Gelation and Time-Dependent Rheological Behavior of Oil / Synthetic Based Drilling Fluids

Transcription

1 AADE-11-NTCE-81 Gelatin and Time-Dependent Rhelgical Behavi f Oil / Synthetic Based Dilling Fluids Gkem M. Gkdemi, Even M. Ozbaglu, Reza Majidi, Stefan Z. Miska, Nichlas Takach, and Mengjia Yu, The Univesity f Tulsa - TUDRP; Antnin Mel, ENI Cpyight 211, AADE This pape as pepaed f pesentatin at the 211 AADE Natinal Technical Cnfeence and Exhibitin held at the Hiltn Hustn Nth Htel, Hustn, Texas, Apil 12-14, 211. This cnfeence as spnsed by the Ameican Assciatin f Dilling Enginees. The infmatin pesented in this pape des nt eflect any psitin, claim endsement made implied by the Ameican Assciatin f Dilling Enginees, thei ffices membes. Questins cncening the cntent f this pape shuld be diected t the individual(s) listed as auth(s) f this k. Abstact Excessive pessue peaks inside the ellbe due t fluid gelatin ae bseved typically at l ellbe tempeatues in deep ate ells. In such ells thee is a na ind beteen the pe pessue and the factue gadient, causing the factue pessue t be eached vey easily. This study examines the tansient stess espnse and gel-beaking pessue f time-dependent dilling fluids by taking int accunt h tempeatue and aging time influence stuctue develpment f the fluid. Aging time and tempeatue effects n fluid gelatin in tems f stess and pessue espnses f synthetic based fluids ae investigated. An expeimental study has been caied ut t evaluate the helgical behavi and gelatin ppeties f a synthetic-based fluid unde a tempeatue ange fm 4 C t C. A high-accuacy hemete has been used t cnduct steady state (uilibium) and stess ve-sht (nn-uilibium) tests ith vane gemeties ith shea ates in the ange f 1.7 s -1 t 8. s -1. Results sh that fluid gelatin is sevee at le tempeatues and lnge static peids. Futhe, fl tests f a synthetic dilling fluid have been cnducted in a fl lp ith an annula test sectin in de t bseve and simulate pessue peaks due t gel beaking pessue and suges ccuing inside a ellbe upn displacing a gelled fluid ith a nn-gelled ne. Finally, a mathematical mdel is develped based n the stuctue kinetic they t descibe the timedependent helgical behavi f the fluid as a functin f tempeatue, shea ate and aging time cnditins. Mdel esults and expeimental bsevatins f pessue peaks and stess cnditins at the uilibium state ae in gd ageement. Intductin Rhelgical ppeties f dilling fluids ae adjusted t fulfill peatinal uiements and t affect the functinality f the mud. These ppeties have a diect impact n dilling hydaulics, cuttings tansptatin, and ell be stability. In additin, dilling fluids shuld pevent settling f cuttings and chemical additives by develping a slid gelled stuctue duing pump-ff peids. Additinal enegy is uied t decmpse these stuctues t e-ciculate the fluid in the dillsting and annulus. The magnitude f this enegy inceases as the nn-ciculating duatin inceases. This exta enegy diectly influences the ciculatin pessue. One f the cnsuential cncens in deep ate ells is t design and select the ppe fluid system in de t maintain the ECD beteen pe pessue and the factue gadient ind f the fmatin t maintain ellbe stability. Insufficient ECD anges may factue the fmatin and cause eithe lst ciculatin bluts. 1 In this study, the tansitinal helgical behavi and pessue espnse f time-dependent fluids have been investigated by cnsideing the yield stess and thixtpic phenmena. Besides the aging effect, effect f fluid tempeatue n gelatin is investigated and a mathematical mdel has been ppsed and cmpaed ith expeimental esults. Backgund Mic-stuctual existence in a fluid esists lage eaangements and is espnsible f the yield stess. The destuctin f such a micstuctue hile sheaing is the suce f thixtpy 2. Mujumda et al. 3 stated that thixtpy is a evesible beakdn f paticulate stuctues unde shea, hich is fuently assciated ith a yield stess. A cntinuus slid-like netk can be fmed in timedependent fluids hen the fluid is nt fling, and a minimum shea stess is uied t initiate fluid mvement. This minimum stess is knn as the yield stess and vaies ith time and tempeatue 4. Bel the theshld f this stess value, elastic plastic defmatin is bseved; n the the hand viscus defmatin is encunteed hen the applied stess exceeds this citical value. 