Chapter 4, Problem 4.88P

Natural gas containing a mixture of methane, ethane, propane, and butane is burned in a furnace with excess air.

1. One hundred kmol/h of a gas containing 94.4mole% methane, 3.40% ethane, 0.60% propane, and 0.50% butane is to be burned with 17% excess air. Calculate the required molar flow rate of the air.
2. Let
hi(kmol/h) = molar flow* of the fuel gas

Xi, x₂, x₃, x» = mole fractions of methane, ethane, propane.

and butane, respectively, in the fuel = percent excess air

n_a( kmol/h) = molar flow^r rate of the air ted to the furnace

Derive an expression for n_a in terms of the other variables. Check your formula with the results of Part (a).

Suppose the feed rate and composition of the fuel gas are subject to periodic variations, and a process control computer is to be used to adjust the flow rate of air to maintain a constant percentage excess. A calibrated electronic flowmeter in the fuel gas line transmits a signal R_tthat is directly proportional to the flow rate (/if = (iRt), with a flow rate of 75.0 kmol/h yielding a signal R_t= 60. The fuel gas composition is obtained with an on-line gas chromatograph. A sample of the gas is injected into the gas chromatograph (GC), and signals A₍, A₂, A₃, and A₄, which are directly proportional to the moles of methane, ethane, propane, and butane, respectively, in the sample, are transmitted. (Assume the same proportionality constant for all species.) The control computer processes these data to determine the required air flow rate and then sends a signal /?_a to a control valve in the air line. The relationship between R₃and the resulting air flow' rate, n_a, is another direct proportionality, with a signal R_a= 25 leading to an air flow rate of 550 kmol/h.

Write a spreadsheet or computer program to perform the following tasks:

Take as input the desired percentage excess and values of R{, Ai, A₂, A₃, and A₄.

Calculate and print out hf, xi, x₂, x₃, x₄, h_a, and /?_a.

Test your program on the data given below, assuming that 15% excess air is required in all cases. Then explore the effects of variations in and R_fon h_afor the values of A_f — A₄ given on the third line of the data table. Briefly explain your results.

Rt	A,	a2	a3	A4
62	248.7	19.74	6.35	1.48
83	305.3	14.57	2.56	0.70
108	294.2	16.61	4.78	2.11

Finally, suppose that when the system is operating as described, stack gas analysis indicates that the air feed rate is consistently too high to achieve the specified percentage excess. Give several possible explanations.