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Yield stress measurement of gelled waxy crude oil: Gap size requirement
Journal of Non-Newtonian Fluid Mechanics 218 (2015) 71–82
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Yield stress measurement of gelled waxy crude oil: Gap size requirement A. Japper-Jaafar a,⇑, P.T. Bhaskoro a, L.L. Sean b, M.Z. Sariman c, H. Nugroho d a
Mechanical Engineering Department, Universiti Teknologi PETRONAS, 32610, Bandar Seri Iskandar, Perak Darul Ridzuan, Malaysia PETRONAS Research Sdn Bhd, Kajang, Selangor, Malaysia c PETRONAS Carigali Sdn Bhd, Kuala Lumpur, Malaysia d Electrical Engineering Department, Universiti Teknologi PETRONAS, 32610, Bandar Seri Iskandar, Perak Darul Ridzuan, Malaysia b
a r t i c l e
i n f o
Article history: Received 21 August 2014 Received in revised form 24 December 2014 Accepted 2 February 2015 Available online 17 February 2015 Keywords: Rheometer Measurement gap Yield stress Waxy crude oil
a b s t r a c t The strength of gelled waxy crude oil is an important parameter required to determine the restart pressure of pipelines filled with the gelled waxy crude oil. Several measurement methods have been proposed in the literature to quantify the yield strength utilizing a rheometer. Minimal discussions, are however, provided on the effects of rheometer geometry gap on the yield stress measurements. This study is intended to propose a systematic protocol to determine the geometry gap settings for better repeatability of the yield stress measurements of gelled waxy crude oils. The reliability of the yield stress data measured has been shown to be highly dependent on the gap selection in the rheometer. The ten-to-one gap ratio has been proven to be inapplicable for the case of gelled waxy crude oils which consists of wax crystal networks entrapping the oil phase. Presence and strong interactions of large wax crystals presents wall effects and subsequently reduces the repeatability of the measurements. The method proposed in this study has been proven to work on a mild waxy crude oil as well as on a more ‘‘severe’’ waxy crude oil. It can be utilized prior to any transient rheological measurements as gap setting is crucial to ensure accurate and reliable measurements. Ó 2015 Elsevier B.V. All rights reserved.
1. Introduction Waxy crude oils are aliphatic hydrocarbon having high molecular weight paraffin with carbon number ranging from C18 to C65 [18]. The paraffin waxes can be classified as either macrocrystalline or micro-crystalline. Macro-crystalline waxes are mainly linear paraffin (n-alkanes) with chain lengths between C18–C30. They have needle-like and plate-like morphology with crystal size up to 100 lm. Their presence within the crude oil promotes strong gel formation. Micro-crystalline waxes on the other hand contain greater percentage of iso-paraffin (branched alkanes) and naphtenes (cyclic alkanes) with carbon number found to be greater than 30. The crystal size is much smaller (up to 10 lm) with spherical morphology. It is amorphous in nature as the crystal growth is hindered by the side and cyclic groups present in the molecules. Misra et al. [13] reported that if the micro-crystalline waxes are present, it will be the main constituent of the sludge at the bottom of crude oil storage tanks. The solubility of paraffin waxes is dependent on the temperature, it decreases with decreasing temperature. At reservoir ⇑ Corresponding author. Tel.: +60 5 368 7022; fax: +60 5 365 6461. E-mail address: [email protected] (A. Japper-Jaafar). http://dx.doi.org/10.1016/j.jnnfm.2015.02.001 0377-0257/Ó 2015 Elsevier B.V. All rights reserved.
conditions where the temperature ranges between 70 and 150 °C with pressure ranges between 50 and 100 MPa, the solubility of the paraffin in the crude oil is adequately high. The wax molecules are fully dissolved in the crude oil mixture resulting in a singlephase crude oil and in the absence of other components and contaminants the crude oil behaves predominantly Newtonian with low viscosity. Once the crude oil leaves the reservoir and flows through cold pipelines placed on the seabed with temperature as low as 5 °C, the crude oil temperature begins to drop dramatically due to the heat loss to the surroundings. The crude oil will then be subjected to phase transformation from liquid state, showing Newtonian behavior, to a gel-like structure exhibiting non-Newtonian characteristics. The three main stages of the phase transformation process are wax precipitation, wax deposition and wax gelation. Wax gelation will be induced when the temperature of the crude oil drops below the pour point temperature of the crude beyond which, the crude oil flow ceases completely. Wax gelation is not a new phenomenon in the petroleum industry and this issue has already captured the interest as early as in the 1920s [14]. Various classical descriptions of gel have been documented in the literature. Flory [8] regards a gel as a homogeneous system within which the liquid is not distinguishable from the solids suspended in the liquid. The liquid tend to disappear
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and the solid mass is formed, which may display either a fluid-dominant characteristics or a more solid-dominant structure. A gel also exhibits greater elastic to viscous properties [4]. Kane´ et al. [11] and Singh et al. [17] proposed that the gelation of waxy crude oil involves three stages; formation of lamellar subcrystals which grows in two dimensions as sheet like crystals, aggregation of sub-crystals to form a large space filling network and finally overlapping and interlocking of the aggregation due to strong interactions and attractions between wax crystals. Subsequently, a 3-D volume spanning network of crystals that traps liquid oils and exhibits both the elastic properties and the viscous properties is formed. The amount of trapped oil, or ‘‘wax porosity’’ within the wax crystals network would influence the strength of the waxy crude gels. For ‘‘soft’’ wax a porosity of up to 90% has been reported while for ‘‘hard’’ wax, the porosity is within the range of 50–70%. Ageing, internal diffusion and large temperature differential within the pipeline, amongst others, could result in ‘‘harder’’ wax and subsequently higher gel strength [5]. The wax gelation has great impact especially during production shutdowns where the crude oil temperature drops below the pour point temperature allowing the formation of a ‘‘candle’’-like structure or solid wax column. This phenomenon can completely block the pipeline and during restart operation, a large pressure may then be required to initiate the crude oil flow again. In order to determine the breakdown pressure required to restart the flow, it is important to estimate the gel strength, measured in terms of the yield stress. The yield strength of waxy crude oil gel has been characterized by many within the literature [1,6,7,16,15,9,19,10], amongst others. As documented, the yield stress can be measured via various experimental protocols; the creep-recovery test, the oscillatory test, the stress ramp test and many more. Several geometries can be utilized to determine the yield stress of gelled crude oil; the cone and plate, the parallel plate and the vane geometry, with the surface of these geometries is maintained smooth, sandblasted or cross hatched. Throughout the study on the yield stress of waxy crude oil documented within the literature, least discussions have been extended on the effects of the geometry gap to the measurements. The rheometer gap size is critical to minimize wall effects and at the same time allowing freedom for the sample to move under shearing action and subsequently behave as a continuum. As highlighted by Marchesini et al. [12], equilibrium flow properties of gelled waxy oils are less influenced by experimental conditions. However, transient measurements including oscillatory measurements are highly dependent on the gap selection in the rheometer which is supported by the work of Wardhaugh and Boger [20]. Barnes [2] proposed a rule of thumb to decide for a geometry gap where a minimum ratio of gap to particle size of 10:1 is recommended. For large particle systems, the requirement is often impossible to be met in small angle cone and plate geometry as it is limited by the truncation height or the gap of the cone and plate. Later in 2000, Barnes discovered that the ‘‘ten-to-one’’ ratio is only applicable for samples with phase volume of up to 25%. Greater gap size is then required in higher phase volume samples, which, may, at times, be unrealistic for a medium containing large particles such as waxy crude oil gel. Cautious treatment of data collected is then required especially on melts and gels obtained using the cone and plate rheometer. The presence of the wax crystals whose characteristic dimension is of the same order of magnitude of the gap within the cone and plate may then introduce measurement errors. The works presented in this paper are intended to propose a systematic assessment on gap determination (for 3 waxy crude oils) and to compare between the thermal cycle tests by Marchesini et al. [12] and the proposed strain sweep test method. Morphology of wax crystal was also investigated for further
understanding on its effects to the rheological behavior. An image processing technique was performed to quantitatively determine wax fraction and maximum aggregated wax crystal length. The values were utilized to theoretically estimate gap size required from Barnes [2,3] and compared with the results from the thermal cycle test and the proposed strain sweep test methods. 2. Characterizations and measurements 2.1. Working fluid and pre-conditioning process The crude oils utilized throughout the study are waxy crude oils produced within the South East Asia. The WAT, as measured using CPM, pour point temperature (ASTM 5985-96) and API gravity (ASTM D1250) of the waxy crude oils are tabulated in Table 1. Conditioning of the crude oil upon received from the operator involves heating at 20 °C above the WAT for 8 h within a large water bath. The crude oil was then poured into smaller containers (20 mL) to ensure minimal sample variations due to light and heavy components, and allowed to cool at room temperature. As thermal history or heat treatment to which the crude oil samples are subjected to influences the flow behavior of the sample, it is important to standardize the pre-conditioning treatment to ensure repeatability of the yield stress measurements. Prior to measurements the crude oil in the smaller container was soaked again in a water bath at 20 °C above the WAT for 2 h to dissolve any wax crystals present ensuring homogeneity and promote a stable composition during testing. 2.2. Equipments A TA instrument controlled stress rheometer, AR-G2, was utilized for all rheological measurements. The geometry (parallel plate) is either a 20 mm or a 40 mm (depending on the strength of the gel) cross hatched plate with the groove to be greater than 10 lm [2] to minimize wall slip phenomena where complete adhesion is violated. A cross hatched surface is suitable as it possesses sufficient rugosity greater than the crystal size aggregates assuming that the crude oil samples contains mainly of macro-crystalline waxes. Assumptions that no flow occurs between the protrusions and shear occurs between the surfaces consisting of the protruding tips were made. It is the same assumption for vane rheometry measurement. Visual observations were performed to verify any presence of slip on smooth surface geometries. When both smooth upper and lower geometries were utilized, the smooth upper surface was practically clean after what is thought to be an apparent yielding of the sample while the sample remained intact on the smooth lower surface. However, yielded sample using the roughened upper surface showed that the gelled crude failed within the sample indicating no slip on the upper roughened surface as well as on the smooth lower surface. Hence, the authors believed that an upper roughened surface is sufficient to minimize the slip effect. The waveforms produced at the same % strain for different gap settings have also been analyzed. The similar waveforms produced at different gaps settings confirmed minimal slip effects as proposed by Yoshimura and Prud’homme [22]. A solvent trap was used to minimize evaporation of the light end components from the sample for all the rheological measurements and subsequently the stability Table 1 Properties of waxy crude oil sample. Properties
Crude A (Se)
Crude B (An)
Crude C (Pe)
WAT (°C) Pour point API gravity (at 15 °C)
41.2 39 33.76
41.1 33 36.86
68.2 60 25.15
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10.00 Cooling Heating Cooling Heating Cooling Heating
viscosity (Pa.s)
1.000
Down Using Gap 300 m icron Up Using Gap 300 m icron Down Using Gap 500 m icron Up Using Gap 500 m icron Down Using Gap 800 m icron Up Using Gap 800 m icron
0.1000
0.01000
1.000E-3 20.0
22.5
25.0
27.5
30.0
32.5
35.0
37.5
40.0
42.5
45.0
temperature (°C) Fig. 1. Thermal cycle test of crude A with gap sizes of 300, 500 and 800 lm.
