RIG HYDRAULICS
This chapter covers the following items:
¾ Pressure losses
¾ Surface connection losses
¾ Pressure drop across the bit
¾ Optimization of bit hydraulics
¾ Surface pressure drop
¾ Hydraulic criteria
¾ Comparison of BHHP and IF
¾ Optimum flow rate
¾ Field methods for optimizing bit hydraulics
¾ A practical check of the efficiency of bit hydraulic program
Pressure Losses
¾ The circulation system consists of: pump, surface connections
(stand pipe, hose, swivel and Kelly), drill pipe, drill collars, bit,
annulus between drill collars and hole, annulus between drill
pipe and hole, mud return lines, and mud tanks.
¾ Friction of fluid through these parts causes pressure losses
¾ The calculation of this pressure losses depend on four parts
• Surface connection losses
• Pipe losses
• Annular losses
• Losses across the bit
¾ Losses depend on the type of fluid used and the type of flow
Surface Connection Losses
¾ Losses caused through surface connections
¾ Depend on the geometry and dimensions of surface connections
¾ These dimensions can vary with time
¾ Evaluated by:
P1 = Eρ0.8Q1.8(PV)0.2
P1
ρ
Q
psi or bar
= pressure loss, psi or bar
= Density, ppg or kg/l
= flow rate, gpm, l/min
PV = plastic viscosity, cp
E
= constant depends type of surface connections
Value of E
Surface Equipment
Type
1
2
3
4
Value of E
Imperial Units
Metric Units
-4
2.5x10
8.8x10-6
9.6x10-5
3.3x10-6
5.3x10-5
1.8x10-6
4.2x10-5
1.4x10-6
Four types of surface equipment
Rotary Hose Swivel
Kelly
Surface Stand Pipe
Equipment Length ID Length ID Length ID Length
Type
(Ft)
(in)
(Ft)
(in)
(Ft)
(in)
(Ft)
1
40
3.0
40
2.0
4
2.0
40
2
40
3.5
55
2.5
5
2.5
40
3
45
4.0
55
3.0
5
3.5
40
4
45
4.0
55
3.0
6
3.0
40
ID
(in)
2.25
3.25
3.25
4.00
Pipe and Annular Losses
¾ Pipe losses takes place inside drill pipe and drill collars
¾ They are designated as P2 and P3
¾ Annular losses takes place around drill collars and drill pipe
They are designated as P4 and P5
¾
¾ The magnitude of these pressures depends on
• Dimension of pipe
• Mud rheological properties, weight, plastic viscosity, and
yield point
• Type of flow, laminar or turbulent
¾ Several models exist to measure pressure losses
¾ Only two are models will be used: the Bingham plastic and the
power law
The following are the equations used for calculations
Bingham Plastic Model
Pipe Flow
¾ Determine average velocity
¾
Va = 24.5Q ft / min
D2
¾ Determine critical velocity
¾ Vc =
97 PV + 97 (PV )2 + 8.2 ρ D2YP
ft /min
ρD
¾ If Va > Vc, flow is turbulent; use
¾
−5 0.8 1.8
0.2
P = 8.91x10 ρ Q (PV ) L psi
D4.8
¾ If Va < Vc, flow is laminar; use
¾
P=
L ⎡⎢YP + (PV )Va ⎤⎥ psi
5D ⎥⎦
300D ⎢⎣
Annular flow
¾ Determine average velocity
¾
Q ft / min
Va = 24.5
Dh2 − ODp2
¾ Determine critical velocity
97 PV + 97 (PV )2 + 6.2 ρ De2YP
ft / min
¾ Vc =
ρ (Dh − ODp )
¾ If Va > Vc, flow is turbulent; use
−5 ρ 0.8Q1.8(PV )0.2 L
x
8.91
10
¾ P=
psi
3
1.8
(Dh − OD) (Dh + OD)
¾ If Va < Vc, flow is laminar; use
¾
P=
L(YP)
L(PV )Va
+
psi
60,000(Dh − OD)2 200(Dh −OD)2
Power Law Model
¾ Determine n and k
¾
¾
⎞
θ
n = 3.32log 600 ⎟⎟
θ
⎟
θ
⎛
⎜
⎜
⎜
⎝
300 ⎠
k = 300n
(511)
⎡ 5.82(104 )k ⎤
¾ Vc = ⎢
⎥
ρ
⎢
⎥
⎣
⎦
(1/(2−n))
1.6 3n+1⎤
.⎡⎢ .
⎥
⎣ D 4n ⎦
(n /(2−n))
¾ If Va >Vc flow is turbulent; use
¾
−5 0.8 1.8
0.2
P = 8.91x10 ρ Q (PV ) L psi
D4.8
¾ If Va < Vc flow is laminar; use
⎡1.6Va (3n +1) ⎤
⎥ psi
.
¾ P = kL ⎢
300D ⎢⎣ D
4n ⎥⎦
n
Annular flow
¾ Determine average velocity
ft /min
¾
Q ft / min
Va = 24.5
2
Dh − ODp2
¾ Determine critical velocity
4 ⎤
⎡
¾ Vc = ⎢ 5.82(10 )k ⎥
ρ
⎢
⎥
⎣
⎦
(1/(2−n))
⎡
1.6
3n+1⎤
.⎢
.
