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
1and Mengbo Li
1,3 1China University of Petroleum, College of Petroleum Engineering, Beijing 102249, China.Phone: + 86 010 89731225 E-mail: lijiwei2009@live.com
2Beijing 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 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).
92 le th in (B ti du T b A st d th co re (C st d n fl d d le w p B ca Ju cu b T m su w 2
evel in the m he safety mar n wells wit Børre and Si Furthermo ioned below uring CMC Therefore, th
etween the f After surface tring will co
rill string, th he annulus u olumn press eached. This Choe et al., 1
Figure 1: S
After a ci teady flow c rilling in C arrow-margi low, the mu rill string du rill string an evel in the ri which may le
earance of th BHP, resultin
an be used t uvkam-world urrently not ring additio Therefore, th must be know
ufficient mo which has mo
marine riser. rgins and dri th narrow o
gbjørn, 2006 ore, the mud w the mud le
drilling but here is a po fluids in the pump is shu ontinue to f hrough the d until an equ sures in the s process co 1998; 1999; 2
Schematic of
irculation br can cause a CMC drilling
in formation d will flow ue to pressu nd the annulu iser may cau ead to a los he friction p ng in kick. D
to solve the d, 2006), bu t very reliab nal restrictio e effect of u wn. Howeve odel in litera tivated us to
This metho ill longer ope operational 6).
level in the a evel inside t not conven otential press drill string a ut down, the m
flow downw drill bit, and uilibrium bet drill string onstitutes an
2007).
the CMC dr
reak, the un significant p g, especially
ns. During into the an ure imbalanc us. The incre use an increa s of circulat pressure loss Drill string se problems ut this addit ble. Moreov ons to drill unsteady flo er, we have atures to add
investigate in
Jiwei Li, Gong
Brazilian Jou od can impro en hole sectio mud windo
annulus is po the drill str ntional drilli sure imbalan and the annul
mud in the d wards along upwards alo tween the m and annulus
unsteady fl
rilling system
ncontrolled problem dur y in deepwa
the unstea nnulus from
ce between ease in the m ase in the BH tion; the dis
can reduce valves (DSV s (Schubert a tional device ver, DSVs c
ing operatio ow on the B not found a dress this iss
nto the proble
ghui Liu, Jun Li a
urnal of Chemica ove ons ows osi-ring ing. nce lus. drill the ong mud s is low m. un-ring ater ady the the mud HP, sap-the Vs) and e is can ons. BHP any sue, em. cha hea dri com and and ing (SM ou Mo the sui aft tio the det cir ma aft is lite tio inv loc pre and siti the beh the con Go ity sul U ity bet
and Mengbo Li
al Engineering The unstea allenge for avy mud of illing, unstea mmon opera d disconnect d co-worker g the unstead
MD) system ut a detailed
oreover, CM e formula de
itable for CM A few stud ter a circulati on study of th
e unsteady f tection meth rculation bre athematical ter surface p
developed an erature (Oga on based on
vestigate the city, mud lev esents an ac d loss of circ ivity analysi e effects of haviors durin e fundament ntrolled mud MA overning Eq The govern y in the annu ltant form is
, 2( ( Ann A f DC An U U t L P L
The first rig y due to the tween the dr
dy flow has operations, f cementing ady flow is a ations, such a tion of the d rs presented
dy flow for m (Choe, 200 theoretical MC drilling is
scribing uns MC drilling. dies have exa
ion break. H he transient flow has not hods for CM eak are scar model desc pump shuttin nd validated awa et al., 20
the explicit e transient b vel in the ann ccurate detec culation afte is was perfo system para ng unsteady tals for desi d-cap drilling
ATHEMATI
quation
ning equation ulus is derive
2 2 , Ann DC Ann Ann DC DC
f Ann bi
Ann nn DC DC U U A L A P P A L A ght-hand side difference i rill string an
s always be such as the (Sauer, 198 also a potent as the conne drill string. I a simple for a subsea mu 07), but they
analysis and s different fr
teady flow f
amined the u However, a de
change in th been publis MC drilling sy
rce. In this ribing the u ng down for d with experi
007). A num t Euler was behaviors of
nulus and BH ction method er a circulatio rmed to bett ameters on
flow. This s igning a saf g operations.
