Hydrostatic Pressure Formula In Oil And Gas

Hydrostatic Pressure Formula In Drilling

Hydrostatic pressure is the pressure created by the weight of a fluid column. In oil and gas wells, it depends primarily on fluid density and the true vertical height of the fluid column.

Hydrostatic Pressure (psi) = 0.052 × Mud Weight (ppg) × TVD (ft)

P_h = 0.052 × MW × TVD

• P_h = hydrostatic pressure, psi
• MW = mud weight or fluid density, ppg
• TVD = true vertical depth of the fluid column, ft
• 0.052 = oilfield conversion factor, psi/ft per ppg

Quick example: For a 10.0 ppg drilling fluid at 10,000 ft TVD, P_h = 0.052 × 10.0 × 10,000 = 5,200 psi.

Hydrostatic pressure is based on true vertical depth (TVD), not measured depth (MD). Therefore, in a deviated or horizontal well, using MD instead of TVD will overestimate the hydrostatic pressure.

More generally, hydrostatic pressure equals the fluid pressure gradient multiplied by the true vertical height of the fluid column:

P_h = Pressure Gradient × TVD

Engineers use hydrostatic pressure to evaluate loads on casing, tubing, completion tools, and other downhole equipment. In directional drilling, use TVD rather than measured depth (MD). For example, a 12,000-ft MD well may have a TVD of only 9,000 ft. In that case, use the 9,000-ft vertical fluid-column height in the calculation.

Formula In API Units

P_h in (PSI) = Pressure gradient in (PSI/FT) × TVD (FT)

Hydrostatic Pressure P_h in (PSI)= 0.052 X Density in (PPG) X TVD (FT)

P_h in (PSI)= 0.006944 X Density in (LB/FT³) X TVD (FT)

• P_h= Hydrostatic Pressure
• TVD: True Vertical Depth
• 0.052: Conversion factor (PSI/FT per LB/GAL) can be calculated as follows:
  • One cubic foot contains 7.48 US gallons.
  • Therefore, a fluid that weighs 1 pound per gallon (PPG) is equivalent to 7.48 pounds per cubic foot.
  • If we consider the pressure exerted by one foot of this fluid over the area of its base, we can calculate the conversion factor of 0.052 psi/ft per lb/gal = 7.48 Ibs / 144 Sq.ins
• 0.006944: Conversion factor (PSI/FT per LB/FT3)
  • One square foot equals 144 inches
  • 1/144 = 0.006944 to convert from 1 square inch to 1 square foot.

Hydrostatic Pressure Formula in Metric Units

In SI units, hydrostatic pressure is calculated from fluid density, gravitational acceleration, and the true vertical height of the fluid column:

P_h = ρ × g × TVD

P_h (Pa) = Density (kg/m³) × 9.81 (m/s²) × TVD (m)

P_h (bar) = 0.0000981 × Density (kg/m³) × TVD (m)

P_h (atm) ≈ 0.0000968 × Density (kg/m³) × TVD (m)

• P_h = hydrostatic pressure
• ρ = fluid density, kg/m³
• g = gravitational acceleration, approximately 9.81 m/s²
• TVD = true vertical height of the fluid column, m

Fluid Gradients

Fluid weight can be expressed in several units. To simplify hydrostatic pressure calculations, drilling engineers commonly use a fluid pressure gradient (psi/ft). This value represents the pressure increase per foot of vertical fluid column. For example, 38° API oil has a density of 52.06 lb/ft³. For a 1-ft-high column, that corresponds to 52.06 lb/ft². Converting square feet to square inches gives the gradient in psi/ft:

52.06 LB/FT³× .006944 FT²/IN²= 0.362 LB/IN²/FT= 0.362 PSI/FT

For fluid density in lb/gal (ppg), multiply by 0.05195 to obtain the pressure gradient in psi/ft. The reference tables below provide common conversions. Once you know the gradient, multiply it by the fluid column’s TVD to calculate P_h.

This is the static hydrostatic component of well pressure. While circulating, annular friction also contributes to bottom-hole pressure and is commonly represented through equivalent circulating density (ECD).

P_h (PSI)= Fluid Gradient (PSI/FT)× TVD (FT)

Fluid Gradients of Mixtures

A well may contain a mixture of liquids, such as oil and water. To calculate its pressure gradient, multiply each liquid’s gradient by its percentage of the mixture. Then add the contributions and divide by 100:

Where:

• fg_mix= fluid gradient of the mixture (psi/ft)
• fg_n = fluid gradient of liquid n (psi/ft)
• f_n = percentage of liquid n

Slurry Gradients

Operations such as hydraulic fracturing and gravel packing may require the pressure gradient of a fluid-sand slurry. Unlike a simple liquid mixture, added sand displaces part of the fluid volume. Therefore, adding the component weights without accounting for the volume change would give an incorrect slurry density. Use the following formulas to calculate slurry weight:

Where:

• ω_slurry = weight of sand slurry (lb/gal)
• ω_f= weight of fluid (lb/gal)

OR

Where:

• ω_slurry = weight of sand slurry (lb/ft³)
• ω_f= weight of fluid (lb/ft³)

Gas Gradients

Gas columns also exert hydrostatic pressure, but their density varies with pressure and temperature. As pressure increases, gas compresses and becomes denser. Conversely, higher temperature generally reduces gas density at a given pressure. Because density changes along the column, gas-gradient calculations differ from those for nearly incompressible liquids. Under the assumptions of the following gas-column equation, calculate bottom-hole pressure as follows:

Where:

• P = pressure at the desired depth (psi)
• P_sur = surface pressure (psi)
• e = natural logarithm base = 2.71828
• G = gas gravity
• h = true vertical depth (ft)
• T_avg = average well temperature (°F) = (surface temperature + temperature at depth) / 2

Gas gravity is the gravity of the gas compared to air. Some common oilfield gas gravities are:

• Air = 1.000
• Carbon Dioxide = 1.529
• Injected Dry Natural Gas = .650
• Methane = .554
• Nitrogen = .967
• Produced Natural Gas = .850
• Propane = 1.554

The oil and gas formulas above apply to gases only; meanwhile, some gases, such as CO2, are normally liquids under high pressure and must be treated as such to determine hydrostatic pressure in drilling.

