Porosity

Purpose

Porosity, Total porosity and Effective porosity, answers how much of the rock is pore space, and therefore how much fluid it can hold. It is the most basic reservoir property and the base of every volumetric calculation: hydrocarbon in place is porosity times the hydrocarbon fraction of it, and the saturation and permeability steps that follow both take porosity as an input. In complex rock, porosity cannot be read from one log, because every porosity log also responds to lithology, clay, organic matter and gas. This step turns the logs into porosity and, where the mineralogy varies, into mineral and fluid volumes at the same time.

Position in the workflow

Upstream. Porosity needs the repaired and normalized density, neutron and sonic logs from Stage 1. A washout shows directly as false porosity. Two earlier steps supply inputs that change the answer:

Clay Volume gives Clay volume, used to convert total to effective porosity and used as a constraint in the mineral inversion.
TOC Analysis gives Kerogen volume, used to remove the low density of kerogen from density porosity and used as a constraint in the mineral inversion.

Mineral inversion is a method of this step. It is one of the ways porosity is computed, not a separate module in front of it. It consumes the clay volume and the kerogen volume as inputs, and does not produce them: if either is wrong the inversion inherits the error. It produces porosity, grain density and the other mineral volumes.

Downstream. Porosity feeds Water Saturation (every Archie-type model uses it directly), permeability, the cutoffs and net pay, and the volumetrics. Effective and total porosity are used by different saturation models, so the choice of which to pass on is part of the saturation choice.

Error propagation. Porosity errors are passed on almost one for one. For an Archie model with equal cementation and saturation exponents, water saturation varies as the inverse of porosity, so a 10% relative error in porosity is a 10% relative error in water saturation. Hydrocarbon in place is porosity times hydrocarbon saturation and carries both. A matrix density error of 0.01 g/cm³ is about 0.005 of porosity at a bulk density of 2.45 g/cm³, which is large in a rock with 0.06 porosity.

Key concepts

Every porosity log is apparent. Density, neutron and sonic porosity are each the porosity that a stated matrix and fluid would need to produce the reading. The apparent value equals the true one only if the assumed matrix, fluid and the absence of other components are right.

Matrix and fluid. Each method needs a matrix response and a fluid response, and these are the main parameters. The matrix is a property of the lithology, and the fluid is that of the zone the tool reads, which for density and neutron is the flushed zone.

Total and effective porosity. Total porosity includes the water bound to clay, Effective porosity does not. The two differ by the clay volume times the clay porosity. See Total vs Effective Porosity.

Corrections. Gas lowers the neutron response, kerogen lowers the bulk density, and salt has a density far from a clastic matrix. Each requires a correction or a separate treatment (Gas and Organic-Matter Corrections).

Volumetric mixing. All the methods rest on the idea that a log reads the volume-weighted sum of the responses of what is in the rock. A single-log method fixes the matrix and solves for porosity. Mineral inversion lets the matrix be a mix and solves for all the volumes at once, using closure (the volumes add to one) and, where available, outside constraints.

Redundancy. Each additional log or constraint gives more information about the volumes, and each additional component asks for more. Whether the answer is reliable depends on the balance, which is why the inversion has its own uncertainty and error QC pages.

Method selection guide

Method	Inputs	Use when	Strengths	Weaknesses
Density porosity	Bulk density; matrix and fluid density	Lithology is known and constant, and a density log is available	Simple, the most reliable single log, shallow and well resolved	Wrong in kerogen, gas, heavy minerals and washouts; needs the right matrix
Neutron-density	Neutron, bulk density; matrix and fluid	Both logs are good; clean or shaly clastic or carbonate; the usual default	Lithology and clay partly cancel; widely understood; a crossplot gives a check	Gas pulls it down (RMS form helps); needs the neutron on the right scale; kerogen not removed
Sonic, Wyllie	Slowness; matrix and fluid slowness; shale slowness	No density or neutron, or an independent check; consolidated rock	Unaffected by washouts to the same degree; reads only connected, intergranular pores	Too high in uncompacted and gassy rock; misses vugs and fractures
Sonic, RHG	Slowness; matrix slowness; exponent	As Wyllie, at higher porosity or where Wyllie reads high	Curved response; no fluid slowness needed	Exponent has to be calibrated; same sonic limits
Gas and organic-matter corrections	Kerogen volume; kerogen density and neutron response; flags	Organic-rich shale, gas, salt	Removes known biases from any of the above	Only as good as the kerogen volume and the gas treatment
Mineral inversion	Density, neutron, sonic, PE or U, constraints (clay volume, kerogen volume)	Mineralogy varies, complex lithology, unconventional rock, or the matrix is itself a result	Matrix is solved, not assumed; gives mineral volumes and grain density; clay and kerogen handled explicitly	Needs a careful component list and endmembers; can fit the logs and be wrong; harder to QC
Total to effective	Total porosity; clay volume; clay porosity	Whenever the saturation or storage calculation needs effective porosity	Simple, transparent	Clay porosity is an assumed number

The inversion has three supporting pages: endmember parameters, uncertainty and confidence and model-error QC.

Decision guidance

Clean, single-lithology reservoir with density and neutron: use neutron-density, with the matrix chosen for the lithology.
Gas is possible: use the RMS form or a gas correction and check the separation of the neutron and density curves.
Organic-rich shale: remove kerogen with the kerogen volume from TOC Analysis, or use the inversion with kerogen as a component.
Mixed or changing mineralogy (carbonate-clastic, pyritic, evaporites, unconventional): use mineral inversion, or at least let the matrix density vary from a grain density derived by inversion.
Only a sonic: use Wyllie in consolidated rock, RHG at higher porosity, and treat the result as less certain.
A required curve is missing in part of the well: use a fixed order of fallback, as described under combining methods.

