Arch. Min. Sci., Vol. 52 (2007), No 4, p. 457–481

.
Arch. Min. Sci., Vol. 52 (2007), No 4, p. 457–481
457
HERNAN DIAZ*, MENGJIAO YU*, STEFAN MISKA*, NICHOLAS TAKACH*
MODELING OF ECD IN CASING DRILLING OPERATIONS AND COMPARISON
WITH EXPERIMENTAL AND FIELD DATA
MODELOWANIE ECD W WIERCENIU Z RÓWNOCZESNYM RUROWANIEM WRAZ
Z PORÓWNANIEM DANYCH EKSPERYMENTALNYCH I TERENOWYCH
Three modeling approaches to the determination of equivalent circulating density (ECD) in Casing
Drilling1 operations are considered in this study; viz., hook-load measurements, pump-pressure measurements and conventional hydraulic models. The bottom-hole pressure is obtained by adding the calculated
annular pressure losses to the hydrostatic pressure. Since the annular clearance is very small in casing
drilling, a narrow-slot flow approximation model is adopted that takes into account the effect of pipe
rotation. A Yield-Power-Law (YPL) drilling fluid is considered in this study.
Results from each of the three approaches are compared with experimental and field data. The differences between the calculated and measured bottom-hole pressures (hence ECD) are within a range of
about ±8%. In terms of the frictional pressure losses in the annulus, this range increases to about ±60%
in some instances.
It is shown that pipe rotation plays an important role in determining ECD. The experimental data
indicate an increase in the annular pressure losses with increasing pipe rotary speed. The hook-load
measurements correlate well with flowing bottom-hole pressures.
Keywords: ECD, Casing Drilling, Modeling, Field Data
W artykule rozważono trzy podejścia do modelowań wykonywanych w celu określenia ekwiwalentnej
gęstości cyrkulacyjnej (ECD) w operacjach wiercenia z równoczesnym rurowaniem1; poprzez pomiary
obciążenia haka, pomiary ciśnienia pomp oraz zastosowanie konwencjonalnych modeli hydraulicznych.
Ciśnienie na dnie otworu otrzymywane jest przez dodanie obliczonych strat ciśnienia w przestrzeni pierścieniowej do ciśnienia hydrostatycznego. W przypadku rur okładzinowych wielkość przestrzeni pierścieniowej
jest bardzo niewielka, dlatego zaadaptowano model wąskiej szczeliny, uwzględniający efekt rotacji rur.
W artykule rozważano płuczkę opisywaną modelem reologicznym Herschela Bulkleya (YPL).
Wyniki zastosowania wymienionych trzech podejść zostały porównane z danymi doświadczalnymi
i terenowymi. Różnice pomiędzy wartościami ciśnienia obliczonego i zmierzonego na dnie otworu (a więc
*
THE UNIVERSITY OF TULSA, TULSA, OK 74104-3189, USA
1
Casing Drilling is a registered trademark of Tesco Corp.
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i ekwiwalentnej gęstości cyrkulacyjnej) pozostają na poziomie ok. ±8%. W przypadku strat ciśnienia
w przestrzeni pierścieniowej w niektórych przypadkach wartość ta ulega zwiększeniu do ok. ±60%
Zwrócono uwagę, że rotacja rur odgrywa dużą rolę w określaniu ekwiwalentnej gęstości cyrkulacji.
Dane doświadczalne wskazują na wzrost strat ciśnienia w przestrzeni pierścieniowej wraz z rosnącą
prędkością obrotową rur. Uzyskano dobrą korelację między pomiarami obciążenia haka i ciśnienia
przepływu na dnie otworu.
