Honarpour Relative Permeability Correlations

Overview

Relative permeability (kr) is a fundamental property controlling multiphase flow in porous media. It represents the reduction in effective permeability to one phase due to the presence of other fluid phases. The Honarpour et al. (1982) correlations provide empirical equations to estimate relative permeability curves when laboratory core data are not available.

These correlations are essential for:

• Reservoir simulation — Predicting oil recovery and water/gas breakthrough
• Well performance — IPR curves for multiphase flow
• Material balance — Fractional flow calculations
• EOR screening — Assessing waterflood and gas injection potential
• Economic evaluation — Recovery factor estimation

Development Background

Honarpour, Koederitz, and Harvey (1982) compiled relative permeability data from:

• 651 data sets from worldwide oil and gas fields
• Continental U.S., Alaska, Canada, Libya, Iran, Argentina, UAE
• Consolidated rocks only (natural formation samples)
• Room temperature and atmospheric pressure measurements
• Both water/oil and oil/gas systems

Using stepwise linear regression analysis, they developed prediction equations segregated by:

1. Lithology: Sandstone/conglomerate vs. carbonate (limestone/dolomite)
2. Wettability: Water-wet vs. intermediate-wet (mixed) vs. oil-wet
3. Fluid system: Water/oil (imbibition) vs. oil/gas (drainage)

Wettability Classification

The correlations distinguish between different wettability states using Craig's rules (modified):

Water-Wet Criteria

1. In oil/water system: $k_{rw}$ at high oil saturation >> $k_{ro}$ in gas/oil system at same oil saturation
2. In oil/water system: $k_{rg}$ in gas/oil system >> $k_{rw}$ at residual oil after waterflood

Physical interpretation: Water preferentially coats rock surface; water occupies small pores, oil in large pores.

Intermediate-Wet (Mixed) Criteria

Rock shows neither clearly water-wet nor oil-wet behavior. Characteristics fall between the two extremes.

Physical interpretation: Rock surface has patches of both water-wet and oil-wet areas.

Oil-Wet Criteria

1. In oil/water system: $k_{ro}$ approximately equal to $k_{ro}$ in gas/oil system
2. $k_{rg}$ in gas/oil approximately equal to $k_{rw}$ in oil/water

Physical interpretation: Oil preferentially coats rock surface; oil occupies small pores, water in large pores.

Note: Honarpour's published equations cover water-wet and intermediate-wet systems only. Oil-wet systems were not included in the regression analysis.

Equation Structure

All equations use normalized saturations to account for irreducible water (Swi) and residual oil (Sor):

Normalized Water Saturation

Normalized Oil Saturation

Where:

• $S_{wi}$ = irreducible (connate) water saturation
• $S_{orw}$ = residual oil saturation to water (after waterflood)
• $S_{org}$ = residual oil saturation to gas (after gas drive)

Typical values:

• Sandstone, water-wet: Swi = 0.15-0.25, Sorw = 0.20-0.35
• Carbonate, water-wet: Swi = 0.10-0.20, Sorw = 0.25-0.40
• Intermediate-wet: Swi lower, Sorw higher than water-wet

Water/Oil System Correlations

Sandstone — Water-Wet

Water Relative Permeability (Equation A-1)

Data basis:

• 84 data sets, 361 data points
• Porosity: 9.9% to 30.3%
• Air permeability: 4.1 to 2,640 md
• Water saturation: 6.7% to 70.0%
• R² = 0.92 (excellent fit)

Physical behavior:

• krw = 0 at Sw = Swi (no water flow below irreducible)
• krw increases with Sw (more water → easier water flow)
• Typical krw endpoint (@ Sorw): 0.05 to 0.30

Oil Relative Permeability (Equation A-3)

Data basis:

• 185 data sets, 1,000 data points
• Porosity: 9.1% to 37.1%
• Air permeability: 0.2 to 4,000 md
• R² = 0.94 (excellent fit)

Physical behavior:

• kro = 0 at So = Sorw (no oil flow at residual)
• kro = 1 at Sw = Swi (oil has full permeability at connate water)
• Porosity term accounts for pore structure effects

Sandstone — Intermediate-Wet

Water Relative Permeability (Equation A-2)

Data basis:

• 101 data sets, 478 data points
• Porosity: 9.1% to 37.1%
• Air permeability: 0.2 to 4,000 md
• R² = 0.87 (good fit)

Physical behavior:

• Higher krw endpoint than water-wet (oil in smaller pores doesn't block water as much)
• Porosity term captures pore structure effects

Oil Relative Permeability

Use Equation A-3 (same as water-wet sandstone). The regression analysis showed wettability has minimal effect on kro in sandstones.

