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NUMERICAL INVESTIGATION OF NON-NEWTONIAN DRILLING … · 29 (T o p o (B su T ci st ch ac pu w th th...
Transcript of NUMERICAL INVESTIGATION OF NON-NEWTONIAN DRILLING … · 29 (T o p o (B su T ci st ch ac pu w th th...
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
*To whom correspondence should be addressed
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: [email protected] E-mail: [email protected]; [email protected]
(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
Drilling fluids are complex mixtures of solids, liquids, chemicals, and sometimes even gases. From the chemical point of view, they can assume aspects of suspension, colloidal dispersion or emulsion, de-pending on the physical state of the components
29
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Kick can bluid by empurpose of ciras to the sureventing br
methods of wo keep constick removal
well, the bottohe formation
margin usuallnnulus (Avel
Accordingwell control uWait and Weig
The Drillend understoouires minimf drilling flu
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methods are as not possib.g., the drill ong distance r when therirculation syided into thtatic Volume
01). Also calned as liquidilling petrolecular require06). luids must bnd safe dril
01), the fluid, such as: it walls of th
keep solids ieatment, phy
nd finally, it sration. Thomfunctions of
f the cuttingsm to the suthe formationfluids (kick);wn and lubric
l
be controlledploying a merculating an
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ant pressure l. To prevenomhole pressn pore pressly equivalentlar, 2008).
g to the literaused today arght Method aer's Method od by the dal calculatioid circulation
nd method icalculations2003; Avel
applied whenble. These s
string is oufrom the bo
re are mechystem. Theshe Dynamicetric Method
led mud, drid compositioeum wells, aements of ea
be specified ling process
d should premust be che
he well, mein suspensionysical and chshould have cmas (2001) af drilling flus generated b
urface; generns to preven; stabilize thcate the drill
d by circulatethod of weinflux of gas
wing the gas he well (Grachave as their
into the botnt further insure should bsure plus ant to the press
ature, the mre: the Drillerand Volumetris simple an
drilling crewn and consisn. s more coms and only lar, 2008). Tn the circulatsituations caut of the welottom, drill jhanical probe methods c Volumetric
d (Avelar, 200
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illing fluids cons to helpnd they depeach perforat
in order to s. Accordingsent some semically stabechanically an when at rehemical, andcost compatialso has writuids are to cleby the drill arate hydrostant the influxhe walls of l string and d
ting the invaell control. Ts is to bring to expand a
ce, 2003). Mbasic princi
ttomhole durnflows into be kept equan added safsure drop in
main methodsr's Method, Tric Methods. nd easily tau
w because it sts of two st
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Fluids can hen under sthere the value known as ear stress isadient. The ry (Sleigh anFluids that
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2009). Newton's la
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ravels removaastic, requirstress, ,L bormation. Theld stress anstress less thad. The mathngham fluid ),
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The Poweories accordalues smalleluids are callhey are callnity, the fluiehavior of Py the appare
The apparent hrough Equa
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Objective an
This papehe bottomholrocess, offerhe behavior ure and amohe pit.
The literathis topic, maan be used tond specificityerformed m
make public evoted to thi
Physical Prob
The case rilling of anped. Figure rilled. For thocated at theil well (drillrrows in thegreen arrowsnnular regio
merical Investigat
Brazi
ald de Waelemodel, shows
n are the rhecy index anado, 2002). r-Law fluids
ding to their ier than one aled pseudopled dilatantsid behaves liPower-Law fent viscosityviscosity of
ation (4) (Ma
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METHO
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e model, alsos the relation
ological parad behavior
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achado, 2002
he Art
nderstand wum wells durthat can be portant varia
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poor in articlthe lack of ine results and drilling proc
rge companing methods. elcome.
ODOLOGY
iption (Case
to analyze tA kick simula
sketch of ann of the kick,stretch withovoir rock). Tigure 2) alonail of Figure ward two-ph
tonian Drilling Fl
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the kick durator was devn oil well be, the gas inleout casing ofThe fluid (blang with the 2) flows in
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the ess,
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Occurrence of a G
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udy was perhase flow pro
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escription of
After makimetry shown cated in the mat the gas isonsidering the tube was tppens in thihole region. e domain to bmputational be was modelt obtained intire area. TheIt is also kn
e-Salt regionve thousand modeling span
ue to the comrformed in o
retch the lensts, it was cong would be n in the pit asigned usingare. The dimble 1 and Fired model wements.