Słowa kluczowe: ECD, wiercenie z równoczesnym rurowaniem, modelowanie, dane terenowe
Nomenclature
A
− annular area, L2, in2
Ai
− area of casing based on internal diameter, L2, in2
An
− area of drill bit nozzles, L2, in2
Ao
− area of casing base on outside diameter, L2, in2
Cv
− in situ cuttings concentration, dimensionless
D
− depth, L, ft
Deff − generalized “effective” diameter, L, in
Dh
− wellbore diameter, L, in
Dhy − Do-Di, hydraulic diameter, L, in
Di, Di1, Di2 − casing internal diameter, L, in
Do
− casing O.D., L, in
Fb
− force due to buoyancy, mL/t2, lbf
Fbit − jetting force, mL/t2, lbf
Fd
− drag force, mL/t2, lbf
− hook load, mL/t2, lbf
Fh
Fp
− force due to piston effect, mL/t2, lbf
f
− friction factor without pipe rotation, dimensionless
f’
− friction factor with pipe rotation, dimensionless
fh
− friction factor at the borehole wall, dimensionless
fo
− friction factor at the casing wall, dimensionless
g
− acceleration due to gravity, L/t2, 9.81 m/s2
K
− Consistency index, mtm–2/L, lbf sm/ft2
Lj
− section casing length, L, ft
m
− flow behavior index of Yield Power Law model, dimensionless
N
− Generalized flow behavior index, dimensionless
NRe − Reynolds number, dimensionless
Ph
− hydrostatic pressure, m/Lt2, psi
Q
− flow rate, L3/t, gal/min
ReYPL − Reynolds Number for Yeild-Power-Law fluids, dimensionless
ri
− casing radius, L, in
rpm − casing rotary speed, rev./min
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u
− mean tangential velocity, L/t, ft/s
vsp
− superficial cuttings velocity, L/t, ft/s
vslip − slip velocity, L/t, ft/s
− mixture velocity, L/t, ft/s
vm
v
− mean axial velocity, L/t, ft/s
Wc
− casing weight in the air, mL/t2, lbf
Wj
− unit weight of casing, m/t2, lbs/ft
wob − weight on bit, mL/t2, lbf
(∆P)ω=0 − pressure drop without pipe rotation, m/Lt2, psi
(∆P)ω
− pressure drop with pipe rotation, m/Lt2, psi
(∆P)bit
− pressure drop through the bit, m/Lt2, psi
∆Pfa, ∆Pa − frictional pressure losses, m/Lt2, psi
æ wr æ
a = arctan ç i ç
è 2v è
γw
− shear rate, t–1, s–1
η
− apparent viscosity, m/Lt, cp
µ
− viscosity, m/Lt, cp
π
− 3.14159…
− equivalent density due to frictional pressure losses, m/L3, lbm/gal
ρfa
ρι
− density inside casing, m/L3, lbm/gal
ρ1
− mud density, m/L3, lbm/gal
ρmh − mixture density, m/L3, lbm/gal
ρο
− density outside casing, m/L3, lbm/gal
ρp
− cuttings density, m/L3, lbm/gal
τi
− wall shear stress in pipe, m/Lt2, psi
τo
− average wall shear stress in annulus, m/Lt2, psi
− wall shear stress, m/Lt2, psi
τw
τy
− yield stress, m/Lt2, psi
ω
− angular velocity, rad/s
1. Introduction
Casing drilling uses a casing string to drill, evaluate and case a well simultaneously.
This technology bypasses some time-consuming steps of conventional drilling that may
take up to 35% of the total time to drill a well (Tessari, 1999; Tarr, 1999). It has been
estimated that casing drilling has the potential to reduce the costs of conventional rotary
drilling by approximately 15% (Tarr, 1999).
The well geometry in casing drilling is a major difference from conventional drilling.
The ratio of hole to pipe diameter is close to unity. The internal diameter of a casing is
460
large so that there is relatively little pressure loss inside the casing. However, the casing
drilling annulus provides more restricted flow so that higher than normal pressure losses
are encountered. Analogies can be drawn to slim-hole hydraulics. It is well documented
(Tao, 1954; DiPrima, 1960; Ustimenko, 1964; Cartalos, 1993; Haciislamoglu, 1994; Hansen, 1999; McCann, 1993) that the narrow clearance between drill pipe and the wellbore
plays an important role in determining the frictional pressure losses in slimhole drilling.
The determination of the flowing bottom hole pressure (hence ECD), during drilling
operations, is an important task of the drilling engineer. In most casing drilling situations
the ECD will be higher than the ECD in conventional drilling, even though a lower flow
rate may be used. ECD is determined using the following equation:
ECD =
Ph + D Pfa
Dg
= rmh + rfa
(1)
The hydrostatic pressure is determined by the average density of mud and cuttings
in the annulus. The frictional pressure losses depend on the borehole geometry, the flow
regime, pipe rotation and drillstring dynamics. In the case of casing drilling the in situ
cuttings concentration may be higher than in conventional drilling due to lower flow
rates and the frictional pressure losses are higher than conventional drilling because of
the narrow clearance between casing and the wellbore. And while the influence of drill
pipe rotation on hole cleaning and ECD has been widely recognized in conventional
drilling (Walker, 1970; Luo, 1989; Lockett, 1993; Hansen, 1995; Wei, 1997; Ooms,
1999; Sterri, 2000; Bailey, 2000), very little is known about the effects of pipe rotation
on ECD in casing drilling operations.
Although casing drilling has been identified as a technology that can potentially solve
many problems in conventional drilling operations, a better understanding of hydraulics
is needed to improve the efficiency of this technology (Tarr, 1999).
In order to obtain a better understanding of the factors that affect ECD in casing
drilling operations, experimental and field data provided to the authors are analyzed
using the models presented in this paper. Particular emphasis is placed on the effect of
pipe rotary speed on ECD.
