ISSN 0104-6632 Printed in Brazil
www.abeq.org.br/bjche
Vol. 33, No. 02, pp. 297 - 305, April - June, 2016 dx.doi.org/10.1590/0104-6632.20160332s20140024
Brazilian Journal
of Chemical
Engineering
NUMERICAL INVESTIGATION OF
NON-NEWTONIAN DRILLING FLUIDS
DURING THE OCCURRENCE OF A GAS
KICK IN A PETROLEUM RESERVOIR
F. F. Oliveira
*, C. H. Sodré and J. L. G. Marinho
Universidade Federal de Alagoas, Centro de Tecnologia, Av. Lourival Melo Mota, Cidade Universitária, Centro de Tecnologia,
CEP: 57000.000, Maceió - AL, Brasil. Phone: + 55 21 82 32141260 *
E-mail: ffreireoliveira@gmail.com
E-mail: chsodre@gmail.com; luis_gmarinho@yahoo.com.br
(Submitted: August 24, 2014 ; Revised: March 15, 2015 ; Accepted: May 6, 2015)
Abstract - In this work, a simplified kick simulator is developed using the ANSYS® CFX software in order to better understand the phenomena called kick. This simulator is based on the modeling of a petroleum well where a gas kick occurs. Dynamic behavior of some variables like pressure, viscosity, density and volume fraction of the fluid is analyzed in the final stretch of the modeled well. In the simulations nine different drilling fluids are used of two rheological categories, Ostwald de Waele, also known as Power-Law, and Bingham fluids, and the results are compared among them. In these comparisons what fluid allows faster or slower invasion of gas is analyzed, as well as how the gas spreads into the drilling fluid. The pressure behavior during the kick process is also compared t. It is observed that, for both fluids, the pressure behavior is similar to a conventional leak in a pipe.
Keywords: Drilling; Kick; Well Control; CFX.
INTRODUCTION
The kick is a fluid flow from the petroleum reser-voir into the well during the drilling process. It can happen if the differential pressure between the for-mation pressure and the fluid circulation (flow) pres-sure and the permeability of the rock are large enough. The main causes of kick are: mud weight less than formation pore pressure; lost circulation of drilling fluid; failure to keep the hole full with fluid while tripping; swabbing while tripping. (Grace, 2003; Avelar, 2008).
The main indications of a well kick are: sudden increase in drilling rate; increase in fluid volume at
the surface; pressure reduction due to the removal of the drilling column, this pressure reduction may gen-erate negative pressure, allowing the formation fluid to flow into the well; gas, oil or water-cut mud; change in pump pressure. (Grace, 2003; Ajienka and Owolabi, 1991).
Drilling Fluids
29 (T o p o (B su T ci st ch ac pu w th th tr p u w b W fl pu g p m to k w th m an w W an qu o m st m is e lo o ci v S 98 Thomas, 200 ften be defin rocess of dri n the partic Barbosa, 200 Drilling fl ure a fast an Thomas (200
ific features, tabilize the hemically; k ccept any tre umpable; an with the oper hat the main he bottom of ransport them
ressure on t ndesirable f well, cool dow
it.
Well Control
Kick can b luid by emp
urpose of cir as to the su reventing br methods of w o keep const
ick removal well, the botto
he formation margin usuall
nnulus (Avel According well control u Wait and Weig
The Drille nd understoo uires minim f drilling flu The secon more precise
tep (Grace, methods are a s not possib .g., the drill ong distance r when ther irculation sy ided into th tatic Volume
01). Also cal ned as liquid illing petrole cular require 06).
luids must b nd safe dril 01), the fluid
, such as: it walls of th keep solids i
eatment, phy nd finally, it s ration. Thom
functions of f the cuttings m to the su the formation fluids (kick);
wn and lubric
l
be controlled ploying a me rculating an urface, allow reakage of th well control h ant pressure l. To preven omhole press n pore press ly equivalent lar, 2008). g to the litera used today ar
ght Method a er's Method
od by the d al calculatio id circulation nd method i
calculations 2003; Avel applied when ble. These s
string is ou from the bo re are mech ystem. Thes he Dynamic etric Method
led mud, dri d compositio eum wells, a ements of ea
be specified ling process d should pre must be che he well, me in suspension ysical and ch should have c mas (2001) a
f drilling flu s generated b urface; gener
ns to preven ; stabilize th cate the drill
d by circulat ethod of we influx of gas wing the gas he well (Grac have as their into the bot nt further in
sure should b sure plus an t to the press
ature, the m re: the Driller and Volumetr is simple an drilling crew n and consis n.
