A liquid mixture containing 50 mole% propane, 30% w-butane, and 20% isobutane is

Question

A liquid mixture containing 50 mole% propane, 30% w-butane, and 20% isobutane is stored in a rigid container at 77 degree F. The container has a maximum allowable working pressure of 400psig. The head space above the liquid contains only vapors of the three hydrocarbons. (a) A form of the Antoine equation for which constants for the three components are available15 is log_l0P^* = A - B/(T + C) where p* is in bar and T is in kelvin. The constants and the data range from which they were obtained are given in the following table: Using these values and Raoult's law, show that use of the container at the given temperature is safe, (b) Assume that upon heating there is little change in the liquid composition, and obtain a rough estimate of the temperature above which the maximum allowable pressure would be exceeded. Explain why the assumption regarding no change in liquid composition is reasonable.

Explanation / Answer

Given temperature = 770F = 298 K

Lets denote propane by 'x', n-butane by 'y' and isobutane by 'z'

Using Antoine equation, calculate the following:

Px0 = 9.49 bar

Py0 = 2.42 bar

Pz0 = 3.47 bar

Xx = 0.5

Xy = 0.3

Xz = 0.2

Using Raoult's law:

P = Px0*Xx + Py0*Xy + Pz0*Xz

P = 9.49*0.5 + 2.42*0.3 + 3.47*0.2 = 6.165 bar = 89.42 psig

Since net pressure is well below the specified limit, the working is completely safe.

(b)

Using hit and trial approach we find that at approx. between 365-370 K , the temperature would be enough to increase the total pressure value beyond 400 psig.

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