Pressure and temperature compensation in flow measurements

Liquids and especially gases expand when the temperature rises, which causes a measurement error in flow measurements. Therefore, when measuring flow, the temperature is often measured to compensate for this.

Another aspect is that when the pressure increases, the volume decreases. With liquids, this is only very small. Gases are very compressible.

So you can not avoid to compensate and express the measured volume in a volume under "standard" conditions. How this works is explained here.

Measuring liquids: P- and T-compensation

For calibrated, volumetric liquid flow measurements, temperature measurements are usually performed as well. Both the measuring signal of the flow meter and that of the temperature sensor are read into a flow computer. The influence of the temperature expansion is calculated and the measured value is corrected. According to the Dutch Meterology Law it is not obligatory to measure temperature.

The influence of pressure on the volume of a liquid is zero. For some liquids, however, the pressure factor is large enough to compensate for it.

Measuring gases: P- and T-compensation

Where a simple temperature correction is sufficient for liquids, the situation is quite different for gases. Because the volume of gases is so strongly influenced by pressure and temperature, it is necessary to express volumes of gases (and thus also of flows) in a way that they would be under standard conditions. That standard is defined as: the volume that the gas has at 1 atmosphere and 0 ºC. And that makes that a quantity of gas is usually expressed in normal cubic metres (Nm³ or nm³ ). This is a good way of comparing quantities of gases and you will find it everywhere in the gas world. For instance in the specifications of components. There you will also often see the derivatives of m³ , such as normal litre (Nl, Ndm³ ) or normal cubic centimetre Ncm³ .

The gas laws

A simple way to arrive at normal m³ (or normal liters) is with Boyle and Gay-Lussac's law. The formula reads:

So, if we compress the volume of 1 m³ gas to half, and the temperature remains constant, that means the pressure is doubled. If the temperature also varies, then the pressure and the actual volume vary.

Here we want to calculate the flow meter value back to the volume of the flow that the gas would have at 0°C and 1 bar. You will then compare 2 situations: the measured value of pressure, volume and temperature and the situation at 0°C and 1 bar. In that case the formula becomes

To arrive at a corrected measurement value, it is a matter of filling in the numbers.

Compressibility factor for real gases

Real life gases are not ideal gases, as the formulae assume. For accurate calculations, especially with hydrocarbons, you need to take into account the compressibility factor Z. This indicates the degree to which a gas is compressible. The reason this factor matters is that the Z-factor is not a constant, but varies with pressure and temperature. The new formula for measured value correction looks like this:

Nevertheless, in daily practice an ideal gas is often assumed and Z=1 is taken. This is due to a number of reasons:

• The pressure and temperature are fairly constant in the system, so the Z factor has become constant. By not taking it into account you introduce a deviation, but it is constant.
• For a control system this is not a problem.
• The effect of the Z-factor is small because pure gases are used.
• The gas system works with hydrogen or helium and these behave like an ideal gas.
• Mass flowmeters (thermal and coriolis flowmeters) measure directly the weight of the gas and are therefore by definition independent of the compressibility factor.

Natural gas flow measurements

The compressibility factor must be taken into account in natural gas flow measurements. That's what we're supposed to do by law, according to the Dutch Metroloy Law. What you have to do with earth gas is the presence of other gases. To determine the compressibility factor there are a number of calculation methods, of which 2 are allowed by law: SGERG and AGA8 (another commonly used method is NX-19).

To give an idea of the influence of the Z-factor on the measured value, the graph below shows the factor for some common hydrocarbons. As we saw before, the compressibility factor is of course dependent on the medium, but also on pressure and temperature. The red line shows that an ideal gas behaves neutrally.

Graph: Ichwarsnur, CC BY-SA 4.0, Wikimedia Commons

Expansion and shrinkage of flow meters

Some flow meters are very dependent on their dimensions for their accuracy. The expansion or contraction of the flow meter itself due to changing temperature and pressure then causes a deviation. This is for example the case with multichannel ultrasonic gas flow meters, where this phenomenon is taken into account.

This is also especially true for differential pressure elements such as nozzles and venturis. Here, the thermal expansion factor of the material is taken into account in the flow computer so that it can compensate for the expansion of the material and thus the diameter.

The end result in the flow computer

In a flow computer the measured flow (in actual volume units) is corrected for the linearity of the measuring instrument and the influences of pressure, temperature and compressibility. Sometimes even the measuring signal of a gas analyser is read into the flow computer for the calculation of:

• compressibility
• mass flow
• calorific values of combustion gas