CamPetro

Swirr from Buckles

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Summary

Buckles observed that at irreducible conditions the product of porosity and water saturation, the bulk volume of water, is nearly constant within one rock type. The method inverts that: Irreducible water saturation is a rock-type constant, Bulk volume water at irreducible saturation, divided by the porosity. Use it when a constant can be picked per rock type and the porosity is reliable.

Inputs and outputs

Item Units
Input Effective porosity v/v
Input Bulk volume water at irreducible saturation v/v
Output Irreducible water saturation v/v

Equations

Bulk volume water at irreducible saturation is the effective porosity times Swirr, and is treated as a constant for a rock type:

\[ \CpBvwIrr = \phie\,\Swirr \]

so Swirr is the constant divided by the porosity, limited to the interval 0 to 1:

\[ \Swirr = \frac{\CpBvwIrr}{\phie} \]

Swirr on a total porosity basis is not the same number: the clay-bound water is part of the total pore volume, so it must be added before dividing by total porosity.

Symbol Variable Units Typical range
\(\phi_e\) Effective porosity v/v 0 to 0.35
\(BVW_{irr}\) Bulk volume water at irreducible saturation v/v 0.005 to 0.10
\(S_{wirr}\) Irreducible water saturation v/v 0.05 to 0.5

Single-value calculator

Behavior

Swirr falls as porosity rises, along a hyperbola. With a Buckles number of 0.04, Swirr is 0.40 at a porosity of 0.10, 0.20 at 0.20 and 0.133 at 0.30. The Buckles number scales the whole curve: at a porosity of 0.20, numbers of 0.02, 0.04 and 0.06 give Swirr of 0.10, 0.20 and 0.30. At low porosity the result is capped at 1, which is a sign the constant does not belong to that rock.

Parameter guidance

The Buckles number is picked from core or from a Buckles plot, which is a cross-plot of bulk volume water against porosity for zones that are at irreducible saturation. Points at irreducible saturation fall along a hyperbola of constant bulk volume water. Published typical ranges depend on grain size: a coarse sandstone is often near 0.02 to 0.025, a fine one 0.035 to 0.05, a very fine or silty one 0.05 to 0.09, and carbonates range from 0.005 for vuggy rock to 0.10 for chalk. Treat those ranges as starting points to review, not as calibration. Pick one number per rock type or flow unit and per porosity basis; the shared choices (basis, rock typing, clamping) are on the Swirr step page.

Worked example

A fine-grained sandstone with a Buckles number of 0.04, at three porosities, and the effect of a 25% error in the constant:

c = 0.04
print(f"{'phie':>6} {'Swirr':>7}")
for phie in (0.08, 0.12, 0.20, 0.30):
    print(f"{phie:6.2f} {min(1.0, c / phie):7.3f}")
phie = 0.20
print()
print(f"C = 0.04 -> Swirr {c / phie:.3f};  C = 0.05 -> Swirr {0.05 / phie:.3f}")

Output

  phie   Swirr
  0.08   0.500
  0.12   0.333
  0.20   0.200
  0.30   0.133

C = 0.04 -> Swirr 0.200;  C = 0.05 -> Swirr 0.250

Assumptions and limitations

  • Bulk volume water is constant at irreducible saturation within the rock type. Where grain size changes with porosity, as it does in most real sections, the constant drifts.
  • The rock is at irreducible saturation. Above the transition zone this is reasonable; in it, a Buckles plot of the actual Sw gives a higher number.
  • The porosity and the constant are on the same basis, effective or total.
  • The number is chosen for a single rock type. A single number across mixed lithology gives a Swirr that follows porosity and not rock quality.

QC checks

  • Plot bulk volume water against porosity for the zone: points at irreducible saturation lie along a line of constant BVW parallel to the hyperbola of the picked number.
  • Swirr is between 0 and 1 and below the water saturation in zones that produce water-free hydrocarbons.
  • Swirr is not capped at 1 in the reservoir intervals.
  • Compare with core capillary pressure or centrifuge Swirr at the same depths.

Going Deeper

The Buckles relation is an empirical observation, made by Buckles in the 1960s from core, that a clean, uniform rock holds a fixed volume of water per unit bulk volume once the hydrocarbon column is tall enough. It is the constant-bulk-volume-water limit of the height-dependent power laws described on the Foil page. The modelling of saturation with height that gives the constant its physical grounding belongs to the SwH Analysis topic. Morris and Biggs used the bulk volume water plot to decide if a zone would produce water-free: when the actual bulk volume water is close to the irreducible value, the zone is at irreducible saturation.

References

  1. Buckles, R.S., 1965. Correlating and averaging connate water saturation data. Journal of Canadian Petroleum Technology, 4(1), 42–52.
  2. Morris, R.L. and Biggs, W.P., 1967. Using log-derived values of water saturation and porosity. Transactions of the SPWLA 8th Annual Logging Symposium, Paper X.

Python reference implementation

Python reference implementation

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