10.00
(a)
viscosity (Pa.s)
1.000
0.1000
Gap 300 - cooling Gap 300 - heating Gap 500 - cooling Gap 500 - heating Gap 800 - cooling Gap 800 - heating
0.01000
1.000E-3 17.5
20.0
22.5
25.0
27.5
30.0
32.5
35.0
37.5
40.0
42.5
temperature (°C)
viscosity (Pa.s)
100.0
Gap 300 - cooling Gap 300 - heating Gap 500 - cooling Gap 500 - heating Gap 800 - cooling Gap 800 - heating
10.00
(b)
1.000
0.1000 35.0
40.0
45.0
50.0
55.0
60.0
65.0
70.0
temperature (°C) Fig. 2. Thermal cycle test at various gap, (a) crude B and (b) crude C.
of the sample composition was assumed to be maintained. All the sample measurements conducted in this study were repeated at least 3 times to confirm repeatability although only 1 or 2 representative data runs were presented.
A cross polar microscopy (Olympus BX 51) equipped with a video camera and recorder is also utilized to observe wax crystallization process as the sample is cooled down to Tmin. A small amount of sample was first heated up to 10 °C above the WAT
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1.000E8
10000
1.000E7
200.0
1.000E8
175.0
1.000E7
150.0
1.000E6
125.0
1.000E5
100.0
10000
75.00
1000
50.00
100.0
25.00
10.00
1000
10000 1000
10.00
osc. stress (Pa)
100.0
Run1 Run2
100.0
G'' (Pa)
G' (Pa)
1.000E5
raw phase (degrees)
1.000E6
1.000 10.00 1.000 0.1000 0.010000
0.10000
1.0000
0 1.000 100.00
10.000
% strain
Fig. 3. Strain sweep test on gelled waxy crude oil A at 25 °C with a gap of 300 lm at 10 Hz with waveforms shown at respective strains.
1.000E5
100.0
10000
1.000
10.00
osc. stress (Pa)
100.0
0.1000 1.000 Run 1 Run 2 0.1000 0.01000 0.010000
0.10000
1.0000
10.000
1.000E5
150.0
10000
125.0 1000 100.0 100.0 75.00
G'' (Pa)
G' (Pa)
1000
raw phase (degrees)
10.00
175.0
10.00 50.00 25.00
1.000
0 0.1000 100.00
% strain
Fig. 4. Strain sweep test on gelled waxy crude oil A at 25 °C with a gap of 500 lm at 10 rad/s with waveforms shown at respective strains.
for 30 min on a small glass crucible. It is to ensure that the wax crystals melt completely prior to cooling. The measurement was conducted from a specified high temperature (above WAT) to a low temperature (below WAT), Tmin. Two various cooling rates were utilized during the measurement: 1 °C/min and 10 °C/min. A lens with 10 magnification was used for all observations.
1 °C/min down to the Tmin (a temperature at which the sample has gelled) at 10 s1. A strain sweep test was performed after the sample was left to rest for another 2 min after gelling from 0.01% to 100% strain at Tmin. Suitable gap required was assessed by considering several aspects: raw phase angle, stress strain waveform, repeatability and achievable strain.
2.3. Procedures 2.3.1. Strain sweep test In this work, a strain sweep test for gap study was proposed. After pre-conditioning the sample was loaded onto the peltier plate, set to a temperature above the WAT to minimize any ‘‘thermal shock’’. Upon loading, the head was lowered gradually to avoid compression overload. An initial gap setting of 300 lm was utilized. As the waxy crude oil system was known to be thixotropic, steps have also been taken to ‘‘standardize’’ the shear history prior to any testing procedure. The sample was pre-sheared at 10 s1 at a temperature higher than WAT, for 3 min and subsequently left for 2 min to rest. To gel the sample, a temperature ramp was applied at
2.3.2. Thermal cycle test A thermal cycle test, as recommended by Marchesini et al. [12], was also performed on the crude samples as comparison and to confirm the selection of gap. The thermal cycle test (under shear rate of 10 s1) started with a cooling of the crude oil at 1 °C/min down to the Tmin (20 °C below PPT) from a starting temperature Ts (5 °C above TWAT). Once the Tmin was achieved, the sample was then subjected to a temperature ramp back to the initial temperature at the same rate. The viscosity was then plotted as a function of temperature. The procedures were repeated with progressively increasing gaps (300, 500, and 800 lm) until the viscosity data was no longer changing with the gap setting indicat-
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1.000E5
100.0
150.0
1.000E5
125.0
1.000
osc. stress (Pa)
1000
Run1 Run2
10000 100.0 75.00
G'' (Pa)
G' (Pa)
10.00
raw phase (degrees)
10000
1000
50.00 100.0
100.0 25.00 0.1000 10.00 0.010000
0.10000
1.0000
0 10.00 100.00
10.000
% strain
Fig. 5. Strain sweep test on gelled waxy crude oil A at 25 °C with a gap of 800 lm at 10 rad/s with waveforms shown at respective strains.
1.000E5
100.0
150.0
1.000E5
Run 1 Run 2
125.0
10000
osc. stress (Pa)
G' (Pa) 100.0
100.0 1000 75.00
G'' (Pa)
10.00
raw phase (degrees)
1000
10000
100.0 50.00 10.00
10.00
25.00
1.000 1.000 0.010000
0.10000
1.0000
10.000
1.000 0 100.00
% strain
Fig. 6. Strain sweep test on gelled waxy crude oil B at 20 °C with a gap of 300 lm at 10 rad/s with waveforms shown at respective strains.
ing gap-independent data. The gap at which gap-independent result was achieved was regarded as minimum gap required.
3. Results and discussions 3.1. Thermal cycle test
2.4. Image processing for wax crystal size determination and distribution Wax crystal size and the distribution were determined by performing a 2D image processing on the image collected from cross polar microscope (CPM) via Matlab software using a threshold technique. 34 wax samples representing low to high threshold values were first taken from the image and plotted to map the distribution of threshold values. General power law model given below was utilized to fit the sample data.
f ðxÞ ¼ axb
ð1Þ 2
In this work, the fitting was accepted if the R -value was equal to or above 0.8 and the threshold value can then be deduced. Based on the threshold value, an algorithm was developed to determine the wax area fraction and maximum aggregated wax crystal length.
Fig. 1 shows viscosity data during the temperature ramp (crude A) for the entire gap setting using the method proposed by Marchesini et al. [12]. The sudden increase in viscosity during cooling corresponded to the crystallization temperature as defined by Marchesini et al. [12]. Under this measurement, appropriate measurement gap was determined when the results no longer change with the increase of gap setting (gap independent result). The Tcrystallization obtained from gap settings of 500 and 800 lm was at 36 °C while a slightly higher value was detected for 300 lm gap setting. The viscosity data obtained at higher gap settings of 500 and 800 lm showed very good agreement except within the Arrhenius portion; i.e. above the temperature of 36 °C. Based on the measurements conducted, the data showed that 500 lm was the minimum gap required to ensure gap independent measurements. It is worth to note that below crystallization temperature,
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1.000E5
100.0
150.0 Run 1 Run 2
125.0
10000
10000
osc. stress (Pa)
100.0
100.0 1000
G'' (Pa)
10.00
raw phase (degrees)
1000
G' (Pa)
1.000E5
75.00 100.0 50.00
10.00
10.00 25.00
1.000 1.000 0.010000
0.10000
1.0000
0 1.000 100.00
10.000
% strain
Fig. 7. Strain sweep test on gelled waxy crude oil B at 20 °C with a gap of 500 lm at 10 rad/s with waveforms shown at respective strains.
