SwH Analysis

Purpose

A saturation-height model gives the water saturation of a reservoir at every height above the free water level. It answers a question that logs alone cannot: what the water saturation would be in a thick, clean, hydrocarbon column in capillary equilibrium, where the resistivity reading has problems or is not available. It is used to check and replace the log Water saturation in low-resistivity and thin-bed pay, to set the water saturation above the logged interval and in cells away from the wells, and to map the transition zone and the contact. This topic covers the whole curve of saturation against height. The Swirr pages cover only its irreducible end point.

Position in the workflow

Upstream. A saturation-height model needs porosity from the Porosity step and permeability from the Permeability step (or a flow unit transform), a rock typing or flow unit assignment, the fluid properties, and a free water level on a depth reference that the logs share. Core capillary pressure data, converted to reservoir conditions, calibrate the model. The Irreducible Water Saturation results supply the lower end of each curve.

Downstream. The result feeds:

the check of log Sw: a modelled Sw that disagrees with the log in thick clean pay points to a problem with m, n, Rw or the free water level,
the transition zone and the contact in the Cutoffs and net pay work,
the water saturation used in volumetrics, where the model supplies Sw above or away from the logs, and
the end points for the Relative Permeability topic.

Error propagation. The free water level shifts every height by the same amount, and near the contact a shift of tens of feet changes Sw by a large factor. In the J-function model, permeability enters as the square root and the density contrast and the product of interfacial tension and contact angle scale all heights. A contrast that is 20% wrong or a \(\sigma\cos\theta\) that is 20% wrong has the same effect as a 20% error in height.

Key concepts

Capillary pressure and height. The hydrocarbon column has a buoyancy pressure that grows with height above the free water level. The pore throats the hydrocarbon can enter at that pressure set the water saturation. Laboratory curves are converted to reservoir conditions with interfacial tension and contact angle. See Capillary Pressure and the Leverett J-Function.

Free water level and contact. The free water level is the zero of capillary pressure. The oil-water contact seen on a log is higher by the entry height. See FWL and Column Height.

Rock types. One curve cannot describe a range of rock quality. The models either carry permeability or RQI as a continuous predictor (Permeability, RQI and FZI), or are fitted separately to each hydraulic flow unit (Flow Units and Winland).

Model versus endpoint. Buckles and Foil appear on the Swirr pages as ways of estimating one number. Here they are saturation-height functions of the whole column: see Foil and Buckles.

Equilibrium. All of these assume capillary equilibrium, which is true for a mature fill in decent rock and not in tight rock, recently filled traps or leaking seals.

Calibration. The models are curve fits to core capillary pressure, to log Sw in thick clean pay, or to both. A fit to log Sw alone makes the saturation-height model a smoothed version of the logs, and not an independent check.

Method selection guide

Method	Inputs	Use when	Strengths	Weaknesses
Capillary pressure and J-function	Lab Pc, interfacial tension and contact angles, permeability, porosity, density contrast	Always, as the first step: it converts core Pc to the reservoir and gives J	Physical basis, collapses curves of one rock type	Interfacial properties and contact angle are uncertain
Permeability, RQI and FZI	Permeability and porosity curves, J-Sw fit, Swirr relation, FWL	Core capillary pressure exists and a good permeability curve is available	Follows rock quality continuously; gives the entry height and the transition zone	Depends on the permeability curve; the power law fits only part of the curve
Foil and Buckles	Porosity, height, two fitted constants or a Buckles number	Only porosity is available, or a quick profile in uniform rock	Simple; needs no capillary pressure curve	No permeability or rock type; the power law has no floor
Flow units and Winland	Porosity and permeability (core and logs)	A section has several rock types and a flow unit assignment is needed	Splits the section into units with their own curves	Statistical grouping; Winland is a sandstone regression
FWL and column height	Depths, depth reference, pressures, entry pressure	Always: the datum of every model above	Sets heights and the contact gap	Pressure data are needed; hydrodynamics complicate it

Decision guidance

Start with the free water level and the Pc conversion. Neither is optional.
If there are core capillary pressure data and a permeability curve, use the J-function model by flow unit. It is the default.
If there is no capillary pressure data, use the Foil or Buckles forms, with constants fitted to log Sw in thick clean zones, and treat the result as a smoothed log, not a check.
In carbonates or where permeability is not set by the same throats as capillary pressure, use rock types, and be careful with a continuous permeability model.
If the zone is in the transition zone, use a height model and not a constant Swirr: the Buckles number is only valid above the transition.
In tight rock, test whether equilibrium is plausible before trusting the model.

