Drilling Hydraulics
Chapter 3
Effect of Bit Hydraulics on Drilling Rate
DRILLING HYDRAULICS
A good understanding of the drilling hydraulics is required for optimum design
ofthe following tasks:
Bottomhole cleaning while drilling
Drill bit cleaning
Cuttings transport to the surface
DRILLING HYDRAULICS
Friction pressure losses through and around the drillstring, through rig piping and the bit nozzles
Equivalent circulating pressure
Hydraulic energy consumption
Cement and well completion fluid circulation
Surge and Swab Pressure Estimation
Borehole wall erosion
MT
SS
DRILLING HYDRAULICS
MP
DP
DC
DB
DB : Drill Bit
DC : Drill Collar
DP : Drill Pipe
MP : Mud Pump
MT : Mud Tank
SS : Shale Shaker
HYDRAULIC HORSEPOWER REQUIREMENT
Pump Hydraulic Horsepower = Q * Pp /1714
Flow rate, Q (gal/min)
Minimum: Cuttings transportMaximum: Borehole wall erosion (hole wash out)
Pump Pressure (psi) Pp = P
Frictional pressure loss is a function of fluid velocity(flow rate), pipe/wellbore geometry, and drilling fluid rheological characteristics.
DRILLING HYDRAULICS
Mud Hydrostatic Pressure : SBHP = 0.052 m D
Buoyancy Effect : We = Wa (1- m /s)
SBHP = Static bottomhole pressure, lbf/in2
D = Depth, ft
We = Effective weight of the drillstring, lbm
Wa = Air weight of the drillstring, lbm
m = Drilling fluid density, lbm/gal
s = Pipe material density, lbm/gal (65.5 lbm/gal for steel)
DYNAMIC PRESSURE BALANCE
Pump Pressure = PS+ PDP+ PDC+ PB+ PA
PS = Pressure losses through surface installations
PDP = Pressure losses through drill pipes
PDC = Pressure losses through drill collars
PB = Pressure losses through drill bit
PA = Pressure losses through annulus
DYNAMIC PRESSURE BALANCE
Circulating Bottomhole Pressure
CBHP (psi) = SBHP + PA
Equivalent Circulating Density
ECD (lbm/gal) = CBHP/(0.052*D)
ECD should always be less than the formation fracture
gradient.
ECD > Fracture Gradient (Lost circulation?)
DYNAMIC PRESSURE BALANCE
ECD < Pore Pressure Gradient
Underbalanced drillingKick?
ECD >Pore Pressure Gradient
Overbalanced drillingFormation Damage?Differential pipe sticking?
ECD = Pore Pressure Gradient
Balanced drilling
ESTIMATION OF FRICTION PRESSURE LOSSES
Friction pressure loss is a function of flow rate (flow regime), rheological properties of fluids, and the pipe/wellbore geometry.
There are four recognized flow regimes: Plug Flow Laminar Flow Transitional Flow Turbulent Flow
ESTIMATION OF FRICTION PRESSURE LOSSES
Plug FlowIf a fluid has a yield strength and its yield strength has a value greater than the shear stress at the wall of a pipe or annulus, then the fluid will be in plug flow.
A suitable criterion is if the value of Reynold’s number is less than 10 and the fluid has a gel strength, then the flow regime is plug.
The other flow regimes are predicted by using Reynold’s number. Depending of the fluid rheology type, however, different criteria need to be used.
Laminar FlowLaminar flow occurs when concentric cylindrical fluid shells (laminae) slide past one another.
The velocity of the shell at the pipe wall is zero, and velocity of the shell at the center of the pipe is maximum.
ESTIMATION OF FRICTION PRESSURE LOSSES
rv
dv/dr=0
ESTIMATION OF FRICTION PRESSURE LOSSES
Turbulent Flow
Fluid flow becomes turbulent at very high flow velocities when (high Reynold’s number) fluid particles show a chaotic(random), diffusive motion with three dimensional vorticity(rotational) fluctuations.
No analytical solution for frictional pressure loss estimation is available.
