Wireline Logging - Tool Physics, Log Interpretation, and Petrophysical Calculations
A wireline log is a continuous record of a formation property measured as a function of depth. The raw measurement coming from the tool - photoelectrons per second, microseconds per foot, ohm-meters - means nothing until it is converted into a petrophysical property that answers the three questions every formation evaluation must answer: What is the porosity? What is the fluid in the pore space? How much hydrocarbon can the formation produce? The engineer who understands what each tool is physically measuring, why the measurement responds to porosity or fluid type, and how to combine multiple logs to reduce interpretation ambiguity is the engineer who can identify a 15 ft pay zone that looks like shale on the gamma ray log alone. This guide gives you the physics, the interpretation equations, and the worked calculations.
1. The Gamma Ray Log - Lithology Identification
1.1 Physical Measurement
The gamma ray (GR) tool measures the natural radioactivity of the formation - specifically the gamma radiation emitted by radioactive isotopes of potassium (K-40), uranium (U-238 series), and thorium (Th-232 series). Shales are radioactive because clay minerals contain potassium and adsorb uranium and thorium. Clean sands and carbonates are generally non-radioactive. The GR log therefore distinguishes shale from reservoir rock:
| Formation Type | Typical GR Value (API units) | Reason |
|---|---|---|
| Clean quartz sand | 15-30 API | SiO2 has no radioactive elements |
| Clean carbonate (limestone/dolomite) | 10-25 API | CaCO3 and CaMg(CO3)2 are non-radioactive |
| Shale | 75-150 API | High clay content - potassium feldspar + uranium adsorption |
| Shaly sand (10-30% clay) | 30-75 API | Mixed - higher GR than clean sand, lower than shale |
| Potassium evaporite (K-salt) | 200-300+ API | Pure K-40 - very high radioactivity. Easy to identify. |
1.2 Shale Volume Calculation (Vsh)
GR Index (IGR) = (GR_log - GR_clean) / (GR_shale - GR_clean)
GR_clean = GR value in the cleanest sand/carbonate on the log (minimum GR in reservoir)
GR_shale = GR value in the adjacent shale (maximum GR)
Linear shale volume: Vsh = IGR (acceptable first approximation)
Larionov correction for older rocks (Tertiary+):
Vsh = 0.083 x (2^(3.7 x IGR) - 1) - gives lower Vsh than linear (shales are less radioactive in older formations)
Example: GR_log = 65 API, GR_clean = 20 API, GR_shale = 120 API:
IGR = (65 - 20) / (120 - 20) = 45/100 = 0.45
Linear: Vsh = 0.45 = 45% shale
Larionov: Vsh = 0.083 x (2^(3.7 x 0.45) - 1) = 0.083 x (2^1.665 - 1) = 0.083 x (3.170 - 1) = 0.083 x 2.170 = 0.180 = 18% shale
The Larionov correction significantly reduces the Vsh estimate - use it to avoid over-estimating shale content in Tertiary reservoirs.
2. The Resistivity Log - Fluid Identification
2.1 Physical Basis
Formation resistivity (Rt, in ohm-meters) measures how strongly the formation resists electrical current flow. The key insight is that formation water is conductive (low resistivity due to dissolved salts) while hydrocarbons are non-conductive (high resistivity). A hydrocarbon-bearing formation has much higher resistivity than the same formation filled with water:
| Formation/Fluid | Typical Resistivity (ohm-m) | Explanation |
|---|---|---|
| Saline formation water | 0.01-0.1 ohm-m | High ion concentration = high conductivity |
| Oil-saturated sandstone | 10-500 ohm-m | Oil is non-conductive - only connate water provides conductivity path |
| Gas-saturated sandstone | 50-2,000+ ohm-m | Gas is non-conductive AND has lower water saturation than oil zones |
| Shale | 1-10 ohm-m | Bound water in clay minerals provides conductivity path |
2.2 Archie's Equation - Water Saturation Calculation
Archie's equation is the fundamental petrophysical relationship that converts resistivity measurements into water saturation - the fraction of the pore space filled with water (vs hydrocarbon):
Sw = (a x Rw / (phi^m x Rt))^(1/n)
Where:
Sw = water saturation (fraction, 0-1)
a = tortuosity factor (typically 0.62-1.0; use 1.0 for carbonates, 0.62 for sands)
Rw = formation water resistivity (ohm-m) - from water sample or Rw catalog
phi = porosity (fraction) - from density or neutron-density log
Rt = true formation resistivity (ohm-m) - from deep resistivity log
m = cementation exponent (typically 2.0 for consolidated sands)
n = saturation exponent (typically 2.0)
Hydrocarbon saturation: Sh = 1 - Sw
Worked example: phi = 0.22, Rt = 45 ohm-m, Rw = 0.04 ohm-m, a = 0.62, m = 2.0, n = 2.0:
Sw = (0.62 x 0.04 / (0.22^2 x 45))^(1/2)