Shared parameter picking

Free water level and depth reference. One free water level per compartment, on one depth reference, true vertical depth or subsea depth, for all wells. See FWL and Column Height.

Fluid properties. The density contrast, interfacial tension and contact angle are shared by all the models. Change them together when the fluid changes (oil to gas, or an oil leg under a gas cap).

Rock typing. Pick flow units or rock types before fitting, and fit each separately. A single set of constants for a mixed section produces a curve that follows porosity or permeability and misses the rock type.

Porosity basis. Effective or total, the same as in the log Sw, the Swirr and the permeability. A mismatch between the fit and its application shifts every saturation.

Irreducible saturation. Irreducible water saturation from the Swirr pages is the lower end of the J-function model. It must come from the same plugs and the same pressure as the Pc fit.

Maximum column height. The height of the top of the trap above the free water level, shared with the Foil and Lucia Swirr methods.

Calibration data. Keep a record of which data (core Pc, mercury injection, log Sw) each fit used, and its pressure range.

Recommended default approach

Absent other information, a careful generalist would:

Set the free water level and the depth reference from pressure data, and compute the height above the free water level for every log sample.
Convert the core capillary pressure to reservoir conditions and compute the J-function.
Group the plugs into hydraulic flow units by FZI, and check them against the Winland R35 classes.
For each unit, fit the J-Sw power law and the Swirr relation to the plugs, and compute the Sw curve from height, with permeability and porosity from logs.
Compare with log Sw in thick, clean, hydrocarbon-bearing intervals well above the transition zone, and adjust the free water level, fluid contrast or rock typing, not the fit constants, when they disagree.
Where there is no capillary pressure data, use the Foil form fitted to those same log intervals, and report that it is calibrated to the logs.
Carry the free water level and fluid property ranges into the volumetrics as a range of saturations.

Combining methods

Do not average saturation-height curves from different models. The models describe the same thing with different assumptions, and a mean of them has no physical meaning. Choose the model by rock type: use the J-function model where core capillary pressure data support it, and use the height power law only where that is all there is. Where both exist, compare them, and use the difference as a measure of uncertainty. A reasonable combination is by interval: the capillary pressure model within the zone it was calibrated for, and log Sw where the model is outside its calibration range, for example above the top of the data. Blending on a height weight across a defined overlap interval is acceptable as long as it is documented.

QC of results

A good result:

is 1 at and below the free water level, falls with height and never goes below Swirr,
has a shorter transition zone and a lower curve for the better rock types,
matches log Sw in thick clean pay above the transition zone with no trend against depth,
matches the contact seen on the logs through the entry height, and
uses the same depth reference, porosity basis and fluids in the fit and the application.

Signs of a bad result: saturation that follows porosity across a lithology change, curves of different rock types that cross, a free water level that has to be moved from well to well, and a model that fits log Sw perfectly (it is probably fitted to the log it should check).

Common pitfalls

Mixing depth references (MD, TVD, TVDSS) between the free water level and the logs.
Treating the oil-water contact as the free water level in tight rock.
Using laboratory pressure without converting to reservoir conditions, or applying the conversion twice.
Using a gas density contrast for an oil column or the reverse.
Fitting one set of constants across several rock types.
Extending a power law beyond the range of data it was fitted to.
Mixing total and effective porosity bases.
Using a permeability curve that depends on Swirr for a Swirr that depends on that permeability.
Calibrating the model to the log Sw and then using it to validate that Sw.
Assuming capillary equilibrium in tight rock or in a young accumulation.

Going Deeper

Saturation-height modelling grew out of the observation that water saturation in a hydrocarbon column falls with height, and the realisation that capillary pressure measurements on core explain it. The Leverett J-function made it possible to combine data from different plugs, and the Brooks-Corey form gave a simple equation for the curve. Later work used the pore throat distribution directly, through mercury injection, and moved to rock types and flow units so that the curve follows the geology. The unresolved questions are practical. The contact angle and interfacial tension at reservoir conditions are rarely measured; the free water level is uncertain in poorly tested fields; and the capillary pressure of tight rock may never have reached equilibrium. A modern workflow treats the saturation-height model as one of two independent estimates of Sw, with the log, and uses the disagreement to find problems in either. Where the two are not independent, that is, when the model was fitted to the log, a good match is not evidence.