ICAL MODE
n for the liqu ed in Append
,0 ) ( ( ) ( DC C Ann it DC A Ann P L L L A L A
e term is the in the cross-d the annulu
en a practic e pumping 87). For CM tial problem ection, trippin
In 2007, Cho rmula descri
ud-lift drillin y did not car
d verificatio om SMD, an for SMD is n
unsteady flo etailed simul he BHP durin
shed yet. Kic ystems after
study, a ne unsteady flo CMC drillin ment from th merical simul
performed f mudflow v
HP. This pap d for the kic on break. Se
ter understan transient flo study provid fe system f
EL
uid flow velo dix A. The r
,0 ) ) ) Ann Ann DC DC Ann Ann DC DC P A L A L g L A ( kinetic velo -sectional ar us. The secon
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, LAnn, in the annulus is ob-tained:
Ann
Ann
L
U 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-second-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 n
n n Ann Ann DC DC
Ann Ann
n Ann n
Ann DC
DC
n n
DC Ann
n Ann n
Ann DC
DC
n n n
f DC f Ann bit
n Ann n
Ann DC
DC
n n
DC Ann
n Ann n
Ann DC
DC
U U U U
U U t
A
L L
A
P P
A
L L
A
P P P
A
L L
A
g L L A
L L
A
(3)
The explicit scheme of the length of the mud col-umn in annulus is
1 1
n n n
Ann Ann Ann
L 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)
DC
U t U (5)
During normal circulation, the length of the mud column within the drill string is equal to the well depth:
( 0)
DC well
L 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) w
ann well w
L 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
94 an m te m ex N st m m
ex 4
nd 3% acry mental device er (ID) of the ment, high-sp xperimental Newtonian flu
tudy to valid matical mode mental param
Figures 3-xperimental
Fluid Typ
68% glycerin solu
1.8% acrylic co-pol 3% acrylic co-pol
Figure 3: glycerin so
ylic co-polym e is shown in
e U- tube is peed camera procedure. uid flow exp date the devel el. The valu meters are sho 5 show the c results and
F
T
pe Lef he
ution 87 lymer 87 lymer 87
(a) HL
Comparison olution in wa
mer solution n Figure 2. Th 40 mm. Dur as were used The data fr periments we
loped unstea ues of the s own in Table comparisons
the calculate
Figure 2: Sc
Table 1: Para
ft-liquid ight HL
70 mm 70 mm 70 mm
L(t) profiles
n of the calc ater.
Jiwei Li, Gong
Brazilian Jou n. The expe he inner diam ring the expe d to record rom the 3 n ere used in t ady flow mat specific expe
1.
of the record ed results fo
hematic illus
ameter valu
Right-liquid height HR
670 mm 670 mm 670 mm
culated resul
ghui Liu, Jun Li a
urnal of Chemica
eri- me- eri-the on-this
the-
eri-ded or 3
dif loc no 2, vel ran par mo and the tio
stration of th
ues in the un
Balanced l surface h
770 mm 770 mm 770 mm
lts of HL and
and Mengbo Li
al Engineering fferent non-N cities and the
n-Newtonian indicating th locity is 3.5 nge of the e
rtially due to odel. The sca
d the capilla e capillary ef on in the math
he experimen
nsteady flow
liquid eight
De
m 1200 m 1030 m 1030
d V with the
Newtonian f e fluid level n fluids. The he maximum 56%, which engineering
o neglecting ale of the exp
ary effect ca ffect has not hematical m
ntal apparatus
experiment
nsity D
0 kg/m3 20. 0 kg/m3 17 0 kg/m3 41
(b) V(t) pr e experiment
fluids. Both l data agree e errors are sh m average err
h is within applications the capillary periment appa an be signifi
been taken i odel.
s.
ts.