s more com s and only lar, 2008). T n the circulat situations ca ut of the wel
ottom, drill j hanical prob e methods c Volumetric d (Avelar, 200
F. F. Oliveira
Brazilian Jou
illing fluids c ons to help nd they depe ach perforat
in order to s. According sent some s emically stab echanically a n when at re hemical, and
cost compati also has writ uids are to cle
by the drill a rate hydrosta nt the influx he walls of l string and d
ting the inva ell control. T
s is to bring to expand a ce, 2003). M
basic princi ttomhole dur nflows into be kept equa n added saf sure drop in
main methods r's Method, T ric Methods. nd easily tau w because it
sts of two st
mplex, requir one circulat The volumet
tion of the k an occur wh ll, the drill i ets are clogg blems with
are further c Method a 08).
, C. H. Sodré and
urnal of Chemica
can the end tion en-g to spe-ble; and est; d be ible tten ean and atic x of the drill ader The the and Most iple ring the al to fety the s of The ught re-eps ring tion tric kick hen, is a ged the di-and No wh wh are she gra go are the bet of Fig So Os flu po the app mi wh L ma giv wh rat a
d J. L. G. Marinho
al Engineering
on-Newtonia
Fluids can hen under st here the valu e known as ear stress is adient. The
ry (Sleigh an Fluids that e known as N er divided i
tween the sh the fluid. Fig
gure 1: Sh ource: Sleigh
Fluids with stwald de W uids used in rtant rheolog The Bingh eoretically th
plied to pro inimum shea hen the fluid
,
L theoretica
atical expres ven by Equat
0 p L
here p, te of shear an
The apparen L a p o an Fluids show large tress. Fluids ue of dynami
Newtonian s linearly d most commo nd Noakes, 2
do not obey Non-Newton nto categori hear stress an
gure 1 shows
hear stress v and Noakes
h Rheologica Waele compos
drilling oil w gical characte
am model, hat a minim oduce some ar stress is c
is subjected ally it behave
sion that def tion (1) (Mac
f
f
and L, r nd yield stres
nt viscosity i
e differences that obey N ic viscosity (
fluids. If μ ependent on on fluids are 2009).
Newton's la nian fluids. T ies based on nd the rate o s these categ
vs. Rate of s (2009).
al behavior o se the major wells, since eristics for gr or ideal pla mum shear s
shear defo called the yie d to a shear s
es as a solid fines the Bin chado, 2002) for for L L epresent pla ss, respective is given by E
s in behavi Newton's law (μ) is consta
is a constan n the veloci
e in this cat
aw of viscosi These are fu n the relatio of shear stra gories.
f shear strai
of Bingham rity of drillin
they have im ravels remova
astic, requir stress, L, b ormation. Th
eld stress an stress less tha
P τ w as ti g v fl th u b by T th O th p th su th th ca an p m d P d op d lo o ar (g an The Ostwa Power-Law m defined as:
nK
where K and n s consistenc ively (Macha The Powe ories accord alues smalle luids are call hey are call nity, the flui ehavior of P y the appare The apparent
hrough Equa
n 1a K Objective an This pape he bottomhol rocess, offer he behavior ure and amo he pit.
The literat his topic, ma an be used to nd specificity erformed m make public evoted to thi
Physical Prob
The case rilling of an ped. Figure rilled. For th ocated at the
il well (drill rrows in the green arrows nnular regio
ald de Waele model, shows
n are the rhe cy index an ado, 2002). r-Law fluids ding to their i er than one a led pseudopl
ed dilatants id behaves li Power-Law f ent viscosity viscosity of ation (4) (Ma
1
d State of th
r aims to un le of petroleu ring a tool t
of some imp ount of form
ture is very p ainly due to t o validate the y of oil well mostly by lar their workin is topic is we
METHO
blem Descri
study was t n oil well. A 2 shows the he simulation e end of the s led in reserv e detail of Fi s, in the deta on in an upw
e model, also s the relation
ological para d behavior
s are divided index behavi and greater t lastics. If n i s. When the ike a Newto fluids can al y variation w
the fluid can achado, 2002
he Art
nderstand w um wells dur that can be
portant varia mation fluid t
poor in articl the lack of in e results and
drilling proc rge compani ng methods. elcome. ODOLOGY iption (Case
to analyze t A kick simula
sketch of an n of the kick,
stretch witho voir rock). T igure 2) alon ail of Figure ward two-ph
o known as n of shear stre
ameters, kno index, resp
d into two ca ior value. Fo than zero, th s greater tha value of n onian fluid. T
lso be analyz with shear ra n be determin
).
