EXPERIMENTAL INVESTIGATION OF CRITICAL STRAIN FOR VISCOPLASTIC MATERIALS WITH DIFFERENT GEOMETRIES AND RHEOMETERS

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1 EXPERIMENTAL INVESTIGATION OF CRITICAL STRAIN FOR VISCOPLASTIC MATERIALS WITH DIFFERENT GEOMETRIES AND RHEOMETERS Guilherme A. S. Balvedi, 2 Diogo E. V. Andrade, 3 Admilson T. Frano e 3 Cezar O. R. Negrão Sientifi Initiation fellow of FUNTEF-PR, student of Mehanial Engineering 2 PhD student at Federal University of Tehnology - Paraná - UTFPR 3 Professor at Federal University of Tehnology - Paraná - UTFPR,2,3 Researh Center for Rheolgy and Non-Newtonian Fluids CERNN, Federal University of Tehnology Paraná UTFPR. Av. Sete de Setembro, 365 Curitiba PR, , Brazil guilhermebalvedi@alunos.utfpr.edu.br, diogoandrade@utfpr.edu.br ABSTRACT Drilling fluids assist drilling operations with leading uttings out of the struture and preventing well from ollapse. At speifi onditions, suh as at rest, these fluids build up a gel-like struture and higher pressures than usual steady state pressures are required to restart the flow. Therefore, a liable property to predit pressure value to restart a flow would be important in suh situations. The existene of a ritial strain for thixotropi materials, suh as drilling fluids and waxy rude oils, has been investigated by several authors in the past few years. This urrent work investigates the presene of a ritial strain in a visoplasti material by means of rheometri tests. Controlled shear rate tests and stress ontrolled tests were performed with different rheometers and geometries. The results have shown that there is a onstant ritial strain for ontrolled stress tests, but not for ontrolled shear rate tests. Keywords: visoplasti material, rheometri tests, ritial strain INTRODUCTION Drilling operations require drilling fluids in order to assist the well from ollapse and to lead uttings out of the struture. Besides, drilling fluids build up a gel-like struture when at rest and high pressures are neessary to restart the irulation within the wellbore. Sine a preise predition for pressure would be important to avoid raks on the walls of the well and fluid loss, a liable property is investigated to foresee the gel break. Da Cruz et al. (203) and Andrade et al. (203) show in spite of yield stress of drilling fluids being dependent of the test type, there is a ritial strain, whih is independent from the test type. In works performed with waxy rude oil, a visoplasti and thixotropi fluid also, Hou (202) and Tarha et al. (205) show that there is also a onstant ritial strain for this fluid. On the other hand, Fernandes (204) and Andrade et al. (204) present that not just the yield stress of strutured materials is dependent from the test type, but also the ritial strain. It worthy of notie that Fernandes (204) analyzed the behavior of a non-aqueous drilling fluid and Andrade et al. (204) of a waxy rude oil at low temperatures. It is notied that the main differene of the tests performed by Fernandes (204) and Andrade et al. (204) and other works (Da Cruz et al., 203; Andrade et al., 203; Hou, 202; and Tarha et al., 205), whih determinate that the ritial strain is onstant, is the use of serrated geometries. In the analyzed works, Da Cruz et al. (203) and Andrade et al. (203) performed ontrolled shear rate tests and Da Cruz et al. (203), Andrade et al. (203), Hou (202) and Tarha et al. (205) performed ontrolled shear stress tests. The authors state that there is a onstant ritial strain. These authors also state that, for both shear rate and shear stress tests, there is a ritial strain, whih is independent from what is imposed to the material. As mentioned by these authors, the ritial strain does not depend on the shear history of the material. With that in mind, its value ould be used to evaluate mathematial models, suh as to restart the flow of drilling fluids at rest. In order to evaluate the existene of ritial strain, a less omplex material than drilling fluids

