SCAL Overview - Relative Permeability Correlations

Introduction

Special Core Analysis (SCAL) provides critical relative permeability (kr) data that controls multiphase flow in reservoirs. Relative permeability determines:

• Oil recovery — waterflood and gas injection efficiency
• Reservoir simulation — fractional flow and displacement physics
• Production forecasting — water/gas breakthrough timing
• Well performance — multiphase IPR curves
• EOR screening — Process selection and optimization

When laboratory SCAL measurements are unavailable, engineers rely on empirical correlations and analytical models developed from measured datasets.

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Correlation Philosophy

When to Use Correlations vs. Laboratory Measurements

Best Practice: Always validate correlations against laboratory data when available. Use correlations to extend measured kr curves beyond tested saturation ranges.

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Fundamental Concepts

Relative Permeability Definition

Relative permeability ($k_r$) is the ratio of effective permeability to absolute permeability:

$$k_{rw} = \frac{k_{ew}}{k} \quad , \quad k_{ro} = \frac{k_{eo}}{k}$$

Where:

• $k_{rw}$, $k_{ro}$ = water and oil relative permeabilities (dimensionless, 0 to 1)
• $k_{ew}$, $k_{eo}$ = effective permeabilities to water and oil (md)
• $k$ = absolute permeability (md)

Critical Saturation Points

      ◄─────────── Mobile Oil ────────────►
┌─────┬────────────────────────────────┬──────┐
│ Swi │         Sw Range              │ Sorw │
└─────┴────────────────────────────────┴──────┘
  │                                       │
  ▼                                       ▼
krw = 0                                 kro = 0
kro = 1.0 (typically)                   krw = krw° (endpoint)

Wettability States

The distribution of fluids in pore space depends on wettability (which fluid preferentially wets the rock):

Modified Craig's Rules (Ibrahim-Koederitz 2000) provide quantitative wettability classification.

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Correlation Types

1. Analytical Models

Power-law relationships with adjustable exponents.

Corey Model (1954)

$$k_{rw} = k_{rw}^{\circ} \left( \frac{S_w - S_{wi}}{1 - S_{wi} - S_{orw}} \right)^{n_w}$$$$k_{ro} = k_{ro}^{\circ} \left( \frac{1 - S_w - S_{orw}}{1 - S_{wi} - S_{orw}} \right)^{n_o}$$

Advantages:

• ✅ Simple (only 4-6 parameters)
• ✅ Smooth, well-behaved curves
• ✅ Works for any rock type or wettability
• ✅ Easy to tune to laboratory data

Limitations:

• ❌ Cannot capture S-shaped curves
• ❌ No physical basis for exponents
• ❌ Single exponent may not fit entire curve

When to use: Quick estimates, sensitivity studies, when tuning parameters to limited lab data.

LET Model (Lomeland et al. 2005)

Three-parameter model with flexible shape:

$$k_{rw} = k_{rw}^{\circ} \frac{S_w^{L_w}}{S_w^{L_w} + E_w (1 - S_w)^{T_w}}$$

Where L, E, T control Lower, Elevation, and Top curvature.

Advantages:

• ✅ Flexible S-shaped curves
• ✅ Better fit to lab data than Corey
• ✅ Can match endpoints and curvature independently

Limitations:

• ❌ More parameters to determine (6 total)
• ❌ Less intuitive than Corey
• ❌ Requires lab data for fitting

When to use: When laboratory data shows S-shaped curves, EOR studies where shape matters.

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2. Empirical Correlations

Regression equations fit to large databases of laboratory measurements.

Honarpour et al. (1982)

• Data basis: 651 kr data sets worldwide
• Coverage: Sandstone/carbonate × water-wet/intermediate-wet
• Form: Polynomial equations (Equations A-1 to A-10)

Advantages:

• ✅ Based on extensive laboratory database
• ✅ Rock type specific (sand vs. carbonate)
• ✅ Wettability differentiation
• ✅ No parameter fitting needed

Limitations:

• ❌ No oil-wet correlations
• ❌ Fixed equations (cannot tune)
• ❌ Limited carbonate data

When to use: Screening studies, when rock type and wettability are known, no lab data available.

