Publication History: This article is based on Chapter 10 of "The Log Analysis Handbook" by E. R. Crain, P.Eng., published by Pennwell Books 1986  Updated 2004. This webpage version is the copyrighted intellectual property of the author.

Do not copy or distribute in any form without explicit permission.

Relative Permeability and Water Cut
Since we are interested in how much oil or gas will flow from a well, and would rather not have any water flow, it is necessary to calculate relative permeability and water cut to determine how good a well might be.

Relative permeability for water.
      1: Krw = (Sw - SWir) / (1 - SWir)

Relative permeability for oil.
      2: Kro = (0.9 - Sw) / (0.9 - SWir)

Relative permeability for gas.
      3: Krg = (1 - (Sw - SWir) / (1 - SWir)) * (1 - ((Sw - SWir) / (1 - Sw)) ^ 0.25 * Sw ^ 0.25)^0.5

Water oil ratio.
      4: KRwo = Krw / Kro
      5: WOr = BO * (VISO / VISW) * (KRwo)

Water gas ratio.
      6: KRwg = Krw / Krg
      7: WGr = BG * (VISG / VISW) * (KRwg)

Water cut for oil wells.
      8: WCo = WOR / (1 + WOR)

Water cut for gas wells:
      9: WCg = WGR / (1 + WGR)

WHERE:
  BG = volume factor for gas (fractional)
  BO = volume factor for oil (fractional)
  Krg = relative permeability to gas (fractional)
  Kro = relative permeability to oil (fractional)
  Krw = relative permeability to water (fractional)
  KRwg = water to gas permeability ratio (fractional)
  KRwo = water to oil permeability ratio (fractional)
  Sw = water saturation (fractional)
  SWir = irreducible water saturation (fractional)
  VISG = viscosity of gas (cp)
  VISO = viscosity of oil (cp)
  VISW = viscosity of water (cp)
  WCg = water cut for gas well (fractional)
  WCo = water cut for oil well (fractional)
  WGr = water gas ratio (fractional)
  WOr = water oil ratio (fractional)

COMMENTS:
Charts for solving the relative permeability relationships and for water cut below. Viscosity data required for water-oil and water-gas ratio are also given for oil and gas.

Relative permeability from log analysis without core data as a control is probably pointless.

RECOMMENDED PARAMETERS:
See Figures.


Relative permeability


Water cut


Viscosity


Viscosity of water and pseudo critical gas properties

NUMERICAL EXAMPLE:
1. Assume data from Sand C
PHIe = 0.30
Sw = 0.50
PHIxSW = 0.06
SWir = 0.06 / 0.30 = 0.20
Krw = (0.50 - 0.20) / (1 - 0.20) = 0.375
Kro = (0.9 - 0.50) / (0.9 - 0.20) = 0.571
Krg = (1 - (0.5 - 0.3) / (1 - 0.2)) * (1 - ((0.5 - 0.3) / (1 - 0.5)) ^ 0.25 * 0.5 ^ 0.25) ^ 0.5
= (0.75 * (1 - 0.4 ^ 0.25 * 0.5 ^ 0.25) ^ 0.5 = 0.431
KRwo = 0.375 / 0.571 = 0.657
KRwg = 0.375 / 0.431 = 0.870

2. Assume oil well data:
BO = 0.8
oil gravity = 40 degrees API
VISO = 1.2 cp
FT = 160 degrees F
VISW = 0.5 cp
| salinity = 120,000 ppm
WOr = 0.8 * (1.2 / 0.5) * 0.657 = 1.26

3. Assume gas well data:
BG = 0.8
VISG = 0.015 cp
VISW = 0.5 cp
dry gas
pressure = 1800 psi
salinity = 120,000 ppm
WGr = 0.8 * (0.015 / 0.5) * 0.870 = 0.021

4. Water Cut:
WCo = 1.26 / (1 + 1.26) = 0.557
WCg = 0.021 / (1 + 0.021) = 0.021

Thus, if this is an oil zone, it will produce over 55% water on initial completion. If it is a gas well, it will produce only 2% water.
 

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