Dynamic viscosity
76×10-3 Pa·s .4×10-3 Pa·s .8×10-3 Pa·s
rofiles tal results fo
the flow v well for the hown in Tab ror of the flo the allowab . The error y effect in th aratus is sma icant, where into consider
Kinematic viscosity
173×10-6 m2/s 169×10-6 m2/s 40.4×10-6 m2/
or the 68%
3 ble ow ble is he all, as
C
as C T fl ci
an d it d lo th st v
Figure 4: acrylic
co-Figure 5: acrylic
co-Table
68% 1.8% 3% a
Case Study
A deep wa s an exampl CMC drilling Table 3. Thes low velocity irculation bre
Figure 6 s nnulus with own. At the ts main powe own of surf ocity decreas he maximum
tring is reach elocity conti
Mode
Brazilia (a) HL
Comparison -polymer sol
(a) HL
Comparison -polymer sol
e 2: Error of
Fluid Type % glycerin soluti
% acrylic co-pol acrylic co-polym
ater well in t e to analyze g system. Th se data were y and mud le
eak. hows the tra
time after e beginning, er source (i.e face pump, th
ses rapidly. W m mud free
hed at point inues to dec
ling and Analysis
an Journal of Ch
L(t) profiles
n of the calc lution in wat
L(t) profiles
n of the exp lution in wat
f calculated
ion lymer mer
the Gulf of M e the unstead
he well data used to calc evel in the a
ansient flow the surface
the mud cir e., the SPP) d herefore, the When the SPP
-fall velocit A. After tha crease linearl
s of Unsteady Flo
emical Engineeri culated resu ter
erimental re ter.
data by the
Average erro
Mexico is us dy flow for t a are shown
culate the m annulus after
velocity in t pump is sh rculation los due to the shu
e mudflow v P reaches zer ty in the dr at the mudflo ly. At point
ow Behavior in D
ing Vol. 33, No. 0 ults of HL an
sults of HL a
e model for 3
or of left-liquid
1.7% 2.21% 2.3%
sed the in mud r a
the hut ses ut- ve-ro, rill ow B,
th na m lik co th sy di be flo re riu sp th le ni po
Deepwater Contro
01, pp. 91 - 104, nd V with th
and V with
3 non-Newto
d height
L
H
E
he flow patte ar flow insi mudflow velo
ke the flow olumn in the he high-fricti ystem preven
ict the time etween in dr ow velocity eached. As c um time is 3 ponding mud he sea level evel in the an ing 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
ern transition de the drill ocity drops e
condition in e drill string ion pressure nts the surge
to reach th rill string and y drops to an be seen f 35 minutes. d level in th versus tim nnulus incre gradually re
rilling
h, 2016 rofiles ntal results f
rofiles ed results fo
flow experim
error of flow v
1.53% 3.56% 2.97%
ns from turb string. Sub exponentially n the experim
does not osc loss in the e. The model he mud leve d annulus. W zero, the e from Figure
Figure 7 sho he annulus m e. As expec eases rapidly eaches its fin
for the 3%
r the 1.8%
ments.
velocity EV
bulent to lam sequently, th y to zero. U ment, the mu cillate becau
CMC drillin l can also pr el equilibriu When the mu equilibrium
6, the equili ows the corr measured fro cted, the mu y at the begi nal equilibriu
95
mi-he
Un-ud use ng re-um
ud-is ib- re-om
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-law
Water 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 is shut 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 50
0 0.2 0.4 0.6 0.8 1 1.2
Time (min)
F
low
ve
loc
it
y
in t
he
a
nn
ulu
s (
m
/s
)
0 0.2 0.4
0.6 0.8 1
0 10 20 30 40 50
600
650
700
750
800
850
Time (min)
M
ud
le
v
e
l d
e
p
th i
n a
nnu
lu
s (
m
)
0 10 20 30 40 50
101 101.2 101.4 101.6 101.8 102
Time (min)
BH
P
(
M
P
a
)
0 2 4
101 101.5 102 A
A
by ra is m nu d ce in as pu p an sy g ci q th y comparing ate. Howeve s shut down masked by th ulus. The no rilling requi ease before ndicator of k ssociated wit However, ump shutdo rovide the tr nnulus after ystem is cou
iven by Eq. irculation bre
( p
qPI P P
When the he liquid flow
, ( 2( ( ( ( A Ann DC D Ann U U t L P L L Figure 9: with and w
Mode
Brazilia g surface pu r, detecting k n is very di he continuou ormal kick d ires a waitin
detecting fl kick. Therefo th a delay and the timely d own is cruci ransient mud
the surface upled to a re
(8). The un eak can be si
) b
P
kick occurs, w velocity in
2 ,0 ,0 - ) ) ( ( ) ) Ann Ann Ann Ann D DC Ann Ann DC Ann Ann n DC DC q U A A L L A P P L L g A L A
: Compariso without a kic
ling and Analysis
an Journal of Ch ump rate and
kick after th ifficult. The us returning
detection me ng period for low within ore, the detec d risks a loss detection of k ial. The abo dflow charac pump is shu servoir prod nsteady flow
imulated.
