A Levenspiel plot graphs FA0/−rA versus X. What does this plot primarily help determine?

A Levenspiel plot graphs FA0/−rA versus X. What does this plot primarily help determine?

• A. The volume of a reactor needed to achieve a given conversion
• B. The heat transfer coefficient
• C. The activation energy of the reaction
• D. The reaction enthalpy

Answer: (A)

The main idea is to use how a plug flow reactor’s volume relates to conversion through an area under a curve. For a reactor in which A is consumed at a rate −rA and the molar flow of A entering is FA0, the differential volume needed to advance the conversion by a small amount dX is dV = dFA/(-rA). Since dFA = −FA0 dX, you get dV = FA0/(-rA) dX. Integrating from zero to the target conversion X gives V = ∫0^X [FA0/(-rA)] dX, so the area under the curve of FA0/(-rA) versus X up to that X equals the reactor volume required. That’s why this plot is used to size a reactor for a desired conversion. It’s not about heat transfer, activation energy, or enthalpy, which involve different analyses and plots.

The main idea is to use how a plug flow reactor’s volume relates to conversion through an area under a curve. For a reactor in which A is consumed at a rate −rA and the molar flow of A entering is FA0, the differential volume needed to advance the conversion by a small amount dX is dV = dFA/(-rA). Since dFA = −FA0 dX, you get dV = FA0/(-rA) dX. Integrating from zero to the target conversion X gives V = ∫0^X [FA0/(-rA)] dX, so the area under the curve of FA0/(-rA) versus X up to that X equals the reactor volume required. That’s why this plot is used to size a reactor for a desired conversion. It’s not about heat transfer, activation energy, or enthalpy, which involve different analyses and plots.