Diffusion Limitations in Porous Catalysts

The concentration of a reactant is not uniform throughout the catalyst, creating a concentration gradient from the bulk fluid to the reaction site within the catalyst's pores.

The rate at which a reactant is transported from the bulk fluid to the external surface of the catalyst.

The rate at which a reactant is transported from the external surface of the catalyst into the catalyst pores to the reaction site.

The total surface area of a catalyst is determined by the external surface area and the surface area of the pores within the catalyst.

The total volume of a porous catalyst is the sum of the solid material volume and the volume of the pores.

The reactant concentration at the external surface of the catalyst.

The reactant concentration inside the catalyst pore, varying with the distance from the external surface.

The reactant concentration in the bulk fluid far away from the catalyst.

The concentration of species A at the center of the catalyst pellet, where radial coordinate r = 0.

The concentration of species A at the external surface of the catalyst pellet, where radial coordinate r = R.

The concentration of species A at a specific point within the catalyst pellet, defined by the radial coordinate r.

A dimensionless concentration defined as the ratio of concentration at any point within the pellet to the concentration at the surface.

A dimensionless radial coordinate representing the ratio of the radial coordinate (r) to the pellet radius (R).

A dimensionless parameter that represents the ratio of the rate of surface reaction to the rate of diffusion inside the catalyst pellet.

The Thiele modulus represents the relative importance of diffusion and reaction rate in a catalyst pellet.

The effective diffusivity of species A in the porous catalyst. It incorporates diffusional resistance due to the porous structure of the catalyst.

The total surface area per unit mass of a catalyst. It is expressed in square meters per kilogram (m2/kg).

The average diameter of the pores within a porous catalyst. It's expressed in meters (m).

The mass of the catalyst per unit volume. Unit: kg/m3

The fraction of the catalyst's volume that is occupied by pores. It's a value between 0 and 1, representing the percentage of the catalyst that's empty space.

The movement of molecules through a porous material, specifically within the catalyst pores.

The rate of diffusion is proportional to the concentration gradient. It is defined as the molar flux of a component through a distance, measured in moles per square meter per second (mol m-2 s-1).

A type of diffusion where molecules collide with each other but not with the pore walls. It occurs in large pores at high pressures.

A type of diffusion where molecules collide with the pore walls but not with each other. It occurs in small pores at low pressures.

A measure of how much the temperature inside a catalyst pellet deviates from the temperature at the surface.

The ratio of the actual reaction rate in a porous catalyst pellet to the rate that would occur if the entire pellet were at the same temperature as the external surface.

The ratio of the activation energy to the product of the gas constant and the surface temperature.

The ratio of the product of the effective thermal conductivity, the surface temperature and the heat of reaction to the product of the reaction rate constant and the surface temperature.

The rate at which heat is conducted through the catalyst pellet.

The temperature at the outer surface of the catalyst pellet.

The energy required to initiate a chemical reaction.

The amount of heat released or absorbed during a chemical reaction.

It describes the movement of a species (A) through a surface, influenced by surface concentration and diffusivity.

A measure of how quickly a component (A) spreads or diffuses across a surface, affected by the activation energy and temperature.

The concentration of species A at the surface, affecting the flux of A.

Represents the total surface area available for reaction per unit volume of the catalyst, influencing the rate of reaction.

Describes the path length taken by a diffusing molecule through a porous material, compared to a straight line. Influences the surface diffusivity.

The minimum energy required for a reaction to occur, impacting the surface diffusivity.

States that at constant conditions, the overall rate of change of a species A within an infinitesimal segment of a spherical catalyst is zero, meaning inflow equals outflow plus the rate of reaction.

The rate at which a reaction takes place, influencing the overall change of a species within the infinitesimal segment.

A dimensionless group that represents the ratio of the rate of reaction inside a catalyst particle to the rate of mass transfer into the particle.

A measure of how effectively a catalyst particle is being used to carry out a reaction. It is the ratio of the actual reaction rate to the rate that would be observed if there were no mass transfer limitations.

For a first-order reaction, the effectiveness factor approaches 1 for small values of the Thiele modulus (φ ≤ 1). For large values of the Thiele modulus (φ ≥ 1), the effectiveness factor is inversely proportional to the Thiele modulus (η = 3/φ).

This criterion helps determine if there are internal diffusion limitations in a catalytic reaction. It compares the diffusional resistance to the reaction rate.

If the Weisz-Prater Criterion (CWP) is greater than 1, it indicates that internal diffusion limitations are present. This means the reaction is slowed down by the rate at which reactants can diffuse into the catalyst particle.

If the Weisz-Prater Criterion (CWP) is less than 1, it indicates that internal diffusion limitations are not significant. The reaction is not limited by diffusion.

In this case, the internal temperature of the catalyst is higher than the temperature on the surface, leading to a higher effectiveness factor (η > 1).

For high exothermic reactions, the rate constant inside the pellet is much larger than at the exterior, resulting in a higher effectiveness factor than 1 (η > 1).