Api report 82 45 1984 scan (american petroleum institute)

Final Report AMERICANPETROLEUM INSTITUTE PRAC PROJECT 82-45 RHEOLOGICAL CHARACTERIZATION OF FRACTURING J?LUIDS Robert K Prud'homme Department of Chemical E n g i n e e r i n g Princeton University Princeton, New Jersey 08544 STD.API/PETRO 82-45-ENGL 2 0577b81, b = OUTLINE I INTRODUCTION 11 SUMMARY OF CONCLUSIONS I I1 RHEOLOGICAL MEASUREMENTS D y n a m i c O s c i l l a t o r y Measurements A, B Steady She+IV Measurements EQUIPMENT Ftheometrics Inc System IV Rheometer Rheametrics Inc P r e s s u r e Rheometer C Impingement Mixing Device D C a p i l l a r y Viscometer A B V MATERIALS AND PREPARATION VI RESULTS AND DISCUSSION A Chemical Effects Hydration of Guar Molecules Order of A d d i t i o n Aging of Titanate S o l u t i o n DiketoneAddition Isopropanol Addition Temperature B Rheology of Guar Gels Dynamic O s c i l l a t o r y Measurements S t e a d y S h e a r Measurements VII KINETIC THEORY MODELING VIII.RECOMMENDATIONS FOR FUTURE RESEARCH IX RECOMMENDATIONS FOR INSTRUMENTATION APPENDICES A Wall S l i p Corrections f o r Coaxial C y l i n d e r Viscometer B ImpingementMixerSchematicand Parts L i s t C C a p i l l a r y Viscometer S c h e m a t i c a n d P a r t s L i s t D Summary of Experiments Performed,prepared by D r John Cameron, API S t e e r i n g Committee Vice-chairman ~~~~~ STD.API/PETRO ~ ~~ ~ 82-45-ENGL ~~~~~ ~~ ~ ~~ ~~ O73229U 7 b 8 2 E I ,INTROD.$TION This is t h e f i n a l report on our research conducted under the American Petroleum I n s t i t u t e ' s PRAC Project 82-45 e n t i t l e d" R h e o l o g i c a lC h a r a c t e r i z a t i o n of Fracturing Fluids" The project was i n i t i a t e d by the American Petroleum I n s t i t u t e (-1) because: 1) the expenseofhydraulicfracturing makes it d e s i r a b l e t o u n d e r s t a n d the process f u l l y , i n c l u d i n g the rheology of t h e f r a c t u r i n gf l u i d , t o ensure a s u c c e s s f u lf r a c t u r i n go p e r a t i o n , and ) during a round-robin t e s t i n g program by s e v e r a ll a b o r a t o r i e st h ev i s c o s i t i e s reported by t h ep a r t i c i p a n t sf o ri d e n t i c a lg e lf o r m u l a t i o n sv a r i e d by 1000% The purpose of t h i s report t o t o provide a workingguide t o rheology of W e first provide, i n S e c t i o n 11, a summary of t h e s i g n i f i c a n t r e s u l t s andconclusions from the f i r s t y e a r of t h i s i n v e s t i g a t i o n I n S e c t i o n I11 dynamic o s c i l l a t o r y shear measurements,which are used t o study guar rheologyandguargelstructure, are described Dynamic o s c i l l a t o r ys h e a r measurementscan be d i r e c t l y related t o t h e number of network c r o s s l i n k s Thesemeasurementsand their i n t e r p r e t a t i o n are d i s c u s s e d i n d e t a i l , s i n c e t h e y are probably less f a m i l i a r t o r e s e a r c h e r i n t h e o i l production research area t h a n are steadyshearmeasurements.InSection I V we describe the rheologic a l instrumentsused i n this s t u d y I n S e c t i o n V t h e p r e p a r a t i o n of guar samples is d e t a i l e d The compositionofthe model g u a rg e lu s e di nt h i ss t u d y w a s s p e c i f i e d by the API S t e e r i n g Committee Our observations on t h ef a c t o r s c o n t r o l l i n g gel rheology,includingchemicaleffects, sample p r e p a r a t i o n In Section V I a e f f e c t s , and flow history effects are p r e s e n t e d i n S e c t i o n model t h a t d e s c r i b e s t h e rheology o fg e l l i n gf l u i d s i s described The model i s based on the temporarynetwork theories used t o describetherheology of polymer melts and s o l u t i o n s To t h i st h e o r y we have incorporated the chem i c a lk i n e t i c so f metal i o na d s o r p t i o no n t o the guar polymer backboneand subsequent polymer-polymer c r o s s l i n k i n g I nt h ef i n a ls e c t i o n s recommendations for rheological instrumentation and for future research are presented guar gels VI A t the q u a r t e r l ym e e t i n g sw i t ht h e A P I Committee several hundred pages of experimental data were d a t a are n o it n c l u d e di n this report Rather the drawn from t h o sdea t a are p r e s e n t eadl o nwgi t h supportthoseconclusions The o r i g i n a l data are on tions department andcan be obtained through the