= (0.0248 / (0.0484 x 45))^0.5
= (0.0248 / 2.178)^0.5
= (0.01139)^0.5 = 0.107 = 10.7% water saturation
Sh = 1 - 0.107 = 89.3% hydrocarbon saturation → Excellent reservoir - commercial accumulation
2.3 Resistivity Tool Depth of Investigation - Why Multiple Curves Matter
During drilling, drilling fluid invades the formation near the wellbore (the invaded zone). Multiple resistivity tools with different depths of investigation measure this invasion profile:
| Tool | Depth of Investigation | What It Measures | Use In Interpretation |
|---|---|---|---|
| Microresistivity (MSFL) | 2-4 inches | Flushed zone resistivity (Rxo) | Porosity estimation, moveable hydrocarbon indicator |
| Medium resistivity (ILM) | 2-3 ft | Invaded zone resistivity (Ri) | Invasion profile analysis |
| Deep resistivity (ILD) | 5-6 ft | True formation resistivity (Rt) | Archie Sw calculation - PRIMARY tool for fluid identification |
3. Density and Neutron Logs - Porosity Measurement
3.1 Density Log - Electron Density to Porosity
The density tool emits gamma rays from a cesium-137 source and measures the backscattered gamma ray count rate at one or two detectors. Denser formations absorb more gamma rays and return fewer counts. The bulk density (rho_b) is calculated from the count rate and converted to porosity:
Density porosity (phi_D):
phi_D = (rho_ma - rho_b) / (rho_ma - rho_fl)
Where:
rho_ma = matrix density (g/cc) - 2.65 for quartz sandstone, 2.71 for limestone, 2.87 for dolomite
rho_b = measured bulk density (g/cc) from log
rho_fl = fluid density (g/cc) - 1.0 for water, 0.9 for oil, 0.2-0.3 for gas
Example (sandstone, water-filled): rho_b = 2.35 g/cc, rho_ma = 2.65, rho_fl = 1.0:
phi_D = (2.65 - 2.35) / (2.65 - 1.0) = 0.30 / 1.65 = 0.182 = 18.2% porosity
Gas effect on density log:
If the formation contains gas (rho_fl = 0.25 g/cc instead of 1.0):
phi_D = (2.65 - 2.35) / (2.65 - 0.25) = 0.30 / 2.40 = 0.125 = 12.5% apparent porosity
The density log UNDER-REPORTS porosity in gas zones because gas is lighter than water. This is the key gas effect that must be recognized in interpretation.
3.2 Neutron Log - Hydrogen Index Measurement
The neutron tool emits fast neutrons from an americium-beryllium (AmBe) source. Neutrons are slowed by collisions with hydrogen nuclei (since hydrogen has nearly the same mass as a neutron, it transfers the most energy per collision). The tool measures the decelerated neutron population and converts it to a Hydrogen Index (HI) which, since hydrogen is primarily in water or hydrocarbons, is equivalent to porosity for water-filled formations.
Gas effect on neutron log - the key diagnostic tool:
Gas has very low hydrogen concentration (low HI) compared to water or oil. In a gas zone, the neutron log reads LOWER porosity than the actual porosity. Combined with the density log effect (density reads lower than actual in gas due to low gas density), the neutron-density crossover pattern is the standard gas indicator:
Neutron-density separation patterns:
Water or oil zone: phi_N ≈ phi_D or phi_N slightly > phi_D (neutron reads slightly higher than density in oil zones)
Gas zone: phi_N < phi_D ("crossover") - neutron reads low (less H), density reads high (less dense gas)
Shale: phi_N >> phi_D - neutron reads very high (bound water in clay), density reads moderate
Best porosity estimate in gas zones:
phi_gas_corrected = sqrt((phi_N^2 + phi_D^2) / 2)
Example: phi_N = 0.12, phi_D = 0.20 (crossover pattern confirming gas):
phi_corrected = sqrt((0.12^2 + 0.20^2) / 2) = sqrt((0.0144 + 0.0400) / 2) = sqrt(0.0272) = 0.165 = 16.5% corrected porosity
4. The Sonic Log - Compressional Wave Travel Time
4.1 Measurement and Wyllie Time-Average Equation
The sonic tool measures the time for a compressional sound wave to travel 1 foot through the formation (Delta-t, in microseconds per foot). Fast formations (hard rock, low porosity) have low Delta-t; slow formations (soft, high porosity) have high Delta-t. The Wyllie time-average equation converts Delta-t to porosity:
Sonic porosity (phi_S):
phi_S = (Delta_t_log - Delta_t_ma) / (Delta_t_fl - Delta_t_ma)
Typical matrix values (Delta_t_ma):
Sandstone: 55.5 microsec/ft
Limestone: 47.5 microsec/ft
Dolomite: 43.5 microsec/ft
Fluid travel time (Delta_t_fl):
Water: 189 microsec/ft
Oil: 230 microsec/ft
Gas: 850+ microsec/ft (very slow)
Example (sandstone, water): Delta_t_log = 87 microsec/ft:
phi_S = (87 - 55.5) / (189 - 55.5) = 31.5 / 133.5 = 0.236 = 23.6% porosity
Sonic log advantage: Less affected by borehole rugosity than density log. Used as quality check against density porosity.