2. Mathematical Modeling
2.1. Calculation of Hydrostatic Pressure
The hydrostatic pressure can be computed from:
Ph = g ( rl (1 - CV ) + rp CV ) D
(2)
where the in situ cuttings concentration in an annulus, CV, can be determined by the
following equation:
461
2
CV =
æ
æ
vsp 1 æ vM
1 æç vM
- 1ç +
- ç
- 1ç
4 çè vslip çè
vslip 2 çè vslip çè
(3)
For small values of Cv, the average slip velocity, vslip, can be assumed to equal the terminal settling velocity. In this paper the settling velocity was calculated from Chien’s
(Chien, 1992) correlations. A detailed derivation was provided by Diaz (Diaz, 2002)
2 . 2 . C a l c u l a t i o n o f A n n u l a r P r e s s u r e L o s s e s f o r a Yi e l d - P o w e r Law Fluid with Pipe Rotation Using Narrow Slot
Approximation
Tao and Donovan (Tao, 1954) proposed the following equation to determine the
pressure losses in a small clearance for a Newtonian fluid.
(D P)w =
f ' (D P)w = 0
f cos a
(4)
This model can be extended for a non-Newtonian fluid if f, f’ and (∆P)ω are calculated using a model for non-Newtonian fluid flow in the annulus. In our study Tao and
Donovan’s model was extended to calculate frictional pressure losses in the annulus for
Yield Power Law fluids using the narrow slot approximation approach. A computational
procedure is shown in Appendix A.
2.3. Calculation of Annular Pressure Losses Using Hook Load
Measurements
During casing drilling operations a noticeable reduction in the hook-load is observed.
This reduction is caused by the upward forces on the outside surface of the casing due
to fluid flowing in the annulus. Thus, this hydraulic lift may be used to estimate the
pressure losses in the annulus.
In order to develop the relationship between hook-load and annular pressure we
assume a casing string composed of two casing sizes, with different lengths and unit
weights. The densities inside and outside the casing are different due to the presence of
cuttings in the annulus. Steady state flow is assumed and convective acceleration terms
are neglected.
From a force balance of the casing drilling string we obtain (see Appendix B):
Fh = Wc Fb Fd Fp – Fbit wob
(5)
The contribution of the factors that cause the reduction of hook load is shown in
Fig. 1. Calculations were done for a depth of 6720 , weight on bit of 10780 lbs, flow rate
of 351 gpm and rate of penetration of 57 ft/hr. The values of these parameters change
462
as the well is drilled. However, the distribution of the effects on the hook load does not
change much. Therefore, the trend can be extended to different conditions. The principal
causes of reduction of hook load are buoyancy, weight on the bit and the piston effect.
From the result obtained with Equation 5, the jetting force is too small to be considered
an important factor. In addition, the contribution of drag force in reduction of the hook
load is not large. The difference of pressure at the end of each section, which causes
the piston effect, depends on many variables such as hole geometry, hole eccentricity,
drill string dynamics and pipe rotation. Thus, in casing drilling operations the hook load
measurement offers a way to estimate the bottom hole pressure.
14000
36.1%
12000
31.4%
Ibs
10000
24.3%
8000
6000
4000
7.8%
2000
0.4%
0
bouyancy
drag
piston
jetting force
wob
effect
Fig. 1. Factors causing reduction in hook load
Rys. 1. Czynniki wpływające na zmniejszenie obciążenia haka
The average shear stresses at the casing wall, τoj, can be related to the annular pressure drops, ∆Paj, through a force balance of forces acting on casing in the annulus (see
Appendix B). Equation 5 can be written in a general form for a casing string composed
of “m” sections as:
m
Fh =
å [w L
j
j
- g ( roj Aoj - r i Aij ) L j -
j =1
p
Dh Doj D Paj ] - D Pbit An - wob
4
(6)
Equation 6 can be used to obtain an expression for the change in hook load, ∆Fh, due
to fluid flowing in the annulus. For a string composed of one casing size the change in
hook load can be determined by the following equation:
D Fh =
p
Dh Do D Pa
4
Warren (2001) derived a similar equation for the same case
(7)
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æ
æ
ç
ç
2
2
ç
p ç Dh - Do
+ Do2ç D Pa
D Fh = ç
4 ç æ fh æ æ Dh æ
ç
1+ ç çç ç
ç ç f çç D ç
ç
è è o èè o è
è
(8)
where fh and fo are the friction factors at the borehole wall and casing wall, respectively. Instead of defining an average friction factor, Warren (Warren, 2001) used different
friction factors for the borehole and the casing wall. Both friction factors were calculated using the same Reynolds number, but different wall roughness. When fh and fo are
equal (as is the case when assuming an average friction factor) Equation 8 reduces to
Equation 7.
