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

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

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

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

5. Fluid Flow in Pipes and Annuli

6. Fluid Flow in Pipes and Annuli
Laminar Flow
Turbulent
LOG
(SHEAR
STRESS)
(psi) n 1

7. Rotating Sleeve Viscometer

8. Rotating Sleeve Viscometer
(RPM * 1.703)
SHEAR RATE
sec -1
5.11
170.3
511
1022
VISCOMETER
RPM 3
100
300
600
ANNULUS
BOB
DRILL STRING
SLEEVE
API RP 13D

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

10. Example: Pressure Drop Calculations
Example Calculate the pump pressure in the wellbore shown on the next page, using the API method.
The relevant rotational viscometer readings are as follows:
R3 = (at 3 RPM)
R100 = 20 (at 100 RPM)
R300 = 39 (at 300 RPM)
R600 = 65 (at 600 RPM)

11. Pressure Drop Calculations
PPUMP
Q = gal/min
r = lb/gal
PPUMP = DPDP + DPDC
+ DPBIT NOZZLES
+ DPDC/ANN + DPDP/ANN
+ DPHYD

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

13. Pressure Drop In Drill Pipe
OD = 4.5 in ID = in
L = 11,400 ft
Effective Viscosity in Pipe (mep):
Reynolds Number in Pipe (NRep):

14. Pressure Drop In Drill Pipe
OD = 4.5 in ID = in
L = 11,400 ft
NOTE: NRe > 2,100, so
Friction Factor in Pipe (fp):
So,

15. Pressure Drop In Drill Pipe
OD = 4.5 in ID = in
L = 11,400 ft
Friction Pressure Gradient (dP/dL)p :
Friction Pressure Drop in Drill Pipe :
DPdp = 665 psi

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

17. Pressure Drop In Drill Collars
OD = 6.5 in ID = 2.5 in
L = 600 ft
Pressure Drop In Drill Collars
Effective Viscosity in Collars(mec):
Reynolds Number in Collars (NRec):

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

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

20. Pressure Drop across Nozzles
DN1 = 11 32nds (in) DN2 = 11 32nds (in) DN3 = 12 32nds (in)
DPNozzles = 1,026 psi

21. Pressure Drop in DC/HOLE Annulus
Q = gal/min
r = lb/gal
8.5 in
DHOLE = 8.5 in
ODDC = 6.5 in
L = 600 ft

22. Pressure Drop in DC/HOLE Annulus
DHOLE = 8.5 in
ODDC = 6.5 in
L = 600 ft
Power-Law Constant (n):
Fluid Consistency Index (K):
Average Bulk Velocity in DC/HOLE Annulus (Va):

23. Pressure Drop in DC/HOLE Annulus
DHOLE = 8.5 in
ODDC = 6.5 in
L = 600 ft
Effective Viscosity in Annulus (mea):
Reynolds Number in Annulus (NRea):

24. Pressure Drop in DC/HOLE Annulus
DHOLE = 8.5 in
ODDC = 6.5 in
L = 600 ft
NOTE: NRe < 2,100
Friction Factor in Annulus (fa):
DPdc/hole = 31.6 psi
So,

25. Pressure Drop in DP/HOLE Annulus
q = gal/min
r = lb/gal
DHOLE = 8.5 in
ODDP = 4.5 in
L = 11,400 ft

26. Pressure Drop in DP/HOLE Annulus
DHOLE = 8.5 in
ODDP = 4.5 in
L = 11,400 ft
Power-Law Constant (n):
Fluid Consistency Index (K):
Average Bulk Velocity in Annulus (Va):

27. Pressure Drop in DP/HOLE Annulus
Effective Viscosity in Annulus (mea):
Reynolds Number in Annulus (NRea):

28. Pressure Drop in DP/HOLE Annulus
NOTE: NRe < 2,100
Friction Factor in Annulus (fa):
DPdp/hole = psi
So,
psi

29. Pressure Drop Calculations - SUMMARY -
PPUMP = DPDP + DPDC + DPBIT NOZZLES
+ DPDC/ANN + DPDP/ANN + DPHYD
PPUMP = ,026
PPUMP = 1, = 2,103 psi

30. PPUMP = 1,918 + 185 = 2,103 psi PPUMP = DPDS + DPANN + DPHYD
DPDS = DPDP + DPDC + DPBIT NOZZLES
= ,026 = 1,918 psi
P = 0
DPANN = DPDC/ANN + DPDP/ANN
= = 185
DPHYD = 0
PPUMP = 1, = 2,103 psi

31. What is the BHP? BHP = 7,985 psig BHP = 185 + 7,800
BHP = DPFRICTION/ANN + DPHYD/ANN
BHP = DPDC/ANN + DPDP/ANN
* 12.5 * 12,000
= ,800 = 7,985 psig
BHP = ,800
BHP = 7,985 psig

32. DRILLPIPE DRILL COLLARS BIT NOZZLES ANNULUS
2103
DRILL COLLARS
BIT NOZZLES
ANNULUS

33. BHP
DRILLSTRING
ANNULUS

34. CIRCULATING
2103
STATIC

35. DRILLSTRING ANNULUS BIT
2103
DRILLSTRING
ANNULUS
(Static)
BIT

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 NRe < 2,100, then
Friction Factor in Pipe (fp):
Then
and

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 NRe > 2,100, then Friction Factor in the Annulus:
Then
and

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. Critical Circulation Rate
In the Drillpipe/Hole Annulus:
Q, gal/min V, ft/sec Nre
,044
,154
,446
,756
,086
,099
,100

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

42. n = 1.0

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

44. Dpf = v 1.75
turbulent flow
Dpf = 9.11 v
laminar flow
Use max. Dpf value