Chapter 5, Problem 5.46P

The ?ow of air to a gas-?red boiler furnace is controlled by a computer. The fuel gases used in the furnace are mixtures of methane (A), ethane (B), propane (C), n-butane (D), and isobutane (E). At periodic intervals the temperature, pressure, and volumetric ?ow rate of the fuel gas are measured, and voltage signals proportional to the values of these variables are transmitted to the computer. Whenever a new feed gas is used, a sample of the gas is analyzed and the mole fractions of each of the ?ve components are determined and read into the computer. The desired percent excess air is then speci?ed, and the computer calculates the required volumetric ?ow rate of air and transmits the appropriate signal to a ?ow-control valve in the air line.

The linear proportionalities between the input and the output signals and the corresponding process variables may be determined from the following calibration data:

Fuel Temperature: T = 25.0°C, R1 = 14

Fuel Temperature: $\begin{array}{c}T=20.0°\text{C,}\\ T=35.0°\text{C,}\end{array}\begin{array}{c}{R}_T=14\\ R_T=27\end{array}$

Fuel Pressure: $\begin{array}{c}{P}_{\text{gauge}}\text{=0kPa},\\ P_{\text{gauge}}\text{=20}\text{.0kPa,}\end{array}\begin{array}{c}{R}_P=0\\ R_P=6\end{array}$

Fuel Flow Rate: $\begin{array}{c}{V}_{\text{f}}=0{\text{m}}^{\text{3}}\text{/h},\\ V_{\text{f}}=2.00\times {10}^3{\text{m}}^{\text{3}}\text{/h,}\end{array}\begin{array}{c}{R}_{\text{f}}=0\\ R_{\text{f}}=10\end{array}$

Air Flow Rate: $\begin{array}{c}{V}_{\text{a}}=0{\text{m}}^{\text{3}}\left(\text{STP}\right)\text{/h},\\ V_{\text{a}}=1.0\times {10}^5{\text{m}}^{\text{3}}\left(\text{STP}\right)\text{/h,}\end{array}\begin{array}{c}{R}_{\text{a}}=0\\ R_{\text{a}}=25\end{array}$

Create a spreadsheet or write a program to read in values of $R_{\text{f}},R_T,R_P$, the fuel gas component mole fractions $x_{\text{A}},x_{\text{B}},x_{\text{C}},x_{\text{D}}$, and $x_{\text{E}}$, and the percent excess air PX, and to calculate the required value of R_A.

Run your program for the following data.

Rf	RT	RP	xA	xB	xC	xD	xE	PX
7.25	23.1	7.5	0.81	0.08	0.05	0.04	0.02	15%
5.80	7.5	19.3	0.58	0.31	0.06	0.05	0.00	23%
2.45	46.5	15.8	0.00	0.00	0.65	0.25	0.10	33%