Pressures

1
14.1-1

• Pressures

2
API Power Law Model
API RP 13D

• K consistency index
• n flow behaviour index

0
3
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
4
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)

5
Pressure DropCalculations
PPUMP
Q 280 gal/min r 12.5 lb/gal
PPUMP DPDP DPDC DPBIT NOZZLES
DPDC/ANN DPDP/ANN DPHYD
6
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 (V)
7
Pressure Drop In Drill Pipe
OD 4.5 in ID 3.78 in L 11,400 ft
Effective Viscosity in Pipe (me)
Reynolds Number in Pipe (NRe)
8
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
(f)
So,
9
Pressure Drop In Drill Pipe
OD 4.5 in ID 3.78 in L 11,400 ft
Friction Pressure Gradient (dP/dL)
Friction Pressure Drop in Drill Pipe
DPdp 665 psi
10
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 (V)
11
OD 6.5 in ID 2.5 in L 600 ft
Pressure Drop In Drill Collars
Effective Viscosity in Collars(me)
Reynolds Number in Collars (NRe)
12
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 (f)
So,
13
OD 6.5 in ID 2.5 in L 600 ft
Pressure Drop In Drill Collars
Friction Pressure Gradient (dP/dL)
Friction Pressure Drop in Drill Collars
DPdc 227 psi
14
Pressure Drop across Nozzles
DN1 11 32nds (in) DN2 11 32nds (in) DN3 12
32nds (in)
DPNozzles 1,026 psi
15
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
16
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 (V)
17
Pressure Dropin DC/HOLE Annulus
DHOLE 8.5 in ODDC 6.5 in L
600 ft
Effective Viscosity in Annulus (me)
Reynolds Number in Annulus (NRe)
18
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
(f)
DPdc/hole 31.6 psi
So,
19
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
20
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)
21
Pressure Dropin DP/HOLE Annulus
Effective Viscosity in Annulus (me)
Reynolds Number in Annulus (NRe)
22
Pressure Dropin DP/HOLE Annulus
NOTE NRe lt 2,100 Friction Factor in Annulus
(f)
DPdp/hole 153.2 psi
So,
psi
23
Pressure Drop Calcs.- 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
24
2,103 psi
PPUMP DPDS DPANN DPHYD
P 0
DPDS DPDP DPDC DPBIT NOZZLES
665 227 1,026 1,918 psi
DPANN DPDC/ANN DPDP/ANN 32 153
185
DPHYD 0
PPUMP 1,918 185 2,103 psi
25
DRILLPIPE
DRILL COLLARS
BIT NOZZLES
ANNULUS
26
BHP
DRILLSTRING
ANNULUS
27
CIRCULATING
STATIC
28
DRILLSTRING
ANNULUS
(Static)
BIT
29
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 (f)
Then
and