1. In a global, single-step mechanism for butane combustion, the reaction order with respect to butane is 0.15 and with respect to oxygen is 1.6. The rate coefficient can be expressed in Arrhenius form: the pre-exponential factor A is 4.16E09 (in SI units), and the activation energy EA is 125,000 kJ/kmol; the temperature exponent is equal to zero.

What are the units of A? Write an expression for the rate of butane destruction, d[C4H10]/dt.

2. Using the results of problem 1, determine the numerical value of the volumetric mass oxidation rate of butane (in kg/m3-s) for a fuel-air mixture with an equivalence ratio of 0.9, temperature of 1200 K, and pressure of 1 atm.

3. Consider the four-step elementary reaction mechanism discussed in lecture and in the textbook for CO oxidation, in the case where there is water present. How many chemical rate equations are needed to determine the chemical evolution of a system defined by this mechanism? Write an expression for the time rate of change of hydroxyl radical concentration, in terms of rate coefficients and species molar concentrations. Consider each elementary reaction to be a reversible reaction.

4. The temperature and pressure of a mixture of gases can be raised rapidly (effectively instantaneously) by passing a shock wave through the mixture. See Example 4.4 in Turns 3rd edition, for example. This is useful for studying chemical kinetics, and can be simulated using CHEMKIN. Here we are not interested in the physics of compressible flows, but rather in the chemical kinetics that start after the shock wave passes through the mixture, and continue until the system eventually reaches steady state. The shock wave essentially sets the initial pressure and temperature of the mixture to sufficiently high values that the chemical reactions can begin to proceed at nontrivial rates.

Here you are to use the GRI-Mech 3.0 chemical mechanism and corresponding thermodynamic data. This is a state-of-the-art chemical mechanism that has been developed for natural-gas combustion, including detailed NOx chemistry (see http://www.me.berkeley.edu/gri_mech/version30/text30.html and Chapter 5 of Turns 3rd edition). Here we are interested primarily in the NOx chemistry. The chemical mechanism file (grimech3.0_chem.inp) and thermodynamic properties file (grimech3.0_therm.dat) have been posted on ANGEL by the instructor.

Follow the same general sequence of operations as you did in earlier CHEMKIN assignments. Don't forget to update/save at appropriate steps in the process.

• Select the "Normal Incident Shock" model under "Shock Tube Reactors." It might be useful to have a look at the corresponding CHEMKIN help files.

• In the "Pre-Processing" panel, specify the GRI-Mech 3.0 chemistry set given above.

• In the "C1_Incident_Shock" panel under "Cluster1 (C1):"
oIn the "Reactor Physical Properties" tab:
 Problem Type = Incident Shock Without Boundary Layer Correction.
 Begin Time = 0.0 s; End Time = 0.02 s (20 ms).
 Incident Shock Velocity = 2.5E5 cm/s.
Temperature Before Incident Shock = 298 K.
Pressure Before Incident Shock = 10 torr.
oIn the "Reactant Species" tab, specify Initial Reactant Fractions corresponding to standard engineering dry air: 21% O2, 79% N2.

• In the "Solver" panel under "Cluster1 (C1):"
oUse the default tolerance values.
oSpecify a Maximum Time Step Size of 0.001 s.

• In the "Output Control" panel under "Cluster1 (C1):"
oCheck the Output in Molar Concentration box.
oSpecify a Time Interval for Printing and a Time Interval for Saving Solution to be 0.001 s.

• In the "Run Model" panel: Run the model (Begin)
• Run the Post Processor to generate plots as specified below.
• Repeat the exercise, replacing a small amount of the N2 in the Initial Reactant Fractions with H2O: 21% O2, 79% N2, 1% H2O.

What are the initial pressure and temperature of the system immediately after the shock wave passes through, in each case (dry air, air with H2O)? Precise values can be found in the output files.

How do the pressure and temperature vary with time after the shock has passed through?

What are the final pressure and temperature of the system when the system reaches steady state, in each case (dry air, air with H2O)?

Comment on the differences that you observe between the dry air case and the air with H2O case. Can you explain the differences?

Remember that NO and NO2 are the primary pollutants of concern.

Temperature and pressure (both on the same plot) versus time

Use different y-axis scales for T and p, so that the plot is legible (see help files if you have trouble figuring out how to do this)

Mole fractions versus time for all species present in >10-8 mole fraction

This should be a very small subset of the 53 species in the mechanism

Don't put all species in one plot

Exercise judgment in how many species to include in each plot

Group species having similar mole fraction values in each plot

Use the same y-axis scale for all species on each plot