Flow Units: RQI and FZI

Part 9, Chapter 9: Permeability Estimation

Learning objectives

  • Define RQI, normalized porosity phiz, and FZI
  • Explain that FZI captures the pore geometry porosity misses
  • Recognize flow units as unit-slope lines on the RQI-phiz plot
  • Use flow units to tighten the permeability-porosity relation

Making Rock Type Rigorous

The last section said to sort by rock type, but how, exactly? Amaefule turned the vague instruction into arithmetic. Define a reservoir quality index, a normalized porosity, and their ratio:

RQI=0.0314kϕ,ϕz=ϕ1ϕ,FZI=RQIϕz.\text{RQI} = 0.0314\sqrt{\frac{k}{\phi}}, \qquad \phi_z = \frac{\phi}{1-\phi}, \qquad \text{FZI} = \frac{\text{RQI}}{\phi_z}.

The flow zone indicator FZI\text{FZI} rolls everything porosity misses, grain size, sorting, tortuosity, and surface area, into one number for the pore geometry. Rocks that share an FZI are a hydraulic flow unit: they flow alike.

Hydraulic flow units (RQI and FZI)0.050.10.20.510.010.1110normalized porosity phiz = phi/(1-phi) (log)RQI = 0.0314 sqrt(k/phi) (log)FZI 1.2 (poor)FZI 3 (moderate)FZI 7 (good)FZI 4.4RQI = FZI x phiz, so each flow unit is a parallel unit-slope line; the cloud splits cleanly.

Flow Units Are Unit-Slope Lines

The plot is where it becomes beautiful. Rearrange the definition and RQI=FZI×ϕz\text{RQI} = \text{FZI}\times\phi_z, so on log-log axes of RQI against ϕz\phi_z every flow unit is a straight line of unit slope whose height is set by its FZI. The fat poro-perm cloud of the last section splits into a few clean, parallel lines, one per flow unit, and each rock falls unambiguously onto one of them. Drop a point with the sliders and read its FZI straight off.

Why It Matters

Two payoffs follow. First, within a flow unit permeability really is a tight function of porosity, so the poro-perm transform finally works without huge scatter. Second, because FZI is a rock-fabric property, a flow unit identified on core can be recognized in uncored wells from the logs, carrying a calibrated permeability everywhere. Flow units are therefore the rigorous backbone of permeability prediction, and the natural unit for the upscaling that feeds a reservoir model.

References

  • Amaefule, J. O. et al. (1993). Enhanced reservoir description: using core and log data to identify hydraulic flow units. SPE 26436.
  • Tiab, D. and Donaldson, E. C. (2015). Petrophysics, 4th ed. Gulf Professional Publishing.

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