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: 

Reference:
 1. Correlating and Averaging Connate Water Saturation Data
     R.S. Buckles, CIM, 1965

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.

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

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.