2.4. Calculation of Bottom Hole Pressure Using Surface Pump
Pressure Measurements
Bottom hole pressure can be calculated from surface pump pressures. Pressure losses
inside the casing are computed using the conventional model for flow in pipes. The pressure drops through the bit and the surface equipment are calculated using the methods
provided in Applied Drilling Engineering (Bourgoyne, 1986). The bottom hole pressure
can be determined by subtracting all these pressure losses from the pump pressure.
2.5. Experimental Data
The Baker Hughes Experimental Test Area (BETA) is located about 20 miles south
of Tulsa, Oklahoma. The data was collected by MoBPTeCh Alliance and provided to
TUDRP (The University of Tulsa Drilling Research Project) as a courtesy of Hughes
Christensen.
2 . 5 . 1 . C a s e d H o l e Te s t s
The well bore schematic is shown in Fig. 2. Three predetermined flow rates, 550 gpm,
450 gpm and 350 gpm of water, were used with the casing rotating at different rates (0,
60, 120 and 180 RPM). The test was repeated using bentonite/water muds of 9 ppg and
10 ppg. Down hole and standpipe pressures were recorded during these tests.
2 . 5 . 2 . D r i l l i n g Te s t s
During the test the flow rate was kept constant at 540 gpm and the rpm and WOB
were changed. The BHA was comprised of the 12 Ľ” bit with TFA 0.746. More detailed
information can be found in Diaz s work (Diaz, 2002).
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Flow outlet @ -1.50’
Hole cased with 13 1/4 ”, 68 #/ft
Ground level @ -12’
11 3/4 ”
drilling casing
Length = 201.13’
BHA length = 60.6’
Bottom of bit @ -282.85
Top of cement @ -300.29’
Casing Shoe @-325’
Fig. 2. Schematic of BETA Wellbore. (Courtesy of BETA facilities)
Fig. 2. Schemat otworu BETA (za zgodą firmy BETA)
2.5.3. Calculation of Bottom Hole Pressure
Three methods were used to estimate the bottom hole pressure. The results of each
method were compared with the field data obtained from the MDP tool. The bottom
hole pressure was finally obtained by adding the calculated annular pressure losses to
the hydrostatic pressure. These methods are as follows:
Method 1: The annular pressure losses are obtained from the measured hook load
using Equation 8.
Method 2: The annular pressure losses are obtained from the measured hook load
using Equation 7.
Method 3: The annular pressure loss is calculated using a narrow slot flow approximation for a Yield-Power-Law fluid. The effect of pipe rotation is included using
an extension of Tao-Donovan s (Tao, 1954) approach for non-Newtonian fluids
(Appendix A).
2.6. Field Data
BP drilled 15 gas wells (Shepard, 2001 and Shepard 2002) using the Tesco Casing
Drilling process in the Wamsutter area of Wyoming. Data was collected while the
production hole was drilled. This data is from a well that we call “Well 1”. The pump
pressure, rpm, ROP, flow rate and hook load measurements were recorded. A schematic
of the well is shown in Fig. 3. Casing string configuration, drilling fluid properties, and
cuttings properties can be found in Tables 1 and 2.
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4 1/2 ’’, 11.6 ppf
casing
7’’,23ppf
@1179’
6 1/4 ’’ Hole
5’’,23ppf
casing
L1 = 1536’
Fig. 3. Schematic of Well 1
Rys. 3. Schemat otworu 1
TABLE 1
Casing String Data
TABLICA 1
Dane techniczne kolumny rur okładzinowych
section no
2
1
Bit
O.D
in
4.50
5.00
6.25
I.D.
Unit Weight
in
lbs/ft
4.00
11.60
4.04
23.20
( 2x13/32 + 3x14/32)
Length
ft
to surface
1536
TABLE 2
Fluid and Cuttings Properties
TABLICA 2
Właściwości płynu i zwiercin
Fluid
Density
ppg
8.33
Viscosity
cp
1
Cutting
Specific Gravity
Diameter
in
2.6
0.25
466
The data collected in the tests was provided to TUDRP (The University of Tulsa
Drilling Research Project) as a courtesy of BP-Tesco.
2.6.1. Calculation of Bottom Hole Pressure
In order to analyze this field data, Methods 2 and 3, described in the previous section,
are used. The pump pressure measurements were also used to estimate the BHP. This
approach is referenced to as Method 4.
3. Discussion of Results
Water and two muds, Muds A and B, were used in the tests. The average rheological
properties of these fluids are listed in Table 3. The Reynolds numbers for different flow
rates and types of fluids were calculated and are shown in Table 4. The flow regime is
fully turbulent for water at all flow rates. For Mud A the flow regime is also turbulent,
but close to the transitional region. The flow regime for Mud B is laminar below 450 gpm
and transitional to turbulent above this flow rate.