1.000E5
100.0
150.0 Run 1 Run 2
125.0
10000
osc. stress (Pa)
G' (Pa) 100.0
10.00
1.000 1.000 0.010000
100.0 1000 75.00 100.0 50.00
25.00
0.10000
1.0000
10.000
10000
G'' (Pa)
10.00
raw phase (degrees)
1000
1.000E5
10.00
0 1.000 100.00
% strain
Fig. 8. Strain sweep test on gelled waxy crude oil B at 20 °C with a gap of 800 lm at 10 rad/s with waveforms shown at respective strains.
the viscosity value under heating process was lower than that under cooling process. Above the crystallization temperature, an opposite phenomena was observed. This is probably due to the kinetics effects experienced by the crude oil samples. Unlike crude A, greater diversity in the data from the thermal cycle test conducted on crude B and C (as presented on Fig. 2) made it difficult to determine appropriate measurement gap. The diversity was observed mostly under heating. If only cooling was considered, close trends were observed on the results at 500 and 800 lm gaps for crude B indicating gap-independent result. For crude C, similar trends were observed at gaps of 300 and 500 lm. Based on these observations, suitable rheology measurement gaps for crude B and C could be assumed at 500 and 300 lm, respectively according to Marchesini et al. [12] thermal
cycle test method. These tests have been repeated more than 3 times and similar trends and patterns were observed. 3.2. Strain sweep test Fig. 3 shows the elastic and loss moduli (for crude A) during the strain sweep from 0.01% to 100% at Tmin of 25 °C with initial angular frequency of 10 Hz (62.8 rad/s) for 2 runs. The figure shows that the gelled waxy crude has a very strong consistency with the elastic and loss moduli to be more than a million at low % strain, hence indicating that the selected initial frequency is too high. The repeatability throughout the procedure was very poor and the raw phase angle at some % strain range was higher than the validity limit of 150°. Possible reasons include
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1.000E6
10000
150.0
125.0
1000 1.000E5
Run 1 Run 2
100.0
75.00
10000
G'' (Pa)
10.00
raw phase (degrees)
10000
osc. stress (Pa)
1.000E5 100.0
G' (Pa)
1.000E6
50.00
1000
1000 1.000
25.00
100.0 0.1000 0.010000
0.10000
1.0000 % strain
0 100.0 100.00
10.000
Fig. 9. Strain sweep test on gelled waxy crude oil C at 35 °C with a gap of 300 lm at 10 rad/s with waveforms shown at respective strains.
1.000E6
10000
150.0 Run 1 Run 2
125.0
1000 1.000E5
1.000E5 osc. stress (Pa)
10.00
100.0
75.00
10000
G'' (Pa)
10000
raw phase (degrees)
100.0
G' (Pa)
1.000E6
50.00
1000
1000 1.000
100.0 0.1000 0.010000
25.00
0.10000
1.0000
10.000
0 100.0 100.00
% strain
Fig. 10. Strain sweep test on gelled waxy crude oil C at 35 °C with a gap of 500 lm at 10 rad/s with waveforms shown at respective strains.
inertia effects and noise possibly due vibration from the surroundings. Further inspection of the waveforms indicated multiple peaks which could be due to the presence of large crystals. Raw data (not shown here) also showed that the prescribed % strain was not achieved which was believed to be due to the strong material consisting of large crystals within the small gap and hence less freedom to move under shearing. A smaller frequency of 10 rad/s (1.59 Hz) and a gap of 500 lm were then employed for the subsequent measurement. The waveforms were also studied as a sinusoidal wave would indicate that the sample is exhibiting viscoelastic features within the linear viscoelastic regimes which is the anticipated response for a gel prior to breakage. A non-sinusoidal response (prior to yielding) would indicate that the gap chosen is also not suitable for the material tested (less freedom to move). Fig. 4 shows the elastic and loss moduli obtained with a gap of 500 lm. Although the raw phase angle for the gap setting of
500 lm was below 150°, the waveforms still showed significant multiple peaks within the region where the sample would be anticipated to behave as a gel and obeying the Hooke’s law (i.e. stress is linear to the strain) indicating possible presence of large crystals and wall effects. Repeatability was also very low at the gap setting. Subsequent testing was then conducted at a gap of 800 lm. Fig. 5 shows the elastic and loss moduli at 800 lm gap setting for two runs. Greater repeatability was obtained with the prescribed % strain achieved throughout most of the points as detected from the raw data file (not shown here). The raw phase angle was well below 150° and the waveforms showed sinusoidal behavior. Hence, 800 lm gap setting was believed to be suitable for this sample. Figs. 6–8 show the elastic and loss moduli of waxy crude oil B obtained with gap settings of 300, 500 and 800 lm. Progressively smoother peaks on the waveforms could be seen as the gap was
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1.000E6
10000
150.0 Run 1 Run 1
125.0
1000 1.000E5
1.000E5 osc. stress (Pa)
10.00
100.0
75.00
10000
G'' (Pa)
10000
raw phase (degrees)
100.0
G' (Pa)
1.000E6
50.00
1000
1000
1.000
25.00
100.0 0.1000 0.010000
0.10000
1.0000
0 100.0 100.00
10.000
% strain
Fig. 11. Strain sweep test on gelled waxy crude oil C at 35 °C with a gap of 800 lm at 10 rad/s with waveforms shown at respective strains.
Table 2 Comparison of gap size required between thermal cycle and strain sweep test. Crude
Gap required Thermal cycle test
Strain sweep test
A B C
500 500 300
800 800 800
increased indicating reduction of the wall effects due to the wax crystals, even at 500 lm. The raw phase angle for all the gap settings were well below 150° implying that the data was free from the instrument inertia. Hence, 500 lm was sufficient for crude oil B. However, though smoother waveform was observed starting from 500 lm, even greater repeatability could be achieved at
800 lm. The repeatability at 500 lm of measured yield stress (taken at the point of deviation from Hooke’s Law) was about 15%. The strain sweep procedure was repeated for a ‘‘severe’’ waxy crude labeled as waxy crude C. Fig. 9 and Fig. 10 showed the measurement conducted at the gap setting of 300 and 500 lm. Even though the waveforms showed sinusoidal behavior prior to deviation from the Hooke’s Law at low strain, the waveform showed multiple peaks indicating possible presence of large crystals within the sample. The gaps then were not sufficient to allow the sample to move freely. Smoother waveforms can be observed prior to deviation from Hooke’s Law at 800 lm (as shown in Fig. 11). Greater repeatability was also obtained at this gap. Comparison between the thermal cycle test and the strain sweep results (as presented in Table 2) showed that all the crudes
100
(a)
100
(b)
100
(c)
100
(d)
Fig. 12. Microscopy images of crude A: (a) at 5 °C below WAT under cooling rate of 1 °C/min., (b) at 15 °C below WAT under cooling rate of 1 °C/min, (c) at 5 °C below WAT under cooling rate of 10 °C/min, (d) at 15 °C below WAT under cooling rate of 10 °C/min.
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100
100
(b)
(a)
100
100
(d)
(c)
Fig. 13. Microscopy images of crude B: (a) at 5 °C below WAT under cooling rate of 1 °C/min, (b) at 15 °C below WAT under cooling rate of 1 °C/min, (c) at 5 °C below WAT under cooling rate of 10 °C/min, (d) at 15 °C below WAT under cooling rate of 10 °C/min.
100
(a)
100
(b)
100
100
(c)
(d)
Fig. 14. Microscopy images of crude C: (a) at 5 °C below WAT under cooling rate of 1 °C/min, (b) at 15 °C below WAT under cooling rate of 1 °C/min, (c) at 5 °C below WAT under cooling rate of 10 °C/min, (d) at 15 °C below WAT under cooling rate of 10 °C/min.
require bigger gap size than that determined by the thermal cycle test. From the strain sweep measurements on the 3 crudes, it can be concluded that the strain sweep test can be used to determine the appropriate gap required especially for transient rheological measurement. Thermal cycle test proposed previously by Marchesini et al. [12] was a continuous flow measurement to determine minimum gap required for rheological measurement at temperatures covering both Newtonian (above WAT) and Non-Newtonian
(below WAT) regions. Gap determination by using strain sweep test has an advantage of minimizing disturbance to the sample structure compared to the continuous flow test. Hence, it is more suitable for a fluid exhibiting time-dependent behavior and/or having irreversible structure changes due to shear/kinetic history. Due to this, it is suggested that the strain sweep test is adopted to determine minimum gap required especially for transient rheological measurements below WAT (at gelled conditions) such as the yield stress determination via dynamic oscillatory tests.
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st_h vs. x1 fit 1
Wax crystals
200
150
100
50
0 0
50
100
150
200
250
Threshold value Fig. 15. Distribution of threshold values of wax crystals.
Table 3 Fraction, size, and number of wax crystals. Crude sample
Cooling rate (°C/min.)
