# Example 2.6: Cryogenic plant

Methane must be condensed for intercontinental transport or when no pipeline is available. What range of operating conditions is necessary? If 10 000 (metric) tons a day is to be transported, how much energy is required per year to accomplish this task?

The data provided are the critical pressure (4600.1 kPa), the critical temperature (190.55 K), the normal boiling temperature (111.66 K) and the molar mass (16.04 kg/kmol). Use corresponding states method for methane.

## Analysis:

To condense methane from vapour to liquid, the heat of vaporization (vaporization enthalpy) has to be eliminated.

Pressure, temperature and enthalpy are required in this problem.

Methane is the only compound and is transported at its bubble point. The corresponding states principle can be applied, and the values can be read from figures 1 and 2.

## Solution:

### See complete results in file (xls):

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The normal boiling point is very low (113.15 K; ~-160 °C or Tr=0.59). Working at higher pressure would make it possible to condense at a higher temperature, thus limiting the amount of cooling. If pressure is 1 MPa (Pr=0.22) temperature of the liquid methane would be near Tr=0.8, which corresponds to slightly over 150 K. Thermal losses against ambient temperature would be very high and insulation is the only way to prevent excessive evaporation from the tanker (up to 0.9 m thick). New steels have been developed to maintain good resistance at low temperature and, nowadays, cryogenic tankers can transport liquids at almost atmospheric pressure. Note, nevertheless, that for road transportation, pressurized vessels are preferably used due to the size of cylinders on trucks together with a smaller insulation. Energy required to condense methane can be read (in its non-dimensional form) from figure 2. The 0.6 isotherm is so low that is not shown on the graph. It is just between the 0 axis and the 0.7 line. At this level, the width of the two-phase zone (difference of height between the dew line on top and the bubble line at the bottom) measures 4.8. Using an approximation for the molar gas constant of 8.3 J/(mol.K), the following value is obtained:

An experimental figure of -8250 J/mol is reported in DIPPR. The molar flow rate of methane and the annual energy necessary for condensation will be:

This value is sometimes expressed as 55 MW. As liquefaction represents almost 40 % of the cost of LNG production, we can see why the price of liquid methane is so high in comparison with gaseous production. This cost is close to 1% of the heat of combustion of methane.