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Well control · field and metric units
Hydrostatic pressure formula in drilling
Hydrostatic pressure is the pressure exerted by a column of fluid at rest. In oilfield units, hydrostatic pressure (psi) = 0.052 × mud weight (ppg) × true vertical depth (ft), so a 10.0 ppg mud at 10,000 ft TVD exerts 5,200 psi. This page sets out the formula in field and metric units, shows where the constant 0.052 comes from, and works through the cases that catch people out: deviated wells, mixed fluid columns and a falling fluid level.
Reference material only. Well-control operations must follow your company's approved procedures, the rig's own kill sheet, and the training standards of IADC WellSharp or IWCF. DrillX calculators are advisory.
1. What hydrostatic pressure is
Hydrostatic pressure is the pressure a column of fluid exerts because of its own weight. In a well it depends on two things only: the density of the fluid and the vertical height of the column. Hole diameter, wellbore length and the volume of mud make no difference. It is the primary barrier in drilling: while the mud column's hydrostatic pressure is at least equal to the formation pressure, formation fluids stay out of the well.
2. The formulas
Hydrostatic pressure, field units
HP (psi) = 0.052 × MW (ppg) × TVD (ft)
Pressure gradient
Gradient (psi/ft) = 0.052 × MW (ppg)
Equivalent mud weight
EMW (ppg) = pressure (psi) ÷ (0.052 × TVD (ft))
Hydrostatic pressure, metric
HP (kPa) = 0.00981 × density (kg/m³) × TVD (m)
Other unit sets use the same idea with a different constant:
| Fluid density in | Depth in | Formula | Result in |
|---|---|---|---|
| ppg (lb/gal) | ft | 0.052 × MW × TVD | psi |
| pcf (lb/ft³) | ft | MW × TVD ÷ 144, or 0.00694 × MW × TVD | psi |
| Specific gravity | ft | 0.433 × SG × TVD | psi |
| kg/m³ | m | 0.00981 × density × TVD | kPa |
| Specific gravity | m | 0.0981 × SG × TVD | bar |
3. Where 0.052 comes from
The constant converts pounds per gallon into psi per foot. Picture a column of fluid one foot high standing on one square inch. Its volume is 12 cubic inches. A US gallon is 231 cubic inches, so the column holds 12 ÷ 231 = 0.0519 gallons. If the fluid weighs 1 ppg, that column weighs 0.0519 lb and presses on one square inch, which is 0.0519 psi for every foot of height. Rounded, that is 0.052 psi/ft per ppg. Some kill sheets use 0.0519 for extra precision; use whichever your company's procedures specify and be consistent.
4. Worked example
| Input | Value |
|---|---|
| Mud weight | 10.0 ppg |
| True vertical depth | 10,000 ft |
| Formation pressure at that depth | 4,900 psi |
| Result | Working | Answer |
|---|---|---|
| Pressure gradient | 0.052 × 10.0 | 0.520 psi/ft |
| Hydrostatic pressure | 0.052 × 10.0 × 10,000 | 5,200 psi |
| Overbalance | 5,200 − 4,900 | 300 psi |
| Formation pressure as EMW | 4,900 ÷ (0.052 × 10,000) | 9.42 ppg |
| Mud weight to balance, rounded up | 9.42 rounded up to the next 0.1 | 9.5 ppg |
The 10.0 ppg mud holds the formation back with 300 psi to spare. A balance mud weight is always rounded up, because rounding down would leave the well underbalanced.
5. Gradient by mud weight
Multiplying mud weight by 0.052 gives the pressure added by every foot of vertical depth. The last column shows the hydrostatic pressure at 10,000 ft TVD.
| Mud weight | Gradient (0.052 × MW) | HP at 10,000 ft TVD |
|---|---|---|
| 8.33 ppg | 0.433 psi/ft | 4,332 psi |
| 9.0 ppg | 0.468 psi/ft | 4,680 psi |
| 10.0 ppg | 0.520 psi/ft | 5,200 psi |
| 11.0 ppg | 0.572 psi/ft | 5,720 psi |
| 12.0 ppg | 0.624 psi/ft | 6,240 psi |
| 13.5 ppg | 0.702 psi/ft | 7,020 psi |
| 15.0 ppg | 0.780 psi/ft | 7,800 psi |
| 18.0 ppg | 0.936 psi/ft | 9,360 psi |
Fresh water is 8.33 ppg, a gradient of 0.433 psi/ft. A commonly used normal formation pressure gradient for salt water is 0.465 psi/ft, about 8.94 ppg. Formations above that gradient are described as abnormally pressured and need heavier mud.
6. Use TVD, not measured depth
In a deviated or horizontal well the wellbore is longer than it is deep. Only the vertical height of the column counts. Take 11.0 ppg mud in a well with a measured depth of 12,000 ft and a true vertical depth of 9,500 ft:
| Depth used | Working | Result |
|---|---|---|
| TVD, correct | 0.052 × 11.0 × 9,500 | 5,434 psi |
| MD, wrong | 0.052 × 11.0 × 12,000 | 6,864 psi |
Using measured depth overstates bottom-hole pressure by 1,430 psi in this case, which would hide a well that is close to balance. Along a horizontal section, hydrostatic pressure does not increase at all.