Temperature taken
Wax area fraction
Max. aggregated wax crystal length (micron)
1 2 3 4
Crude A
1
5 °C < WAT 15 °C < WAT 5 °C < WAT 15 °C < WAT
4.09 19.78 9.38 46.12
39.42 74.34 42.48 152.63
5 6 7 8
Crude B
5 °C < WAT 15 °C < WAT 5 °C < WAT 13 °C < WAT
1.6 6.63 1.71 27.48
29.77 38.81 30.04 114.54
9 10 11 12
Crude C
5 °C < WAT 25 °C < WAT 5 °C < WAT 25 °C < WAT
0.99 1.03 0.11 1.04
21.96 33.82 18.47 30.81
No
10 1 10 1 10
3.3. CPM images Fig. 12 showed the images of crude A as captured using a CPM of the wax-oil samples cooled down to the same final temperature at two different cooling rates of 1 °C/min and 10 °C/min and captured at 5 °C and 15 °C below WAT (from Cross Polar Microscopy), respectively. The individual wax crystals formed at the lower cooling rate of 1 °C/min (same as that utilized in the rheological measurements) were observed to be larger up to 50 lm compared to those formed at the higher cooling rate. The morphologies of the wax crystals were mainly rod or needle-like with presence of spherical crystals in between. Hence the images indirectly confirmed that the waxy crude contains mainly macro-crystalline with some micro-crystalline waxes. The amount of wax crystals at the higher cooling rate was also greater compared to that formed at 1 °C/min implying that as the cooling rate increased, crystals size reduced and the number density increased. Higher number density was also observed with reduction in temperature. Based on the gap requirement of 800 lm as obtained from the strain sweep test, it was confirmed that the ten-to-one ratio was not applicable for crude A sample which contained wax crystals up to approximately 50 lm. Fig. 13 showed CPM images of crude B when it was cooled down to the same final temperature at two different cooling rates of 1 °C/ min and 10 °C/min and captured at 5 °C and 15 °C below WAT, respectively. Similar to crude oil A, the individual wax crystals formed at the lower cooling rate of 1 °C/min were observed to be larger up to approximately 30 lm compared to those formed at the higher cooling rate with lesser number density. Similar wax crystal morphology in crude A was also observed in crude B. The
smaller crystal sizes as compared to that of crude A indicated that appropriate measurement gap required may also be smaller. According to ten-to-one ratio, the minimum gap required should be 300 lm. The strain sweep test however, confirmed that the ten-to-one ratio was not applicable and that the gap required was in fact similar to crude A. Unlike crude A and B, CPM images for crude C (as presented in Fig. 14) showed less wax crystals with crystal size as small as 1 lm or less. However, similar trend of wax crystal formation as crude A and B was observed. With the ten-to-one ratio, the gap required should be 10 lm which was much smaller than that obtained from the strain sweep test. The CPM images from these waxy crude oils also showed that crude A and B exhibit rapid wax precipitation process compare to crude C. Comparing the CPM observation with rheological results from the thermal cycle test, it can be concluded that the viscosity increased below WAT upon cooling correlate to the wax precipitation process and that the degree of viscosity increase would depend on the wax precipitation rate. This explains the phenomena observed under the thermal cycle tests where crude A and B exhibited sharp viscosity increase below WAT while crude C exhibited slow viscosity increase upon cooling. 3.4. 2D image processing 2D-image processing for the CPM images from the three waxy crude oils were conducted mainly to estimate the maximum crystal aggregation diameter. 34 wax crystals sample representing low to high threshold values (taken from the CPM images) were first collected to map the distribution of threshold values and was fitted by using general power law model as shown in Fig. 15, Threshold value
f ðxÞ ¼ 225:1x0:9187
ð2Þ
From the graph, it can be deduced that the threshold value for wax crystal is 15. The value was then use in the algorithm to determine the wax area fraction at the final temperature and maximum aggregated wax crystal length. The results are shown in Table 3. Images for crude C captured at lower temperatures (25 °C below WAT) were utilized instead due to the lower number density obtained at 15 °C below WAT. The image processing results showed that crudes A, B, and C have similar trends. The wax area fraction and maximum aggregated wax crystal length were larger as the temperature decreased (indicating formation of stronger network) and as the cooling rate increased. The maximum aggregated crystal length was found to be as big as 152.63 lm (crude A). Since the calculation of wax length during image processing considered aggregated wax as a single wax, the maximum wax length mentioned above is believed to be the maximum diameter of clustered wax within the network in the respective sample. The maximum size was then utilized to assess and compare against the gap determined from the rheological methods. 3.5. Theoretical gap [2,3] required for rheological measurement of fluid with suspended particles Similar gap analysis performed by Barnes [3] for the worst case of hard wax with wax porosity of 50% was also conducted, assuming that the wax crystals could be treated as suspended particles. A ratio of the apparent to real viscosity of a suspension as a function of the radius of suspended particles, a, geometry gap, H, phase volume, /, and a constant n was given as [3]
ga ¼ g
1 2 1 1 þ ð2an=HÞ 1 //m
ð3Þ
A. Japper-Jaafar et al. / Journal of Non-Newtonian Fluid Mechanics 218 (2015) 71–82
condition, the wax crystals could not be treated as suspended particle. If aggregated wax crystal size (from 2D-image processing) was used for gap size determination rather than single wax crystal, the ten-to-one gap estimation is good for crude A. However, the estimations were poor for crude B and C. Summary of gap size required from different methods are presented in Table 4.
Gap/particle diameter, H/2a
103
102
4. Conclusions
101
100
0
0.1
0.2
0.3
0.4
0.5
Phase volume, φ Fig. 16. Predicted minimum gap to particle diameter ratio as a function of phase volume.
Table 4 Summary of gap size required under different methods. Crude
A B C
Gap size required (lm) Thermal cycle test
Strain sweep test
10:1 rule (CPM, estimated size)a
10:1 rule (CPM, image processing)b
500 500 300
800 800 800
500 300 100
800 400 400
a The gap is 10 times maximum single wax crystal size estimated from CPM image. b The gap is 10 times maximum aggregated wax crystal determined from an image processing technique.
By limiting the viscosity measurement error to 5%, i.e. the difference between the measured viscosity to the ‘‘real’’ viscosity was within 0.05, taking the n value to be 0.25 which was typical for concentrated suspension as recommended by Yilmazer and Kalyon [21], a maximum phase volume of 0.5 (/m), the predicted minimum gap-to-particle diameter ratio can be obtained via
H ¼ 4:75 2a
81
" # 2 / 1 1 0:5
ð4Þ
and shown graphically in Fig. 16. The figure indicated that if the wax was soft and had an oil porosity of 90%, the ten-to-one ratio as suggested previously by Barnes [2] is valid. However, samples with oil porosity lesser than 80% may require larger gap for the rheology measurement. The minimum gap required for ‘‘harder’’ wax also increased almost exponentially as predicted by Eq. (4). For the case of waxy crude samples under study, the wax phase volumes were all below 0.2 under the cooling rate of 1 °C/min. Hence, the ten-to-one rule [2] should be applicable if we consider single wax and neglected wax aggregation. However, rheological measurement results (from both thermal cycle and strain sweep tests) showed that the gap size required was larger than the gap size determined from the ten-to-one rule. The findings indicated that wax crystallization and gelation is a complex and random process which lead to random wax crystals interaction and aggregation. The results also showed strong indication that, in gel
The reliability of the yield strength measurements via oscillatory tests of gelled waxy crude oil has been proven to be highly dependent on the gap selection in the rheometer. Presence of large crystals encompassing the trapped oil forming a gel network could interfere with the rheology measurements. The ten-to-one ratio is not applicable for gelled waxy crude oils even with wax porosity greater than 80% and hence, care should be taken in deciding the suitable gap. Smaller gap measurements of gelled waxy crude oil are subjected to the wall effects which also subsequently reduce the measurement repeatability. The thermal cycle test as proposed by Marchesini et al. [12] could be a good start in deciding the gap parameter. Nevertheless a detailed analysis using a strain sweep test is a better option for greater accuracy while maintaining repeatability to be within 10% without the need to determine the crystals size under a microscope. It is also important to note that the gap selection is crude specific and highly dependent on the shear and cooling conditions as reported in the literature [19] and confirmed in this study. Under medium shear for instance, the wax crystals formed may be smaller than that formed under no shear condition. Even greater imposed shear may induce crystals aggregations changing the effective size of the wax crystals. Aggregates of wax crystals sizes as large as 74 lm at a cooling rate of 1 °C/min. (standard measurement cooling rate) has been observed in this study which would then require a minimum gap greater than that provided by the cone and plate system. However, very large gap within the parallel plate system also has limitations such as lack of temperature control and reduce surface adhesion by samples of low surface tension. Hence, a minimum gap can be selected through the proposed strain sweep procedure such that these limitations are not violated. Using a suitable gap setting ensures achieved prescribed strain, minimized instrument inertia effect where the ratio between raw phase and delta angles (i.e. the inertia correction) is maintained below 10, good measurement repeatability with gap-independent results and well respond from the sample to the applied load as seen from the sinusoidal waveforms. This study also confirms that the wax crystal size and aggregations are not the only indicator to be considered in determining the gap required especially when the testing protocol involves dynamic oscillatory shear measurements on gelled waxy crude oil. The strong interlocking and interactions between the wax crystals forming the gelled network complicate the gap analysis based on crystal size alone.
Acknowledgements The authors would like to thank PETRONAS Carigali Sdn Bhd (PCSB) for providing samples and the continuous information input extended throughout the project. Also to PETRONAS Research Sdn Bhd (PRSB) for letting us to use the Cross Polar Microscopy. We also wish to extend our gratitude to our technician, Mr. Hazri Shahpin and the personnel from PCSB and PRSB for their technical assistance. Last but not least, the Universiti Teknologi PETRONAS for providing the platform for the research to be conducted.
