ISSN 0104-6632 Printed in Brazil www.abeq.org.br/bjche Vol. 33, No. 01, pp. 91 - 104, January - March, 2016 dx.doi.org/10.1590/0104-6632.20160331s20150530 *To whom correspondence should be addressed Brazilian Journal of Chemical Engineering MODELING AND ANALYSIS OF UNSTEADY FLOW BEHAVIOR IN DEEPWATER CONTROLLED MUD-CAP DRILLING Jiwei Li 1* , Gonghui Liu 1,2 , Jun Li 1 and Mengbo Li 1,3 1 China University of Petroleum, College of Petroleum Engineering, Beijing 102249, China. Phone: + 86 010 89731225 E-mail: [email protected]2 Beijing University of Technology, Beijing 100192, China. 3 China National Offshore Oil Corporation Research Institute, Beijing 100010, China. (Submitted: August 24, 2015 ; Revised: November 13, 2015 ; Accepted: November 30, 2015) Abstract - A new mathematical model was developed in this study to simulate the unsteady flow in controlled mud-cap drilling systems. The model can predict the time-dependent flow inside the drill string and annulus after a circulation break. This model consists of the continuity and momentum equations solved using the explicit Euler method. The model considers both Newtonian and non-Newtonian fluids flowing inside the drill string and annular space. The model predicts the transient flow velocity of mud, the equilibrium time, and the change in the bottom hole pressure (BHP) during the unsteady flow. The model was verified using data from U-tube flow experiments reported in the literature. The result shows that the model is accurate, with a maximum average error of 3.56% for the velocity prediction. Together with the measured data, the computed transient flow behavior can be used to better detect well kick and a loss of circulation after the mud pump is shut down. The model sensitivity analysis show that the water depth, mud density and drill string size are the three major factors affecting the fluctuation of the BHP after a circulation break. These factors should be carefully examined in well design and drilling operations to minimize BHP fluctuation and well kick. This study provides the fundamentals for designing a safe system in controlled mud-cap drilling operatio． Keyword: Deep water; Controlled mud-cap drilling; Unsteady flow; Mathematical model; Kick detection. INTRODUCTION Due to the depletion of onshore oil and gas re- sources, the oil-gas industry has extended its search for resources to deep-water areas. However, deep- water drilling is facing many problems and chal- lenges, including pore pressure prediction uncertain- ties, narrow pressure margins, and high equivalent circulation density (ECD) (Shaughnessy et al., 1999; 2007; Stave, 2014). These problems and challenges not only lead to the inability to design wells for tradi- tional kick tolerances, but also make a well techni- cally undrillable due to lack of drilling window right below the previous casing/liner shoe. Controlled mud cap (CMC) drilling is the solution to all of these problems and challenges, and improve safety and efficiency in the well construction process (JPT staff, 2013; Stave, 2014; Malt and Stave, 2014; Godhavn et al, 2014; Børre and Sigbjørn, 2014). CMC drilling is a kind of subsea mud-lift pump drilling system technologies. Figure 1 shows a sche- matic of a CMC drilling system. The mud-lift pump is placed in water and return mud and cuttings to surface through a mud return line (MRL). The tech- nique allows for precise control of bottom hole pres- sure (BHP) during drilling by regulating the mud
Transcript
ISSN 0104-6632 Printed in Brazil
www.abeq.org.br/bjche
Vol. 33, No. 01, pp. 91 - 104, January - March, 2016 dx.doi.org/10.1590/0104-6632.20160331s20150530
*To whom correspondence should be addressed
Brazilian Journal of Chemical Engineering
MODELING AND ANALYSIS OF UNSTEADY FLOW BEHAVIOR IN DEEPWATER CONTROLLED
MUD-CAP DRILLING
Jiwei Li1*, Gonghui Liu1,2, Jun Li1 and Mengbo Li1,3
1China University of Petroleum, College of Petroleum Engineering, Beijing 102249, China. Phone: + 86 010 89731225
E-mail: [email protected] 2Beijing University of Technology, Beijing 100192, China.
3China National Offshore Oil Corporation Research Institute, Beijing 100010, China.
(Submitted: August 24, 2015 ; Revised: November 13, 2015 ; Accepted: November 30, 2015)
Abstract - A new mathematical model was developed in this study to simulate the unsteady flow in controlled mud-cap drilling systems. The model can predict the time-dependent flow inside the drill string and annulus after a circulation break. This model consists of the continuity and momentum equations solved using the explicit Euler method. The model considers both Newtonian and non-Newtonian fluids flowing inside the drill string and annular space. The model predicts the transient flow velocity of mud, the equilibrium time, and the change in the bottom hole pressure (BHP) during the unsteady flow. The model was verified using data from U-tube flow experiments reported in the literature. The result shows that the model is accurate, with a maximum average error of 3.56% for the velocity prediction. Together with the measured data, the computed transient flow behavior can be used to better detect well kick and a loss of circulation after the mud pump is shut down. The model sensitivity analysis show that the water depth, mud density and drill string size are the three major factors affecting the fluctuation of the BHP after a circulation break. These factors should be carefully examined in well design and drilling operations to minimize BHP fluctuation and well kick. This study provides the fundamentals for designing a safe system in controlled mud-cap drilling operatio． Keyword: Deep water; Controlled mud-cap drilling; Unsteady flow; Mathematical model; Kick detection.