API work o v e r s e e i n gt h i s d i s t r i b u t e d A l l of that important conclusions t hr e l e v a nd ta t a that f i l e w i t h t h e API p u b l i c a - - I I SUMMARY OF CONCLUSIONS t o study Dynamic o s c i l l a t o r y a n d s t e a d y s h e a r measurements havebeenused t h e r h e o l o g y of guar gels Dynamic o s c i l l a t o r y measurementshavebeenused to s t u d y t h e slow hydration of guar polymer and t h e e f f e c t s of chemical composition andmixingon guar g e l s t r u c t u r e S t e a d y s h e a r measurementshavebeenused to Major c o n c l u s i o n s ,p r e s e n t e di nt h e body of t h i s s i m u l a t ep r o c e s sc o n d i t i o n s report, includethefollowing: R e s u l t s from polymer k i n e t i ct h e o r yc a n be used t o relate the measured storage modulus, G ' , t o t h e c r o s s l i n k d e n s i t y i n t h e g u a r gel Aged t i t a n a t es o l u t i o n sp r o d u c eg e l sw i t h iower values of G I ; and t h e r e f o r e , dynamic o s c i l l a t o r y measurementscan be used t o q u a n t i f y titanate reactivity S T D - A P I I P E T R O 82-45-ENGL 2 05'77b83 b ' Adding d i k e t o n e( t h a t is, a c e t y l a c e t o n e ) to modify the rate of r e a c t i o n down t h e r e a c t i o n , b u t it also p r e v e n t s t h e gel from does not just slow c r o s s l i n k i n g t o t h e same e x t e n t a t room temperature as g e l s w i t h o u t added acetylacetone Mixing i s shown to p l a y a crucial role i n t h e development of gel s t r u c t u r e Poor mixing appears t o producemicroscopically inhomogeneous gel networks that have h i g h e r l e v e l s of e l a s t i c i t y t h a n homogeneous gels To Produceintimately&xedfluids mixing device - we havedeveloped a novelimpingement Measurementsof the s t e a d ys h e a rv i s c o s i t y of gels i n d i c a t et h a t wall s l i p is occurring However, c o n v e n t i o n a lr h e o l o g i c a lt e c h n i q u e sf o r c a l c u l a t i n g wall s l i p velocities h a v e g i v e n c o n t r a d i c t o r y r e s u l t s There i s a need f o r direct measurementsof v e l o c i t y f i e l d s i n s h e a r flow t o c l a r i f y t h e mechanism of wall s l i p I n t h e next y e a r we w i l l be conducting laser doppler measurements t o address t h i s problem Under q u i e s c e n tc o n d i t i o n s dynamic o s c i l l a t o r y measurements show t h a t the guar continues to crosslink over a time scale of about 15 minutes The s t e a d y s h e a r measurements show t h a t s h e a r i n c r e a s e s the rate of reaction A novel network theorycoupledwithchemicalreactionkinetics is proposed; material f u n c t i o n sc a n be expressed a n a l y t i c a l l y This model p r o v i d e s a framework f o r modelingand p r e d i c t i n g r h e o l o g i c a l p r o p e r t i e s of reacting g e l s 111 RHEOLOGICAL MEASUREMENTS A Dynamic O s c i l l a t o r y Measurements Dynamic o s c i l l a t o r y s h e a r e x p e r i m e n t s , whichmeasure the l i n e a r viscoe l a s t i c response of materials, are acknowledged t o be t h e most valuable probes of g e l o r network s t r u c t u r e Though s t e a d ys h e a r measurements are necessary t o d u p l i c a t e process c o n d i t i o n s , the o s c i l l a t o r y measurementsgive more i n s i g h t s t e a d y s h e a r measurements When i n t o the properties o f t h e g e l t h a n i n t e r p r e t e d u s i n g classical network theory, linear viscoelastic measurementscan be used t o d e t e r m i n e t h e k i n e t i c s of g e l f o r m a t i o n , t h e c r o s s l i n k d e n s i t y of a gel, or t h e s h e a r d e g r a d a t i o n o f g e l s t r u c t u r e The g e l a t i o n of p o l y v i n y l alcoh o l andgelatingelshasbeenstudied by a number of r e s e a r c h e r s ( , , ) , and a t P r i n c e t o n we have used these measurements t o study polyacrylamide gels used as p e r m e a b i l i t y c o n t r o l a g e n t s i n enhanced o i l r e c o v e r y ( , s ) Foranintroduct i o n t o t h e f i e l d of l i n e a r v i s c o e l a s t i c i t y t h e reader i s r e f e r r e d t o t h e t e x t by Ferry ( ) In a linear visco-elastic y ( t ) , is imposed on a sample, measurementan o s c i l l a t o r y shear s t r a i n , STD.API/PETRO - - E N G L PI 2 0577bA4 h T m where Yo is t h e maximum value of t h e s t r a i n