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Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.jnnfm.2015.02. 001. References [1] C. Bai, J. Zhang, Effect of carbon number distribution of wax on the yield stress of waxy oil gels, Ind. Eng. Chem. Res. 52 (2013) 2732–2739. [2] H.A. Barnes, A review of the slip (wall depletion) of polymer solutions, emulsions and particle suspensions in viscoemeters: its cause, character and cure, J. Nonnewton. Fluid Mech. 56 (1995) 221–251. [3] H.A. Barnes, Measuring the viscosity of large-particle (and flocculated) suspensions — a note on the necessary gap size of rotational viscometers, J. Nonnewton. Fluid Mech. 94 (2000) 213–217. [4] M. Bolourchifard, An Experimental Study of the In Situ Gelation of a Polyacrylamide-Chromium Acetate System in a Polymer-Treated Porous Medium (MSc Thesis), University of Kansas, 2006. [5] K.K. Botne, Modelling wax thickness in single phase turbulent flow (MSc Thesis), NTNU, 2012. [6] C. Chang, D.V. Boger, Q.D. Nguyen, The yielding of waxy crude oils, Ind. Eng. Chem. Res. 37 (1998) 1551–1559. [7] C. Chang, D.V. Boger, Q.D. Nguyen, Influence of thermal history on the waxy structure of statically cooled waxy crude oil, SPE J. 5 (2000) 148–157. [8] P.J. Flory, Principles of Polymer Chemistry, Cornell University Press, Ithaca, NY, 1953. pp. 347–398. [9] I. Henaut, O. Vincke, F. Brucy, Waxy crude oil restart: mechanical properties of gelled oils, in: Paper SPE 56771 presented at the SPE Annual Technical Conference and Exhibition Houston, 3–6 October, 1999.
[10] B. Jia, J. Zhang, Yield behaviour of waxy crude gel: effect of isothermal structure development before prior applied stress, Ind. Eng. Chem. Res. 51 (2012) 10977–10982. [11] M. Kane´, M. Djabourov, J. Volle, J. Lechairec, G. Frebourg, Morphology of paraffin crystals in waxy crude oils cooled in quiescent conditions and under flow, J. Fuel 82 (2003) 127–135. [12] F.H. Marchesini, A.A. Alicke, P.R.D.S. Mendes, C.M. Ziglio, Rheological characterization of waxy crude oils: sample preparation, Energy Fuels 26 (2012) 2566–2577. [13] S. Misra, S. Barauah, K. Singh, Paraffin problems in crude oil production and transportation: a review, SPE 28181, 1995. [14] F.W. Padgett, D.G. Hefley, A. Henriksen, Wax crystallization – a preliminary report, J. Ind. Eng. Chem. 18 (1926) 832–835. [15] H.P. Ronningsen, Rheological behavior of gelled, waxy North Sea crude oils, J. Petrol. Sci. Eng. 7 (1992) 177–213. [16] R.J. Russell, E.D. Chapman, The pumping of 85 °F Pour point Assam (Nahorkatia) crude oil at 65 °F, J. Inst. Petrol. 57 (1971) 117–128. [17] P. Singh, R. Venkatesan, H.S. Fogler, N. Nagarajan, Formation and aging of incipient thin film wax-oil gels, J. Am. Inst. Chem. Eng. 46 (2000) 1059–1074. [18] S.P. Srivastava, J. Handoo, K.M. Agrawal, G.C. Joshi, Phase-transition studies in n-alkanes and petroleum-related waxes – a review, J. Phys. Chem. Solids 54 (1993) 639–670. [19] R. Venkatesan, N.R. Nagarajan, K. Paso, T.B. Yi, A.M. Sastry, H.S. Fogler, The strength of paraffin gels formed under static and flow conditions, Chem. Eng. Sci. 60 (2005) 3587–3598. [20] L.T. Wardhaugh, D.V. Boger, Measurement of the unique flow properties of waxy crude oil, Chem. Eng. Res. Des. 65 (1987) 74–83. [21] U. Yilmazer, D.M. Kalyon, Slip effects in capillary and parallel disk torsional flows of highly filled suspensions, J. Rheol. 33 (1989) 1197. [22] A.S. Yoshimura, R.K. Prud’homme, Wall slip on dynamic oscillatory measurements, J. Rheol. 32 (6) (1988) 575–584.
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Journal of Non-Newtonian Fluid Mechanics journal homepage: http://www.elsevier.com/locate/jnnfm
Yield stress measurement of gelled waxy crude oil: Gap size requirement A. Japper-Jaafar a,⇑, P.T. Bhaskoro a, L.L. Sean b, M.Z. Sariman c, H. Nugroho d a
Mechanical Engineering Department, Universiti Teknologi PETRONAS, 32610, Bandar Seri Iskandar, Perak Darul Ridzuan, Malaysia PETRONAS Research Sdn Bhd, Kajang, Selangor, Malaysia c PETRONAS Carigali Sdn Bhd, Kuala Lumpur, Malaysia d Electrical Engineering Department, Universiti Teknologi PETRONAS, 32610, Bandar Seri Iskandar, Perak Darul Ridzuan, Malaysia b
a r t i c l e
i n f o
Article history: Received 21 August 2014 Received in revised form 24 December 2014 Accepted 2 February 2015 Available online 17 February 2015 Keywords: Rheometer Measurement gap Yield stress Waxy crude oil
a b s t r a c t The strength of gelled waxy crude oil is an important parameter required to determine the restart pressure of pipelines filled with the gelled waxy crude oil. Several measurement methods have been proposed in the literature to quantify the yield strength utilizing a rheometer. Minimal discussions, are however, provided on the effects of rheometer geometry gap on the yield stress measurements. This study is intended to propose a systematic protocol to determine the geometry gap settings for better repeatability of the yield stress measurements of gelled waxy crude oils. The reliability of the yield stress data measured has been shown to be highly dependent on the gap selection in the rheometer. The ten-to-one gap ratio has been proven to be inapplicable for the case of gelled waxy crude oils which consists of wax crystal networks entrapping the oil phase. Presence and strong interactions of large wax crystals presents wall effects and subsequently reduces the repeatability of the measurements. The method proposed in this study has been proven to work on a mild waxy crude oil as well as on a more ‘‘severe’’ waxy crude oil. It can be utilized prior to any transient rheological measurements as gap setting is crucial to ensure accurate and reliable measurements. Ó 2015 Elsevier B.V. All rights reserved.
1. Introduction Waxy crude oils are aliphatic hydrocarbon having high molecular weight paraffin with carbon number ranging from C18 to C65 [18]. The paraffin waxes can be classified as either macrocrystalline or micro-crystalline. Macro-crystalline waxes are mainly linear paraffin (n-alkanes) with chain lengths between C18–C30. They have needle-like and plate-like morphology with crystal size up to 100 lm. Their presence within the crude oil promotes strong gel formation. Micro-crystalline waxes on the other hand contain greater percentage of iso-paraffin (branched alkanes) and naphtenes (cyclic alkanes) with carbon number found to be greater than 30. The crystal size is much smaller (up to 10 lm) with spherical morphology. It is amorphous in nature as the crystal growth is hindered by the side and cyclic groups present in the molecules. Misra et al. [13] reported that if the micro-crystalline waxes are present, it will be the main constituent of the sludge at the bottom of crude oil storage tanks. The solubility of paraffin waxes is dependent on the temperature, it decreases with decreasing temperature. At reservoir ⇑ Corresponding author. Tel.: +60 5 368 7022; fax: +60 5 365 6461. E-mail address: [email protected] (A. Japper-Jaafar). http://dx.doi.org/10.1016/j.jnnfm.2015.02.001 0377-0257/Ó 2015 Elsevier B.V. All rights reserved.