what happens ring the drill used to pred ables like pr that can inva
les dealing w nformation t
the complex cedures that ies that do Thus, resea
e Studied)
the kick dur ator was dev n oil well be
, the gas inle out casing of The fluid (bla
ng with the 2) flows in hase flow. T
the ess, (3) own pec- ate-or n hese an 1 n is
The zed ate. ned (4) s in ling dict res-ade with that xity are not arch ring vel-eing et is f an ack gas the The stu ph Fig the De om loc tha Co the hap wh the com tub sul ent pre fiv mo du per str tes lon pen de wa Tab tur ele
udy was per hase flow pro
gure 2: Rep e final stretch
escription of
After maki metry shown
cated in the m at the gas is onsidering th
e tube was t ppens in thi hole region. e domain to b
mputational be was mode
lt obtained in tire area. The
It is also kn e-Salt region ve thousand m
odeling span ue to the com
rformed in o retch the len sts, it was co ng would be n in the pit a signed using are. The dim ble 1 and Fi red model w ements. rformed by ofiles. presentation h. f Geometry
ng the abov in Figure 3 middle of the s equally di he symmetry aken to perf is slice app This was req be studied an effort. A sec eled and, as n this region e section is sh nown that an n, frequently
meters in the nning that len mputational e order to def ngth of the oncluded tha
suitable to r at the time o g the ANSY mensions of t
igure 3 C. Th ith 237 476
analyzing t
of the well
of the Studi
ve considera 3 was The w e reservoir, it istributed at
of the well, form the sim roximately r quired in ord nd especially ction of 45 d suming sym can be extra hown in Figu n oil well, esp
reaches dep e final phase ngth would b effort require fine the leng
desired pipe at a tube ab represent wh of the studied YS® ICEM 13 the geometry he mesh use
predominant
transient tw
and detail
ied Domain
ations, the g well studied
t was assume the entranc only a slice mulation. Wh represents th der to simpli y to reduce th
degrees of th mmetry, the r
apolated to th ure 3 A and B
pecially in th pths exceedin e of drilling. be impractic ed. Tests we gth that wou e. After som
out 20 mete hat would ha d phenomeno
30
D
S
D
du fi fo ar
T
S
v a th
00
F r
Table 1: F Dimension
L1 = di /2 L2 L3 L4 L5 = Hres
Source: AVELAR
Drilling Fluid
The behav uring the ki ive being Po our Bingham
re shown in T
Table 2: Rhe
Parameters
Fluid 1 Fluid 2 Fluid 3 Fluid 4 Fluid 5 Source: WALDM
The natura alues above l., 1966). Th he modeling
Figure 3: D representatio
Features of th Value
(in) Va
(cm
2.1 5.3 0.4 1.0 1.5 3. 2.5 6. 10 25 R (2008); Author
ds and Natu
vior of nine d ick process, ower-Law flu m fluids. Th
Table 2.
eological pr Power-L
K (Pa.sn)
2.4 0.855 0.42 1.154 2.096 MANN (2012)
al gas found 90% methan hus, in this it was consi
Dimensions o on; (B) Detail
he develope alue
m)
D
334 Inner rad 016 Drill stri .81 Annular .35 Drilling 5.4 Gas inle
ural Gas Use
drilling fluid all non-New uids (all pseu
e parameter
operties of d Law
n τL
0.376 5. 0.549 3. 0.634 2. 0.543 3. 0.468
d during dril ne in its comp
study, in or idered that t
F. F. Oliveira
Brazilian Jou
of the geom l of the mode
ed geometry. Description
dius of drill stri ing thickness r length
fluid inlet heig et height
ed
ds was analyz wtonian flui udoplastic) a s of each fl
drilling fluid Bingham (Pa) µp(Pa. 966 0.012 527 0.019 612 0.017 561 0.029
lling may sh position (Lee rder to simpl the composit
, C. H. Sodré and
urnal of Chemica
metry used in eled section;
.
ing
ght
zed ids, and luid
ds.
