Shear Degradation and Possible viscoelastic properties of High Molecular Weight Oil Drag Reducer Polymers

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1 ANNUAL TRANSACTIONS OF THE NORDIC RHEOLOGY SOCIETY, VOL. 3, 2005 Sher Degrdtion nd Possible viscoelstic properties of High Moleculr Weight Oil Drg Reducer Polymers A.A. Hmoud, C. Elissen, C. Idsøe nd T. Jcobsen, University of Stvnger, Stvnger, Norwy ABSTRACT High moleculr weight polymers re susceptible to mechnicl sher degrdtion. Oil soluble polymer drg reducers (DRA) re long chin molecules with verge moleculr weight in excess of 0*0 6, reching n verge of bout 50*0 6. Polymer drg reducers exhibit Weissenberg effect, which is chrcteristic of viscoelstic behvior. Severl mechnisms hve been suggested for the drg reduction mechnism in turbulent flow. The extent of the sher degrdtion of DRA is studied when the polymer ws exposed to 3395, 6790 nd 3582 sec -. It is lso studied the effect of the temperture on the sher degrdtion. The pper shows the effect of 5 nd 60 o C. Also, the effect of sher degrdtion on the viscoelstic properties of the polymers is ddressed s shown from the G trend s function of scnned frequency () between 0.0 to 0 sec -. Polymer recovery fter sher degrdtion is determined by the regin properties of the polymer. Key words: Polymer drg reducers, sher degrdtion, viscoelstic properties of degrded polymers. INTRODUCTION There is very little work reported in literture tht ddresses the oil soluble drg reducers. However, there re lot of studies done on wter soluble drg reducers. A recent pper by Peiwen et l (200) hs utilized the degrdtion phenomenon in their investigtion with wter/surfctnt to enhnce the het trnsfer in drg-reducing flow. The pper presented her is n extension to our first reported effect of the temperture on degrdtion of the drg reducer polymers 2 t 20 nd 40 o C to 5 nd 60 o C. A comprison between the degree of degrdtion of two polymers re mde bsed on their reltive verge moleculr weight before nd fter being exposed to mechnicl sher degrdtion rtes of 3395, 6790 nd 358 sec -, where the verge moleculr weight of the polymers re estimted from the intrinsic viscosity. Intrinsic viscosity [] of polymer solution is generlly determined by mesuring reltive viscosities t series of different concentrtions. Rudin 3 proposed determintion of intrinsic viscosity from single point. In most cses, [] cn be evluted conveniently using the grphic representtions of Huggins 4 nd Kremer 5. Although, nonliner lest squres fitting of the ctul curviliner reltion is universl method for estimting [] from reltive viscosity dt t series of concentrtions 5. In our previously work, the nonliner lest squre ws used by determining the verge viscosity t low sher rtes for different concentrtions. However when this method of clcultion ws pplied in this work, there ws hrdly ny difference in the clculted intrinsic viscosity for some of the experiments, especilly where the difference in the reltive viscosity is not lrge enough. This my be due to the fct tht the nonliner best fit suppresses the rel difference, hence overshdowed the smll differences. Rudin s 3 pproch ws followed fter verifiction by nother similr pproch by Solomon et l 6. 65

2 RESULTS nd DISCUSSIONS In order to ddress the sher degrdtion of the polymers, two min steps were followed in this work. The first is to estblish the properties of the polymer (sher viscosity mesurements) nd then expose the polymer to different sher degrdtion t constnt time, followed by ssessing the chnge in the polymers properties immeditely fter the sher degrdtion nd fter 72 hrs (recovered) where the polymers were kept with no disturbnces under the sme degrdtion temperture. The work hs been done for severl concentrtions, however polymer concentrtion tht is presented here is for 5000 ppm(w). When the DRA ws exposed to low sher degrdtion 3395 sec - t 5 o C, there ws lmost no difference between the shered nd the recovered sttus s shown in fig., except for DRA2 t 5 o C, where it shows prtil regin of its property fter 72 hrs t 5 o C s shown in fig.b. On the other hnd t 60 o c, the low sher degrdtion of 3395 sec - showed no chnge in DRA properties s shown in fig 2.&b. When the polymers were exposed to high sher degrdtion rte of 3582 sec -, no regin of their viscoelstic properties ws observed for the two tempertures, s shown in fig.c&d nd fig.2 c&d. It is interesting to observe tht the recovery tests show slightly lower viscosity thn the mesured sher viscosity immeditely fter the sher degrdtion. More work is on going, however, this phenomenon is not cler on why it occurs t this stge DRA_5C_5000 ppm DRA_3395_5C_5000 ppm_ DRA_rec.3395_5C_5000ppm DRA2_5C_5000 ppm DRA2_3395_5C_5000 ppm DRA2_rec.3395_5C_5000 ppm b DRA_5C_5000 ppm DRA_3582_5C_5000 ppm DRA_ rec.3582_5c_5000 ppm c DRA2_5C_5000 ppm "DRA2_3582_5C_5000 ppm" DRA2_rec.3582_5C_5000 ppm d Fig. Sher viscosity of mechnicl sher degrded polymers DRA nd DRA2 t 3395 sec - for DRA () nd DRA2 (b) nd t 3582 sec - fter 72 hrs for DRA (c) nd DRA2 (d) t 5 o C. 66

