PERMEABILITY
The sixth step in a log analysis is to estimate permeability and productivity. These values
determine whether a zone is commercially attractive. There are a number of methods for
calculating matrix permeability.
Although it is not a quantitative measure of permeability, the separation between the two
microlog curves is an excellent indicator. The log can still be run today as part of a density log
survey.
Log analysis matrix permeability is calibrated to maximum core permeability (absolute
permeability or air permeability). Allowance must be made to eliminate fractured samples from
the core data set. Permeability to liquids is lower than absolute permeability. Flow capacity
from logs (KH) can be compared to pressure buildup analysis. Again fractures will cause a
difference.
PERMEABILITY FROM THE WYLLIE-ROSE METHOD
The general form of this equation has been used by many authors, with various correlations
between log and core data. Individual analysts routinely calibrate their core and log data to this
equation.
STEP 1: Calculate permeability
1: PERMw = CPERM * (PHIe ^ DPERM) / (SWir ^ EPERM)
If we recall that SWir = KBUCKL / PHIe, we see that this equation is strictly a function of
porosity if KBUCKL is a constant. However, KBUCKL varies with shale volume and grain size,
so Perm will vary also.
he permeability from the Wyllie method (PERMw) is called the effective permeability, Perm. The
result is in millidarcies. It can be calibrated to air, absolute, maximum, or Klinkenberg
corrected permeability from core analysis, You should state which type of core analysis you
calibrated to.
USAGE RULES:
Use anytime, usually when no core data is available.
Not reliable in fractures or heterogeneous reservoirs.
Calibrate to core by adjusting CPERM, DPERM, and EPERM. Sw, PHIe and Vsh should have
been accomplished earlier.
PARAMETERS:
RESEARCHER
CPERM DPERM
EPERM
* OIL or WATER GAS
Morris-
Biggs 65000 6500 6.0 2.0
Timur 6500 650 4.5
2.0
Values of CPERM as low as 10 000 and as high as 1 000 000 have been used in the Morris -
Biggs equation. It is also called the Tixier equation.
PERMEABILITY FROM POROSITY
Permeability is often a semi-logarithmic function of porosity, unfortunately with a fairly large
deviation. Core data is usually plotted to determine the equation of the best fit line: it can be
calibrated to air, absolute, maximum, or Klinkenberg corrected permeability from core analysis,
STEP 1: Calculate permeability
1: PERMp = 10 ^ (HPERM * PHIe + JPERM)
The permeability from the Porosity method (PERMp) is called the effective permeability, Perm.
The result is in millidarcies.
USAGE RULES:
Use anytime that parameters can be calibrated to core, especially in low porosity.
Not reliable in fractures or heterogeneous reservoirs.
A best fit line of the logarithm of core permeability vs. core porosity is often used to obtain
this relationship for a particular zone.
PARAMETERS:
Sandstones Carbonates
JPERM HPE
RM
Very fine grain Chalky –
3.00 16
Fine grain Cryptocrystalline- –
2.50 18
Medium grain Intercrystalline –
2.20 20
Coarse grain Sucrosic- –
2.00 22
Conglomerate Fine vuggy –
1.80 24
Unconsolidated Coarse vuggy –
1.50 26
Fractured Fractured –1.00 30
The medium grain parameters approximate the Wyllie - Rose equation. These parameters
should be calibrated to core data whenever possible.
PERMEABILITY FROM THE COATES METHOD
This is a simplification of an earlier method proposed by Dumanoir and Coates. It is more
optimistic than other methods in low porosity.
1: PERMc = 5000 * (PHIe ^ 4) * ((PHIt – PHIe * SWir) / (PHIe * SWir)) ^ 2
OR in clean zones:
2: PERMc = 5000 * (PHIe ^ 4) * ((1 - SWir) / SWir) ^ 2
Heslop (pere et fils) fitted core data in very young sediments in two wells and obtained
parameters for an equation similar to the Coates equation (caution: there was no low or high
porosity data in the calibration data set):
3: PERMh = 100 000 * (PHIe ^ 3.9) * (1 - SWir) ^ 3.9
It is clear that the constant and exponents are mutable and should be calibrated with core data.
Equation 3 has the advantage that low porosity cannot have high permeability, whereas the
other equations that rely on SWir can generate high perms in low porosity when SWir is
extremely low. The disadvantage is that SWir is needed from capillary pressure studies, along
with the permeability for the same core samples, in order to calibrate the equation.
The permeability from the Coates method (PERMc) is called the effective permeability, Perm.
The result is in millidarcies.
USAGE RULES:
Use anytime. Porosity method may be better if core data is available.
Not reliable in fractured or heterogeneous reservoirs.
Parameters need to be calibrated to core data for most zones.
FRACTURE PERMEABILITY
There are a few published methods for
calculating fracture permeability from
conventional open hole logs or from
some arbitrary estimate of fracture
porosity. The only correct approach is
to use formation micro-scanner fracture
aperture and frequency data:
1: Kfrac = 833 * 10^11 *
PHIfrac^3 / (Df^2 * KF1^2)
2: Kfrac = 833 * 10^5 * PHIfrac *
Wf^2
3: Kfrac = 833 * 10^2 * Wf^3 * Df
* KF1
Where: KF1 = number of main
fracture directions
= 1 for sub-horizontal or
sub-vertical
= 2 for orthogonal sub-
vertical
= 3 for chaotic or
brecciated
PHIfrac = fracture porosity (fractional)
Df = fracture frequency (fractures per meter)
Wf = fracture aperture (millimeters)
Kfrac = fracture permeability (md)
Kfrac can be many thousands of millidarcies. Equations 1, 2, 3 give identical results.
