Pollutant P undergoes first-order degradation. An aqueous stream containing 2 kmole/m3 of P at 1 m3/h requires volume V in a mixed reactor to reach 0.5 kmole/m3. If inlet concentration doubles and flow rate triples while outlet concentration remains 0.5 kmole/m3, by what factor must the mixed reactor volume be scaled up_______________?
Show answer Hide answer
Answer: A. 7
Explanation
CSTR design equations for first-order reactions relate volume, flow rate, and concentrations. Doubling inlet concentration and tripling flow rate alters mass balance requirements. Solving the steady-state reactor design equation yields a volume scale-up factor of 7. Continuous stirred tank reactor mass balances assume perfect mixing and uniform composition. Space time is calculated as reactor volume divided by volumetric feed rate. First-order degradation kinetics simplify algebraic reactor design calculations.
Environmental engineering relies on CSTR models to design wastewater treatment aeration basins. Industrial pollutant degradation units must scale up when influent loading rates increase. Reactor volume scaling calculations prevent undersizing biological or chemical treatment systems. Alternative scale-up factors fail to satisfy the stoichiometric mass balance equations. Simple proportional scaling ignores the non-linear nature of CSTR kinetics. Rigorous mathematical derivation confirms a scale-up factor of 7 is required.
- Subject
- Engineering
- Category
- Chemical Engineering
- Topic
- —
- Difficulty
- medium
Related questions
Q1. A second-order liquid reaction A → B is run in a semi-batch mixed reactor (no outflow). Reactant A at feed concentration CAF is supplied at volumetric flow rate F, maintaining a constant liquid volume V and constant density. The component mass balance for A is_______________________?
Show answer Hide answer
Answer: D. d(VCA)/dt = FCAF – kCA2V
Mass balance equations for semi-batch reactors account for reactant mass input minus consumption. Inlet volumetric flow rate supplies reactant mass at feed concentration into the reactor. Second-order reaction kinetics c...
Q2. An acid-catalyzed reaction is also promoted by any species exhibiting a tendency to _________________?
Show answer Hide answer
Answer: A. Lose a proton
Brønsted-Lowry acids function as chemical species that donate or lose protons readily. Substances exhibiting a strong tendency to lose a proton promote acid-catalyzed reactions. Proton donation activates reactant molecul...
Q3. A reversible, endothermic, liquid-phase reaction is conducted in a plug flow reactor. To minimize reactor volume, the temperature profile along the length should be operated such that ?
Show answer Hide answer
Answer: C. Is at the highest allowable temperature throughout
Endothermic reactions absorb heat, so higher temperatures shift equilibrium toward product formation. Reaction rates also increase exponentially with temperature according to the Arrhenius relationship. Operating at the...
Q4. A second-order reaction A + B → C behaves as a pseudo-first-order reaction when____________________?
Show answer Hide answer
Answer: D. CB0 ≥ CB0
A second-order reaction becomes pseudo-first-order when one reactant is present in large excess compared to the other.
Q5. A space time of 3 hours in a flow reactor signifies that___________________?
Show answer Hide answer
Answer: A. The time required to process one reactor volume of feed (measured at specified conditions) is
Space time represents the exact duration required to process one reactor volume of feed. Volumetric feed rates must be measured at specified reference conditions for accuracy. A three-hour space time means three hours of...
Q6. A space velocity of 5 hr-1 denotes that ___________________?
Show answer Hide answer
Answer: A. Five reactor volumes of feed (at specified conditions) are being fed into the reactor per hour
Space velocity indicates the number of reactor volumes of feed treated per unit time. A value of five inverse hours means five reactor volumes pass through per hour. Reactor sizing calculations frequently utilize space v...