Experimentally this is accomplished by placing a sample i n a coneand p l a t e in a geometry, a parallel plate geometry, o r between concentric cylinders Couettegeometry,andthenimposing a t o r s i o n a l o s c i l l a t i o n on one plate, cone, o r cylinder The r e s u l t i n g stress on t h e s t a t i o n a r y plate, cone, o r c y l i n d e r w i l l oscillate with the imposed frequency w, b u t will be o u t of phase with the t o components, f o r c i n g o s c i l l a t i o n The measured stress can be f a c t o r e d i n t o w 90 degrees out of phase with the one i n phase with the displacepent and one displacement: The in-phase stress d e f i n e s a s t o r a g e modulus G I t h a t gives information about t h e e l a s t i c i t y andnetwork structure, whereas the out-of-phase component d e f i n e s a loss modulus G" t h a t gives information about the viscous or dissipative prop e r t i e s of t h e f l u i d The frequency and s t r a i n dependenceof t h e s t o r a g e and loss moduli, G I and G" respectively,provideinformationaboutthe s t a t e of the f l u i d For a n uncrosslinked guar solution both G I and G" decrease with decreasingfrequency, w i t h G" l y i n g above G I As a g e l c r o s s l i n k s G I rises u n t i l i t is horizontal independentoffrequency As an example, t h i s p r o g r e s s i o n i s shown i n Fig f o r t h e g e l a t i o n of a p o l y s t y r e n e / c a r b o n d i s u l f i d e s o l u t i o n as temperature is decreased As we will show i n S e c t i o n V I , G I can be monitored as the amplitude of t h e s t r a i n deformation i s i n c r e a s e d I f s t r a i n d e s t r o y s t h e network s t r u c t u r e , t h e n G I will decrease with i n c r e a s i n g s t r a i n Classical network theory ( ) shows t h a t G ' , i n t h e low frequencyregion i s p r o p o r t i o n a l t o t h e number d e n s i t y of where G I i s independentoffrequency, crosslinks in the gel: G' = gnkT + Ge (3) where g i s a constant of o r d e r one, n is t h e number density of c r o s s l i n k s , k is t h e Boltzmann constant, T is the absolute temperature, and Ge is a contribution t o the modulusfram molecularentanglements.Foraqueous gels G e i s verysmall It i s p o s s i b l e t o f o l l o w the k i n e t i c s of gel formation by t a k i n g t h e time deriv a t i v e of 3: Eq dn dt dG' c= kT d t Likewise, t h e d e s t r u c t i o n o f gel s t r u c t u r e by shear can be monitored by measuring G I a f t e r exposure t o steady shear The r e s u l t s c a n be i n t e r p r e t e d i n terms of t h e breakdown i n t h e number of c r o s s l i n k p o i n t s S T D - A P I I P E T R O 82-45-ENGL c1732290 7 L 5 R rad/sec w rad/sec Fig 1a Fig 1b rad/sec o rad/sec Fig 1c , Fig.1a-d : - - Fig 1d - Storage ((3') and loss (G") moduli as afunction of frequencyof a 8.5 wt % polystyrene (900,000molecular weight) in carbon disulfide solution at temperature as indicated in each figureandrun at 3% strain.(Clark, et.al., Polym Preprintrs between parallel plates 24,87( 1983)) IV ,EQUIPMENT A Rheometrics System I V Rheometer: Most of the measurements reported here were conducted on our Rheometrics Inc System I V rheometer (Rheometrics, Inc.,Piscataway, NJ) This state-of-the-art instrument shown i n Fig has s e v e r a l motor and transducer options The instrument i s f u l l y automatedand a l l data a c q u i s i t i o n and manipuFor measurements w i t h the FluidsTransducer l a t i o n i s undercomputercontrol a c i r c u l a t i n g water bath is aiailable with a temperature range from -2OOC t o 8OoC For most of the g u a r s o l u t i o n measurements a Fluids Transducer w i t h a g-cm maximum torque and 100 g maximum normal force was used This F l u i d s Transducer allows s t e a d y shear measuremements of f l u i d v i s c o s i t y , dynamic w i t h a some modification t o t h e d r i v e u n i t , o s c i l l a t o r y s h e a r measurements,and, s t e a d y shear followed by o s c i l l a t o r y shear For polymer s o l u t i o n s and g e l s t h e be made i s range of frequencies and shear rates over whichmeasurementscan usually determined by t h e minimum torque range of the t r a n s d u c e r ( a b o u t 1/1000 t o 1/500 of the maximum torque).Frequencies from 0.01 t o 100 rad/$ a r e accessible and s t e a d y s h e a r rates from 0.01 t o 10,000 s-l The F l u i d s with