conditions where the temperature ranges between 70 and 150 °C with pressure ranges between 50 and 100 MPa, the solubility of the paraffin in the crude oil is adequately high. The wax molecules are fully dissolved in the crude oil mixture resulting in a singlephase crude oil and in the absence of other components and contaminants the crude oil behaves predominantly Newtonian with low viscosity. Once the crude oil leaves the reservoir and flows through cold pipelines placed on the seabed with temperature as low as 5 °C, the crude oil temperature begins to drop dramatically due to the heat loss to the surroundings. The crude oil will then be subjected to phase transformation from liquid state, showing Newtonian behavior, to a gel-like structure exhibiting non-Newtonian characteristics. The three main stages of the phase transformation process are wax precipitation, wax deposition and wax gelation. Wax gelation will be induced when the temperature of the crude oil drops below the pour point temperature of the crude beyond which, the crude oil flow ceases completely. Wax gelation is not a new phenomenon in the petroleum industry and this issue has already captured the interest as early as in the 1920s [14]. Various classical descriptions of gel have been documented in the literature. Flory [8] regards a gel as a homogeneous system within which the liquid is not distinguishable from the solids suspended in the liquid. The liquid tend to disappear
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and the solid mass is formed, which may display either a fluid-dominant characteristics or a more solid-dominant structure. A gel also exhibits greater elastic to viscous properties [4]. Kane´ et al. [11] and Singh et al. [17] proposed that the gelation of waxy crude oil involves three stages; formation of lamellar subcrystals which grows in two dimensions as sheet like crystals, aggregation of sub-crystals to form a large space filling network and finally overlapping and interlocking of the aggregation due to strong interactions and attractions between wax crystals. Subsequently, a 3-D volume spanning network of crystals that traps liquid oils and exhibits both the elastic properties and the viscous properties is formed. The amount of trapped oil, or ‘‘wax porosity’’ within the wax crystals network would influence the strength of the waxy crude gels. For ‘‘soft’’ wax a porosity of up to 90% has been reported while for ‘‘hard’’ wax, the porosity is within the range of 50–70%. Ageing, internal diffusion and large temperature differential within the pipeline, amongst others, could result in ‘‘harder’’ wax and subsequently higher gel strength [5]. The wax gelation has great impact especially during production shutdowns where the crude oil temperature drops below the pour point temperature allowing the formation of a ‘‘candle’’-like structure or solid wax column. This phenomenon can completely block the pipeline and during restart operation, a large pressure may then be required to initiate the crude oil flow again. In order to determine the breakdown pressure required to restart the flow, it is important to estimate the gel strength, measured in terms of the yield stress. The yield strength of waxy crude oil gel has been characterized by many within the literature [1,6,7,16,15,9,19,10], amongst others. As documented, the yield stress can be measured via various experimental protocols; the creep-recovery test, the oscillatory test, the stress ramp test and many more. Several geometries can be utilized to determine the yield stress of gelled crude oil; the cone and plate, the parallel plate and the vane geometry, with the surface of these geometries is maintained smooth, sandblasted or cross hatched. Throughout the study on the yield stress of waxy crude oil documented within the literature, least discussions have been extended on the effects of the geometry gap to the measurements. The rheometer gap size is critical to minimize wall effects and at the same time allowing freedom for the sample to move under shearing action and subsequently behave as a continuum. As highlighted by Marchesini et al. [12], equilibrium flow properties of gelled waxy oils are less influenced by experimental conditions. However, transient measurements including oscillatory measurements are highly dependent on the gap selection in the rheometer which is supported by the work of Wardhaugh and Boger [20]. Barnes [2] proposed a rule of thumb to decide for a geometry gap where a minimum ratio of gap to particle size of 10:1 is recommended. For large particle systems, the requirement is often impossible to be met in small angle cone and plate geometry as it is limited by the truncation height or the gap of the cone and plate. Later in 2000, Barnes discovered that the ‘‘ten-to-one’’ ratio is only applicable for samples with phase volume of up to 25%. Greater gap size is then required in higher phase volume samples, which, may, at times, be unrealistic for a medium containing large particles such as waxy crude oil gel. Cautious treatment of data collected is then required especially on melts and gels obtained using the cone and plate rheometer. The presence of the wax crystals whose characteristic dimension is of the same order of magnitude of the gap within the cone and plate may then introduce measurement errors. The works presented in this paper are intended to propose a systematic assessment on gap determination (for 3 waxy crude oils) and to compare between the thermal cycle tests by Marchesini et al. [12] and the proposed strain sweep test method. Morphology of wax crystal was also investigated for further
understanding on its effects to the rheological behavior. An image processing technique was performed to quantitatively determine wax fraction and maximum aggregated wax crystal length. The values were utilized to theoretically estimate gap size required from Barnes [2,3] and compared with the results from the thermal cycle test and the proposed strain sweep test methods. 2. Characterizations and measurements 2.1. Working fluid and pre-conditioning process The crude oils utilized throughout the study are waxy crude oils produced within the South East Asia. The WAT, as measured using CPM, pour point temperature (ASTM 5985-96) and API gravity (ASTM D1250) of the waxy crude oils are tabulated in Table 1. Conditioning of the crude oil upon received from the operator involves heating at 20 °C above the WAT for 8 h within a large water bath. The crude oil was then poured into smaller containers (20 mL) to ensure minimal sample variations due to light and heavy components, and allowed to cool at room temperature. As thermal history or heat treatment to which the crude oil samples are subjected to influences the flow behavior of the sample, it is important to standardize the pre-conditioning treatment to ensure repeatability of the yield stress measurements. Prior to measurements the crude oil in the smaller container was soaked again in a water bath at 20 °C above the WAT for 2 h to dissolve any wax crystals present ensuring homogeneity and promote a stable composition during testing. 2.2. Equipments A TA instrument controlled stress rheometer, AR-G2, was utilized for all rheological measurements. The geometry (parallel plate) is either a 20 mm or a 40 mm (depending on the strength of the gel) cross hatched plate with the groove to be greater than 10 lm [2] to minimize wall slip phenomena where complete adhesion is violated. A cross hatched surface is suitable as it possesses sufficient rugosity greater than the crystal size aggregates assuming that the crude oil samples contains mainly of macro-crystalline waxes. Assumptions that no flow occurs between the protrusions and shear occurs between the surfaces consisting of the protruding tips were made. It is the same assumption for vane rheometry measurement. Visual observations were performed to verify any presence of slip on smooth surface geometries. When both smooth upper and lower geometries were utilized, the smooth upper surface was practically clean after what is thought to be an apparent yielding of the sample while the sample remained intact on the smooth lower surface. However, yielded sample using the roughened upper surface showed that the gelled crude failed within the sample indicating no slip on the upper roughened surface as well as on the smooth lower surface. Hence, the authors believed that an upper roughened surface is sufficient to minimize the slip effect. The waveforms produced at the same % strain for different gap settings have also been analyzed. The similar waveforms produced at different gaps settings confirmed minimal slip effects as proposed by Yoshimura and Prud’homme [22]. A solvent trap was used to minimize evaporation of the light end components from the sample for all the rheological measurements and subsequently the stability Table 1 Properties of waxy crude oil sample. Properties
Crude A (Se)
Crude B (An)
Crude C (Pe)
WAT (°C) Pour point API gravity (at 15 °C)
41.2 39 33.76
41.1 33 36.86
68.2 60 25.15
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10.00 Cooling Heating Cooling Heating Cooling Heating
viscosity (Pa.s)
1.000
Down Using Gap 300 m icron Up Using Gap 300 m icron Down Using Gap 500 m icron Up Using Gap 500 m icron Down Using Gap 800 m icron Up Using Gap 800 m icron
0.1000
0.01000
1.000E-3 20.0
22.5
25.0
27.5
30.0
32.5
35.0
37.5
40.0
42.5
45.0
temperature (°C) Fig. 1. Thermal cycle test of crude A with gap sizes of 300, 500 and 800 lm.
10.00
(a)
viscosity (Pa.s)
1.000
0.1000
Gap 300 - cooling Gap 300 - heating Gap 500 - cooling Gap 500 - heating Gap 800 - cooling Gap 800 - heating
0.01000
1.000E-3 17.5
20.0
22.5
25.0
27.5
30.0
32.5
35.0
37.5
40.0
42.5
temperature (°C)
viscosity (Pa.s)
100.0
Gap 300 - cooling Gap 300 - heating Gap 500 - cooling Gap 500 - heating Gap 800 - cooling Gap 800 - heating
10.00
(b)
1.000
0.1000 35.0
40.0
45.0
50.0
55.0
60.0
65.0
70.0
temperature (°C) Fig. 2. Thermal cycle test at various gap, (a) crude B and (b) crude C.
of the sample composition was assumed to be maintained. All the sample measurements conducted in this study were repeated at least 3 times to confirm repeatability although only 1 or 2 representative data runs were presented.
A cross polar microscopy (Olympus BX 51) equipped with a video camera and recorder is also utilized to observe wax crystallization process as the sample is cooled down to Tmin. A small amount of sample was first heated up to 10 °C above the WAT
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1.000E8
10000
1.000E7
200.0
1.000E8
175.0
1.000E7
150.0
1.000E6
125.0
1.000E5
100.0
10000
75.00
1000
50.00
100.0
25.00
10.00
1000
10000 1000
10.00
osc. stress (Pa)
100.0
Run1 Run2
100.0
G'' (Pa)
G' (Pa)
1.000E5
raw phase (degrees)
1.000E6
1.000 10.00 1.000 0.1000 0.010000
0.10000
1.0000
0 1.000 100.00
10.000
% strain
Fig. 3. Strain sweep test on gelled waxy crude oil A at 25 °C with a gap of 300 lm at 10 Hz with waveforms shown at respective strains.
1.000E5
100.0
10000
1.000
10.00
osc. stress (Pa)
100.0
0.1000 1.000 Run 1 Run 2 0.1000 0.01000 0.010000
0.10000
1.0000
10.000
1.000E5
150.0
10000
125.0 1000 100.0 100.0 75.00
G'' (Pa)
G' (Pa)
1000
raw phase (degrees)
10.00
175.0
10.00 50.00 25.00
1.000
0 0.1000 100.00
% strain
Fig. 4. Strain sweep test on gelled waxy crude oil A at 25 °C with a gap of 500 lm at 10 rad/s with waveforms shown at respective strains.
for 30 min on a small glass crucible. It is to ensure that the wax crystals melt completely prior to cooling. The measurement was conducted from a specified high temperature (above WAT) to a low temperature (below WAT), Tmin. Two various cooling rates were utilized during the measurement: 1 °C/min and 10 °C/min. A lens with 10 magnification was used for all observations.
1 °C/min down to the Tmin (a temperature at which the sample has gelled) at 10 s1. A strain sweep test was performed after the sample was left to rest for another 2 min after gelling from 0.01% to 100% strain at Tmin. Suitable gap required was assessed by considering several aspects: raw phase angle, stress strain waveform, repeatability and achievable strain.
2.3. Procedures 2.3.1. Strain sweep test In this work, a strain sweep test for gap study was proposed. After pre-conditioning the sample was loaded onto the peltier plate, set to a temperature above the WAT to minimize any ‘‘thermal shock’’. Upon loading, the head was lowered gradually to avoid compression overload. An initial gap setting of 300 lm was utilized. As the waxy crude oil system was known to be thixotropic, steps have also been taken to ‘‘standardize’’ the shear history prior to any testing procedure. The sample was pre-sheared at 10 s1 at a temperature higher than WAT, for 3 min and subsequently left for 2 min to rest. To gel the sample, a temperature ramp was applied at
2.3.2. Thermal cycle test A thermal cycle test, as recommended by Marchesini et al. [12], was also performed on the crude samples as comparison and to confirm the selection of gap. The thermal cycle test (under shear rate of 10 s1) started with a cooling of the crude oil at 1 °C/min down to the Tmin (20 °C below PPT) from a starting temperature Ts (5 °C above TWAT). Once the Tmin was achieved, the sample was then subjected to a temperature ramp back to the initial temperature at the same rate. The viscosity was then plotted as a function of temperature. The procedures were repeated with progressively increasing gaps (300, 500, and 800 lm) until the viscosity data was no longer changing with the gap setting indicat-
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1.000E5
100.0
150.0
1.000E5
125.0
1.000
osc. stress (Pa)
1000
Run1 Run2
10000 100.0 75.00
G'' (Pa)
G' (Pa)
10.00
raw phase (degrees)
10000
1000
50.00 100.0
100.0 25.00 0.1000 10.00 0.010000
0.10000
1.0000
0 10.00 100.00
10.000
% strain
Fig. 5. Strain sweep test on gelled waxy crude oil A at 25 °C with a gap of 800 lm at 10 rad/s with waveforms shown at respective strains.