INTRODUCTION
Due to the depletion of onshore oil and gas re-sources, the oil-gas industry has extended its search for resources to deep-water areas. However, deep-water drilling is facing many problems and chal-lenges, including pore pressure prediction uncertain-ties, narrow pressure margins, and high equivalent circulation density (ECD) (Shaughnessy et al., 1999; 2007; Stave, 2014). These problems and challenges not only lead to the inability to design wells for tradi-tional kick tolerances, but also make a well techni-cally undrillable due to lack of drilling window right
below the previous casing/liner shoe. Controlled mud cap (CMC) drilling is the solution to all of these problems and challenges, and improve safety and efficiency in the well construction process (JPT staff, 2013; Stave, 2014; Malt and Stave, 2014; Godhavn et al, 2014; Børre and Sigbjørn, 2014).
CMC drilling is a kind of subsea mud-lift pump drilling system technologies. Figure 1 shows a sche-matic of a CMC drilling system. The mud-lift pump is placed in water and return mud and cuttings to surface through a mud return line (MRL). The tech-nique allows for precise control of bottom hole pres-sure (BHP) during drilling by regulating the mud
92
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evel in the mhe safety marn wells witBørre and Si
Furthermoioned belowuring CMC
Therefore, thetween the f
After surface tring will corill string, thhe annulus uolumn presseached. ThisChoe et al., 1
Figure 1: S
After a citeady flow crilling in Carrow-margilow, the murill string durill string anevel in the ri
which may leearance of th
BHP, resultinan be used tuvkam-worldurrently notring additio
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ore, the mud w the mud le
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ontinue to fhrough the duntil an equsures in the s process co1998; 1999; 2
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CMC drillingin formationd will flow ue to pressu
nd the annuluiser may cauead to a loshe friction p
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odel in literativated us to
This methoill longer opeoperational 6). level in the aevel inside t not convenotential pressdrill string a
ut down, the mflow downwdrill bit, and uilibrium bet
drill string onstitutes an 2007).
the CMC dr
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g, especiallyns. During into the an
ure imbalancus. The increuse an increas of circulat
pressure loss Drill string se problems
ut this additble. Moreovons to drillunsteady floer, we have atures to addinvestigate in
Jiwei Li, Gong
Brazilian Jou
od can improen hole sectiomud windo
annulus is pothe drill str
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and the annulmud in the d
wards along upwards alo
tween the mand annulusunsteady fl
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ncontrolled problem dury in deepwa
the unsteannulus from ce between ease in the mase in the BHtion; the discan reduce valves (DSV
The unsteaallenge for avy mud ofilling, unsteammon operad disconnectd co-workerg the unsteadMD) system
ut a detailed oreover, CMe formula deitable for CMA few stud
ter a circulation study of the unsteady ftection methrculation breathematical ter surface pdeveloped anerature (Oga
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MA
overning Eq
The governy in the annultant form is
,
2(
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Ann
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An
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P
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The first rigy due to the tween the dr
dy flow hasoperations,
f cementing ady flow is aations, such ation of the drs presented dy flow for
m (Choe, 200theoretical
MC drilling isscribing uns
MC drilling. dies have exaion break. Hhe transient
flow has not hods for CMeak are scarmodel desc
pump shuttinnd validated
awa et al., 20the explicit
e transient bvel in the annccurate detecculation afteis was perfosystem para
ng unsteady tals for desid-cap drilling
ATHEMATI
quation
ning equationulus is derive
2 2
,
Ann DC
AnnAnn DC
DC
f Ann bi
Annnn DC
DC
U UA
LA
P P
AL
A
ght-hand sidedifference i
rill string an
s always besuch as the(Sauer, 198
also a potentas the connedrill string. Ia simple fora subsea mu
07), but theyanalysis and
s different frteady flow f
amined the uHowever, a de
change in thbeen publis
MC drilling syrce. In this ribing the u
ng down for d with experi007). A numt Euler was behaviors of nulus and BHction methoder a circulatiormed to bettameters on flow. This s
igning a safg operations.
ICAL MODE
n for the liqued in Append
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(
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C Ann
it DC
AAnn
P
L
L LA
LA
e term is the in the cross-d the annulu
en a practice pumping 87). For CMtial problem ection, trippinIn 2007, Chormula descriud-lift drillin
y did not card verificatioom SMD, an
for SMD is n
unsteady floetailed simulhe BHP durinshed yet. Kicystems afterstudy, a ne
unsteady floCMC drillinment from th
merical simulperformed
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EL
uid flow velodix A. The r
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(
kinetic velo-sectional arus. The secon
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Modeling and Analysis of Unsteady Flow Behavior in Deepwater Controlled Mud-Cap Drilling 93
Brazilian Journal of Chemical Engineering Vol. 33, No. 01, pp. 91 - 104, January - March, 2016
right-hand side term takes into account the boundary pressure at the mud level in the drill string and the annulus. The third right-hand side term is related to friction, and the last right-hand side term represents the driving mechanism caused by the hydrostatic pressure imbalance between the drill string and the annulus. All symbols are defined in the Nomencla-ture section.