⎥
⎢⎣ (Dh −OD p ) 4n ⎥⎦
(n /(2−n))
ft / min
¾ If Va > Vc, flow is turbulent; use
¾
−5 0.8 1.8
0.2
P = 8.91x10 ρ Q (PV ) L psi
De4.8
¾ If Va < Vc, flow is laminar; use
n
⎡
1.6Va (3n +1) ⎤⎥
kL
⎢
psi
.
¾ P=
300(Dh − OD) ⎢⎢⎣ (Dh −OD) 4n ⎥⎥⎦
Pressure loss across bit
¾ Need to be optimized to achieve maximum cleaning
¾ For given length of drill string and given mud properties,
pressure from 1 to 5 remain constant
¾ The smaller the nozzle the greater the pressure drop
¾ For soft formation, large nozzle is required
¾ To calculate pressure loss across and nozzle size use
¾
P =P
− (P + P + P + P + P ) psi
bit stand pipe
¾ Nozzle velocity
P
¾ Vn = 33.36 bit ft / s
ρ
¾ Total area of nozzles
1
2
3
4
5
¾
A = 0.32 Q in2
Vn
¾ Nozzle size
¾
dn =
⎛
⎜
⎜⎜
⎝
4 A ⎞⎟.32
3π ⎟⎟⎠
OD
D
L
PV
YP
= outside diameter, in
= inside diameter, in
= length, ft
= plastic viscosity, cp
= yield value, lb/100ft2
Optimizing bit hydraulics
¾ All hydraulic programs start by calculating pressure drops in the
various parts of the circulating systems
¾ The pressure loss in the circulating system, except bit, is given
the symbol Pc
Several hydraulic slide rules are available for calculating Pc
¾
¾ The slide rule is inadequate for calculating annular pressure loss
¾ Either annular pressure loss is beyond the sale or flow is laminar
and most slide rules used turbulent flow
Surface pump pressure
¾ The system pressure shoes how much pressure loss can be
tolerated at bit
¾ The value of Pbit is controlled by the maximum allowable surface
pump pressure
¾ Most rigs have limits on maximum surface pressure with high
volume rates (500 gpm)
¾ On land rigs typical limits on surface pressure are in the rang
2500 to 3000 psi for well depth of around 12000 ft
¾ For deep wells, heavy-duty pump can give 5000 psi surface
pressure
¾ Therefore, optimization of bit hydraulics is necessary
Hydraulic criteria
¾ Two criteria for optimization
¾
¾
¾
¾
• Maximum bit hydraulic horsepower (BHHP)
• Maximum impact force (IF)
Each criteria yields different value of bit pressure loss
Engineer is faced with the task to decide which one to choose
In most drilling operations the circulation rate is kept constant
Pbit is the factor to be optimized
Maximum bit hydraulic horsepower
¾ The bit pressure is the difference between stand pipe pressure
and Pc
¾ For optimum hydraulic Pbit must be fraction of stand pipe
pressure
¾ Surface hydraulic horsepower (HHPs) is the sum of hydraulic
horse power at bit (BHHP) and hydraulic horsepower in the
circulating system (HHPc)
¾
BHPs= BHHP - HHPc
¾ BHHP = BHPs - HHPc
¾ Hence HHP = PQ/1714
¾ Then
¾
PQ PQ
BHHP = s − c
1714 1714
¾ Pc = KQn
K = constant
n = index represents degree of turbulence in the circulating
system
¾
n+1
PQ
BHHP = s − KQ
1714 1714
¾ Differentiating equation with respect to Q
¾ Ps
= (n+1)KQn
¾ Ps = (n+1) Pc
¾ Also
¾
¾
Pc
= Ps - Pbit
P = n Ps
bit n +1
¾ The value of n falls in the range 1.8 – 1.86
¾ For n = 1.86, Pbit = 0.65 Ps
¾ This means the for optimum hydraulic horsepower, the pressure
drop across the bit is 65% of surface pump pressure
¾ The actual value of n can be determined in fields by running the
pump pressure at several speeds and reading the resulting
pressure
¾ A graph of Pc=(Ps – Pbit) against Q is then drawn
¾ The slope of the graph is taken as the index n
Maximum impact force
¾
P = n Ps
bit n + 2
¾ Impact force is given by
Q ρP
bit
¾ IF =
58
Comparison of BHHP and IF criteria
¾ The ratio R, of pressure drop across bit is given by the BHHP
criteria and IF criteria
n P
R = n +1 s n
P
n+2 s
¾ or
R = n+2
n +1
¾ The following table shows the value of n and R
¾ It shows that R decreases parabolic ally with increasing value of
n, but never assumes unity
¾ It means that the pressure loss calculated by BHHP is greater
than that calculated by IF
R as a function of n
N
R
1
1.50
1.2
1.45
1.5
1.4o
1.8
1.36
2.0
1.33
Optimum flow rate
¾ Optimum flow rate is obtained by plotting circulating pressure
versus Q
¾ The intersection of optimum Pc with the curve gives the
optimum flow rate
Field method of optimizing bit hydraulics
¾ Prior to POH current bit for next bit change, run the pump at
four or five speeds and record the resulting stand pipe pressure
¾ From current nozzle size and stand pipe pressure and mud
weight determine pressure loss across the bit
¾ Subtract Pbit from stand pipe pressure to get Pc
¾ Plot a graph of Pc against Q on log-log paper and determine the
slope to get n
¾ For the next bit run calculate Pbit using BHHP or IF equations
¾ Select nozzle size to for the value of Pbit calculated
¾ For particular rig and field the index n will not vary widely if the
same parameters are used