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```BASIC WELL LOGGING ANALYSIS –
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Hsieh, Bieng-Zih
Fall 2009
ARCHIE EQUATION SW

Water saturation (Sw) of a reservoir’s uninvaded zone is calculated
by the Archie (1942) formula.
Sw








 a Rw 

  m


R
t 

1
n
Where:
Sw＝ water saturation of the uninvaded zone (Archie method)
Rw＝ resistivity of formation water at formation temperature
Rt＝ true resistivity of formation
Φ＝ porosity
a ＝ tortuosity factor (1.0 for carbonates; 0.81 for consolidated
sandstone; 0.62 for unconsolidated sandstone)
m＝ cementation exponent (2.0 for carbonates and consolidated
sandstone; 2.15 for unconsolidated sandstone)
n＝saturation exponent (normally equal to 2.0)
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ARCHIE EQUATION SW (CONT.)

The uninvaded zone’s water saturation (Sw), determined
by the Archie equation, is the most fundamental
parameter used in log evaluation.

But, merely knowing a zone’s water saturation (Sw) will
not provide enough information to completely evaluate a
zone’s potential productivity.

A geologist must also know whether: (1) hydrocarbons are
moveable, (2) water saturation is low enough for a waterfree completion, (3) the zone is permeable, and (4)
whether (volumetrically) there are economic, recoverable
hydrocarbon reserves.
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ARCHIE EQUATION SXO

Water saturation of a formation’s flushed zone (Sxo) is
also based on the Archie equation, but two variables are
changed:
S xo
 a R mf
  m
  R xo




1
n
Where:
 Sxo＝ water saturation of the flushed zone
 Rmf＝ resistivity of the mud filtrate at formation
temperature
 Rxo＝ shallow resistivity

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ARCHIE EQUATION SXO (CONT.)

Water saturation of the flushed zone (Sxo) can be used as
an indicator of hydrocarbon moveability.

For example, if the value of Sxo is much larger than Sw,
then hydrocarbons in the flushed zone have probably
been moved or flushed out of the zone nearest the
borehole by the invading drilling fluids (Rmf).
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RATIO METHOD

The Ratio Method identifies hydrocarbons from the
difference between water saturations in the flushed zone
(Sxo) and the uninvaded zone (Sw).

When water saturation of the uninvaded zone (Sw) is
divided by water saturation of the flushed zone (Sxo), the
following results:
Sw
S xo
 a R 
  m w 
  Rt 
 a R mf
  m
  R xo




1
n
1
n
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RATIO METHOD – WITHOUT KNOWING POROSITY

When Sw is divided by Sxo, the formation factor (F＝a/Φm)
is cancelled out of the equation because formation factor
is used to calculate both Sw and Sxo.

This can be very helpful in log analysis because, from the
ratio of (Rxo/Rt)/(Rmf/Rw), the geologist can determine a
value for both the moveable hydrocarbon index (Sw/Sxo)
and water saturation by the Ratio Method without
knowing porosity.

Therefore, a geologist can still derive useful formation
evaluation log parameters even though porosity logs are
unavailable.
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RATIO METHOD -- MOVEABLE HYDROCARBON INDEX

Formulas for calculating the moveable hydrocarbon index
and water saturation by the Ratio Method are:

If the ratio Sw/Sxo is equal to 1.0 or greater, then
hydrocarbons were not moved during invasion.

Whenever the ratio of Sw/Sxo is less than 0.7 for
sandstones or less than 0.6 for carbonates, moveable
hydrocarbons are indicated (Schlumberger, 1972).
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RATIO METHOD
To determine water saturation (Sw) by the Ratio Method,
you must know the flushed zone’s water saturation.
 In the flushed zone of formations with moderate invasion
and “average” residual hydrocarbon saturation, the
following relationship is normally true:


by substituting the above equation in the relationship:
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RATIO METHOD

Where: Swr ＝ water saturation uninvaded zone, Ratio
Method
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RATIO METHOD – QUALITY CHECK

After the geologist has calculated water saturation of the
uninvaded zone by both the Archie and Ratio methods, he
should compare the two values using the following
observations:

(1) If Sw (Archie) ≈ Sw (Ratio)
the assumption of a step-contact invasion profile is indicated
to be correct,
 all values determined (Sw, Rt, Rxo, and di) are correct.

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RATIO METHOD – QUALITY CHECK

(2) If Sw (Archie) ＞ Sw (Ratio)
the value for Rxo/Rt is too low.
 Rxo is too low because invasion is very shallow, or Rt is too high
because invasion is very deep.
 Also, a transition type invasion profile may be indicated
 Sw (Archie) is considered a good value for Sw

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RATIO METHOD – QUALITY CHECK

If Sw (Archie) ＜ Sw (Ratio)



the value for Rxo/Rt is too high because of the effect of
an annulus type invasion profile may be indicated
or Sxo ＜ Sw1/5
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RATIO METHOD – QUALITY CHECK


In the case of Sw (Archie) ＜ Sw (Ratio), a more accurate
value for water saturation can be estimated using the
following equation (from Schlumberger, 1977):
Where:
(Sw)COR ＝ corrected water saturation of the uninvaded zone
 Swa ＝ water saturation of the uninvaded zone (Archie Method)
 Swr ＝ water saturation of the uninvaded zone (Ratio Method)

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BULK VOLUME WATER

The product of a formation’s water saturation (Sw) and its
porosity (Φ) is the bulk volume of water (BVW).

If values for bulk volume water, calculated at several
depth in a formation, are constant or very close to
constant, they indicate that the zone is homogeneous and
at irreducible water saturation (Sw irr).
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BULK VOLUME WATER

When a zone is at irreducible water saturation, water
calculated in the uninvaded zone (Sw) will not move
because it is held on grains by capillary pressure.

Therefore, hydrocarbon production from a zone at
irreducible water saturation should be water-free (Morris
and Biggs, 1967).
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BULK VOLUME WATER

A formation not at irreducible water saturation (Sw irr) will
exhibit wide variations in bulk volume water values.

Figure 39 illustrates three crossplots of porosity (Φ)
versus Sw irr for three wells from the Ordovician Red River
B-zone, Beaver Creek Field, North Dakota.

Note, that with increasing percentages of produced water,
scattering of data points from a constant value of BVW
(hyperbolic lines) occurs.
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PERMEABILITY FROM LOGS

Log-derived permeability formulas are only valid for
estimating permeability in formations at irreducible water
saturation (Sw irr; Schlumberger, 1977).

The common method for calculating log-derived
permeability is the Wyllie and Rose (1950) formulas.
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PERMEABILITY FROM LOGS

Before these formulas can be applied, a geologist must
first determine whether or not a formation is at
irreducible water saturation.

Whether or not a formation is at irreducible water
saturation depends upon bulk volume water (BVW＝Sw×
Φ) values.
When a formation’s bulk volume water values are constant, a
zone is at irreducible water saturation.
 If the values are not constant, a zone is not at irreducible
water saturation .

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PERMEABILITY FROM LOGS

The Wyllie and Rose (1950) method for determining
permeability utilizes the following two formulas:
Where:
 K1/2 ＝ square root of permeability (K is equal to
permeability in millidarcies)
 Φ＝ porosity
 Sw irr ＝ water saturation (Sw) of a zone at irreducible
water saturation

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HOMEWORK #6
Rt
Rxo
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Depth Rxo
Rt
Φ
Sw
Sxo
Sw/Sxo
Swr
BVW
K
7600
7610
7620
….
….
….
Information:
….
Consolidated sandstone
a = 0.81
m = 2.0
n = 2.0
….
….
….
7840
7850
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