Reaction rate per unit volume for

The reaction rate per unit volume for gas oil cracking is given by ... 

The catalyst support may either be inert or play a role in catalysis. Supports typically have a high internal surface area. Special shapes (e.g., trilobed particles) are often used to maximize the geometric surface area of the catalyst per reactor volume (and thereby increase the reaction rate per unit volume for diffusion-limited reactions) or to minimize pressure drop. Smaller particles may be used instead of shaped catalysts however, the pressure drop increases and compressor costs become an issue. For fixed beds, the catalyst size range is 1 to 5 mm (0.04 to 0.197 in). In reactors where pressure drop is not an issue, such as fluidized and transport reactors, particle diameters can average less than 0.1 mm (0.0039 in). Smaller particles improve fluidization however, they are entrained and have to be recovered. In slurry beds the diameters can be from about 1.0 mm (0.039 in) down to 10 Jim or less. 

Here JT] is the chemical reaction rate per unit volume for reaction j, v1 the specific stoichiometric coefficient of species i in the chemical reaction j, and Mt the molecular mass of component i. 

With several small changes in notation, the mass and energy balances of Eqs. 14.1-1 and 14.1-2 can be made to look more like those commonly u.sed in reactor analysis. By letting q n and r/om represent the volurnetric flow rates into and out of the reactor, O, be the molar concentration of species i, V be the fluid volume in the reactor (so that C V = N ), and rj = Xj/ V be the specific reaction rate (reaction rate per unit volume) for the jth reaction, Eqs. 14.1-1 and I4.I-2can be rewritten as... 

The analysis of steady-state and transient reactor behavior requires the calculation of reaction rates of neutrons with various materials. If the number density of neutrons at a point is n and their characteristic speed is v, a flux effective area of a nucleus as a cross section O, and a target atom number density N, a macroscopic cross section E = Na can be defined, and the reaction rate per unit volume is R = 0S. This relation may be appHed to the processes of neutron scattering, absorption, and fission in balance equations lea ding to predictions of or to the determination of flux distribution. The consumption of nuclear fuels is governed by time-dependent differential equations analogous to those of Bateman for radioactive decay chains. The rate of change in number of atoms N owing to absorption is as follows ... 

The flow terms represent the convective and diffusive transport of reactant into and out of the volume element. The third term is the product of the size of the volume element and the reaction rate per unit volume evaluated using the properties appropriate for this element. Note that the reaction rate per unit volume is equal to the intrinsic rate of the chemical reaction only if the volume element is uniform in temperature and concentration (i.e., there are no heat or mass transfer limitations on the rate of conversion of reactants to products). The final term represents the rate of change in inventory resulting from the effects of the other three terms. 

For the control volume, the heat flux at the boundary is given as if = hc(T — T. ). The diffusion mass flux supplying the reaction is given as m" = hm(yFj00 — yF ), where from heat and mass transfer principles hm — hc/cv. Let Vand S be the volume and surface area of the control volume. The reaction rate per unit volume is given as m " — AYf E ilRT] for the fuel in this problem. 

A further important result which arises because of the functional form of is that the apparent order of reaction in the diffusion controlled region differs from that which is observed when chemical reaction is rate determining. Recalling that the reaction order is defined as the exponent n to which the concentration CAm is raised in the equation for the chemical reaction rate, we replace f(CA) in equation 3.8 by CJ . Hence the overall reaction rate per unit volume is (1 - e)rjkCA. When diffusion is rate determining, tj is (as already mentioned) equal to f1 from equation... 

The rate constant is defined as the reaction rate per unit volume of the reaction chamber divided by the product of the reactant concentrations. Thus, for a bimolecular reaction... 

The concept of an effectiveness factor is useful in estimating the reaction rate per catalyst pellet (volume or mass). It is, however, mainly useful for simple reactions and simple kinetics. When there are complex reaction pathways, the concept of effectiveness factor is no longer easily applicable, and species and energy balance equations inside the particle may have to be solved to obtain the reaction rates per unit volume of... 

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... 

The reaction rate per unit volume of catalyst as well as its selectivity depend on both the specific catalytic activity and the surface area of the active component per unit catalyst volume, as well as on its pore structure. These characteristics are determined by the conditions of catalyst preparation. Therefore, when developing a new catalyst, it is extremely important to be able to determine in advance the required internal surface area and the most suitable pore structure of the catalyst for the given reaction. 

In Section II,D,1 we have developed an expression, formula (7), for the maximum dimension between two parallel planes representing the two different catalytic surfaces of a reaction sequence, containing the reaction rate per unit surface area. Now let us imagine a reaction space (of unit volume) filled with such surfaces of catalyst X and Y. Then, the number of such planar reaction units will be n = 1 /L, and the maximum attainable reaction rate per unit volume will be... 

Consider first the isothermal, first order reaction for which the true reaction rate per unit volume of catalyst is pi,Sgicc, The observed rate of reaction, r (say), is a function of the observed concentration c, and is in fact... 

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