Density Measurement

Key Takeaways

• The formation density log (also called the litho-density log or FDC — formation density compensated log) uses a cesium-137 radioactive source that emits gamma rays into the formation at two different distances from the detector, measuring the density of the formation through the relationship between the source intensity, the formation's electron density, and the detected gamma ray flux at each detector; the Compton scattering process (in which gamma rays lose energy by interacting with electrons in the formation) is the dominant attenuation mechanism at the energy level of Cs-137 emissions (662 keV), and the amount of attenuation is proportional to the electron density of the formation, which is in turn proportional to the bulk density; the two-detector compensated design (near and far detectors at 6 and 16 inches from the source) allows the tool to correct for the effect of rugose borehole surfaces and mud cake between the tool and the formation wall, which would otherwise read as artificially low density; the bulk density measurement is converted to porosity using the Wyllie matrix-fluid model (phi = (rho_matrix - rho_bulk) / (rho_matrix - rho_fluid)), where rho_matrix is the grain density of the reservoir rock (2.65 g/cc for sandstone, 2.71 for limestone, 2.87 for dolomite) and rho_fluid is the density of the pore fluid (approximately 1.0 g/cc for brine, 0.8 for oil, 0.3 for gas at reservoir conditions).
• Coriolis mass flow meters are the highest-accuracy technology for produced fluid density measurement in fiscal and allocation applications, operating on the principle that a fluid flowing through a vibrating tube causes a Coriolis force proportional to the mass flow rate, and that the resonant frequency of the vibrating tube changes in proportion to the fluid density within it; a single Coriolis meter simultaneously measures mass flow rate, volumetric flow rate (derived from mass flow rate and density), density, and temperature directly without requiring separate measurement devices, making it the preferred technology for multiphase fluid allocation in facilities where the cost of measurement errors (in royalty payments, production sharing agreements, or commercial billing) justifies the premium of Coriolis meters over differential pressure meters; the accuracy of a Coriolis meter for density measurement is typically 0.001-0.003 g/cc (or 0.0001-0.0003 g/cc for laboratory versions) across flow rates from near-zero to the maximum rated flow, providing a turndown ratio far superior to differential pressure meters that lose accuracy at low flow rates; the limitation of Coriolis meters in oilfield applications is the sensitivity of the vibrating tube to gas entrainment (which damps the tube vibration and gives erroneous low-density readings) and the requirement for tube cleaning or replacement when scale or wax accumulates inside the measurement tubes.
• Drilling fluid density measurement by mud balance is performed routinely (every 15-30 minutes during active drilling and at each connection during tripping operations) because the drilling fluid hydrostatic pressure — which depends directly on the mud density — is the primary mechanism for balancing formation pressure and preventing kicks; the standard API-calibrated mud balance consists of a fixed-volume cup that is filled with mud, a balance arm with a rider weight that is adjusted until the arm is level, and a calibrated scale that reads the mud density directly; the pressurized version (PMB) adds a sealed cap and pressurizing mechanism to prevent gas evolution from aerated mud or foam systems; the mud balance accuracy (approximately 0.05 ppg for standard balances, 0.01-0.02 ppg for premium calibrated balances) is sufficient for routine mud density monitoring but insufficient for the precise density control needed in ultradeep or HPHT wells where the mud weight window between pore pressure and fracture gradient may be only 0.1-0.2 ppg; electronic flow-line density sensors (using pressure differentials across a vertical section of flow line or using gamma-ray attenuation through the flow line) provide continuous density monitoring with better precision than the intermittent mud balance checks, enabling automated mud density control systems that adjust the barite addition rate to maintain target density.
• Rock grain density (also called particle density or matrix density) measured on disaggregated core samples provides the reference density used in porosity calculations from density logs and is measured in the laboratory by helium pycnometry or by a gravimetric method: helium pycnometry measures the volume of the solid grains directly by measuring the pressure change when a known volume of helium gas is introduced into a sealed chamber containing the sample, and grain density is calculated as the measured dry sample mass divided by the pycnometric grain volume; gravimetric methods use the principle of Archimedes to measure the volume of the grains by the weight loss of the sample when immersed in a fluid of known density (typically saturated brine or a non-reactive organic liquid); grain densities for common reservoir minerals range from 2.65 g/cc for quartz, 2.71 g/cc for calcite, 2.87 g/cc for dolomite, 4.48 g/cc for siderite (iron carbonate), to 2.55-2.75 g/cc for various clay minerals, and the bulk grain density of a mixed-mineralogy sample is the volume-weighted average of the component mineral densities; accurate grain density determination is critical for porosity calculations from the density log because a 0.05 g/cc error in assumed grain density produces an error of approximately 2.5 porosity units in the calculated porosity for a typical sandstone reservoir.
• Phase density measurement in multiphase flow (where oil, gas, and water flow simultaneously in different proportions that vary with time) is the most challenging density measurement problem in the production facilities context, because a conventional density meter measures the bulk density of whatever mixture passes through it but cannot directly determine the proportions of each phase without additional measurements; multiphase flow meters (MPFM) combine bulk density measurement with measurements of water fraction (by electrical impedance, capacitance, or microwave attenuation), volumetric flow rate, and velocity (by cross-correlation of upstream and downstream sensors) to simultaneously determine the flow rates of each phase; the calibration of MPFMs for density-based phase fraction measurement is particularly sensitive to the fluid properties (which change as the reservoir depletes and the gas-oil ratio changes over time) and to the flow regime (stratified, slug, bubbly, annular) that affects how representative the sensor measurement is of the bulk mixture; regular recalibration of MPFMs against test separator measurements is required to maintain the accuracy needed for production allocation in fields with multiple wells commingled into a common production facility.