Irreducible Water Saturation (Swirr)

Purpose

Irreducible water saturation, Irreducible water saturation, is the water that stays in the pore space however far a hydrocarbon column drains it. It answers two questions. How much of the water in a zone can move, and so whether the zone will produce water-free hydrocarbons? And what is the lower bound of the water saturation a model can return?

It is also an input. Several of the permeability models use it as their saturation term, and relative permeability and saturation-height models take it as an endpoint. This page covers the Swirr result and the ways to estimate it; the capillary pressure and saturation-height modelling behind some of the methods belongs to SwH Analysis.

Position in the workflow

Upstream. Swirr needs porosity (Effective porosity or Total porosity) from the Porosity step, clay volume from Clay Volume, and, for some methods, a permeability curve, a rock type or an NMR distribution. Core capillary pressure or centrifuge data calibrate most of them.

Downstream. Swirr feeds:

the Permeability step, where Coates, Timur, Tixier and similar models take Swirr as the saturation term. Swirr has to be computed first, and with a permeability source that does not depend on it,
the checks on Water Saturation: Sw below Swirr is not physical, and Sw close to Swirr indicates a zone producing water-free,
Cutoffs, where a saturation cutoff is judged against Swirr, and
relative permeability and saturation-height models.

Error propagation. The permeability models are steep functions of Swirr. In a Coates-type model the permeability is proportional to ((1 - Swirr) / Swirr) squared, so raising Swirr from 0.25 to 0.30 lowers the permeability by 40%. In a Timur-type model, where it goes as Swirr to the power -2, the same change gives -31%. Swirr errors therefore matter more through permeability than directly.

Key concepts

Irreducible is relative to the drive. Swirr is not a single number of the rock: it is the saturation at the capillary pressure, or height above the free water level, that was reached. A core drained to a high pressure gives a lower Swirr than one drained at a lower pressure, and the field value depends on the column height.

Bulk volume water. The product of porosity and water saturation, BVW. At irreducible saturation it is close to constant within a rock type, which gives the Buckles method and the bulk-volume-water plot used to see whether a zone is at irreducible saturation.

Three families of estimate. Empirical constants applied to log porosity (Buckles, Foil), relations to rock quality (permeability, RQI, Lucia) and a direct log measurement (NMR).

Porosity basis. Swirr on an effective porosity basis excludes the clay-bound water. On a total porosity basis it includes it, and is higher in shaly rock. Mixing the two is a common error; see Total vs Effective Sw.

Calibration to core. Every method here is an empirical fit or a calibration. The core data that define Swirr (porous plate, mercury injection or centrifuge) are the reference.

Method selection guide

Method	Inputs	Use when	Strengths	Weaknesses
Buckles	Porosity; constant per rock type	Rock types are clear and a Buckles plot or core gives the constant	Simplest, needs only porosity	The constant drifts with grain size; no sense of column height
Foil	Total porosity; maximum column height; two fitted constants	A height-BVW fit from core or thick clean zones exists	Includes column height	Origin of the name not documented; sensitive to the height pick
Permeability	Permeability; two fitted constants	Core gives a Swirr-permeability fit and a good permeability curve exists	Follows rock quality, not just porosity	Cannot be used with a permeability that depends on Swirr
RQI	Permeability and porosity; two fitted constants	Core fits better against RQI than permeability, flow units are known	Uses both properties, links to flow units	Still depends on permeability; fit constants are specific to the unit
Lucia	Total porosity; height; rock fabric number	Carbonates with a fabric assignment	Built for carbonate pore structure	Steps at class boundaries; needs RFN; vuggy rock is difficult
NMR	T2 distribution; porosity; T2 cutoff	An NMR log and a core-calibrated cutoff exist	Measured at the well, no permeability needed	Cutoff is a calibration; hydrocarbon effects; log availability

Decision guidance

If NMR is available with a calibrated cutoff, use it as the reference and compare the others to it.
In clastics without NMR, start with Buckles by rock type and check against a Swirr-permeability or RQI fit to core.
In carbonates, use Lucia if the fabric can be assigned, and Buckles as a check. Be careful in vuggy rock, where porosity does not control Swirr.
If the Swirr is wanted only as an input to permeability, use a method that does not use permeability (Buckles, Foil, Lucia, NMR).
If there is no core and no NMR, treat all results as ranges. Vary the constant and carry the range into permeability.