2 Yield stess is difficult t measue. In de t undestand the yield stess cncept and t btain a tue value f yield stess, dynamic and static yield stess tems shuld be taken int accunt and evaluated sepaately. Dynamic yield stess, knn as a yield pint, shs the stess value bel hich fluid defms in an elastic ange and stuctues in the system egain thei iginal shapes hen the applied stess is emved. 6 Dynamic yield stess shs the stess hich is needed t stp the fluid fl afte the fling sheaing pcess is ve. Static yield stess, als knn as gel stength, is the minimum stess uied t stat the fluid fl fm a static cnditin 7. Time-dependent

2 2 G.M. Gkdemi, E.M. Ozbaglu, R. Majidi, S.Z. Miska, N. Takach, M. Yu, and A. Mel AADE-11-NTCE-81 fluids can ste sme enegy and fm a eak gel stuctue. Accding t Hezhaft et al. 8 cllidal inteactin beteen slid additives in dilling fluids can lead t develpment f a stuctual netk hen the fluid is at est. The stength f this gel netk is sensitive t sheaing histy and tempeatue. The helgy f mst dilling fluids shs thixtpic chaacte. Thixtpic fluids fm a 3-D netk as in gels and the 3-D stuctue is bken dn t get a minimum thickness as in sls; hence thixtpy is efeed t as the slgel tansitin phnemena. 7 Accding t Banes et al. 9 the finite time needed f a evesible change f micstuctues fm ne stage t anthe stage in liquid systems is knn as thixtpy. Thixtpic systems cnsist f fine paticles at the cllidal level and the inteactin beteen these paticles as they build-up micstuctues. The build-up pcess is the assciatin f paticles t fm a stuctual netk due t shea-induced cllusin and a andm mvement f paticles that ae suspended in the liquid. In this pcess viscsity f the thixtpic fluid can incease as the build-up phenmenn cntinues. Cntaily, sheaing fce beaks the develped netk due t viscus dag and is knn as the stuctue beak-dn pcess. Appaent viscsity deceases duing this pcess. When thixtpic mateials ae sheaed, build-up and beak-dn kinematics cmpete ith each the and eventually each an uilibium ate. Time-dependency thixtpy is bseved hen the ates f the t kinematic pcesses ae diffeent 1.. Time-Dependent Rhelgical Behavi f Thixtpic Systems ith Yield Stess Tansitinal pessue espnses at the initiatin f fl, hen cmpaed t steady fl cases, ae bseved in thixtpic fluids. Time-dependent helgical mdels ae necessay t calculate the pessue peaks f a given duatin f nn-ciculatin. A mathematical fm f the yielding cnditin in the thixtpic mdel is needed f cnstitutive uatins, because bth indicate the influence f an intenal stuctue n the helgical behavi. Numeus studies fund in the liteatue belng t time-dependent tansient stess uatins based n stuctue kinetic they ith diffeent appaches 11 ae based n cuve=fitting methdlgy. Gandelman et al. 12 develped a gel stess uatin ith diffeent aging time and tempeatue cnditins t calculate the pessue peaks geneated afte a pump-ff time. Bjkall et al. 13 develped a gel stength uatin based n the diffeence beteen initial stess peak and steady shea stess unde diffeent esting cnditins. Mujumda et al. 3 used the indiect mic stuctual appach and ppsed a timedependent stess uatin. They claimed that the ttal stess is the cmbinatin f elastic and viscus stesses in the system. Henandez et al. 4 eseached the uilibium and nnuilibium helgical behavi f fesh cement paste and chaacteizes the time-dependent helgical espnse as ageeing ith the Bingham Plastic mdel unde uilibium cnditins. They stated that initial stuctue affects the yield stess tem, and instantaneus stuctue level in the system affects the viscsity tem. Thei stess uatin is: (1) p hee is the initial stuctue paamete, τ is the yield stess at hich all f the stuctue is assumed t be built-up in the system (=1), and µ p is the plastic viscsity at hich all the stuctue is assumed t be built-up in the system (=1). Tehani et al. 1 analyzed the thixtpic behavi f atebased dilling fluids and mdeled thei gelling ppeties. In thei study, Me`s 14 stuctue ate