Perforation friction pressure
Pressure drop across the perforations: for limited-entry fracturing and for estimating the number of open perforations from a step-down test.
ΔP_pf = 8 · ρ · q² / (π² · C_d² · N² · d⁴)ΔP_pf [psi] = 0.2369 · q² [bbl/min] · ρ [ppg] / (N² · d⁴ [in] · C_d²)Orifice equation: ΔP = ρ · v² / (2 · C_d²). As proppant erodes the holes the discharge coefficient grows and the friction falls during the job. The field constant 0.2369 is 0.3 % below the exact 0.2376.
Source: Economides & Nolte, Reservoir Stimulation; discharge coefficient: Crump & Conway, JPT (1988)
Inputs
You can change a field's unit: the value is converted to the formula's units automatically.
Taking fluid; fewer than shot in a limited-entry design.
The hole in the casing, from the charge data: usually 0.3–0.6 in (8–15 mm).
0.56–0.65 for new perforations, up to 0.85–0.95 after proppant erosion.
Unit converter for this formulaLiquid rate · Density and °API · Length · Pressure · Velocity
- m³/d1
- m³/h0.0416667
- L/s0.0115741
- L/min0.694444
- m³/min0.000694444
- bbl/d6.28981
- Mbbl/d0.00628981
- ft³/d35.3147
- US gpm0.183453
- bbl/min0.00436792
A day is 24 hours.
- q/N — Rate per perforation–
- v — Velocity through a perforation–
More in Fracturing and acidizing
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.
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.
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.