2 Shear Stress [Pa] Shear Stress [Pa] was hosen to arry out the tests desribed in the next setions. Gel for ultrasound purposes, suh as arbopol, was hosen for its known well-behaved visoplastiity and quik properties reovery after shearing. EXPERIMENTAL SECTION Materials and Methods Carbopol in its original pakage was used to ondut the tests on two different rotational rheometers, Thermo Sientifi Haake MARS III (Haake Co., Germany) and TA Instruments DHR- 3 (TA Instruments, USA). Serrated and sandblasted 35 mm parallel plate geometry (.0 mm gap) were employed on the Haake rheometer and serrated and lathed 40 mm parallel plate geometry (.0 mm gap) on the TA rheometer. All tests were performed at 25 C with an aging time of 0 minutes at the beginning for temperature equalization. Besides, a sample hood was used to prevent material degradation. After the initial proedure the following tests were exeuted: ontrolled shear rate test; ontrolled shear stress rate test; and ontrolled shear stress test. The values presented in the work are average values of tests repeated three times. It was notied that the repeatability obtained for tests with this material is around 90%. RESULTS AND DISCUSSION Controlled Shear Rate Tests This test onsisted of shearing the material with variation of shear rate ( ). In other words, the shear rate applied on the material varied from 0 to a final pre-established shear rate in 5 seonds in order to ensure the break of the gellike struture. The following were used: 0.02, 0., 0.2,, 2, 0, 20, 200 s -2. Figure illustrates shear stress as a funtion of logarithmi strain sale. It an be noted that the eight tests performed have omparable urves. At the beginning, strain inrease is not as relevant as shear stress inrease. This indiates a predominant elasti behavior. At some point the strain is too high to be supported by the material and the gel struture is finally broken, starting a predominant visous behavior. From this ritial point the material easily flows without an expressive inrease of shear stress ,02 s -2 0, s -2 0,2 s -2 s -2 2 s -2 0 s s s Strain [-] Figure Shear stress as a funtion of strain for Haake serrated geometry at 25 C The exat point that separates both elasti and visous behavior is not obvious. With that in mind, it was established that the yield point would be the intersetion between two lines traed over the experimental points just before and just after in the region of behavior hange. As shown in Figure 2, shear stress as a funtion of strain with =2 s -2 for Haake serrated geometry, the ritial point was determined as explained. The two blak dotted lines interset eah other and their intersetion is indiated with a red irle. After that it is possible to analyze its position, whih in this ase orrespond to a ritial strain of 0.90 and ritial shear stress of 36 Pa Strain [-] Figure 2 Determination of the ritial point for ontrolled shear rate of 2 s -2 test Table ontains ritial strain and ritial shear stress from the tests of this work setion. It is important to note that it was not possible to determinate the ritial points of the tests performed with the grinded sensor on the TA rheometer, sine the surfae is not rough enough to prevent sample slipping.

3 Critial strain [-] Table Data from the ontrolled rate of hange of shear rate tests on Haake and TA rheometers Sandblasted Haake Serrated Haake Serrated TA [s -2 ] [-] [Pa] [-] [Pa] [-] [Pa] As an be observed from Table, ritial shear stress ( ) are approximately the same for every tested, independent from rheometers or sensors. For example, the highest perentage hange is for = 200 s -2, 6.3%. In other words, the rheometers indiate values for ritial shear stress with good repeatability. On the other hands, the same is not notied for ritial strain, whih the lowest perentage hange is 3% for = 200 s Serrated - TA Serrated - Haake Sandblasted - Haake Variation of Shear Rate [s -2 ] Figure 3 Critial strain as a funtion of variation of shear rate for different rheometers and geometries at 25 C Figure 3 shows ritial strain as a funtion of variation of shear rate. For range tested, from 0.0 to 200 s -2, the ritial strain range varies signifiantly. For example, the ritial strain for sandblasted geometry Haake varies from 0.58 to For serrated geometry Haake its value varies from 0.78 to Furthermore, ritial strain values also vary meaningly. For example = 0. s -2 leaded to a ritial strain of 0.6 for sandblasted geometry Haake and also to a ritial strain of 0.89 for serrated geometry TA. The perentage differene for these two last values is 45%. It is noted that the highest ritial strains values are obtained for serrated geometries when ompared to the ones from the sandblasted geometry. This was not an expeted result sine wall slip is more often observed in surfaes with low roughness. The ourrene of this event is assoiated to higher measured strains, whih is not noted. Higher the, higher the orresponding value for ritial strain. Besides, all ritial strain values are higher for the serrated sensor on TA rheometer than for the serrated sensor on Haake rheometer. These tests orroborate the results obtained by Fernandes et al. (204) for drilling fluids and by Andrade et al. (204) for waxy rude oil. It is worth noting that ritial strain in ontrolled shear rate tests is not onstant for both geometries used. Controlled Stress Tests The ontrolled stress tests were performed by applying variable shear stress ( ) on the sample. The following were used: 0, 25, 50, 00, 500, 000 and 0000 Pa.min -. At the beggining, shear stress onstantly inreases and strain remains in low values, as an be seen in Figure 4, strain as a funtion of shear stress for serrated geometry on Haake rheometer. When the shear stress is high enough to break the gellike struture, the sample flows and a high shear rate is notied.

