Densitometer

Key Takeaways

• Coriolis densitometers measure fluid density by detecting the effect of the fluid's mass on the oscillation frequency of a vibrating tube through which the fluid flows: the fundamental principle is that a tube vibrating at its natural resonant frequency will oscillate at a lower frequency when filled with a denser fluid (because the inertia of the fluid mass adds to the tube's effective inertia), with the relationship between oscillation frequency and density being approximately linear over the density range of interest; the Coriolis meter simultaneously measures the mass flow rate (from the phase shift of the oscillation between inlet and outlet caused by the Coriolis force on the flowing fluid) and the fluid density (from the oscillation frequency), making it a true mass flow meter that does not require knowledge of the volumetric flow rate or separate density measurement; Coriolis densitometers achieve measurement accuracies of 0.0005 g/cc or better under ideal conditions of single-phase flow, stable temperature, and no entrained gas or solids; entrained gas bubbles are the most significant source of error in Coriolis density measurement for multiphase petroleum applications, because gas bubbles attenuate the tube vibration and produce density readings that underestimate the true liquid density; slugging flow (alternating slugs of gas and liquid) can cause severe measurement errors or tube stalling that requires the instrument to be re-synchronized before measurements resume.
• Radiometric (nuclear) densitometers use the attenuation of gamma rays transmitted through a pipe cross-section to infer the average density of the fluid in the pipe, based on the Beer-Lambert law that relates gamma-ray attenuation to the thickness and density of the absorbing material: the source (typically Cs-137 or Am-241) and detector are mounted on opposite sides of the pipe in a clamp-on configuration that requires no contact with the process fluid and no intrusion into the pipe, making the radiometric densitometer suitable for hostile process conditions (high pressure, high temperature, corrosive fluids, abrasive slurries) where contact instruments would be damaged; the density measurement accuracy depends on the pipe diameter, the gamma-ray energy (higher energy provides better penetration through thick-walled or high-density pipes), and the stability of the source-detector geometry; gamma-ray transmission densitometers are widely used in drilling mud return lines for kick detection, in produced water treatment systems for measuring oil content, and in separator trains for level detection and phase density monitoring; the radioactive source requires regulatory licensing, periodic leak testing, and secure storage when not in use, and international shipping of radioactive sources for offshore and remote locations requires compliance with IATA and IMDG dangerous goods regulations; the NORMs (naturally occurring radioactive materials) deposited on the inside of production tubing from radioactive scale (barium sulfate containing Ra-226 and Ra-228) can affect the calibration of radiometric densitometers if the scale thickness or activity changes over time.
• Downhole formation density logs use a different principle from surface densitometers but serve a related purpose of measuring the bulk density of the formation rock and pore fluid for porosity calculation: the compensated density log (LDT, litho-density tool) emits gamma rays from a Cs-137 source into the formation and measures the backscattered gamma-ray flux at two detectors at different distances from the source, with the ratio of the detector readings corrected for borehole effects (the short-spaced detector primarily measures the near-wellbore zone including mudcake, while the long-spaced detector penetrates deeper into the formation); the formation bulk density (rho_b) measured by the density log is converted to porosity using the formula phi = (rho_matrix - rho_b) / (rho_matrix - rho_fluid), where rho_matrix is the grain density of the rock (2.65 g/cc for quartz sandstone, 2.71 g/cc for calcite limestone, 2.87 g/cc for dolomite) and rho_fluid is the density of the pore fluid (approximately 1.0 g/cc for salt water, 0.8 g/cc for oil, 0.1-0.3 g/cc for gas); the density-neutron crossplot is the primary tool for lithology identification in petrophysical analysis, because different minerals (quartz, calcite, dolomite, anhydrite, halite) plot at characteristic positions on the density-neutron plane, allowing the petrophysicist to identify the mineral assemblage and correct the porosity calculation for the appropriate matrix density.
• Process densitometers for gas measurement use Equation of State calculations to convert the measured process conditions (pressure, temperature, and gas composition from chromatography) to a calculated gas density at standard conditions, which is then used in conjunction with the volumetric flow rate to compute the mass flow rate of gas for custody transfer: the AGA-8 (American Gas Association Report No. 8) or GERG-2008 equation of state is the international standard for computing the compressibility factor (Z-factor) of natural gas mixtures, from which the density at standard conditions is calculated as rho_standard = P_standard * MW / (Z * R * T_standard), where MW is the molecular weight of the gas mixture from chromatographic analysis; errors in the gas composition (inaccurate chromatograph calibration, unrepresentative sample, liquid dropout in the sample line) translate directly to density errors and hence to volume measurement errors in custody transfer; the energy content (heating value) of the gas is calculated from the same composition analysis as the density, so accurate chromatography is critical to both the volumetric and energy content of gas sold; for liquids, densitometry at standard conditions (15 degrees C, 1 atmosphere) is used for custody transfer of crude oil, condensate, and NGL, with the most accurate method being a precision laboratory densitometer (digital oscillating U-tube type, achieving 0.0001 g/cc accuracy) applied to samples taken from the process stream after thorough mixing to ensure representative sampling.
• Multiphase flow measurement using dual-energy gamma-ray densitometers (or Dual Energy Gamma-ray absorption, DEGA) allows the simultaneous measurement of oil, water, and gas holdups in a three-phase mixture by using two gamma-ray sources at different energies whose attenuation coefficients through oil, water, and gas are sufficiently different to mathematically separate the three-phase composition: the low-energy source (typically Am-241 at 59.5 keV) is more strongly attenuated by dense materials (water, steel) than the high-energy source (Cs-137 at 662 keV), and the ratio of attenuation at the two energies provides information about the density and atomic number of the mixture that allows simultaneous determination of the gas, oil, and water volume fractions without a test separator; DEGA-based multiphase meters are used on offshore platforms for well-by-well production allocation, subsea well testing, and production monitoring where the cost and space of conventional test separators is prohibitive; the measurement accuracy depends on the flow regime (homogeneous dispersed flow is more accurately measured than slug flow, where the gas and liquid alternate rather than being uniformly mixed across the pipe cross-section), the fluid properties (oil density, water salinity), and the cleanliness of the pipe wall (scale deposits change the apparent transmission even with no change in the process fluid).