Question

Compressed natural gas is fed into a small underground pipeline having an inside diameter of 5.9 in. The gas enters at an initial temperature of 120oC and constant pressure of 132.3 psig. The metered volumetric flow rate at standard pressure of 14.7 psia and standard temperature of 25oC is 195.4 ft3/min. The ground temperature is constant at 15oC and serves as an “infinite sink” for heat transfer. a) Show that the mass flow rate is 0.0604 kg/sec, volumetric flow rate is 0.01 m3/s at 50oC and 10 atm, the total system pressure is 10 atm, and the gas density assuming ideal behavior is 6.04 kg/m3 at 50oC. You may assume other properties not dependent on pressure for methane at 50oC are k = 0.035 W/m K, Cp = 220 J/kg K and μ = 1.2x10-5 kg/m-sec. b). Develop an energy balance model to predict the steady state temperature profile of the natural gas in the pipe. c). Is the gas flow laminar or turbulent? d). What are the Prandtl, Nusselt, and Stanton numbers, and also the heat transfer coefficient of methane in the pipe?

Answer 1

Diameter of pipe = 5.9 in = 0.14986 m

We have gas conditions at 25⁰C and 14.7 psia (101352.9 Pa)

Volumetric flowrate of gas at 50⁰C is given as

Density of gas at 50⁰C = 6.04 kg/m³

Hence mass of gas, M

b)

Initial temperature of gas = 120⁰C

Initial pressure of gas = 912176.39 Pa

So energy balance model will be

..................................................................(1)

Equation 1 is the model equation

c)

Hence

Therefore flow is turbulent

d)

As we know that