Pseudo-volumetric, kinetic rate constant

Hint Universal gas constant in the appropriate units, as required to make the kinetic rate constant pseudo-volumetric Rgas = 82.057 cm -atmo-sphere/(mol-K)... 

Step 11. Make the kinetic rate constant psendo-volumetric with units of inverse seconds. The product of and Papparent is equivalent to twice the intrapellet porosity divided by the average pore radius. Hence, fei, pseudo =... 

The kinetic rate constant kj corresponds to the kinetics of heterogeneous surface-catalyzed chemical reactions in the boundary conditions, whereas the rate law is written on a pseudo-volumetric basis when chemical reaction terms are included in the mass transfer equation. 

The Hougen-Watson rate law lEinw, with units of moles per area per time, is written on a pseudo-volumetric basis using the internal surface area per mass of catalyst S , and the apparent mass density of the pellet Papp. k is the nth-order kinetic rate constant with units of (volume/mole)" per time when the rate law is expressed on a volumetric basis using molar densities. 

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

The Hougen-Watson model is approximated by the best pseudo-volumetric zeroth-order rate law with kinetic rate constant 0, pseudovoiumetric such that Papp Hw Can be replaced by o.pseudovoiumetric- The questions below are based on pseudo-volumetric zeroth-order kinetics. 

Notice that the molar density of key-limiting reactant A on the external surface of the catalytic pellet is always used as the characteristic quantity to make the molar density of component i dimensionless in all the component mass balances. This chapter focuses on explicit numerical calculations for the effective diffusion coefficient of species i within the internal pores of a catalytic pellet. This information is required before one can evaluate the intrapellet Damkohler number and calculate a numerical value for the effectiveness factor. Hence, 50, effective is called the effective intrapellet diffusion coefficient for species i. When 50, effective appears in the denominator of Ajj, the dimensionless scaling factor is called the intrapellet Damkohler number for species i in reaction j. When the reactor design focuses on the entire packed catalytic tubular reactor in Chapter 22, it will be necessary to calcnlate interpellet axial dispersion coefficients and interpellet Damkohler nnmbers. When there is only one chemical reaction that is characterized by nth-order irreversible kinetics and subscript j is not required, the rate constant in the nnmerator of equation (21-2) is written as instead of kj, which signifies that k has nnits of (volume/mole)"" per time for pseudo-volumetric kinetics. Recall from equation (19-6) on page 493 that second-order kinetic rate constants for a volnmetric rate law based on molar densities in the gas phase adjacent to the internal catalytic surface can be written as... 

The heterogeneous rate law in (22-57) is dimensionalized with pseudo-volumetric nth-order kinetic rate constant k that has units of (volume/mol)" per time. k is typically obtained from equation (22-9) via surface science studies on porous catalysts that are not necessarily packed in a reactor with void space given by interpellet. Obviously, when axial dispersion (i.e., diffusion) is included in the mass balance, one must solve a second-order ODE instead of a first-order differential equation. Second-order chemical kinetics are responsible for the fact that the mass balance is nonlinear. To complicate matters further from the viewpoint of obtaining a numerical solution, one must solve a second-order ODE with split boundary conditions. By definition at the inlet to the plug-flow reactor, I a = 1 at = 0 via equation (22-58). The second boundary condition is d I A/df 0 as 1. This is known classically as the Danckwerts boundary condition in the exit stream (Danckwerts, 1953). For a closed-closed tubular reactor with no axial dispersion or radial variations in molar density upstream and downstream from the packed section of catalytic pellets, Bischoff (1961) has proved rigorously that the Danckwerts boundary condition at the reactor inlet is... 

Step 1. Enter the first-order kinetic rate constant for the surface-catalyzed chemical reaction based on gas-phase molar densities. This rate constant has units of cm/min and is known as the reaction velocity constant. It is not a pseudo-volumetric rate constant. 

The parameter has dimensions of (volume/mol)" because >S m/Oapp n,sur ce is a pseudo-volumetric nth-order kinetic rate constant with units of (volume/mol)" /time. In dimensionless notation, equation (30-62) yields the following nonlinear polynomial that relates the molar densities of reactant A in the bulk gas stream and at the external surface of the catalyst ... 

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. 

GL 16] [R 12] [P 15] As excess of cyclohexene was used, the kinetics were zero order for this species concentration and first order with respect to hydrogen [11]. For this pseudo-first-order reaction, a volumetric rate constant of 16 s was determined, considering the catalyst surface area of 0.57 m g and the catalyst loading density of1g cm. ... 

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