cone-and-plate, parallel plate, or Couette Transducerscanberun geometries For dynamic o s c i l l a t o r y measurements on g u a r g e l s t h e g-cm t r a n s ducer i s ideal; however, the torque range of this t r a n s d u c e r i s quicklyexceeded i f s t e a d y shear measurements are attempted on gels Therefore, f o r the bulk of t h e gel measurements a Fluids Transducer with a 100 g-cm torque range was used For our System I V rheometer we have a high temperature and pressure c e l l t h a t allows measurement of f l u i d v i s c o s i t y anddynamicmoduliunder p r e s s u r e s t o p s i and temperatures t o 300'C However we generally found it more convenient to perform high temperature measurements on a Rheometrics P r e s s u r e Rheometer, described below, rather then on ourSystem I V B RheometricsInc.Pressure Rheometer: Measurements of gel properties a t elevated temperatures were performed on a Rheometrics Pressure Rheometer located a t Rheometrics Inc laboratories i n Piscataway, NJ The i n s t r u m e n t has a unique sealed sample chamber w i t h a Couette dynamic o s c i l l a t o r y shear measurements over the same geometry.Steadyshearand rangeof shear rates and frequencies spanned by the System I V Fluids Transducer are possible The t o r q u e s e n s i t i v i t y of the P r e s s u r e Rheometer corresponds approximately t o t h a t of the 100 g-cm FluidsTransducer It i s possible t o seal and pressurize the sample cell t o run samples a t temperatures above the normal b o i l i n g p o i n t of water It is somewhat awkward to load and mount the sample cup the process takes 2-3 minutes.Modifications t o allow o n - l i n e i n t r o d u c t i o n of the sample t o the cup have b e e n s u g g e s t e d t o the manufacturer Fig.2 System IV Rheometer STD.API/PETRO B2-L.I5-ENGL C ImpingementMixing m 0732270 7 b B d SS Device: The homogeneity achieved d u r i n g the mixingof the guar and t i t a n a t e s o l u t i o n s and s h e a r h i s t o r y of the f l u i d as it crosslinks determines the g e l properties The recommended procedure of mixing the g u a r s o l u t i o n a n d t i t a n a t e s o l u t i o n i n a blender and then t r a n s f e r r i n g the preformed gel t o t h e v i s c o m e t e r will be discussed below To circumvent this yields irreproducible results This problem, animpingement mixing d e v i c e was f a b r i c a t e d t h a t i n t i m a t e l y mixes the w t o streams and i n j e c t s t h e m d i r e c t l y i n t o the rheometer t e s t c e l l (Fig ) The d e v i c e c o n s i s t s of a s t a i n l e s s ' steel double acting pneumatic cylinder that is mechanicallycoupled t o a-microliter glass syringe The pneumatic cylinder i s p r e s s u r i z e d w i t h n i t r o g e n at 200 psi t o f o r c e g u a r s o l u t i o n i n the cylinder and t i t a n a t e s o l u t i o n i n the syringe through an impingementmixinghead; the mixture then flows through a packed bed mixing section The packed bed c o n s i s t s of t h r e e i n c h e s of a 1/4" OD s t a i n l e s s steel tube packedwith 24-32 mesh (0.71 - 0.50 mm) sand.During i n j e c t i o n through the sandpack the Reynolds number is aboutone, based on a mean h y d r a u l i c radius f o r the sandpackand t h e v i s c o s i t y of t h e uncrosslinkedguar The c o n n e c t i o n s i n the device are made with 1/8" t e f l o n tubing A three-way valve is used t o d i v e r t f l u i d either to waste or t o t h e rheometer cell The f l u i d fhws d i r e c t l y i n t o the rheometer c e l l and the dynamic o s c i l l a t o r y measurement can be i n i t i a t e d e v e n b e f o r e t h e f l u i d f i l l s the gap The t o t a l time between the i n i t i a l c o n t a c t i n g of the guar and metal i o n s o l u t i o n s and t h e start of a dynamic o s c i l l a t o r y e x p e r i m e n t is on t h e order of t o seconds.For a s t e a d y shear experiment the tube connecting the impingement cup must be disconnected so that time t o i n i t i a t e a n mixer and the rheometer experiment i s less t h a n minute The schematicand parts l i s t f o r the impingement mixer is g i v e n i n Appendix D C a p i l l a r y Viscometer: A p r e l i m i n a r y capillary viscometer has been designed and assembled The s h e a r h i s t o r y d e p e n d e n c e of these gels, as shown i n S e c t i o n VI, convincedus t h a t r a