Petrophysics in Weller Logs

Weller Logs does a deterministic quick-look interpretation. Every equation is in app/js/petro.js and unit-tested in tests/petro.test.mjs. Parameters live in the Interpretation panel and are saved with the project. Computed curves are added to each well with the mnemonics below, so they can be plotted, crossplotted, averaged and exported like any log.

Equations

Shale volume. Gamma-ray index IGR = (GR − GRclean) / (GRshale − GRclean), clipped to 0–1, then one of: linear (Vsh = IGR), Larionov Tertiary 0.083 (2^(3.7 IGR) − 1), Larionov older rocks 0.33 (2^(2 IGR) − 1), or Clavier 1.7 − √(3.38 − (IGR + 0.7)²). Automatic baselines: clean is the 2nd percentile of the well's GR; shale is the 95th percentile after dropping samples above median + 2.5 × MAD. That exclusion matters in organic or uranium-rich shales (Sharon Springs, Niobrara marls, many source rocks), which read far above ordinary shale and would otherwise make real shale look clean. Set the baselines per well in the panel when you know better.

Porosity. PHID = (ρma − ρb) / (ρma − ρfl). Total porosity is the neutron-density average, or root-mean-square √((φN² + φD²)/2) for gas-bearing rock, or density alone. PHIE = PHIT × (1 − Vsh). Matrix density "Match neutron" uses the matrix the neutron was recorded on (MATR in the LAS header, or in older files the neutron curve's description, such as "NEUTRON POROSITY SANDSTONE"): sandstone 2.65, limestone 2.71, dolomite 2.87 g/cc. Keeping both logs in the same matrix units is what makes the neutron-density average close to lithology-independent.

Water resistivity at depth. Formation temperature is a linear gradient from the surface temperature to BHT at TD (TVD in deviated wells). Wells with no BHT in the header use a geothermal gradient instead, 1.5 °F/100 ft by default (set in the Interpretation panel), near the continental U.S. average of about 25–30 °C/km. Rw is carried to that temperature with Arps: Rw2 = Rw1 (T1 + 6.77)/(T2 + 6.77) (°F).

Water saturation. Archie Sw = (a Rw / (φ^m Rt))^(1/n), or Simandoux (n = 2) 1/Rt = φ^m Sw²/(a Rw) + Vsh Sw / Rsh, solved as a quadratic. Rsh is the median deep resistivity where Vsh > 0.8. Sw can use effective or total porosity: effective suits shaly sands; total is the usual choice in organic mudrocks and chalk-marl systems, where GR-derived Vsh overstates clay.

TOC. Passey et al. (1990), density form: ΔlogR = log10(Rt/Rt_base) − 2.5 (ρb − ρb_base) and TOC = ΔlogR × 10^(2.297 − 0.1688 LOM). The baseline is the median Rt and ρb of the chosen baseline zone (on "Auto", the zone above the first top), or of the lower-resistivity half of the shaly samples when there are no tops. TOC is left blank where the rock is not fine-grained (Vsh < 0.35 and PE < 3.5) and in bad hole, because resistivity separation in a clean sand or chalk carrying oil or gas comes from the hydrocarbons, not organic matter. Values are clipped at 20 wt%. LOM (level of organic metamorphism) should come from vitrinite reflectance or Tmax.

Flags and cutoffs. Washout: caliper more than 1 in over bit size (bit from the header, else the caliper's P10 as gauge). Bad hole: washout, or |DRHO| > 0.15 g/cc. Net reservoir: Vsh < cut, porosity ≥ cut, not bad hole, and not RHOB < 2.0 g/cc (coal, washout or a log behind casing, which would otherwise read as very high porosity). Porosity from the neutron alone never makes net reservoir: apparent neutron porosity reads 0.3–0.5 in shale and through casing. That includes depths in a neutron-density well where only the neutron was logged. Net pay: net reservoir and Sw ≤ cut. The flags track also takes any log with a threshold (e.g. metal loss % for corrosion).

Reduced log suites. Older wells often have only GR or SP and one or more resistivities. The workflow uses what is there:

The Notes button in the Interpretation panel lists which fallbacks each well used.

Zone summations (Zone stats tab). Zones run from each top to the next top. Thickness is true vertical in deviated wells (from the survey). Per zone: gross, net reservoir, net-to-gross, net pay, average porosity over net reservoir, average Sw over net pay (pore-volume weighted, Σ φ Sw h / Σ φ h), porosity-feet Σ φ h over net reservoir and hydrocarbon-feet Σ φ (1 − Sw) h over net pay. Curve means are depth-weighted; resistivity, gas and permeability use geometric means. Wells without porosity logs use the Vshale-only net sand flag. Click a zone in the legend to hide it from the table, box plots, crossplot and histograms (exports keep every zone).