uatin is used t explain the evlutin in tems f a single stuctue paamete. This uatin shs the time, thixtpic effect n helgical paametes (bth n the yield stess and appaent viscsity) at a mlecula and paticle level: d dt t t bt a 1 (2) Cheng and Evans 11 use an uatin f state that is simila t Henandez et al. s mdel 4 t develp a timedependent cnstitutive uatin. t t ct y m (3) hee τ(t) is the instantaneus stess, τ y is the dynamic yield stess and µ is the infinite viscsity value (viscsity value at uilibium cnditins). They Classical time-independent helgical mdels such as the Bingham Plastic (BP) the Yield Pe La (YPL), explain steady state stess behavi and ae aduate f classical calculatins in t chaacteize the helgical behavi f yield stess fluids. Heve, these mdels d nt cnside the tansient defmatin espnse because f thixtpy aging. In me challenging and cmplex situatins like pessue peaks afte pump stat-up, these steady-state mdels cannt be used since they d nt take thixtpic behavi int accunt. 8 F this study, the fllings assumptins ae made in develping a mathematical mdel f bth stess and fictinal pessue lss uatins: i) the sample fluid is incmpessible, ii) the system is hmgenus, iii) steady-state helgical paametes, i.e., the dynamic yield stess, τ y, the cnsistency index, K, and the fluid fl behavi index, m, ae all timeindependent and nly change ith tempeatue. In de t take thixtpy int cnsideatin, stuctue kinetic they and the stuctue paamete, λ, hich shs the ati f unbken links in the ttal netk f the system, ae used in the ppsed mdel. The stuctue paamete as intduced and used by Me 14 t investigate ceamic paste fl. Me s fm f the stuctual ate uatin is d dt t f Buildup ate & Beakdn ate

3 AADE-11-NTCE-81 Gelatin and Time-Dependent Rhelgical Behavi f Oil / Synthetic Based Dilling Fluids 3 d dt t t Dt (4) U 1 () hee U is the build-up ate cefficient and D is the beakdn ate cefficient. Equatin states that, the ate f stuctue develpment inceases ith the incease in numbe f unstuctued paticles in the system, epesented by 1-(t) in the uatin. Similaly, the ate f stuctue beak-dn is pptinal t the instantaneus stuctue, (t), hich exists in the system at that time, and the applied shea ate. In dynamic uilibium the ates f stuctue build-up and stuctue beak-dn ae ual, i.e., d(t)/dt=. The value f the stuctue paamete at uilibium depends n the applied shea ate: the highe the shea ates, the highe the beakdn ates, hich deceases the value f λ. Cnvesely, the le the ate f stain, the highe the build-up ates, hich bings n highe uilibium values. Theefe, the uilibium value f the stuctue paamete can be expessed as: U U D (6) Equatin 8 is slved ith the help f t limiting cnditins: i) at t= (t) = (hich is the uilibium stuctue paamete), and ii) at t= (t) = (hich is the initial stuctue paamete). Finally, the ate uatin becmes U Dt t e (7) Stuctue effects n the helgical behavi f the fluid ae cnsideed nly in the yield stess tem. The cnsistency index, K, and the fluid behavi index, m, ae assumed t be cnstant at a cnstant tempeatue. Based n these assumptins, the time-dependent cnstitutive uatin can be expessed as t t K m (8) hee τ is the maximum value f the static yield stess at hich all the stuctue is cmpletely built-up (=1). The fist tem n the ight side f the uality, (t)τ, is the instantaneus static yield stess. Cmbining Equatins 7 and 8 yields U Dt t e K m The initial stuctue paamete, is fund by using the stuctue kinetic uatin (Equatin ). When the thixtpic (9) system is mtinless, nly the build-up pcess ccus in the system and the build-up dynamic detemines the stuctue develpment. Theefe, the ate uatin f the initial stuctue paamete in tems f esting time is edefined as d dt t t U 1 (1) We then apply the limiting cnditins: i) at t = () = 1 (hich is the cmplete build-up stuctue) and ii) at t = () = (hich is the uilibium value f the stuctue). Finally the ate uatin f λ, hich is a functin f aging time, becmes: U t t 1 1e (11) Thus, the time-dependent cnstitutive uatin (Equatin 8) can be defined as a functin f U, D, t and t by t hee 1 U t 1e U U D e U Dt m K (12) This uatin des nt explain elastic and