t h e r t h a n making a c i r c u l a t i n g loop using a pump, a better d e s i g n f o r o u r v e r y small scale l a b work would be a l o n g c a p i l l a r y i n which the f l u i d i s pumped backand f o r t h I n t h i s way the f l u i d is under constant shear (excluding the s h o r t times needed t o reverse t h e d i r e c t i o n of t h e f l o w ) The viscometer is b e i n g c o n t r o l l e d by a n IBM p e r s o n a l computerwith a Tecmar Inc A/D and D/A board F u r t h e r d e t a i l s and r e s u l t s on t h i s d e v i c e will be p r e s e n t e d i n f u t u r e p r o g r e s sr e p o r t su n d e rn e x ty e a r ' sr e s e a r c hp r o j e c t The schematicofthe c a p i l l a r y v i s c o m e t e r i s given i n Appendix C V MATERIALS PREPARATION The e x a c t f o r m u l a t i o n of the guar g e l was s p e c i f i e d by the API Committee monitoring this project Special l o t s ofhydroxypropylguarandTyzor AA t i t a n a t e were r e s e r v e d f o r this s t u d y by Celaneseand DuPont, r e s p e c t i v e l y The following formulation was used t o produce a 40 lb/Mgal g e l : 500 m l d i s t i l l e d water 2.4 g hydroxypropyl guar (Celanese SCN 9574) STD.API/PETRO - - E N G L 1111 2 0 7 b 8 double-actin Pneumatic reservoir of microliter syringe reservoir of titanate solution , -load ing - injection STD.API/PETRO 82-45-ENGL Is 2 00 7 32 R : c * g e l s i n t o t h e sample Thisarrangement is, Rheometrics Pressure data a c q u i s i t i o n and , chamber through the a i r l i n e used t o p r e s s u r i z e &e'system however, awkward.Compared t o t h e Pam viscometer, t h e Rheometer i s more s e n s i t i v e and more accurate, has*modern display, and allows dynamic o s c i l l a t o r y measurements ~ i c ACKNOWLEDC;MENTS W e wish t o acknowledge t h e f i n a n c i a l a s s i s t a n c e p r o v i d e d by t h e American Petroleum Institute The work was conducted by Alice Chu, a p o s t - d o c t o r a l r e s e a r c h a s s o c i a t e , and Jeffrey'Kramer, a d o c t o r a l s t u d e n t a t Princeton University.Specialthanks go to Dr RalphVeatch, PRAC Committee Chairman, f o r h i s encouragementand d i r e c t i o n i n administrative and t e c h n i c a l matters, and to D r John Cameron, PRAC Committee Vice-Chairman, f o r h i s c a r e f u l c r i t i q u e of experiments and drafts of t h i s f i n a l r e p o r t Dr Cameron's c o n t r i b u t i o n i n f i n d i n g the e r r o r i n the o r i g i n a l m l l s l i p c a l c u l a t i o n s (Appendix A ) i s acknowledged Also, I want t o thank the PRAC Committee members for their p a t i e n c ei nt e a c h i n g a rheologistabout the a r t , science, and mystery of hydraulic fracturing 24 ._ REFEREKES - ~ Chem., i,1 J D Ferry, Adv Protein '2 R '" - , Roscoe, Rheologica 19, 737980) (1 - Personalcommunication Jeffersontown, ICY Personalcommunication Laboratory,Deepwater, Personalcommunication Point, NY G .,L -'I (submitted) F Halverson, SOC Pet W KO Graessley,Macromolecules, ( 981 1' J D Ferry, Viscoelastic P r o p e r t i e s of Polymers,3rd Sons, NY, 1980 S Pearsonand ' R D - ( 948) J T Uhl, R K Prud'bmme, Macromolecules 10 A c t a , E, 522 KO Prud'homme, J; To Uhl, J P Poinsatte,and Engrs J., 804-808, Oct 11 - _ K te Jigen Nuis, Colloid Polymer Science, ed., JohnWileyand 13, 1001, L (1980) from D r William Stivers, Celanese Chemical Co., from D r Donald Putzig, du PontInc.,Jackson HiT, frm Dr James Steinmutz,Kay-Fries,Inc.,Stony RummO, O i l and Gas J., Sep 13, 84 ( 982) 12 P Kolodziej, C W Macosko, and W ( 982) E Ranz, P o l p Eng and Sci., 13 C Tucker, 111, and N P Suh, Polym Eng and Sci., 14 R B Bird and P J Carreau, Chem Engr Sci., 15 R 16 P J Carreau,Trans 17 A 18 A S Lodge, Rheol A c t a 19 R 20, 875(1980) g, 427-434 (1968) z, 388 - B B i r d , Hassager, R C Armstrongand C F Curtiss, Dynamics of Polymeric Liquids, V o l John Wiley: New York (1 977) , 15 Ch Kaye, B r i t J Apl I Tannerand J M Soc R h e O l l6, 99-127 Phys., E, 803-806 ,;zI 379-392 Sinnmons, Chem (1972) (1966) (1968) Engr Sci., 22, 1803-1815 (1967) S T D - A P I / P E T R O 82-45-ENLL E 2 00 7 - "48 M ApPE,NDIX A WALL SLIP CORRECTIONS FOR THE COAXIAL CYLINDER VISCOMETER Ann S Yoshimura Robert K Prud'homme Department of Chemical Engineering Princeton University Princeton, New J e r s e y 08544 Rheological measurementson gels,concentratedsuspensions,and foams