Design an outside storage facility for methane gas (CH4). 110 kg is the maximum

Question

Design an outside storage facility for methane gas (CH4). 110 kg is the maximum mass of methane to be stored at this facility. The container to be designed is spherical and is not insulated. The temperature range the tank must be able to withstand is -10oC and 30oC . the maximum pressure is set by a pressure relief valve at 5MPa. If a container costs $1000/M^2 installed. Determine the dimensions of the lowest cost container considering the provided environmental factors. Consider the following when making the determination: - ideal gas law -compressability Z chart - using the vanderwaals equation

Explanation / Answer

P = 5 Mpa

m = 110 kg

cost will be minimum , at -10 C, bu t we have to design the constainer so that it can withstand the 30 C

so T = 30 C = 303 K

Now, Pv =m.R.T

for Co2, R = 8.314/48 = 0.173 KJ/Kg.K

so, 5 x 1000 x v = 110 x 0.173 x 303

so, Voume = v = 1.15 m^3

let r = raidus of the constanier.

then volume = 4/3.pi.r^3 =1.15

so, radius = r = 0.65 m

so area of container = 4.pi.r^2 = 4 x pi x 0.65^2

= 5.3 m^2

so COST = $1000 x 5.3 = % 5300

B0 with compressibility cahrt and vander wall equation volume cones out to be = 1.165 m^3

so, 4/3. pi.r^3 = 1.165

so, radius = r = 0.66 m

so, cost = area x $1000

= 4 x pi x 0.66^2 x $1000

= $5474

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