Display conventions

• Density-neutron overlay. The density scale follows the neutron's recorded matrix so the two curves overlay in clean matrix rock and crossover means the same thing in every well: limestone 1.95–2.95 g/cc, sandstone 1.90–2.90 g/cc, dolomite 2.12–3.12 g/cc, all against neutron 0.45 to −0.15 v/v. The header shows which scale is in use. Editing the density limits by hand turns the matching off for that track.
• Neutron-density crossplot. The line for the neutron's calibration matrix is exact. The other two lithology lines are linear-mixing approximations of the service-company chartbook curves and are drawn dashed. The lines hold for clean rock only: clay-bound water lifts the neutron, so shale plots below and right of the dolomite line. The ◇ shale point is the median NPHI and RHOB of samples with Vsh ≥ 0.65 (the lithology track's shale cutoff), joined to the calibration matrix by a dotted line; shaly, low-porosity rock falls between them.
• PE-density crossplot. Matrix points for quartz, calcite, dolomite and anhydrite, with porosity lines toward fresh water (ticks every 10 p.u.). PE mixes by volume through U = PE × ρe, not PE itself, so porosity lowers PE as well as density (limestone at 20% reads about 4.6 b/e, not 5.08). Clay minerals are shown as muted reference points at chartbook log values. Bad-hole samples (washout or |DRHO| > 0.15) are hidden by default on the neutron-density, PE-density and Pickett plots, because PE and density are the readings most affected by rugose hole and barite mud.
• Pickett plot. Log deep resistivity (x) against log porosity (y), the usual layout, with equal decades on both axes so the Sw lines show their true slope of −1/m. Archie Sw lines use the current a, m, n and Rw, corrected to the median formation temperature of the plotted points. Only clean samples are plotted by default (Vsh < 0.2, editable on the chart), since Archie assumes clean rock. Click a zone in the legend to hide it.
• Curve families, aliases and colors follow petroplots so figures made in the app and in petroplots agree; the families are listed below. One deliberate difference: petroplots' default density and neutron limits (1.9–2.9 g/cc against 0.45 to −0.05 v/v) do not overlay a limestone or sandstone matrix, so Weller keeps the matrix-matched scales above.
• Horizontal wells (Lateral tab). A well counts as horizontal when its survey holds 300 ft (100 m) or more of hole at 70° or more; landing is the first station at 70°. The path is TVDSS (or TVD when a well has no KB or GL) against vertical section or MD. Vertical section is the offset from the wellhead projected on the azimuth from the wellhead to the last station; between stations, position is linear in MD. Beds are the type well's tops in TVDSS, shifted so one top (by default the deepest the two wells share) meets the lateral's own pick, then bent by dip segments the user sets. Each segment starts at an MD and has an apparent dip (positive where beds deepen toward the toe) and a throw at its start (positive where beds drop on the toe side); within a segment beds are straight. With d the vertical section (or MD without offsets), the bed offset is O(d) = Σ tan(dipᵢ) × (length of segment i crossed) + Σ throws, set to 0 at the tie, and a bed sits at z_type + shift + O(d). Stratigraphic depth is z − O(d): the lateral's log drawn there on the type log traces it where the dips are right. The zone at the bit and the in-zone shares (landing to TD, by MD) come from the same lines. Nothing is fitted automatically.
• Laterals in Correlation. With dip segments set, a lateral hangs on stratigraphic depth (TVD − O(d)) in every hang but MD, so its log sits at the depth of the beds it drilled; passes up and down through the same beds overlap. With no dips it hangs on TVD and the lateral stacks into a few feet.
• GR level steps. Along the lateral, the largest difference between the mean GR over 100 ft (30 m) before and after any depth is flagged when it is at least 60 API and a factor of 1.5: usually a run or tool change. Leveling shifts the part after it by the difference, for display and matching only.

Curve families and groups

A family is every mnemonic that means the same measurement, named by its PWLS property kind: deep resistivity covers ILD, AT90, LLD and many more. A group gathers related families: Resistivity holds deep, medium and shallow. A track is what is drawn together on screen and is set in the track editor.

A track curve takes the mnemonics listed for its family first. After all of them come the vendor mnemonics the PWLS Curve Catalog files under the same property kind ("more" below), so a listed curve always wins. Families tag curves; they never rename them. Units are tagged the same way with their Energistics UoM symbol (OHMM is ohm.m). "PWLS parent" is the next kind up in PWLS 4.0. Families with no track of their own (shear slowness, NMR porosity, hook load) show example names from the catalog. Select a group to open it.

Known limits

• GR-derived shale volume overstates clay where uranium or organic matter raises GR. Spectral GR (thorium and potassium) or a neutron-density clay volume would be better; neither is implemented yet.
• PHIE = PHIT × (1 − Vsh) is a simplification. There is no shale-porosity correction or clay-bound water model.
• The ΔlogR TOC is a screening estimate. Calibrate LOM and the baseline against core TOC before quoting numbers.
• There are no environmental corrections (borehole size, mud weight, temperature for the neutron).
• No depth matching between runs, or between core and log, yet.

References

• Archie, G.E., 1942, The electrical resistivity log as an aid in determining some reservoir characteristics: Trans. AIME 146, 54–62.
• Arps, J.J., 1953, The effect of temperature on the density and electrical resistivity of sodium chloride solutions: Trans. AIME 198.
• Clavier, C., Hoyle, W., and Meunier, D., 1971, Quantitative interpretation of TDT logs: J. Petroleum Technology 23.
• Larionov, V.V., 1969, Borehole radiometry: Nedra, Moscow.
• Passey, Q.R., Creaney, S., Kulla, J.B., Moretti, F.J., and Stroud, J.D., 1990, A practical model for organic richness from porosity and resistivity logs: AAPG Bulletin 74(12), 1777–1794.
• Simandoux, P., 1963, Dielectric measurements on porous media, application to the measurement of water saturations: Revue de l'IFP 18.
• U.S. Geological Survey data release, doi:10.5066/P14CRSQQ: produced-water chemistry from Niobrara wells, Denver-Julesburg Basin, Weld County, Colorado. Source of the example's Rw: the maximum specific conductance, 61.3 mS/cm at 25 °C, is 0.16 Ω·m at 77 °F.