A mixture of methane, ethane, and argon at 25°C is burned with excess air in a power plant boiler. The hydrocarbons in the fuel are completely consumed. The following variable definitions will be used throughout this problem:

xm mole fraction of methane in the fuel

xa mole fraction of argon in the fuel

Pxs (%) = percent excess air fed to the furnace

Ta (°C) = temperature of the entering air

Ts (°C) = stack gas temperature

r = ratio of CO2 to CO in the stack gas (mol CO2/mol CO) Q (kW) = rate of heat transfer from the furnace to the boiler tubes

(a) Without doing any calculations, sketch the shapes of the plots you would expect to obtain for plots of Q versus (i) xm, (ii) xa, (iii) Pxs, (iv) Ta, (v) Ts, and (vi) r, assuming in each case that the other variables are held constant. Briefly state your reasoning for each plot.

(b) Take a basis of 1.00 mol/s of fuel gas draw and label a flowchart, and derive expressions for the molar flow rates of the stack gas components in terms of xm, xa, Pxs, and r. Then take as references the elements at 25°C prepare and fill in an inlet–outlet enthalpy table for the furnace and derive expressions for the specific molar enthalpies of the feed and stack gas components in terms of Ta and Ts.

(c) Calculate Q (kW) for xm = 0.85 mol CH4/mol, xa = 0.05 mol Ar/mol, Pxs = 5%, r = 100 mol CO2/mol CO, Ta = 150°C, and Ts = 700°C.

(d) Prepare a spreadsheet that has columns for xm, xa, Pxs, Ta, r, Ts, and Q, plus columns for any other variables you might need for the calculation of Q from given values of the preceding six variables (e.g.. component molar flow rates and specific enthalpies). Use the spreadsheet to generate plots of Q versus each of the following variables over the specified ranges:

xm 0.00—0.85 mol CH4imol

xa = 0.01-0.05 mol Ar/mol

Pxs = 0%-100%

T = 25°C—250°C

r = 1 – 100 mol CO2/mol CO (make the r axis logarithmic)

Ts = 500°C-10O0°C When generating each plot, use the variable values given in part (c) as base values. (For example. generate a plot of Q versus xm for xa = 0.05, Pxs = 5%. and so on, with xm varying from 0.00 to 0.85 on the horizontal axis.) If possible, include the plots on the same spreadsheet as the data.