The final expression for the equation of motion for the length of mud, AnnL , in the annulus is ob-tained:
AnnAnn
LU
t
(2)
These two equations are solved numerically in a
computer program. Numerical Formulation
Because the mud level is not changing very rap-idly, the numerical integration need not to be exces-sive. The explicit Euler method is locally second-order accurate but first-order globally accurate (Bew-ley, 2012). Provided that the time step is small enough, the explicit Euler method will yield good results for the problem. The simplest and most intui-tive way of integrating the above scheme is by using the explicit Euler method, which takes the following form for Equation (1):
1
,0 ,0
, ,
2( )
( )
( )
( )
( )
n n n nn n Ann Ann DC DCAnn Ann
n nAnnAnn DC
DC
n nDC Ann
n nAnnAnn DC
DC
n n nf DC f Ann bit
n nAnnAnn DC
DC
n nDC Ann
n nAnnAnn DC
DC
U U U UU U t
AL L
A
P P
AL L
A
P P P
AL L
A
g L LA
L LA
(3)
The explicit scheme of the length of the mud col-
umn in annulus is
1 1n n nAnn Ann AnnL L U t (4)
Eq. (3) can be easily solved using the velocity
and position of the previous time step to solve for the acceleration of mud in annulus in each time step. The acceleration is then used to obtain the velocity of mud in annulus, which in turn is used to calculate the position of the liquid level in annulus. In practice, the routine can be summarized as follows: Use Eq. (3) to update the acceleration based
on the level position and velocity at the previous time step; Use Eq. (4) to update the level position based
on the new velocity. This procedure is repeated for each time step until
the maximum time is reached. Initial Conditions
After a circulation break, the initial mudflow ve-locity in the drill string is equal to that in the string before a circulation break:
0( 0)DCU t U (5)
During normal circulation, the length of the mud column within the drill string is equal to the well depth:
( 0)DC wellL t L (6)
The annulus pressure at subsea level is ap-
proximately equal to the seawater hydrostatic pres-sure; therefore, the length of the mud column within the annulus can be calculated using the following equation:
( 0) wann well wL t L h
(7)
RESULT AND ANALYSIS Model Verification
Field experimental test for the unsteady flow after a circulation break are not currently available for a CMC drilling system. In 2007, Akira Ogawa et al. studied the flow in a U-tube in a laboratory (Ogawa et al, 2007). They adopted 3 non-Newtonian fluids to carry unsteady flow experiments in a U-tube: 68% glycerin solution, 1.8% acrylic co-polymer solution
94
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nd 3% acrymental deviceer (ID) of the
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matical modemental param
Figures 3-xperimental
Fluid Typ
68% glycerin solu
1.8% acrylic co-pol
3% acrylic co-pol
Figure 3:glycerin so
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uid flow expdate the develel. The valu
meters are sho5 show the cresults and
F
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lymer 87
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Comparisonolution in wa
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Figure 2: Sc
Table 1: Para
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70 mm
70 mm
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Jiwei Li, Gong
Brazilian Jou
n. The expehe inner diamring the exped to record rom the 3 nere used in t
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hematic illus
ameter valu
Right-liquid height HR
670 mm
670 mm
670 mm
culated resul
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urnal of Chemica
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fferent non-Ncities and then-Newtonianindicating thlocity is 3.5nge of the ertially due toodel. The scad the capillae capillary efon in the math
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liquid eight
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fluids. Both l data agree e errors are shm average errh is within applicationsthe capillary
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Dynamic viscosity
76×10-3 Pa·s
.4×10-3 Pa·s
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rofiles
tal results fo
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Figure 6 snnulus with own. At thets main poweown of surfocity decreashe maximumtring is reachelocity conti
Mode
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Comparison-polymer sol
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ater well in te to analyze
g system. Thse data were y and mud leeak. hows the tratime after
e beginning, er source (i.eface pump, thses rapidly. Wm mud freehed at point inues to dec
ling and Analysis
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L(t) profiles
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ion lymer mer
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used to calcevel in the a
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When the SPP-fall velocitA. After tha
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ow Behavior in D
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ults of HL an
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Deepwater Contro
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nd V with th
and V with
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d height LHE
he flow pattear flow insi
mudflow veloke the flow olumn in thehe high-frictiystem prevenict the timeetween in drow velocity
eached. As cum time is 3ponding mudhe sea level evel in the aning and then osition.
olled Mud-Cap Dr
January - Marc
(b) V(t) pr
he experimen
(b) V(t) pr
the calculate
onian fluid f
Average
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ocity drops econdition in
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to reach thrill string andy drops to an be seen f35 minutes. d level in th
versus timnnulus incregradually re
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rofiles
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error of flow v
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ns from turbstring. Sub
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from Figure Figure 7 sho
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ments.
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95
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Un-ud
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96 Jiwei Li, Gonghui Liu, Jun Li and Mengbo Li
Brazilian Journal of Chemical Engineering
Table 3: Basic parameter values.
