1. Basic Formulas

Table of Content

1. Pressure Gradient
2. Hydrostatic Pressure
3. Converting Pressure into Mud Weight
4. Specific Gravity
5. Equivalent Circulation Density
6. Maximum Allowable Mud Weight
7. Pump Output
8. Annular Velocity
9. Capacity Formulas
10. Control Drilling
11. Buoyancy Factor
12. Hydrostatic Pressure Decrease POOH
13. Loss of Overbalance Due to Falling Mud Level
14. Formation Temperature
15. Hydraulic Horsepower
16. Drill Pipe, Drill Collar Calculation
17. Pump Pressure, Pump Strokes
18. Cost Per Foot
19. Temperature Conversion Formulas

1.8 Annular Velocity (AV)

Annular velocity (AV), ft/min - Formula 1

AV = pump output, bbl/min ÷ annular capacity, bbl/ft

Example: pump output = 12.6 bbl/min, and, annular capacity = 0.1261 bbl/ft
AV = 12.6 bbl/min ÷ 0.1261 bbl/ft
AV = 99.92 ft/min

Annular velocity (AV), ft/min - Formula 2

$\mathrm{AV,\; ft/mim}=\frac{24.5\times Q}{{\mathrm{Dh}}^2-{\mathrm{Dp}}^2}$

where Q = circulation rate, gpm, Dh = inside diameter of casing or hole size, in. Dp = outside diameter of pipe, tubing or collars, in.

Example: pump output = 530 gpm, hole size = 12-1/4 in, and, pipe OD = 4-1/2 in.
$\mathrm{AV}=\frac{24.5\times 530}{{12.25}^2-{4.5}^2}$
$\mathrm{AV}=\frac{\mathrm{12,985}}{129.8125>}$
AV = 100 ft/min

Annular velocity (AV), ft/min - Formula 3

$\mathrm{AV,\; ft/mim}=\frac{\mathrm{PO,\; bbl/min}\times \mathrm{1,029.4}}{{\mathrm{Dh}}^2-{\mathrm{Dp}}^2}$

Example: pump output = 12.6 bbl/min, hole size = 12-1/4 in, and, pipe OD = 4-1/2 in.
$\mathrm{AV}=\frac{\mathrm{12.6\; bbl/min}\times \mathrm{1,029.4}}{{12.25}^2-{4.5}^2}$
$\mathrm{AV}=\frac{\mathrm{12,970.44}}{129.8125>}$
AV = 99.92 ft/min

Annular velocity (AV), ft/sec

$\mathrm{AV,\; ft/sec}=\frac{17.6\times \mathrm{PO,\; bbl/min}}{{\mathrm{Dh}}^2-{\mathrm{Dp}}^2}$

Example: pump output = 12.6 bbl/min, hole size = 12-1/4 in, and, pipe OD = 4-1/2 in.
$\mathrm{AV}=\frac{17.6\times \mathrm{12.6\; bbl/min}}{{12.25}^2-{4.5}^2}$
$\mathrm{AV}=\frac{216.216}{129.8125>}$
AV = 1.6656 ft/sec

Pump output, gpm, required for a desired annular velocity, ft/mm

$\mathrm{Pump\; output,\; gpm}=\frac{\mathrm{AV,\; ft/mm}\times ({\mathrm{Dh}}^2-{\mathrm{Dp}}^2)}{24.5}$

where AV = desired annular velocity, ft/min
Dh = inside diameter of casing or hole size, in.
Dp = outside diameter of pipe, tubing or collars, in.

Example: desired annular velocity = 120 ft/mm, hole size = 12-1/4 in, and, pipe OD = 4-1/2 in.
$\mathrm{PO}=\frac{120\times ({12.25}^2-{4.5}^2)}{24.5}$
$\mathrm{PO}=\frac{120\times 129.8125}{24.5}$
$\mathrm{PO}=\frac{15577.5}{24.5}$
PO = 635.8 gpm

Strokes per minute (SPM) required for a given annular velocity

$\mathrm{SPM}=\frac{\mathrm{annular\; velocity,\; ft/mm}\times \mathrm{annular\; capacity,\; bbl/ft}}{\mathrm{pump\; output,\; bbl/stk}}$

Example: annular velocity = 120 ft/min, annular capacity = 0.1261 bbl/ft, Dh = 12-1/4 in, Dp = 4-1/2 in, and, pump output = 0.136 bbl/stk.
$\mathrm{SPM}=\frac{\mathrm{120\; ft/mm}\times \mathrm{0.1261\; bbl/ft}}{\mathrm{0.136\; bbl/stk}}$
$\mathrm{SPM}=\frac{15.132}{0.136}$
SPM = 111.3

⬆ Table of Content