Bioreactors mass balances

Expression of the mass balances around the bioreactor (process). 

Evolution of the component concentrations in the two phases of the bioreactor are modeled by using an iteractive program (Runge-Kutta). All the kinetic equations and the experimentally determined constants are introduced into the program. The mass balance equation is included. 

In this section we shall use the standard notation employed by biochemical engineers and industrial microbiologists in presenting the material. Thus if we denote by Xv the viable cell (cells/L) or biomass (mg/L) concentration, S the limiting substrate concentration (mmol/L) and P the product concentration (immol/L) in the bioreactor, the dynamic component mass balances yield the following ODEs for each mode of operation ... 

Integration with the (micro) kinetics, in other words the kinetics of the pertinent free biocatalysts or of the immobilized biocatalysts including mass transfer, yields the overall reactor description or macrokinetics in later sections. In order to come up with these descriptions, a mass balance over the bioreactor should be drawn up (Figure 11.11). 

In the ideal plug-flow reactor (Figure 11.16) the continuous phase flows as a plug through the reactor i.e., there is no mixing or, in other words, no axial dispersion. Consequently, if a compound is consumed or produced, a concentration gradient will exist in the direction of flow. The mass balance is therefore first set up over an infinite small slice perpendicular to the direction of the flow with volume dV of the bioreactor. Assuming steady state and F =Fq=F, Equation (11.5) then is reduced to ... 

Tremaine et al. (1994) conducted pilot-scale studies to compare the effect of a suspended-growth reactor and a fixed-film bioreactor with a constructed wetland environment in removing creosote-PAHs from contaminated water recovered from a wood-preserving facility. Mass balanced chemical analysis of 5 PAHs used as model constituents of creosote showed that the wetland yielded between 20 and 84% removal, whereas the fixed-film reactor yielded 90 to 99% PAH removal. Biodegradation accounted for >99% of the losses observed in the fixed-film reactor, but only 1-55% of the compounds removed in the artificial wetland was attributable to biodegradation. Again, physical sorption of PAHs, especially HMW PAHs, was found to be significant. 

Knowing the concentrations in the absorber-outlet liquid stream C k. 0, the model of the bioreactor allows calculation of the concentrations in the reactor-outlet stream Ck =1. The model consists of mass-balance equations for FeEDTA complexes ... 

The starch plant for continuous sweet syrup production consists of a container for summer wheat, mill, fermenter, exchangers, bioreactors, and filter as individual process stages, or equipment items as shown in Fig.l(a),(b)and Fig.2. The overall mass balance... 

A comprehensive model of a membrane bioreactor has been developed by Moueddeb et al [5.103] for a simple irreversible reaction A B. The goal of the model was to describe their experimental reactor system, which was described earlier in Chapter 4. The model equations were established by taking into account the effect of the biomass on the permeate flow rate in the annular volume. The mass balance equations for the substrate (A) and the product (B) in cylindrical coordinates, utilized by Moueddeb et al [5.103] are given as ... 

A bioreactor or fennenter is a chemical reactor in which microbes (e.g., bacteria or yeast) act on an organic material (referred to as a substrate) to produce additional microbes and other desired or undesired products. A schematic diagram of a bioreactor is - given in Fig. 15.9-1. Mass balances for a biochemical reactor or fermenter are slightly... 

We now want to consider the completely general steady-state mass balance equations for the bioreactor of Fig. 15.9-1. The balances will be written for each species of atoms C, H, N, and O, and we will use the following notation ... 

The bioreactor behavior is based on mass balances for the key chemical species of the fermentative process. The reaction stoichiometric considered was... 

Elementary regions of bioreactor. A more simple description of the flow characteristics of a reactor than that by a local mass balance is done by introducing the residence time distribution concept (RTD), which provides macro-mixing characteristics (determination of the elementary regions of the reactor). In fact, using the residence time concept a particular situation may be described by mixed-type models considering "the reactor as... 

The total mass balance gives the rate of change of volume with inlet and outlet flow rates for a well-mixed constant-density system. A fed batch is a special case of a variable-volume CSTR operation It has been defined as a bioreactor with inflowing substrate but without outflow. For this system, the equation becomes... 

During operation of the bioreactors, samples were collected for the analysis of key operating parameters, such as dissolved oxygen, nutrient levels, total organic carbon and suspended solids. Microbial analysis was performed to assess the cell concentration of the specialized bacteria being added. All cultures were prepared in advance and added to the bioreactors. Additional samples were collected to measure the contaminant concentration across the bioreactor, as well as in the various portions of the treatment system, in order to calculate a mass balance. 

Corollary In warm-up examples 4 and 5 (chemical reactors), we had information about stoichiometry and conversion, and the proposed procedure was to construct a table to take into account the moles entering the reactor, moles reacting, and the moles leaving the reactors (reagents and products). This is a convenient procedure and facilitates the material balance in the reactor. On the other hand, in the bioreactor problems, we had information about the disappearance of the substrate (kinetics), and in that case it was easier just to formulate the mass balance like (8.6). 

The basic concepts related to biocatalytic reactions, in terms of the kinetics and mass transport phenomena involved, have to be introduced in order to formulate detailed mass balance within the systems. Furthermore, in order to predict the performance of a membrane bioreactor, a detailed analysis of the effectiveness of the biocatalysed processes is necessary. 

When the substrate is first transported in a boundary layer surrounding the particle, before diffusing within the catalyst support where reaction occurs, external resistance needs to be considered (Calabro et al, 2008 Truskey et al., 2004). An example is the case of a packed bed bioreactor, where fluid-dynamics play a significant role in the optimization of system performances. In such a case the kinetic contribution has to be expressed in terms of overall effectiveness factor ri y. To estimate it, the mass balance. Equation [1.29], has to be solved by imposing the continuity of mass flux at the wall. For a flat-sheet support it corresponds to ... 

In designing a bioreactor, the mass balance of products is usually required. The simplest way to give a kinetic expression for the product generation is to link this quantity to the rate of substrate consumption or to the behavior of the cell population. Two kinds of product generation can occur one is associated with the growth of the cells, the other one is non-growth associated. In the former mechanism, the production rate is proportional to... 

Characterization of a process occurring in a bioreactor where living cells are involved requires mass balances for cells, substrate, and extracellular product, all of them ultimately interlinked. 

In this section we return to the mass balance equations on the cells [Equatlcm (9-75)] and substrate [Equation (9-76)) and consi r the case where the volumetric flow rates in and out are the same and that no live (i.e.. viable) cells enter the chemostat. We next define a parameter common to bioreactors called the dilution rate, D. The dilution rate is... 

A simple dynamic model of a fed-batch bioreactor was given in Chapter 2, Eqs. 2-98 to 2-101. This model can be converted into mass balances on individual components as follows ... 

A model can be defined as a set of relationships between the variables of interest in the system being investigated. A set of relationships may be in the form of equations the variables depend on the use to which the model is applied. Therefore, mathematical equations based on mass and energy balances, transport phenomena, essential metabolic pathway, and physiology of the culture are employed to describe the reaction processes taking place in a bioreactor. These equations form a model that enables reactor outputs to be related to geometrical aspects and operating conditions of the system. 

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). 

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