TABLE 3
Average Properties of Muds
TABLICA 3
Średnie właściwości płuczek
Fluid
Density (ppg)
A
B
8.7
9.8
600
11
35
Fann Viscometer Reading
300 200 100
6
7
6
4
1
23
18
12
3
3
1
3
TABLE 4
Generalized Reynolds Number
TABLICA 4
Uogólniona liczba Reynoldsa
Q (GPM)
350
450
550
Water
29836
38360
46885
Generalized Reynolds Number
Mud A
Mud B
4972
1765
7089
2500
9402
3298
Figs. 4 to 6 show the bottom hole pressure as a function of the casing rotary speed at
different water flow rates (350 gpm, 450 gpm and 550 gpm). Both model predictions show
a similar trend compared to the experimental data: the annular pressure losses increase
467
as pipe rotary speed increases. The results obtained from the hook load measurement
show a better agreement with the experimental data as compared to the predictions using
the narrow slot approximation.
Bottom hole pressure, psi
140
136
132
128
MDP tool
Method 1
Method 2
Method 3
124
120
0
60
120
180
RPM
Fig. 4. Bottom hole pressure vs. rotary speed.
Water, Dh = 12.715”, OD = 11.75”, TD = 283’, Q = 350 gpm
Rys. 4. Zależność ciśnienia na dnie otworu od prędkości obrotowej.
Woda, Dh = 12.715”, OD = 11.75”, TD = 283’, Q = 350 gpm
Bottom hole pressure, psi
145
140
135
MDP tool
Method 1
Method 2
Method 3
130
0
60
120
180
RPM
Fig. 5. Bottom hole pressure vs. rotary speed.
Water, Dh = 12.715”, OD = 11.75”, TD = 283’, Q = 450 gpm
Rys. 5. Zależność ciśnienia na dnie otworu od prędkości obrotowej.
Woda, Dh = 12.715”, OD = 11.75”, TD = 283’, Q = 450 gpm
468
Bottom hole pressure, psi
160
155
150
145
MDP tool
Method 1
Method 2
Method 3
140
135
0
60
120
180
RPM
Fig. 6. Bottom hole pressure vs. rotary speed.
Water, Dh = 12.715”, OD = 11.75”, TD = 283’, Q = 550 gpm
Rys. 6. Zależność ciśnienia na dnie otworu od prędkości obrotowej.
Woda, Dh = 12.715”, OD = 11.75”, TD = 283’, Q = 550 gpm
The differences between the calculated and measured bottom-hole pressures (hence
ECD) are within a range of about ±8%. However, in terms of the frictional pressure
losses in the annulus, this range increases to about ±60%.
Similar tests were conducted using Muds A and B. Figs. 7 to 9 show the bottom hole
pressure as a function of rotary speed. The model predictions and measured data show
trends similar to those observed in the water tests. Again, the results obtained from the
hook load measurements show better agreement with the experimental data as compared
to the narrow slot approximation.
The difference between the calculated and measured bottom-hole pressures are within
a range of about ±8%. However, in terms of the frictional pressure losses in the annulus,
about ±40% difference is obtained.
Another fluid, Mud B, was tested in this study at the same flow rates (350 gpm,
450 gpm and 550 gpm). Fig. 10 shows the bottom hole pressure as a function of rotary
speed at a flow rate of 350gpm. The axial flow is laminar under this test condition. The
predicted pressure losses obtained from Method 3 decrease as pipe rotary speed increases. These results agree well with the theoretical (Haciislamoglu, 1994; Hansen, 1995)
and experimental (Cartalos, 1993; Luo, 1989) results for laminar helical flow of a shear
thinning fluid in a concentric pipe. However, the experimental data shows an increase
in the annular pressure losses when the casing rotary speed increases. The flow of Mud
B becomes less laminar with increasing rotary speeds of the casing. Again, a better
agreement was obtained from the hook load measurements.
469
Bottom hole pressure, psi
145
141
137
133
MDP tool
Method 1
Method 2
Method 3
129
125
0
60
120
RPM
Fig. 7. Bottom hole pressure vs. rotary speed.
Mud A, Dh = 12.715”, OD = 11.75”, TD = 283’, Q = 350 gpm
Rys. 7. Zależność ciśnienia na dnie otworu od prędkości obrotowej.
Płuczka A, Dh = 12.715”, OD = 11.75”, TD = 283’, Q = 350 gpm
Bottom hole pressure, psi
155
150
145
140
MDP tool
Method 1
Method 2
Method 3
135
0
60
120
180
RPM
Fig. 8. Bottom hole pressure vs. rotary speed.
Mud A, Dh = 12.715”, OD = 11.75”, TD = 283’, Q = 450 gpm
Rys. 8. Zależność ciśnienia na dnie otworu od prędkości obrotowej.