Carbonate — Water-Wet

Water Relative Permeability (Equation A-6)

Data basis:

• 8 data sets, 57 data points
• Porosity: 10.1% to 15.7%
• Air permeability: 0.05 to 800 md
• R² = 0.77 (acceptable for limited data)

Physical behavior:

• Strong porosity effect (carbonate pore structure more variable)
• Permeability term accounts for pore connectivity
• Generally lower krw than sandstones at same Sw

Oil Relative Permeability (Equation A-8)

Data basis:

• 54 data sets, 593 data points
• Porosity: 6.5% to 31.1%
• Air permeability: 0.05 to 713.4 md
• R² = 0.95 (excellent fit)

Physical behavior:

• Higher exponent (4 vs 1.8-2 for sandstone) → steeper kro curve
• Reflects more heterogeneous pore structure in carbonates

Carbonate — Intermediate-Wet

Water Relative Permeability (Equation A-7)

Data basis:

• 26 data sets, 197 data points
• Porosity: 8.0% to 29.1%
• Air permeability: 0.04 to 490 md
• R² = 0.84 (good fit)

Physical behavior:

• More complex functional form reflects wettability effects
• Generally higher krw endpoint than water-wet carbonate

Oil Relative Permeability

Use Equation A-8 (same as water-wet carbonate).

Oil/Gas System Correlations

Sandstone (All Wettabilities)

Oil Relative Permeability (Equation A-4)

Data basis:

• 133 data sets, 822 data points
• Porosity: 9.0% to 45.0%
• Air permeability: 0.2 to 4,000 md
• R² = 0.93

Note: Wettability effect on kro (gas/oil) was found to be negligible.

Gas Relative Permeability (Equation A-5)

Data basis:

• 133 data sets, 766 data points
• Critical gas saturation: 0.0001% to 34%
• R² = 0.92

Special feature: Requires $k_{rg}(S_{org})$ = endpoint gas relative permeability at residual oil saturation. Typical range: 0.60 to 0.95.

Carbonate (All Wettabilities)

Oil Relative Permeability (Equation A-9)

Same functional form as sandstone Equation A-4, but with carbonate-specific coefficients.

Gas Relative Permeability (Equation A-10)

More complex than sandstone, includes permeability and porosity terms to account for heterogeneous carbonate pore structure.

Applicability and Limitations

Validated Range

Assumptions

1. Consolidated rocks — Not valid for unconsolidated sands or fractures
2. Room temperature — Temperature effects not explicitly included
3. Imbibition (water/oil) — Displacement of oil by water
4. Drainage (oil/gas) — Displacement of oil by gas
5. Primary process — First imbibition or drainage cycle

Strengths

• Based on extensive laboratory data (651 data sets)
• Worldwide geographic coverage
• Segregated by lithology and wettability
• High R² values (0.77 to 0.95)
• Better than older correlations (Wyllie, Pirson, Naar)

Limitations

1. No oil-wet equations published
2. Limited carbonate data (especially water-wet)
3. Endpoint values (krw°, krg°) must be known or estimated
4. Rock properties (φ, ka) required for some equations
5. Wettability must be determined (can use Craig's rules or contact angle)

When to Use Honarpour

Best for:

• Preliminary reservoir studies when core data unavailable
• Sensitivity analysis on relative permeability effects
• Initial reservoir simulation model
• Comparison with laboratory measurements
• Estimating missing kr curves when only one system measured

Alternatives:

• Ibrahim-Koederitz (2000) — More comprehensive (all wettabilities, more data)
• Corey (1954) — Simpler power-law model
• LET model (2005) — Three-parameter flexible shape
• Laboratory measurement — Most accurate, always preferred

Functions Covered

The following functions implement Honarpour's relative permeability correlations. See each function page for detailed parameter definitions, Excel syntax, and usage examples.

Water/Oil System

Note: Oil/gas system functions for krg and kro are not currently exposed (use Ibrahim-Koederitz for gas systems).

Related Documentation

• SCAL Overview — Correlation selection guide
• Ibrahim-Koederitz Correlations — More comprehensive kr equations
• Corey and LET Models — Analytical kr models
• PVT Properties — Fluid property correlations for fractional flow

References

1. 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.

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

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

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

5. Lake, L.W. (1989). Enhanced Oil Recovery. Englewood Cliffs, NJ: Prentice Hall. Chapter 3: Rock-Fluid Interactions.

6. Tiab, D. and Donaldson, E.C. (2016). Petrophysics: Theory and Practice of Measuring Reservoir Rock and Fluid Transport Properties, 4th Edition. Cambridge, MA: Gulf Professional Publishing.