Permeability from Porosity

This simple regression of core porosity versus core permeability:
      1: PERMp = 10 ^ (HPERM * PHIe + JPERM)
      2: IF PERMp > 20000
      3: THEN PERMp = 20000

Where:
  JPERM = permeability constant (fractional)
  HPERM = porosity exponent (fractional)
  PERMp = calculated permeability (millidarcies)
  PHIe = effective porosity (fractional)

COMMENTS:
Because a poor choice of HPERM could create very large values of permeability, the computation is usually constrained to prevent unreasonable answers. Results have been very good in low and high porosity when calibrated to core.

You can fit a regression line to anything - look at the graph and check the R-squared to confirm that the regression line is rational.

RECOMMENDED PARAMETERS:
ROCK TYPE                HPERM            JPERM
Carbonates
  chalky                         10 - 20               -2.5
  fine sucrosic or
  intercrystalline            20 - 30                -2.5
  coarse sucrosic or
  intercrystalline            25 - 50               -2.5
  small vuggy                 30 - 100             -2.5
  large vuggy                  50 - 200             -2.5
  fractures 200 -                  300                 -3.0

Sandstones
  very fine grains            10 - 20                -3.0
  fine grains                    15 - 25                -3.0
  medium grains             20 - 30                -3.0
  large grains                  25 - 50                -3.0
  conglomerate               20 - 50                 -3.0
  unconsolidated             20 - 50                 -3.5
  fractures                      200 - 300                -3.0

Permeability from Porosity - example of a "good" regression line.

NUMERICAL EXAMPLE
Assume data from Classic Example Sand B.
PHIe = 0.30
SWir = Sw = 0.25

1. Wylie-Rose formula / Morris-Biggs parameters:
CPERM = 62500
DPERM = 6.0
EPERM = 2.0
PERMw = 62500 * (0.30 ^ 6) / (0.25 ^ 2) = 730 md

2. Wylie-Rose formula / Timur parameters:
CPERM = 3400
DPERM = 4.4
EPERM = 2.0
PERMw = 3400 * (0.30 ^ 4.4) / (0.25 ^ 2) = 272 md

Permeability from Formation Factor
Since Formation Factor (F) is a function of porosity, F is also a predictor of permeability:
      4: F = A / (PHIe ^ M)
      5: PERMff = FPERM / (F ^ GPERM)

Where:
  A = tortuosity exponent (fractional)
  FPERM = permeability constant (fractional)
  GPERM = porosity exponent (fractional)
  F = formation factor (fractional)
  M = cementation exponent
  PERMf = calculated permeability (millidarcies)
  PHIe = effective porosity (fractional)

COMMENTS:
This formula has not been as successful as the Wylie - Rose approach.

RECOMMENDED PARAMETERS:
ROCK TYPE               FPERM              GPERM
  Sandstone             7.0 * 10 ^ 6              4.5
  Limestone             4.0 * 10 ^ 6              3.5

Data from individual core studies varies considerably from these average values.

NUMERICAL EXAMPLE
Assume data from Classic Example Sand B.
PHIe = 0.30
A = 0.62
M = 2.15

Formation factor method:
FPERM = 7.0 * 10 ^ 6
GPERM = 4.50
F = 0.62 / (0.30 ^ 2.15) = 8.25
PERMf = 7.0 * 10 ^ 6 / (8.25 ^ 4.5) = 526 md

META/LOG "PERM"  Compare Permeability Calculated from Various Methods
 
Download this spreadsheet:
SPR-24 META/LOG PERMEABILITY CALCULATOR
  Calculate and compare permeability derived from well logs, 5 Methods.