RHEOLOGY OF DRILLING FLUIDS
Newtonian Fluids (Water, High gravity oil)
=
= Shear stress, dynes/cm2
= Shear rate, 1/sec = Viscosity, poise (dyne-sec/cm2)
Field Units: = lbf/100 ft2
= centipoise
RHEOLOGY OF DRILLING FLUIDS
Non-Newtonian Fluids (Drilling Fluids)
Bingham Plastic Model = Y + pPower Law Model = Kn
Yield Power Law Model = Y +Kn
K : Fluid consistency index, lbf-sn/cm2
Y : Yield stress, lbf/100 ft2
p : Plastic viscosity, cp.
n : Flow behavior index
RHEOLOGY OF DRILLING FLUIDS
Bingham Plastic
Yield Power Law
Power Law
p
Y
ESTIMATION OF FRICTIONAL PRESSURE LOSSES
Nomenclature
d: Diameter, in.L: Length, ft.: Viscosity, cp.: Density, lbm/galq: Flow rate, gal/minv : Average fluid velocity, ft/sec
Pipe: v = q/2.448d2
Annulus: v = q/2.448(d22 - d1
2)
EQUIVALENT DIAMETER CONCEPT
An equivalent diameter is used to extend pipe
flow equations to annular geometry. Use hydraulic radius concept
4221212
21
2
1
2
2 ddrrrrrrr H
ddrd He 124
EQUIVALENT DIAMETER CONCEPT
Use geometry term in laminar pressure loss
equations derived for pipe flow and concentric
annular flow.
ddddddd
1
2
2
1
2
22
1
2
2
2
ln
~
ddddddd e
1
2
2
1
2
22
1
2
2
ln
EQUIVALENT DIAMETER CONCEPT
Use slot approximation
Use Crittendon’s equivalent diameter
ddd e 12816.0
2
ln
21
22 2
1
2
24
1
2
2
4
1
4
2 ddd
ddddd
d e
NEWTONIAN FLUIDS
Laminar Flow
Reynold’s Number:
Check for Flow Regime: NRE < 2100
Pressure Losses in Pipe Flow:
Pressure Losses in Annulus:
vd
N RE
928
ddP v
dLf
15002
dddP v
dLf
1221000
NEWTONIAN FLUIDS
Turbulent Flow Check for Flow Regime: NRE > 2100 Use the Fanning equation for pressure
losses
Pipe flow Flow in Annulus
ddLvfdP f
8.25
2 dd
vfdPdL
f
12
2
2.21
NEWTONIAN FLUIDS
Friction factor, f
Colebrook Equation
fdf N Re
255.1269.0log4
1
Stanton Chart
BINGHAM PLASTIC FLUIDS
Laminar Flow
Pressure Losses in Pipe Flow:
Pressure Losses in Annulus:
ddLypf
ddP v
22515002
dddddP ypf
v
dL12
2 2001000 12
BINGHAM PLASTIC FLUIDS
Turbulent Flow
Use apparent viscosity in Reynold’s number
criterion developed for Newtonian fluids.
Pipe:
Annulus:
v
dy
pa
66.6
vddy
pa
125
BINGHAM PLASTIC FLUIDS
If NRE > 2100 , then the flow is turbulent!
Use the Colebrook equation to determine friction factor.
Determine the frictional pressure loss using the Fanning equation;
a
vdN RE
928
ddLvfdP f
8.25
2 dd
vfdPdL
f
12
2
2.21
POWER LAW FLUIDS
Reynold’s Number (Pipe Flow)
Reynold’s Number (Annulus Flow)
n
dN
n
RE Kvn
13
0416.0289100
n
ddN
n
RE Kvn
12
0208.0 122109000
POWER LAW FLUIDS
Use Fig. 4.34 (Applied Drilling Engineering by Bourgoyne et al.) to determine the critical Reynold’s number.
Following approximate equations can also be used to determine flow regime for power law fluids:
Laminar Flow
NRE < 3470 - 1370n
Turbulent Flow
NRE > 4270 - 1370n
POWER LAW FLUIDS
Laminar Flow Frictional pressure loss in pipes
Frictional Pressure Loss in Annulus
ddL n
n
n
f
nvK
dP
1144000
0416.0
13
dd
n
n
nvK
dLdP
n
f
121144000
0208.0
12
POWER LAW FLUIDS
Turbulent Flow Use the Dodge and Metzner friction factor correlation
(given only for smooth pipes)
Use the Fanning equation to determine frictional pressure loss.