4 Strain [-] Critial Strain [-] Strain [-] Pa/min 25 Pa/min 50 Pa/min 00 Pa/min 500 Pa/min 000 Pa/min 0000 Pa/min Figure 6, in whih strain is plotted as a funtion of shear stress rate Shear Stress [Pa] Figure 4 Strain as a funtion of shear stress for Haake serrated geometry at 25 C In the same line from the previous setion, the ritial point is not obvious to determine. Therefore, an analog proedure was used to determinate the ritial point for every urve. As shown in Figure 5, shear stress as funtion of strain for with = 50 Pa.min - for Haake serrated geometry, two lines are traed over the experimental points just before and just after in the region of behavior hange and the intersetion point is onsidered the ritial point. In this ase, ritial strain is 0.5 and ritial shear stress is 9 Pa Shear Stress [Pa] Figure 5 Determination of a ritial point for ontrolled stress rate of 50 Pa.min - test Table 2 presents data olleted from shear stress rate tests for every geometry and rheometer used. Sine the ritial strain values are lose to eah other for eah geometry and rheometer used, its average value is also presented. As an be seen from Table 2, the ritial shear stress inreases as the shear stress rate inreases for all geometries. With respet to ritial strain, the results are better visualized in 0.2 Shear Stress Rate [Pa.min - ] Figure 6 Critial strain as a funtion of shear stress rate for different rheometers and geometries at 25 C The average ritial strain values for eah geometry are also plotted in Figure 6 as interrupted lines. It is worth noting that the sale for ritial strain is preise, logarithmially varying from 0. to. Even though the ritial strain does not have wide variations for the shear stress rate range studied. For example, the widest variation ours for both Haake geometries, Based on the values obtained for ritial strain is possible to state that they are onstant for the same geometry, regardless to shear stress rate. Besides, the values for serrated geometries in both rheometers are lose to eah other, around 0.5, and higher with respet to values from the sandblasted Haake, Therefore, there is for ontrolled shear stress rate test a onstant ritial value whih does not depends on shear stress rate and rheometer. This result orroborates the results obtained by Da Cruz et al. (203), Andrade et al. (203), Hou (202) and Tarha et al. (205). Creep Tests Serrated - TA Serrated - Haake Sandblasted - Haake The reep test onsists in applying a onstant shear stress on the sample for 600 s and observe if the gel-like struture breaks or if strain remains onstant, indiating only elasti deformation. As an be seen in Figure 7, strain as funtion of time for Haake serrated geometry, shear stress of 80 Pa is not high enough to break the gel-like struture in 600 s for this material. On the other hand, shear stress of 00 Pa was high enough to break the gel and resume the flow in 70 s. One an observe that when 20 Pa is applied the gel breaks in less than s. In addition, the ritial strain obtained for both shear stresses

5 Strain [-] apable of breaking the gel-like struture has a onstant value around 4. Table 2 Data from the ontrolled shear stress rate tests on Haake and TA rheometers Sandblasted Haake Serrated Haake Serrated TA [Pa.min - ] [-] [Pa] [-] [Pa] [-] [Pa] Average Pa 80Pa 00Pa 20Pa Time [s] Figure 7 Strain as a funtion of time for Haake serrated geometry at 25 C Therefore, for ontrolled shear stress test, ritial strain is onstant for this material. The result aquire in this setion also orroborates the results obtained by Cruz et al. (203), Andrade et al. (203), Hou (202) and Tarha et al. (205). CONCLUSION In the urrent work, ritial strain of visoplasti materials is analyzed for different types of tests. For the variation of shear rate test, the higher the, the higher the ritial strain. In the other words, the ritial strain is not onstant for this type of test. Both ontrolled shear stress rate and reep tests resulted in onstant ritial strain, although not the same. The ritial strain value obtained for onstant shear stress test is around 8 times higher than the ones found for onstant shear stress rate tests with serrated geometry. With respet to ritial shear stress, their values are lose to the same test and same parameters. It inreases as inreases and as shear stress rate inreases. For both ontrolled shear rate and ontrolled stress rate tests it is obvious the dependene of the results on the type of geometry. Serrated geometries showed higher ritial strains than the sandblasted geometry. Higher values were expeted for sandblasted sensor sine slipping event is more often observed in surfaes with low roughness. REFERENCES ANDRADE, D. E. V.; RODRIGUES, M. T.; CECCON, E. V.; CRUZ, A. C. B.; FRANCO, A.T.; NEGRÃO, C. O. R., 203. Proposal of Curve Fitting for Shear Stress During Gel Breaking of Thixotropi Drilling Fluids. 22nd International Congress of Mehanial Engineering - COBEM, 437 ANDRADE, D. E. V.; TAKII, B. A.; FRANCO, A. T.; NEGRÃO, C. O. R., 204. The influene of the initial ooling ondition on the flow urve of waxy rude oil, ENCIT 204. DA CRUZ, A. C. B.; RODRIGUES, M. T.; ANDRADE, D. E. V.; FRANCO, A. T.; NEGRÃO, C. O. R.; MARTINS, A. L., 203. Curve fitting for gel braking of drilling fluids, ENAHPE 203. FERNANDES, R. R.; 204. Metodologia para preparação de amostras em testes reológios e avaliação da tensão limite de esoamento de fluidos de perfuração. Trabalho de Conlusão de Curso Curso de Engenharia Meânia, Universidade Tenológia Federal do Paraná. HOU, L., 202. Experimental study on yield behavior of Daqing rude oil, Rheologia Ata, 5: TARCHA, B. A.; FORTE, B. P. P.; SOARES, E. J.; THOMPSON, R. L., 205. Critial quantities of the yielding proess of waxy rude oils, Rheologia Ata.

6 ACKNOWLEDGEMENTS The authors aknowledge the finanial support of PETROBRAS S/A, ANP (Brazilian National Oil Ageny) by means of the PRH/ANP and PFRH/PETROBRAS (PRH0-UTFPR) and FINEP.