Parameter Value Mud density, g/cm3 1.50 Seawater density, g/cm3 1.03 Fluid model Power-lawWater depth, m 2500 Plastic viscosity, cP 45 Bingham yield point, Pa 0.87 Number of bit nozzles 3 Bit nozzle diameter, 1/32nd in 14 Well vertical depth, m 5000 Length of drill collars, m 91.5 Inner diameter of the last casing, m 0.22289 Open hole diameter, m 0.22225 OD and ID of drill string, m 0.127×0.1086 OD and ID of drill collars, m 0.1778×0.0762 ID of return line, m 0.1524
Figure 6: Change of annulus flow velocity over time after the surface pump is shut down
Figure 7: Change of mud level in annulus over time after the surface pump is shut down
The BHP can be predicted based on the mudflow
velocity and mud level in the annulus (Figure 8).
Figure 8: Transient BHP after the surface pump isshut down.
The BHP is the sum of the hydrostatic pressure
and friction pressure loss in the annulus. During un-steady flow, a fluctuation in the BHP can occur. Fig. 8 shows that the BHP rapidly decreases within the first few seconds due to the disappearance of the SPP. Subsequently, the BHP increases as the increase in the pressure resulting from the rising mud level in the annulus is larger than the decrease in the pressure caused by reduced annulus flow velocity; when these two equal to each other, the BHP reaches to a new high point; and then the increase in the pressure re-sulting from the rising mud level in the annulus be-comes less than the decrease in the pressure caused by reduced annulus flow velocity, and the BHP de-creases gradually and tends to a constant. The fluc-tuation in the BHP can threaten drilling safety as it can lead to the occurrence of kick. Applications
Under normal circulation conditions in CMC drilling, the SPP is non-zero, a kick can be detected
0 10 20 30 40 500
0.2
0.4
0.6
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ump rate andkick after thifficult. The us returning detection meng period forlow within ore, the detecd risks a loss detection of kial. The abodflow characpump is shu
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uring unsteaeasures to prveloping furad may be adss of circulatque needs to
The model re drilling syessure, but nsses.
igure 10: Cith and witho
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January - Marc
er, the emphalow behavioderivation ofuation just apr large kick, rom single psteady frictiirements. Thflow need t
tion results athe beginninssure, and ththan the formade into thestarts to be
w velocity aner than those. 10. The moof circulatione real-time mnd. If real-tim
in annulus kick is indicaindicated. Thd loss of circady flow arevent kick orther in the wdopted to detion has occbe further inis also appliystems, such
needs to be tu
Comparison out a kick.
rilling
h, 2016
asis is laid ur of the puref Eq. (9) is pplied in ththe fluid in
phase into twion factor cahe frictional to be introd
are shown inng, the BHP here is no kimation pressue wellbore. different fro
nd mud levele of no kickodel can be n during unsmonitored tr
me monitoredare higher thated. Converhis method culation in a tand helps or loss of cirwell. A changetermine whecurred. Howenvestigated aied to other mh as constanuned with fri
of annulus
upon analyzine liquid phasnot presente
he situation the annulus
wo-phase. Thannot meet th
pressure loduced into th
n Figure 9 anis higher thaick. When thure, formatioThe unstead
om that of nl in annulus k, as shown
used to detesteady flow brend with th
d flow velocihan the calcrsely, a loss can be used timely manndrillers tak
rculation froge in the hooether a kick ever, the tecand developemanaged prent bottom hoiction pressu
mud level
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1) Water De
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SENSITIVIT
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TY ANALYS
side the drillow are influe
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Jiwei Li, Gong
Brazilian Jou
ct. The transithe CMC drin this mat
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SIS
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HP during cie critical derectly correlaed the BHP ay result in aless than theease as the w
well kick. uring narrow-illing operati
) Mud Densi
The annulnsitized to m5 g/cm3, 1.6 (a), increase
ow velocity tween the ing. 12 (b) demcts the fluctuow. Again, aeate fluctuati
BHP over tim
e with the wes a greaterside of the uently increathe drill strinn Fig. 11 (b),or a given wes not create
mined. At thie friction pre
the increasfinal equilibrirculation. Ifepth, the finate with theprior to the
a loss of circe critical depwater depth dTherefore, a-margin presions.
ity
lus flow vmud densitieg/cm3 and 1es in the mudue to a grside of the d
monstrates thuation in thea critical mions in the B
(b) B
me for differ
water depth br pressure ddrill string
ases the mudng after a circ, the BHP lev
well depth. A a fluctuatiois water depessure loss ise in the murium BHP if the water dnal equilibriu water depth
e circulationculation. If thpth, the finaldecreases, wa fluctuationssure drilling
velocity ands of 1.3 g/cm.7 g/cm3. As
ud density wireater pressu
drill string anhat the mud d BHP during
mud density HP can be id
BHP
ent water dep
because deepdifference b
and annuludflow into thculation breavel drops wi
A critical waton in the BHpth, the disas compensate
ud level in ths equal to thdepth exceeum BHP wh and can e break, whiche water depl BHP will d
which may lean in the BHg is a threat
d BHP wem3, 1.4 g/cmshown in Fi
ill increase thure differen
nd the annuludensity also ag the unsteadthat does n
dentified.