Sonic log disadvantage: Over-estimates porosity in vuggy carbonates (secondary porosity not well-characterized by sonic). Also affected by gas (reads slow = high apparent porosity in gas zones).
5. Integrated Log Interpretation - The Complete Petrophysical Workflow
5.1 Gross Pay vs Net Pay vs Net Productive Pay
Log interpretation must distinguish between the total formation interval, the potentially productive portion, and the actually productive portion. Three cutoffs are applied sequentially:
| Pay Classification | Cutoff Applied | Typical Values | Purpose |
|---|---|---|---|
| Gross pay | GR cutoff: GR < GR_cutoff (identifies reservoir vs shale) | GR cutoff = GR_clean + 0.5 x (GR_shale - GR_clean) | Total sand/carbonate thickness above shale baseline |
| Net pay | Porosity cutoff: phi > phi_min AND Vsh < Vsh_max | phi_min = 5-10%, Vsh_max = 30-50% | Reservoir quality sufficient for production |
| Net productive pay | Sw cutoff: Sw < Sw_max (hydrocarbon saturation above abandonment) | Sw_max = 50-75% (field-specific) | Contains enough hydrocarbon to produce above WOR/GOR limits |
5.2 Complete Worked Log Interpretation Example
Formation interval 8,450-8,510 ft: GR = 35 API (GR_clean = 20, GR_shale = 120), rho_b = 2.26 g/cc, Delta_t = 92 microsec/ft, ILD = 38 ohm-m, Rw = 0.05 ohm-m.
Step 1 - Shale volume:
IGR = (35-20)/(120-20) = 15/100 = 0.15. Larionov Vsh = 0.083 x (2^(3.7x0.15)-1) = 0.083 x (2^0.555 - 1) = 0.083 x (1.469-1) = 0.083 x 0.469 = 0.039 = 3.9% shale. Clean sand confirmed.
Step 2 - Porosity:
phi_D = (2.65 - 2.26)/(2.65 - 1.0) = 0.39/1.65 = 0.236 = 23.6%. phi_S = (92-55.5)/(189-55.5) = 36.5/133.5 = 0.273 = 27.3%. Average = (23.6+27.3)/2 = 25.5% porosity. Density and sonic agree within 4% - consistent, reliable estimate.
Step 3 - Water saturation:
Sw = (0.62 x 0.05 / (0.255^2 x 38))^0.5 = (0.031 / (0.0650 x 38))^0.5 = (0.031/2.471)^0.5 = (0.01254)^0.5 = 0.112 = 11.2% water saturation
Step 4 - Pay summary:
- Vsh = 3.9% < 50% cutoff: Net pay ✓
- phi = 25.5% > 10% cutoff: Net pay ✓
- Sw = 11.2% < 75% cutoff: Productive pay ✓
- Sh = 88.8% → Excellent hydrocarbon saturation
- Conclusion: 60 ft productive pay zone with 25.5% porosity and 88.8% hydrocarbon saturation. Perforate and test.
6. Cased-Hole Logging - Post-Completion Applications
| Cased-Hole Log Type | Measurement | Primary Application |
|---|---|---|
| Cement Bond Log (CBL/VDL) | Acoustic amplitude at casing OD | Primary cement quality evaluation - Bond Index calculation |
| Production logging tool (PLT) | Spinners + density + capacitance + temperature | Flow profiling - which perforations contribute, water entry identification |
| Pulsed neutron log (PNC/GST) | Neutron capture cross-section (Sigma) | Saturation monitoring through casing - water flood front tracking |
| Casing inspection log (EMIT) | Electromagnetic thickness measurement | Casing wall loss quantification - corrosion assessment |
| Temperature log | Downhole temperature profile | Gas entry identification (cooling effect), cement top confirmation, SCP source location |
Conclusion
The 60 ft productive pay zone example in this article was identified from three numbers: a GR of 35 API that confirmed clean sand, a density-derived porosity of 23.6% that confirmed reservoir quality, and a deep resistivity of 38 ohm-m that yielded an Archie Sw of 11.2%. These are not complex measurements. The physics behind each is well understood, the equations are established, and the interpretation workflow is reproducible. The engineer who performs this workflow on every potential pay interval makes perforation decisions based on quantified petrophysical evidence. The engineer who perforates based on a general "that interval looks like it might have hydrocarbons" read of a GR log misses pay intervals that look shaley but are actually clean paying reservoirs, and perforates water zones that have high resistivity due to tight rock rather than hydrocarbons.
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