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1 PETE 411 Well Drilling Lesson 13 Pressure Drop Calculations API Recommended Practice 13D Third Edition, June 1, 1995.

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Presentation on theme: "1 PETE 411 Well Drilling Lesson 13 Pressure Drop Calculations API Recommended Practice 13D Third Edition, June 1, 1995."— Presentation transcript:

1 1 PETE 411 Well Drilling Lesson 13 Pressure Drop Calculations API Recommended Practice 13D Third Edition, June 1, 1995

2 2 Homework u HW #7. Pressure Drop Calculations u Due Oct. 9, 2002 u The API Power Law Model

3 3 Contents u The Power Law Model u The Rotational Viscometer u A detailed Example - Pump Pressure l Pressure Drop in the Drillpipe l Pressure Drop in the Bit Nozzles l Pressure Drop in the Annulus u Wellbore Pressure Profiles

4 4 Power Law Model K = consistency index n = flow behaviour index 0

5 5 Fluid Flow in Pipes and Annuli

6 6 LOG (SHEAR STRESS) (psi) Laminar FlowTurbulent n 1

7 7 Rotating Sleeve Viscometer

8 8 VISCOMETER RPM (RPM * 1.703) SHEAR RATE sec BOB SLEEVE ANNULUS DRILL STRING API RP 13D

9 9 API RP 13D, June 1995 for Oil-Well Drilling Fluids u API RP 13D recommends using only FOUR of the six usual viscometer readings: u Use 3, 100, 300, 600 RPM Readings. u The 3 and 100 RPM reading are used for pressure drop calculations in the annulus, where shear rates are, generally, not very high. u The 300 and 600 RPM reading are used for pressure drop calculations inside drillpipe, where shear rates are, generally, quite high.

10 10 Example: Pressure Drop Calculations u Example Calculate the pump pressure in the wellbore shown on the next page, using the API method. u The relevant rotational viscometer readings are as follows: u R 3 = 3 (at 3 RPM) u R 100 = 20 (at 100 RPM) u R 300 = 39 (at 300 RPM) u R 600 = 65 (at 600 RPM)

11 11 P PUMP =  P DP +  P DC +  P BIT NOZZLES +  P DC/ANN +  P DP/ANN +  P HYD Q = 280 gal/min  = 12.5 lb/gal Pressure Drop Calculations P PUMP

12 12 Power-Law Constant (n): Pressure Drop In Drill Pipe Fluid Consistency Index (K): Average Bulk Velocity in Pipe (V p ): OD = 4.5 in ID = 3.78 in L = 11,400 ft

13 13 Effective Viscosity in Pipe (  ep ): Pressure Drop In Drill Pipe Reynolds Number in Pipe (N Rep ): OD = 4.5 in ID = 3.78 in L = 11,400 ft

14 14 NOTE: N Re > 2,100, so Friction Factor in Pipe (f p ): Pressure Drop In Drill Pipe OD = 4.5 in ID = 3.78 in L = 11,400 ft So,

15 15 Friction Pressure Gradient (dP/dL) p : Pressure Drop In Drill Pipe OD = 4.5 in ID = 3.78 in L = 11,400 ft Friction Pressure Drop in Drill Pipe :  P dp = 665 psi

16 16 Power-Law Constant (n): Pressure Drop In Drill Collars Fluid Consistency Index (K): Average Bulk Velocity inside Drill Collars (V dc ): OD = 6.5 in ID = 2.5 in L = 600 ft

17 17 Effective Viscosity in Collars (  ec ): Reynolds Number in Collars (N Rec ): OD = 6.5 in ID = 2.5 in L = 600 ft Pressure Drop In Drill Collars

18 18 OD = 6.5 in ID = 2.5 in L = 600 ft Pressure Drop In Drill Collars NOTE: N Re > 2,100, so Friction Factor in DC (f dc ): So,

19 19 Friction Pressure Gradient (dP/dL) dc : Friction Pressure Drop in Drill Collars : OD = 6.5 in ID = 2.5 in L = 600 ft Pressure Drop In Drill Collars  P dc = 227 psi

20 20 Pressure Drop across Nozzles D N1 = 11 32nds (in) D N2 = 11 32nds (in) D N3 = 12 32nds (in)  P Nozzles = 1,026 psi

