Fracture pressure and gradient (Eaton)
Formation fracture pressure by Eaton's method: the minimum horizontal stress from the overburden and pore pressures through Poisson's ratio. The gradient is given in kPa/m or as an equivalent density.
P_frac = ν / (1 − ν) · (σ_v − P_p) + P_pG_frac = P_frac / HUniaxial-strain model: tectonic stresses are ignored, so in tectonically active areas the fracture pressure is higher. The result is close to the minimum stress, the fracture opening pressure; the tensile strength of the rock is not included. Calibrate with a mini-frac or a leak-off test.
Source: Eaton, "Fracture gradient prediction and its application in oilfield operations", JPT (1969); with ν = 0.25 and σ_v/H = 1 psi/ft it equals the Hubbert & Willis (1957) minimum
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Integral of the density log; roughly 0.0226 MPa/m × H (average bulk density 2.3 g/cm³, 1 psi/ft).
The current one: fracture pressure drops as the reservoir depletes.
From sonic logs or core: sandstones 0.2–0.3, shales 0.3–0.45; in Eaton's chart it rises with depth towards 0.5.
Unit converter for this formulaPressure · Length · Pressure gradient and equivalent density
- MPa1
- kPa1,000
- bar10
- atm9.86923
- kgf/cm²10.1972
- mmHg7,500.62
- MPa(g)0.898675
- barg8.98675
- psi145.038
- psia145.038
- psig130.342
- ksi0.145038
psi and psia are absolute pressure; gauge units (barg, MPa(g), psig) are above atmospheric (101.325 kPa = 14.696 psi). Pressure differences in the formulas do not depend on this.
- G_frac — Fracture gradient–
- ν/(1 − ν) — Effective stress ratio–
More in Fracturing and acidizing
Expected surface pressure while pumping: the bottomhole treating pressure minus the hydrostatic head plus the friction in the pipe and through the perforations, and the hydraulic power of the pump fleet.
Pressure drop across the perforations: for limited-entry fracturing and for estimating the number of open perforations from a step-down test.
Proppant mass and slurry volume and density for a frac stage from the clean fluid volume and the proppant concentration in kilograms per cubic metre of fluid (in ppa, pounds added per gallon).
Dimensionless fracture conductivity F_CD, the equivalent skin and effective wellbore radius after fracturing from the Cinco-Ley and Samaniego chart, and the fold increase in productivity in pseudo-steady-state flow.
How much calcite or dolomite a cubic metre of acid dissolves: the gravimetric (β) and volumetric (X) dissolving power from the reaction stoichiometry, the mass of rock dissolved and the CO₂ released.
Volume of acid to fill the pores and dissolve the carbonate minerals in a ring around the well out to a given radius: in total and per metre of pay. The typical case is the hydrochloric acid preflush ahead of a mud acid treatment of a sandstone.
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.