Catalysts void area fraction

However, the void area fraction is equivalent to the void volume fraction, based on equation (21-76) and the definition of intrapellet porosity Sp at the bottom of p. 555. Effectiveness factor calculations in catalytic pellets require an analysis of one-dimensional pseudo-homogeneous diffusion and chemical reaction in a coordinate system that exploits the symmetry of the macroscopic boundary of a single pellet. For catalysts with rectangular symmetry as described above, one needs an expression for the average diffusional flux of reactants in the thinnest dimension, which corresponds to the x direction. Hence, the quantity of interest at the local level of description is which represents the local... 

The void area fraction in (21-76) is based on the fractional area in a plane at constant x that is available for diffusion into catalysts with rectangular symmetry. A rather sophisticated treatment of the effect of g 6) on tortuosity is described by Dullien (1992, pp. 311-312). The tortuosity of a porous medium is a fundamental property of the streamlines or lines of flux within the individual capillaries. Tortuosity measures the deviation of the fluid from the macroscopic flow direction at every point in a porous medium. If all pores have the same constant cross-sectional area, then tortuosity is a symmetric second-rank tensor. For isotropic porous media, the trace of the tortuosity tensor is the important quantity that appears in the expression for the effective intrapellet diffusion coefficient. Consequently, Tor 3 represents this average value (i.e., trace of the tortuosity tensor) for isotropically oriented cylindrical pores with constant cross-sectional area. Hence,... 

Dixon and coworkers [25] have performed several CFD simulations of fixed beds with catalyst particles of different geometries (Figure 15.9). The vast number of surfaces and the problems with meshing the void fraction in a packed bed have made it necessary to limit the number of particles and use periodic boundary conditions to obtain a representative flow pattern. Hollow cylinders have a much higher contact area between the fluid and particles at the same pressure drop. However, with a random packing of the particles, there wiU be a large variation... 

In the model equations, A represents the cross sectional area of reactor, a is the mole fraction of combustor fuel gas, C is the molar concentration of component gas, Cp the heat capacity of insulation and F is the molar flow rate of feed. The AH denotes the heat of reaction, L is the reactor length, P is the reactor pressure, R is the gas constant, T represents the temperature of gas, U is the overall heat transfer coefficient, v represents velocity of gas, W is the reactor width, and z denotes the reactor distance from the inlet. The Greek letters, e is the void fraction of catalyst bed, p the molar density of gas, and rj is the stoichiometric coefficient of reaction. The subscript, c, cat, r, b and a represent the combustor, catalyst, reformer, the insulation, and ambient, respectively. The obtained PDE model is solved using Finite Difference Method (FDM). 

One must understand the physical mechanisms by which mass transfer takes place in catalyst pores to comprehend the development of mathematical models that can be used in engineering design calculations to estimate what fraction of the catalyst surface is effective in promoting reaction. There are several factors that complicate efforts to analyze mass transfer within such systems. They include the facts that (1) the pore geometry is extremely complex, and not subject to realistic modeling in terms of a small number of parameters, and that (2) different molecular phenomena are responsible for the mass transfer. Consequently, it is often useful to characterize the mass transfer process in terms of an effective diffusivity, i.e., a transport coefficient that pertains to a porous material in which the calculations are based on total area (void plus solid) normal to the direction of transport. For example, in a spherical catalyst pellet, the appropriate area to use in characterizing diffusion in the radial direction is 47ir2. 

The pellets leave a fraction e unoccupied as they pack into the reactor so the fraction 1 — is occupied by the catalyst. The pellet is usually porous, and there is fluid (void space) both between catalyst pellets and within pellets. We measure the rate per unit area of pellet of assumed geometrical volume of pellet so we count only the void fraction external to the pellet. 

A monolith catalyst has a much higher void fraction (between 65 and 91 percent) than does a packed bed (which is between 36 and 45 percent). In the case of small channels, monoliths have a high geometric surface area per unit volume and may be preferred for mass-transfer-limited reactions. The higher void fraction provides the monolith catalyst with a pressure drop advantage compared to fixed beds. 

The commercial catalyst used in this work contains 12 wt% Ni and 83 wt% a-Al203. It has a BET total surface area of 3.4m /g and a unimodal pore size distribution with volume 0.155 cc/g, mean pore radius 1600 A and void fraction 0.362. Its activation required a reduction which was carried out under atmospheric pressure in situ, for 72 hrs at 850°C by means of a pure dried hydrogen flow of lOO Nl/hr. These severe reduction conditions were required because 20 wt% of the Ni was present as NiAl204-spinel phase, which could only be reduced above 770°C. It led to a very active catalyst, with a specific Ni-surface area of 0.68 m Ni/g.cat. 

Most catalysts of high surface area are to some extent porous. Porosity is a concept related to texture and refers to the pore space in a material. It can be defined as the fraction of the bulk volume that is occupied by pore or void space. An open pore is a cavity or channel communicating with the surface of a particle, as opposed to a closed pore. Void is the space or interstices between particles. 

Typically, commercial catalysts have a void fraction (porosity) ef of about 0.5. Therefore an approximate relationship between the internal surface area per unit particle volume and average pore size rt is ... 

A recycle reactor containing 101 g of catalyst is used in an experimental study. The catalyst is packed into a segment of the reactor having a volume of 125 cm. The recycle lines and pump have an additional volume of 150 cm. The particle density of the catalyst is 1.12 g cm , its internal void fraction is 0.505, and its surface area is 400 m g . A gas mixture is fed to the system at 150 cm s . The inlet concentration of reactant A is 1.6 mol m . The outlet concentration of reactant A is 0.4 mol m . Determine the intrinsic pseudohomogeneous reaction rate, the rate per unit mass of catalyst, and the rate per unit surface area of catalyst. The reaction isA- - Psov.4 = —1. 

A catalyst considered by Satterfield [40] has a void fraction of 0.40, an internal nfaoe area of 180 mVg. and a pellet density of 1.40 g/ cm Estimate the efliective difliisivity of... 

The measurable physical properties of catalyst particles commonly used in geometric models are the total surface area Sg (m /g), pore volume Vg (cm /g), solid density ps (g/cm ), void fraction or porosity Gp, and occasionally pore-volume distribution. 

The catalyst bed void fraction / is related to the hydraulic diameter and external surface area per unit volume of bed by = dhSsutf/(, Vbed)- A correlation of the form of Equation 8.61 can he generalized for other geometries ... 

Consider the packed-bed tubular reactor whose schematic diagram is shown in Figure P4.ll. It is a hollow eylindrical tube of uniform cross-sectional area A, packed with solid catalyst pellets, in which the exothermic reaction A Bis taking place. The packing is such that the ratio of void space to the total reactor volume— the void fraction—is known let its value be represented by E. The reactant flows in at one end at constant velocity v, and the reaetion takes place within the reactor. Obtain a theoretical model that will represent the variation in the reactant concentration C and reactor temperature r as a function of time and spatial position z. Consider that the temperature on the surface of the catalyst pellets Tg is different from the temperature of the reacting fluid and that its variation with time and position is also to be modeled. 

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