.s)
2 9 7 9
how e et lify tion
of pro
So
M
the em rep tio cal as is, a m tio uti
M
reg
d J. L. G. Marinho
al Engineering
n the model (C) Size.
natural gas operties of th
Table Properties
Molar mas Density Dynamic v Reference t Reference p ource: PEACE (20
athematical
The mathem e Finite Volu mbedded in th presenting an ons in the fo
lculated at d fluxes at th the small vo mesh. The ti ons per times
ilized in the s
odeling Con
The follow gard to the pr All drilli
o
l: (A) Three
consists mos his gas are sh
e 3: Methan s
s
viscosity temperature pressure 013); LEE et al. (
l Model
matical mod ume Model he software u nd evaluating orm of algeb
discrete plac he surfaces o
olume surrou mestep was step and the simulations.
nsiderations
wing conside roperties of t ng fluids are
e-dimensiona
stly of metha hown in Tabl
e gas proper V
0.01 22 2.8242x
4.997 (1966)
del used in t (FVM), wh used. FVM i g partial diff braic equation
es on a mes of each finite
unding each 0.1 s with u k-ϵ turbulen
erations wer the fluids inv
considered in al
ane. The ma le 3.
rties. Value
16 kg/mol 3.7 kg/m³ x10-5Pa.s 365 K 77x107 Pa
this work w hich is alread
s a method f ferential equ ns. Values a shed geomet e volume, th node point o up to ten iter nce model w
re made, wi volved:
ncompressibl ain
was dy for ua-are
try hat on ra-was
ith
The variation of the gas compressibility was considered to be very small, and therefore neglected;
The temperature variation in the evaluated stretch was neglected;
The physicochemical properties of drilling fluids and gas remained constant in the analyzed section;
The drilling fluid and gas inlet pumping speeds were considered constant in the analyzed time interval.
Initial Conditions
The initial condition of the well represents a nor-mal drilling situation, with known constant flow rate of circulating drilling fluid and without the presence of gas within the well. In this case, the drilling veloc-ity vle at the entrance of the well is calculated by Equation (5),
2 / 4
l le
i
Q v
d
(5)
where Q is the volumetric flowrate of drilling fluid injected into the well, and di is the diameter of the drill string.
The pressure (pformation) at the point where the
en-trance of drilling fluid occurs is given by Equation (6).
formation l p
p SIDPPgD (6)
where SIDPP is the shut-in drill pipe pressure; l is the density of the drilling fluid; g is the acceleration of gravity, and Dp is the depth of the well at that point.
After a determined period of time, a formation with pressure above the one exerted by the drilling fluid is reached, the gas from this formation begins to enter the well. The pressure of this porous for-mation was estimated to be 10% greater than that exerted by the drilling fluid at the same point, which was also calculated by Equation (6).
During the entry of gas into the well, the fluid pumping conditions remain unchanged and the ve-locity of the liquid at the entrance of the well can be calculated by Equation (5). In this step, the input flow of gas is determined by the equation of perma-nent radial flow in porous medium for compressible fluids, shown in Equation (7) (Rosa et al., 2006).
2 ( )
ln
res res formation bottom
g
res g
e
K H p p
Q
d d
(7)
The entrance velocity of the gas into the well is calculated by Equation (8).
2 ( ) 1
ln
res res formation bottom
ge
res e res
g
e
K H p p
v
d d H
d
(8)
where Kres and Hres are the permeability and
reser-voir height, respectively, (pformationpbottom) is the
differential pressure in the bottomhole; g is the gas viscosity; dres and de are the diameters of the reser-voir and the well, respectively; d He res is the sur-face area of the gas entrance. The gas density is cal-culated using Equation (9).
'
bottom atm
g
p p M
Z RT
(9)
where pbottom and patm are the pressures in the bot-tomhole and the atmospheric pressure, respectively, M is the molecular mass of the gas, Z' is the com-pressibility factor, R is the universal gas constant, T is the temperature in the bottomhole.
The gas viscosity (g) given in micropoise was calculated by Equation (10), which was developed by Lee et al. (1966).
' 'exp ' Y
g K X g
(10)
where
1.57.77 0.063 '
122.4 12.9 M T K
M T
(11)
1914.5
' 2.57 0.0095
X M
T
(12)
' 1.11 0.04 '
Y X (13)
30 in ri
S
D
su th 02
nitial conditi ized in Table
Table 4:
Source: AVELAR
Data Acquisi
Several si ults were an hese points a Paramete
Total dept Thickness Height of t Well diam Outside di Thickness SIDPP Density of Surface tem Pressure o Geotherma Reservoir Reservoir Reservoir Accelerati Pressure in Temperatu Speed of d Speed of th
ons used in t e 4.