, the governi n the annulus
2 , , ) ) ( DC DC
f DC f Ann
Ann DC DC DC DC Ann U P P A L A L A L
on of annulu ck.
s of Unsteady Flo
emical Engineeri d subsea pu e surface pu kick is eas flow in the ethod for CM
r circulation the well as ction of kick of well contr kick after ev ove model c
cteristics in ut down. If ductivity mod
of kick afte
ing equation s is as follow
) ) bit C Ann DC P q
A L t
us flow velo
ow Behavior in D
ing Vol. 33, No. 0 ump ump sily an-MC n to an k is rol. very can the the del, er a (8) for w: (9) the Th her sm tra app acc of equ Fig for BH flu flo kic kic Fig kic com cal and lat cir det du me dev loa los niq sur pre los
ocity Fi
wi
Deepwater Contro
01, pp. 91 - 104, In this pape e unsteady fl he detailed d re. The equ mall kick. For
ansformed fr plication of curacy requi two-phase uation. The simulat gure 10. At t rmation pres HP is lower t uid will inva ow of kick s ck. The flow ck are highe g. 9 and Fig ck and loss o
mparing the lculated tren d mud level ted trend, a k rculation is i
tect kick and uring unstea easures to pr veloping fur ad may be ad ss of circulat que needs to The model re drilling sy essure, but n sses.
igure 10: C ith and witho
olled Mud-Cap Dr
January - Marc er, the empha
low behavio derivation of uation just ap
r large kick, rom single p steady fricti irements. Th
flow need t
tion results a the beginnin ssure, and th than the form ade into the starts to be w velocity an er than those . 10. The mo of circulation e real-time m nd. If real-tim
in annulus kick is indica indicated. Th d loss of circ ady flow a revent kick o rther in the w dopted to de tion has occ be further in is also appli ystems, such needs to be tu
Comparison out a kick.
rilling
h, 2016 asis is laid u
r of the pure f Eq. (9) is pplied in th the fluid in phase into tw
ion factor ca he frictional
to be introd
are shown in ng, the BHP here is no ki mation pressu e wellbore.
different fro nd mud level
e of no kick odel can be n during uns monitored tr me monitored are higher th ated. Conver his method c ulation in a t and helps or loss of cir well. A chang etermine whe curred. Howe nvestigated a ied to other m h as constan uned with fri
of annulus
upon analyzin
e liquid phas not presente he situation
the annulus wo-phase. Th annot meet th pressure lo duced into th
n Figure 9 an is higher tha ick. When th ure, formatio The unstead om that of n l in annulus k, as shown used to dete steady flow b
rend with th d flow veloci
98
g in m qu ti su fl er to ac b in ti
nu p b th af fo in
(1
pu 3 la an 1
8
The drillin elling effect ng system h matical mode uent flow is ion must be ure loss. For low lengths
ration make ors adequate cceleration o e insufficien ntroduced in ion factors.
