If kt is too small, a steady-state reaction cannot be sustained even with initial spiking of component B. A continuous fermentation process will have a maximum flow rate beyond which the initial inoculum of cells will be washed out of the system. At lower flow rates, the cells reproduce fast enough to achieve and hold a steady state. 

Many reviews and several books [61,62] have appeared on the theoretical and experimental aspects of the continuous, stirred tank reactor - the so-called chemostat. Properties of the chemostat are not discussed here. The concentrations of the reagents and products can not be calculated by the algebraic equations obtained for steady-state conditions, when ji = D (the left-hand sides of Eqs. 27-29 are equal to zero), because of the double-substrate-limitation model (Eq. 26) used. These values were obtained from the time course of the concentrations obtained by simulation of the fermentation. It was assumed that the dispersed organic phase remains in the reactor and the dispersed phase holdup does not change during the process. The inlet liquid phase does not contain either organic phase or biomass. 

The two extreme hypotheses on mixing produce lumped models for the fluid dynamic behavior, whereas real reactors show complex mixing patterns and thus gradients of composition and temperature. It is worthwhile to stress that the fluid dynamic behavior of real reactors strongly depends on their physical dimensions. Moreover, in ideal reactors the chemical reactions are supposed to occur in a single phase (gaseous or liquid), whereas real reactors are often multiphase systems. Two simple examples are the gas-liquid reactors, used to oxidize a reactant dissolved in a liquid solvent and the fermenters, where reactions take place within a solid biomass dispersed in a liquid phase. Real batch reactors are briefly discussed in Chap. 7, in the context of suggestions for future research work. 

Putting these important issues aside, the production of ethanol by batch fermentation is an important example of a batch reactor. The basic regulatory control of a batch ethanol fermentor is not a difficult problem because the heat removal requirements are modest and there is no need for very intense mixing. In this section we develop a very simple dynamic model and present the predicted time trajectories of the important variables such as the concentrations of the cells, ethanol, and glucose. The expert advice of Bjom Tyreus of DuPont is gratefully acknowledged. Sources of models and parameter values are taken from three publications.1 3... 

Chen VCP, Rollins DK (2000), Issues regarding artificial neural network modeling for reactors and fermenters, Bioprocess. Eng. 22 85-93. 

Several special terms are used to describe traditional reaction engineering concepts. Examples include yield coefficients for the generally fermentation environment-dependent stoichiometric coefficients, metabolic network for reaction network, substrate for feed, metabolite for secreted bioreaction products, biomass for cells, broth for the fermenter medium, aeration rate for the rate of air addition, vvm for volumetric airflow rate per broth volume, OUR for 02 uptake rate per broth volume, and CER for C02 evolution rate per broth volume. For continuous fermentation, dilution rate stands for feed or effluent rate (equal at steady state), washout for a condition where the feed rate exceeds the cell growth rate, resulting in washout of cells from the reactor. Section 7 discusses a simple model of a CSTR reactor (called a chemostat) using empirical kinetics. 

The fermentation section is modeled by means of two stoichiometric reactors placed in parallel, followed by a flash for separation of the vapor products (see Figure 5.12). The first reactor (SSCF) describes the saccharification and... 

In addition to sacharification and fermentation, loss to other product occurs (Table 15.12). This is modeled by a side stream bypassing the SSCF reactor that reacts to lactic acid. A total of 7% of the sugars available for fermentation are considered lost to contamination. 

A number of fine reviews have appeared recently which address in part the problems mentioned and the models employed. Rietema (R12) discusses segregation in liquid-liquid dispersion and its effect on chemical reactions. Resnick and Gal-Or (RIO) considered mass transfer and reactions in gas-liquid dispersions. Shah t al. (S16) reviewed droplet mixing phenomena as they applied to growth processes in two liquid-phase fermentations. Patterson (P5) presents a review of simulating turbulent field mixers and reactors in which homogeneous reactions are occurring. In Sections VI, D-F the use of these models to predict conversion and selectivity for reactions which occur in dispersions is discussed. 

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