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INPUT   DATA

Title

Mud weight		ppg
Plastic viscosity		cps
Yield point		lb/100ft2
Hole diameter		in
Drill pipe OD		in
Drill pipe ID		in
Drill pipe length		ft
Drill collar OD		in
Drill collar ID		in
Drill collar length		ft
Bit Nozzle diameter		inch
Number of Nozzles
Pipe running speed		ft/min.

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OUTPUT   VARIABLES   &   GRAPHS

Pressure losses psi	Closed Pipe	Open Pipe
	Annulus	Annulus	Inside
♦  Drill pipe
♦  Drill collar
♦  Bit nozzle
♦  Total
♦  Surge/Swab
♦  Mud weight (ppg)

Surge and Swab Pressures Produced By Drillpipe Movement

During tripping, pipe run into the wellbore too fast may generate large surge pressures inside the hole which can lead to lost circulation and formation fracture. On the other hand, when pipe is pulled out too fast, it may generate large swab (negative surge) pressures that can lead to kicks and blowouts.

Surge pressures are generally calculated using the steady-state model developed by Burkhardt. The method is based on the Bingham plastic behavior of drilling mud, and essentially involves estimating and summing the frictional pressure losses arising from the normal circulation of mud inside and outside the drill string components. These pressures losses are added to the mud's hydrostatic pressure in the hole to obtain the Surge pressure, and subtracted to obtain Swab pressure. There are 2 string configurations to consider: Closed pipe or Open pipe.

CLOSED-PIPE: Here, the pressure losses due to annular flow around the drillpipe and collars are considered. Laminar flow is assumed around the pipe and turbulent flow around the collar. The relevant equations are:

 -  drillcollar pressure losses:

Where:

   V_p = pipe velocity, ft/minute
   V_m = max pipe velocity, ft/min.
   P_s = pressure loss, psi
   ρ = mud weight, ppg
   n = derived parameter of mud, dimensionless
   K = derived parameter of mud, dimensionless
   θ₃₀₀ = 300 viscometer dial reading
   θ₆₀₀ = 600 viscometer dial reading
   θ₃₀₀ = PV + YP;
   θ₆₀₀ = θ₃₀₀ + PV
   PV = plastic viscosity of mud, cps
   YP = yield point of mud, lb/100ft²
   L = length of pipe, ft
   TVD = true vertical depth, ft
   D_h = hole diameter, inches
   D_p = drill pipe or collar OD, inches
   D_i = drill pipe or collar ID, inches

OPEN-PIPE: Here, the relative flow in the annulus and in the drillstring are considered separately. That is, the pressure losses attendant to a) annular flow over the drillpipe plus collars, and b) drillstring flow through the pipe plus the collars plus the drillbit nozzles. The mean of a) and b), or the max (larger) of a) and b) can be considered representative of the surge pressure. Laminar flow is assumed inside and outside the pipe. Turbulent flow is assumed in and outside the collars and also in the nozzles.

The expressions for annular pressure losses is similar to that of the closed-pipe, except that the fluid velocity is now lower and includes the pipe's inner diameter term:

The following equations are employed to estimates pressure losses inside the drillstring components:

 -  inside drill collars:

 -  inside drillbit nozzles:

Surge pressure can be converted to the equivalent mud weight increment via the expression:

       ρ = 19.23*P_surge / TVD.

BIBLIOGRAPHY

• Moore P.L.; Drilling Practices Manual; Pennwell Books, Tulsa, Oklahoma, 1986, chap. 7.
• Lapeyrouse N.J.; Formulas & Calculations for Drilling, Production and Workover; Gulf Professional Publ. Co, Amsterdam, 2002, chap.5.
• Mitchell B.; Advanced Oilwell Drilling Handbook; Mitchell Engineering, Lakewood, Colorado, 1995.