S
The transi ulus during arameters, in it nozzle siz he mud, etc. ffect flow be ormed for ea ng the other p
1) Water De
The annul uted for wat 500 m and ated transien nd BHP for d 1 (a), the fl
Figu
ng fluid has a of low-velo has not been el. After a ci s unsteady fl exercised to r the CMC in combinat the applica for friction of mud, the nt. Unsteady to the mode
SENSITIVIT
ient flow ins unsteady flo ncluding the ze, water de . To underst ehavior, a se ach of these
parameters c
epth
lus flow vel ter depths of
4500 m. Fig nt flow veloc different wat flow velocity
(a) Flow ve
ure 11: Chan
a gelling effec ocity mud in n considered
irculation br low, which m o calculate th
drilling syst tion with sm ation of stead
pressure los steady frict friction fact l to replace
TY ANALYS
side the drill ow are influe
drill string, epth, physica tand how th ensitivity an parameters w constant.
locity and B f 500 m, 15 gure 11 pres city of mud ter depths. A y and equilib
elocity in ann
nges of flow
Jiwei Li, Gong
Brazilian Jou ct. The transi the CMC dr in this mat reak, the sub means that c he friction pr tem, long mu mall fluid acc
dy friction f ss. But for la tion factors c
tors need to the steady fr
SIS
l string and enced by ma
well geome al properties hese paramet nalysis was p while mainta
BHP were co 00 m, 2500 sents the cal
in the annu As shown in F brium time
nulus
velocity in a
ghui Liu, Jun Li a
urnal of Chemica ient
rill- the- bse- cau- res- ud- cel- fac-arge
can be
fric- an-any
try, s of
ters per-
ain- om-m, lcu-ulus Fig.
di-rec wa tw wh ann As wa dep can pea com ann BH the dir cee ma is cre to du dri
(2)
sen 1.5 12 flo bet Fig fec flo cre
annulus and B
and Mengbo Li
al Engineering ctly correlate ater generate ween the ins
hich consequ nulus from t s indicated in ater depth fo pth that doe n be determ arance of the mpletely by nulus. The f HP during ci e critical de rectly correla
ed the BHP ay result in a
less than the ease as the w well kick. uring narrow-illing operati
) Mud Densi
The annul nsitized to m 5 g/cm3, 1.6
(a), increase ow velocity tween the in g. 12 (b) dem cts the fluctu ow. Again, a eate fluctuati
BHP over tim
e with the w es a greater side of the uently increa the drill strin n Fig. 11 (b), or a given w es not create mined. At thi e friction pre the increas final equilibr irculation. If epth, the fin ate with the prior to the a loss of circ e critical dep water depth d Therefore, a -margin pres ions.
ity
lus flow v mud densitie g/cm3 and 1 es in the mu due to a gr side of the d monstrates th uation in the a critical m ions in the B
(b) B
me for differ
water depth b r pressure d
drill string ases the mud ng after a circ , the BHP lev well depth. A
a fluctuatio is water dep essure loss is e in the mu rium BHP i f the water d nal equilibriu water depth e circulation culation. If th pth, the final
decreases, w a fluctuation ssure drilling
velocity and s of 1.3 g/cm .7 g/cm3. As ud density wi reater pressu drill string an hat the mud d BHP during mud density
HP can be id
BHP
ent water dep
because deep difference b and annulu dflow into th culation brea
vel drops wi A critical wat on in the BH pth, the disa
s compensate ud level in th s equal to th depth excee um BHP w h and can e break, whic he water dep l BHP will d which may lea
n in the BH g is a threat
d BHP we m3, 1.4 g/cm
shown in Fi ill increase th
ure differen nd the annulu density also a g the unstead that 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
fr m th in cr d ti
(3
fo an
Figu
At the cri riction pressu mud level in t
he critical d nitial BHP reases. If th ensity, the st ial BHP as m
3) Well Dept
The calcul or well depth nd 9500 m a
Figur
Mode
Brazilia (a) Flow ve
ure 12: Chan
itical density ure loss is o the annulus. density, the f while circul he mud dens tabilized BH mud density d
th
lated annulu hs of 5500 m are shown in
(a) Flow ve
re 13: Chang
ling and Analysis
an Journal of Ch locity in ann
nges of flow
y, the decre offset by the If the mud d final BHP w lating as m sity is less th HP will be le
decreases.
s flow veloc m, 6500 m, 7 n Figure 13.
elocity in ann
ges in the flo
s of Unsteady Flo
emical Engineeri nulus
velocity in a
ease in annu increase in density exce will exceed mud density han the criti ess than the i
cities and BH 500 m, 8500 As 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
Fig rat cre equ fric dep cor sur no fie sta we cal as
n annulus an
Deepwater Contro
01, pp. 91 - 104, BHP over tim
g. 13 (a), inc te at which eases, which
uilibrium. T ction pressur pth. Fig. 13 rrelates with re fluctuation t result in fl ed. If the wel abilized BHP ell deepens.