plastic egin defmatin, but mdels the tansitin egin beteen elasticplastic defmatins t viscus fl. The maj fcus f this study is the pessue peaks due t gelatin and the pessue espnses ith time. Expeimental Wk and Deteminatin f Mdel Paametes Labaty tests ee cnducted t chaacteize fluid helgical behavi ith diffeent aging times and tempeatues using a hemete. Als, fl-lp expeiments ee pefmed t bseve the time effect n tansitinal pessue espnses. A Synthetic-Based dilling fluid (SBM) as used in the expeiments. The fluid has the physical ppeties f 11 ppg density and 7/2 il/ate ati, ith 17% ate phase salinity. In the fist stage f expeimental k, an Antn Paa Physica MCR 31 hemete as used, ith diffeent measuement gemeties, t detemine the static yield stess and t chaacteize the fluid. Afte analyzing the test esults, the cefficients f Equatin 12 ee detemined. F tansient helgical tests a vane measuement gemety as fund t be the best. The ppsed mdel des nt cve the elastic defmatin pat f the stess espnse, hich is illustated in Figue 1 (.32 s -1 shea ate, 4 C tempeatue, 6-minute aging time). In this figue, it is clealy stated that fist elastic, then plastic

4 4 G.M. Gkdemi, E.M. Ozbaglu, R. Majidi, S.Z. Miska, N. Takach, M. Yu, and A. Mel AADE-11-NTCE-81 stess espnses ae bseved against the applied ate f stain ithin the fist secnd. The peak stess is bseved afte.611 secnds f shea applicatin; hence, this time is assumed t be the stating time f sheaing and time data ae efined accding t this cnsideatin. In the helgical tests stain-cntlled measuement methdlgies ae selected, l and cnstant shea ate is applied t the sample and shea stess vesht peak stess is ecded as the static yield stess value; i.e., the stess value at hich the ceeping fl patten changes t viscus fl. 1 This technique is knn as the stess-vesht test (SOT). Figue 2 illustates the SOT esults at a cnstant.27 s -1 shea ate and a 17 C cnstant tempeatue afte 1,, 1, 2, 3, 4 and 6 minutes f aging times. The aim f this gaph is t highlight the aging effect n shea stess eadings. Theefe, this figue is limited t 2 secnds in de t demnstate the ealy time-dependent stess espnse. All f the aging time gaphs stat fm the peak pints and then stess decay flls because the develped stuctual netk is bken by sheaing fce. The theshld peak values incease as the aging is inceased. Finally, all the stess cuves cme t an uilibium value because steady state shea stess is independent f aging peid and is nly affected by ambient tempeatue and applied shea ate, as illustated in Figue 3. Heve the elaxatin peid, i.e., the time inteval beteen t peak pint and the uilibium pint, inceases hen the aging time is inceased due t the highe netk develpment pssible duing lnge esting peids. Accding t SOT esults pesented in Figue 4, stuctue develpment cntinues afte 3 minutes f aging ith a ys value f Pascal, hich inceases t Pascal afte 6 minutes. Theefe, the stuctue develpment stuctual netk inceases hen the duatin f the aging peid is extended, as shn in the gel stength peak stess eadings f the SBM. Pesented in Figue is the stess measuement f SBM at 4, 1, 17, 24, 3, 4 and C at the.84 s -1 aveage shea ate applicatin afte 3 minutes f aging. Bth the uilibium stesses and the peak stesses incease hen the fluid tempeatue is deceased, as seen in Figue 6. It can be bseved that the gelatin pcess stuctual build-up is me significant at l tempeatues. Als, the stess decline ates incease as the tempeatues incease, as seen in Figue. Deteminatin f the Mdel Cefficients Equatin 12 cntains cefficients hich need t be detemined via dynamic tests. These cefficients ae all mateial-dependent and affected by tempeatue change in the fluid system. Rhelgical paametes (the cnsistency index, K, dynamic yield stess, y, and the fl behavi index, m) ae btained fm the steady state expeimental data at vaius shea ates and a cnstant tempeatue. The uilibium shea stess data ae pltted against the cespnding shea ate t cnstuct a hegam. This cuve is fitted t a Yield Pe La mdel t btain the thee mdel paametes. As mentined, these uilibium helgical paametes ae tempeatue sensitive; the pcedue must be