IRREDUCIBLE Water
Saturation  BUCKLE'S METHOD
Many permeability calculation models based on log analysis
require knowledge of the irreducible water saturation. In a
reservoir at initial conditions, above the water contact,
the irreducible saturation is equal to the actual or initial
saturation, as found from conventional water saturation
calculations. However in transition zones, water zones, and
depleted zones, irreducible is less than the actual
saturation. So we need to find irreducible saturation in
these zones some other way.
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
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
SWir2  Irreducible Water Saturation from NMR LOGS
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
EXAMPLES
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.