l depth, the the well dep
nd BHP over
olled Mud-Cap Dr
January - Marc (b) B
me for the di
creases in th mudflow ve h prolongs th This phenom
re loss direct (b) shows th h the BHP, w
n. Again, a c fluctuations o
ll depth exce P will be les If the well d final BHP w pth decreases
(b) B
time for diff
rilling
h, 2016 BHP
ifferent mud
he well depth elocity in th
he time requ menon occurs tly correlates hat the well which also af ritical well d of the BHP eeds the criti ss than the i depth is less will exceed th
s.
BHP
ferent well d
densities.
h decrease th he annulus d
uired to reac s because th s with the we depth direct ffects the pre depth that do can be ident ical depth, th initial BHP
than the crit he initial BH
depths.
99
he
de-ch he ell tly
es-es ti-he
10 (4 ti 4 tr fo (a th G cr eq v (5 fo 1 an th fl eq ti th m g lu ti th ti n d th d b v m 00
4) Mud Visc
The annul igated at mu
5 mPa·s, 50 ransient flow or different m a), the mud he time to re Generally, a rease in the f quilibrium. A iscosity will
5) Drill Strin
The calcul or drill string 19.5 mm an nd Figure 15 he drill strin low velocity
quilibrium. F ional area of he annulus c metric flow r enerates a h us. Increasin ion pressure he annulus fr ion pressure ant role in t rill string ID he annulus. A rill string ID ecause the c ersely correl more mud wi
Figure 14:
cosity
lus flow velo ud viscositie
mPa·s and w velocity in
mud viscosit viscosity aff each equilibr high viscosi flow velocity As shown in reduce the f
ng Size
lated annulu g IDs of 82.5
d 130.5 mm (b), respectiv ng size sign y in the annu
For a given f the drill strin cross-sectiona rate conditio higher initial ng the drill st loss inside th rictional pres
loss inside th the total fric D will genera As revealed i D results incr cross-section lates with th ill flow into
(a) Flow ve
: Changes in
ocity and BH es of 35 mP
55 mPa·s. F n the annulu ties. As indic ffects the flo
rium in a co ity will yiel y and a longe n Fig. 14 (b) fluctuation in
s flow veloc 5 mm, 93.2 m m are shown
vely. As show nificantly im ulus and the wellbore ID ng inversely al area. For ons, a larger
flow veloci tring ID dec he drill strin ssure loss. B he drill string ction pressur ate a higher f n Fig. 15 (b) reases the eq nal area of t he drill string the annulus
locity in ann
the flow vel
Jiwei Li, Gong
Brazilian Jou HP were inv Pa·s, 40 mPa igure 14 sho us and the B
cated in Fig. ow velocity a omplex mann d a slower er time to rea ), a higher m n the BHP.
cities and BH mm, 107.4 m in Figure 15 wn in Fig. 15 mpacts the m
e time to rea D, the cross-s
y correlates w the same vo drill string ity in the an creases the fr ng and increa
ecause the fr g plays a dom re loss, a lar flow velocity ), increasing quilibrium BH
the annulus g ID; therefo s 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 str dri str tua (6) tiz in, sis dis lea ing ind typ ste aff (7) we L/s for cir of tot of the m/ cu occ sur and 0.6 mu sys annulus and
and Mengbo Li
al Engineering ring. The BH
ill string size ring size doe
ation in the B
) Nozzle Size
The annulu zed to nozzle 16/32nd in, a s are presente splayed in Fi ads to a fast g in a short dicated in Fig pically incre eady flow, bu
fect the final
) Volumetric
The calcula ere sensitized s, 30 L/s, 35 r the same d rculation rate transient m tal time for e
seconds afte e annulus mu /s for differe
ssed in the curs because re imbalance d the annulu 68 m/s indic um free fall v stem in Table
BHP over tim
HP shows si es during th es not signifi BHP.
e
us flow veloc e sizes of 10/
and 18/32nd in ed in Figure 1 ig. 16 (a), a l
flow velocit ter time to r
g. 16 (b), an eases the BH
ut this incre BHP.
c Flow Rate
ated annulus d to volumetr L/s and 40 L drill string ge e does not c mud flow vel
equilibrium er the surfac
ud flow velo nt initial vol
previous s e the mud flo e between th us, and the cates zero S
velocity insid e 3.
