CamPetro

Total vs Effective Sw

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Summary

Total water saturation Total water saturation counts the clay-bound water in the pore volume, and effective water saturation Effective water saturation does not. Each shaly-sand model returns one of them, and each downstream use needs one of them, so the two have to be converted in a consistent way through the bound-water saturation Bound-water saturation. The hydrocarbon volume is the same on either basis.

Inputs and outputs

Item Units
Input Total water saturation v/v
Input Total porosity v/v
Input Clay volume v/v
Input Shale total porosity v/v
Output Bound-water saturation v/v
Output Effective porosity v/v
Output Effective water saturation v/v

Equations

The bound-water saturation, as a fraction of the total pore volume, is the clay volume times the total porosity of the clay, divided by total porosity:

\[ \SwB = \frac{\Vcl\,\phiSh}{\phit} \]

Effective porosity is the total porosity with the bound water removed:

\[ \phie = \phit\left(1 - \SwB\right) = \phit - \Vcl\,\phiSh \]

Converting between the saturations:

\[ \SwE = \frac{\SwT - \SwB}{1 - \SwB} \qquad\qquad \SwT = \SwB + \left(1 - \SwB\right)\SwE \]

The conversion preserves the water and hydrocarbon volumes. Bulk volume water is \(\BVW = \phit\,\SwT = \phie\,\SwE + \Vcl\,\phiSh\), and the hydrocarbon volume is \(\phit\,(1 - \SwT) = \phie\,(1 - \SwE)\).

The result for \(\SwE\) is limited to the interval 0 to 1, and set to 0 when \(\SwB \ge 1\).

Symbol Variable Units Typical range
\(S_{w,t}\) Total water saturation v/v 0 to 1
\(\phi_t\) Total porosity v/v 0 to 0.40
\(V_{cl}\) Clay volume v/v 0 to 1
\(\phi_{sh}\) Shale total porosity v/v 0.05 to 0.35
\(S_{w,b}\) Bound-water saturation v/v 0 to 0.5
\(\phi_e\) Effective porosity v/v 0 to 0.35
\(S_{w,e}\) Effective water saturation v/v 0 to 1
\(\mathrm{BVW}\) Bulk volume water v/v 0.02 to 0.3

Single-value calculator

Behavior

The effective saturation is always at or below the total saturation, and the two differ more as the clay volume rises. With total porosity 0.225 and a shale porosity of 0.15, a total saturation of 0.45 converts to 0.450, 0.365 and 0.250 at clay volumes of 0, 0.2 and 0.4 (bound-water saturation 0, 0.133 and 0.267). With clay at 0.3 (bound water saturation 0.200 and effective porosity 0.180), a total saturation of 0.45 is an effective saturation of 0.312. Each curve ends at 1 when the total saturation is 1, since a fully water-filled rock is fully water-filled on either basis. The curves reach zero where the total saturation equals the bound-water saturation: the rock has no free water, so all the water is clay-bound.

Parameter guidance

Which basis does a method need? Archie in a clean sand (either), Simandoux, modified Simandoux and Indonesian use effective porosity and return an effective saturation, as given in the Porosity step. Dual water and Waxman-Smits use total porosity and return a total saturation. Lucia's relation uses the porosity of the rock fabric. Shale porosity Shale total porosity is the one new input: use the same value that the porosity step used to get effective porosity from total porosity, so the conversion is the inverse of the porosity calculation (see Total vs Effective Porosity). Which basis does the next step need? Volumetrics and hydrocarbon pore volume are the same on either basis if the matching porosity is used. A cutoff on Sw needs a basis stated with it. Permeability and irreducible-saturation relations are each defined on one basis (for example Coates uses effective, Timur total), so convert before applying them. Water Saturation lists the choice for each method.

Worked example

A total saturation of 0.45 in a rock with 22.5% total porosity, 30% clay and a shale porosity of 0.15, with the volume balance:

phit, vcl, phish, swt = 0.225, 0.30, 0.15, 0.45

swb = vcl * phish / phit
phie = phit * (1.0 - swb)
swe = (swt - swb) / (1.0 - swb)
print(f"Swb  = {vcl:g} x {phish:g} / {phit:g} = {swb:.3f}")
print(f"phie = {phit:g} x (1 - {swb:.3f}) = {phie:.3f}    (check: {phit - vcl * phish:.3f})")
print(f"Swe  = ({swt:g} - {swb:.3f}) / (1 - {swb:.3f}) = {swe:.3f}")
print()
print("volume balance (v/v of the rock)")
print(f"  total BVW           = {phit * swt:.4f}")
print(f"  bound water         = {vcl * phish:.4f}")
print(f"  effective BVW       = {phie * swe:.4f}   (bound + effective = {vcl * phish + phie * swe:.4f})")
print(f"  hydrocarbon, total basis     = {phit * (1 - swt):.4f}")
print(f"  hydrocarbon, effective basis = {phie * (1 - swe):.4f}")
print(f"back to total: Swt = {swb + (1 - swb) * swe:.3f}")

Output

Swb  = 0.3 x 0.15 / 0.225 = 0.200
phie = 0.225 x (1 - 0.200) = 0.180    (check: 0.180)
Swe  = (0.45 - 0.200) / (1 - 0.200) = 0.312

volume balance (v/v of the rock)
  total BVW           = 0.1013
  bound water         = 0.0450
  effective BVW       = 0.0563   (bound + effective = 0.1013)
  hydrocarbon, total basis     = 0.1238
  hydrocarbon, effective basis = 0.1238
back to total: Swt = 0.450

Assumptions and limitations

  • The bound-water volume is the clay volume times a constant shale porosity. If the shale porosity varies with depth (compaction) or clay type, the conversion shifts.
  • The clay volume and shale porosity are the same as those used to compute effective porosity. Different values in the porosity step and here break the volume balance.
  • Silt and other non-clay volume in the shale carries its own porosity. The conversion treats only clay as bound water.
  • Total saturation counts all the water in the total porosity, including the clay-bound water, and the water that is bound has no hydrocarbon in it.

QC checks

  • Total BVW equals the bound water plus effective porosity times effective saturation. The worked example prints this check.
  • Hydrocarbon volume is the same on both bases, to rounding.
  • SwE is at or below SwT, and equals it at zero clay.
  • Total saturation is never below the bound-water saturation. Where it is, the clay volume, shale porosity or saturation is inconsistent.
  • The basis of every saturation curve, cutoff and volumetric result is stated on the display or in the result name.

Going Deeper

Most confusion about saturation in shaly sands is a confusion of basis. A water saturation of 0.45 might mean 45% of the total pore volume, or 45% of the effective pore volume, and the hydrocarbon volume implied differs by the whole clay-bound water. The convention that effective saturation excludes the clay-bound water and total includes it is standard, but different tools and papers use a different name for the same quantity. The safe practice is to write down the porosity each saturation multiplies. The equivalence of the volumes is the useful check: convert both ways and compare hydrocarbon pore volume. The same bookkeeping carries through to permeability transforms and capillary-pressure based saturation-height functions, which are fitted on one basis.

References

References will be added once verified.

Python reference implementation

Python reference implementation

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