pths.
per be-us, he
ak. ith ter HP ap-ed he he ds
will x-ch
pth de-ad
HP to
ere m3, ig. he ce
us. af-dy
not
frmthincrdti (3
foan
Figu
At the cririction pressu
mud level in the critical dnitial BHP reases. If thensity, the stial BHP as m
3) Well Dept
The calculor well depthnd 9500 m a
Figur
Mode
Brazilia
(a) Flow ve
ure 12: Chan
itical densityure loss is othe annulus.
density, the fwhile circul
he mud denstabilized BH
mud density d
th
lated annuluhs of 5500 mare shown in
(a) Flow ve
re 13: Chang
ling and Analysis
an Journal of Ch
locity in ann
nges of flow
y, the decreoffset by the
If the mud dfinal BHP wlating as m
sity is less thHP will be ledecreases.
s flow velocm, 6500 m, 7n Figure 13.
elocity in ann
ges in the flo
s of Unsteady Flo
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nulus
velocity in a
ease in annuincrease in
density excewill exceed
mud density han the criti
ess than the i
cities and BH500 m, 8500As indicated
nulus
ow velocity in
ow Behavior in D
ing Vol. 33, No. 0
annulus and
ulus the eds the in-
ical ini-
HPs 0 m d in
Figratcreequfricdepcorsurnofiestawecalas
n annulus an
Deepwater Contro
01, pp. 91 - 104,
BHP over tim
g. 13 (a), incte at whicheases, whichuilibrium. Tction pressurpth. Fig. 13 rrelates withre fluctuationt result in fl
ed. If the welabilized BHPell deepens. l depth, the the well dep
nd BHP over
olled Mud-Cap Dr
January - Marc
(b) B
me for the di
creases in thmudflow ve
h prolongs thThis phenomre loss direct(b) shows th
h the BHP, wn. Again, a c
fluctuations oll depth exceP will be lesIf the well dfinal BHP w
pth decreases
(b) B
time for diff
rilling
h, 2016
BHP
ifferent mud
he well depthelocity in thhe time requ
menon occurstly correlateshat the well
which also afritical well dof the BHP eeds the critiss than the idepth is less will exceed ths.
BHP
ferent well d
densities.
h decrease thhe annulus duired to reacs because ths with the wedepth direct
ffects the predepth that docan be identical depth, thinitial BHP than the crit
he initial BH
depths.
99
he de-ch he ell tly es-es ti-he as ti-
HP
10
(4
ti4trfo(athGcreqv (5
fo1anthfleqtithmglutithtindthdbvm
00
4) Mud Visc
The annuligated at mu5 mPa·s, 50 ransient flowor different ma), the mud he time to re
Generally, a rease in the fquilibrium. Aiscosity will
5) Drill Strin
The calculor drill string19.5 mm annd Figure 15he drill strinlow velocityquilibrium. Fional area of he annulus c
metric flow renerates a hus. Increasinion pressure he annulus frion pressure ant role in trill string IDhe annulus. Arill string IDecause the cersely correl
more mud wi
Figure 14:
cosity
lus flow veloud viscositie mPa·s and
w velocity inmud viscositviscosity aff
each equilibrhigh viscosiflow velocityAs shown inreduce the f
ng Size
lated annulug IDs of 82.5d 130.5 mm(b), respectivng size signy in the annuFor a given
f the drill strincross-sectionarate conditio
higher initial ng the drill st
loss inside thrictional presloss inside ththe total fric
D will generaAs revealed iD results incrcross-sectionlates with thill flow into
(a) Flow ve
: Changes in
ocity and BHes of 35 mP55 mPa·s. F
n the annuluties. As indicffects the florium in a coity will yiely and a longen Fig. 14 (b)fluctuation in
s flow veloc5 mm, 93.2 m
m are shown vely. As shownificantly imulus and thewellbore IDng inverselyal area. For
ons, a larger flow veloci
tring ID deche drill strinssure loss. Bhe drill string
ction pressurate a higher fn Fig. 15 (b)
reases the eqnal area of the drill string the annulus
locity in ann
the flow vel
Jiwei Li, Gong
Brazilian Jou
HP were invPa·s, 40 mPaigure 14 sho
us and the Bcated in Fig.ow velocity aomplex mannd a slower er time to rea), a higher mn the BHP.
cities and BHmm, 107.4 min Figure 15
wn in Fig. 15 mpacts the me time to rea
D, the cross-sy correlates w
the same vodrill string
ity in the ancreases the frng and increa
ecause the frg plays a dom
re loss, a larflow velocity), increasing
quilibrium BHthe annulus g ID; therefos from the d
nulus
locity in the a
ghui Liu, Jun Li a
urnal of Chemica
ves-a·s, ows
BHP 14 and ner. de-ach
mud
HPs mm, 5(a) (a),
mud ach sec-with olu-
ID nu-
fric-ases fric-mi-rger y in the
HP, in-
ore, drill
strdristrtua (6)
tizin,sisdisleaingindtypsteaff (7)
weL/sforcirof totof them/cuoccsurand0.6musys
annulus and
and Mengbo Li
al Engineering
ring. The BHill string sizering size doeation in the B
) Nozzle Size
The annuluzed to nozzle 16/32nd in, a
s are presentesplayed in Fiads to a fast g in a shortdicated in Figpically increeady flow, bufect the final
) Volumetric
The calculaere sensitizeds, 30 L/s, 35 r the same drculation rate
transient mtal time for eseconds afte
e annulus mu/s for differessed in thecurs becausere imbalanced the annulu68 m/s indicum free fall vstem in Table
BHP over tim
HP shows sies during thes not signifiBHP.
