Cells mass balances

Substituting into the mass balance yields, the cell mass balance is arranged. At steady-state condition ... 

The theory and verification of the mixing-cell mass balance equation has been reported previously (2). For a cell with initial concentration of tracer, C, flushed with tracer-free... 

Equations 8 and 9, previously shown for the substrate and product mass balances in continuous cultures, can also be applied to this cultivation mode. However, due to cell retention, the equation that expresses the cell mass balance is altered, when compared with the mass balance of cells in a continuous culture (Equation 11) ... 

Solve the cell mass balance for the substrate concentration and calc... 

Tables 1 and 2 list the complete set of mass balance equations for the hydrolysis model and the SSF model. Dilution due to cell growth was not included in the model, nor was a cell mass balance. As cells were grown to maximal exponential phase before the batch runs and the fermentation was 90% complete in 5 h or less, any maintenance or growth requirements were neglected, and yield coefficients were used to determine the conversion yield for each reaction rate.

Tower reactors are usually described by means of dispersion models. According to Chen (1) the cell mass balance yields for nonsterile feed Xq> O ... 

To investigate whether it is possible to switch from batch to continuous operation the nonsteady state cell mass balance equation must be solved ... 

When assuming that (a) the tower can be described by a one-dimensional dispersion model, (b) the liquid residence time in the loop is negligible, and (c) the axial dependence of the local relative gas holdup is negligible, the following cell mass balance is obtained (5,6) ... 

For steady-state cell mass balance eq. (63) is valid ... 

The cell mass balance for a steady state in the tower is given by... 

From the cell mass balance equation for steady state. Equation 7.38, with sterile feed and assuming negligible cell death. 

Overall Water Balance Fuel Cell Mass Balance... 

Fuel cell mass balance requires that the sum of all mass inputs must be equal to the sum of all mass outputs. The inputs are the flows of fuel and oxidant plus water vapor present in those gases. The outputs are the flows of unused fuel and oxidant, plus water vapor present in those gases, plus any liquid water present in either fuel or oxidant exhaust. 

The previous set of equations (5-36 through 5-60) represents the fuel cell mass balance. For a given set of inlet conditions (temperatures, pressures, flow rates, relative humidities), and some known or estimated stack performance characteristics (such as current, pressure drop, temperature difference, electroosmotic drag, and back diffusion), it allows one to calculate the flow rates and particularly water conditions at the outlet, or it may be used to tailor the inlet conditions so that desired conditions at the outlet are obtained, as demonstrated in an example at the end of this chapter. 

In most cases the third function of the electrolyte is not required (or very limited), therefore from the point of view of the cell mass balance, the electrolyte is considered as a dead mass which should be cut down to the indispensable minimum. Taking into account simple Zn-Mn02 cells, the change that took place between the first and commercial design is more than clear when looking at the geometry evolution which allowed the amount of the electrolyte to be decreased dramatically (Fig. 2.1). 

The requirement for oxygen and carbon source for cell biosynthesis are calculated using nitrogen-limited mass balance equations for growth during exopolysaccharide production 01 res (nitrogen-limited cultures). These balances are derived from experimentally determined values of ... 

Carbon from the substrate glucose is converted into the carbon of the cells, phenylalanine, carbon dioxide and byproducts. Carbon balance calculations thus give us more understanding of the amount of carbon in glucose used for cell mass production, for synthesis of the wanted produd, maintenance energy and byproduct formation. 

Steady-state material balance is used for cell mass. 

Before energy balance is calculated, we need to make mass balance. Figure 9.1 shows the material balance for ethanol and glycerol fermentation. Put simply, mass into the system is equal to mass out of die system. The mass of carbon dioxide is calculated by adding mass of dry cell, mass of glycerol, mass of edianol and mass of water at product stream and then subtracting die sum from die feed stream. As a result, die mass of carbon dioxide is defined. The heat of the reaction is calculated by the following equation ... 

The mass balance for each combustible species j in cell i is... 

After dark-condition equilibrium was established, as indicated by the visible spectra, the photo-shift in equilibrium was observed to be completely reversed when the illumination ceased. This photogalvanic effect maintained a mass balance in the system, with no reagent consumed or generated during the dark-light-dark cycle. This observation suggested that the plutonium system in the proper network of a concentration cell... 

Turning to the substrate balance, yeast cells contain about 50% carbon. The cell mass is measured as total dry weight, not just carbon. This gives Yx/s = 2 when S is measured as the carbon equivalent of glucose. A reasonable value for Yxis is 1 so that half the carbon goes into biomass and half meets the associated energy requirements. The maintenance coefficient in carbon-equivalent units is 0.008 h . Using these parameter estimates, the three simultaneous ODEs for 5" > 0, become... 

At the end of 24 hours of continuous process the system was shut down. The knowledge of flowed buffer volumes and of the optical densities inside and downstream each ultrafiltration stage allowed to estimate product distribution (see appendix for mass-balance equations and the calculation procedure). The content of each cell was recovered and ffeeze-dried in order to be stored and used for subsequent kinetic experiments. A schematic flow-sheet of the whole procedure is illustrated in figure 1. 

The vessels were indexed by the subscript "j" (j = 0 refers to the reactor and j from 1 to 4 to the UF cells) and oligomers were lumped in two categories "P" (Permeated) and "R" (Rejected). Let label "in" species entering a cell and "out" those leaving it. Instantaneous mass-balance in the stream leaving a cell and feeding the following one is ... 

Although the Lewis cell was introduced over 50 years ago, and has several drawbacks, it is still used widely to study liquid-liquid interfacial kinetics, due to its simplicity and the adaptable nature of the experimental setup. For example, it was used recently to study the hydrolysis kinetics of -butyl acetate in the presence of a phase transfer catalyst [21]. Modeling of the system involved solving mass balance equations for coupled mass transfer and reactions for all of the species involved. Further recent applications of modified Lewis cells have focused on stripping-extraction kinetics [22-24], uncatalyzed hydrolysis [25,26], and partitioning kinetics [27]. 

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 ... 

The specific death rate can be obtained by considering the corresponding mass balance for nonviable (dead) cells. Normally nonviable cell concentration is measured at the same time the measurement for viable cell concentration is made. If viability (Q data are available, the nonviable cell concentration can be obtained from the viable one as Xd=Xv(l-y/. ... 

The dynamic mass balance for nonviable cells in a batch or perfusion culture yields. 

Example 4.8 Develop a fermentor model which consists of two mass balances, one for the cell mass (or yeast), Cl5 and the other for glucose (or substrate), C2. We have to forget about the... 

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