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THERMODYNAMIC PROPERTIES OF SUPERCRITICAL FLUIDS

A supercritical fluid changes from gas-like to liquid-like as the pressure is increased and its thermodynamic properties change in the same way. Close to the critical temperature, this change occurs rapidly over a small pressure range. A facility is provided on this website for the calculation of some thermodynamic properties from an equation of state.

The most familiar property is the density and its behaviour is illustrated in the figure above. This shows three density-pressure isotherms and at the lowest temperature, 6 K above the critical temperature, the density change is seen to increase rapidly at around the critical pressure. As the temperature is raised, the change is less dramatic and moves to higher pressures. One consequence is that it is difficult to control the density near the critical temperature and, as many effects are correlated with the density, control of experiments and processes can be difficult. Other properties, such as enthalpy also show these dramatic changes near the critical temperature.

To illustrate the significance and behaviour of enthalpy and entropy for those not familiar with process engineering design, a simple supercritical-fluid process is now discussed. The example chosen is an extraction with carbon dioxide in which the fluid is recycled and this is shown in the figure above, where the process is illustrated schematically as a graph of enthalpy versus entropy. Although extraction is taking place, for the purposes of illustration it will be assumed that the properties of the fluid are those of pure carbon dioxide. Point A represents liquid carbon dioxide in a condenser or storage vessel at -3°C and 40 bar. It is pressurized to 200 bar to point B and then heated to 47°C at point C, where extraction occurs. The pressure is then reduced, with heating, to 40 bar at the same temperature for separation at point D. The carbon dioxide is then cooled again to -3°C at point A for recycling.

During pumping, passing from point A to point B no heat is put into the fluid (ignoring friction), the entropy is therefore constant and the line A–B is vertical. However, the temperature will rise as the fluid is compressed. The entropy of carbon dioxide at 270 K and 40 bar is 136 J mol^–1 K^–1 and at 200 bar carbon dioxide has the same value of entropy at 280 K. Therefore the carbon dioxide has increased in temperature by 10 K due to the compression work done on it. At 270 K and 40 bar the enthalpy is 21.7 kJ mol^–1, whereas at 280 K and 200 bar it is 22.4 kJ mol^–1. The difference of 0.7 kJ mol^-1 is the work done by the pump and this value can be used, with the required flow rate to estimate the power output required for the pump. The carbon dioxide is still liquid and heat is required to bring it into the supercritical state between B and C before extraction. The enthalpy at 320 K and 200 bar is 26.2 kJ mol^–1 and so 3.8 kJ mol^–1 is required from the heat exchanger. This value, with the flow rate, provides information for the design of the heat exchanger. Following extraction, the pressure is reduced through a control with heating. The enthalpy of carbon dioxide at 320 K and 40 bar is 34.8 kJ mol^–1 and so 8.6 kJ mol^–1 is required. This is the largest amount of heating required from a heat exchanger in the process and this is because on passing from C to D the fluid is changing from liquid-like to gas-like. Finally to condense the carbon dioxide to a liquid at 40 bar the enthalpy must be reduced to its value at A requiring 13.1 kJ mol^–1 to be removed by a cooler between D and A. With the flow rate, the size of the refrigeration unit needed can be calculated from this value. The amount of energy removed by the cooler equals, of course, the total of the compression and heat energy put into the system between A and D.

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