PERMEABILITY from Dumanoir and Coates
The original model is somewhat complicated and not very accurate in water bearing zones due to a number of assumptions that need to be made. The simplofied model is popular because it treats the porosity in the same way as the dual-water saturation model. Both total and effective porosity are used, so there is an implicit shale correction to the permeability calculation.

PERMd - Permeability from Dumanoir and Coates Method
First find the resistivity log reading in the irreducible water zone:
      1: IF Sw > 0.70
      2: THEN SWir = KBUCKL / PHIe
      3: AND RESir = A * RW@FT / (PHIe ^ M) / (SWir ^ N)
      4: OTHERWISE RESir = RESD

Then calculate the porosity exponent (LPERM)
      5: LPERM = (3.75 - PHIe + ((log (RW@FT / RESir) + 2.2) ^ 2) / 2) ^ 0.5

And finally:
      6: PERMd = LPERM * ( 0.077 + 1.55 * DENShy - 0.627 * DENShy ^ 2)
                      * (PHIe ^ (2 * LPERM)) / ((LPERM ^ 4) * (RW@FT / RESir))) ^ 2

WHERE:
  A = tortuosity exponent (fractional)
  KPERM = permeability constant (fractional)
  LPERM = porosity exponent (fractional)
  DENShy = hydrocarbon density (gm/cc)
  M = cementation exponent (fractional)
  N = saturation exponent (fractional)
  PERMd = calculated permeability (millidarcies)
  PHIe = effective porosity (fractional)
  KBUCKL = porosity saturation product (fractional)
  RESD = resistivity log reading (ohm-m)
  RESir = resistivity at irreducible water saturation (ohm-m)
  RW@FT = water resistivity at formation temperature (ohm-m)
  Sw = water saturation (fractional)
  SWir = irreducible water saturation (fractional)

COMMENTS:
This complex formula does not lend itself to graphical solution, although some charts are provided in the original technical paper. A simpler version of this algorithm can be found below.

RECOMMENDED PARAMETERS:
KPERM is usually set at 90,000, but can be modified with local experience.

NUMERICAL EXAMPLE
Assume data from Classic Example Sand B.
PHIe = 0.30
RW@FT = 0.02 ohm-m
A = 0.62
M = 2.15
SWir = Sw = 0.25
RESD = 20 ohm-m
N = 2.00
DENShy = 0.8 gm/cc

Dumanoir and Coates method:
KPERM = 90,000
LPERM = (3.75 - 0.30 + ((log (0.2 / 20) + 2.2) ^ 2) / 2) ^ 0.5 = 1.86
PERMd = 90,000*(0.077+1.55*0.8-0.627*0.8*0.8)*(0.3^(2*1.86)) / ((1.86^4)*(0.2/20)))^2
PERMd = 90,000 * (0.915 * 0.0


Permeability From the Coates Simplified Method

PERMc - Permeability From the Coates Simplified Method
This is a simplification of an earlier method proposed by Dumanoir and Coates. It is more optimistic than other methods in low porosity.
      7: PERMc = GPERM * PHIe ^ 4 * ((PHIt - PHIe * SWir) / (PHIe * SWir)) ^ 2

OR in clean zones:
      8: PERMc = GPERM * PHIe ^ 4 * ((1 - SWir) / SWir) ^ 2

WHERE:
  GPERM = permeability scale factor (fractional)
  PERMc = calculated permeability (millidarcies)
  PHIe = effective porosity (fractional)
  PHIt = total porosity (fractional)
  SWir = irreducible water saturation (fractional)

COMMENTS:
This method works well in shaly sands. As the difference between PHIt and PHIe increases, PERMc decreases.

RECOMMENDED PARAMETERS:
GPERM = 6500 to 10000 for oil, 650 to 1000 for gas

"META/PERM"  Compare Permeability Calculated from Various Methods
         

 

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