In today’s blog I would like to take you with me into the world of thermodynamics and explain how the ideal gas law helped us creating a software tool called Fluidat on the Net.

**Fluidat®**

As an R&D Engineer at Bronkhorst High-Tech calculating pressure drops of an instrument and using physical properties in gas conversion models of thermal mass flow instruments are frequently recurring activities. At Bronkhorst, these physical properties are used to design and select flow devices, and to calibrate the flow devices during the production process on the customers’ requirements.

Therefore an application was developed which can easily generate the physical fluid properties based on theoretical calculation methods. The application is called Fluidat on the Net, which can also be accesed through the Bronkhorst website.

**The ideal gas law**

The origin of Fluidat is directly related to the ideal gas law - the combination of Boyle, Gay-Lussac, Charles, and Avogadro Law - resulting in the following equation of state and thermodynamic law of a hypothetical ideal gas:

where:

- P is the pressure of the gas;
- V is the volume of the gas;
- n is the amount of gas (molecules);
- R is the universal gas constant;
- T is the absolute temperature of the gas.

Equations of state like the ideal gas law are thermodynamic equations relating state variables, like pressure and temperature, and are useful in describing properties of fluids, either gas or liquid. For example, if in closed volume the pressure is increased by moving a piston, one is able to calculate the resulting temperature.

However, the ideal gas law is based on an ideal model, but in practice I have experience that real gases do not behave in this way. Molecules are not point particles, but do have volume and can also interact with each other. The first adaption to the ideal gas law was performed by Johannes Diderik van der Waals, a famous Dutch theoretical physicist:

where:

- a is the interaction energy between molecules;
- b is the occupied volume by the molecules.

This equation gives a much better prediction of real gas behavior in practice. Each gas (or mixture) has different a en b coefficient. When the molecules do not interact (a=0) and do not occupy space (b=0), the result is again the ideal gas law.

The equation of state used in Fluidat is based on a more advanced virial equation of state (an expression of a system derived from statistical mechanics, usually describing a system in equilibrium as a power series of particle interactions). It is called the Benedict-Webb-Rubin equation, named after the three researchers (M. Benedict, G.B. Webb and L.C. Rubin) working at the research laboratory of M. W. Kellogg Limited who determined the model.

From this equation of state the non-ideal behavior of fluids can be derived, a required input for the calculation of physical properties like:

- density
- heat capacity
- thermal conduction
- viscosity
- and vapor pressure

The Benedict-Webb-Rubin equations are calculated using intrinsic properties, like molar mass, critical properties, polarity, accentric factor and other parameters. These intrinsic properties characterize the fluid, taken into account effects like compressibility, variable specific heat capacity, and Van der Waals forces. These properties will influence the physical properties of a fluid.

For example the accentric factor (the shape of the molecule) will influence the viscosity for large hydrocarbon molecules. And the critical properties are most important to calculate the reduced (or normalized) properties; all calculations perfomed in the Benedict-Webb-Rubin equations are based on reduced properties, thus resulting in a universal gas model . The reduced properties are calculated by deviding the actual state properties by the critical properties (for example P_r=P/P_c, where P_r is the reduced pressure and P_c is the critical pressure).

Basically, the Benedict-Webb-Rubin equation is a model to derive the compressibility factor (the deviation from ideality) of fluids:

Generalized compressibility factor Z diagram. The compressibility factor is required for property calculations and can be found in this graph by looking up the value for a certain reduced temperature T_r=T/T_c and reduced pressure p_r=p/p_c (solid lines).

The total non-ideal behavior of fluids is summarized in the compressibility factor Z:

where Z=1 for an ideal gas. Under normal operating conditions, usually the compressibility factor is Z<1 for common gases, except Hydrogen and Helium for which under normal circumstances the compressibility factor is Z>1 resulting in different behavior compared to other gases, for example the Joule-Thomson effect when a real gas is throttled through a valve or porous plug.

When the compressibility factor is known, the physical properties like density, specific heat capacity, thermal conductivity, and viscosity can be calculated using specific calculation methods. These physical properties can be used in other calculations.

It is important to include real gas behavior in a mass flow controller (MFC), because the ideal gas law can differ significantly from the real gas behavior, especially near the critical point and vapour pressure line. Some important gases, like CO2 and SF6 are at critical tempeture at room temperature, thus real gas compensation is important to achieve high accuracy for these gases.

The physical properties are also required for calibration and gas conversion, thus an accurate fluid database is necessary te deliver customer requirements. Without the Fluidat database, for me as an engineer it would be impossible to accurately predict the behavior of mass flow controllers, because you require highly accurate property calculations, for example for conversion model for thermal instruments.

In conclusion, Fluidat is a valuable fluid database when it comes to mass flow meters, both for our internal use and to our customers, either indirect during the calibration process or directly on our website.

Do you already benefit from Fluidat? Have a look at our previous blog to find out what Fluidat can do for you: Software to access the world of properties for mass flow meter or controller

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