# Direct Measurement of Mass Flow Rate in Industrial Process Operations

Increasingly, industrial process operators are recognizing the advantages of the direct measurement of mass flow rate for monitoring gases. The following article discusses the difference between volumetric flow and mass flow measurement for gas control applications, and is excerpted from the Magnetrol® Thermal Dispersion Mass Flow Measurement Handbook.

An Introduction to and Benefits of Thermal Dispersion Mass Flow Measurement

Accurate mass flow measurement of gas is difficult to obtain. The main reason is that gas is a compressible fluid. This means that the volume of a fixed mass of gas depends upon the pressure and temperature it is subject to

Consider a balloon containing one actual cubic foot of gas at room temperature (70° F) and atmospheric pressure. An increase in the room temperature causes the balloon to expand. An increase in the pressure surrounding the balloon results in a decrease in volume. Although the volume of the balloon changes with variations in pressure and temperature, the mass of the gas inside the balloon has remained the same. This illustrates how pressure and temperature affect the actual volume

There are many well-established methods of measuring the actual volumetric flow rate. However, the measured flow rate will vary with changes in temperature and pressure. For virtually all industrial process operations, the user wants to measure the mass flow rate instead of the actual flow rate. Chemical reactions work on the basis of mass relationships of ingredients. Combustion is based upon the mass flow rate of the air and the fuel. Gas consumption in a facility is based upon mass flow rate. To accurately measure mass flow, the actual flow rate must be adjusted to correct for any change in temperature and pressure.

Thermal mass flow technology is a method of gas flow measurement that does not require correction for changes in process temperature or pressure. Thermal mass flow technology also has a benefit of measurement at low velocities and greater turndown capabilities than those obtainable with other flow measurement devices. Turndown is the flow range for which the device is accurate (maximum flow / minimum flow).

What is Mass Flow Rate?

Mass Flow is the measurement of the flow rate without consideration of the process conditions. Mass flow is equivalent to the actual flow rate multiplied by the density. M = Q x ρ, where Q is the actual flow and ρ is the density. As the pressure and temperature change, the volume and density change, however the mass remains the same.

To obtain standardization of gas flow measurement, Standard conditions of Temperature and Pressure (STP conditions) are utilized. Gas flow measured at STP conditions is corrected from the actual process conditions to standard conditions (more information about standard versus actual process conditions can be found in our Thermal Dispersion Mass Flow Measurement Handbook).

The simplest way of measuring mass flow of gas is in units of cubic feet per minute or cubic meters per hour, corrected to STP conditions. This is referred to as SCFM (standard cubic feet per minute) or the metric equivalent of Nm3/h (normal cubic meters per hour). The density of a gas at standard conditions is known, thus providing a relationship between SCFM and pounds per hour or between Nm3/h and kg/h.

The conversion between the volume at actual conditions and the volume at standard conditions is based on the ideal gas law — actual volume increases in direct proportion to an increase in absolute temperature, and decreases in direct portion to an increase in absolute pressure. Consider the balloon example — as the temperature increases, the volume expands; as the pressure increases, the volume shrinks.

Absolute pressure of zero psia (pounds per square inch at absolute conditions) is a perfect vacuum. One atmosphere of pressure is defined as 14.69 psia or zero psig. The conversion between psia and psig is easy: PSIA = PSIG + 14.69. If you have a pressure gauge calibrated for psig, it will read zero at sea level and only measure gauge pressure above atmospheric pressure. The following chart will help clarify this.

Absolute zero is defined as the temperature where molecular motion stops. It is defined as 0 K (Kelvin) which is -273.16° C or 0° R (Rankine) which is -459.67° F. To convert between actual temperature and absolute temperature, simply add 460 to the temperature in degrees Fahrenheit or 273 to the temperature in Celsius.

Once we establish a set of conditions as a standard temperature and pressure (STP conditions), we can convert between the flow rate at actual conditions and the flow rate at standard conditions.

The subscript (a) refers to actual conditions; the subscript (s) refers to standard conditions.

Unfortunately, not all STP conditions are universal. Many users consider one atmosphere and 70° F as STP. Some industries use one atmosphere and 60° F as standard; others use one atmosphere and 32° F as standard. The metric equivalent is Normal conditions which are based on a pressure of one bar (14.5 psia) and 0° C.

The important issue is that Standard Conditions are not Standard and a mass flow meter needs to be able to permit the user to select the desired STP condition. An error of approximately 8% will occur if there is a difference in STP conditions between 70° F and 32° F.

Once a set of standard conditions is identified, the density of that gas at these conditions is known. Therefore, it is a simple matter to convert from SCFM to mass in pounds per hour:

In this formula, the density in pounds per cubic foot is the density at the specified STP conditions.