Hydraulics

2. Importance of Hydraulics
Cuttings removal in the annulus
Hydrostatic pressure to balance pore pressure and
prevent the wellbore from collapsing
ECD (Equivalent Circulating Density)
Surge/swab pressures during tripping
Limitation of pump capacity
Optimisation of the drilling operation
It becomes more important for HPHT and extended
reach wells:
Small margin between pore and fracture
pressures
Increased ECD for extended reach wells

3. Circulating System
Drill pipe
Annulus
Casing & cement
Open hole
Drill collar
Mud pump
Mud pit
Drill bit

4. Components of the Pressure Losses
 Pressure loss through the surface equipment
 From the pump to the top of the drill pipe
 Difficult to calculate due to the variation from rig to rig
 It is usually taken as 100 psi. Consult the rig personnel.
 Pressure loss through the drill string
 Downhole tool pressure loss
 Varied from 200 psi up to 2000 psi depending on the tools
 No general model available.
 Consult the service company
 Bit hydraulics
 Pressure loss through the annulus

5. Pore Pressure & Fracture Pressure
 Pore pressure
 The pressure of the formation fluids.
 Fracture pressure
 The pressure to fracture the formation.
 Design criteria
 Pore Pressure < Mud Pressure < Fracture Pressure
 Consequences of poor design:
 Formation fluids flows into the borehole if mud pressure is less
than the pore pressure.
 Lost circulation occurs if mud pressure exceeds the fracture
pressure.

6. Operating Margin of Mud Pressures
Pore
pressure
Fracture
pressure
Pressure
Depth
Mud
pressure

7. Basic Concepts
 Average fluid velocity:
 Fluid velocity through the annulus Vf (ft/min)
24.51


f d d
Q
2 2
h p
( )
v

 Fluid velocity through the drill string Vf (ft/min)
v
Q
24 .
51
d f 
2
 Where: Q = pump rate (gpm)
d2 = wellbore diameter (inch)
d1 = Outer diameter of the drill string (inch)
d = Inner diameter of the drill string (inch)

8. Basic Concepts
 Hydrostatic pressure:
 The pressure acting on the hole bottom due to mud weight.
 For a given mud density rf, the pressure imposed by the mud
at a given true vertical depth (TVD) is:
Pst  0.052rf TVD
rf: = Mud density (ppg)
TVD: = The true vertical depth (ft)
Pst : = Hydrostatic mud pressure (psi)
 Criteria for the hydrostatic mud pressure:
 High enough to balance the pore pressure of the formation
 Low enough to avoid fracturing the formation.

9. Basic Concepts
 Equivalent circulating density (ECD):
 Mud weight rf (ppg)
 Pressure loss through the annulus Pa (psi)
 True Vertical Depth (TVD) (ft)
ECD
p
TVD f
a  

r
0.052
ECD = Equivalent Circulating Density (ppg)
 Factors affecting the ECD:
 Mud density.
 Annular pressure loss Pa.
 TVD. The smaller the TVD, the higher the ECD.
 Rate of penetration and cuttings size

10. Basic Concepts
 Equivalent viscosity meq:
 In the pressure loss calculations for non-Newtonian fluids, the
equations for Newtonian fluids are usually used. The effective
viscosity for non-Newtonian fluids is the equivalent Newtonian
viscosity of the fluid which would give the same friction factor
versus Reynolds number relationship as that for Newtonian
fluids.
 Equivalent diameter Deq:
 The equivalent diameter of a non-circular conduit is the
geometric parameter of the conduit based on which a laminar
Newtonian fluid flow through the conduit would give the same
friction factor vs. Reynolds number relationship as that for
Newtonian laminar flow through a circular pipe.

11. Basic Concepts
 Reynolds number NRe:
 Reynolds number is defined as follows (in consistent unit
system):
 Critical Reynolds number NRec:
 The number for the transition from laminar flow to turbulent flow.
 If the fluid Reynolds number is greater than the critical Reynolds
number, the fluid is in turbulent flow regime. Otherwise, the fluid
is in laminar flow regime.
 For Newtonian and Bingham plastic fluids: NRec = 2100
 For Power Law fluids
NRec n  34701370
N
D v eq f f
eq
Re 
 r
m m
r f f
a
D D v
N
  

15.47( 2 1)
Re

12. Reynolds Number
 Reynolds number Drill Pipe (NRe)):
Q
378.78 .
D PV
N
.
Re
 r

NRe = Reynolds Number
D = Pipe diameter, (in).
PV = Plastic Viscosity (cps).
Q = Flow Rate (gpm).
r = Density (lb/gal).

