Several other equations are available to calculate water saturation (SwS_wSw) in reservoirs,
each designed for specific conditions. Here’s an overview of the major ones, their
applications, and why they may not be suitable for certain scenarios (like shaly sands where
the Simandoux equation is often preferred):
1. Archie's Equation
Equation:
Swn=a⋅Rwϕm⋅RtS_w^n = \frac{a \cdot R_w}{\phi^m \cdot R_t}Swn=ϕm⋅Rta⋅Rw
Where:
o RtR_tRt: True resistivity.
o RwR_wRw: Formation water resistivity.
o ϕ\phiϕ: Porosity.
o a,m,na, m, na,m,n: Empirical constants.
Why It’s Used:
o Simple and widely applicable for clean (shale-free) formations.
o Highly effective in high-porosity, homogeneous reservoirs.
Why It’s Not Used:
o Does not account for shale conductivity, leading to overestimation of water
saturation in shaly sands.
o Assumes all conductivity is from formation water, which is invalid for shaly
or mixed lithology reservoirs.
2. Indonesia Equation
Equation:
1Rt=Vsh(1Rsh)+(1−Vsh)(ϕma⋅Rw⋅Swn)\frac{1}{R_t} = V_{sh} \left( \frac{1}
{R_{sh}} \right) + (1 - V_{sh}) \left( \frac{\phi^m}{a \cdot R_w \cdot S_w^n} \
right)Rt1=Vsh(Rsh1)+(1−Vsh)(a⋅Rw⋅Swnϕm)
Why It’s Used:
o Specifically designed for shaly sands.
o Incorporates shale resistivity (RshR_{sh}Rsh) and shale volume
(VshV_{sh}Vsh).
Why It’s Not Used:
o Requires precise knowledge of shale resistivity and shale volume, which may
vary laterally and vertically.
o Slightly less accurate than Simandoux in highly laminated or complex shaly
sands.
3. Waxman-Smits (WS) Equation
Equation:
1Rt=B⋅QvSw+1ϕm⋅Rw⋅Swn\frac{1}{R_t} = \frac{B \cdot Q_v}{S_w} + \frac{1}{\
phi^m \cdot R_w \cdot S_w^n}Rt1=SwB⋅Qv+ϕm⋅Rw⋅Swn1
Where:
o BBB: Counterion conductance (depends on water salinity and temperature).
o QvQ_vQv: Cation exchange capacity (CEC) per unit pore volume.
Why It’s Used:
o Accounts for cation exchange in clay minerals, making it highly accurate for
shaly sands.
o Incorporates the effects of clay type and distribution.
Why It’s Not Used:
o Requires detailed lab measurements (e.g., QvQ_vQv and BBB), making it
time-consuming and expensive.
o Overly complex for routine applications in reservoirs with simpler lithologies.
4. Dual Water (DW) Model
Equation:
Swn=(Fw⋅Rt−Fw⋅Rsh⋅Vsh)(Fw−Fsh)S_w^n = \frac{(F_w \cdot R_t - F_w \cdot
R_{sh} \cdot V_{sh})}{(F_w - F_{sh})}Swn=(Fw−Fsh)(Fw⋅Rt−Fw⋅Rsh⋅Vsh)
Where:
o FwF_wFw: Formation factor for water-saturated rock.
o FshF_{sh}Fsh: Formation factor for shale.
Why It’s Used:
o Differentiates between bound water in clays and free water in pores.
o Effective in formations with high clay-bound water content.
Why It’s Not Used:
o Complex to parameterize, requiring accurate estimates of clay-bound and free
water.
o Less commonly used due to the need for specialized log and core data.
5. Modified Simandoux
Equation: Similar to the Simandoux equation, but includes additional terms to
account for laminated shaly sands or specific reservoir characteristics.
Why It’s Used:
o Provides improved accuracy in complex shaly sand systems.
Why It’s Not Used:
o Requires detailed and site-specific calibration.
o More computationally intensive compared to standard Simandoux.
Comparison Table
Equation Best for Limitations
Archie's Clean sands Inaccurate for shaly or laminated reservoirs.
Shaly sands with known Sensitive to RshR_{sh}Rsh and VshV_{sh}Vsh
Indonesia
shale properties accuracy.
Waxman- Clay-rich, high-CEC
Requires detailed lab data (e.g., QvQ_vQv).
Smits formations
Dual Water Clay-bound water systems Complex to parameterize, less widely adopted.
Shaly sands with mixed Relies on RshR_{sh}Rsh and shale
Simandoux
lithology homogeneity, but widely applicable.
Why Simandoux is Preferred
Simandoux strikes a balance between accuracy and complexity:
o Accuracy: Accounts for shale conductivity and provides reasonable estimates
in shaly sands.
o Ease of Use: Requires fewer specialized measurements compared to Waxman-
Smits or Dual Water models.
o Versatility: Works well in mixed lithology reservoirs with moderate to high
shale content.
For highly laminated, heterogeneous reservoirs or clay-rich systems, Waxman-Smits or Dual
Water models may be more accurate but are not commonly used due to their complexity and
data requirements. Let me know if you'd like to calculate water saturation for a specific
dataset using any of these models!