epeated f diffeent tempeatues. Thee ae thee paametes t descibe a YPL fluid: the dynamic yield stess yield pint, y, the cnsistency index, K, and the fl behavi index, m. The mdel is m y K (13) In the liteatue numeus methds ae used t get the hegam. The hegam is the plt f vaius shea stesses at the cespnding shea ates. L shea ate eadings in timedependent stuctued fluids sh highe stesses cmpaed t actual steady state cnditins, as illustated in Figue 7. This is due t inaduate time f stuctues t each uilibium. This pblem is eliminated by selecting the shea stesses at the cespnding shea ates n SOT at cnstant tempeatue test intevals. Time duatin is adjusted f stess espnse t each the steady state; i.e., uilibium is eached at the stuctual level. F example, the uilibium stess eadings f a 4 C test at an applied cnstant 6.31 s -1 shea ate ae: 14.86, and Pascal f 1-, 2- and 3- minute esting times, espectively. The steady state stess value f this shea ate is fund by taking the aveage f the seven aging peid stabilized eadings and is fund t be Pascal (see Figue 8). The pcedue is epeated f evey shea ate inteval t sketch the hegam. Table-1 illustates the thee paametes that ee detemined. The definitin f the maximum value f static yield stess (gel stength),, is the static yield stess peak stess measuement f a thixtpic fluid in hich all the stuctues in the system ae cmpletely built-up (λ=1). The paamete is affected by tempeatue and applied shea ate. Theefe, it is btained by pltting the stess peaks f stess ve-sht data vesus esting time at a cnstant shea ate and tempeatue. The value is btained by extending the plt f esting time t infinity. This pcedue is epeated f diffeent shea ates at each tempeatue t find the influence f shea ate. Expeiments ae epeated at diffeent tempeatues t bseve the effect f tempeatue n. The numeical value f is btained by pltting the stess peak eadings at cnstant tempeatue and cnstant shea ates at diffeent aging times. Figue 9 is such a plt at 17 C and at.37 s -1 shea ate. The stess peaks sh a lgaithmic incease ith aging time and stess can be stabilized afte 9 minutes. Theefe the limiting time f the stuctue gth develpment in the system is assumed t be 9 minutes. Figue 1 pesents an example f values detemined at 17 C and seven diffeent shea ate esults. Fm this gaph, a cnstant 4. Pascal is used t find the cefficients f U and D tems in Equatin 12. When the stess peak eadings f SOT ae encunteed, sheaing time is assumed t be ze (t=) sheaing is assumed t stat at the instant f stess-vesht; i.e., inetia and elastic defmatin ae eliminated. The mdel ppsed in Equatin 12 is mdified hen t=:

5 AADE-11-NTCE-81 Gelatin and Time-Dependent Rhelgical Behavi f Oil / Synthetic Based Dilling Fluids peak U t m t 1 1 e K U U D (14) The build-up ate cefficient, U, and beak-dn ate cefficient, D, ae bth ate functins, detemined by cnducting a cuve-fitting pcedue using the stessvesht expeimental data f all shea ates ith vaius aging times at a cetain tempeatue. The paamete U is assumed t be independent f shea ate. On the the hand, D is assumed t be shea ate-dependent. Figue 11 shs the mdel pedictin and expeimental stess peak data at 3 C and.2 s -1 shea ate ith a Pascal value. U and D tems ae detemined using a cuve-fitting pcedue applied t Equatin 14. Table-2 shs the U and D tems btained using this appach. Then, all the expeimental data having diffeent aging times and shea ates ae applied t a cuve-fitting pcedue using Equatin 12 at a cnstant tempeatue. It is assumed that D is shea-ate-dependent f sheaing times geate than ze. This assumptin is based n stuctue kinetic they because the build stuctue is bken dn (at a ate f D) int paticles due t the sheaing fce. The D tem is edefined as a functin f shea ate, such that D d 1 d 2 (1) The numeical values f U, d 1 and d 2 cefficients at diffeent tempeatues based n this appach ae pesented in Table 3. Fl-Lp Expeiments Fl lp expeiments ee cnducted n a fl lp system called the Dynamic Testing Facility at The Univesity f Tulsa Dilling Reseach Pjects (DTF) (Figue 12). The pupse f the fl lp expeiments is t validate the ppsed mdel in