PETE 411 Well Drilling

1
PETE 411Well 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

0
5
Fluid Flow in Pipes and Annuli
6
Fluid Flow in Pipes and Annuli
Laminar Flow
Turbulent
LOG
(SHEAR STRESS)
(psi)
n
1
7
RotatingSleeveViscometer
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
DRILLSTRING
SLEEVE
API RP 13D
9
API RP 13D, June 1995for 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 3 (at 3 RPM)
• R100 20 (at 100 RPM)
• R300 39 (at 300 RPM)
• R600 65 (at 600 RPM)

11
Pressure DropCalculations
PPUMP
Q 280 gal/min r 12.5 lb/gal
PPUMP DPDP DPDC DPBIT NOZZLES
DPDC/ANN DPDP/ANN DPHYD
12
Pressure Drop In Drill Pipe
OD 4.5 in ID 3.78 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 3.78 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 3.78 in L 11,400 ft
NOTE NRe gt 2,100, so Friction Factor in Pipe
(fp)
So,
15
Pressure Drop In Drill Pipe
OD 4.5 in ID 3.78 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
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
OD 6.5 in ID 2.5 in L 600 ft
Pressure Drop In Drill Collars
NOTE NRe gt 2,100, so Friction Factor in DC
(fdc)
So,
19
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 Dropin DC/HOLE Annulus
Q 280 gal/min r 12.5 lb/gal
8.5 in
DHOLE 8.5 in ODDC 6.5 in L
600 ft
22
Pressure Dropin 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 Dropin 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 Dropin DC/HOLE Annulus
DHOLE 8.5 in ODDC 6.5 in L
600 ft
NOTE NRe lt 2,100 Friction Factor in Annulus
(fa)
DPdc/hole 31.6 psi
So,
25
Pressure Dropin DP/HOLE Annulus
q 280 gal/min r 12.5 lb/gal
DHOLE 8.5 in ODDP 4.5 in L
11,400 ft
26
Pressure Dropin 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 Dropin DP/HOLE Annulus
Effective Viscosity in Annulus (mea)
Reynolds Number in Annulus (NRea)
28
Pressure Dropin DP/HOLE Annulus
NOTE NRe lt 2,100 Friction Factor in Annulus
(fa)
DPdp/hole 153.2 psi
So,
psi
29
Pressure DropCalculations- SUMMARY -
PPUMP DPDP DPDC DPBIT NOZZLES
DPDC/ANN DPDP/ANN DPHYD
PPUMP 665 227 1,026 32
153 0
PPUMP 1,918 185 2,103 psi
30
2,103 psi
PPUMP DPDS DPANN DPHYD
DPDS DPDP DPDC DPBIT NOZZLES
665 227 1,026 1,918 psi
P 0
DPANN DPDC/ANN DPDP/ANN 32 153
185
DPHYD 0
PPUMP 1,918 185 2,103 psi
31
2,103 psi
What is the BHP?
P 0
BHP DPFRICTION/ANN DPHYD/ANN
BHP DPDC/ANN DPDP/ANN 0.052
12.5 12,000 32 153 7,800
7,985 psig
BHP 185 7,800
BHP 7,985 psig
32
DRILLPIPE
2103
DRILL COLLARS
BIT NOZZLES
ANNULUS
33
BHP
DRILLSTRING
ANNULUS
34
CIRCULATING
2103
STATIC
35
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 lt 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 gt 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 280
2.197 1,044 300 2.354 1,154
350 2.746 1,446 400
3.138 1,756 450 3.531 2,086
452 3.546 2,099 452.1
3.547 2,100
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.

41
(No Transcript)
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 11.41 v 1.75 turbulent flow
Dpf 9.11 v laminar flow
Use max. Dpf value