13. Pressure Loss Equations – Bingham Fluids
 The critical velocity (drill pipe):
97 97 8.2 . 2 2
PV PV D YP
  r
Vc .
Vc = Critical Velocity (ft/min)
D = Pipe diameter, (in).
PV = Plastic Viscosity (cps).
YP = Yield Point (lb/100ft2).
r = Density (lb/gal).
D
r


14. Pressure Loss - Pipe
)
 Pressure Loss in Laminar Flow (V<Vc):
PV V
5
.
YP
(
300. D
D
L
Pd  
Pd = Pressure Loss (psi)
D = Drill Pipe diameter, (in).
PV = Plastic Viscosity (cps).
L = Length of pipe (ft)
V = Fluid Velocity (ft/min)
YP = Yield Point (lb/100ft2).

15. Pressure Loss – Pipe
 Pressure Loss in Turbulent Flow (V>Vc):
5 0.8 1.8 0.28.91 10 . . . .
x Q PV L
4.8
D
Pd
r 

Pd = Pressure Loss (psi)
D = Drill Pipe diameter, (in).
PV = Plastic Viscosity (cps).
L = Length of pipe (ft)
Q = Flow rate (gpm)
YP = Yield Point (lb/100ft2).
r = Density (lb/gal).

16. Reynolds Number
 Reynolds number Annulus (NRe)):
Q
378 .78 .
Re 

D D PV
N
( h p).

r
NRe = Reynolds Number
Dh = Hole diameter, (in).
Dp = Pipe diameter, (in).
PV = Plastic Viscosity (cps).
Q = Flow Rate (gpm).
r = Density (lb/gal).

17. Pressure Loss – Annulus
 The critical velocity (annulus):
97 97 6.2( ) . 2 2
PV  PV  D 
D YP
Vc 
Vc = Critical Velocity (ft/min)
Dh= Hole diameter, (in).
Dp = Pipe diameter, (in).
PV = Plastic Viscosity (cps).
YP = Yield Point (lb/100ft2).
r = Density (lb/gal).
.( h p
)
h p
D D

r
r

18. Pressure Loss - Annulus
 Pressure Loss (annulus) in Laminar Flow (V<Vc):
YP .
L
Pd 
200.( )
PV . V .
L
D D
60000 .( )
2

h 
p Dh Dp

Pd = Pressure Loss (psi)
Dh = Hole diameter, (in).
Dp = Pipe diameter, (in).
PV = Plastic Viscosity (cps).
L = Length of pipe (ft)
V = Fluid Velocity (ft/min)
YP = Yield Point (lb/100ft2).

19. Pressure Loss – Annulus
 Pressure Loss (annulus) in Turbulent Flow (V>Vc):
5 0.8 1.8 0.2
x Q PV L
8.91 10 . . . .
Pd  
3 1.8
DH Dp Dh Dp
( ) ( )

 r
Pd = Pressure Loss (psi)
Dh = Hole diameter, (in).
Dp = Pipe diameter, (in).
PV = Plastic Viscosity (cps).
L = Length of pipe (ft)
Q = Flow Rate (gpm)
YP = Yield Point (lb/100ft2).
r = Density (lb/gal).

20. Bit Hydraulics
 Pressure loss at bit PN:
PN =
156.8 rQ2
( D1
2)2
PN = Nozzle pressure loss (psi).
r = Fluid density (ppg).
Q = Flow rate (gpm).
 D1
2 = Sum of square of nozzles (32nd inch).
Pbit = Pstandpipe – (Pdrillpipe + Pannulus)

21. Bit Hydraulics
ECD = Equivalent Circulating Density (ppg)
ECD
p
TVD f
a  

r
0.052
Factors affecting the ECD:
 Mud density.
 Annular pressure loss Pa.
 TVD. The smaller the TVD, the higher the ECD.
 Rate of penetration and cuttings size

22. Nozzle Velocity
Nozzle Velocity Vn:
Vn = Nozzle velocity (fps).
Pbit = Pressure Loss at Bit (psi).
r = Mud density (ppg).
Pbit
 If the nozzle velocity is too high hole erosion will occur.
 Guidelines for nozzle velocities.
Formation. Nozzle Velocity. (ft/sec)
Hard competent 380 - 450
Medium hard 340 - 380
Fractured, faulted, dipped 320 - 400
or rubble like, soft
Soft, gummy, sticky formations 290- 320
r
VN  33.36

23. Nozzle Size
Nozzle Size:
0.32.
VN
Q
AT

Vn = Nozzle velocity (fps).
Q = Flow rate (gpm).
4
3
32.
At
Nsize 

24. Bit Hydraulics
 Hydraulics impact force Fim:
F
Q v
im
r  
1930
n 
r = Fluid density (ppg).
Q = Flow rate (gpm).
Fim = Impact force (lbs)
Vn = Nozzle velocity (f/sec)

