Physics:Density meter

A density meter, also known as a densimeter, is a device that measures the density. Density is usually abbreviated as either [math]\displaystyle{ \rho }[/math] or [math]\displaystyle{ D }[/math]. Typically, density either has the units of [math]\displaystyle{ kg/m^3 }[/math] or [math]\displaystyle{ lb/ft^3 }[/math]. The most basic principle of how density is calculated is by the formula:

[math]\displaystyle{ \rho = \frac {m} {V} }[/math]

Where:

[math]\displaystyle{ \rho }[/math] = the density of the sample.

[math]\displaystyle{ m }[/math] = the mass of the sample.

[math]\displaystyle{ V }[/math] = the volume of the sample.

Many density meters can measure both the wet portion and the dry portion of a sample. The wet portion comprises the density from all liquids present in the sample. The dry solids comprise solely of the density of the solids present in the sample.

A density meter does not measure the specific gravity of a sample directly. However, the specific gravity can be inferred from a density meter. The specific gravity is defined as the density of a sample compared to the density of a reference. The reference density is typically of that of water. The specific gravity is found by the following equation:

[math]\displaystyle{ SG_s = \frac {\rho_s} {\rho_r} }[/math]

Where:

[math]\displaystyle{ SG_s }[/math] = the specific gravity of the sample.

[math]\displaystyle{ \rho_s }[/math] = the density of the sample that needs to be measured.

[math]\displaystyle{ \rho_r }[/math] = the density of the reference material (usually water).

Density meters come in many varieties. Different types include: nuclear, coriolis, ultrasound, microwave, and gravitic. Each type measures the density differently. Each type has its advantages and drawbacks.

Density meters have many applications in various parts of various industries. Density meters are used to measure slurries, sludges, and other liquids that flow through the pipeline. Industries such as mining, dredging, wastewater treatment, paper, oil, and gas all have uses for density meters at various points during their respective processes.

Different types of Density Meter

Gravimetric

Gravimetric density meters work on the principle of gravity to calculate the density of a sample. A flexible hose is used to determine the change in weight. Using the principle of beam deflection of two fixed ends, the weight can be calculated. Increases in weight result in a larger deflection. Decreases in weight result in a smaller deflection. The volume inside of the hose never changes. Since the volume is constant and the weight is known, the density is easily calculated from this information.

Displacement is measured with a high precision displacement laser. Micron scale deflections can be read by the density meter. Minute changes in weight are seen at this scale.

The entire volume is measured using gravimetric methods. This means that the sample size is the entire volume of what needs to be measured.

Gravimetric density meters use the least amount of theory, making them the most accurate choice, depending on the application. Using the equation [math]\displaystyle{ \rho = \frac {m} {V} }[/math] the volume is known, once we find the mass, we can find the density.

Coriolis

Coriolis density meters, also known as mass flow meters or inertial flow meters, work on the principle of vibration to measure phase shifts in the vibration of a bent thin walled tube. The bent thin walled tube is rotated around a central axis. When there is no mass in the bent section, the tube remains untwisted. However, when the density inside the bent section increases, the inbound flow portion of the bent pipe drags behind the out flow portion. This twisting causes phase shifts which result in changes in the resonant frequency of the thin walled tube. Therefore, the resonant frequency is directly affected by the density. Higher density media causes a larger Coriolis effect if the volumetric flow rate is constant. Flowing media causes a frequency and a phase shift of the bent pipe, which are proportional to the mass flow rate of the sample.

Coriolis meters measure the mass flow of the system. They do not measure the volumetric flow. However, a volumetric flow can be inferred from the mass flow measurement. These measurements are restricted to small diameters for flow tubes. However, this measurement technique results in high accuracy and high repeatability. Coriolis meters also have a fast response time.

Coriolis meters need to be calibrated for temperature and pressure. The zero points for these values are used to calibrate the system. Coriolis meters cannot be calibrated while in use. The span difference is used to see how temperature and pressure have changed.

Nuclear

Nuclear density meters work on the principle of measuring gamma radiation. Gamma radiation is emitted from a source. This source is typically caesium-137 (half-life: ~30 years). The radiation is seen by a scintillator device. The radiation is converted into flashes of light. The number of flashes of light is counted. Radiation that is absorbed by the mass is not seen by the scintillator device. Therefore, the density of the media is inversely proportional to the radiation captured and seen by the scintillator.

Nuclear density meters are limited in scope to what is seen by the gamma radiation beam. The sample size is a single, thin column with small longitudinal length.

Nuclear equipment requires certified and licensed staff in order to operate the instruments.

Microwave

Microwave density meters have various ways to measure what solids are in the sample. All microwave meters measure microwaves but some use different methods such as measuring the microwave propagation speed change, amplitude reduction, time of flight, single phase difference, or dual phase shift. Each technique has certain accuracies.

Some microwave meters use a ceramic probe that is directly inserted into the sample. This allows the meter to have direct contact to the sample in question. However, this limits the types of slurries and sludges that can flow through the pipe line. Abrasive slurries with particulates can damage the sensor probe.

Microwave meters are also limited to liquids with unvarying dielectric constants. The percentage of solids of the slurry affects the dielectric constant for the entire sample. Typically, percent solids greater than 20% result in large errors. Similar inconsistencies happen with large pipe diameters.

Microwave meters are very good at detecting dissolved solids. Homogeneous solutions are easily seen by microwave meters. This makes them a fit for applications where the solution is consistent and non-abrasive.

Ultrasonic

Ultrasonic density meters work on various principles to calculate the density. One of the methods is transit-time principle (also known as the time of flight principle). In this technique, two transducers are mounted to the sides of the pipe walls. The transducers alternate between sending and receiving ultrasonic signals. From this transit time measurement, the flow velocity and volume flow based on the diameter of the pipe are calculated.

Another method this is used is ultrasonic attenuation method. This method measures the count of various signals with certain amplitudes. The density of the media flowing through the pipe affects the signal sent through the pipe. This changes the strength of the signal, causing a weaker signal and smaller amplitude.

Another method that is utilized in ultrasonic meters is the envelope energy average method. This method is based on not only the amplitude of the signal but also the shape of the signal. These packets of information are called envelopes.

Doppler ultrasonic meters measure the suspension flow where the concentration of solids in the slurry is above 100ppm and the particles that are suspended are larger than 100 microns in diameter. However, the Doppler method only works on concentrations of less than 10% solids.

Compensations

Temperature

Temperature affects the density of fluids. In most cases, an increase in temperature indicates that the density of the media will decrease. This indicates that temperature and density are inversely proportional to each other. Temperature also affects the meters themselves. Mass flow meters have different resonant frequencies at different temperatures.

Pressure

Pressure changes the rigidity of the mass flow tube. Pressure affects the rigidity of gravimetric meters.

Vibration

Vibration from plant noise can be filtered out. Vibration is apparent in microwave, ultrasonic, gravimetric, and Coriolis meters. Vibration causes these types of meters to accumulate error

Damage

Coriolis meters have compensations from pitting, cracking, coating, erosion, and corrosion. These damages affect the way that the tube resonates. These changes affect the baseline. Compensations cannot be made dynamically. These damages typically cause offsets that can be added to the existing calibration factors that will ensure that a consistent reading is still acquired.