1.000E5
100.0
150.0
1.000E5
Run 1 Run 2
125.0
10000
osc. stress (Pa)
G' (Pa) 100.0
100.0 1000 75.00
G'' (Pa)
10.00
raw phase (degrees)
1000
10000
100.0 50.00 10.00
10.00
25.00
1.000 1.000 0.010000
0.10000
1.0000
10.000
1.000 0 100.00
% strain
Fig. 6. Strain sweep test on gelled waxy crude oil B at 20 °C with a gap of 300 lm at 10 rad/s with waveforms shown at respective strains.
ing gap-independent data. The gap at which gap-independent result was achieved was regarded as minimum gap required.
3. Results and discussions 3.1. Thermal cycle test
2.4. Image processing for wax crystal size determination and distribution Wax crystal size and the distribution were determined by performing a 2D image processing on the image collected from cross polar microscope (CPM) via Matlab software using a threshold technique. 34 wax samples representing low to high threshold values were first taken from the image and plotted to map the distribution of threshold values. General power law model given below was utilized to fit the sample data.
f ðxÞ ¼ axb
ð1Þ 2
In this work, the fitting was accepted if the R -value was equal to or above 0.8 and the threshold value can then be deduced. Based on the threshold value, an algorithm was developed to determine the wax area fraction and maximum aggregated wax crystal length.
Fig. 1 shows viscosity data during the temperature ramp (crude A) for the entire gap setting using the method proposed by Marchesini et al. [12]. The sudden increase in viscosity during cooling corresponded to the crystallization temperature as defined by Marchesini et al. [12]. Under this measurement, appropriate measurement gap was determined when the results no longer change with the increase of gap setting (gap independent result). The Tcrystallization obtained from gap settings of 500 and 800 lm was at 36 °C while a slightly higher value was detected for 300 lm gap setting. The viscosity data obtained at higher gap settings of 500 and 800 lm showed very good agreement except within the Arrhenius portion; i.e. above the temperature of 36 °C. Based on the measurements conducted, the data showed that 500 lm was the minimum gap required to ensure gap independent measurements. It is worth to note that below crystallization temperature,
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1.000E5
100.0
150.0 Run 1 Run 2
125.0
10000
10000
osc. stress (Pa)
100.0
100.0 1000
G'' (Pa)
10.00
raw phase (degrees)
1000
G' (Pa)
1.000E5
75.00 100.0 50.00
10.00
10.00 25.00
1.000 1.000 0.010000
0.10000
1.0000
0 1.000 100.00
10.000
% strain
Fig. 7. Strain sweep test on gelled waxy crude oil B at 20 °C with a gap of 500 lm at 10 rad/s with waveforms shown at respective strains.
1.000E5
100.0
150.0 Run 1 Run 2
125.0
10000
osc. stress (Pa)
G' (Pa) 100.0
10.00
1.000 1.000 0.010000
100.0 1000 75.00 100.0 50.00
25.00
0.10000
1.0000
10.000
10000
G'' (Pa)
10.00
raw phase (degrees)
1000
1.000E5
10.00
0 1.000 100.00
% strain
Fig. 8. Strain sweep test on gelled waxy crude oil B at 20 °C with a gap of 800 lm at 10 rad/s with waveforms shown at respective strains.
the viscosity value under heating process was lower than that under cooling process. Above the crystallization temperature, an opposite phenomena was observed. This is probably due to the kinetics effects experienced by the crude oil samples. Unlike crude A, greater diversity in the data from the thermal cycle test conducted on crude B and C (as presented on Fig. 2) made it difficult to determine appropriate measurement gap. The diversity was observed mostly under heating. If only cooling was considered, close trends were observed on the results at 500 and 800 lm gaps for crude B indicating gap-independent result. For crude C, similar trends were observed at gaps of 300 and 500 lm. Based on these observations, suitable rheology measurement gaps for crude B and C could be assumed at 500 and 300 lm, respectively according to Marchesini et al. [12] thermal
cycle test method. These tests have been repeated more than 3 times and similar trends and patterns were observed. 3.2. Strain sweep test Fig. 3 shows the elastic and loss moduli (for crude A) during the strain sweep from 0.01% to 100% at Tmin of 25 °C with initial angular frequency of 10 Hz (62.8 rad/s) for 2 runs. The figure shows that the gelled waxy crude has a very strong consistency with the elastic and loss moduli to be more than a million at low % strain, hence indicating that the selected initial frequency is too high. The repeatability throughout the procedure was very poor and the raw phase angle at some % strain range was higher than the validity limit of 150°. Possible reasons include
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1.000E6
10000
150.0
125.0
1000 1.000E5
Run 1 Run 2
100.0
75.00
10000
G'' (Pa)
10.00
raw phase (degrees)
10000
osc. stress (Pa)
1.000E5 100.0
G' (Pa)
1.000E6
50.00
1000
1000 1.000
25.00
100.0 0.1000 0.010000
0.10000
1.0000 % strain
0 100.0 100.00
10.000
Fig. 9. Strain sweep test on gelled waxy crude oil C at 35 °C with a gap of 300 lm at 10 rad/s with waveforms shown at respective strains.
1.000E6
10000
150.0 Run 1 Run 2
125.0
1000 1.000E5
1.000E5 osc. stress (Pa)
10.00
100.0
75.00
10000
G'' (Pa)
10000
raw phase (degrees)
100.0
G' (Pa)
1.000E6
50.00
1000
1000 1.000
100.0 0.1000 0.010000
25.00
0.10000
1.0000
10.000
0 100.0 100.00
% strain
Fig. 10. Strain sweep test on gelled waxy crude oil C at 35 °C with a gap of 500 lm at 10 rad/s with waveforms shown at respective strains.
inertia effects and noise possibly due vibration from the surroundings. Further inspection of the waveforms indicated multiple peaks which could be due to the presence of large crystals. Raw data (not shown here) also showed that the prescribed % strain was not achieved which was believed to be due to the strong material consisting of large crystals within the small gap and hence less freedom to move under shearing. A smaller frequency of 10 rad/s (1.59 Hz) and a gap of 500 lm were then employed for the subsequent measurement. The waveforms were also studied as a sinusoidal wave would indicate that the sample is exhibiting viscoelastic features within the linear viscoelastic regimes which is the anticipated response for a gel prior to breakage. A non-sinusoidal response (prior to yielding) would indicate that the gap chosen is also not suitable for the material tested (less freedom to move). Fig. 4 shows the elastic and loss moduli obtained with a gap of 500 lm. Although the raw phase angle for the gap setting of
500 lm was below 150°, the waveforms still showed significant multiple peaks within the region where the sample would be anticipated to behave as a gel and obeying the Hooke’s law (i.e. stress is linear to the strain) indicating possible presence of large crystals and wall effects. Repeatability was also very low at the gap setting. Subsequent testing was then conducted at a gap of 800 lm. Fig. 5 shows the elastic and loss moduli at 800 lm gap setting for two runs. Greater repeatability was obtained with the prescribed % strain achieved throughout most of the points as detected from the raw data file (not shown here). The raw phase angle was well below 150° and the waveforms showed sinusoidal behavior. Hence, 800 lm gap setting was believed to be suitable for this sample. Figs. 6–8 show the elastic and loss moduli of waxy crude oil B obtained with gap settings of 300, 500 and 800 lm. Progressively smoother peaks on the waveforms could be seen as the gap was
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1.000E6
10000
150.0 Run 1 Run 1
125.0
1000 1.000E5
1.000E5 osc. stress (Pa)
10.00
100.0
75.00
10000
G'' (Pa)
10000
raw phase (degrees)
100.0
G' (Pa)
1.000E6
50.00
1000
1000
1.000
25.00
100.0 0.1000 0.010000
0.10000
1.0000
0 100.0 100.00
10.000
% strain
Fig. 11. Strain sweep test on gelled waxy crude oil C at 35 °C with a gap of 800 lm at 10 rad/s with waveforms shown at respective strains.
Table 2 Comparison of gap size required between thermal cycle and strain sweep test. Crude
Gap required Thermal cycle test
Strain sweep test
A B C
500 500 300
800 800 800
increased indicating reduction of the wall effects due to the wax crystals, even at 500 lm. The raw phase angle for all the gap settings were well below 150° implying that the data was free from the instrument inertia. Hence, 500 lm was sufficient for crude oil B. However, though smoother waveform was observed starting from 500 lm, even greater repeatability could be achieved at
800 lm. The repeatability at 500 lm of measured yield stress (taken at the point of deviation from Hooke’s Law) was about 15%. The strain sweep procedure was repeated for a ‘‘severe’’ waxy crude labeled as waxy crude C. Fig. 9 and Fig. 10 showed the measurement conducted at the gap setting of 300 and 500 lm. Even though the waveforms showed sinusoidal behavior prior to deviation from the Hooke’s Law at low strain, the waveform showed multiple peaks indicating possible presence of large crystals within the sample. The gaps then were not sufficient to allow the sample to move freely. Smoother waveforms can be observed prior to deviation from Hooke’s Law at 800 lm (as shown in Fig. 11). Greater repeatability was also obtained at this gap. Comparison between the thermal cycle test and the strain sweep results (as presented in Table 2) showed that all the crudes
100
(a)
100
(b)
100
(c)
100
(d)
Fig. 12. Microscopy images of crude A: (a) at 5 °C below WAT under cooling rate of 1 °C/min., (b) at 15 °C below WAT under cooling rate of 1 °C/min, (c) at 5 °C below WAT under cooling rate of 10 °C/min, (d) at 15 °C below WAT under cooling rate of 10 °C/min.