Pipe flow Flow in annulus
nfN
n
n
f 2.121
Re75.0
395.0log
0.4/1
ddLvfdP f
8.25
2 dd
vfdPdL
f
12
2
2.21
FLOW THROUGH JET BITS
ACQ
Ptd
b 22
25
10*311.8
At=Total flow area, in2
Cd=Discharge coefficient (0.95)
d= Nozzle diameter, in
vn= Nozzle velocity, ft/sec
Q=Mud flow rate, gal/min
=Mud density, lb/gal
Pb= Bit pressure drop, psi
dddAt2
3
2
2
2
14
PRESSURE DROP ACROSS BIT NOZZLES
FLOW THROUGH JET BITS
Bit Hydraulic Horsepower
BHHP= Q Pb /1714
The higher the BHHP, the faster the drilling rate!
Hydraulic (Jet) Impact Force
Fj= Jet impact force, lbf
PCF bdjQ 01823.0
OPTIMIZATION OF DRILLING HYDRAULICS
ObjectiveTo maximize the drilling rate (or to minimize the drilling cost)
Required
• Instantaneous removal of the cuttings from the
rock face, • Effective upward transportation of cuttings to
the surface
OPTIMIZATION OF DRILLING HYDRAULICS
Two types of energy sources are brought from the surface to the rock face and
should be applied in an optimal manner:
• Mechanical Energy (WOB, RPM)• Hydraulic Energy (Flow rate, nozzle
area)
OPTIMIZATION OF DRILLING HYDRAULICS
Methods of optimal hydraulic design:
• Determine the bit hydraulic horsepower required in order to balance the mechanical energy level
• Maximize arbitrarily selected criterion of estimation, e.g. bit hydraulic horse-power, jet impact force, etc.
Minimum Bit Hydraulic Horsepower vs.WR to Prevent Hydraulic Flounder (After Fullerton)
Example :Is there a proper balance between hydraulic and mechanical energy which has been delivered to therock face ?
Available BHHP : 400 HP Db: 12 ¼”
WOB/ Db : 7000 lbf/in N: 80 RPM
(WOB/Db)*N = 7000*80 = 560X103
From Fullerton Chart Required BHHP = 650 HP < 400 HP
Answer: No
OPTIMIZATION OF DRILLING HYDRAULICS
Optimization Criteria
• Maximum Bit Hydraulic Horsepower• Maximum Jet Impact Force• Maximum Nozzle Velocity
OPTIMIZATION OF DRILLING HYDRAULICS
Once the objective function for optimal hydraulic program design is selected, the limitations connected with “performance characteristics of the mud pump”
have to be considered.
Pump Performance Characteristics
I Pump Operating Range
Pp = Constant for 1 < Q < Qm
Pp = PD+ PB
II Pump Operating Range
HPp = HPD + HPb = Constant
Mud Pump Performance Characteristics
(Pp)max
I II
q’max
Continental EMSCO F 1600 (Triplex) Pump Performance Characteristics
Continental EMSCO F 1600 (Triplex) Pump Performance Characteristics
OPTIMIZATION OF DRILLING HYDRAULICS
Pp = PS+ PDP+ PDC+ PB+ PDCA + PDPA
PD = PS+ PDP+ PDC+ PDCA + PDPA
PD= Parasitic pressure losses
Pp = PD+ PB
PD= cQm
m is constant (1.3 < m < 2.1 theoretically 1.75)
c is a function of mud properties and hole geometry
PARASITIC PRESSURE LOSSES vs. FLOW RATE
Q1
Log PD
Log QQ2
PD2
PD1
Slope = m
Log c
OPTIMIZATION OF DRILLING HYDRAULICS
OBJECTIVE:Determine the optimum combination of flow rate and nozzle sizes (total flow area across the bit): CONSTRAINTS:
• Adequate cuttings transport (Qmin)
• Maximum Available Pump Flow Rate/ Wellbore erosion (Qmax)
PATH OF OPTIMUM HYDRAULICS
Log PD
Slope = m
Qmin Log QQmax
(PD)opt
I
IIIII
(Pp)max
MAXIMUM BIT HYDRAULIC HORSEPOWER
Determine the flow rate, Q, at which the bit hydraulic horsepower is maximum.