are o f t e n confounded by s l i p a t s o l i d b o u n d a r i e s with t h e r e s u l t t h a t t h e f l o w f i e l d , or kinematics, is unknown necessary t o correct f o r slip a t b o u n d a r i e s I n t h i s n o t e sis of Couetteflowbetweencoaxialcylinders t o Couette geometries on w it is To i n t e r p r e te x p e r i m e n t a ld a t a we p r e s e n t t h e a n a l y - w i t h wall s l i p we show how t o c a l c u l a t e t h e t o t a l From experiments wall s l i p v e l o c i t y , and, f o r t h e case of small g a p s , t h e f l u i d v i s c o s i t y The coaxial Couettegeometry i s held stationary, the cup on the bob i s measured endof t o be considered i s shown i n Fig is rotated a t angularvelocity A l i s t of nomenclatureand The bob a, and t h e t o r q u e T symbols can be found a t t h e the t e x t I t can be shown from the e-equation given by of motion t h a t t h e s h e a r stress is The r a t e of s t r a i n i n a c y l i n d r i c a l c o o r d i n a t e system i s defined by For a f l u i d a t s t e a d y s t a t e the rate of s t r a i n is a unique function of the imposed stress; t h e r e f o r e 431,2 can be w r i t t e n n can be used t o changeindependentvariables i n Eqn from r t o rre, which can then be i n t e g r a t e d from t h e bob ( r = R) t o t h e cup (r = KR) t o y i e l d , The s l i p v e l o c i t i e s Sb and Sc are defined as the difference between the v e l o c i t y of the s o l i d wall and the f l u i d v e l o c i t y a t the wall; 'b el r =R I (7) and are assumed t o depend only on the wall shear stresses Tb and be noted that the slip velocities Q I t should a t the cup and bob surfaces are not equal S T D - A P I I P E T R O - - E N G L sls 2 0577727 A10 Appendix A Page s i n c e , as can be s e e n from theseexpressionswith4n Eqn ( l ) , the stresses are n o t equal Combining ( ) yields The f i r s t term on the r i g h t i n b r a c k e t s r e p r e s e n t s the s l i p c o n t r i b u t i o n t o t h e a n g u l a r v e l o c i t y p, while t h e i n t e g r a l term accounts for deformation liquid of the The s l i p v e l o c i t i e s and t r u e r a t e of s t r a i n i n the f l u i d c a n be determined from experimental data i n the following manner C a l c u l a t i o n of S l i p Velocities A I - The s l i p tem can be e v a l u a t e d by u s i n g t w o Couette tools of d i f f e r e n t R b u t w i t h the same if the torques K For bobs of r a d i i R1 and R2, and of l e n g t h s L1 and L2, are chosensuch that *l -= T2 Ll Rl I L2R2 t h e n t h e same shear stress will be producedon fc Since K i s t h e same for both devices, From Eqn (11, ( 10 ) the s h e a r stresses a t t h e cups are a l s o equal % Applying n each bob ( ) t o each device g i v e s S T D - A P I / P E T R O 82-qS-ENGL H 0732290 057772d 757 M Appendix A Since 'bl - Tb2 e and (1 3) fcl = 'e2 ? i t follows that b ' = 'b2 scl - sc2 r and (1 ) I Therefore, Eqns ( 1 ) and (12) can &,subtracted From n (15) the total t o yield slip velocity can be calculated then be inserted i n t o e i t h e r Eqn ( 1 ) angular velocity experienced by the liquid, This expression can or ( ) t o give the actual (corrected) S T D A P I / P E T R O 82-45-ENGL m 2 0 7 7 b73 Appendix Page B A Calculation of FluidViscosity I _ The determination of the corrected angular velocity from measurements with w t o s e t s of geometrically similar Couette coaxial cylindaers new r e s u l t The d e r i v a t i o n makes no assumptionaboutwhether thecylinders i s "narrow" Ci.e., t i o n of f l u i d v i s c o s i t y , K 1) o r "wide" ( i e , ICI 16) is a the gapbetween > 1) The calcula- however, from measured torque and corrected angular v e l o c i t y i s accomplishedconvenientlyonly approximationscanbe K (i.e., made ( ) when e i t h e r "narrow" o r "wide" gap For the case of "wide" gapsKrieger (2) has resented a series s o l u t i o n t h a t converges rapidly so t h a t the "narrow"gapapproxima- Most Couette viscometers are designed t i o n i s valid, For a d i f f e r e n c e i n r a d i i between the cupand t h e bob of 5%, t h e stress across the gap will deviate from i t s mean v a l u e by t 5% ofaccuracy i s acceptable, then the If t h i s l e v e l stress can be considered approximately constant across the gap, and the viscosity and r a t e of s t r a i n can be calculated from (3,l): I References &ch.mics of Schowalter, W R., 1978, pp.94-96 Krieger, I M Bird, R B., W E Stewart, and E N Lightfoot,Transport Wiley and Sons, NY, 1960, p 95 , Trans Non-Newtonian F.luid.s, Pergamon Press, NYt SOC Rheol, E, (1968) Phenomena, John , :- A"; i r r8 radial, tangential coordinates T torque on bob EF.21 Tre re-component of the stress tensor(shear Tb shear s t r e s s a t bob =C shear stress a t cup rate of s t r a n It"I Y , bob radius t g l R ratio of cup radius to K , L bob radius length of bob [ aI , , respectively stress) [F/a2] STD.API/PETRO - - E N G L APPENDIX B An impingementmixingdevice was c o n s t r u c t e d t o mix guar and t i t a n a t e s o l u t i o n s s i n c e mixing i n a blenderproduced gels with i n c o n s i s t e n t properties The concept for the mixing device comes fromimpingementmixersused in reaction i n j e c t i o n moldingofpolyurethane A schematic of the mixer is attached and a parts list i s included Mixing occurs as t h e g u a r a n d t i t a n a t e s o l u t i o n s impinge on e a c h o t h e r i n a three-way tee f i t t i n g , and further mixing occurs as the mixed solution flows through a 3" s e c t i o n of1/4* OD s t a i n l e s s steel tubing f i l l e d w i t h 24-32mesh (0.71 0.50 mm) sand The guar and t i t a n a t e are loaded steel h y d r a u l i c c y l i n d e r and microliter syringe, i n t o a double-acting, stainless r e s p e c t i v e l y , by p o s i t i o n i n g a six-port chromatographyvalve so that s o l u t i o n s i s sucked i n t o t h e g u a r can be drawn i n t o t h e cylilider andsyringe.Fluid c y l i n d e r b u t is i n j e c t e d i n t o t h e t i t a n a t e s y r i n g e u s i n g a larger 10 ml s y r i n g e as t h e t i t a n a t e " r e s e r v o i r * shown i n t h e f i g u r e The p i s t o n r o d of the double a c t i n g h y d r a u l i c c y l i n d e r i s mechanically coupled t o a rod that d r i v e s t h e The cross-sections of thecylinder(17/16*) and m i c r o l i t e rs y r i n g ep l u n g e r s y r i n g e (250 m i c r o l i t e r volume) determine the r a t i o of guar t o t i t a n a t e s o l u tions - Afterloading,the6-portvalve i s r o t a t e dt ot h e" i n j e c t "p o s i t i o n Mixing i s opened to p r e s s u r i z e t h e backof the double begins when an on/off valve a c t i n g c y l i n d e r w i t h 200 psi nitrogen The f i r s t few milliliters of mixed g e l are discarded by d i r e c t i n g t h e f l o w t o a waste v e s s e l u s i n g a three-position valve, and then the flow is directed i n t o the stem of a special cup we have c o n s t r u c t e d f o r o u r Sys tern Iv Rheometer A f t e r a n i n j e c t i o n , the l i n e s andsand-pa& are flushed w i t h HC1 s o l u t i o n , t o remove r e s i d u a l gel Nitrogengas is used t o dry the l i n e s andsand-pack before the n e x t i n j e c t i o n D I water, and thenmethanol Parts L i s t -1 Bimba double acting, t u r i n g , Monee, IL) stai2less-steel c y l i n d e r Model D4173A-6 (Bimba ManufacThis c y l i n d e r may be disassembled f o r cleaning Hamilton m i c r o l i t e r Gas-TightSyringe, Inc., Reno, N V ) C a t No 1725-TEFLL (Hamilton Ekcton-Dickinsonthree-way Rutherford, NJ.) Teflonchromatographytubing:1/8" OD X 2.4 mm I D , C a t No x 1.0 mm I D , C a t No 3132 (Alltech, Deerfield, I L ) A l l t e c hp l a s t i cl i q u i d Six-portvalve screw-type stopcock(Becton-Dickinson,Inc., 3134; 1/16" OD chromatography f i t t i n g s similar t o Valco (ValcoInstruments Co., Houston, TX) FIG 61 load ing injection hpingement mixing "device FIG €32 U cy I mder IO" - PI STD.API/PETRO 82-95-ENGL 0'7322700577734 TSU W i AF'PE.NDIX C Continuous Shear Flow Apparatus _ Theory of Operation showing t h e r e v e r s a l of flow The schematic of t h e c a p i l l a r y v i s c o m e t e r d i r e c t i o n i s shown i n Fig C l The g u a rs o l u t i o na n dc r o s s - l i n k i n ga g e n t are mixed and i n j e c t e d i n t o t h e flow system by a m i x i n g d e v i c e d e s c r i b e d ' i n Appendix B N o n - r e a c t i v ed r i v i n gf l u i d i s s u p p l i e d from a h i g h p r e s s u r e l i q u i d r e s e r v o i r is c o n t r o l l e d by t h r e e l o c a t e d a t t h e t o p of t h e system The d i r e c t i o n offlow pneumaticallydrivencomputer-controlledvalves The v a l v e s are switched, and t h e d i r e c t i o n of flow r e v e r