Surface treating pressure and pump power for a frac job
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.
P_s = G_frac · H − ρ · g · H + ΔP_fr + ΔP_pfN = P_s · qFriction and density change from stage to stage, so check the pressure for each stage. Size the pump fleet with a margin and a standby unit, and compare the surface pressure with the limits of the tubing, packer and wellhead.
Source: Economides & Nolte, Reservoir Stimulation; in field units HHP = P [psi] · q [bbl/min] / 40.8
Inputs
You can change a field's unit: the value is converted to the formula's units automatically.
Best from a mini-frac: (ISIP + ρ · g · H) / H. Eaton's estimate gives the minimum stress; add the net pressure to it.
Clean fluid 1.00–1.05 g/cm³; a proppant slurry is heavier, so the surface pressure is lower.
From the fluid friction curves of the service company for this rate and pipe size.
Usually 2–6 m³/min (13–38 bbl/min).
Unit converter for this formulaPressure gradient and equivalent density · Length · Density and °API · Pressure · Liquid rate · Power
- g/cm³ (equiv.)1.2
- kg/m³ (equiv.)1,200
- kPa/m11.768
- bar/m0.11768
- ppg (equiv.)10.0145
- psi/ft0.520233
- lb/ft³ (equiv.)74.9136
Gradient = equivalent density × g (9.80665 m/s²): 1 g/cm³ = 9.807 kPa/m = 0.4335 psi/ft = 8.345 ppg. This is how mud weight, pore pressure and fracture gradients convert.
- P_bh — Bottomhole treating pressure–
- P_h — Hydrostatic pressure–
- N — Hydraulic horsepower–
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.
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.