Chapter 9, Problem 9.68P

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:

x_m= mole fraction of methane in the fuel

x_A= mole fraction of argon in the fuel

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

T_a(°C) = temperature of the entering air

T_s(°C) = stack gas temperature

r = ratio of CO₂to CO in the stack gas (mol CO₂/mol CO)

$\stackrel{\dot{}}{Q}\left(kW\right)$= rate of heat transfer from the furnace to the boiler tubes

1. Without doing any calculations, sketch the shapes of the plots you would expect to obtain for plots of Q versus (i) x_M, (ii) x_A, (iii) P_xs, (iv) T_a, (v) T_s, and (vi) r, assuming in each case that the other variables are held constant. Briefly state your reasoning for each plot.
2. 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 x_M, x_A, P_xs, 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 T_aand T_s.
Calculate $\stackrel{\dot{}}{Q}\left(kW\right)$for x_M= 0.85 mol CH ₄/mol, x_A= 0.05 mol Ar/mol. P _{x s}= 5%, r = 10.0 mol CO ₂/mol CO, T _a= 150°C, and T _s= 700°C (Solution: $\stackrel{\dot{}}{Q}$
3. = -655 kW.)
Prepare a spreadsheet that has columns for. x_M, x_A, P _{x s , ,} T_a, r, T_s, and $\stackrel{\dot{}}{Q}$ . 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:

x_M= 0.00—0.85 mol CH₄/mol

x_A= 0.01—0.05 mol Ar/mol

P_xs= 0%-100%

T_a= 25°C—25O°C

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

T_s= 500°C-1000°C

When generating each plot, use the variable values given in Part (c) as base values. (For example, generate a plot of $\stackrel{\dot{}}{Q}$versus x_Mfor x_A= 0.05, P_xs= 5%, and so on, with x_Mvarying from 0.00 to 0.85 on the horizontal axis.) If possible, include the plots on the same spreadsheet as the data.