Drilling guides › Hydrostatic pressure, mud gradient and equivalent mud weight
Hydrostatic pressure, mud gradient and equivalent mud weight
Almost every drilling calculation starts from the pressure a column of fluid exerts at the bottom of the hole. Get this one right and kill sheets, leak-off tests and ECD all follow from it. Get it wrong and every number built on it is wrong in the same direction, which is why it is worth understanding rather than just memorising.
Hydrostatic pressure
Hydrostatic pressure depends only on the fluid density and the true vertical depth (TVD), not on the measured depth or the hole size.
The constant 0.052 converts pounds per gallon and feet into psi: a column of 1 ppg fluid one foot high presses 0.052 psi on its base (7.48 gallons per cubic foot ÷ 144 square inches per square foot).
Picture a column of mud one foot square. Each foot of height holds one cubic foot, which is 7.48 gallons, so at 1 ppg it weighs 7.48 lb. That weight rests on 144 square inches, so it adds 7.48 ÷ 144 = 0.0519 psi per foot. Rounded to 0.052, that is the number on every rig floor. Because the weight of the column is all that matters, a wide hole and a narrow one give the same pressure at the same vertical depth, and so does a long, inclined path that ends at the same TVD.
In metric units:
Here 0.00981 is simply gravity (9.81 m/s²) with the units tidied up, and the bar version uses specific gravity, so water at 1.00 sg adds about 0.098 bar per metre.
Worked example
Mud weight 10.5 ppg, TVD 9,500 ft.
The same well in metric: 1,258 kg/m³ (1.26 sg) and 2,896 m TVD gives 0.00981 × 1,258 × 2,896 ≈ 35,740 kPa, about 357 bar. 5,187 psi ÷ 14.504 is also about 357 bar, so the two agree.
Worked example: a deviated well
The bit is at 12,800 ft measured depth but only 9,800 ft TVD, with 11.2 ppg mud.
Using measured depth overstates the bottomhole pressure by about 1,750 psi. A crew working from that figure would think the well is far more overbalanced than it is.
Columns of more than one fluid
A well often holds several fluids at once: a heavy slug at the top of the string, spacer and cement in the annulus, or a kill mud that has only reached part of the way round. Work out the pressure of each section from its own density and its own vertical height, then add them together.
Worked example: cement below mud
After a cement job the annulus holds 3,000 ft (vertical) of 15.8 ppg slurry below 6,500 ft of 10.5 ppg mud, 9,500 ft TVD in all.
This is the figure to compare with the fracture pressure of the weakest zone before the job, because losses during cementing usually happen when the heavy slurry is all in the annulus.
Pressure gradient
The gradient is the pressure added per foot of depth. It is handy for comparing a mud weight with formation pressure or fracture gradients from the well plan.
10.5 ppg mud has a gradient of 0.546 psi/ft. Fresh water (8.33 ppg) is 0.433 psi/ft, and a typical normal formation pressure is about 0.465 psi/ft (8.95 ppg).
Pore pressure charts and fracture gradient curves on a well plan are often drawn in psi/ft or in ppg EMW. Converting your mud weight to the same scale lets you see at a glance where you sit in the drilling window.
Equivalent mud weight (EMW)
EMW turns any pressure at a depth back into the mud weight that would give it. It is how formation pressures, leak-off results and circulating pressures are compared on one scale.
Worked example
A formation pressure of 6,000 psi at 9,500 ft TVD:
With 10.5 ppg mud in the hole, this zone is underbalanced by 6,000 − 5,187 = 813 psi. The well would flow if it were drilled into without raising the mud weight.
Worked example: metric check
1.20 sg mud at 2,500 m TVD: 0.0981 × 1.20 × 2,500 = 294.3 bar, or about 4,268 psi. Converted first to oilfield units (10.01 ppg, 8,202 ft) the answer is 4,271 psi. The 3 psi difference comes from rounding the constants and is not significant.
Common mistakes
- Using measured depth instead of TVD, especially in directional and horizontal wells.
- Taking the mud weight from the suction pit when the hole holds something different: a slug, a pill, cuttings-loaded mud or a weighted-up section.
- Forgetting that density changes downhole. In deep, hot wells mud expands with temperature and compresses with pressure, so the true hydrostatic can differ from the surface calculation. Your mud company can correct for this.
- Ignoring the air gap or riser on offshore rigs when depths are referenced to different datums (rotary table, mean sea level, seabed).
Good practice
- Keep the datum for every depth on the well data sheet and use it consistently.
- Weigh mud in and out regularly with a calibrated balance, and use a pressurised balance when the mud may hold entrained air or gas.
- Recalculate the overbalance every time the mud weight or the planned pore pressure changes, not only at the start of a section.
Questions people ask
Does the hole size change hydrostatic pressure?
No. Only density and vertical height matter. Hole size affects volumes, strokes and friction, not the static pressure.
Does gas-cut mud at surface mean a big loss of bottomhole pressure?
Usually not. Gas expands mostly near surface, so a badly cut sample at the flowline often reflects only a small drop at the bottom. It still needs attention: it can be an early kick sign, and the drop grows if the gas keeps coming.