Fracture porosity is the ratio between the volume of open fractures and the rock's
bulk volume. The fracture porosity, if present, is one of the contributions to the
rock's porosity. The other porosity contributions are other sources of secondary
porosity like vugs or vugular porosity, effective matrix porosity, and non effective
matrix porosity like clay cement porosity.
Secondary porosity is classically estimated from well logs as the difference of
total density porosity minus total sonic porosity
φ_{f} ≅ φ_{d}  φ_{s}.
It is applicable to either carbonate rocks or clastic sandstones that may or
may not contain clays. The porosity difference should be similar to that of
effective density porosity minus the effective sonic porosity.
If the only source of secondary porosity are fractures, then the porosity
difference could be a good estimator of the fracture porosity.
Since the sonic speed is higher for the solid rock's fabric or matrix
(it's denser than fluid filled pores and fracture gaps), the compressive sonic
pulse or wave is mostly transmitted through the matrix. However,
the bulk density log and its derived density porosity curve,
measures all the porosity spaces. That's why the difference
φ_{d}  φ_{s}
is an estimator to the secondary porosity and fracture porosity.
If the rock is shaly and the effective density porosity is not available,
it can be replaced by the effective neutron porosity log, but only after it is
converted to the correct matrix mineral blend.
Density  sonic porosity estimates fracture porosity: (brown + blue pore volume)  (brown pore volume) = blue pore volume
Fracture porosity estimation from the density porosity  sonic porosity difference
φ_{d}  φ_{s}
requires good quality logs, knowledge of the rock's minerals, and some properties.
The figure below shows the GeolOil Porosity Functions panel equations for:
 Density porosity
 Wyllie sonic porosity
 Raymer sonic porosity
 Modified Raymer sonic porosity
 Effective Porosity
 Secondary Porosity (Fracture porosity if there are no vugs)
The figure below shows the GeolOil porosity functions panel.
The Wyllie sonic porosity equation is one of most well known
models to estimate sonic porosity. However, it depends upon the sonic travel time
of pore fluid, which may be unknown if the fluid column is variable, or if there is
a transition zone with a blend of fluids.
The modified Raymer sonic porosity removes the fluid dependency
and could behave as a robust estimator.
The most critical parameter to calculate sonic porosity is perhaps the
matrix compressional travel time Δt_{matrix}.
It is not only usually unknown, but in many reservoirs is not a constant
parameter, but a curve that depends on the variable column lithology,
its matrix fabric, and rock's stiffness. Since typical values of fracture
porosity barely range 0%4%, its computation may be unstable, requiring good
quality curves, and precise parameters. The following methodology provides
some guidance to achieve a reasonable estimation of fracture porosity from
logs:
 Calculate a first draft of fracture porosity as the algebraic difference
φ_{d}  φ_{s}
without trimming or discarding any negative estimates.
 Name this difference curve itself as Quality indicator curve Q(md)

If Q(md) yields too big negative values, or too big positive values,
the fracture porosity estimation is completely unreliable and should be discarded
at least for the problematic depths.

If Q(md) absolute value magnitude is not so big, try to shift it to the right to remove
most of the negative estimates by slightly tunning the
matrix compressional travel time Δt_{matrix}

Finally, replace all negative values with 0 (no fractures at such depths),
and trim values exceeding 4% to 4%. Make sure only few depths exceeds 4%,
otherwise discard the fracture porosity estimation as it looks unreliable large.
The figure below shows an estimation of fracture porosity with a quality index curve for a gas reservoir
The figure below shows another estimation of fracture porosity: the more plastic the rock, less fractures
⚠ WARNING:
The techniques presented in this article can only estimate fractures at the log resolution scale
—that is, fractures that may be enclosed in the log scale of around few feet—.
Any fractures out of this volume would be overlooked, given the false impression that the reservoir
has no fractures.
∎

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