(b) B
me for the di
imilar trends e unsteady f ficantly influ
city and BH /32nd in, 12/3 n. The results 16 (a) and Fig larger nozzle
y and flow d reach the eq increase in t HP fluctuatio ease does no
s flow veloc ric flow rates L/s. As shown eometry, a d
ause noticea locity in the except for th e pump is sh ocity rapidly lumetric flow section, this ow is powere he inside of t annular flo PP which m de the drill st
BHP
ifferent mud
s for differe flow. The dr uence the flu
HP were sens 32nd in, 14/32 s of this anal gure 16 (b). A e size normal
decline, resu quilibrium. A the nozzle siz on during u ot significant
city and BH s of 20 L/s, 2 n in Figure 1 different initi able differen
e annulus an he first coup hut down, an y drop to 0.6 w rate. As di
phenomeno ed by the pre
the drill strin w velocity means a max
tring for give
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.
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 connecdetec-tion 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 columnin the annulus (m)
LDC Length of mud columninside the drill
string (m)
Lwell Well depth below the Kelly bushing (m)
N Time node
OD Outside diameter
PAnn, 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)
ρw 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).
Man-JP M O O S S A E sc af ti im th m in fl st is d d d th F th u le co tr agement T shore Tec (2014). PT Staff, EC
circulating ogy, 65(8) Malt, R., and
drilling fo shore Tech pur, Malay Ochoa, M. V and Tool J lics Calcul versity (20 Ogawa, A., Sugawara, wada, T., oscillation Newtonian Thermal S auer, C. W., state of the 39(9), 109 chubert, J. J.
APPENDIX Equation
In order to cribe the tran fter surface p ions were ma mmediately; he surface p mud is incom
nside the dril low is one-d tant; 7) the sothermal.
The well h rill string an rill string in efined as po he wellbore First, the drill he upper and
me are B1 a evel in drill
ontrol volum rol volume.
Modeli
Brazilia Toolbox for F chnology Co
C-drill elim g density. Jou
, 38-40 (201 d Stave, R., E
or challengin hnology Con ysia (2014). V., Analysis o
Joint Effect to lations. Ph.D 006).
Tokiwa, S. , T., Watana
Shishido, K n of liquid co n and non-Ne Science, 16(4
Mud displac e art. Journa 91-1101 (198 . and Juvkam
A: Derivati
o develop the nsient flow c pump shutdo ade: 1) all p
2) the drill pumps and o mpressible; 4 ll string and dimensional; mud does n
hole can be nd the annulu nto the annu
sitive. Figur at any time l string was s d lower bou and B2, resp l string is c me can be reg
ing and Analysis
an Journal of Ch Floating Dril onference, H
inates effect urnal of Petro
3).
EC-drill MPD ng pressure nference-Asi
of Drilling F o Reduce Er D. Thesis, Te
., Mutou, M abe, M., Sa K., Matumoto
olumn in vert ewtonian liq 4), 289-300 (2
cement durin al of Petroleu
7).