e
us flow veloce sizes of 10/and 18/32nd ined in Figure 1ig. 16 (a), a lflow velocit
ter time to rg. 16 (b), an
eases the BHut this increBHP.
c Flow Rate
ated annulusd to volumetrL/s and 40 L
drill string gee does not c
mud flow velequilibrium er the surfacud flow velont initial vol
previous se the mud floe between thus, and the cates zero Svelocity inside 3.
(b) B
me for the di
imilar trendse unsteady f
ficantly influ
city and BH/32nd in, 12/3n. The results16 (a) and Figlarger nozzley and flow dreach the eqincrease in t
HP fluctuatioease does no
s flow velocric flow ratesL/s. As showneometry, a dause noticealocity in theexcept for the pump is shocity rapidlylumetric flowsection, this ow is powerehe inside of t
annular floPP which mde the drill st
BHP
ifferent mud
s for differeflow. The dr
uence the flu
HP were sens32nd in, 14/32s of this analgure 16 (b). A
e size normaldecline, resuquilibrium. Athe nozzle sizon during u
ot significant
city and BHs of 20 L/s, 2n in Figure 1
different initiable differene annulus anhe first couphut down, any drop to 0.6w rate. As di
phenomenoed by the prethe drill strinw velocity
means a maxtring for give
viscosities.
ent rill uc-
si-2nd ly-As lly lt-As ze
un-tly
HP 25 7,
ial ce nd ple nd 68 is-on es-ng of
xi-en
Figure
Figu
Figure 17:
Modeli
Brazilia
(a) Flow ve
e 15: Change
(a) Flow vel
ure 16: Chan
(a) Flow ve
: Changes in
ing and Analysis
an Journal of Ch
locity in ann
es in flow ve
locity in ann
ges in the flo
locity in ann
the flow velo
of Unsteady Flow
emical Engineeri
nulus
elocity in the
nulus
ow velocity i
nulus
ocity in the an
w Behavior in De
ing Vol. 33, No. 0
annulus and
in the annulu
nnulus and B
eepwater Controll
01, pp. 91 - 104,
d BHP over ti
us and BHP o
BHP over time
led Mud-Cap Dri
January - Marc
(b) B
ime for the d
(b) B
over time for
(b) B
e for differen
illing
h, 2016
BHP
different drill
BHP
r different no
BHP
nt volumetric
1
l string sizes
ozzle sizes.
flow rates.
101
102 Jiwei Li, Gonghui Liu, Jun Li and Mengbo Li
Brazilian Journal of Chemical Engineering
CONCLUSIONS
A new mathematical model for the unsteady flow during CMC drilling was developed in this study to simulate the annular after-flow and BHP after a circu-lation break. The following conclusions are drawn:
1. The mathematical model was verified using experimental obtained from U-tube flow. This veri-fication indicated that the model is accurate, with a maximum average error of 3.56% for the flow velocity.
2. Based on the new mathematical model, a method of early kick detection during the unsteady flow was formulated. This method identifies abnor-malities in the mudflow by comparing the model-calculated and measured return flow in the annulus. If the real-time measured flow trend differs from the model-calculated trend, a kick or loss of circulation can be detected in time. This approach will help to overcome the current difficulty of early kick detec-tion during the connection of pipes. Accordingly, drillers can take well control actions in a timely man-ner to prevent well blowout.
3. Sensitivity analysis of various parameters indi-cate that the velocity of continuous flow in the annu-lus is directly proportional to the water depth, mud density, drill string size, and nozzle size and in-versely proportional to the well depth and mud vis-cosity. The time required for the unsteady flow to reach equilibrium is directly proportional to the wa-ter depth, well depth, mud density, mud viscosity, drill string size and inversely proportional to the nozzle size.
4. The water depth, mud density and drill string size were identified to be three major factors affect-ing the fluctuation in the BHP after a circulation break. Whereas the water depth cannot be controlled, the mud density and drill string size should be care-fully selected to minimize the risk of well blowout.
ACKNOWLEDGMENT
The authors wish to acknowledge the Key Program of National Natural Science Foundation of China (Contract No. 51334003 and 51434009) for the fi-nancial support.
