Heating and Cooling Due to Expansion

Hydrocarbon fluid systems undergo rapid expansion around the wellbore and in production facilities, As a result of expansion, the temperature may rise or fall. The following establishes the criteria for cooling and heating due to free expansion. The derivations are limited to 

TABLE 3.6 Enthalpy of ternary mixture of methane, ethane, and CO2 (data of Ng and Mather, 1978) 

Consider the sketch. Fig. 3.34, in which a fluid is expanding from pressure P to pressure P., at steady state conditions. The system is rigid and insulated. Assume two imaginary pistons at points A and B at time t. During time interval At, piston 1 moves from point A to A and piston 2 moves from point B to S. The fluid contained between pistons 1 and 2 is our thermodynamic system. The work done on the system in the time interval At is given by 

149) implies that if ju is positive, the free expansion results in cooling. For a negative pL, the free expansion leads to heating. 

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Chapter 3 contains a simple presentation of cubic equations of state and their strengths for pure components and mixtures. It is shown that cubic equations can be used to calculate (1) volumetric properties, (2) gas and liquid phase compositions, (3) thermal properties, and (4) sonic velocities. The last two items, thermal properties and sonic velocity, are related. Three types of problems are solved in this chapter (1) two-phase compressibility, (2) two-phase sonic velocity, and (3) heating and cooling due to expansion for multicomponent mixtures. For the two-phase compressibility and two-phase sonic velocity, it is shown that the two-phase gas-liquid compressibility can be greater than the gas compressibility and the two-phase sonic velocity can be less than the gas-phase sonic velocity. The calculation procedures for these two problems are provided in detail. The problem of heating and cooling from expansion is well known, and is much simpler than the first two problems. 

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