21 21 Pressure Drop in DC/HOLE Annulus D HOLE = 8.5 in OD DC = 6.5 in L = 600 ft Q =  gal/min  =  lb/gal 8.5 in

22 22 Power-Law Constant (n): Fluid Consistency Index (K): Average Bulk Velocity in DC/HOLE Annulus (V a ): D HOLE = 8.5 in OD DC = 6.5 in L = 600 ft Pressure Drop in DC/HOLE Annulus

23 23 Effective Viscosity in Annulus (  ea ): Reynolds Number in Annulus (N Rea ): D HOLE = 8.5 in OD DC = 6.5 in L = 600 ft Pressure Drop in DC/HOLE Annulus

24 24 So, D HOLE = 8.5 in OD DC = 6.5 in L = 600 ft Pressure Drop in DC/HOLE Annulus NOTE: N Re < 2,100 Friction Factor in Annulus (f a ):  P dc/hole = 31.6 psi

25 25 q =  gal/min  =  lb/gal Pressure Drop in DP/HOLE Annulus D HOLE = 8.5 in OD DP = 4.5 in L = 11,400 ft

26 26 Power-Law Constant (n): Fluid Consistency Index (K): Average Bulk Velocity in Annulus (V a ): Pressure Drop in DP/HOLE Annulus D HOLE = 8.5 in OD DP = 4.5 in L = 11,400 ft

27 27 Effective Viscosity in Annulus (  ea ): Reynolds Number in Annulus (N Rea ): Pressure Drop in DP/HOLE Annulus

28 28 So,psi Pressure Drop in DP/HOLE Annulus NOTE: N Re < 2,100 Friction Factor in Annulus (f a ):  P dp/hole = psi

29 29 Pressure Drop Calculations - SUMMARY - P PUMP =  P DP +  P DC +  P BIT NOZZLES +  P DC/ANN +  P DP/ANN +  P HYD P PUMP =  +  +  +  +  +  P PUMP =  psi

30 30 P PUMP = 1, = 2,103 psi  P HYD = 0 P PUMP =  P DS +  P ANN +  P HYD  P DS =  P DP +  P DC +  P BIT NOZZLES = ,026 = 1,918 psi  P ANN =  P DC/ANN +  P DP/ANN = = 185 2,103 psi P=0P=0

31 31 BHP = ,800 What is the BHP? BHP =  P FRICTION/ANN +  P HYD/ANN BHP =  P DC/ANN +  P DP/ANN * 12.5 * 12,000 = ,800 = 7,985 psig 2,103 psi P=0P=0 BHP= 7,985 psig

32 32 DRILLPIPE DRILL COLLARS BIT NOZZLES ANNULUS 2103

33 33 BHP DRILLSTRINGANNULUS

34 34 STATIC CIRCULATING 2103

35 35 DRILLSTRING ANNULUS (Static) BIT 2103

36 36 Pipe Flow - Laminar In the above example the flow down the drillpipe was turbulent. Under conditions of very high viscosity, the flow may very well be laminar. NOTE: if N Re < 2,100, then Friction Factor in Pipe (f p ): Thenand

37 37 Annular Flow - Turbulent In the above example the flow up the annulus was laminar. Under conditions of low viscosity and/or high flow rate, the flow may very well be turbulent. NOTE: if N Re > 2,100, then Friction Factor in the Annulus: Thenand

38 38 Critical Circulation Rate Example The above fluid is flowing in the annulus between a 4.5” OD string of drill pipe and an 8.5 in hole. The fluid density is 12.5 lb/gal. What is the minimum circulation rate that will ensure turbulent flow? (why is this of interest?)

39 39 Critical Circulation Rate In the Drillpipe/Hole Annulus: Q, gal/minV, ft/sec N re , , , , , , ,100

40 40 Optimum Bit Hydraulics u Under what conditions do we get the best hydraulic cleaning at the bit? l maximum hydraulic horsepower? l maximum impact force? Both these items increase when the circulation rate increases. However, when the circulation rate increases, so does the frictional pressure drop.

41 41

42 42 n = 1.0

43 43 Importance of Pipe Size or, *Note that a small change in the pipe diameter results in large change in the pressure drop! (q = const.) Eq. 4.66e Decreasing the pipe ID 10% from 5.0” to 4.5” would result in an increase of frictional pressure drop by about 65% !!

44 44  p f = v 1.75 turbulent flow  p f = 9.11 v laminar flow Use max.  p f value


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