Gas Kick in a Pet
05, April - June,
rformed by ofiles.
presentation h.
f Geometry
ng the abovin Figure 3
middle of thes equally di
he symmetry aken to perfis slice appThis was reqbe studied aneffort. A sec
eled and, asn this regione section is shnown that ann, frequently meters in the
nning that lenmputational eorder to defngth of the oncluded thasuitable to r
at the time og the ANSY
mensions of tigure 3 C. Thith 237 476
troleum Reservoi
2016
analyzing t
of the well
of the Studi
ve considera3 was The we reservoir, itistributed at of the well,
form the simroximately rquired in ordnd especiallyction of 45 dsuming sym can be extrahown in Figu
n oil well, espreaches dep
e final phasength would beffort requirefine the lengdesired pipe
at a tube abrepresent wh
of the studiedYS® ICEM 13
the geometryhe mesh usepredominant
ir 2
transient tw
and detail
ied Domain
ations, the gwell studiedt was assumethe entranc
only a slice mulation. Wh
represents thder to simpliy to reduce thdegrees of th
mmetry, the rapolated to thure 3 A and Bpecially in th
pths exceedine of drilling. be impracticed. Tests wegth that woue. After somout 20 mete
hat would had phenomeno3.0 CFD sofy are given
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30
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Table 1: F
Dimension
L1 = di /2 L2 L3 L4
L5 = Hres
Source: AVELAR
Drilling Fluid
The behavuring the kiive being Poour Binghamre shown in T
Table 2: Rhe
Parameters Fluid 1 Fluid 2 Fluid 3 Fluid 4 Fluid 5
Source: WALDM
The naturaalues above l., 1966). Thhe modeling
Figure 3: Drepresentatio
Features of th
Value (in)
Va(cm
2.1 5.30.4 1.01.5 3.2.5 6.10 25
R (2008); Author
ds and Natu
vior of nine dick process, ower-Law flum fluids. ThTable 2.
eological pr
Power-LK (Pa.sn)
2.4 0.855 0.42
1.154 2.096
MANN (2012)
al gas found90% methanhus, in this it was consi
Dimensions oon; (B) Detail
he develope
alue m)
D
334 Inner rad016 Drill stri.81 Annular.35 Drilling 5.4 Gas inle
ural Gas Use
drilling fluidall non-New
uids (all pseue parameter
operties of d
Law n τL
0.376 5.0.549 3.0.634 2.0.543 3.0.468
d during drilne in its compstudy, in oridered that t
F. F. Oliveira
Brazilian Jou
of the geoml of the mode
ed geometry.
Description
dius of drill striing thickness r length fluid inlet heig
et height
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drilling fluid
Bingham (Pa) µp(Pa.966 0.012527 0.019612 0.017561 0.029
lling may shposition (Lee
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Table
PropertiesMolar masDensity Dynamic vReference tReference p
ource: PEACE (20
athematical
The matheme Finite Volu
mbedded in thpresenting anons in the folculated at dfluxes at ththe small vo
mesh. The tions per timesilized in the s
odeling Con
The followgard to the pr All drilli
o
l: (A) Three
consists moshis gas are sh
e 3: Methan
s s
viscositytemperature pressure
013); LEE et al. (
l Model
matical modume Modelhe software und evaluating
orm of algebdiscrete plache surfaces oolume surroumestep was step and thesimulations.
nsiderations
wing consideroperties of tng fluids are
e-dimensiona
stly of methahown in Tabl
e gas proper
V0.0122
2.8242x
4.997
(1966)
del used in t(FVM), wh
used. FVM ig partial diff
braic equationes on a mes
of each finiteunding each 0.1 s with uk-ϵ turbulen
erations werthe fluids invconsidered in
al
ane. The male 3.
rties.