m-world, H. C
ion Process
e mathematic characteristic own, the foll pumps involv
string is disc open at the 4) the cross-annulus are 6) the mud not gel; and
divided into us. The mud ulus, and this e A1 shows during the studied as a c undaries of t
pectively. Be continuously
garded as a d
of Unsteady Flow
emical Engineeri ling Units. O Houston, Te
t of equival oleum Techn
D dual gradi regimes. O ia, Kuala Lu
Fluid Rheolo rrors in Hydr exas A&M U
M., Mogi, atou, K., Ki
o, N., Damp tical U-tube uids. Journal 2007). ng cementing um Technolo C., Well-cont for Govern
cal model to c in the annu lowing assum ved are stopp connected fr
surface; 3) -sectional ar constant; 5) density is c 8) the well
o two parts, flows from s direction w
the mudflow unsteady flo control volum the control v ecause 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-Fig any is e d dt wh vo is eepwater Controll
01, pp. 91 - 104, procedures to conventi Completion haughnessy, J P., Problem IADC Drill lands (1999 haughnessy, J
Durkee, T., lems. SPE/ dam, The N ave, R., Imp Offshore Te (2014). ewley, T. R
Copy. Rena engel, Y. A. Fundamenta Higher Edu egler, R., Du time: The b well contro flat time red ence, Houst
gure A1: Illu y time during
For this situ expressed as
CVBdV
t
hereBcan re lume, such a the local ma
led Mud-Cap Dri
January - Marc for dual-gra ional riser n, 21(04), 287
J. M., Armag ms of Ultra-ling Confere 9).
J. M., Daugh , More ultra /IADC Drill Netherlands (2 plementation echnology C R., Numerica aissance Pres and Cimbala als and Ap ucation, Ame ual gradient d
benefits of a l, enhanced w duction. Off ton, Texas (2
ustration of m g the unstead
uation, the R s follows (Çe
CV B dV t
epresent sev as the mass, aterial velociilling
h, 2016 adient drilling
drilling. SP 7-295 (2006) gost, W. K., -deepwater ence, Amster
herty, W. T., a-deepwater
ling Confere 2007). n of dual gra
onference, H
al Renaissan ss, La Jolla (2 a, J. M., Flu pplications. M
rica (2010). drilling is rea a retrofit sys
water depth fshore Techn 2014).
mudflow in t dy flow.
Reynolds tran engel and Cim
(
CSB
VVveral parame momentum ity; VCS is
1 g as compare
E Drilling ).
Herrmann, R drilling. SP rdam, Nethe
, Graff, R. L drilling pro ence, Amste adient drillin Houston, Tex nce, Advan 2012). uid Mechanic
McGraw H
ady for prim stem for bett capability an nology Confe the wellbore nsport theore mbala, 2010) )
CS dA
V n
eters per un or energy; V the local co
n-104 Jiwei Li, Gonghui Liu, Jun Li and Mengbo Li
Brazilian Journal of Chemical Engineering trol surface velocity at the surface elementdA; n
represents 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
( )
( ) 0
DC
DC DC DC B
L
A 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 U
A U U U
t
PA P A L A g
(A2)
whereis 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);
,DC f
P 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 ( P PB2PB1, PB1PDC,0);
,0 DC
P is the atmospheric pressure in Pa because the drill string is open at the surface after the surface pump is shut down (PB2PDC); and PDC 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 DC,0 f DC
DC
DC DC
P
P P
U
L L g
t
(A3)
Similarly, the momentum balance equation for the annulus can also be obtained:
,
,0 f Ann
Ann Ann
Ann
Ann Ann
P
P P
U
L 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. PAnnis the bottom hole pressure in the
annulus in Pa; Pf Ann, 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 ,0
DC
, ,
( )
Ann DC
Ann DC
DC Ann
Ann
f DC f Ann
DC Ann
U U
L L
t t
P P
P P
P P
L 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 Ann
DC Ann
U U
A A
t t
(A6)
According to the energy balance equation, the fol-lowing formula can be obtained:
2 2
2 2
DC DC Ann Ann bit
P U P U P
(A7)
where AAnn is the cross-sectional area of annulus in
m2; Pbit 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 DC
P , Pf Ann, and Pbit can be obtained from the
literature (Ochoa, 2006).
According to Equations (A5) (A6) (A7), UDC is eliminated, and the equation governing the liquid flow velocity in the annulus can be derived as follows:
2 2
,0 ,0
, ,
2( ) ( )
( )
( ) ( )
DC Ann
Ann Ann DC
Ann Ann
Ann DC Ann DC
DC DC
f DC f Ann bit DC Ann
Ann Ann
Ann DC Ann DC
DC DC
P P U U U
A A
t L L L L
A A
P P P L L g
A A
L L L L
A A
(A8)
Thus, the final expression for the motion equation for the length of mud columnLAnn in the annulus can be obtained:
Ann
Ann
L
U t