: Parameter
R (2008); PERRY
ition
mulations w nalyzed at fo are presented er
th of the well of the water de the well meter
iameter of the d of the drill stri
f the drilling flu mperature on the surface
al gradient permeability height diameter ion of gravity n the bottomhol ure in the bottom drilling fluid in
he gas at the in
the simulatio
s used in sim
Y (1999), REID e
were perform our points. T d in Table 5 a
Figu V
epth
drill string ng
3 uid
9.8
le 4
mhole the inlet let
F. F. Oliveira
Brazilian Jou
ons are summ
mulations.
t al. (1986)
med and the The locations and Figure 4.
ure 4: Locati Value (SI Units
3 600 m 1 000 m 20.32 m 0.2032 m 0.1219 m 0.01016 m 3.1026x106 Pa 1 199 kg/m3
300 K 101 325 Pa
0.025 K/m 8692x10-13 m2 0.254 m 1 000 m 9.8066 m/s2 4.9977x107 Pa 365 K 3.9831 m/s 0.1838 m/s
, C. H. Sodré and
urnal of Chemica
ma- re-s of
P
Inf
pse sis flu ior on set
um tim the of sio dec mo exp in
ion of data a s)
d J. L. G. Marinho
al Engineering
Table 5 Point/coordina
Point 1 Point 2 Point 3 Point 4
RES
fluence of V
Five Power eudoplastic stency and b uid are presen r of each flu nly the drillin ttings unchan
Figures 5 a me fraction o me at the po e graph in Fi the simulati on of gas fa crease in th ore quickly plained beca comparison
cquisition po o
5: Points for ates X (cm
9.906 9.906 9.906 9.906
SULTS AND
Viscosity in P
r-Law fluids type with behavior. Th nted in Table uid, five sim ng fluid was r
nged. and 6 show t of the drilling oints 2 and 4 igure 5, it can ion, that the aster than th he concentra at the obser ause this flui to the others
oints.
r data acqui m) Y (cm)
6 254 6 508
6 1 016
6 1 778
D DISCUSSI
Power-Law
were analyz different ind he character e 2. To comp mulations we replaced, kee
the comparis g fluid as a f 4, respective n be seen, at e third fluid he other flui ation of the
rved point. T id has the lo s.
isition. ) Z (cm)
0 0 0 0
ION
Fluids
zed, all of th dices of co
istics of eac pare the beha
ere performe eping all oth
son of the vo function of th ely. Analyzin t the beginnin allowed inv ids, causing
drilling flu This could b
west viscosi he n-ch av-ed; her
ol-he ng ng
F (P
fl g g m
F L
In
ly w an fo in u fo
p F d la th p
Figure 5: V Power-Law)
Figure 6 sh luids at the p
as invasion i esting that t most at the sa
Figure 6: Vo Law) at the po
nfluence of P The chara yzed are sho with different
nalyzed. To our simulatio ng fluid wa
nchanged. T or these simu Figures 7 a oints 3 and Figure 7 show
ecrease of d ater time than hat, for fluid
rogress is slo
Volumetric f at the point
hows the vo point 4. At th in the drillin the invading ame time for
lume fractio oint 4.
Plastic Visco acteristics of
own in Tabl t plastic visco
compare th ons were per as replaced, The k-ε turbu
ulations. and 8 show t d 4, respecti ws the densi ensity for Bi n for the oth d with highe ow.
fraction of 2.
lumetric frac his point, the ng fluids are g gas reache all fluids ana
n of drilling
osity in Bing f each Bingh le 2. Four B osities and fl he behavior
rformed and keeping all ulence model
the fluid den ively, for B ity profiles a ingham fluid her fluids. Th er plastic vis
drilling flu
ction of drill e differences very little, s s this point alyzed.
g fluids (Pow
gham Fluids ham fluid a Bingham flu flow limits w of each flu d only the dr l other settin
l was also u
nsity behavio Bingham flui
at point 3. T d #4 occurs a his result sho scosity, the
uids
ling s in
ug-
al-
wer-s ana-uids were uid, rill-ngs sed
r at ids. The at a ows gas
Th wi
Fig po
Fig po
Inf
rhe Bin par per La scr var vad Po the un tha mi
vo the
Figure 8 sh he same patte
th a slight de
gure 7: Den int 3.
gure 8: Den int 4.
fluence of F
Two types o eological beh ngham fluid re the beha rformed usin aw fluid #1;
ribed in Tabl riation of th ding the dr ower-Law flu e fluids beh ntil they reac ane. From th ismatch.