Shared parameter picking

Porosity basis. Decide whether Swirr is effective or total, and use that basis for every downstream model. Permeability models differ in the basis they were written for.

Rock typing. Every constant in this step is for a single rock type or hydraulic flow unit. Pick the zones and the rock typing before the constants. Constants for a mixed section produce a Swirr that follows porosity alone.

Column height. Height above free water level, the maximum height of the hydrocarbon column, is shared by the Foil and Lucia methods. Pick it from the contact and free water level picks and use the same value for both.

Bulk volume water constant. The Buckles number (Bulk volume water at irreducible saturation) is read from a plot of BVW against porosity for zones that are at irreducible saturation, and is also used to judge whether a zone produces water-free.

Core definition of Swirr. Record the pressure or height at which the core Swirr was measured, so that the log result can be compared like with like.

Limits. Clamp Swirr to the interval 0 to 1, and cap it at the water saturation where a model requires Sw to be at least Swirr.

Recommended default approach

Absent other information, a careful generalist would:

Decide the porosity basis and divide the section into rock types.
Pick the Buckles number per rock type from a BVW-porosity plot of the clean zones, or from core, and compute Swirr.
Fit a Swirr-permeability or Swirr-RQI relation to core, if there is core, and compare.
In carbonates, add Lucia by fabric class. Where NMR exists, compute NMR Swirr with a core-calibrated cutoff.
Choose one result as the Swirr curve, per rock type, and carry the spread of the others as the uncertainty into permeability.
Check Swirr against Sw: Sw should not be below Swirr, and zones with Sw close to Swirr should test water-free.

Combining methods

Do not average the estimates blindly. Each is a different calibration and they do not share errors, so averaging gives a smooth result with no clear meaning. The more defensible approach is to use the estimate that is calibrated best to core in each rock type, and use the others as a cross-check and as the range. Where NMR and a rock-quality method disagree, the explanation is usually the cutoff, the porosity basis or the rock type assigned. A weighted combination is acceptable if the weights come from a comparison with core.

QC of results

A good result:

lies between 0 and 1, and is not capped at either limit in the reservoir,
falls with rising porosity or permeability within a rock type,
is below the water saturation in hydrocarbon-bearing zones, and close to it in zones that produce water-free,
matches core capillary pressure or centrifuge Swirr at the same depths, with no bias, and
agrees in size between independent methods for the same rock.

Signs of a bad result: Swirr that follows porosity across a lithology change, Swirr above Sw in a pay zone, a jump in Swirr at a rock-type boundary with no change in the rock, and Swirr that changes when the permeability model changes.

Common pitfalls

Using one constant for several rock types.
Mixing total and effective porosity bases between Swirr and the permeability or Sw model.
Computing permeability from Swirr and Swirr from that permeability.
Comparing a core Swirr measured at a low pressure with a log Swirr for a tall column.
Using Swirr in a transition zone as if the zone were at irreducible saturation.
Using a typical NMR cutoff without core calibration.
Using total porosity in a Lucia relation that was fitted to interparticle porosity (or the reverse).

Going Deeper

Irreducible water saturation was an empirical concept first: connate water saturation data were correlated with porosity and permeability from the 1950s, and Buckles formalised the constant bulk volume water in the 1960s. Capillary pressure theory then explained why: the saturation at a given height is set by the pore throat size distribution, so Swirr is the end of a saturation-height curve and not a separate property. That is the reason the modern view treats the methods here as shortcuts to what a saturation-height model gives directly. NMR added a direct log measure, at the cost of a core-calibrated cutoff. The main open difficulty is that there is no single number: the Swirr depends on the pressure that defines 'irreducible', the fluid pair and the wettability.