# Summary

The Joule-Thomson Effect describes the change in temperature of a gas as it experiences a rapid change in pressure from passing through a valve, orifice or nozzle. It may represent a safety hazard, or an opportunity depending on the process.

# Definitions

 : Enthalpy : Temperature : Critical temperature : Reduced temperature : Pressure : Critical pressure : Reduced pressure : Entropy : Joule-Thomson coefficient

# Introduction

The Joule-Thomson effect (also known as Joule-Thomson Expansion and the Joule-Kelvin effect) is the change in temperature of a fluid as it flows from a region of high pressure to a region of low pressure.

## Basic Principles

The thermodynamic basis of the Joule-Thomson effect is best understood by considering a discrete packet of gas upstream of a restriction. In order for the packet of gas to pass through the restriction the upstream gas must do some work to push the packet through. This work is equal to volume of the packet times the upstream pressure:

Once the packet clears the restriction it must make room for itself by displacing some of the downstream gas which involves doing work equal to the product of the downstream pressure and packet volume:

Due to various compressibility effects the amount of work done upstream will not equal the amount of work downstream for real gases i.e. . As depressuring can be viewed as an adiabatic process, meaning that the gas does not exchange heat or work with its surroundings, a change in internal energy is required to satisfy the first law of thermodynamics:

The internal energy of the gas is the sum of kinetic and potential energy associated with the random motion of the gas molecules. It is the kinetic portion of internal energy that can be experienced as temperature.

In a real gas molecules are subject to attractive and repulsive forces (van der Waals forces) as they move randomly past each other. As the pressure of a gas is lowered (i.e. the average distance between molecules increases) attractive forces become dominant over repulsive forces for most gases at ambient temperature resulting in an increase in potential energy component of internal energy.

However due to compressibility effects most real gases require more work downstream than upstream at ambient temperatures:

This implies that internal energy must decrease as the gas passes through the restriction. Given that the potential energy component will increase as the pressure of the gas is lowered the kinetic energy component of internal energy must decrease. As kinetic energy is realised as temperature this means that a reduction in temperature will be observed.

Although it is often generalised that for most real gases there is a decrease in temperature during a pressure reduction this is not true for all gases and conditions. Depressureing is an isenthalpic process which means enthalpy remains constant. For any gas the temperature could either increase or decrease depending on how the internal energy has to change to keep enthalpy constant. Therefore the direction of the temperature change is dependent on the upstream temperature and pressure of the gas relative to its inversion temperature.

## Inversion Temperature

The inversion temperature is the temperature of a gas at which a reduction in pressure causes no temperature change. Above this temperature the gas heats on expansion, below this temperature the gas cools on expansion.

## Applications

Applications of the Joule-Thomson effect generally use the cooling potential, rather than heating, as there are almost always more convenient ways to heat a process. Some applications where the cooling of expanding gases is employed are:

• Refrigeration - The pressurisation and expansion of refrigerants in a closed loop systems are the basis of most refrigerators and freezers.
• Air conditioning - Identical to a refrigerator in principal, but optimised for a building, vehicle or other inhabitable space.
• Gas separations - By cooling a gas through an expansion the heavier components will condense into a liquid phase. This is often employed in LPG production, with cooling the first step before fractionation is used to refine the liquids further.
• Liquid Gas Production - The Liquefaction of Gases such as; Ammonia, Chlorine, Nitrogen, Oxygen and Argon is achieved through expansion of the pressurised gases. Often employing several expansion and compression steps.

## Hazards

Where a gas is handled at high pressure there is always a risk of unintended Joule-Thomson effects. This is a risk that is faced in the Natural Gas industry where high pressures are frequently used to transport and store gases. Potential consequences of unintended low temperatures are:

• Valve Freezing - Where a large pressure drop occurs through a valve it may freeze. This can occur either through the seizure of components within the valve, or the valve becoming inoperable because ice has formed on the outside of the valve.
• Low Temperature Embrittlement - Below certain temperatures metals can become brittle and the pressure or load they can withstand reduced. Aluminium and ordinary carbon steel are both susceptible to this at temperatures that can be expected in a gas plant. Low temperature carbon steels and stainless can be used where the temperature reduction is unavoidable or the risk of Joule-Thompson cooling can not be removed. Control systems and heating (such as a water bath heater) may be employed to protect equipment from potential low temperatures
• Hydrate formation - When cooling a natural gas system to below the dew point of water hydrate may form, which can cause safety hazards and loss of efficiency.

# Calculation of Temperature Effect

## Joule-Thomson Coefficient

As Joule-Thompson expansion is considered an adiabatic process the Joule-Thomson coefficient can be calculated as the ratio of change in temperature to change in pressure:

Once calculated, the Joule-Thompson coefficient can then be used to predict the direction of temperature change based on the following criteria:

• - no temperature change, ideal gases
• - gas heats on expansion
• - gas cools on expansion

## Determining Temperature changes

### Joule-Thomson Coefficient

Where the change in fluid pressure is small it can be assumed that the rate of change in temperature with respect to pressure (the Joule-Thompson coefficient) is constant. Therefore for small changes in pressure the downstream temperature can be estimated by multiplying the Joule-Thompson coefficient by the pressure change . However as with any extrapolation care should be taken, the error in the expansion temperature prediction increases with the change in pressure.

### Temperature-Entropy Diagrams

Where thermodynamic charts are available, a Temperature-Entropy diagram can be used to accurately determine the final temperature. The expansion of gas through a nozzle is isenthalpic, so by following a constant enthalpy line from the start pressure to the final pressure the final temperature can be determined.

In the below example the final temperature of steam being let down from 60 MPa and 590°C to 2 MPa can be determined by following the constant enthalpy line.

### Process Simulations

Alternatively, software packages such as HYSYS or Pro/II can be used to model the pressure drop process using one of many thermodynamics packages available. Care should always be taken to match the correct thermodynamics package to the composition of the fluid being modelled.