Płuczka A, Dh = 12.715”, OD = 11.75”, TD = 283’, Q = 450 gpm
470
Bottom hole pressure, psi
170
165
160
155
MDP tool
Method 1
Method 2
Method 3
150
145
0
60
120
180
RPM
Fig. 9. Bottom hole pressure vs. rotary speed.
Mud A, Dh = 12.715”, OD = 11.75”, TD = 283’, Q = 550 gpm
Rys. 9. Zależność ciśnienia na dnie otworu od prędkości obrotowej.
Płuczka A, Dh = 12.715”, OD = 11.75”, TD = 283’, Q = 550 gpm
168
Bottom hole pressure, psi
164
160
156
152
MDP tool
Method 1
Method 2
Method 3
148
144
0
60
120
180
RPM
Fig. 10. Bottom hole pressure vs. rotary speed.
Mud B, Dh = 12.715”, OD = 11.75”, TD = 283’, Q = 350 gpm
Rys. 10. Zależność ciśnienia na dnie otworu od prędkości obrotowej.
Płuczka B, Dh = 12.715”, OD = 11.75”, TD = 283’, Q = 350 gpm
Figs. 11 and 12 show the results for Mud B at the flow rates of 450 gpm and 550
gpm, respectively. The flow regime is turbulent when the flow rates go beyond 450 gpm.
471
Similar trends were observed and the results using hook load data are better than the
predictions using narrow slot approximation.
190
Bottom hole pressure, psi
185
180
175
170
MDP tool
Method 1
Method 2
Method 3
165
160
0
60
120
180
RPM
Fig. 11. Bottom hole pressure vs. rotary speed.
Mud B, Dh = 12.715”, OD = 11.75”, TD = 283’, Q = 450 gpm
Rys. 11. Zależność ciśnienia na dnie otworu od prędkości obrotowej.
Płuczka B, Dh = 12.715”, OD = 11.75”, TD = 283’, Q = 450 gpm
Bottom hole pressure, psi
205
200
195
190
185
MDP tool
Method 1
Method 2
Method 3
180
175
0
60
120
180
RPM
Fig. 12. Bottom hole pressure vs. rotary speed.
Mud B, Dh = 12.715”, OD = 11.75”, TD = 283’, Q = 550 gpm.
Rys. 12. Zależność ciśnienia na dnie otworu od prędkości obrotowej.
Płuczka B, Dh = 12.715”, OD = 11.75”, TD = 283’, Q = 550 gpm
472
The differences between the calculated and measured bottom-hole pressures are
within a range of about ±20% for Mud B. However, in terms of the frictional pressure
losses in the annulus, this range increases to about ±40%.
A flow test was conducted in which the flow rate was kept constant at 540 gpm but
the rotary speed and WOB were changed. The properties of the fluids used are shown
in Table 5.
TABLE 5
Properties of Muds Used in Drilling Test
TABLICA 5
Właściwości płuczek użytych w badaniach wiertniczych
Fluid
Density ppg
C
D
9.3
9.7
600
18
29
Fann Viscometer Reading
300
200
100
6
10
7
4
1
19
13
9
1
3
1
1
The measured and calculated bottom hole pressure for the interval from 435’ to 665’
are shown in Fig. 13 when Mud C was used in the test. Both Method 2 and Method 3
over-predict the bottom hole pressure.
400
Bottom hole pressure, psi
380
360
340
320
300
280
260
240
MDP tool
Method 2
Method 3
220
200
415
465
515
565
615
665
715
Depth, ft
Fig. 13. Bottom hole pressure vs. depth. BETA drilling tests.
Mud C, Interval: 435’-665’, Dh = 12.25”, OD = 10.75”, Q = 540 gpm
Rys. 13. Zależność ciśnienia na dnie otworu od głębokości.
Badanie otworu BETA. Płuczka C, Interwał: 435’-665’, Dh = 12.25”, OD = 10.75”, Q = 540 gpm
473
Similar tests were conducted with Mud D. Fig. 14 shows the bottom hole pressure,
measured and calculated values for the interval from 665’ to 887’ (TD). Both models
under-predict the bottom hole pressure in this interval.
Bottom hole pressure, psi
600
550
500
450
400
350
650
MDP tool
Method 2
Method 3
700
750
800
850
900
Depth, ft
Fig. 14. Bottom hole pressure vs. depth. BETA drilling tests.
Mud D, Interval: 665’-887’, Dh = 12.25”, OD = 10.75”, Q = 540 gpm
Rys. 14. Zależność ciśnienia na dnie otworu od głębokości.
Badanie otworu BETA. Płuczka D, Interwał: 665’-887’, Dh = 12.25”, OD = 10.75”, Q = 540 gpm
5000
Bottom hole pressure, psi
4500
4000
3500
3000
2500
Method 2
Method 3
Method 4
2000
1500
2800
3800
4800
5800
6800
7800
8800
Depth, ft
Fig. 15. Bottom hole pressure as a function of depth.