Fluid Gradients Tables

The tables below convert oil API gravity and fluid weight into pressure gradient. To calculate hydrostatic pressure, multiply the appropriate gradient by TVD: P_h = Fluid Gradient × TVD. For an oil-water mixture, add the separate oil and water gradient contributions to obtain the total mixture gradient.

Oil API Gravity and Pressure Gradient

Fluid Weight and Pressure Gradient

Mobile: Swipe the table horizontally to view all percentages.

Oil-Water Mixture Gradient Components

Mobile: Swipe the table horizontally to view all percentages.

Download Hydrostatic Pressure Formula Excel Sheet For Oil & Gas

Download Calculation Sheet

Example 1

What is the hydrostatic pressure 1,000 FT below the surface in a well filled with 14 lb/gal drilling fluid?

• Fluid density: 14 lb/gal
• Depth: 1,000 ft

Using the “Fluid Gradients” tables above, the fluid gradient of 14 lb/gal fluid is 0.728 psi./ft. Therefore, the hydrostatic pressure is:

P = Fg × TVD = 0.728 psi/ft × 1,000 ft = 728 psi

Tubing or casing diameter does not change static hydrostatic pressure. Instead, the calculation depends on fluid density and vertical fluid-column height. If the well is partially filled, use the actual vertical height of the fluid column rather than the full well TVD.

Example 2 For Hydrostatic Pressure Formula In Oil & Gas

Calculate the hydrostatic pressure at the bottom of a 5,000 ft well considering the following:

• The fluid level is at 1,275 ft.
• The well fluid is 15° API oil.

Solution:

From the “Fluid Gradients” table: F_g = 0.418 psi/ft

The true vertical height of the fluid column is: h = 5,000 ft – 1,275 ft = 3,725 ft

Therefore: P = 0.418 psi/ft × 3,725 ft = 1,557.05 psi ≈ 1,557 psi

Hydrostatic Pressure Formula In Oil & Gas – Example 3

Given the following well conditions,

• Fluid (CMT): 800 ft of 15 ppg
• 5,600 ft of 9 lb/gal water
• Well Depth: 6,400 ft
• Pump Pressure: 1,450 psi

Determine the following:

1. The total bottom hole pressure.
2. The total pressure at the surface.
3. The total pressure at 2,500 ft.

Solution:

From the “Fluid Gradients” tables:

• F_gc =0.780 psi/ft
• F_gw = 0.468 psi/ft

Bottom Hole Pressure

Hydrostatic pressure due to cement slurry:

P_c = fg_c × h_c = 0.780 psi/ft × 800 ft = 624 psi

Hydrostatic pressure due to water:

P_w = fg_w × h_w = 0.468 psi/ft × 5,600 ft = 2,620.8 psi

Total hydrostatic pressure in drilling:

P_hydro = P_c + P_w = 624 psi + 2,620.8 psi = 3,244.8 psi

Total bottom hole pressure:

P_total = P_app + P_hydro = 1,450 psi + 3,244.8 psi = 4,694.8 psi

Total Surface Pressure

Since there is no hydrostatic pressure at the surface, the surface pressure is the applied pressure of 1,450 psi.

Pressure at 2,500 ft:

At 2,500 ft there is no cement, so only the water is considered.

Hydrostatic pressure at 2,500 ft:

P_hydro = fg × h = .468 psi/ft × 2,500 ft = 1,170 psi

Total pressure at 2,500 ft: Adding P_app to P_hydro

P_total= 1,450 psi + 1,170 psi = 2,620 psi

Example 4

What is the fluid gradient of an oil-water mixture that is 60% water cut, if the water weighs 9.2 lb/gal and the oil is 35° API?

Solution:

From the “Fluid Gradients” tables:

fg_w = 0.478 psi/ft

fg_o = 0.366 psi/ft

Fluid gradient of the mixture:

Using the “Fluid Gradients of Oil-Water Mixtures” table above:

fg_mix = water component + oil component = 0.287 psi/ft + 0.147 psi/ft = 0.434 psi/ft

Example 5

Calculate the pressure in a 1,500 ft well filled with 9.0 ppg water to which 3 pounds of sand per gallon is added.

Solution:

Slurry weight:

Multiply the weight by the conversion factor 0.05195 gal/(ft.in²) to determine the slurry pressure gradient

fg_slurry = 10.56 lb/gal × 0.05195 gal/(ft.in²)= 0.548 psi/ft

Hydrostatic pressure: P = 0.548 psi/ft × 1,500 ft= 823 psi

Example 6

Determine the bottom hole pressure of a well under the following conditions:

Well Data:

• Depth: 9,500 ft
• Bottom Hole Temp.: 275°F
• Surface Temperature: 75°F
• Surface Pressure: 2,500 psi
• G_N2= 0.967

Solution:

Average well temperature:

Bottom hole pressure:

References:

• Schlumberger Completions Hydraulics Handbook
• Aberdeen Well Control Manual