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Drilling

Hydrostatic pressure and equivalent density, well control, ECD, bit and annular hydraulics, pipe capacities and displacement, string weight in mud, cementing, dogleg severity and cost per metre.

22 calculators

Pressures and drilling fluid

Hydrostatic pressure of a fluid column

Pressure of a column of drilling or kill fluid at a true vertical depth, and its gradient (equivalent density).

P = ρ · g · H
Well kill: kill mud weight and circulating pressures

Kill mud weight from the shut-in drill pipe pressure, and the initial and final circulating pressures for the driller's and the wait-and-weight methods.

ρ_kill = ρ + P_dp / (g · H) + Δρ
Mud weight from the pore pressure

Equivalent density of the pore pressure and the mud weight that keeps the hydrostatic pressure above it by the margin of the Kazakhstan industrial safety rules (item 85-2), with the depth-dependent cap on the overbalance.

ρ_e = P_p / (g · H)
Equivalent circulating density (ECD)

The density equivalent to the bottomhole (or shoe) pressure while circulating: the static mud column plus the annular friction loss above that point.

ECD = ρ + ΔP_a / (g · H)
Leak-off test: fracture gradient at the shoe and MAASP

Fracture (leak-off) equivalent density and pressure at the shoe from a LOT or FIT, and the maximum allowable annular surface pressure (MAASP) for the current mud weight.

ρ_fr = ρ_t + P_lo / (g · H_sh)
Weighting up, diluting and blending fluids

How much weighting material (barite, hematite, calcium carbonate), water or another fluid to add to bring the mud to the required density, and the final volume.

V_a = V_1 · (ρ_2 − ρ_1) / (ρ_a − ρ_2)

Hydraulics

Mud pump output

Output per stroke and flow rate of a single-acting triplex or quintuplex pump from the liner size, stroke length, pump speed and volumetric efficiency.

q = z · π/4 · D² · S · η
Bit hydraulics: nozzles, pressure drop and power

Total flow area (TFA), jet velocity, bit pressure drop, hydraulic power at the bit and per unit of hole area (HSI), jet impact force.

TFA = π/4 · (n_1 · d_1² + n_2 · d_2²)
Annular velocity

Average mud velocity in the annulus between the hole (or casing) and the pipe at a given pump rate.

v_a = Q / (π/4 · (D² − d²))
Circulation times: surface to bit, bottoms up, full circulation

Pump strokes and time to pump the string and annulus volumes: when the mud reaches the bit, when the bottoms-up (cuttings, gas) reaches surface, and how long a full circulation takes.

n_sb = V_s / q; t_sb = n_sb / N

Drill string and volumes

Pipe capacity and displacement

Internal volume per metre and for the whole string, metal (open-end) and closed-end displacement — for the trip sheet: hole fill when pulling and returns when running in.

C = π/4 · d²
Annular capacity and volume

Volume per metre and over an interval of the annulus between the hole (or casing) and the pipe.

C_a = π/4 · (D² − d²)
String weight in mud and hook load

String weight in air and in mud (buoyancy factor) for one or two pipe sections, and the hook load including the travelling block and top drive.

k_b = 1 − ρ / ρ_s
Hoisting system: line tension and derrick load

Fast-line and dead-line tension, derrick load and the rope breaking strength needed to lift the string on n lines, allowing for the efficiency of the block and tackle.

F_f = W / (n · E); F_d = W / n

Cementing

Casing cementing: slurry and displacement volumes

Slurry volume for a single-stage casing job: the open-hole annulus with excess, the overlap with the previous casing, the shoe track and the rat hole, plus the displacement volume down to the float collar.

V_oh = π/4 · (D_b² − D_c²) · (H_s − max(H_c, H_p)) · (1 + k)
Cement slurry: density, yield, cement and water

Slurry density and yield from the water-cement ratio, and the dry cement mass and mix water volume for a given slurry volume.

Y = 1/ρ_c + m/ρ_w
Balanced cement plug

Slurry volume for a plug of a given length, the slurry height with the pipe in the hole, the spacer volume behind the cement that balances the columns, and the displacement volume.

V_c = π/4 · D² · L · (1 + k)

Trajectory

Dogleg severity between two survey stations

Dogleg angle and severity (°/10 m, °/30 m, °/100 ft), and the changes in vertical depth, north and east between two survey stations, by the minimum curvature method.

cos β = cos I_1 · cos I_2 + sin I_1 · sin I_2 · cos(A_2 − A_1)

Drilling economics

Drilling cost per metre

Cost per metre of a bit run: the bit cost plus the rig time (rotating, connections, trip), divided by the footage; rate of penetration and cost of the run.

C = (C_b + C_r · (t_r + t_c + t_t) / 24) / ΔH

Other areas

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_pFrom Reservoir engineering and stimulation
Free point from pipe stretch

Length of the free pipe above the stuck point from the stretch measured for an increase in pull — an estimate of where tubing or drill pipe is stuck.

L = E · A · ΔL / ΔFFrom Workover and well servicing
Spotting pill to free stuck pipe

Volume of a spotting fluid (oil, water or acid) that covers the stuck zone in the annulus with a reserve inside the pipe, the displacement volume, and the drop in bottomhole pressure caused by the lighter pill.

V_a = π/4 · (D² − d_o²) · h · (1 + k)From Workover and well servicing

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.