Value 16 kg/mol 3.7 kg/m³ x10-5 Pa.s
365 K 77x107 Pa
this work which is alreads a method fferential equns. Values ashed geomete volume, thnode point o
up to ten iternce model w
re made, wivolved: ncompressibl
ain
was dy for ua-are try hat on ra-
was
ith
le;
Numerical Investigation of Non-Newtonian Drilling Fluids During the Occurrence of a Gas Kick in a Petroleum Reservoir 301
Brazilian Journal of Chemical Engineering Vol. 33, No. 02, pp. 297 - 305, April - June, 2016
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 lev at the entrance of the well is calculated by
Equation (5),
2
/ 4l
lei
Qv
d
(5)
where Q is the volumetric flowrate of drilling fluid
injected into the well, and id is the diameter of the
drill string. The pressure ( )formationp at the point where the en-
trance of drilling fluid occurs is given by Equation (6).
formation l pp SIDPP gD (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 bottomg
resg
e
K H p pQ
dd
(7)
The entrance velocity of the gas into the well is
calculated by Equation (8).
2 ( ) 1
ln
res res formation bottomge
res e resg
e
K H p pv
d d Hd
(8)
where and res resK H are the permeability and reser-
voir height, respectively, ( )formation bottomp p is the
differential pressure in the bottomhole; g is the gas
viscosity; resd and ed are the diameters of the reser-
voir and the well, respectively; e resd H is the sur-
face area of the gas entrance. The gas density is cal-culated using Equation (9).
'
bottom atmg
p p M
Z RT
(9)
where bottomp and atmp 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 ' Yg gK X (10)
where
1.57.77 0.063 '
122.4 12.9
M TK
M T
(11)
1914.5
' 2.57 0.0095 X MT
(12)
' 1.11 0.04 'Y X (13)
where g is the gas density, g/cm3; T is the local
temperature given in °R and M is the molecular weight of the gas, in g/mol. Other parameters and
30
inri
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D
suth
02
nitial conditiized in Table
Table 4:
Source: AVELAR
Data Acquisi
Several siults were anhese points a
ParameteTotal deptThickness Height of tWell diamOutside diThickness SIDPP Density ofSurface temPressure oGeothermaReservoir Reservoir Reservoir AcceleratiPressure inTemperatuSpeed of dSpeed of th
ons used in te 4.
: Parameter
R (2008); PERRY
ition
mulations wnalyzed at foare presented
er th of the well
of the water dethe well
meter iameter of the dof the drill stri
f the drilling flumperature
on the surface al gradient permeability height diameter
ion of gravity n the bottomholure in the bottomdrilling fluid in he gas at the in
the simulatio
s used in sim
Y (1999), REID e
were performour points. Td in Table 5 a
Figu
V
epth
drill string ng
3uid
9.8
le 4mhole the inlet let
F. F. Oliveira
Brazilian Jou
ons are summ
mulations.
t al. (1986)
med and the The locationsand Figure 4.
ure 4: Locati
Value (SI Units3 600 m1 000 m20.32 m
0.2032 m0.1219 m
0.01016 m3.1026x106 Pa
1 199 kg/m3
300 K 101 325 Pa0.025 K/m
8692x10-13 m2
0.254 m 1 000 m
9.8066 m/s2
4.9977x107 Pa365 K
3.9831 m/s0.1838 m/s
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Table 5
Point/coordinaPoint 1 Point 2 Point 3 Point 4
RES
fluence of V
Five Powereudoplasticstency and buid are presenr of each flu
nly the drillinttings unchanFigures 5 a
me fraction ome at the poe graph in Fithe simulati
on of gas facrease in thore quickly plained becacomparison
cquisition po
o
5: Points for
ates X (cm9.9069.9069.9069.906
SULTS AND
Viscosity in P
r-Law fluids type with
behavior. Thnted in Tableuid, five simng fluid was rnged. and 6 show tof the drillingoints 2 and 4igure 5, it canion, that theaster than thhe concentraat the obser
ause this fluito the others
oints.
r data acqui
m) Y (cm)6 254 6 508 6 1 016 6 1 778
D DISCUSSI
Power-Law
were analyzdifferent indhe charactere 2. To comp
mulations wereplaced, kee
the comparisg fluid as a f4, respectiven be seen, at
e third fluid he other fluiation of the rved point. Tid has the los.
isition.
