petrophysics · rock physics
Pore Volume Compressibility (Hall)
cf = 12.287 × φ^(−0.438) [Hall 1953; output in μkPa⁻¹; equivalent to 1.782×10⁻⁶ × φ^(−0.438) psi⁻¹]
click formula to derive ↑
Inputs
fraction
Description
Estimates pore volume compressibility (cf) from porosity alone using Hall's (1953) empirical correlation, derived from laboratory compressibility measurements on consolidated sandstone cores. Used in material balance calculations to quantify the rock expansion drive term in undersaturated oil reservoirs when no direct core compressibility measurements are available.
Variables
| Symbol | Unit | Description |
|---|---|---|
| cf | μpsi⁻¹ | Pore volume compressibility |
| φ | fraction | Total porosity of the reservoir rock. Hall's calibration range is 5–40%; extrapolation outside this range should be treated as approximate. Use the porosity representative of the rock being evaluated in material balance. |
Assumptions
- The rock is a consolidated sandstone similar to Hall's original dataset; the correlation was not derived from carbonates, chalk, or friable sands.
- Compressibility is evaluated at initial reservoir pressure (above bubble point for oil reservoirs); the correlation does not account for pressure dependence of cf.
- The pore volume compressibility dominates rock compressibility; grain and bulk compressibilities are assumed negligible compared to cf in the material balance context.
- Porosity is total porosity representative of the reservoir rock frame, not vugs or fractures, which have different compressibility behavior.
Limitations
- Newman (1973) showed that Hall's correlation overestimates cf for many consolidated carbonates and underestimates cf for friable or unconsolidated sands by factors of 2–5×. Use direct core measurements whenever available.
- The exponent −0.438 was fit to a small dataset of consolidated sandstones; for chalk (North Sea Ekofisk), cf can be 5–10× higher than Hall predicts at the same porosity.
- cf is pressure-dependent — it increases as reservoir pressure declines below initial pressure. Hall's correlation provides a single-value estimate at initial conditions; for depletion studies, pressure-dependent cf from core tests should be used.
- For limestone or lithology-selectable Newman (1973) coefficients, see pore_compressibility_newman — built as a separate calc rather than a mode of this one, since Newman's sandstone and limestone regressions are not a drop-in extension of Hall's single-lithology correlation.
Use Cases
- → Undersaturated material balance: Supply the rock expansion term (cf × Δp × Vp) in the undersaturated oil material balance equation, quantifying how much additional production comes from pore volume reduction as reservoir pressure declines above bubble point.
- → First-estimate cf without core data: Provide a first-estimate cf baseline for sensitivity analysis when no laboratory core compressibility measurements are available, with appropriate uncertainty disclosure.
- → Drive mechanism screening: Screen whether rock compressibility drive is significant relative to fluid expansion drive. For φ > 15%, rock drive is typically < 5% of total expansion above bubble point — this calculation quantifies that fraction.
- → Lab data quality validation: Benchmark measured cf values from core tests against Hall's expected range to identify outliers, instrument errors, or samples unrepresentative of the bulk reservoir rock.
Related Calculations
Region Notes
Global (sandstone)
Hall (1953) is the de facto standard for sandstone cf estimation when no core measurements exist. Typical values: φ = 0.10 → cf ≈ 5.2 μpsi⁻¹; φ = 0.20 → cf ≈ 3.6 μpsi⁻¹; φ = 0.30 → cf ≈ 2.9 μpsi⁻¹.
North Sea (chalk)
Ekofisk chalk: measured cf values of 20–50 μpsi⁻¹ at φ = 0.30–0.45 — 7–17× above Hall's prediction. Chalk compaction drive is a major production mechanism in Ekofisk; always use core-derived cf for chalk reservoirs.
Gulf of Mexico (deepwater sands)
High-porosity GOM turbidite sands (φ = 0.28–0.38): Hall predicts cf ≈ 2.8–3.5 μpsi⁻¹. Measured values for well-consolidated sands are within ±30% of this range. For poorly consolidated sands, expect cf 1.5–3× higher.
Permian Basin (tight sandstone)
Wolfcamp tight sand φ = 0.05–0.10: Hall predicts cf ≈ 5–7 μpsi⁻¹. Rock compressibility drive is typically less than 3% of total energy for tight unconventional reservoirs where fluid expansion and desorption dominate.
References
Primary source
Need geoscience support? BauerCalc is just one of the tools we build. If you're looking for independent expertise in well planning, geosteering, reservoir characterization, or opportunity evaluation, visit BauerSubsurface.com.