📖 Full Documentation: Honarpour Correlations

Ibrahim-Koederitz (2000)

• Data basis: 416 kr data sets (SPE literature 1950-1998)
• Coverage: ALL combinations (sand/carb × 4 wettabilities × 4 fluid systems)
• Form: Linear regression with 3-10 terms per equation

Advantages:

• ✅ Most comprehensive coverage
• ✅ Includes oil-wet systems
• ✅ Gas-oil, gas-water, gas-condensate systems
• ✅ Modified Craig's wettability rules

Limitations:

• ❌ Complex equations (many terms)
• ❌ Cannot tune to local data
• ❌ Room temperature data only

When to use: When Honarpour doesn't cover your system, oil-wet reservoirs, gas systems.

📖 Full Documentation: Ibrahim-Koederitz Correlations

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Selection Matrix

By Rock Type and Wettability (Oil-Water System)

Legend: WW = Water-wet | ✅ = Available | ❌ = Not available | A1, A-3 = Equation numbers

By Fluid System

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Correlation Comparison

Prediction Quality

Based on validation against independent laboratory data:

Note: Actual accuracy depends on how well your reservoir matches the correlation database.

Computational Complexity

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Recommended Workflow

Step 1: Classify Your Reservoir

Step 2: Select Initial Correlation

Step 3: Apply Correlation

1. Determine endpoints:

   • Swi (from log analysis or default 20%)
   • Sorw (from waterflood data or default 25%)
   • krw° (typically 0.05-0.30)
   • kro° (typically 0.8-1.0)

2. Calculate kr curves:

   • Use selected correlation equations
   • Compute kr at each saturation step (ΔSw = 0.05)

3. Validate results:

   • Check crossover point matches wettability
   • Verify endpoint values are reasonable
   • Compare with regional data if available

Step 4: Sensitivity Analysis

Always run cases with ±20% variation in:

• Sorw (changes EUR significantly)
• krw° (affects water breakthrough)
• Corey exponents nw, no (if using Corey)

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Typical Correlation Parameters

Corey Exponents by Rock Type and Wettability

Higher exponent → Steeper curve → Lower average kr → Reduced mobility

Endpoint Relative Permeability

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Available Functions by Correlation

Corey Model Functions

📖 Full Documentation: Corey and LET Models

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Honarpour Functions

Sandstone

Carbonate

📖 Full Documentation: Honarpour Correlations

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Ibrahim-Koederitz Functions (24 total)

Oil-Water: Sandstone (8 functions)

Oil-Water: Carbonate (8 functions)

Gas-Oil Systems (4 functions)

Gas-Water and Gas-Condensate (4 functions)

📖 Full Documentation: Ibrahim-Koederitz Correlations

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Related Documentation

• Honarpour Correlations — Empirical kr for sand/carb × WW/IW
• Ibrahim-Koederitz Correlations — Comprehensive kr (all combinations)
• Corey and LET Models — Analytical kr models
• Rock Compressibility — Formation compressibility

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References

1. Corey, A.T. (1954). "The Interrelation Between Gas and Oil Relative Permeabilities." Producers Monthly, 19(1), pp. 38-41.

2. Honarpour, M., Koederitz, L.F., and Harvey, A.H. (1982). "Empirical Equations for Estimating Two-Phase Relative Permeability in Consolidated Rock." Journal of Petroleum Technology, 34(12), pp. 2905-2908. SPE-9966-PA.

3. Ibrahim, M.N.M. and Koederitz, L.F. (2000). "Two-Phase Relative Permeability Prediction Using a Linear Regression Model." SPE-65631-MS, presented at SPE Eastern Regional Meeting, Morgantown, WV.

4. Lomeland, F., Ebeltoft, E., and Thomas, W.H. (2005). "A New Versatile Relative Permeability Correlation." SCA2005-32, International Symposium of the Society of Core Analysts, Toronto, Canada.

5. Craig, F.F. Jr. (1971). The Reservoir Engineering Aspects of Waterflooding. Monograph Series, SPE, Richardson, TX. Vol. 3.

6. Ahmed, T. (2019). Reservoir Engineering Handbook, 5th Edition. Cambridge, MA: Gulf Professional Publishing. Chapter 6: Relative Permeability Concepts.

7. Honarpour, M., Koederitz, L.F., and Harvey, A.H. (1986). Relative Permeability of Petroleum Reservoirs. Boca Raton, FL: CRC Press.