NOMENCLATURE AAnn Cross-sectional area of annulus (m2) ADC Cross-sectional area of drill string (m2)G Gravitational acceleration (m/s2) HL Left-liquid height (mm)
HR Right-liquid height (mm) hw Water depth (m) ID Inner diameter LAnn Length of mud column in the annulus (m) LDC Length of mud column inside the drill
string (m)Lwell Well depth below the Kelly bushing (m) N Time nodeOD Outside diameterPAnn, 0 Boundary pressure of mud level in the
annulus (Pa) Pb Bottom hole pressure (Pa) Pbit Friction pressure loss in drill bit (Pa) PDC, 0 Boundary pressure of mud level inside
the drilling string (Pa) Pf, Ann Friction pressure loss in the annulus (Pa)Pf, DC, 0 Friction pressure loss in the drill
string (Pa)PI Productivity index (m3/(Pa·s)) Pp Pore pressure (Pa) Q Reservoir inflow rate (m3/s) U0 Mud flow velocity in drill string before
the surface pump is shut down (m/s) UAnn Average flow velocity of fluid in the
annulus (m/s) UDC Average flow velocity of fluid inside
the drill string (m/s) ρ Density of mud (kg/m3) ρ
w Seawater density (kg/m3) t Unit time step (s)
REFERENCES Børre, F. and Sigbjørn, S., Controlled mud-cap drill-
ing for subsea applications: Well-control chal-lenges in deep water. SPE Drilling & Completion, 21(2), 133-140 (2006).
Choe, J. and Juvkam-Wold, H. C., Well control as-pects of riserless drilling. SPE Annual Technical Conference and Exhibition, Society of Petroleum Engineers. New Orleans, Louisiana (1998).
Choe, J., Analysis of riserless drilling and well-con-trol hydraulics. SPE Drilling & Completion, 14(1), 71-81(1999).
Choe, J., Schubert, J. J. and Juvkam-Wold, H. C., Analyses and procedures for kick detection in sub-sea mud-lift drilling. SPE Drilling & Completion, 22(4), 296-303 (2007).
Børre, F. and Stave, R., Drilling depleted reservoirs using controlled mud level technology in mature subsea fields. SPE Bergen One Day Seminar, Bergen, Norway (2014).
Godhavn, J. M., Hauge, E., Molde, D. O., Kjøsnes, I., Gaassand, S., Fossli, S. B., Stave, R., ECD Man-
JP
M
O
O
S
S AE
scaftiimthminflstis
dddthFthulecotr
agement Tshore Tec(2014).
PT Staff, ECcirculatingogy, 65(8)
Malt, R., and drilling foshore Techpur, Malay
Ochoa, M. Vand Tool Jlics Calculversity (20
Ogawa, A., Sugawara,wada, T., oscillationNewtonianThermal S
auer, C. W., state of the39(9), 109
chubert, J. J.
APPENDIX Equation
In order tocribe the tranfter surface pions were mammediately; he surface p
mud is incomnside the drillow is one-dtant; 7) the sothermal.
The well hrill string anrill string inefined as pohe wellbore
First, the drillhe upper andme are B1 aevel in drillontrol volumrol volume.
Modeli
Brazilia
Toolbox for Fchnology Co
C-drill elimg density. Jou, 38-40 (201
d Stave, R., Eor challenginhnology Conysia (2014).
V., Analysis oJoint Effect tolations. Ph.D006).
Tokiwa, S., T., WatanaShishido, K
n of liquid con and non-Ne
Science, 16(4Mud displace art. Journa
91-1101 (198. and Juvkam
A: Derivati
o develop thensient flow cpump shutdoade: 1) all p2) the drill
pumps and ompressible; 4ll string and
dimensional; mud does n
hole can be nd the annulunto the annusitive. Figurat any time
l string was sd lower bouand B2, respl string is c
me can be reg
ing and Analysis
an Journal of Ch
Floating Drilonference, H
inates effecturnal of Petro3).
EC-drill MPDng pressure nference-Asi
of Drilling Fo Reduce Er
D. Thesis, Te
., Mutou, Mabe, M., Sa
K., Matumotoolumn in vertewtonian liq
4), 289-300 (2cement durinal of Petroleu7).
m-world, H. C
ion Process
e mathematiccharacteristicown, the follpumps involvstring is disc
open at the 4) the cross-annulus are 6) the mud
not gel; and
divided intous. The mud ulus, and thise A1 shows during the studied as a cundaries of tpectively. Becontinuouslygarded as a d
of Unsteady Flow
emical Engineeri
ling Units. OHouston, Te
t of equivaloleum Techn
D dual gradiregimes. O
ia, Kuala Lu
Fluid Rheolorrors in Hydrexas A&M U
M., Mogi,atou, K., Kio, N., Damptical U-tube uids. Journal2007).
ng cementingum Technolo
C., Well-cont
for Govern
cal model to c in the annulowing assumved are stoppconnected frsurface; 3) -sectional arconstant; 5) density is c8) the well
o two parts, flows from
s direction wthe mudflowunsteady flo
control volumthe control vecause the fl changing, deforming c
w Behavior in De
ing Vol. 33, No. 0
Off-xas
lent nol-
ient Off-um-
ogy rau-Uni-
K., ika-ped for l of
g: A ogy,
trol
Sh
Sh
Sta
Be
Çe
Zie
ing
de-ulus mp-ped rom the
reas the on-l is
the the
was w in ow. me; vol-luid the on-
Figany
is e d
dt whvois
eepwater Controll
01, pp. 91 - 104,
procedures to conventiCompletion
haughnessy, JP., ProblemIADC Drilllands (1999
haughnessy, JDurkee, T.,lems. SPE/dam, The N
ave, R., ImpOffshore Te(2014).
ewley, T. RCopy. Rena
engel, Y. A. FundamentaHigher Edu
egler, R., Dutime: The bwell controflat time redence, Houst
adient drillingdrilling. SP7-295 (2006)gost, W. K., -deepwater ence, Amster
herty, W. T.,a-deepwater ling Confere2007).
n of dual graonference, H
al Renaissanss, La Jolla (2a, J. M., Flu
pplications. Mrica (2010). drilling is reaa retrofit syswater depth
fshore Techn2014).
mudflow in tdy flow.
