•The sum of these interval pressure drops is equal to the total system pressure loss or the measured standpipe pressure.
•The total pressure loss for this system can described mathematically as:
PTotal= PSurf Equip+ PDrillstring+ PBit+ PAnnulus
•Surface pressure losses include losses between the standpipe pressure gauge and the drill pipe.
–This includes the standpipe, kellyhose, swivel, and kellyor top drive.
–To calculate the pressure loss in the surface connections, use the API pipe formula for pressure loss in the drill pipe.
•Top Drive Surface connections
–There is no current standard case for top drive units.
–The surface connections of most of these units consist of an 86-ft standpipe and 86 ft of hose with either a 3.0-or 3.8-in. ID. In addition, there is an “S”pipe that is different on almost every rig.
•Drill String Pressure losses
–The pressure loss in the drillstring is equal to the sum of the pressure losses in all of the drillstring intervals, including drill pipe, drill collars, mud motors, MWD/LWD/PWD or any other downhole tools.
•Friction Factor
–Before calculating the pressure loss, the Fanning friction factor (fp) is calculated next with different equations being used for laminar and turbulent flow.
–This friction factor is an indication of the resistance to fluid flow at the pipe wall.
–The friction factor in these calculations assumes a similar roughness for all tubulars.
•Formulas for friction Factor–If the Reynolds number is less than or equal to 2,100:
fp= 16/NRep
–If the Reynolds number is greater than or equal to 2,100
fp=((log n + 3.93)/50)/NRep((1.75 –log n)/7)
•Pipe Interval Pressure loss
–Drillstring (including drill collars) intervals are determined by the ID of the pipe.
–The length of an interval is the length of pipe that has the same internal diameter.
–The following equation is used to calculate the pressure loss for each drillstring interval.
•Formula for Pipe Pressure loss
•Pp(psi) =( fp x Vp*2 x r x L)/(92,916 x D)
•Vp= Velocity (ft/min)
•D = ID pipe (in.)
•r = Density (lb/gal)
•L = Length (ft)
•Pressure loss for motors and tools
–If the drillstring contains a downhole motor; an MWD, LWD or PWD tool; a turbine or a thruster, their pressure losses must be included in the system pressure losses when calculating the system’s hydraulics.
–These pressure losses can significantly change the pressure available at the bit, as well as bypass flow around the bit.
–The pressure loss through MWD and LWD tools varies widely with mud weight, mud properties, flow rate, tool design, tool size and the data transmission rate.
–Some manufacturers publish pressure losses for their tools but these pressure losses can be conservative, because they are usually determined with water.
–The pressure loss across motors and turbines cannot be accurately determined by formula, but, again, this pressure loss data is available from the suppliers.
–Regular nozzle type bit
Pbit= 156rQ*2/(Dn1*2+ Dn2*2+ Dn3*2+ …)*2
–Diamond type coring bitPbit= rQ*2/10,858(TFA)*2
–r = Density (lb/gal)
–Q = Flow ratio (gpm)
•Pressure loss in the annulus
–The total annular pressure loss is the sum of all of the annular interval pressure losses.
–Annular intervals are divided by each change in hydraulic diameter.
–A change in drillstring outside diameter and/or a change in casing, liner or open hole inside diameter would result in a hydraulic diameter change.
–As with the drillstring pressure loss equations, the friction factor must first be determined before calculating the pressure loss for each annular section.
–The pressure loss for each interval must be calculated separately and added together for the total annular pressure loss.
This equation is used to calculate the individual interval pressure losses.
Pa(psi) =( fa xVa x 2r x Lm)/((92,916 x D2)-D1)
–Va= Velocity (ft/min)
–D2= ID hole or casing (in.)
–D1= OD Drill pipe or collars (in.)
–r = Density (lb/gal)
–Lm= Length (ft)
-fa as before
–TFA = Total Flow Area (in.2)
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