
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.
This
webpage version is the copyrighted intellectual
property of the author.
Do not copy or distribute in any form without explicit
permission. 
IRREDUCIBLE Water
Saturation  BUCKLE'S METHOD
Hydrocarbon zones with water saturation (Sw)
above irreducible saturation (SWir) will produce some water
along with hydrocarbons. This can occur in transition zones
between the oil and water leg, or after water influx into a
reservoir due to production of oil or gas. SWir is equivalent to
the minimum water saturation found from capillary pressure
curves determined from special core analysis. Typical
capillary pressure curve relationships are shown below.
Capillary pressure curves define irreducible water
saturation SWir (vertical
dashed line near left edge of graph).
Irreducible water saturation varies
inversely with porosity: Sw
= Constant / Porosity, but the Constant can
vary with pore
geometry. A reservoir with Sw > SWir will produce
some
water with the hydrocarbons.
The difference between Sw and SWir, and relative
permeability of water and hydrocarbon, determine the water cut.
These concepts are best described by the capillary pressure
curve and relative permeability curves illustrated above.
Irreducible water saturation is a necessary value
for water cut and permeability calculations.
STEP 1: Find Buckles number from special core
analysis or from log analysis in a known clean pay zone that
produced initially with zero water cut.
1: KBUCKL =
PHIe * Sw (in a CLEAN zone that produced initially with no
water, or from core data)
STEP 2: Solve for irreducible water saturation in
each zone.
2: IF zone is
obviously hydrocarbon bearing
3: THEN SWir =
Sw
4: OTHERWISE
SWir = KBUCKL / PHIe / (1 – Vsh)
5: IF SWir > Sw
6: THEN SWir =
Sw
An easier,
but equivalent, model is:
7: SWir =
Min (1.0, Sw, KBUCKL / PHIe / (1 – Vsh))
COMMENTS:
·
Use always in preparation for permeability
calculations.
· Buckles Number can be found by observing the
porosity times water saturation product in pay zones where RW@FT
is known, or where a water zone can be used to calibrate RW@FT.
Data can also be found from capillary pressure data.
· If Sw is greater than SWir, then the zone will
produce with some water cut (if it produces anything at all).
· If Sw is less than SWir, then the Buckles number
for the layer is wrong.
· The (1 – Vsh) term can be replaced by (1 – Vsh^2)
if needed.
· Calibrate water saturation to core by preparing a
porosity vs SWir graph from capillary pressure data. Adjust
KBUCKL, Vsh, PHIe until a satisfactory match is achieved.
PARAMETERS:
Sandstones Carbonates KBUCKL
Very
fine grain Chalky 0.120
Fine
grain Cryptocrystalline 0.060
Medium
grain Intercrystalline 0.030
Coarse
grain Sucrosic 0.020
Conglomerate Fine vuggy 0.010
Unconsolidated Coarse vuggy 0.005
Fractured Fractured
0.001
The
illustrations below demonstrate the difference between actual and
irreducible water saturation in a partially depleted or long
transition zone.
Actual saturation (blue curve in
Track 3) compared to irreducible water saturation (black curve) in
two wells. Where the two curves are close together, little water
will be produced. Where they are separated, water will flow with the
oil. Production histories on these two wells bear out this
interpretation.
Irreducible Water Saturation from Nuclear Magnetic Log
The NMR
transform is illustrated below. The matrix and dry clay terms of NMR response are
zero. An NMR log run today can display clay bound water (CBW),
irreducible water (capillary bound water, BVI), and mobile
fluids (hydrocarbon plus water, BVM), also called free fluids or
free fluid index (FFI). On older logs, only free fluids (FFI) is
recorded and some subtractions, based on other open hole logs,
are required.
Nuclear Magnetic Resonance Response to Fluids
For modern logs:
7: PHIt = CBW +
BVI + BVM
8: PHIe = BVI +
BVM
9: SWir = BVI /
(BVI + BVM)
OR 9A: SWir = BVI / PHIe
Some or all of the sums defined above may be
displayed on the delivered log. Log presentation is far from
standard for NMR logs. PHIt and PHIe from NMR do
not always agree with that derived from density neutron methods,
which see much larger volumes of rock.
For older logs, the BVI measurement was not
possible, so:
10: IF PHIe > 0.0
11: AND IF FFI < PHIe
12: THEN SWir = (PHIe  FFI ) / PHIe
13: OTHERWISE SWir = 1.0
14: IF SWir > 1.0
15: THEN SWir = 1.0
IRREDUCIBLE WATER SATURATION FROM CAP PRESSURE DATA
Capillary
pressure data is often used to estimate irreducible water saturation
or to calibrate other methods, especially the Buckle's Number
approach. A
capillary pressure (Pc) data set, along with some calculated
parameters, is summarized in the table below.
CAPILLARY PRESSURE SUMMARY 
Sample 
Depth 
Perm 
PHIe 
SWir 
SWir 
PHI*SW 
PHI*SW 
sqrt/PHIe) 
Pore Throat 

m 
mD 

425m 
100m 
425m 
100m 

Radius um 
Bakken 









1 
03.5 
2.40 
0.118 
0.12 
0.19 
0.014 
0.022 
4.51 
1.358 
2 
04.3 
0.24 
0.137 
0.62 
0.94 
0.085 
0.129 
1.32 
0.036 
3 
04.5 
0.32 
0.139 
0.39 
0.64 
0.054 
0.089 
1.52 
0.100 
4 
05.2 
0.77 
0.149 
0.31 
0.62 
0.046 
0.092 
2.27 
0.113 
Average 
04.4 
0.93 
0.136 
0.36 
0.60 
0.050 
0.083 
2.41 
0.402 










Torquay 









5 
16.8 
0.05 
0.163 
1.00 
1.00 
0.163 
0.163 
0.55 
0.008 
6 
20.4 
0.07 
0.145 
0.59 
0.97 
0.086 
0.141 
0.69 
0.038 
7 
21.8 
0.09 
0.174 
0.79 
0.96 
0.137 
0.167 
0.72 
0.019 
8 
23.8 
0.03 
0.157 
1.00 
1.00 
0.157 
0.157 
0.44 
0.009 
9 
31.4 
0.07 
0.138 
0.83 
0.98 
0.115 
0.135 
0.71 
0.017 
Average 
24.4 
0.07 
0.154 
0.80 
0.98 
0.124 
0.150 
0.64 
0.021 
In
higher permeability rock, the cap pressure curve quickly reaches an
asymptote and the minimum saturation usually represents the
irreducible water saturation in an undepleted hydrocarbon reservoir
above the transition zone. In tight rock, the asymptote is seldom
reached, so we pick saturation values from the cap pressure curves
at two heights (or equivalent) Pc values) to represent two extremes
of reservoir condition.
Only sample 1 in the above table behaves close to
asymptotically, as in curve A in the schematic illustration at the
right. All other samples behave like curves B and C (or worse). The
real cap pressure curves for samples 1 and 2 are shown below.
Examples of capillary pressure curves in good quality rock (sample 1
– left) and poorer quality rock
(sample 2 – right)
The summary table shows wetting phase saturation
selected by observation of the cap pressure graphs at two different
heights above free water, namely 100 meters and 425 meters in this
example. In this case, the 100 meter data gives water saturations
that we commonly see in petrophysical analysis of well logs in
hydrocarbon bearing Bakken reservoirs in Saskatchewan. This is a
pragmatic way to indicate the water saturation to be expected when a
Bakken reservoir is at or near irreducible water saturation. The
data for the 450 meter case is considerably lower and probably does
not represent reservoir conditions in this region of the Williston
Basin.
