(a) Prove that for a first order decay reaction (k1= 2 days-1) taking place in reactors of identical size at steady state, it does not matter if you use a CMFR followed by a PFR or a PFR followed by a CMFR (i.e. show that the final treated effluent concentration, in mg/L, is approx. the same in each scenario). Assume the volume of each reactor is 15 L and the reactors in series will be used to treat a wastewater containing 5 mg/L of contaminant “C” at a flowrate of 10 L/day. (b) Does this remain true if a second order decay reaction was taking place? If not, which sequence of reactors is more efficient (i.e. removes more of the contaminant)? Assume the same reactor volumes, flow rate and contaminant concentration as in part (a), and k2 = 2 Lmg-1day-1 . You must show your derivation of the expression for a PFR with 2nd order decay.

(a) Prove that for a first order decay reaction (k1= 2 days-1) taking place in reactors of identical size at steady state, it does not matter if you use a CMFR followed by a PFR or a PFR followed by a CMFR (i.e. show that the final treated effluent concentration, in mg/L, is approx. the same in each scenario). Assume the volume of each reactor is 15 L and the reactors in series will be used to treat a wastewater containing 5 mg/L of contaminant “C” at a flowrate of 10 L/day. (b) Does this remain true if a second order decay reaction was taking place? If not, which sequence of reactors is more efficient (i.e. removes more of the contaminant)? Assume the same reactor volumes, flow rate and contaminant concentration as in part (a), and k2 = 2 Lmg-1day-1 . You must show your derivation of the expression for a PFR with 2nd order decay.

Materials Science And Engineering Properties

1st Edition

ISBN:9781111988609

Author:Charles Gilmore

Publisher:Charles Gilmore

Chapter4: Temperature Effects On Atom Arrangements And Atom Motion

Section: Chapter Questions

Problem 4.14P

See similar textbooks

Similar questions

3. A CFSTR receives a flow rate of 100 m³/sec. There is one influent stream coming into the reactor and one effluent stream leaving the reactor. The concentration of a chemical in the influent stream is reduced by 95% in the reactor. Given, the chemical has a first order decay rate of 0.15/d. Find the volume of the CFSTR (in m³).
Consider the reactor shown in the figure. The flow rate through the reactor is Q m/h. The concentrations (in mg/L) of a compound in the influent and effluent are C, and C, respectively. The compound is degraded in the reactor following the first order reaction. The mixing condition of the reactor can be varied such that the reactor becomes either a completely mixed flow reactor (CMFR) or a plug-flow reactor (PFR). The length of the reactor can be adjusted in these two mixing conditions to LCMFR and LPER while keeping the cross-section of the reactor constant. Assuming steady state and for C/C, = 0.8, the value of LoMER/LPER (round off to 2 decimal places) is_ Q, C Co
When a slug of tracer is injected into a cascade of CFSTRs, a maximum value of C₁ occurs at t> 0 for all reactors except the first. Determine the time when the peak occurs in the nth reactor in terms of OH.
A 9.00-mol sample of H₂ gas is contained in the left side of the container shown below, which has equal volumes on the left and right. The right side is evacuated. When the valve is opened, the gas streams into the right side. H₂ Valve Vacuum (a) What is the entropy change of the gas? J/K (b) Does the temperature of the gas change? Assume the container is so large that the hydrogen behaves as an ideal gas. The temperature decreases. O The temperature increases. The temperature does not change. ✓
Environmental Engineering: Water Treatment Please consider each of the following points: a. Determine the required residence time for each reactor of 3 equal volume CSTRs in series given a zero-order reaction with a reaction rate constant, k = -5 mg/L hr. The influent concentration is 125 mg/L and 95% conversion is required across the three-reactor system. What is the total reactor system residence time? b. Determine the required residence time for a single CSTR given the same conditions. c. Determine the required residence time for a PFR given the same conditions. d. Why are all three residence time the same?
3. A first order decay reaction is occurring in a single CFSTR. Dividing the reactor into two smaller CFSTRs that are operated in series (effluent from one serving as the influent to the other) reduces the overall mixing and therefore makes the flow more PFR-like. Because reaction efficiency is greater in a PFR than a CFSTR, we might expect that dividing the reactor would improve the efficiency. To test that hypothesis, consider a system receiving an influent with C = 100 mg/L of a reactant that undergoes a first order decay reaction with a rate constant of 0.1 min ¹. Assume that the system has a total hydraulic detention time of 1 hour, but that it can be operated in three different ways: as a PFR, a CFSTR, or as two CFSTRs in series with the detention time split equally between the two. Find the effluent concentrations for the three possible operating modes
The rise times (unit: min) of a reactor for two batches are measured in experiment. 1.Define the sample space of the experiment. 2.Define E1 where the reactor rise time of the first batch is less than 55 min and E2 where the reactor rise time of the second batch is greater than 70 min. 3.Find E1 ∪ E2, E1 ∩ E2, and E1’. 4.Are E1 and E2 mutually exclusive? 5. Are E1 and E2 exhaustive?
An ideal continuous stirred tank reactor (CSTR) has an influent containing Chemical X at a concentration of 150 mg/l and a flow rate of 100 gpm (380 liters/min). Chemical X undergoes a first-order decay reaction having k = 0.40 hr –1 . Determine: 1a. The required detention time and volume of the CSTR if the effluent concentration contains 20 mg/l of Chemical X. Express the volume in both gallons and liters. 1b. Use a spreadsheet to perform the necessary calculations and then use the spreadsheet's graphing tools to plot two graphs; i. Pollutant removal efficiency, 1e, on the vertical or y-axis versus hydraulic detention time on the horizontal or x-axis. ii. Effluent concentration, CX1 , on the vertical or y-axis versus hydraulic detention time on horizontal or x-axis. Analyze and comment on the significance of the graphs. 1c. How many times larger must a CSTR be than a PFR to achieve 80 percent pollutant removal or conversion? 1d. How many times larger must a CSTR be than a PFR to…
When the system is at equilibrium at a particular temperature, C(s) + CO2(g) =2 CO(g) a 4-L flask contains 0.40 mol CO, 0.80 mol CO2, and 0.45 mol C. What is the value of K, at that temperature? O 0.050 O 0.20 1.8 O 0.44
A medium containing 50 g/L of S (substrate) is continuously fed into a completely mixed reaction vessel at a certain liquid flow rate. The working volume of the reactor is maintained at a constant liquid volume of 10 L by overflowing. The following table shows the steady state concentrations of X (biomass or cell), S, and P (product). X (g cells/L) S (g/L) P (g/L) 2.0 30.0 18.0 3.0 20.0 27.0 4.0 10.0 36.0 4.5 5.0 40.5 4.8 2.0 43.2 If cell growth follows the Monod equation, no cell death occurs at steady state, and the product formation is growth-associated, determine (1) μmax, (2) Ks, (3) Yx/s, and (4) Yp/s.
You are designing a reactor that uses chlorine in a plug flow reactor or a completely stirred tank reactor to destroy pathogens in water. A minimum contact time of 30 min is required to reduce the pathogen concentration from 100 pathogens/L to below 1 pathogen/L through a first-order decay process. You plan on treating water at a rate of 1,000 gal/min. (a) What is the first-order decay rate constant? (b) What is the minimum size (in gallons) of the reactor required for a plug flow reactor? (c) What size (in gallons) of CSTR would be required to reach the same outlet concentration?
(9A metal rod made of some alloy is to be used as a thermometer. At OoC its length is 40000cm, and at 1000C its length is 40060cm. (a) What is the linear expansion coefficient of the alloy? (b) what is the temperature when its length is 39975cm?