The graph i lumetric fra e point 4. A
hows the den ern of density ecrease in tim
nsity of drillin
nsity of drillin
Fluid Type: P
of non-Newt havior were
and Ostwal avior of thes
ng the Bing all properti le 2. The gra he volumetri
rilling fluid uids at the po have identica ch the maxim
hat point bo
in Figure 10 ction of me At this point,
sity profiles y drop with me for the Bin
ng fluids (Bi
ng fluids (Bi
Power-Law
tonian fluids used: the id d de Waele f se, two sim
ham fluid # ies of these aph in Figur ic fraction o for both B oint 1. It can ally in the f mum concen oth graphs b
shows the v thane invadi the concent
at the point time was ke ngham fluid #
ingham) at th
ingham) at th
vs. Bingham
with differe deal plastic fluid. To com mulations we
#1 and Powe fluids are d re 9 shows th of methane i
Bingham an n be noted th
first momen ntration of m begin to sho
variation of th ing drilling tration of m
4. ept #4.
he
he
m
ent or m-ere
er- de-he in-nd hat nts
me-ow
me-30 th re th
sh d (B
F
p d re
04
hane in the each the max hat observed Considerin hows that the rilling fluid Bingham flui
Figure 9: M
Figure 10: M Figure 11 oint 3. When rops abruptly eaching its lo
Figure 1
simulation ximum value
with the Pow ng the case
e gas propag has ideal p id).
Methane volu
Methane volum
shows the n the gas inv y, causing a owest value.
11: Pressure v
with a Bing e at slightly e
wer-Law flui s studied h gates more qu plastic rheolo
ume fraction
me fraction a
pressure v vades the we kind of insta
variation at t
F. F. Oliveira
Brazilian Jou
gham fluid c earlier time th
id.
here, the res uickly when ogical behav
at the point
at the point 4
variation at ell, the press ant vacuum a
the point 3.
, C. H. Sodré and
urnal of Chemica
can han
sult the vior
1.
4.
the sure and
ref ate
sim con pre
tem req po pre for
vel dy fra ga
ob all con ob it vis
son sho ing is a
wh sha bac bac liz tio pre kin
abo com in sub con nee trib vel int fie
d J. L. G. Marinho
al Engineering
Then it goe ference press e level which The pressu milar to the nventional le essure drop i
Well drillin mperatures ar quires high t ints in the essure within rmation fluid
In this work loped to aid ynamic behav actions of bo
s-liquid mixt During the served that owed faster ncentration o served point was noted t scosity, allow Considering n between th owed that th g fluid has i a Bingham f For the pre hen gas inv arply and re ck up to a l ck to an inte ze over time. onal leak in a
essure drop nds of fluids As has bee out this topi mpare the re the future, th bject and su ntributing po er responsib bute to an i lopment, as terpretation eld.
o
es back up to sure and furt h tends to sta ure behavior e one obser eak in a pip is almost equ
CONCL
ng in areas re becoming technology. O
drilling pr n the well. ds can invade
k, a simplifi the analysis vior of some th drilling fl ture in the w analysis with
fluid #3, be gas invasion of the drilling
. For the ana that the flui wed slower ad
g the cases an he Power-Law he gas spread
ideal plastic fluid.
essure variab vades the w eaches its lo
level close t ermediate le This behav a pipe. It wa was almost were compa en said, there
ic in the lite esults obtaine
here will be uch compar ositively to ble for the dr
mprovement well as a of the phen
o a level clos ther back to abilize over ti r shown in rved in the
e. It is also ual for both f
LUSION
with high more comm One of the m rocess is co If this con e the well, cau
ed kick simu s, through gr
variables, su uid and gas, well and press h Power-Law eing less vis n, causing a d g fluid more alyses with B
id #4, with dvance of the nalyzed here w fluid and B ds quickly w
rheological
ble, it was o well, the p owest value; to the initial evel, which t ior is similar s further obs t the same w ared.
e is a lack o rature that c ed here. It is more papers isons can b the decision rilling. It wo t in training better unde nomena occ
se to the initi an intermed ime.
