Practice and answer pack
Darcy flow practice set with field and SI units
This practice set connects Darcy flow in field and SI units, rate ratios, radial resistance and the distinction between local and stock-tank volume.
By PetroCalcHub Team · Updated October 24, 2026 · Free to read and use
Begin from dimensions
In SI, q = kAΔp/(μL) with k in m², area in m², pressure in Pa, viscosity in Pa·s and length in m gives m³/s. A field coefficient incorporates a different set of units.
Do not use the field coefficient with SI inputs. The same physical case should agree after converting all quantities, apart from rounding in published field constants.
Use ratio questions to expose model assumptions
Changing permeability, viscosity or pressure gradient one at a time gives predictable Darcy ratios. Changing geometry from linear to radial requires a different resistance expression rather than a new coefficient alone.
The worked example specifies a local volume rate. A separate exercise applies Bo to obtain a stock-tank rate, making the fluid-volume basis explicit.
Audit the completed solution
Show each substitution, units and the held assumptions. Reverse-check pressure drop from the calculated rate. For radial questions retain the logarithm and skin convention.
The printable answer pack includes conceptual questions because a correct number from the wrong geometry is not a correct engineering explanation.
Explore the example
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.
Select one of 5 recorded scenarios. Intermediate states are not interpolated.
Permeability (mD) = 100. q (bbl/day): 2.8175.
- q (bbl/day)
Worked example
Darcy's Law for Linear Single-Phase Flow
Fixed controls: A = 500 ft²; DeltaP = 100 psi; mu = 2 cP; L = 1000 ft. k is varied as shown.
Relation and unit basis
q = 0.001127 k A DeltaP / (mu L)
k: Permeability (mD). A: Cross-Sectional Flow Area (ft²). DeltaP: Pressure Drop (psi). mu: Fluid Viscosity (cP). L: Flow Length (ft).
1. Define the baseline
Permeability (mD) = 100
Fixed controls: A = 500 ft²; DeltaP = 100 psi; mu = 2 cP; L = 1000 ft. k is varied as shown.
2. Select the relation
q = 0.001127 k A DeltaP / (mu L)
k: Permeability (mD). A: Cross-Sectional Flow Area (ft²). DeltaP: Pressure Drop (psi). mu: Fluid Viscosity (cP). L: Flow Length (ft).
3. Substitute the values
k = 100; A = 500; DeltaP = 100; mu = 2; L = 1000 → q = 2.8175 bbl/day
Retain intermediate precision. The displayed values are rounded only after evaluation.
4. Read the result
q (bbl/day) = 2.8175
The local fluid-volume rate is proportional to permeability at fixed linear geometry, viscosity and gradient.
Result and interpretation
q (bbl/day) = 2.8175
The local fluid-volume rate is proportional to permeability at fixed linear geometry, viscosity and gradient.
Solve the baseline with units, then use the additional questions to test ratios and geometry choices.
Exact scenario data
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.
| Permeability (mD) | q (bbl/day) |
|---|---|
| 25 | 0.704375 |
| 50 | 1.40875 |
| 100 | 2.8175 |
| 200 | 5.635 |
| 400 | 11.27 |
Scroll the table to see all columns. The highlighted row is the worked baseline. Downloads retain full numerical precision.
Practice problems and answer key
Work through the question before revealing its answer. Use the stated assumptions and include units in every numerical step.
1. In SI Darcy flow, what units should k have?
Show the worked answer
Square metres. Millidarcies must be converted before using the unscaled SI expression.
2. Reproduce the baseline q (bbl/day) without rounding intermediate values.
Show the worked answer
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. Compare the first and last recorded scenarios. Which input changes?
Show the worked answer
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. What would be needed to apply this example to a different physical system?
Show the worked answer
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. 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.
Show the worked answer
q = kAΔp/(μL) = 10⁻⁵ m³/s. The unscaled SI formula requires all these SI units.
6. What does doubling viscosity do to Darcy rate at fixed k, geometry and Δp?
Show the worked answer
It halves rate. Doubling k simultaneously would preserve the original rate.
Before using the result
- Match coefficients and units.
- State the flow geometry.
- Label local versus stock-tank rate.
The local fluid-volume rate is proportional to permeability at fixed linear geometry, viscosity and gradient.
Continue learning
Start with the broader workflow guide · Related method guide
Sources and method
The explanation and synthetic examples are original PetroCalcHub teaching material. The references below support the definitions and model context. They do not supply field validation for the synthetic scenarios.