Lammert Heijnen
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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:

Hypothetical ideal gas law

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:

Ideal gas law van der waals

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 factorz diagram

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:

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.

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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

Register for a FREE account of Fluidat today!

Adam Mumford
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What is FLUIDAT?

FLUIDAT is Bronkhorst’s online calculation software. It allows our end users to make many theoretical calculations for their instruments and also have access to over 1800 different fluid properties and corresponding data.

Working with fluids and ever changing process conditions can provide many challenges, especially when trying to understand the behaviour of the given fluid depending on the actual pressure and temperature of the process. Along with understanding the behaviour of your particular fluid or fluid mixture making sure that you select an instrument that is able to operate effectively to the level you expect and that meets your application’s demands. In this case the initial selection of the correct instrument is fundamental, understanding what is possible for the future of your instrument can however be just as important.

This is where FLUIDAT can assist by allowing our end users to fully understand their instruments capability. If it’s working at different pressure conditions or using a completely different fluid for example, FLUIDAT can allow you to make an informed decision about whether or not the instrument is up for the task at hand. Of course, sometimes we have to accept that returning the instrument for recalibration is the only option but with FLUIDAT at your fingertips you have the ability to make an informed choice.

Traditionally, fluid data has been stored in technical handbooks and manuals with graphs and tables of data in a listed format demonstrating fluid properties along with their coefficients. However, this is a very inflexible format and does not allow immediate access to changing fluid behaviour (due to external factors) without making what can sometimes be complex calculations.

Knowing that these challenges were sometimes a hindrance to our end users, Bronkhorst released this on-line fluid management programme to support our customers in a way we never had before. This on-line programme allows immediate data and calculations relating to the behaviour of thousands of fluids under different working conditions.

One example of this is our Controlled Evaporation Mixing (CEM) vapour generation calculation tool. To calculate the output vapour to the process you need to calculate the combination and vaporisation properties of both a liquid and gas at differing temperatures and flow rates. Our CEM calculation tool can make this task easy, at just a click of a button.

The newly added interactive Vapour-Pressure line allows users to simply glide the cursor over the chosen fluid graph to establish the phase at the given temperature and pressure. Added value comes from the ability to create and save your own fluid mixtures, which alone can remove hours of calculations and research from a single project.

OK, so let’s have a look in more detail at some of the calculation tools available in FLUIDAT.

Gas Conversion Factor:

Here, the end user can choose a pure gas or create a gas mixture to find the conversion factor for a different gas to which an instrument can be sized on. As with most thermal mass flow controllers the output signal from the MFC is determined by which gas it has been calibrated for. With the gas conversion factor tool you simply choose the ‘Fluid from’ and ‘Fluid to’ to find out the conversion / correction factor. You can also select your exact model to improve the accuracy of the conversion. This function also allows you to add the specific pressure and temperature conditions you are converting from and to, for even more accuracy. The conversion factor can then be applied to the output measurement of the MFC to know the actual flow of the new gas.

Example of a gas conversion made in FLUIDAT: Image description

Controlled Evaporation Mixing (CEM) Calculation Tool:

A CEM system can be an extremely versatile addition to any vapour generation requirement. FLUIDAT allows the end user to make various calculations to not only enable the correct CEM heater temperature setting , the flow rates required for both the liquid and gas instruments and the relative humidity of the generated vapour. It is also possible to back calculate the flow rates needed to achieve the required relative humidity of your vapour. All of the fluid data is stored within the FLUIDAT software, the heat capacity, thermal conductivity and heat of vaporisation to name a few. This data can also be accessed by the user under the ‘Fluid Properties’ calculation.

The possibilities of the CEM calculation tool are endless, from knowing the pressures needed to supply the liquid and gas MFCs to calculating the vapour temperature on the outlet, or knowing the flow of the vapour output and having the ability to choose between thousands of different fluids to make your calculations. This makes FLUIDAT a ‘must-have’ for any Bronkhorst customer using our CEM vapour delivery systems.

Example of a CEM calculation in FLUIDAT: Fluidat CEM calculation

Pressure Drop Calculations:

For most applications it is important for the end user to understand the pressure drop across the instrument. It is not only important to understand the pressure loss across a device but sometimes it can also be critical to know the required pressure for the instrument to function correctly, especially when using control valves.

In FLUIDAT it is possible to calculate the pressure drop for both our gas instruments and our mini-Coriolis Series. Calculating the pressure drop using FLUIDAT is easy, all you need to do is select the correct pressure drop calculation tool. You have the choice of selecting our MASS-STREAM, EL-FLOW/IN-FLOW or Coriolis Instruments.

The calculation tool for the Coriolis Instruments is called ‘CoriCalc’ and for the other instruments are referred to as ‘Pressure Difference D-6300’ or ‘Pressure Difference LOW-dP-FLOW and EL-FLOW'. Once you have selected the correct tool and instrument type you can then select the fluid and flow rate and simply hit the calculate button. You can choose to readout the pressure drop in many different units from mbar to psi for example. For meters this is pretty straight forward, the pressure drop will be displayed across the sensor and fittings and yes, you can also choose the fitting size and type in many situations.

This calculation tool can also demonstrate the minimum required inlet pressure to flow the fluid you want at the required flow rate. Without the complication of the control valve calculating for meters is relatively straight forward. When making calculations involving both a meter and control valve (e.g. in a controller), it is important to make sure your calculation includes the correct selected orifice for your given controller, the easiest way to do this is using the inlet and outlet pressures to be used.

Example of a Pressure Drop Calculation in FLUIDAT: Fluidat pressure drop calculation

FLUIDAT is an extremely useful and powerful tool for those using Bronkhorst instruments. It allows an end user access to additional information which can be used to not only enhance the potential of our instruments but also allows our customers to gain an advantage over competitors and gain an understanding of mass flow. The above examples are just a snippet of some of the tools available.

Please register at www.fluidat.com to take full advantage of this free online software.