Question

A pressure vessel is being designed to hold compressed methane to fuel a liquid rocket motor at a maximum pressure of 50 bar. If the methane is to be stored at 40 bar, -18 C, determine the mass contained in a 10 m3 tank using the following assumptions:

a) The ideal gas equation of state.

b) The van der Waals equation of state.

c) Using CoolProp. Comment on the accuracy of each.

Answer 1

SOLUTION : -

a) Ideal gas equation is -

PV = n RT

P = 40 x 10⁵ Pa = 40 x 10² kpa

R = 8.314 J/mole/K

V = 10m³

T = - 18 +273 = 255K

so that n = PV/RT

n = 40 x10² x10/(8.314 x 255)

n = 18.86 mol

n = m/Molecular weight of Methane

Molecular weight of = CH₄ = 12 +4= 16g/mole

so that,

n = m/16

mass, m = n x16 = 18.86 x 16

m = 301.87 gm = 0.301 kg

b) By Van Der Waals Equation of state -

Vander waals constants for methane gas -

a = 2.3 bar L²/mole²

b = 0.04301 L/mole

By Vander Waal's gas equation-

( P + n²a/V²) (V - nb) = n R T

(40 + n²x2.3/10²) (10 - n x 0.04301) = n x 8.314 x 255

- 0.00098n³ + 0.23n² - 2137.21n +400 =0

n = 0.187, 117.25+1472i,117.25 +1472i

0.187 is acceptable

so that

n = m/16

m= 2.992 gm

m = 0.00292kg

c)

CoolProp is a C++ library that implements:

• Pure and pseudo-pure fluid equations of state and transport properties for 122 components
• Mixture properties using high-accuracy Helmholtz energy formulations
• Correlations of properties of incompressible fluids and brines
• Highest accuracy psychrometric routines
• User-friendly interface around the full capabilities of NIST REFPROP
• Cubic equations of state (SRK, PR)