Well 1. Water, Interval: 2850’-9070’, Dh = 6.25”, OD1 = 5”, OD2 = 4.5”
Rys. 15. Ciśnienie na dnie otworu jako funkcja głębokości.
Otwór 1. Woda, Interwał: 2850’-9070’, Dh = 6.25“, OD1 = 5“, OD2 = 4.5“
474
Fig. 15 is a plot of the bottom hole pressure as a function of depth for the interval from
2850 ft to 9070 ft. Water was used as the drilling fluid in this test. The results obtained
using Methods 2 and 3 are similar. The bottom hole pressure obtained from Method 4
(using pump pressure measurements) is greater than the values obtained from the other
two methods (using hook load measurements and narrow slot approximation).
4. Concluding Remarks
Three modeling approaches are proposed and evaluated in this paper for estimating
ECD in Casing Drilling operations:
1. A mathematical model for estimation of bottom hole pressure using hook load
measurements;
2. An extension of Tao and Donovan s method for calculating pressure losses, using
the narrow slot approximation approach;
3. Use of surface pump pressures for estimation of bottom hole pressure.
Experimental data was analyzed to estimate the bottom-hole pressure by adding the
calculated annular pressure losses to the hydrostatic pressure.
Comparisons of the models with the experimental data show good agreement. The
differences between the calculated and measured flowing bottom hole pressure are within
a range of about 8%. However, in terms of the frictional pressure losses in the annulus,
this range increases up to about 60%. These frictional pressure losses represent about
10-30% of the total bottom hole pressure.
It is shown in this study that pipe rotation plays an important role in determining the
Equivalent Circulating Density in the annulus of a wellbore. The experimental results
indicate that an increase in the annular pressure losses is observed with increasing pipe
rotary speed.
The hook-load measurements correlate well with flowing bottom-hole pressures.
Hook load measurements as well as surface pump pressure measurements can be
used to determine the bottom hole pressure (hence Equivalent Circulating Density) in
casing drilling operations.
Acknowledgement
We would like to express our appreciation to Peter Bern of BP, Allen Sinor of Hughes
Christensen, Tommy Warren of Tesco, the MoBPTeCh Alliance and Tulsa University
Drilling Research Projects for making this study possible.
This paper was originally presented as SPE 87149 at the SPE IADC Meeting held
in Dallas TX in March 2-4 2004.
475
REFERENCES
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SPE 56638, presented at the Annual Meeting.
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Received: 03 September 2007
476
Appendix A
Procedure for calculating effect of pipe rotation on pressure losses
Suppose we have a yield power law fluid and are given the following data: Do, Di,
Q, ρ, k, m, τy and rpm.
Then we:
Calculate the angular velocity, ω
2p
rpm
60
A.1
Q
A
A.2
w ri w Di
=
2
4
A.3
w=
Calculate mean axial velocity, ν:
v=
Calculate mean tangential velocity, u:
u=
Calculate shear stress at the wall, τw from:
1+ m
(t w - t y ) m æ 3m æ æ
12v
m
æ
=
t yç
ç
ç çt w +
1
Do - Di
1+ m è
è 1 + 2m è è
K m t w2
A.4
Calculate wall Shear Rate, γ·w:
1
æt -t æ m
g&w = çç w y çç
è K è
A.5
Calculate Generalized Fluid Behavior Index, N from:
g&w =
1 + 2N 12V
3 N Do - Di
A.6
Calculate Reynolds Number, ReYPL:
N Re, slot =
Deff r v
h
A.7
477
where:
Deff =
3N æ 2
æ
ç Dh y ç
1 + 2N è 3
è
h=
t w , av
gw
A.8
A.9
Determine whether flow is Laminar or Turbulent:
If N Re, slot < (N Re )cr Þ Laminar flow
Otherwise, flow is Turbulent
Calculate friction factor, f:
For laminar flow,
f =
2t w
16
=
2
N Re, slot
rV
A.10
For turbulent flow, find f from:
N
é
1- ù
1
4
0.4
= 0.75 Log10 êRe YPL f 2 ú - 1.2
N
f
êë
ûú N
A.11
æ dP æ
Calculate annular pressure drop gradient without rotation, ç ç :
è dl èw = 0
4t
2 fr v 2
æ dP æ
ç ç = w =
Dhy
è dl èw = 0 Dhy
A.12
Where Dhy is hydraulic diameter Do – Di
Calculate annular pressure drops, (dP)ω=0:
(dP)w = 0 =
2 fr v 2
dL
Dhy
A.13
Calculate v' = v sec α, where
æ wr æ
a = arctan ç i ç
è 2v è
A.14
We substitute v = v' and repeat the above calculations. The annular pressure loss with
the effect of pipe rotation is:
(dp)w =
f ' (dP)w = 0
f cos a
A.15
478
APPENDIX B
Relationship between hook load and annular pressure drops
In order to develop this relationship we assume:
• Casing string composed of two casing sizes, with different lengths and unit weights.