3 DRA Unshered DRA_3395_60C_5000 ppm DRA_ rec.3395_60c_5000 ppm DRA2 Unshered DRA2_3395_60C-5000 ppm DRA2_rec.3395_60C_5000 ppm DRA Unshered b DRA_3582_60C_5000 ppm DRA_rec.3582_60C_5000 ppm c DRA2 Unshered DRA2_3582_60C_5000 ppm DRA2_rec.3582_60C d Fig.2 Sher viscosity of mechnicl sher degrded polymers DRA nd DRA2 t 3582 sec - for DRA () nd DRA2 (b) nd t 3582 sec - fter 72 hrs for DRA (c) nd DRA2 (d) t 60 o C. MOLECULAR WEIGHT In order to determine the degree of degrdtion, similr pproch to our previous work is followed here 2. This is done by relting the intrinsic viscosity to moleculr weight for the shered nd unshered polymers. The intrinsic viscosity [] is defined by the following eqution []=[(ln r )/c] c 0 () Huggins 4 hs pointed out tht plots for given polymer/solvent system vry pproximtely s the squre of intrinsic viscosity s expressed by the following eqution: C 0 2 = [ ] + k [ ] C (2) H Where, nd 0 re the viscosity of polymer solution nd the solvent, respectively, ( =, reltive viscosity), C is the r 0 polymer concentrtion expressed s g.dl - nd k H is Huggins constnt. In prctice it is customry to mesure the reltive viscosity t two or more concentrtions, chosen to give reltive viscosities in the rnge of. to.5, nd then extrpolted to C=0. Series of sher rtes re then required in order to extrpolte to very low sher rte of zero. This prctice my produce errors due to forcing rel curviliner reltion into rectiliner form. In our previous work 2, the power series expressions re solved directly by non-liner regression nlysis 5 of the following eqution = C0 2 H H 2 ` 3 [ ] + k [ ] C + k [ ] C +... (3) This pproch, hs shown tht the clculted []in different cses of sher degrdtion nd recovery did not show pprecible difference. This my be explined tht the slight chnge in the sher viscosity occurs t certin window of sher rtes, hence overshdowed by the low differences. 67

4 Rudin 3 proposed n pproch to clculte intrinsic viscosity from single point t low concentrtion nd sher rte. The intrinsic viscosity [] is clculted by the following equtions [ ] = φ(.3ρ 2.5c) ( cρ)( φ) (4) where ρ is the density of the solution g ( 3 ), nd φ is the swelling fctor obtined cm by r 5 7 = 2.5φ + φ.5φ (5) The obtined intrinsic viscosity ws verified by similr pproch by Solomon et l 5. The results were lmost identicl Intrinsic viscosity cn then be relted to verge moleculr weight using Houwink- Skurd s reltion given by [ ] = K M (6) where K nd re polymer constnts. Exponent rnges from 0, to. Flory 7 stted tht this exponent does not fll below 0.5 nd seldom exceeds 0.8. Rudin et l 0 tested vrious polymers with different solvents, found tht the exponent () is between 0.5 nd 0.7. Prk nd Choi found tht for liner polymer system the Mrk-Houwink exponent () is bout 0.7 in good solvent nd 0.5 in the thet condition. In this work exponent () of 0.7 nd 0.5 re used. The trend for the degree of degrdtion of the polymers is clculted reltive to the un-shered polymer. This reltion is shown below. M M 2 [ ] [ ] = 2 (7) where, the subscript nd 2 represent the un-shered nd the shered polymer, respectively. As shown in fig 3 nd b, for the un-shered polymer t 60 nd 5 o C, respectively tht DRA is more susceptible to sher degrdtion thn DRA2 s expected, since it hs higher moleculr weight. M 2 /M M 2 /M Moleculr weight shered/unshered DRA nd DRA2_60C Mechnicl sher degrdtion rte [s - ] DRA 60C_=0.7 DRA 60C_=0.5 DRA2 60C_=0.7 DRA2_60C_=0.5 Moleculr weight shered/unshered DRA nd DRA2_ 5C DRA _5C_=0.7 DRA _5C_=0.5 DRA2 _5C_=0.7 DRA2_5C_= Mechnicl sher degrdtion rte [s - ] b Fig. 3 Rtio of the moleculr weight of the shered to the un-shered polymers DRA nd DRA2 t 60 o C () nd 5 o C (b) using exponent of 0.5 nd 0.7. It lso demonstrtes tht t high temperture 60 o C the polymers re less susceptible to mechnicl sher degrdtion rtes. This phenomenon is not well understood, however, since this reltion reflects the viscosity, it my, then be explined bsed on tht the moleculr ctivity t 60 o C is higher thn tht for 5 o C, the degrdtion my then be msked. 68