7. More than one fluid in the hole
When the column is made up of different fluids, such as a slug, a spacer, cement, or kill mud partway round, work out each section with its own density and its own vertical height, then add them. With 6,000 ft of 10.0 ppg mud sitting above 4,000 ft of 12.0 ppg mud:
| Section | Working | Pressure |
|---|---|---|
| 10.0 ppg, 6,000 ft | 0.052 × 10.0 × 6,000 | 3,120 psi |
| 12.0 ppg, 4,000 ft | 0.052 × 12.0 × 4,000 | 2,496 psi |
| Total at 10,000 ft TVD | 3,120 + 2,496 | 5,616 psi |
| Equivalent mud weight | 5,616 ÷ (0.052 × 10,000) | 10.8 ppg |
8. Metric example
A 1,200 kg/m³ mud at 3,000 m TVD exerts 0.00981 × 1,200 × 3,000 = 35,316 kPa, which is about 353 bar or 5,122 psi. The same well in field units is roughly 10.0 ppg at 9,843 ft, and 0.052 × 10.0 × 9,843 gives the same answer to within rounding.
9. How hydrostatic pressure is lost
- The fluid level drops. Every foot the level falls removes one foot of gradient. With 10.0 ppg mud, a 200 ft drop in level takes away 0.52 × 200 = 104 psi. This is why the hole is kept full while tripping, and why lost circulation is a well-control problem as well as a mud-cost problem.
- The mud gets lighter. Gas-cut mud, water dilution, or barite settling out all lower the density of part of the column.
- A lighter fluid enters the column. An influx of gas, oil or water displaces mud in the annulus, which is why casing pressure reads higher than drill pipe pressure after a kick is shut in. See kill sheet calculations.
- Swabbing. Pulling pipe too fast lowers the pressure below the bit for a moment, even though the mud weight has not changed.
Hydrostatic pressure is the static figure. While the pumps are running, friction in the annulus adds to it; that is equivalent circulating density (ECD). At the casing shoe, the difference between the formation's tested strength and the mud's hydrostatic pressure is the MAASP.
10. Mistakes to avoid
- Using measured depth instead of TVD in a deviated well.
- Mixing unit sets, such as a ppg mud weight with a depth in metres.
- Rounding a balance or kill mud weight down. Round up to the next 0.1 ppg.
- Treating the whole column as one density when there is a slug, spacer or kill mud in the hole.
- Using the mud weight on the morning report when the weight in and out of the hole is no longer the same.
- Forgetting that surface pressure adds to hydrostatic pressure. In a shut-in well, bottom-hole pressure is the hydrostatic pressure plus the gauge pressure on that side of the well.
How DrillX helps
DrillX includes a hydrostatic pressure calculator alongside ECD, annular pressure loss, MAASP from leak-off test, triplex pump output, annular capacity and velocity, buoyancy and string weight, and a Driller's and Wait & Weight kill sheet. Values update as you type, in field units, and in English or Arabic. To turn shut-in pressures into a kill mud weight, with a lookup table, see kill mud weight and kick tolerance. DrillX is in final testing; email info@drillx.app for a demo or early access, or see what DrillX does.
Questions
What is the formula for hydrostatic pressure in drilling?
Hydrostatic pressure (psi) equals 0.052 multiplied by the mud weight in pounds per gallon and by the true vertical depth in feet. A 10.0 ppg mud at 10,000 ft TVD exerts 0.052 × 10.0 × 10,000 = 5,200 psi.
Where does the constant 0.052 come from?
It converts pounds per gallon to psi per foot. A column of fluid one foot high over one square inch holds 12 cubic inches, and a US gallon is 231 cubic inches, so the column holds 12 ÷ 231 = 0.0519 gallons. Each 1 ppg of mud weight therefore adds 0.0519 psi per foot of depth, rounded to 0.052.
Do you use measured depth or true vertical depth for hydrostatic pressure?
Always true vertical depth. Hydrostatic pressure depends only on the vertical height of the fluid column, not on the length of the wellbore. Using measured depth in a deviated well overstates the pressure.
What is the hydrostatic pressure gradient of fresh water?
Fresh water weighs 8.33 ppg, so its gradient is 0.052 × 8.33 = 0.433 psi per foot. A commonly used normal formation pressure gradient for salt water is 0.465 psi per foot, equal to about 8.94 ppg.
How do you calculate hydrostatic pressure in metric units?
Hydrostatic pressure (kPa) equals 0.00981 multiplied by the fluid density in kilograms per cubic metre and by the true vertical depth in metres. A 1,200 kg/m³ mud at 3,000 m TVD exerts 0.00981 × 1,200 × 3,000 = 35,316 kPa, about 353 bar.
How do you calculate hydrostatic pressure with two different fluids in the well?
Calculate each fluid separately using its own density and its own vertical height, then add the results. With 6,000 ft of 10.0 ppg mud above 4,000 ft of 12.0 ppg mud, the pressure at 10,000 ft is 3,120 + 2,496 = 5,616 psi.
Sources and further reading
- International Association of Drilling Contractors, WellSharp well-control training: iadc.org/wellsharp
- International Well Control Forum, well-control certification and standard kill sheets: iwcf.org
- American Petroleum Institute, RP 59, Recommended Practice for Well Control Operations: api.org