25. Hydraulic Horsepower
 At bit:
 At pump:
HHP bit =
(PN)(Q)
1714
HHP pump =
(PT)(Q)
1714
HHP = Hydraulic horse power.
PN = Nozzle pressure loss (psi).
PT = Total pressure loss (psi).
Q = Flow rate (gpm).
 Bit hydraulic horsepower relates to the rate at which the fluid
performs work at the bit. (efficiency of cuttings removal from
beneath the bit).
 As a rule of thumb the bit HHP should be 3.5 - 4 HHP per
square inch of hole cross section area being drilled.

26. Surge and Swab Pressures (I)
Surge pressure. Mud pressure increase when running
into the hole.
Swab pressure. Mud pressure decrease when tripping
out of hole.
Affecting parameters:
Viscosity
Tripping speed
Annular geometry
Mud density

27. Surge and Swab Pressures (II)
The effect is similar to that of a plunger:
A large proportion of kicks while tripping are due to
swabbing.
Excessive surges cause lost circulation, the resultant
loss of hydrostatic head could cause a kick.
The pressure changes caused by surges and swabs
may cause hole sloughing, solids bridges and solids fill
on bottom.
Swab pressures may result in mud contamination by
formation fluids entering the system.
Surge and swab pressures can be reduced by
reducing the pipe running / pulling speed and by
reducing the viscosity.

28. Effects of P & T on Mud Density
 Compressed by pressure
 Expanded by temperature
 Overall density variation depending on the thermal gradient and
compositions of the fluid.
 Water is less compressible than oil or synthetic fluids.
 The effects of P & T are more pronounced for OBM than for WBM.
 The variation in solids content of mud at a given weight has small
influence on the variation of mud density at depth.

29. Hole Cleaning Efficiency
Rheology, higher viscosities give better hole cleaning.
Flow rate, needs to be greater than settling velocity.
Particle size, shape; and density will affect its settling
velocity.
Fluid density, higher densities will be more buoyant.
ROP, the rate the particles come to the surface will be the
annular velocity - the settling rate - the R.O.P.
Hole angle, deviated holes are more difficult to clean.
Hole geometry, washed out sections will have lower
annular velocities.

30. Particle Slip Velocity - Stokes Law
The particle slip velocity is given by:
 
v
r r
d
2 m
s
  
p p

(N
. )
Re 8160
01
vs = Particle slip velocity (fpm).
dp = Diameter of particle (inch).
rp = Density of particle (ppg).
r = Density of Fluid.
h = Viscosity of fluid around the particle (cps).

31. Procedure for Pressure Loss calculations
 Select rheology model and derive rheology parameters based
on viscometer readings
 Select the pressure loss equations
 Calculate the followings for each section of the string and
annulus:
Critical flow rate
Pressure loss
 Compute the bit pressure loss
 Estimate the pressure loss through downhole tools and surface
lines
 Add all the pressure losses to obtain the pump pressure

32. Dilemmas in Rheology & Hydraulics Design
Parameters Advantages Disadvantages
Good hole cleaning
No kicks or blowouts
Stable hole
Good hole cleaning
Good hole cleaning
Lower torque, drag
Good suspension of
barite
High pump pressure
High ECD
More hole washouts
Loss circulation
Low ROP
Pressure sticking
High ECD
High pump pressure
Low ROP
Diff. for solids control
High
flow rate
High mud
density
High mud
viscosity

33. Design Philosophy and Necessary Tools
Definition of optimum rheology and hydraulics:
 Best compromises (rheology, hydraulics and related drilling
parameters)
Design philosophy:
 Modify mud rheology and hydraulics to meet drilling
requirements
Modify drilling parameters to meet the needs of hydraulics
Necessary tools:
Hydraulics programme
 Hole cleaning model

34. Criteria of Optimum Hydraulics Design
Design criteria
Pump capacity
Tripping in/out
Hole cleaning Bit hydraulics
Maximum ROP
BHA design
Weighting
agent sag
Cementing
operations
Running casing
Pore pressure < mud pressure
Frac. pressure > mud pressure Breaking circulation

35. Optimisation of Rheology & Hydraulics
Given parameters
Hole
cleaning
yes
Pump
pressure
Mud pressures
Bit hydraulics
Barite
sagging
yes yes yes
Other
criteria
OK? OK? Tolerable? Tolerable? All met?
no
no no no no
yes
Optimum design
Modify parameters parameters