Publication History: This article is based on Chapter 8 of "The Log Analysis Handbook" by E. R. Crain, P.Eng., published by Pennwell Books 1986  Updated 2004, 2016, 2018. This webpage version is the copyrighted intellectual property of the author.

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

Apparent Water Resistivity (Rwa) Method
The Rwa method involves a three step procedure:

STEP 1. Calculate apparent water resistivity for all prospective zones in a well, including water zones:
      1: Rwa = (PHIt ^ M) * RESD / A

STEP 2. Select Rw from minimum of Rwa values for all the other defined clean water zones.
      2: IF Vsh < 0.2
      3: AND IF RESD < RESWET
      4: THEN RwaFLAG = 1.0
      5: OTHERWISE RwaFLAG = 10 ^ 6
      6: RW@FT = min (Rwai * RwaFLAG)

STEP 3. Calculate water saturation from Rwa for each level:
      7: Swa = (RW@FT / Rwa) ^ (1 / N)

WHERE:
  A = tortuosity exponent (fractional)
  M = cementation exponent (fractional)
  N = saturation exponent (fractional)
  PHIt = total porosity from any method (fractional)
  RESD = resistivity reading on deep log (ohm-m)
  RESWET = cut off resistivity for possible water zones (ohm-m)
  Rwa = apparent water resistivity (ohm-m)
  Rwai = water resistivity of any point in the zone (ohm-m)
  RW@FT = formation water resistivity (ohm-m)
  Swa = water saturation from Rwa method (fractional)
  Vsh = volume of shale (fractional)

COMMENTS:
This is merely a restatement of the Archie equation described earlier. The basic Rwa formula is displayed below.

Shale corrected versions of the Rwa equation can be created by rearranging the Simandoux or Dual Water equations. They should be restricted to shaly sands where Vsh < 0.40.

RECOMMENDED PARAMETERS:
for carbonates A = 1.00  M = 2.00  N = 2.00  (Archie Equation as first published)
for sandstone  A = 0.62  M = 2.15  N = 2.00  (Humble Equation)
                          A = 0.81  M = 2.00  N = 2.00  (Tixier Equation - simplified version of Humble Equation)

Asquith (1980 page 67) quoted other authors, giving values for A and M, with N = 2.0, showing the wide range of possible values:
Average sands              A = 1.45  M = 1.54
Shaly sands                  A = 1.65  M = 1.33
Calcareous sands         A = 1.45  M = 1.70
Carbonates                   A = 0.85  M = 2.14
Pliocene sands S.Cal.  A = 2.45  M = 1.08
Miocene LA/TX             A = 1.97  M = 1.29
Clean granular             A = 1.00  M = 2.05 - PHIe
 


Nomograph for RWA equation (no shale correction)

NUMERICAL EXAMPLE:
1. Using data from Sands A, B, C and D as before:
  Sand A Sand B Sand C Sand D
RESD 20 40 1.2 1.0
PHIe 0.33 0.23 0.30 0.11
A 0.62 0.62 0.62 0.62
M 2.15 2.15 2.15 2.15
Rwa 2.97 2.73 0.145 0.014
RW @ FT 0.9 0.9 0.036 0.015
N 2.0 2.0 2.0 2.0
Swa 0.55 0.57 0.50 1.03

Sample:
Rwa = (0.33 ^ 2.15) * 20 / 0.62 = 2.97
Swa = (0.9 / 2.97) ^ (1 / 2.0) = 0.55
 

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