Drilling Hydraulics Calculator: Pump Pressure Loss Breakdown

Every psi a mud pump generates has to go somewhere, and knowing where it goes is the difference between a well planned circulating system and a pump working against a pressure limit it cannot clear. Use the calculator above to split total system pressure loss into its three biggest pieces, drill string friction, bit nozzle pressure drop, and annulus friction, based on standard turbulent flow drilling hydraulics equations.

Three Places Pressure Goes

Mud pumped down the drill string loses pressure to friction against the pipe wall the entire way down. At the bit, the mud is forced through small nozzles at high velocity, creating a large, deliberate pressure drop that converts pump pressure into jetting energy for hole cleaning at the bit face. Back up the annulus, the mud loses more pressure to friction, this time against both the pipe and the borehole wall. Add a smaller loss through surface equipment, and the sum is the total pressure the pump has to supply.

The Formulas

For turbulent flow in the drill string and annulus, oilfield unit pressure loss equations take the form:

Drill string loss = C1 x MW^0.8 x Q^1.8 x PV^0.2 x L / ID^4.8

Annulus loss = C2 x MW^0.8 x Q^1.8 x PV^0.2 x L / ((Dh – Do)^3 x (Dh + Do)^1.8)

where MW is mud weight in ppg, Q is flow rate in gpm, PV is plastic viscosity in centipoise, L is length in feet, and the diameters are in inches. Bit nozzle pressure loss follows a separate, simpler relationship based on flow rate squared and the total nozzle flow area:

Bit nozzle loss = MW x Q squared / (12031 x total flow area squared)

Worked Example

For a 10 ppg, 15 cP mud pumped at 400 gpm down an 8000 ft, 4.276 inch ID drill string, back up an 8000 ft annulus between an 8.5 inch open hole and 5 inch drill pipe, through a bit with 0.66 square inches of total flow area, the drill string loses about 323 psi, the annulus about 160 psi, and the bit nozzles about 305 psi, for a total system loss around 788 psi before adding surface equipment losses. Notice how close the bit and drill string losses are here, which is typical, since bit hydraulics are usually sized to take up a large, deliberate share of total system pressure.

Why the Split Matters

• Bit nozzles are typically sized to take somewhere between a third and two thirds of total system pressure, to maximize jetting hydraulic horsepower at the bit
• If drill string and annulus losses eat up too much of the available pump pressure, there is little left for bit hydraulics and hole cleaning suffers
• These simplified turbulent flow equations assume constant viscosity behavior and do not capture every rheology model, but they match published worked examples closely
• Real planning should add surface equipment losses and account for eccentric pipe position and cuttings loading in the annulus

Related Calculator and Reference

For the mud weight values used in this calculation, see the Mud Weight and Hydrostatic Pressure Gradient Calculator. The pressure loss equations and constants used here were checked directly against the worked examples in Drilling Formulas and Drilling Calculations, based on Bourgoyne et al., Applied Drilling Engineering (SPE Textbook Series).