petrophysics · porosity
Apparent Matrix Density
ρmaa = (ρb − φ·ρfl) / (1 − φ)
click formula to derive ↑
Inputs
g/cc
fraction
g/cc
Description
Back-solves the apparent matrix (grain) density implied by a bulk density log reading and an independently-known porosity, most commonly core plug porosity. This is a log-QC and lithology-calibration tool, not a primary reservoir-characterization output: its purpose is to check or refine the ρma assumption fed into phi_den over a cored interval, not to replace core or mineralogy data with a computed answer.
Variables
| Symbol | Unit | Description |
|---|---|---|
| ρmaa | g/cc | Apparent Matrix Density |
| ρb | g/cc | Formation bulk density read directly from the density log over the interval being calibrated. |
| φ | fraction | Porosity from a source independent of the density log — core plug porosity is the standard choice. This is NOT phi_den's own output; using φD here would just return the ρma already assumed, not calibrate it. |
| ρfl | g/cc | Density of the fluid occupying the pore space at the depth of interest — about 1.0 g/cc for fresh mud filtrate, up to 1.1 g/cc for saline mud filtrate. |
Assumptions
- φ comes from a source genuinely independent of the density log being calibrated — core plug porosity is standard; do not feed phi_den's own output back in, since that returns the ρma already assumed rather than calibrating it
- Single dominant matrix mineral over the interval — a mixed-lithology interval will average out to a value that does not represent any single mineral
- Density log is properly calibrated and corrected for borehole effects, and the core plug depth is accurately matched to the log depth
Limitations
- A QC/calibration tool, not a reservoir-characterization output — it does not produce a porosity, saturation, or volumetric result on its own
- Only as good as the depth-matching between core and log; a few centimeters of depth mismatch in a heterogeneous interval can shift ρmaa significantly
- Cannot distinguish a genuine matrix-density change from a bad log reading, gas effect, or a bad core porosity measurement — an outlier ρmaa can result from any of the three
Use Cases
- → Calibrating ρma for phi_den over a cored interval: Compute ρmaa at each cored depth and compare against the standard mineral densities (2.65 sandstone, 2.71 limestone, 2.87 dolomite) to select or refine the ρma used in phi_den across the rest of the (uncored) log.
- → Detecting lithology changes within a formation: Where core control exists at multiple depths, a systematic drift in ρmaa away from the expected mineral value can flag an unrecognized lithology change or heavy-mineral content the density log alone would not reveal.
- → Sanity-checking an unusual phi_den result: If phi_den porosity looks implausible over a cored zone, back-solve ρmaa here with the core porosity to check whether the assumed matrix density — rather than the density log itself — is the source of the discrepancy.
Related Calculations
Region Notes
Permian Basin
Wolfcamp/Spraberry core studies often back out ρmaa 2.68-2.71 g/cc rather than pure sandstone 2.65, reflecting carbonate cement — a common reason to recalibrate ρma away from the sandstone default.
Eagle Ford
Mixed carbonate-clay mudrock typically backs out ρmaa ≈ 2.68-2.70 g/cc; kerogen content can pull this lower where TOC is not separately accounted for.
Middle East Carbonates
Alternating limestone/dolomite intervals make a single field-wide ρma unreliable — use core control at multiple depths to back out ρmaa zone-by-zone rather than assuming one value.
Global
Always run this against several cored depths, not just one — a single ρmaa value could reflect a depth-matching error rather than a real lithology signal.
References
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