tems f pessue peaks and timedependent pessue espnse. A schematic daing f the DTF test sectin is pesented in Figue 13. The test system is cmpsed f seven main cmpnents: mixing eciculatin tank, mud pump, tempeatue senss, heating/cling system ith an annula heat exchange, vetical pipe test sectin (2 in. in), pessue senss and a cmpute-based data acquisitin system. The test pcedue stats by ciculating the SBM t get a hmgeneus mixtue and adjusting the test tempeatue. Afte this, ciculatin in the vetical annula sectin is bypassed and ciculatin cntinues in the hizntal pipe sectin by clsing the valve and aiting f diffeent esting times f the develpment f gelled stuctues. As the desied aging time is btained, ciculatin is diveted t the vetical test sectin and t measue the gel beaking pessue is measued by ciculating the nn-gelled fluid. Ciculatin in the vetical sectin cntinues until steady pessue eadings ae bseved. Figue 14 is a typical example f DTF test esults. In this figue, the expeimental esults at 24 C ith 4.7 gpm fl ate at diffeent aging times emphasize the gelatin stuctue develpment effect n tansitinal pessue espnses. Afte 1 minute f aging, the pessue peak stats at.8 psi/ft and eaches a.22 psi/ft steady state gadient afte 3. secnds f peak bsevatin. The 1-minute peak stats at.1 psi/ft and takes aund 4 secnds t each.24 psi/ft steady state eadings. This pessue decline takes me than secnds, fm.14 psi/ft t.21 psi/ft, hen the fluid is stagnant f 3 minutes in the vetical sectin. Pessue eadings sh.174 psi/ft and dp t.26 psi/ft in aund secnds hen the SBM is subjected t a 6-minute aging peid. In this figue, all the pessue cuves ith diffeent aging times cme t the same steady state pessue gadient,.2 psi/ft. This is expected because aging des nt affect the uilibium pessue dp and if the tempeatue is kept cnstant at a cnstant fl ate, the steady state fictinal pessue lss gadient shuld be cnstant. The pessue peaks in Figue 14 incease as the esting peid inceases. This is due t stnge gel stuctues ith lnge aging times. F example, the maximum pessue gadient dubles hen the aging time inceases fm 1 minute t 6 minutes and the pessue peak at 3 minutes is 4% highe than the pessue peak at 1 minutes. This is illustated in Figue 1. Pesented in Figue 16 is the DTF expeiment cnducted at a cnstant 4.6 gpm fl ate at diffeent tempeatues. Simila t the pessue peaks, steady state pessue gadients tend t decease hen fluid tempeatue inceases. Fictinal Pessue Lss f YPL Fluids A calculatin methdlgy f fictinal pessue lsses f YPL fluids in annula gemeties is pesented in Advanced Dilling and Well Technlgy. 16 The auths assume that the inne pipe is cncentically lcated in the annula sectin, fluid is incmpessible and fl is isthemal. Ttal fl aea in the annula gemety is epesented by the pduct f h and. Accding t Netn s La f Mtin, the pessue gadient is defined as a functin f all shea stess, : h dp 2 dl (16) The fl behavi f a YPL fluid can be defined as: 2 h 1 1 y m 2 1 2m Q 2 K m y m 1 1m m (17) It shuld be nted that Equatins 16 and 17 ae develped ithut cnsideing thixtpy time-dependent effects.

6 6 G.M. Gkdemi, E.M. Ozbaglu, R. Majidi, S.Z. Miska, N. Takach, M. Yu, and A. Mel AADE-11-NTCE-81 Dynamic yield stess is cnstant in the uatins; i.e., they ae shea ate velcity-independent. The fist tem in the ppsed mdel, Equatin 12, epesents the instantaneus yield stess, hich is a time-dependent ppety f the thixtpic system, hee y U t U Dt t 1 1e e hee U U D (18) If the dynamic yield stess, y, is eplaced by the instantaneus yield stess, y (t), in Equatin 17 and fl ate is cnveted t aveage velcity, the fl uatin f a YPL fluid in an annula gemety f a given aveage velcity in stuctued fluids becmes 12v D D i K 1 m y t 2 1m m 3m 1 2m m y t 1 m (19) Equatin 19 must be slved iteatively t find shea stess at the all. Mdel Validatin The stess uatin, Equatin 12, is validated ith the pedicted and measued shea stess values. In additin t shea stesses, the calculated fictinal pessue lss gadient, based n the stess uatin, is cmpaed ith esults btained fm the fl lp expeiments. Figue 17 cmpaes the mdel pedictin and SOT at a.81 