Darcy flow practice set with field and SI units
PetroCalcHub · Original synthetic teaching exercise · 2026-10-24

This practice set connects Darcy flow in field and SI units, rate ratios, radial resistance and the distinction between local and stock-tank volume.

Fixed controls: A = 500 ft²; DeltaP = 100 psi; mu = 2 cP; L = 1000 ft. k is varied as shown.

1. In SI Darcy flow, what units should k have?

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2. Reproduce the baseline q (bbl/day) without rounding intermediate values.

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3. Compare the first and last recorded scenarios. Which input changes?

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4. What would be needed to apply this example to a different physical system?

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5. Evaluate SI Darcy rate for k = 10⁻¹² m², A = 0.01 m², Δp = 100,000 Pa, μ = 0.001 Pa·s and L = 0.1 m.

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6. What does doubling viscosity do to Darcy rate at fixed k, geometry and Δp?

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ANSWER KEY

1. Square metres. Millidarcies must be converted before using the unscaled SI expression.
2. k = 100; A = 500; DeltaP = 100; mu = 2; L = 1000 → q = 2.8175 bbl/day. q (bbl/day) = 2.8175. The local fluid-volume rate is proportional to permeability at fixed linear geometry, viscosity and gradient.
3. Permeability (mD) changes from 25 to 400. Other controls remain as stated in the premise. q (bbl/day) changes from 0.704375 to 11.27.
4. Replace the synthetic controls with compatible documented inputs and check the relation's assumptions. k: Permeability (mD). A: Cross-Sectional Flow Area (ft²). DeltaP: Pressure Drop (psi). mu: Fluid Viscosity (cP). L: Flow Length (ft). The local fluid-volume rate is proportional to permeability at fixed linear geometry, viscosity and gradient.
5. q = kAΔp/(μL) = 10⁻⁵ m³/s. The unscaled SI formula requires all these SI units.
6. It halves rate. Doubling k simultaneously would preserve the original rate.

Method: Replayed with the same equation record and calculation engine as /calculators/darcy-s-law-for-linear-single-phase-flow. Original synthetic inputs; engine outputs are saved in the downloadable record.
Sources:
USGS: porosity, permeability and formation-specific controls: https://pubs.usgs.gov/publication/70016961
NIST SP 811: pressure, temperature and volume conversions: https://www.nist.gov/pml/special-publication-811/nist-guide-si-appendix-b-conversion-factors/nist-guide-si-appendix-b9