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: 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

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

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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

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nd finally, it sration. Thomfunctions of

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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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Brazilian Jou

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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The volumettion of the k

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The Poweories accordalues smalleluids are callhey are callnity, the fluiehavior of Py the appare

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Objective an

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make public evoted to thi

Physical Prob

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ding to their ier than one aled pseudopled dilatantsid behaves liPower-Law fent viscosityviscosity of

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achado, 2002

he Art

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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

Chemical Enginee

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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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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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Fr

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

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ural Gas Use

drilling fluidall non-New

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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

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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

S

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

he at

me-

30

threth

shd(B

F

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.

here, the resuickly when ogical behav

at the point

at the point 4

variation atell, the pressant vacuum a

the point 3.

, C. H. Sodré and

urnal of Chemica

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vior

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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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