s -1 shea ate and a test tempeatue f 17 C. In this analysis, SBM is subjected t a 3-minute aging peid. The mdel gives a 3.47 Pascal value hen the measued value is 3.92 Pascal. The stess cuve btained fm the pedictin shs a faste stess decline espnse cmpaed t measued data. This may be due t the assumed linea elatinship beteen the shea ate and beak-dn ate cefficient shn in Equatin 1. Figue 18 shs the calculated fictinal pessue lss gadients, based n the stess uatin, and the measued values at a 4.7 gpm fl ate and 24 C tempeatue ith 6 f minutes esting. The pessue peak encunteed in the expeimental k is.198 psi/ft and a.194 psi/ft pessue gadient is calculated based n the time-dependent cnstitutive uatin. The pedicted and measued uilibium pessue gadient values ae bth.38 psi/ft. These esults validate the mdel s applicability f pactical applicatins. Cnclusins The aim f this study is t analyze the gelatin and time effects n thixtpic fluid helgy and t estimate the pump stat-up pessue and tansitinal pessue behavi. A timedependent cnstitutive uatin as ppsed in de t addess these pints. Rhelgical and fl expeiments ee cnducted t chaacteize the defmatin behavi f a test fluid and t sh the applicability f the uatin. Fm this study, the flling cnclusins can be eached: The static value f yield stess (gel stength), τ ys, inceases as aging time inceases. Als, it inceases as the fluid tempeatue deceases. The enegy uied t beak the gel stuctue and t initiate fluid fl shs a espnse simila t the stess behavi in thixtpic fluids. Pessue peaks incease ith inceasing esting time. Expeimental esults sh that the magnitude f the measued pessues at peak pints is significantly highe than the pessue values afte uilibium cnditins ae established. The mdel can estimate pessue gadients f bth peak and uilibium cnditins ith easnable accuacy. Nmenclatue a = Build-up cnstant, s -1 b = Beak-dn cnstant, s -1 c = Cnstant in Equatin 3 d = Cuve fitting paamete in Equatin 1 D = Beakdn ate cefficient in Equatin 8, s -1 G = Shea mdulus, Pa h = Height, in H = Cnstant in Equatin 1, Pa K = Cnsistency index, Pa.sm l = Length, in m,n = Fl behavi index P = Pessue, Pa Q = Fl ate, m 3 /s t = Time, secnds t = Resting (aging) time, minutes t ef = Refeence time, secnds U = Buildup ate cefficient in Equatin, s -1 v = Velcity, m/s = Wide, in y = Cleaance fm cente f slt, in Geek lettes γ e = Equilibium stain γ = Shea ate, s -1 γ = Wall shea sate, s -1 µ p = Plastic viscsity, P λ = Stuctue paamete λ e = Equilibium stuctue paamete λ = Initial stuctue paamete = Shea stess, Pa g = Gel stength, Pa = Stess vesht peak, Pa y = Dynamic yield stess, Pa = Limiting value f static Yield stess, Pa ys = Static yield stess, Pa = Aveage all shea stess, Pa

7 AADE-11-NTCE-81 Gelatin and Time-Dependent Rhelgical Behavi f Oil / Synthetic Based Dilling Fluids 7 Refeences 1. Pe, D., Catalian, D., Ivan and Steve W., 23, The Tp 1 lst Ciculatin Cncen in Deepate Dilling, SPE pesented at the SPE Latin Ameican Petleum Engineeing Cnfeence held in Pt f Spain, Tinidad, 27-3 Apil. 2. Pede, C.F.M, Jan, M., Daniel, B., Yield Stess and Thixtpy: On the Difficulty f Measuing Yield Stesses in Pactice, 26, Sft Matte. 3. Mujumda, A., Beis, A.N., Metzne, A.B.,: Tansient phenmena in thixtpic systems, Junal f Nn-Netnian Fluid Mechanics, 22, 12, Rubinh, H., Galind, R., Rhelgical Chaacteizatin f a Time-Dependent Fesh Cement Paste, Mech. Time-Dependent Mateials, 29, Cusst, P., Nguyen, O.D., Huynh, H.T., Bnn, D.,: Viscsity Bifucatin in Thixtpic, Yielding Fluids, The Sciety f Rhelgy, May/June 22, 46(3), Bge, D., Paste and Thickened Tailings, 2 nd Editin, Steefe, J.F., Rhelgical Methds in Fd Pcess Engineeing, Feeman Pess, 1996, 2 nd Editin, Hezhaft A., Raguillaux A., 26, H t Unify L-Shea Rhelgy and Gel Ppeties f Dilling Muds: A Tansient Rhelgical and Stuctual Mdel f Cmplex Well Applicatins, SPE 998 pesented at the IADC/SPE Dilling Cnfeence held in Miami, Flida, USA, Febuay. 9. Banes, H.A.: Thixtpy, Junal f Nn-Netnian Fluid Mechanics, 1997, 7, Ahmadi T., Andy P., 29, Mdeling The Gelling Ppeties f Wate-Based Dilling Fluids, AADE-29-NTCE-12-2 pesented at 29 Natinal Technical Cnfeence and Exhibitin held in Ne Oleans, Luisiana. 