Shared parameter picking

Matrix density (Matrix density) is shared by density, neutron-density and the corrections, and sets the grain density that an inversion should reproduce. Use about 2.65 for quartz sandstone, 2.71 for limestone and 2.87 for dolomite, or a volume-weighted value for a mix. Check it against core grain density.

Fluid density (Pore fluid density) is the filtrate density in the flushed zone: about 1.0 g/cm³, a little higher for salty filtrate.

Sonic matrix and fluid slowness (Matrix slowness and Fluid slowness): about 55.5, 47.5 and 43.5 µs/ft for sandstone, limestone and dolomite, and 189 µs/ft for fresh water. Shared by the Wyllie and RHG pages.

Kerogen properties (Kerogen density, and its neutron response Kerogen neutron response) must be the same as those used in the TOC step to convert TOC to kerogen volume, and the same ones used for the kerogen endmember in the inversion.

Clay porosity (Clay porosity) converts total to effective porosity. It must match the clay endmember of the inversion and the definition of clay volume.

Upper limit on porosity. A physical maximum is often applied to the result to stop bad hole and noise producing porosity above what the formation can have. Choose it from core and apply it in one place.

Picking once. Pick these per zone, not per well, and use the same values in every method so that the methods can be compared. Where matrix density is itself calculated by inversion, use that curve in place of a constant.

Recommended default approach

Absent other information, a careful generalist would:

Check that the density, neutron and sonic logs are repaired and on known units and lithology scales, and flag washouts.
Choose a matrix density and fluid density for each zone from lithology and core, and compute neutron-density porosity. Use the RMS form, or look at the neutron-density separation, in zones where gas is possible.
Remove kerogen where the kerogen volume from TOC Analysis is significant, using the same kerogen properties as in the TOC step.
Compute a sonic porosity (RHG, or Wyllie in consolidated rock) as an independent check, and compare.
Where the mineralogy varies or the zone is unconventional, run the mineral inversion with the clay volume and kerogen volume as constraints, and compare its porosity and grain density with step 2 and with core.
Take total porosity from the best-supported method, convert to effective porosity with the clay volume and a clay porosity, and calibrate against core porosity by adjusting the matrix density, not the porosity itself.
Carry the model-error flags from the inversion and the gas and bad-hole flags to the results.

Combining methods

Fallback order. If curves are missing, a fixed order is simple and transparent: neutron-density where both logs exist, then density alone, then sonic. Keep the transitions visible, since each change of method can be a step in the result.

Comparison. Porosity from different logs is not redundant, it is diagnostic. Neutron below density in a clean interval suggests gas. Neutron above density suggests clay or a heavier matrix. Sonic below density or neutron in a carbonate is commonly read as porosity the sonic does not see, such as vugs or fractures. Sonic above them points to uncompaction or gas.

Inversion against the single-log methods. The inversion porosity and the neutron-density porosity share their inputs, so they are not independent. Their difference is nevertheless useful: where they differ by more than the combined uncertainty the mineralogy is not as assumed in one of them.

Averaging. Averaging porosities from methods with different biases (neutron and density) works because the biases are of opposite sign. Averaging methods that share a bias (density porosity and an inversion that uses the same density log) does not.

Calibration to core. Core porosity is the anchor. When log and core porosity differ, check depth shifts, the core's confining stress and drying method, and then adjust the matrix density, not a constant added to the porosity.

QC of results

A good result:

lies between 0 and the physical maximum, with values near zero in tight and cemented intervals and in salt,
compares with core porosity (total with total, effective with effective) with no trend against depth, clay volume or lithology,
agrees with the other porosity logs except where a known effect (gas, clay, vugs) explains the difference,
has a grain density, from the matrix choice or from an inversion, that matches core grain density, and
is not driven by caliper, washouts or the density correction curve.

Signs of a bad result: porosity that follows the caliper, a negative or clipped-at-zero run over a long interval (matrix density too low, or kerogen over-corrected), porosity above the physical maximum, density and neutron porosity that separate systematically in clean rock, and mineral volumes that change sharply from sample to sample in an inversion.

Common pitfalls

Using the wrong lithology scale on the neutron, or the wrong matrix density, which is a systematic error of several porosity units.
Ignoring kerogen in an organic-rich shale, which makes density porosity read high by about 0.84 times the kerogen volume.
Using the RMS form and a gas correction together, or the RMS form in very tight rock.
Subtracting kerogen twice: once with a correction and again with an inversion that has kerogen as a component, or with a matrix density that already includes it.
Using different kerogen densities, clay endmembers or clay porosities in the TOC, clay, porosity and inversion steps.
Treating the inversion as a source of truth because the logs are fitted well. A missing component can be absorbed with little misfit.
Letting the inversion recompute clay or kerogen volume that was supposed to be an input, or passing it shale volume instead of clay volume.
Giving the inversion more components than the logs and constraints can resolve, such as quartz and calcite from density and neutron alone.
Passing effective porosity to a saturation model that wants total porosity, or the reverse.
Reading density porosity in salt or through washouts.

Going Deeper

The porosity logs and their crossplots were interpreted by hand for decades, with chart books for lithology and gas. The time-average sonic equation dates from the 1950s and the Raymer-Hunt-Gardner transform from 1980. Computer-based multi-mineral inversion, which replaces the chart reading with a simultaneous solution, became routine from the 1980s. Unconventional reservoirs, in which kerogen, pyrite and clay are a large part of the rock, made the matrix itself the main unknown and led to inversions constrained by clay volume and TOC. The unresolved problems are the same ones throughout: every log responds to more than one thing, the endmembers are not known well, and a model that fits the logs is not evidence that it is right. Core remains the only independent check, and the most useful use of it is to calibrate the matrix density and the endmembers, not the result.