Mobility ratio and water fractional flow
The water-oil mobility ratio from the end-point relative permeabilities, and the water fractional flow at a given water saturation with Corey curves: the stability of the displacement front and the water cut.
M = (k_rw° / μ_w) / (k_ro° / μ_o)S_wn = (S_w − S_wc) / (1 − S_wc − S_or), k_rw = k_rw° · S_wn^n_w, k_ro = k_ro° · (1 − S_wn)^n_of_w = 1 / (1 + (k_ro · μ_w) / (k_rw · μ_o))M ≤ 1 gives a stable, piston-like displacement; with M > 1 the water fingers through and the sweep drops. The end-point M is an upper estimate: Craig uses the water relative permeability at the average saturation behind the front. The fractional flow is for horizontal flow without capillary and gravity forces, at reservoir conditions; the surface water cut differs by the formation volume factors.
Source: Craig, The Reservoir Engineering Aspects of Waterflooding, SPE Monograph 3 (1971); relative permeability: Corey (1954); fractional flow: Buckley & Leverett (1942)
Inputs
You can change a field's unit: the value is converted to the formula's units automatically.
Between S_wc and 1 − S_or.
Usually 0.1–0.3 in water-wet rock, higher in oil-wet rock.
Usually 0.6–1.
Usually 1.5–4.
Usually 1.5–4.
0.3–1 mPa·s depending on temperature and salinity.
Unit converter for this formulaViscosity · Fraction and percent
- mPa·s1
- Pa·s0.001
- cP1
- P0.01
1 cP = 1 mPa·s.
- f_w — Water fractional flow (reservoir)–
- k_rw — Water relative permeability at S_w–
- k_ro — Oil relative permeability at S_w–
More in Waterflooding and pressure maintenance
Results are engineering estimates from standard formulas; for design decisions check them against the codes, project documents and specialists' calculations. The formulas carried over from the original set are unchanged, and their errors are described in the notes.