) Z (cm)0 0 0 0
ION
Fluids
zed, all of thdices of coistics of eac
pare the behaere performeeping all oth
son of the vofunction of thely. Analyzint the beginninallowed inv
ids, causing drilling flu
This could bwest viscosi
he n-ch
av-ed; her
ol-he ng ng
va-a
uid be ity
F(P
flggm
FL In
lywanfoinufo
pFdlathp
Num
Figure 5: VPower-Law)
Figure 6 shluids at the pas invasion iesting that t
most at the sa
Figure 6: VoLaw) at the po
nfluence of P
The charayzed are sho
with differentnalyzed. To our simulationg fluid wanchanged. Tor these simu
Figures 7 aoints 3 and
Figure 7 showecrease of dater time thanhat, for fluidrogress is slo
merical Investigat
Brazi
Volumetric fat the point
hows the vopoint 4. At thin the drillinthe invadingame time for
lume fractiooint 4.
Plastic Visco
acteristics ofown in Tablt plastic visco
compare thons were per
as replaced, The k-ε turbuulations. and 8 show t
d 4, respectiws the densiensity for Bin for the othd with higheow.
tion of Non-Newt
ilian Journal of C
fraction of 2.
lumetric frachis point, the
ng fluids are g gas reache
all fluids ana
n of drilling
osity in Bing
f each Binghle 2. Four Bosities and flhe behavior rformed andkeeping all
ulence model
the fluid denively, for Bity profiles aingham fluid
her fluids. Ther plastic vis
tonian Drilling Fl
Chemical Enginee
drilling flu
ction of drille differencesvery little, ss this point alyzed.
g fluids (Pow
gham Fluids
ham fluid aBingham fluflow limits w
of each flud only the drl other settinl was also u
nsity behavioBingham fluiat point 3. Td #4 occurs ahis result shoscosity, the
luids During the O
ering Vol. 33, No
uids
ling s in ug-al-
wer-
s
ana-uids
were uid, rill-ngs sed
r at ids. The at a ows gas
Thwi
Figpo
Figpo Inf
rheBinparperLascrvarvadPotheunthami
vothe
Occurrence of a G
o. 02, pp. 297 - 3
Figure 8 shhe same patteth a slight de
gure 7: Denint 3.
gure 8: Denint 4.
fluence of F
Two types oeological behngham fluid re the beharformed usin
aw fluid #1;ribed in Tablriation of thding the dr
ower-Law flue fluids beh
ntil they reacane. From thismatch.
The graph ilumetric frae point 4. A
Gas Kick in a Pet
05, April - June,
hows the denern of densityecrease in tim
nsity of drillin
nsity of drillin
Fluid Type: P
of non-Newthavior were and Ostwal
avior of thesng the Bingall properti
le 2. The grahe volumetririlling fluid uids at the pohave identicach the maximhat point bo
in Figure 10 ction of me
At this point,
troleum Reservoi
2016
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 fse, two simham fluid #
ies of these aph in Figuric fraction o
for both Boint 1. It canally in the fmum concenoth graphs b
shows the vthane invadithe concent
ir 3
at the point time was ke
ngham fluid #
ingham) at th
ingham) at th
vs. Bingham
with differedeal plasticfluid. To com
mulations we#1 and Powe
fluids are dre 9 shows thof methane iBingham an
n be noted thfirst momen
ntration of mbegin to sho
variation of thing drilling tration of m
303
4. ept #4.
he
he
m
ent or
m-ere er-de-he in-nd hat nts
me-ow
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me-
30
threth
shd(B
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pdre
04
hane in the each the maxhat observed
Considerinhows that therilling fluid Bingham flui
Figure 9: M
Figure 10: M
Figure 11oint 3. Whenrops abruptlyeaching its lo
Figure 1
simulation ximum value
with the Powng the casee gas propaghas ideal p
id).
Methane volu
Methane volum
shows then the gas invy, causing a owest value.
11: Pressure v
with a Binge at slightly ewer-Law fluis studied h
gates more quplastic rheolo
ume fraction
me fraction a
pressure vvades the wekind of insta
variation at t
F. F. Oliveira
Brazilian Jou
gham fluid cearlier time thid.
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Numerical Investigation of Non-Newtonian Drilling Fluids During the Occurrence of a Gas Kick in a Petroleum Reservoir 305
Brazilian Journal of Chemical Engineering Vol. 33, No. 02, pp. 297 - 305, April - June, 2016
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)
gQ Flow of gas (m³.s-¹)
lQ 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)
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