• The densities inside and outside the casing are different, due to the presence of
cuttings in the annulus.
• Steady state and acceleration terms are neglected.
From force balances at different sections of a casing drilling string we obtain:
At the bottom of the first section (Fig. B.1):
F b + (P b + D Pbit)( Ai1 - An ) - P b (Ao1 - An ) = 0
B.1
F b = P b(Ao1 - Ai1) - D Pbit (An - Ai1)
B.2
At the top of the second section (Fig. B.2):
F T - P T Ai 2 - Fh = 0
B.3
F T = P T Ai 2 + Fh
B.4
From a force balance of the whole string, we get (Fig. B.3):
Fb
Fb
Fh
PT
pump
Pcb
wob
PB
Ft
Ft
Fig. B.1. Boundary condition at the
bottom of the 1st section
Fig. B.2. Boundary condition at the
top of 2dn section
Rys. B.1. Warunki graniczne w dolnej
części 1-ej sekcji przewodu
Rys. B.2. Warunki graniczne w górnej
części 2-giej sekcji przewodu
479
F T - w1 L1 - w2 L 2 + Pc12 (Ai1 - Ai 2) - Po12 (Ao1 - Ao 2 ) +
to1p Do1 L1 - t i1p Di1 L1+ t o 2 p Do 2 L 2 - t i2p Di 2 L 2 + F b = 0
B.5
where:
P T = D Pc1 + D Pc 2 + D Pbit + D Pa1 + D Pa 2 +
g ( ro1 - ri ) L1 + g ( ro 2 - ri ) L2
B.6
P b = D Pa1 + D Pa 2 + g ro1 L1 + g ro 2 L 2
B.7
Pc12 = D Pc1 + D Pbit + D Pa1 + D Pa 2 +
g ( ro1 - ri ) L1 + g ( ro 2 - ri ) L2 + g ri L2
Pa12 = D Pa 2 + g ro 2 L2
Ft
W2
t o2
t i2
Section 2, L 2
Pa12
Pc12
t o1
W1
Section 2, L 1
Fb
Fig. B.3. Force balance of a casing string
Rys. B.3. Bilans sił działających na przewód rur okładzinowych
B.8
B.9
480
From a balance of viscous forces acting on a fluid element in the pipe the following
equations are obtained (Fig. B.3):
t i1p Di1 L 1 = D Pc1 Ai1
B.10
t i 2 p Di 2 L2 = D Pc 2 Ai 2
B.11
Combining Eqns. B.1 to B.11 we have:
Fh = Wc Fb Fd Fp – Fbit wob
B.12
WC = w1 L1 + w2 L 2
B.13
Fb = g ( ro1 Ao1 - ri Ai1)L 1 + g (ro 2 Ao 2 - ri Ai ) L 2
B.14
Fd = t o1p Do1 L1 + t o 2p Do 2 L 2
B.15
Fp = D Pa1 Ao1 + D Pa 2 Ao 2
B.16
Fbit = D Pbit An
B.17
where
Casings weight in air:
Buoyancy effect:
Fluid drag:
Piston effect:
Jetting force
The average shear stresses at the casing wall, τoj, can be related to the annular pressure
drops, ∆Paj, through a balance of forces acting on a fluid element in the annulus. See Fig. B.4.
t oj
P+D Paj
P
rh
t oj
roj
Fig. B.4. Forces acting on a fluid element in the annular space
Rys. B.4. Rozkład sił działający na element płynu w przestrzeni pierścieniowej
481
Then, for annular flow:
t oj p (Dh + Doj ) L j @ D Paj
p 2
(Dh - Doj2 )
4
B.18
Thus, Eqn. B.15 can be rewritten as:
Fp =
Do1 p (Dh - Do1 )
D p (Dh - Do 2)
D Pa1 + o 2
D Pa 2
4
4
B.19
Combining Eqn. B.19 and Eqns B.12 through B.17 and rearranging:
Fh = w1 L1 + w2 L2 - g ( ro1 Ao1 - ri Ai1) L1- g ( ro 2 Ao 2 - ri Ai ) L2
-
p
p
Dh Do1 D Pa1 - Dh Do 2 D Pa 2 - D Pbit An - wob
4
4
B.20
In general, for a casing string of m sections:
Fh =
m
å[ w L
j
j =1
j
- g ( roj Aoj - ri Aij ) L j -
p
Dh Doj D Paj ] - D Pbit An - wob
4
B.21