Rates per unit volume of reactor

Then, the rate in terms of the fluid bulk-phase concentration (overall rate per unit volume of reactor) is... 

It is obvious that this form of reaction rate becomes very complicated to work with when the surface concentration is introduced. In this case, we can use the concept of the ratecontrolling step. In our case, we assume that kt -> x or kt km, the resistance to the overall rate is owing to the intrinsic reaction rate. Then, due to the equality of the individual rates, if kt -> co then (CA- CAS) -> 0 or CA -> CAS, and so the individual rates are finite and equal to the overall rate. The rate in terms of the fluid bulk-phase concentration (overall rate per unit volume of reactor) is... 

As discussed in Sec. 7, the intrinsic reaction rate and the reaction rate per unit volume of reactor are obtained based on laboratory experiments. The kinetics are incorporated into the corresponding reactor model to estimate the required volume to achieve the desired conversion for the required throughput. The acceptable pressure drop across the reactor often can determine the reactor aspect ratio. The pressure drop may be estimated by using the Ergun equation... 

When the values shown in Table 2 are used to calculate the overall molar production rates per unit volume of reactor for monolith reactors, values of 40 mol/mreactor s are foimd. Figure 14 illustrates that this value is very high in comparison with those foimd in conventional catalytic reactors used in industry. 

It may be seen that there are disadvantages in making any considerable increase of scale in either case. If the activity is constant, the particle size increases so much that great stress is put on the approximations used in calculating the parameters. If the activity is inversely proportional to the diameter of the particles, the production rate per unit volume of reactor is seriously decreased. 

We next want to deterroine the other extreme for the dilution rate, which is the rate of maximum cell production. The cell production rate per unit volume of reactor is the mass flow rate of cells out of the reactor (i.e., = C Vq)... 

Space velocity, a term commonly used to describe the extensive operating characteristics of a tubular-flow reactor, is the maximum feed rate per unit volume of reactor that will give a stated conversion. Also space velocity is a measure of the ease of the reaction job. A high space velocity means that the reaction can be accomplished with a small reactor or that a given conversion can be obtained with a high feed rate. 

This correlation is based on data for both liquid-solid and gas-solid beds. The coefficients calculated from Eq. (10-36) are not particularly large. However, when this coefficient is multiplied by the external surface area per unit volume of bed, very high transport rates are obtained. From Eq. (10-1), the mass-transfer rate per unit volume of reactor is... 

This rate may be expressed in terms of the rate per unit volume of reactor by multiplying —dNJdt by the particle density (particles per unit volume). 

Deactivation is loss of activity. The rate per unit volume of reactor is given by... 

When the reaction is carried out in a low-boiling-point solvent or when one of the reactants is quite volatile, heat can be removed by allowing the solvent or reactant to vaporize. The vapors are condensed in an overhead condenser, and the liquid is returned to the reactor. The limiting factor in this design may be the allowable vapor velocity in the reactor. Too high a velocity will cause foaming or excessive entrainment of liquid, and the reaction rate per unit volume of reactor will decrease because of greater gas holdup. 

Just as knowledge of the reaction rate per unit volume is very helpful in determinations of the size of a partieu-lar type of reactor for carrying out a homogeneous phase reaction (see Table 8.1), so too is it beneficial to be able to relate the various -rates to reaction rates per unit volume. The several -rates are expressed per unit of biomass. Hence, the corresponding rates per unit volume of reactor can be expressed as... 

The second term in the heat balance accounts for heat removal by a circulating liquid at temperature from the surface of the volume element dV, assuming an overall heat transfer coefficient U across the tube wall. Note that represents the rate per unit volume of reactor. Hence... 

The average residence time t, introduced in Equation (10.14) deserves further comment. Another convenient term relating the feed rate and reactor volume in any type of flow process (including the tubular flow unit) is the space velocity (SV). This term is defined as the volumetric feed rate per unit volume of reactor. The SV has the units of reciprocal time and is therefore equal to 1 /t. In a variable-density... 

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