11. Cheng, D.C., Evans, F., Phenmenlgical Chaacteizatin f the Rhelgical Behavi f Inelastic Revesible Thixtpic and Antithixtpic Fluids, Bit. J. Appl. Phys, Vl.16, Gandelman, R.A., Leal, R.F., Gncalves, J.T., Aaga, A.L., Lmba, R.F. and Matins, A.L., 27, Study n Gelatin and Feezing Phenmena f Synthetic Dilling Fluids in Ulta Deepate Envinments, SPE/IADC 1881 pesented at the SPE/IADC Dilling Cnfeence held in Amstedam, The Netheland, 2-22 Febuay. 13. BjØkvll, K.S., Rmmetveit, R., Aas, B., Gjealdstveit, H. and Mel, A., 23, Tansient Gel Beaking Mdel f Citical Wells Applicatins ith Field Data Veificatin, SPE/IADC pesented at the SPE/IADC Dilling Cnfeence held in Amstedam, The Nethelands, Febuay. 14. F. Me, The helgy f ceamic slips and bdies, Tans. B. Ceamic Sc. 8 (199) Stkes, J.R., Telfd J.H., Measuing the Yield Behavi f Stuctued Fluids, 24, J. Nn-Netnian Fluid Mech. Vl. 124, Aadny B.S., Cpe I., Miska S.Z., Mitchell R.F., Payne M.L., Advanced Dilling and Well Technlgy, SPE Pess, 29, Table 1 Rhelgical ppeties detemined using uilibium stess values Tempeatue y (Pa) K (Pa-sec m ( C) m ) Table 2 U and D values t be used f detemining stess peaks Tempeatue ( C) U (min -1 ) D (min -1 ) Table 3 Cefficients f U and D f detemining timedependent shea stess Tempeatue ( C) U (sec -1 ) d 1 (sec -1 ) d 2 (sec -1 ) Shea Stess vs Measuement Time at 4 C-.32 1/s Shea Rate Sheaing Time= Measuement Ra Data Used Data Figue 1: Example f data pcessing

8 Peak Stess (Pa) Stess Peak (Pa) 8 G.M. Gkdemi, E.M. Ozbaglu, R. Majidi, S.Z. Miska, N. Takach, M. Yu, and A. Mel AADE-11-NTCE-81 Stess Peaks vs Time at.27 1/s Shea Rate-17 C Shea Stess vs Time at.84 1/s Shea Rate afte 3 mins. Aging min. min. 1 min. 2 min. 3 min. 4 min. 6 min C 1 C 17 C 24 C 3 C 4 C C Figue 2: SOT Results (limited time scale) Figue : Tempeatue Effect n SOT Results at.84 s -1 3 minutes aging Stess Peaks vs Time at.27 1/s Shea Rate-17 C 2 1 min. min. 1 min. 2 min. 2 3 min. 4 min. 6 min Figue 3: SOT esults (full vesin) Stess Peaks vs Tempeatue at.84 1/s Shea Rate afte 3 mins. Aging Tempeatue (C) Figue 6: Tempeatue effect n stess peaks at.84 s -1 3 minutes aging 2 Peak Stess vs Aging Time at.27 1/s Shea Rate-17 C 9 Rhegam 2 1 y = 1.878Ln(x) R 2 = Thixtpic Effect Eq. Stess Aging Time (Min) Figue 4: Aging effect n Stess Peaks at.27 s -1 and 17 C Shea Rate (1/s) Figue 7: Thixtpy effect n hegam

9 Maximum Static Yield Stess (Pa) Stess Peak (Pa) Stess Peak (Pa) AADE-11-NTCE-81 Gelatin and Time-Dependent Rhelgical Behavi f Oil / Synthetic Based Dilling Fluids 9 Rhegam at 4C Stess Peak vs Aging Time at.2 1/s Shea Rate-3 C 3 2 Ra Data Pa 2 1 Mdel Pedictin 1 1 Measued YPL Mdel Shea Rate (1/s) Figue 8: Rhegam at 4 C Aging Time (min) Figue 11: Expeimental and mdel stess peak cmpaisn at.2 s -1 and 3 C Aging Time vs Stess Peaks at.37 1/s Shea Rate-17 C Aging Time (mins) Figue 9: Stess peaks at.37 s -1 and 17 C t = Figue 12: Dynamic Testing Facility (DTF) Shea Rate vs Maximum Static Yield Stess at 17 C 6. Ty ave. = 4. Pa Shea Rate (1/s) Figue 1: Shea ate effect n τ at 17 C Figue 13: Schematic f expeimental sectin f DTF

10 dp/dl (psi/ft) Pessue Peak Gadient (psi/ft) dp/dl (psi/ft) dp/dl (Psi/ft) 1 G.M. Gkdemi, E.M. Ozbaglu, R. Majidi, S.Z. Miska, N. Takach, M. Yu, and A. Mel AADE-11-NTCE-81.3 Fictinal Pessue Gadient vs Time at 4.7 gpm-24 C 1 min. 1 min. 3 Shea Stess vs Time at.81 1/s Shea Rate-17 C afte 3 mins. Aging min. 6 min. 3 2 Expeimental Data Mdel Pedictin Figue 14: DTF esults at 4.7 gpm and 24 C Figue 17: Stess mdel-expeimental data cmpaisn at.81 s -1 and 17 C - 3 minutes aging Pessue Peak Gadient vs Aging Time at 4.6 gpm-24c Aging Time (min.) Figue 1: Aging effect n pessue peaks at 4.6 gpm and 24 C Fictinal Pessue Gadient vs Time at 4.6 gpm ith 1 mins. Aging Fictinal Pessue Gadient vs Time at 24C-4.7 gpm. ith 6 mins. Aging Expeimental Data Mdel Pedictin Figue 18 Fictinal pessue gadient, mdel-expeimental Data cmpaisn at 4.7 gpm and 24 C - 6 minutes aging C 1 C 17 C 24 C 4 C Figue 16: Tempeatue effect n DTF esults at 4.6 gpm-1 minutes aging