5 VISCOELASTIC PROPERTIES of the POLYMERS Viscoelstic properties re dominted by rerrngements of moleculr segments. Polymer moleculr weight nd moleculr weight distribution hve importnt effect on the viscoelstic properties of the polymer. Interprettion of polymer behviour using the storge modulus (G ) trend s function of scnned frequencies from 0.0 to 0 sec - t strin mplitude of 50% is believed to give n insight to the moleculr behviour tht my propose possible explntion to some of the observed phenomen. The mesurements re done using Pr Physic rheometer (model Physic USD 200 ) Fig.4, 5, 6, 7 nd 8 show plots of the storge modulus (dyn/cm 2 ) versus the ngulr frequency (sec - ) for un-shered polymers (DRA nd DRA2), shered polymers t 3395 sec - (5 nd 60 o C) nd 3582 sec - (5 nd 60 o C), respectively for polymer concentrtion of ppm(w). At ngulr frequencies () below bout 0.0 sec - high fluctution responses were obtined, it ws therefore decided to sty within the shown frequencies for this work(0.0-0 sec - ). G'dyn/cm 2 DRA_US_5C_5000 ppm.iwd: storge modulus G' DRA2_US_5C_5000 ppm.iwd: storge modulus G' DRA_3395_5C_5000 ppm.iwd: storge modulus G' DRA2_3395_5C_5000 ppm.iwd: storge modulus G' ω(/s) Fig.5 A comprison between G for the un-shered nd shered t 3395 sec - polymers DRA (open symbols) nd DRA2 (filled symbols) t 5 o C. Oyngi et l 8 from their work on nrrow distribution polystyrenes identified three distinct zones, which re the terminl, plteu nd trnsition zones. DRA2_US_60C.iwd: storge modulus G' DRA s^-_60c-5000ppm.iwd: storge modulus G' DRA_3395_60_5000ppm.iwd: storge modulus G' DRA_US_60C_5000 ppm.iwd: storge modulus G' 5000 US_DRA2_5C_dt.iwd: storge modulus G' DRA2_US_60C.iwd: storge modulus G' DRA_US_5C_5000 ppm.iwd: storge modulus G' DRA_US_60C_5000 ppm.iwd: storge modulus G' ω(sec - ) Fig.4 Storge modulus of polymer for DRA (open symbols) nd DRA2 (filled symbols) t 60 nd 5 o C. ω(sec - ) Fig.6 A comprison between G for the un-shered nd shered t 3395 sec - polymers DRA (open symbols) nd DRA2 (filled symbols) t 60 o C. In this work here, there is generl feture in ll the presented figures (4-8), where four zones were observed zones. The first is long plteu zone. Within this zone, the polymer behviour is shown not to be 69

6 much ffected by differences in moleculr weight or moleculr weight distribution. At frequency of bout 0.2sec - shrp increse of G from bout 5 * to bout 3* dyn/cm 2 ws observed, which is US_DRA2_5C_dt.iwd: storge modulus G' 5000_3582_DRA2_5C_dt.iwd: storge modulus G' DRA_US_5C_5000 ppm.iwd: storge modulus G' DRA_3582_5C_5000 ppm.iwd: storge modulus G' ω(sec - ) Fig.7 A comprison between G for the un-shered nd shered t 3582 sec - polymer DRA nd DRA2 t 5 o C. DRA2_US_60C.iwd: storge modulus G' DRA_US_60C_5000 ppm.iwd: storge modulus G' DRA2_3582_60C_5000 ppm.iwd: storge modulus G' DRA_3582_60_5000 ppm.iwd: storge modulus G' ll the curves converge. So the terminl is perhps wht is identified s second zone followed by the short plteu (zone 3) nd then trnsition zone (zone 4). The difference between the trnsition zone in this work nd the reported in the literture is tht fter the plteu G decresed to the rnge of bout 0-6 dyn/cm 2 where the curves converged. In order to confirm tht zone 3 is the equivlent to the reported plteu in litertures, this zone ws further exmined. Qyngi nd Ferry 9 showed tht in the plteu zone, the loss tngent (tnδ ), psses through minimum, where the minimum deepens with moleculr weight. Plots of tnδ nd G vs re shown in fig.9, where the minimum coincides with the third zone, hence it my represent the plteu. The trnsition between the terminl nd plteu nd the mgnitude nd the shpe of the plteu my give informtion on the polymer behviour. G'dyn/cm DRA2_US_5C_5000 ppm.iwd: loss tngent DRA2_US_5C_5000 ppm.iwd: storge modulus G' DRA_US_5C_5000 ppm.iwd: loss tngent DRA_US_5C_5000 ppm.iwd: storge modulus G' tn δ ω (sec - ) ω(sec - ) Fig.8 A comprison between G for the un-shered nd shered t 3582 sec - polymer DRA nd DRA2 t 60 o C. followed by third zone with plteu (low slope). The fourth zone shows drop in G fter which ll G converged. The forth zone hs the sme criteri s the reported trnsition zone in literture, where Fig.9 G nd tn (filled symbols) for the un-shered polymers DRA (open tringles) & DRA2 (open circles) t 5 o C. It is interesting to observe tht the shered nd un-shered polymers hve longer plteu t lower temperture (5 o C) thn t the high temperture (60 o C). This is true for both low nd high sher rtes, 3395 nd 3582 sec -, except tht the shered DRA t high sher rte 3582 sec - (60 o C) hs long plteu tht is comprble, to some 70

