Rock Compressibility Correlations

Overview

Rock compressibility ($c_f$) quantifies the change in pore volume with pressure. It is a critical parameter for:

• Material balance calculations — affects OOIP/OGIP estimates
• Pressure transient analysis — controls total system compressibility
• Reservoir simulation — impacts fluid expansion and pressure behavior
• Stress-sensitive reservoirs — unconsolidated sands and high-porosity formations
• Compaction drive — contributes to reservoir energy

This document covers empirical correlations for estimating formation compressibility from basic rock properties.

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Theory

Definition

Rock compressibility is defined as the fractional change in pore volume per unit change in pressure:

$$c_f = -\frac{1}{V_p} \left(\frac{\partial V_p}{\partial p}\right)_T$$

Where:

• $c_f$ = formation (rock) compressibility, psi⁻¹
• $V_p$ = pore volume, ft³
• $p$ = pressure, psia
• $T$ = temperature (constant)

The negative sign ensures $c_f$ is positive, as pore volume decreases with increasing pressure.

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Physical Significance

Rock compressibility varies widely:

Key Dependencies:

• Decreases with pressure — pore space becomes stiffer as it compacts
• Increases with porosity — higher porosity = more compressible
• Depends on lithology — grain packing and cementation
• Affected by overburden stress — shallow reservoirs more compressible

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Total System Compressibility

In reservoir engineering, formation compressibility combines with fluid compressibility:

$$c_t = c_f + S_o c_o + S_w c_w + S_g c_g$$

Where:

• $c_t$ = total system compressibility, psi⁻¹
• $c_o$, $c_w$, $c_g$ = oil, water, gas compressibility, psi⁻¹
• $S_o$, $S_w$, $S_g$ = oil, water, gas saturation, fraction

Typical Magnitudes:

• Oil: $c_o \approx 10-20 \times 10^{-6}$ psi⁻¹
• Water: $c_w \approx 3 \times 10^{-6}$ psi⁻¹
• Gas: $c_g \approx 100-1000 \times 10^{-6}$ psi⁻¹ (highly pressure-dependent)
• Rock: $c_f \approx 3-25 \times 10^{-6}$ psi⁻¹

Important: In gas reservoirs, $c_g \gg c_f$ so rock compressibility is often negligible. In oil reservoirs, $c_f$ can be significant, especially for unconsolidated formations.

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Hall (1953) Correlation

Hall developed an early $c_f$-$\phi$ correlation using limited data. This correlation is included for historical completeness but has been superseded by Newman's more comprehensive work.

$$c_f = 1.86 \times 10^{-6} \phi^{-0.415}$$

Where:

• $c_f$ = formation compressibility, psi⁻¹
• $\phi$ = formation porosity, fraction

Data Range:

• Porosity: $0.20 < \phi < 0.26$
• Sample size: 12 samples (7 limestones, 5 sandstones)

Limitations: Limited data range and poor to fair accuracy. Use Newman's correlations for better results.

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Newman (1973) Correlations

Newman developed empirical correlations for pore volume compressibility using extensive laboratory data on consolidated sandstones and limestones. The data were fit with hyperbolic equations providing improved accuracy over earlier correlations.

Newman Sandstone Correlation

For consolidated sandstones, Newman used 79 samples to develop:

$$c_f = \frac{a}{(1 + bc\phi)^{1/b}}$$

Where:

• $a = 97.3200 \times 10^{-6}$
• $b = 0.699993$
• $c = 79.8181$
• $\phi$ = formation porosity, fraction
• $c_f$ = formation compressibility, psi⁻¹

Data Range:

• Porosity: $0.02 < \phi < 0.23$
• Sample size: 79 consolidated sandstone samples
• Average absolute error: 2.60%

Application: Best for consolidated sandstones with moderate to low porosity. For unconsolidated sands, expect higher compressibility than predicted.

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Newman Limestone Correlation

For limestones (carbonates), Newman developed a separate correlation:

$$c_f = \frac{a}{(1 + bc\phi)^{1/b}}$$

Where:

• $a = 0.853531$
• $b = 1.07538$
• $c = 2.30304 \times 10^6$
• $\phi$ = formation porosity, fraction
• $c_f$ = formation compressibility, psi⁻¹

Data Range:

• Porosity: $0.02 < \phi < 0.33$
• Sample size: Limestone samples
• Average absolute error: 11.8%

Application: Suitable for dense to moderately porous limestones. Higher error reflects natural variability in carbonate pore structures (vugs, fractures).

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Applicability and Limitations

When to Use Correlations

✅ Recommended:

• Preliminary reservoir studies
• Material balance calculations when lab data unavailable
• Sensitivity analysis on $c_f$ impact
• Quick estimates for well test analysis

❌ Not Recommended:

• Critical compaction drive reservoirs (use lab measurements)
• Geomechanical modeling (requires stress-strain curves)
• Subsidence prediction (needs comprehensive geomechanics)

Laboratory Measurements Preferred

For accurate $c_f$ values, laboratory measurements on core samples are essential:

• Uniaxial strain test — simulates overburden conditions
• Hydrostatic test — equal confining pressure on all sides
• Stress cycling — captures hysteresis effects

Newman correlations provide estimates only. Use lab data when available.

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Related Topics

• SCAL Overview — Special core analysis property selection
• Oil Compressibility — Oil compressibility correlations
• PTA Dimensionless Variables — Total compressibility in well testing

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References

1. McCain, W.D., Jr. (1991). "Reservoir-Fluid Property Correlations—State of the Art." SPE Reservoir Engineering, May 1991, 266-272.

2. Hall, H.N. (1953). "Compressibility of Reservoir Rocks." Transactions of the AIME, 198, 309-311.

3. Newman, G.H. (1973). "Pore-Volume Compressibility of Consolidated, Friable, and Unconsolidated Reservoir Rocks Under Hydrostatic Loading." Journal of Petroleum Technology, June 1973, SPE-3835-PA.

Related Reading

For background on rock compressibility:

• Craft, B.C., Hawkins, M., and Terry, R.E. (2014). Applied Petroleum Reservoir Engineering. Prentice Hall.
• Ahmed, T. (2019). Reservoir Engineering Handbook. Gulf Professional Publishing.
• Dake, L.P. (1978). Fundamentals of Reservoir Engineering. Elsevier.
• Zimmerman, R.W. (1991). Compressibility of Sandstones. Elsevier.

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Typical Values Reference Table

For quick reference when lab data and correlations are unavailable:

Source: Typical ranges from industry experience. Use Newman correlations for more specific estimates.