Problems
(Those with an asterisk require a numerical solution and use of an appropriate software program—See Appendix I.)
1. In hydrocarbon oxidation a negative reaction rate coefficient is possible. (a) What does this statement mean and when does the negative rate occur? (b) What is the dominant chain branching step in the high-temperature oxidation of hydrocarbons? (c) What are the four dominant overall steps in the oxidative conversion of aliphatic hydrocarbons to fuel products?
2. Explain in a concise manner what the essential differences in the oxidative mechanisms of hydrocarbons are under the following conditions:
a. The temperature is such that the reaction is taking place at a slow (measurable) rate—that is, a steady reaction.
b. The temperature is such that the mixture has just entered the explosive regime.
c. The temperature is very high, like that obtained in the latter part of a flame or in a shock tube.
Assume that the pressure is the same in all three cases.
3. Draw the chemical structure of heptane, 3-octene, and isopropyl benzene.
4. What are the first two species to form during the thermal dissociation of each of the following radicals?
5. Toluene is easier to ignite than benzene, yet its overall burning rate is slower. Explain why.
6. Determine the generalized expression for the α criteria when the only termination step is radical–radical recombination.
7. In examining Eqn (3.8), what is the significance of the condition?
9. Using the forward reactions 3.20–3.24 and reaction rate constant data from Appendix C, determine the criteria for explosion of a stoichiometric hydrogen–oxygen mixture. At a pressure of 0.5 atm, what is the temperature at which the explosive reaction will occur?
10. ∗The reaction rate of a dilute mixture of stoichiometric hydrogen and oxygen in N2 is to be examined at 950 K and 10 atm and compared to the rate at 950 K and 0.5 atm. The mixture consists of 1% (by volume) H2. Perform an adiabatic constant-pressure calculation of the reaction kinetics at the two different conditions for a reaction time that allows you to observe the complete reaction. Use a chemical kinetics program such as SENKIN (CHEMKIN II and III) or the CLOSED HOMOGENEOUS_TRANSIENT code (CHEMKIN IV) to perform the calculation. Plot the temperature and major species profiles as a function of time. Discuss and explain the differences in the reaction rates. Use a sensitivity analysis or rate-of-progress analysis to assist your discussion. The reaction mechanism can be obtained from Appendix C or may be downloaded from the Internet (e.g., from the database of F.L. Dryer at http://www.princeton.edu/∼combust/database/other.html, the database from LLNL at http://www-pls.llnl.gov/?url=science_and_technology-chemistry-combustion, or the database from Leeds University, http://garfield.chem.elte.hu/Combustion/methane.htm).
11. ∗Investigate the effect of moisture on the carbon monoxide–oxygen reaction by performing a numerical analysis of the time-dependent kinetics, for example, by using SENKIN (CEMKIN II and III) or the CLOSED HOMOGENEOUS_TRANSIENT code (CHEMKIN IV). Assume a constant-pressure reaction at atmospheric pressure, an initial temperature of 1150 K, and a reaction time of approximately 1 s. Choose a mixture consisting initially of 1% CO and 1% O2 with the balance N2 (by volume). Add to this mixture, various amounts of H2O starting from 0 ppm, 100 ppm, 1000 ppm, and 1% by volume. Plot the CO and temperature profiles for the different water concentrations and explain the trends. From the initial reaction rate, what is the overall reaction order with respect to water concentration? Use a mechanism from Appendix C or download one from the Internet.
12. ∗Calculate the reaction kinetics of a methane–oxygen mixture diluted with N2 at a constant pressure of 1 atm and initial temperature of 1100 K. Assume an adiabatic reaction with an initial concentration of CH4 of 1% by volume, an equivalence ratio of 0.2, and the balance of the mixture nitrogen. Use the GRI-Mech 3.0 chemical mechanism for methane oxidation (which may be obtained from G. P. Smith, D. M. Golden, M. Frenklach, N. W. Moriarty, B. Eiteneer, M. Goldenberg, C. T. Bowman, R. K. Hanson, S. Song, W. C. Gardiner, Jr., V. V. Lissianski, and Z. Qin, http://combustion.berkeley.edu/Combustion_Laboratory/gri-mech/). Plot the major species and temperature profiles as a function of time. Determine the induction and ignition delay times of the mixture. Also, analyze the reaction pathways of methyl radicals with sensitivity and rate-of-progress analyses.
13. ∗Compare the effects of pressure on the reaction rate and mechanism of methane (see Problem 12) and methanol oxidation. Calculate the time-dependent kinetics for each fuel at pressures of 1 and 20 atm and an initial temperature of 1100 K. Assume the reaction occurs at constant pressure and the mixture consists of 1% by volume fuel, 10% by volume O2, and the balance of the mixture is nitrogen. A methanol mechanism may be obtained from the database of F.L. Dryer at http://www.princeton.edu/∼combust/database/other.html.
14. ∗Natural gas is primarily composed of methane, with about 2–5% by volume ethane and smaller concentrations of larger hydrocarbons. Determine the effect of small amounts of ethane on the methane kinetics of Problem 12 by adding to the fuel various amounts of ethane up to 5% by volume maintaining the same total volume fraction of fuel in the mixture. In particular, discuss and explain the effects of ethane on the induction and ignition delay periods.
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