Petrophysical Interpretation
Saturation Computation

The ideal log
0.35
porGas 0.3
0.25
0.2
porOil 0.15
0.1
porWat 0.05
% of rock filled with gas, 0
1000 1005 1010 1015 1020 1025 1030
% of rock filled with oil,
% of rock filled with water,
perm 10000
Gas
recovery factors
1000
perm
Oil 100
relative permeability 10
perm 1000 1005 1010 1015 1020 1025 1030
Wat
Unfortunately we currently 0.8
0.7
cannot directly measure any recGas
0.6
0.5
of these quantities
0.4
recOil
0.3
0.2
0.1
0
1000 1005 1010 1015 1020 1025 1030

In reality we have to make indirect measurements
• GR
• Resistivity in various flavors
• Spectroscopy (natural or induced)
• Density and PEF
• Neutron Porosity
• Sigma
• etc.

Water Saturation : Volumes

Fraction of porosity
Vw
Porosity, Ø
Vo
Sw = Vw / Ø
So = Vo / Ø

Archie

Resistivity variation due to fluids
Resistivity is the resistance of 1 m3 of a material.
Oil has high resistivity, saline water has low resistivity.
Rt Rt

Resistivity variation due to porosity
Higher porosity rock has lower resistivity
than lower porosity rock, given the same Sw.
Rt Rt

Saturation Equations: Archie 1942
Ro a
F= = m
Rw φ
a Rw
= m
n
Sw
Sw =
n Ro
φ Rt
Rt
φ Sw Cw
m n
F = Formation factor
Rt = True formation resistivity
Ct =
Ro = True formation resistivity when Sw=1 a
Rw = Resistivity of the formation water
Ø = Total formation porosity
m = empirical fudge factor (cementation factor)
n = empirical fudge factor (saturation exponent)
a = yet another fudge factor

Archie a, m and n
Ro/Rw (log scale)
Slope = -m
a Rw a
= m
n
Sw
φ Rt 0.01
Ø (log scale)
1.0
Effect of m
(tortuosity)
Rt/Ro (log scale)
Slope = -n
Effect of m+n
(tortuosity) 1.0
0.01 Sw (log scale) 1.0

Archie a & m values
General form
where a ~ 1
and m ~2
sandstones a = .81, m=2
‘Humble’ formula
carbonates a = 1, m > 2

Archie equation - complications
Archie’s equation assumes “clean” sand, with saline water.
In shaley sand, with fresh water, the simple Archie equation is not accurate:
There are many variations on Archie equation derived for different
environments. They all reduce to simple Archie in the case of clean sand
with various values of a, m & n.

Water Saturation : n
n is saturation dependent in
fresh water, the error due to
variation on n decreases at
higher saturations.
n measurements can be made
on core, but they are difficult
and expensive.
n may also be saturation
equation dependent.

Water Saturation : Archie equation - variations
2
1 ⎛ Vcl φe ⎞ n
m
•Nigeria Equation =⎜
1.4
+ ⎟S 2
Rt ⎜ Rcl aR ⎟ w
⎝ w
⎠
2
•Indonesia Equation ⎛
1 ⎜V
⎛ Vcl ⎞
⎜ 1− ⎟
φe ⎞
⎟
cl ⎝
2 ⎠
=⎜ +
2
Rt ⎜ Rcl ⎟ Sw
Rw ⎟
⎝ ⎠
•Waxman-Smits Equation 1 Sw BQ Sw
2
= * + v*
Rt F Rw F
•Dual Water Equation φtm S wt ⎛
n
⎞
⎜ Cw + wb (Cwb − Cw )⎟
S
Ct = ⎜ ⎟
a ⎝ S wt ⎠

The CCD
model
⎛ ⎞
⎜ ⎟
m' ⎜ 1.93 'Qv
m ⎟
Ct = φ (1− 0.28 v ) ⎜Cw +
m
Q −n ⎟ + 1.3φ m'Qv
0.7Sw
⎜
⎜ 1+ ⎟
⎟
⎝ Cw ⎠
1/ 2
⎛ φ ⎞
⎜
⎜ (1− φ ) ⎟
m' = 1.79+ 0.27 Qv ⎟
⎝ ⎠
Clavier, Coats, Dumanoir

The SGS
model n m 1.93 m µT QV m
σ= Swφ σw + + β 0 µ T φ QV
1+0.7 µ T Sw /σw
-n
µT =1+0.0414 T-22
1/2
φ
m =1.62+1.37 QV
1-φ
Sen, P.N.; Goode, P.A.; and Sibbit, A.M.: “Electrical conduction in clay bearing sandstones at low and high salinities,” Journal
of Applied Physics 63 no.10 (15 May 1988), pp 4832-4840.
Sen, P.N.; Goode, P.A.:”Influence of temperature on electrical conductivity in shaly sands,” Geophysics 57 no. 1 (January
1992) pp 89-96.
Sen, P.N.; Goode, P.A.: “Shaly sand conductivity at low and high salinities,” presented at the 29th annual logging symposium
of the SPWLA (June 1988) paper F.

For this course simple Archie is enough
a Rw
= m
n
Sw
φ Rt

Resistivity of NaCl Solutions
0.16 Ohm-m
0.052 Ohm-m
25°C 120°C
Chart Gen-9

Water Saturation : Rw
Rw depends on the water
salinity and the temperature.
Even if water salinity is know,
temperature can be an issue.
Temperature sensors in the tool
string measure the mud temperature
or the temperature inside the tool
(slightly warmer than the mud
temperature).
Formation temperature is usually
higher than mud temperature.

Formation temperature from gradient
Chart Gen-6
Formation temperature can be
estimated from a known
temperature gradient, and
may be more accurate than
mud temperature.

Quick Look – D Log R

Quick Look – D Log R

Flowchart of Petrophysical Analysis

Interpretation Method
• Quick Look : D LOG R (DELTA LOG R)
• Interpretation (Cross Plot Method)
a. Lithological Model
- Cross Plot N-D
- Cross Plot N-S
- Cross Plot S-D
- Cross Plot M-N
b. Petrophyisical Parameter
- Picket Plot (a, m & Rw)
- Hingle Plot (Rw)
- Cross Plot RWA-GR (Rclay & water salinity)
- Cross Plot PHIE-RHOMAU ( RhoH)
c. Permeability
K = (kcoef x PHIEkexp)/(SWirr2) , mD

Cross Plot S-D
Cross Plot M-N

Picket Plot (a, m & Rw)
Hingle Plot (Rw)

Cross Plot RWA-GR

Log Header

D LOG R (DELTA LOG R)

Composite Log

SUMUR-X
PETRAN