Reynolds tranengel and Cim
(CS
B V V
veral paramemomentum
ity; CSV is
1
g as compareE Drilling ). Herrmann, Rdrilling. SPrdam, Nethe
, Graff, R. Ldrilling pro
ence, Amste
adient drillinHouston, Tex
nce, Advan2012).
uid MechanicMcGraw H
ady for primstem for bettcapability an
nology Confe
the wellbore
nsport theorembala, 2010)
)CS dAV n
eters per unor energy; Vthe local co
103
ed &
R. E/ er-
L., b-
er-
ng. xas
ce
cs: Hill
me-ter nd er-
at
em ):
nit Vn-
104 Jiwei Li, Gonghui Liu, Jun Li and Mengbo Li
Brazilian Journal of Chemical Engineering
trol surface velocity at the surface element dA ; nrepresents the outward-pointing unit normal vector associated with dA ; CV denotes the control volume; CS represents the surface area of the control volume.
According to the Reynolds transport theorem of a deforming control volume, the mass balance equa-tion for the drill string can be written as follows:
2( )
( ) 0DCDC DC DC B
LA A U U
t
(A1)
The momentum balance equation for the annulus
can be written as follows:
2
,
( )( )DC DC DC
DC DC DC B
DC f DC DC DC DC
A L UA U U U
t
PA P A L A g
(A2)
where is the density of the mud in kg/m3; ADC is the cross-sectional area of the drill string in m2; UDC is the fluid velocity in the drill string in m/s; LDC is the length from the bottom to the fluid level in the drill string in m; UB2 is the average velocity of the lower boundary of the control volume in m/s (when the lower boundary is fixed, the velocity is 0 m/s);
,DCfP is the friction pressure loss in the drill string in
Pa; g is the gravitational acceleration in m/s2. P is the pressure difference between two boundaries of the control volume in Pa ( 2 1B BP P P , 1 ,0B DCP P );
,0DCP is the atmospheric pressure in Pa because the
drill string is open at the surface after the surface pump is shut down 2( )B DCP P ; and DCP is the bottom hole pressure in the drill string in Pa.
Expanding the time derivative of the momentum balance equation and combining Equations (A1) and (A2) yields the following expression for the momen-tum balance equation of the drill string:
,DC ,0 f DCDCDCDC DC
PP PUL L g
t
(A3)
Similarly, the momentum balance equation for the annulus can also be obtained:
,,0 f AnnAnn AnnAnnAnn Ann
PP PUL L g
t
(A4)
where LAnn is the length from the bottom to the fluid level in the annulus in m; UAnn is the average flow velocity of the fluid in the annulus in m/s; PAnn, 0 is the atmospheric pressure because the annulus is open at the surface. PAnn is the bottom hole pressure in the
annulus in Pa; ,f AnnP is the friction pressure loss in
the annulus in Pa. Combining the drill string and annulus momen-
tum balance Equations, (A3) and (A4), yields the following expression for the momentum balance equation for the fluid in the entire well:
,0 ,0DC
, , ( )
Ann DCAnn DC
DC AnnAnn
f DC f AnnDC Ann
U UL L
t tP PP P
P PL L g
(A5)
The wellbore mud is incompressible; therefore,
the volumetric flow is conserved, which implies that the rate of volumetric change over time is the same inside the drill string and the annulus:
DC AnnDC Ann
U UA A
t t
(A6)
According to the energy balance equation, the fol-
lowing formula can be obtained:
2 2
2 2DC DC Ann Ann bitP U P U P
(A7)
where AAnn is the cross-sectional area of annulus in m2; bitP is the friction pressure loss in the drill bit in Pa. The friction pressure loss calculation is well es-tablished, and the detailed method used to calculate
,f DCP , ,f AnnP and bitP can be obtained from the
literature (Ochoa, 2006). According to Equations (A5) (A6) (A7), DCU is
eliminated, and the equation governing the liquid flow velocity in the annulus can be derived as follows:
2 2,0 ,0
, ,
2( ) ( )
( )
( ) ( )
DC AnnAnn Ann DC
Ann AnnAnn DC Ann DC
DC DC
f DC f Ann bit DC Ann
Ann AnnAnn DC Ann DC
DC DC
P PU U UA At L L L LA A
P P P L L gA A
L L L LA A
(A8)
Thus, the final expression for the motion equation
for the length of mud column AnnL in the annulus can be obtained:
