Proppant and slurry: mass, volume and density
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).
M = c · V_fV_sl = V_f · (1 + c / ρ_p)ρ_sl = (ρ_f + c) / (1 + c / ρ_p)The concentration is per clean fluid (like ppa), not per slurry. The absolute volume of the proppant M/ρ_p adds to the fluid volume; the bulk density (with the pack porosity) matters only for the storage volume. The slurry density sets the hydrostatic head in the pipe for the surface pressure.
Source: Economides & Nolte, Reservoir Stimulation: mass and absolute volume balance
Inputs
You can change a field's unit: the value is converted to the formula's units automatically.
Carrier fluid for the stage.
Kilograms added per m³ of clean fluid, like ppa: 1 ppa = 119.8 kg/m³.
Not the bulk density: sand 2 650, ceramic 2 700–3 300, bauxite 3 500–3 600 kg/m³.
Water and water-based gels 1 000–1 030 kg/m³.
Unit converter for this formulaLiquid volume · Density and °API · Mass · Fraction and percent
- m³1
- 10³ m³0.001
- 10⁶ m³1·10⁻⁶
- L1,000
- bbl6.28981
- Mbbl0.00628981
- MMbbl6.28981·10⁻⁶
- ft³35.3147
- US gal264.172
- V_sl — Slurry volume–
- ρ_sl — Slurry density–
- c_sl — Concentration per slurry volume–
- φ_p — Proppant volume fraction in the slurry–
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.
Pressure drop across the perforations: for limited-entry fracturing and for estimating the number of open perforations from a step-down test.
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.