Calculation of reactor volume
Thread Content
Adipic acid and hexanediol in equimolar ratio are reacted in a batch reactor using sulfuric acid as a catalyst. Second-order reaction: –ra = kCa²⁺kmor·m⁻³·h⁻¹, where k = 0.1182 m³·kmor·h. The initial concentration of adipic acid is CA₀ = 4 kmor·m⁻³. If 2400 kg of adipic acid is processed per day, each batch processing takes 1 hour, the reactor loading factor is 0.75, and the conversion rate is 80%, what is the required volume of the reactor? Solution: For a second-order batch reactor, tr = 1 × 0.8 / [(0.1182 × 4) × (1 – 0.8)] = 8.5 hours; tt = 8.5 + 1 = 9.5 hours. FA₀ = 2400 / (24 × 146) = 0.684 kmor/h. V₀ = FA₀ / CA₀ = 0.684 / 4 = 0.171 m³/h. The effective volume is v₀ × tt = 0.171 × 9.5 = 1.63 m³. The total volume is 1.63 / 0.75 = 2.17 m³. Question: Since both FA₀ and CA₀ are values related to adipic acid, why isn’t the volume flow rate the flow rate related to adipic acid itself? An equimolar amount of hexanediol should also require a certain reaction volume, right? If the initial concentration of hexanediol is also 4, does that mean the required reaction volume needs to be doubled?
CA0 refers to the concentration of component A at the moment when the reaction begins, after the material has been loaded into the reactor; at this point, component B must also already be present in the reactor, and the reaction mixture consists of A and B. A:B=1:1, and the CB0 in the material is naturally the same as CA0. If A and B enter the reactor in two streams at a flow ratio of 1:1, with the concentration of one stream being CA and that of the other stream being CB before entry, then the concentration after mixing will be 1/2CA and 1/2CB. At this point, the concentrations of A and B (1/2CA and 1/2CB) are respectively equal to CA0 and CB0. This situation needs to be specifically stated in the problem conditions. There is an issue with the expression of the reaction equation in this question; it should be -ra=kCaCbkmor.m-3.h-1. If written as in the original question, it would imply a second-order reaction with respect to adipic acid and a zero-order reaction with respect to hexanediol.
Because the concentration is used to calculate volume, not the amount of substance. The concentration can already represent the overall condition of the material.