7 extent, with tht obtined with the unshered polymer t the low temperture (5 o C). The plteu, where G chnges only slightly with frequency my be explined to be due to entnglements 8&9, s result, the polymer behviour is not much ffected by differences in moleculr weight or moleculr weight distribution. Fig 5, nd 7 show tht for sher degrdtion of 3395 nd 3582 sec -, respectively t 5 o C hve slightly but consistently indiction of higher moleculr weight thn the un-shered polymers. However, t 60 o C, the shered DRA t 3395 nd 3582 sec -, s shown in fig. 6 nd 8, respectively show comprble behviour to the un-shered polymers (DRA nd DRA2) t 5 o C in the plteu zone tht my indicte tht the shered DRA (high verge moleculr weight) hs lrge moleculr distribution, hence promoting entnglement phenomenon to occur. This phenomenon hs not been observed for the shered DRA2 t 60 0 C CONCLUSIONS The tested polymer drg reducers seem to be less susceptible to sher degrdtion t 60 o C thn t the low temperture of 5 o C. This my be explined bsed on tht the degrdtion effect is msked by the higher level moleculr ctivities t 60 o C. At the high temperture the degrded DRA, hs indicted (from the plteu) possible occurrence of more entnglement when shered t 3852 sec-. Combining the polymer ctivities nd the wide moleculr weight distribution fter the sher degrdtion my enhnce the entnglement phenomenon. On the other hnd this phenomenon ws not observed for DRA2, to the sme extent s for DRA. This, perhps, is due to nrrower moleculr weight distribution thn for DRA. This is not unrelistic, since the verge moleculr weight of DRA2 is bout 5 times less thn tht for DRA. The moleculr weight rtio estimted from the intrinsic viscosity does give insight to moleculr weight distribution but rther verge moleculr weight rtio between the shered nd the un-shered polymers. REFERENCES. Peiwen L., Ysuo K., Hisshi D., Akir Y., Koichi H. nd Msnobu M. (200), Het trnsfer enhncement to the drg-reducing flow of surfctnt solutionin twodimensionl chnnel with mesh-screen inserts t the inlet Journl of Het Trnsfer, Trnsctionof the ASME, Vol. 23, pp Hmoud, A.A., nd Sveinung, T, Annul Trnsctions of the Nordic Rheology Society,, Rudin, A.nd Wgner,R.A. Journl of Applied Polymer Science, 9, , Huggins, M.,L, J.Am. Chem. Soc , Kremer,E.O., Ind. Eng. Chem., 30, 200, Solomon, O.F. nd Ciut, I.Z., J. ppl. Polym. Sci. 6, 683, 962). 7. Flory, P.J., Prinsiples of polymer chemistry, Cornell University Press, New York, 953). 8. Oyngi. S., Musud. T, nd Kitgw.K, Mcromolecules, 3, 09, ) Oyngi. Y nd Ferry,J.D, Proc. 4 th intern. Cong. Rheology, Prt 2, Interscience, New York, 49, Rudin, A., Strthdee, G.B.nd, Edey, W.B., J. Appl. Polym. Sci. 7, 3085 (973). 7

Fig. 1. Open-Loop and Closed-Loop Systems with Plant Variations

Fig. 1. Open-Loop and Closed-Loop Systems with Plant Variations ME 3600 Control ystems Chrcteristics of Open-Loop nd Closed-Loop ystems Importnt Control ystem Chrcteristics o ensitivity of system response to prmetric vritions cn be reduced o rnsient nd stedy-stte responses