Sigma (Thermal Neutron Capture Cross Section)
Sigma (symbol Σ, also written as sigma or capture cross section) is the thermal neutron capture cross section of a formation — a measure of the formation's ability to absorb thermal neutrons, expressed in capture units (c.u., where 1 c.u. = 10⁻³ cm⁻¹) — and is the primary formation evaluation parameter measured by pulsed neutron capture (PNC) logs run in cased holes to determine water saturation in reservoirs where open-hole logging was not performed or where formation conditions have changed during production; the physical basis for the sigma measurement is that thermal neutrons (slow neutrons with energies around 0.025 eV) are captured by atomic nuclei in the formation, with each element having a characteristic capture cross section that determines its probability of neutron absorption; chlorine, the dominant anion in saline formation water, has an exceptionally high thermal neutron capture cross section (approximately 33.2 barns per atom) compared to the rock matrix minerals (silicon, carbon, oxygen have very low cross sections), oil and gas hydrocarbons (hydrogen has low cross section, carbon has low cross section), and fresh water (oxygen dominates, very low cross section); this contrast in capture properties between saline water and hydrocarbons is the physical basis for the sigma log's usefulness in cased-hole water saturation determination — saline-water-bearing zones have high sigma values while hydrocarbon-bearing zones have low sigma values, allowing the two to be distinguished in the logged sigma profile.
Key Takeaways
- Chlorine's high capture cross section is the foundation of the sigma log's salinity sensitivity — among all common elements in oil and gas formations, chlorine has by far the highest thermal neutron capture cross section; brine-filled reservoirs with high chloride concentration (NaCl dissolved in formation water) have sigma values 3-5 times higher than the same reservoir filled with oil or gas; the sigma contrast depends on the salinity of the formation water — highly saline brines (100,000+ ppm NaCl) give very high sigma values (25-35 c.u.) that clearly distinguish them from oil (15-20 c.u.) and gas (8-15 c.u.); in low-salinity formations (<20,000 ppm NaCl), the sigma contrast between brine and hydrocarbon is small and may not provide reliable saturation discrimination without supplemental measurements.
- Pulsed neutron tools measure sigma by observing the decay rate of thermal neutron population in the formation — the tool emits a burst of fast neutrons from a neutron generator, and as the neutrons slow down (thermalize) and are captured by the formation, the count rate at the detector decreases exponentially with time; the decay time constant (Tc) of this thermal neutron die-away is inversely proportional to sigma: Tc = 4545 / Σ (where Tc is in microseconds); by fitting an exponential to the measured count rate decay after each neutron burst, the tool derives sigma directly from the measured die-away rate; the ratio of near and far detector responses provides additional information to separate formation sigma from the borehole fluid sigma contribution, which must be corrected for to obtain the true formation sigma.
- Time-lapse sigma logging tracks fluid contact movement during production — because sigma changes significantly when brine replaces oil or gas in the reservoir pore space, repeated sigma logging surveys over time reveal how the oil-water contact (OWC) or gas-water contact (GWC) has moved during production and water/gas injection; the comparison of sigma from a baseline survey (before injection) to a monitor survey (after injection) shows clearly which intervals have been swept by injected water (higher sigma) versus which remain hydrocarbon-bearing (lower sigma); this time-lapse cased-hole logging is a routine production monitoring tool in mature fields where re-entry and open-hole logging are not practical but understanding remaining hydrocarbon distribution is essential for well recompletion decisions.
- The sigma measurement requires knowledge of formation water salinity for saturation calculation — the sigma of any formation volume is the volume-weighted average of the sigma contributions from rock matrix, formation water, oil, and gas; calculating water saturation from sigma requires knowing the end-member sigma values for the formation water (which depends on salinity and temperature) and the reservoir hydrocarbons; formation water salinity is typically determined from water samples, resistivity logs, or regional knowledge of the formation brine chemistry; the sensitivity of sigma to salinity means that the method is most reliable and precise in high-salinity formations (above 50,000-80,000 ppm NaCl) where the contrast between brine and hydrocarbon sigma is large relative to measurement uncertainty.
- Sigma is combined with other cased-hole measurements for more robust formation evaluation — in addition to sigma, pulsed neutron tools typically measure the inelastic scatter gamma ray and thermal capture gamma ray spectra, providing elemental yields (silicon, calcium, iron, sulfur, gadolinium, chlorine) that allow lithology and mineralogy characterization alongside the saturation measurement; the carbon/oxygen (C/O) ratio tool uses the inelastic scatter gamma ray spectrum to separately determine the carbon and oxygen contributions to the formation response, providing a salinity-independent saturation measurement that is particularly valuable in low-salinity formations where the sigma contrast between brine and hydrocarbon is insufficient for reliable sigma-based saturation.
Fast Facts
Pulsed neutron capture logging tools were developed in the late 1950s and early 1960s to allow formation evaluation in cased holes — wells where open-hole logging opportunity had been missed or where the open-hole logs needed to be supplemented with production-time reservoir monitoring. The sigma measurement's reliance on chlorine's high neutron capture cross section means it only works reliably in formations with saline connate water — a limitation that drove development of the carbon-oxygen log for low-salinity environments where sigma alone cannot distinguish brine from hydrocarbon.
What Is Sigma in Well Logging?
Sigma is the formation's thermal neutron capture cross section — a measure of how aggressively the rock and its fluids absorb slow neutrons. In salty water, chlorine absorbs neutrons voraciously, giving brine a high sigma value. Oil and gas barely absorb them at all. That contrast is the entire basis for using pulsed neutron tools in cased holes to monitor water saturation without ever having to pull the casing and re-log the well open-hole.
Synonyms and Related Terminology
Sigma is also written as Σ or as capture cross section. Related terms include pulsed neutron log (the measurement tool), water saturation (the calculated property), cased-hole logging (the application context), thermal neutron (the absorbed particle), capture unit (the measurement unit), carbon-oxygen log (the salinity-independent alternative), time-lapse logging (the production monitoring application), oil-water contact (the boundary tracked by sigma), and formation water salinity (the key input to sigma interpretation).
Why Sigma Is the Production Engineer's Cased-Hole Saturation Tool
Once a well is cased, open-hole logging is no longer an option. But the reservoir keeps changing as production proceeds and water floods advance — and knowing where the remaining oil is determines where to perforate, which zones to shut off, and whether a workover is worth the cost. Sigma gives you that picture without disturbing the well, using nothing more than a wireline neutron source and chlorine's extraordinary appetite for slow neutrons. In high-salinity reservoirs, it's one of the most cost-effective diagnostic tools available for mature field management.