Figure 11 profile of noted that th fluids.
pressures an mon, although
most importa ontrolling th ntrol fails, th using the kick ulator was d raphics, of th uch as volum density of th sure.
w fluids, it w scous, initial decrease in th
quickly at th Bingham fluid higher plast e invading ga e, the compar Bingham flu when the dri behavior, i.e
observed tha ressure drop ; then it go l pressure an tends to stab r to a conve served that th when the tw
of informatio can be used
expected tha s related to th be made, thu ns of the eng
ould also co and staff d erstanding an curring in th ial
di-is a he
nd h it ant he he k. de-he me he
was lly he he ds, tic as. ri-uid
ll-e.,
at, ps es nd
bi- n-he wo
on to at, he us
NOMENCLATURE
de Well outer diameter (m)
di Inner diameter of drill string (m)
Dp depth of the well (m)
dres Reservoir diameter (m)
g acceleration of gravity (m.s-²) Hres Reservoir height (m)
K consistency index (kg.m-¹s-²sn) K' LEE equation parameter --- Kres Reservoir permeability (m²)
M Molecular mass of the gas --- n behavior index ---
patm Atmospheric pressure (Pa)
pformation Formation pressure (Pa)
Pbottom Bottomhole pressure (Pa)
g
Q Flow of gas (m³.s-¹)
l
Q Flow of drilling fluid (m³.s-¹) R Universal gas constant (m².s-².T-¹) SIDPP shut-in drill pipe pressure (Pa) T Bottomhole temperature (K)
vge Velocity of the gas in the entrance (m.s-¹)
vle Velocity of the drilling fluid in the entrance (m.s-¹)
X Cartesian coordinate (m) X' LEE equation parameter --- Y Cartesian coordinate (m) Y' LEE equation parameter --- Z Cartesian coordinate (m) Z' Compressibility factor ---
Greek Letters
γ Shear stress rate (s-¹) µa Apparent viscosity (Pa.s)
μg Gas viscosity (Pa.s) µp Plastic viscosity (Pa.s)
ρg Gas density (kg.m-³)
ρl density of the drilling fluid (kg.m-³)
τ Shear stress (Pa)
τL Yield stress (Pa)
REFERENCES
Ajienka, J. A. and Owolabi, O. O., Application of mass balance of kick fluid in well control. Journal
of Petroleum Science and Engineering, 6(2), 161-174 (1991).
Avelar, C. S., Well Control Modeling: A Finite Dif-ference Approach. Master Thesis, State Univer-sity of Campinas, Campinas, Brasil (2008). Barbosa, M. I. R., Bentonites Treated with Polymeric
Additives for Application in Drilling Fluids. Mas-ter Thesis Federal University of Campina Grande, Campina Grande, Brasil (2006).
Grace, R. D., Blowout and Well Control Handbook. With contributions by Cudd, B. et al. Elsevier Science, USA (2003).
Lee, A. L., Gonzalez, M. H. and Eakin, B. E., The viscosity of natural gases. Journal of Petroleum Technology, 18(8), 997-1000 (1966).
Machado, J. C. V., Reologia e escoamento de fluidos: Ênfase na indústria do petróleo. Interciência, Rio de Janeiro (2002). (In Portuguese).
Peace Software, Some scientific and engineering data online. 2013. Available in: <http://www. peacesoftware.de/einigewerte/einigewerte_e.html> (Accessed: October 10, 2013).
Perry, R. H., Perry’s Chemical Engineers’ Handbook. 7th Ed. McGraw-Hill, USA (1999).
Reid, R. C., Prausnitz, J. M. and Poling, B. E., The Properties of Gases and Liquids. 4th Ed. Singa-pore, Mc-Graw-Hill (1986).
Rosa, A. J., Carvalho, R. S. and Xavier, J. A. D., Engenharia de Reservatórios de Petróleo. Inter-ciência, Rio de Janeiro (2006). (In Portuguese). Sleigh, A. and Noakes C., An introduction to fluid
mechanic: Fluid mechanics and fluid properties. School of Civil Engineering, University of Leeds, (2009). Available in: <http://www.efm.leeds.ac. uk/CIVE/CIVE1400/Section1/Fluid_mechanics.h tm> (Accessed: January 2, 2014).
Thomas, J. E., Fundamentos de Engenharia de Petró-leo. Interciência, Rio de Janeiro (2001). (In Portu-guese).