0
dQ
BHHPd
171417141714
QPPPPm
pDpbcQQQ
BHHP
1
mDP
P p
opt
MAXIMUM BIT HYDRAULIC HORSEPOWER
• If the intersection occurs in zone 1 Qopt=Qmax
• If the intersection occurs in zone 3 Qopt=Qmin
• If the intersection occurs in zone 2
1
/1
mcP
Q pm
opt
PPP Db optpopt
CP
QA
dboptt 2
25
10*311.8
MAXIMUM JET IMPACT FORCE
Determine the flow rate, Q, at which the jet
impact force is maximum.
0
dQ
d F j
22
mP
P p
D
PPCF pQDdj 01823.0
MAXIMUM JET IMPACT FORCE
• If the intersection occurs in zone 1 Qopt=Qmax
• If the intersection occurs in zone 3 Qopt=Qmin
• If the intersection occurs in zone 2
2
2/1
mcP
Q pm
opt
PPP Db optpopt
CP
QA
dboptt 2
25
10*311.8
Example :Using maximum bit hydraulic horsepower criterion,determine the optimum nozzle sizes to be used to drill the next depth interval.
Given the following well data:
Drillpipe: 4.5”, 20 lb/ft (ID:3.64”) Drill collar: 7” x 2” 120.3 lb/ft, 1000 ft.Drill Bit: 12 7/8”-tricone, 3-14 nozzles to 12,000 ftNext bit: 8 7/8” (assume hole washed out to 9 7/8” )Pump: 1600 HP- National Duplex-Double acting
(Pp)max : 5440 psi Volumetric Efficiency: 80%Cuttings Slip Velocity: vsl : 25 ft/min
Required Net transport velocity: vt : 60 ft/minLast casing set : 9 7/8” @ 12,000 ft.
Mud Data:Bingham plasticDial reading @ 300 rpm : 21Dial reading @ 600 rpm: 29Density: 15.5 ppg
Field data @ 12,000 ft while using 8 7/8” bit, 3-14 nozzles
Q, gpm
Pp, psi
300 2966
400 4883
Solution :
Total bit nozzle area:
TFA: (3*/4)*(14/32)2 = 0.4509 in2
Bit pressure losses at 300 and 400 gpm:
Pb = 8.311*10-5*15.5*3002/ (0.952*0.45092)=632 psi
Pb = 8.311*10-5*15.5*4002/ (0.952*0.45092)=1123 psi
Parasitic pressure losses at 300 and 400 gpm:
PD @ 300 gpm = 2966-632 = 2334 psi
PD @ 400 gpm = 4883-1123 = 3760 psi
The slope and the intercept of the PD vs.Q line:m = log(3760/2334) / Log (400/300) = 1.657C =2334/3001.657 = 0.18345
The maximum flow rate: Qmax = 1714*E*HPp/(Pp)max
= 1714*0.8*1600/5440 = 403 gpm
The minimum required flow rate:Qmin = 2.448*(Dh
2-Dp2)*vmin = 2.448*(9.8752-4.52)*(85/60)
= 268 gpm
Optimum Parasitic pressure losses using Maximum BHHP Criterion:(PD )opt = 5440/(1+1.657) = 2047 psi
Optimum bit pressure drop: (Pb )opt = 5440-2047 = 3393 psi
Optimum Flow Rate: Qopt = (2047/0.18345)1/1.657 = 277 gpm
Qmax > Qopt > Qmin , Region – 2 in optimum hydraulic path!
Optimum nozzle area:
TFA = (8.311*10-5*15.5* 2772/(0.952*3393))0.5 = 0.1797 in2
For 3 equal-sized nozzles the diameter will be:
dn = (0.1797*4*322/(3*))0.5 = 8.83
Therefore 3 - 9/32 in nozzles need to be installed for the next bit run.