s e d when a s p e c i f i e d amount of d r i v i n g f l u i d h a s been c o l l e c t e di nt h ee l e c t r o n i cb a l a n c ea p p a r a t u s The b a l a n c e i n t e r f a c e s with t h e RS-232 l i n k The amount of d r i v i n g f l u i d c o l l e c t e d i s chocomputerthroughan t e s t i n g s e c t i o n andunder s e n so t h a t t h e c r o s s l i n k e d gel i s k e p t i n t h e c e n t e r s t e a d ys h e a rc o n d i t i o n s C a p i l l a r yp r e s s u r ed r o p s are determined by t h r e e pressure t r a n s d u c e r s and a r e r e c o r d e d by thecomputingsystemthroughan A/D converter Specifications I D tubing: 1/32" C a p i l l a r y Length(Middle D r i v i n gP r e s s u r e : testingsection): 200 p s i Shear Rate a t Wall: 1500 s-' F l u i d Flow Rate: 0.0737 cm/s PressureTransducers:Celesco Model P7D V a l v e s Switching Time: approx 15 m s ComputingSys tern: IBM PC 910 cm LEGEIJD : PMEUMATIC COMPUTER COI?TROLLED VALBE PRESSURETRANSDUCERS -FELECTRICAL L U I D FLOW e - + +FLUID SIGIJALS NOT FLOWING = , ' : I * S T D - A P I / P E T R O 82-45-ENGL R 0732270 057773b 823 U APPENDIX D P r e p a r e d by D r JohnCaneron PRAC Committee Vice- Chairman, Dec Outline Summary of PRAC Project82-45 Research During 1983 I Measurement of Viscous and Elastic Properties at Low Shear Rates A Hydration and Strticture of Guar solutions@ 25 C using the Systems IV Mechanical spectrometer steady shear sweeps (2/28/83) strain sweeps (2/28/83) frequency sweeps (2/28/83) effect of mixing sequence viaG' from strain and frequency sweeps (6/12/83) effect of isopropanol via G' from strain and frequency sweeps (6/12/83) B Properties and structure of 0.4% Tyzor TE gel @ 25 C using the I Systems IV Mechanical Spectrometer (2/28/83) strain sweep frequency sweep temperature sweep from 25 to 100 C gelation time @ 25 C step shear rate (1, 10, 100, and l/s) C Properties and structure of -04% Tyzor AA gel @ 27 C using the Systems IV Mechanical Spectrometer or the Rheometrics Pressure Rheometer (RPR) gelation time @ 27 C via G' by varying guar and TyzorAA concentration (6/12/83 Systems IV) effect of mixing sequence via G' from strain and frequency -sweeps (6/12/83) and (9/5/83 Systems IV) effect of Tyzor AA aging via G from dynamic time sweep Systems IV) (6/12/83 effect of diketone via G' from dynamic time sweepat various diketone concentrations (6/12/83 Systems IV) effects of shear viaG' from alternating steady shear and oscillatory testing (6/12/83 RPR) and (9/5/83 Systems IV) Equilibrium viscosity tests via steady shear tests using fresh samples at each shear rate; two cone angles used (9/5/83 Systems IV) Viscosity of guar solutions at high shear rates using parallel plate geometry'(procedure using rotational viscometer being written up) (9/5/83 Systems IV ? ) (results of this work has not yet been presented to the API TAC) - D Construction of a pneumatic syringe for the continuous injection of guar and cross-linker during rheometer loading (9/5/83) - _ , * ' ' Slip Flow Studies 11 A Cone-and plate wall s l i p and inertial effects testing.using Brookfield standard solution 1000 and mineral oil @ 25 C; two cone anglesuSed ( / / Systems IV) I B Equilibrium viscosity tests @ 25 C via steady shear tests using fresh samples at each shear rate; two cone angles used (9/5/83 Systems IV) C Construction of new Couette Systems IV) slip (9/5/83 tools for measuring wall D Derivations of equations for analysisof Couette flow with slip (assuming s l i p velocity to be a function of wall shear stress) ( / / ) 111 Gel Rheology at High Shear Rates A Ordering of hardware for reciprocating capillary viscometer (computer received and functioning) IV KineticModeling - A Modification of existing polymer network theory models to incorporate chemical reaction kinetics (9/5/83) (Results of this work has not yet been reported to the API TAC) V Projected PRAC Project 82-45 Research for Balance of 1983 A Use of Couette geometry to quantify slip B Continuation of dynamic testing immediately following steady shear testing to show effects of steady shear on gel viscoelasticity C Continuation of model development forgel cross-linking r D Development ofreciprocatingcapillary viscometer for time at temperature studies (slip and high shear studies too? E- Rheological testing of gels at high temperature and pressure (Systems IV or RPR) JRC 83340ART0246 L$Io~ I