Volumetric reaction rate constant

When the surface reaction rate constant is multiplied by the specific internal area, one gets the volumetric reaction rate constant per unit catalyst volume, which is analogous to the reaction rate constant of a homogeneous reaction ... 

A hydrogenation is carried out batchwise in a liquid phase, with a suspended catalyst (mean particle size 10 [im) in a stirred laboratory autoclave, at 80 C, under pressures between 10 and 100 bar. By varying pressure and concentrations it is found that the reaction is first order with respect to hydrogen, and zero order with respect to the dissolved reactant, until a degree of conversion of 90% of that reactant is reached. The volume of the liquid phase is 200 ml. When at least 10 g of catalyst is used, the reaction rate is not increased by addition of more catalyst. The autoclave is kept at constant temperature by regulating the cooling water flow. From these experiments an effective first order volumetric reaction rate constant (for the hydrogen conversion) is found. 

By varying the average volumetric reaction rate constant, e.g. with... 

If the initial specific surface area of the char Aq in m /kg or the initial volumetric mass distribution of carbon expressed as density Pq in kg/m are known, the surfece-related or volumetric reaction rate constants, k" in kg/(m s Pa ) and k " in kg/(m -s-Pa ), respectively, can be calculated. 

In this equation the reaction is taken to be pseudo first-order with respect to A (as is the case for hydrogen in the reaction with thiophene) with an effectiveness factor r). The factor er appearing in this equation converts the basis of the reaction rate constant from unit volume of particles to unit volume of bed in order to be consistent with the basis used for the volumetric mass transfer coefficients. 

The design equations for a CFSTR with perfect mixing, constant fluid density, and steady state operation are as follows. If u is the volumetric flowrate and K = k1/k2, relative reaction rate constant, where k1 k2, and k3 are the specific reaction rate constants for reactions 5-357, 5-358, and 5-359. The rate expressions of A, B, R, S, and T are... 

Let us now apply the above equation in order to calculate the conversion of a varying number of CSTRs in series with total volume Vtot = 0.6 m3 and volumetric flow rate V = 0.1 m3 h"1 for a first-order reaction with reaction rate constant k = 0.25 h The results are presented in Table 1. 

The pseudo-volumetric kinetic rate constant for the forward reaction with units of (volume/mole)/time in equation (19-39) is... 

Inlet gas-phase molar density of reactant A, Cao = 3 x 10 g-mol/cm First-order kinetic rate constant for the surface-catalyzed chemical reaction based on gas-phase molar densities, surface = 5 x 10 cm/min (also known as the reaction velocity constant) — this is not a pseudo-volumetric kinetic rate constant Diameter of spherically shaped catalytic pellets = 1 cm Intrapeiiet porosity factor = 65% (i.e., 0.65)... 

Use the following data to analyze the performance of a packed catalytic tubular reactor that contains porous spherical pellets. The heterogeneous kinetic rate law is pseudo-first-order and irreversible such that / surface, with units of moles per area per time, is expressed in terms of the partial pressure of reactant A, only (i.e., surface = i.siufacePA), and ki, surface has dimensions of moles per area per time per atmosphere, ki, surface is not a pseudo-volumetric kinetic rate constant. Remember that the kinetic rate constant in both the intrapellet and interpellet Damkohler numbers must correspond to a pseudo-volumetric rate of reaction, where the rate law is expressed in terms of molar densities, not partial pressures. 

Assuming a constant-volume reaction (V = 0), the volumetric reaction rate is expressed as Equation (3.1.3-3a) ... 

The effects of SCFs on the catalytic activity of methanol synthesis are shown in Table 3. It is obvious that the gas phase (He) exhibited the lowest total carbon conversion (about 16.4%). As methanol synthesis is a highly exothermic reaction, the low conversion in gas phase possibly resulted from the heat of reaction which cannot be removed rapidly from the catalyst bed. The total carbon conversion increased to 45.6% when SC-Ce was introduced into the reaction. This illustrates that the SCF enhanced the reaction activity of methanol synthesis. The rate of reaction was possibly enhanced while the experiment was operated in the mixture critical region because of a favorable pressure dependence of the reaction rate constant as well as the imusual volumetric behavior of heavy solutes solubilized in an SCF solvent [16]. 

In (5.37), r stands for the volumetric reaction rate, Ci represents the concentration of acid groups per unit volume of catalyst, and a, is the liquid-phase activity of component i. The temperature dependence of the reaction rate constant k can be expressed by the Arrhenius equation. All kinetic and thermodynamic parameters can be found elsewhere [7]. 

An exothermic reaction that obeys a second-order rate expression (r = kC ) is to be accomplished in a cascade of three identical stirred tanks operating in series. To (approximately) balance the heat loads on the various reactors, each of the reactors will be operated at a different temperature. These temperatures are to be selected in a manner such that the rates of reaction are to be the same in each reactor. To minimize losses of the organic solvent during operation, it will be necessary to operate the third reactor at 140°C. At this temperature the reaction rate constant is equal to 500 L/(mol h). If the effluent from the third reactor corresponds to 99% conversion and if the volumetric flow rate to the cascade is equal to 1.8 m /h when the concentration of A in the feed stream is 1.5 M, how large must each of the reactors be If the activation energy for the reaction is 20 kcal/g-mol, at what temperatures should the first and second reactors be operated ... 

A further increase of the intrinsic reaction rate at constant volumetric mass transfer coefficient (/rg, ) results in Hatta numbers greater than 3 Ha > 3). The reaction rate can be considered as very fast compared to the mass transfer rate. As a consequence, the reactants do not reach the bulk phase (Cg jj 0) the reaction takes place only in the boundary layer (Figure 2.12c). Under these conditions, the reaction rate increases proportionally with the specific interfacial area between the phases ( ), the square root of the reaction rate constant, and the catalyst concentration as indicated in Equation 2.93. 

L is the length and A is the cross-sectional area of the tubular vessel, q is the volumetric fluid flow rate and u = q/A is the mean velocity of the fluid. C q arid C f are the feed and the exit concentrations of A C (Z) is the concentration of A in the fluid, at a distance Z from the inlet. (-r,i) = kC is the specific reaction rate, where k is the specific reaction rate constant. 

The surface reaction rate constant, e.g., for a first order surface reaction, should be expressed per unit of surface area of the carrier, so that its dimension is m/s compare eq. (5.9). The product of the surface reaction rate constant and the specific surface area is the volumetric rate constant. It has the dimension s and is comparable to the rate constant of a homogeneous first order reaction compare eq. (3.1). 

The liquid side volumetric physical mass transfer coefficient was determined from the desorption rate of oxygen. Detailed description of the experimental set up, procedure and analysis of data is given by Tosyali [30]. Methods of estimating the interfacial CO2 concentration, diffusivities of CO2 and OH in the liquid phase, reaction rate constant, which are all required in data analysis, can be found elsewhere [31, 32]. ... 

Area-based physical mass transfer coefficient, m/s Area-based chemical mass transfer coefficient, m/s Volumetric physical mass transfer coefficient, 1/s Volumetric chemical mass transfer coefficient, 1/s Second order reaction rate constant, 1/s Generalized variable for a second-order reaction,... 

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