Methane enters a heat exchanger at a volumetric flow rate of 120.0 m ^3/min, at an absolute...

Question:

Methane enters a heat exchanger at a volumetric flow rate of 120.0 m{eq}\displaystyle ^3 {/eq}/min, at an absolute pressure of 1.013 bar and temperature of 10.0{eq}\displaystyle ^oC. {/eq} At these conditions, the specific enthalpy of methane is -34.199 kJ/Kg. The methane leaves the heat exchanger at an absolute pressure of 1.013 bar and temperature of 90.0{eq}\displaystyle ^oC. {/eq} The corresponding specific enthalpy at these conditions is 149.614 kJ/kg. The methane is heated by a stream of saturated steam entering the heat exchanger at 2.6 bar (absolute) and leaving as a liquid at 54{eq}\displaystyle ^oC. {/eq} Find the volumetric flow rate of saturated steam into the heat exchanger by following the steps below.

What is the mass flow rate of methane into the heat exchanger?

What rate of heat is supplied to the methane stream in order to heat it from 10.0{eq}\displaystyle ^oC {/eq} to 90.0{eq}\displaystyle ^oC? {/eq}

What is the minimum mass flow rate of saturated steam into the heat exchanger?

What is the volumetric flow rate of saturated steam into the heat exchanger?

1) First, we'll calculate the mass flow rate of methane using ideal gas equation:

PV = mRT

101.3 * 2 = m * (8.314 / 16) * 283

m = 1.3777 kg/seconds

2) The heat absorbed by the gas will be:

Heat absorbed = 1.3777 * (149.614 - (-34.199))

Heat absorbed = 253.244 kj/seconds

3) To calculate the parameters of the steam, we need to refer to the steam table.

According to the steam table at 2.6 bar and 128.73 degree c:

Latent heat of condensation = 2177.3 kj/kg.

Now we need to determine the heat extracted:

Heat extracted from saturated steam = latent heat of condensation + heat released from condensation of saturated liquid to liquid.

Heat extracted from saturated steam = 2177.3 + (4.1868(128.73 - 54))

Heat extracted from saturated steam = 2490.12 kj/kg

According to the principle of energy conservation, the heat released from saturated steam is equal to the heat absorbed by the methane:

Mass flow of steam * 2490.12 = 253.244

Mass flow of steam = 0.1017 kg/seconds

Finally, we need to find the value of density at pressure 2.6 bar from the steam table.

According to the steam table: Density = 1.444 kg/m^3 at 2.6 bar.

Therefore:

Volume flow rate = Mass flow rate * Density

Volume flow rate = 0.1017 * 1.444

Volume flow rate = 0.1468548 m^3/seconds

Volume flow rate = 8.811288 m^3/minutes