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100
100
(b)
(a)
100
100
(d)
(c)
Fig. 13. Microscopy images of crude B: (a) at 5 °C below WAT under cooling rate of 1 °C/min, (b) at 15 °C below WAT under cooling rate of 1 °C/min, (c) at 5 °C below WAT under cooling rate of 10 °C/min, (d) at 15 °C below WAT under cooling rate of 10 °C/min.
100
(a)
100
(b)
100
100
(c)
(d)
Fig. 14. Microscopy images of crude C: (a) at 5 °C below WAT under cooling rate of 1 °C/min, (b) at 15 °C below WAT under cooling rate of 1 °C/min, (c) at 5 °C below WAT under cooling rate of 10 °C/min, (d) at 15 °C below WAT under cooling rate of 10 °C/min.
require bigger gap size than that determined by the thermal cycle test. From the strain sweep measurements on the 3 crudes, it can be concluded that the strain sweep test can be used to determine the appropriate gap required especially for transient rheological measurement. Thermal cycle test proposed previously by Marchesini et al. [12] was a continuous flow measurement to determine minimum gap required for rheological measurement at temperatures covering both Newtonian (above WAT) and Non-Newtonian
(below WAT) regions. Gap determination by using strain sweep test has an advantage of minimizing disturbance to the sample structure compared to the continuous flow test. Hence, it is more suitable for a fluid exhibiting time-dependent behavior and/or having irreversible structure changes due to shear/kinetic history. Due to this, it is suggested that the strain sweep test is adopted to determine minimum gap required especially for transient rheological measurements below WAT (at gelled conditions) such as the yield stress determination via dynamic oscillatory tests.
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st_h vs. x1 fit 1
Wax crystals
200
150
100
50
0 0
50
100
150
200
250
Threshold value Fig. 15. Distribution of threshold values of wax crystals.
Table 3 Fraction, size, and number of wax crystals. Crude sample
Cooling rate (°C/min.)
Temperature taken
Wax area fraction
Max. aggregated wax crystal length (micron)
1 2 3 4
Crude A
1
5 °C < WAT 15 °C < WAT 5 °C < WAT 15 °C < WAT
4.09 19.78 9.38 46.12
39.42 74.34 42.48 152.63
5 6 7 8
Crude B
5 °C < WAT 15 °C < WAT 5 °C < WAT 13 °C < WAT
1.6 6.63 1.71 27.48
29.77 38.81 30.04 114.54
9 10 11 12
Crude C
5 °C < WAT 25 °C < WAT 5 °C < WAT 25 °C < WAT
0.99 1.03 0.11 1.04
21.96 33.82 18.47 30.81
No
10 1 10 1 10
3.3. CPM images Fig. 12 showed the images of crude A as captured using a CPM of the wax-oil samples cooled down to the same final temperature at two different cooling rates of 1 °C/min and 10 °C/min and captured at 5 °C and 15 °C below WAT (from Cross Polar Microscopy), respectively. The individual wax crystals formed at the lower cooling rate of 1 °C/min (same as that utilized in the rheological measurements) were observed to be larger up to 50 lm compared to those formed at the higher cooling rate. The morphologies of the wax crystals were mainly rod or needle-like with presence of spherical crystals in between. Hence the images indirectly confirmed that the waxy crude contains mainly macro-crystalline with some micro-crystalline waxes. The amount of wax crystals at the higher cooling rate was also greater compared to that formed at 1 °C/min implying that as the cooling rate increased, crystals size reduced and the number density increased. Higher number density was also observed with reduction in temperature. Based on the gap requirement of 800 lm as obtained from the strain sweep test, it was confirmed that the ten-to-one ratio was not applicable for crude A sample which contained wax crystals up to approximately 50 lm. Fig. 13 showed CPM images of crude B when it was cooled down to the same final temperature at two different cooling rates of 1 °C/ min and 10 °C/min and captured at 5 °C and 15 °C below WAT, respectively. Similar to crude oil A, the individual wax crystals formed at the lower cooling rate of 1 °C/min were observed to be larger up to approximately 30 lm compared to those formed at the higher cooling rate with lesser number density. Similar wax crystal morphology in crude A was also observed in crude B. The
smaller crystal sizes as compared to that of crude A indicated that appropriate measurement gap required may also be smaller. According to ten-to-one ratio, the minimum gap required should be 300 lm. The strain sweep test however, confirmed that the ten-to-one ratio was not applicable and that the gap required was in fact similar to crude A. Unlike crude A and B, CPM images for crude C (as presented in Fig. 14) showed less wax crystals with crystal size as small as 1 lm or less. However, similar trend of wax crystal formation as crude A and B was observed. With the ten-to-one ratio, the gap required should be 10 lm which was much smaller than that obtained from the strain sweep test. The CPM images from these waxy crude oils also showed that crude A and B exhibit rapid wax precipitation process compare to crude C. Comparing the CPM observation with rheological results from the thermal cycle test, it can be concluded that the viscosity increased below WAT upon cooling correlate to the wax precipitation process and that the degree of viscosity increase would depend on the wax precipitation rate. This explains the phenomena observed under the thermal cycle tests where crude A and B exhibited sharp viscosity increase below WAT while crude C exhibited slow viscosity increase upon cooling. 3.4. 2D image processing 2D-image processing for the CPM images from the three waxy crude oils were conducted mainly to estimate the maximum crystal aggregation diameter. 34 wax crystals sample representing low to high threshold values (taken from the CPM images) were first collected to map the distribution of threshold values and was fitted by using general power law model as shown in Fig. 15, Threshold value
f ðxÞ ¼ 225:1x0:9187
ð2Þ
From the graph, it can be deduced that the threshold value for wax crystal is 15. The value was then use in the algorithm to determine the wax area fraction at the final temperature and maximum aggregated wax crystal length. The results are shown in Table 3. Images for crude C captured at lower temperatures (25 °C below WAT) were utilized instead due to the lower number density obtained at 15 °C below WAT. The image processing results showed that crudes A, B, and C have similar trends. The wax area fraction and maximum aggregated wax crystal length were larger as the temperature decreased (indicating formation of stronger network) and as the cooling rate increased. The maximum aggregated crystal length was found to be as big as 152.63 lm (crude A). Since the calculation of wax length during image processing considered aggregated wax as a single wax, the maximum wax length mentioned above is believed to be the maximum diameter of clustered wax within the network in the respective sample. The maximum size was then utilized to assess and compare against the gap determined from the rheological methods. 3.5. Theoretical gap [2,3] required for rheological measurement of fluid with suspended particles Similar gap analysis performed by Barnes [3] for the worst case of hard wax with wax porosity of 50% was also conducted, assuming that the wax crystals could be treated as suspended particles. A ratio of the apparent to real viscosity of a suspension as a function of the radius of suspended particles, a, geometry gap, H, phase volume, /, and a constant n was given as [3]
ga ¼ g
1 2 1 1 þ ð2an=HÞ 1 //m
ð3Þ
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condition, the wax crystals could not be treated as suspended particle. If aggregated wax crystal size (from 2D-image processing) was used for gap size determination rather than single wax crystal, the ten-to-one gap estimation is good for crude A. However, the estimations were poor for crude B and C. Summary of gap size required from different methods are presented in Table 4.
Gap/particle diameter, H/2a
103
102
4. Conclusions
101
100
0
0.1
0.2
0.3
0.4
0.5
Phase volume, φ Fig. 16. Predicted minimum gap to particle diameter ratio as a function of phase volume.
Table 4 Summary of gap size required under different methods. Crude
A B C
Gap size required (lm) Thermal cycle test
Strain sweep test
10:1 rule (CPM, estimated size)a
10:1 rule (CPM, image processing)b
500 500 300
800 800 800
500 300 100
800 400 400
a The gap is 10 times maximum single wax crystal size estimated from CPM image. b The gap is 10 times maximum aggregated wax crystal determined from an image processing technique.
By limiting the viscosity measurement error to 5%, i.e. the difference between the measured viscosity to the ‘‘real’’ viscosity was within 0.05, taking the n value to be 0.25 which was typical for concentrated suspension as recommended by Yilmazer and Kalyon [21], a maximum phase volume of 0.5 (/m), the predicted minimum gap-to-particle diameter ratio can be obtained via
H ¼ 4:75 2a
81
" # 2 / 1 1 0:5
ð4Þ
and shown graphically in Fig. 16. The figure indicated that if the wax was soft and had an oil porosity of 90%, the ten-to-one ratio as suggested previously by Barnes [2] is valid. However, samples with oil porosity lesser than 80% may require larger gap for the rheology measurement. The minimum gap required for ‘‘harder’’ wax also increased almost exponentially as predicted by Eq. (4). For the case of waxy crude samples under study, the wax phase volumes were all below 0.2 under the cooling rate of 1 °C/min. Hence, the ten-to-one rule [2] should be applicable if we consider single wax and neglected wax aggregation. However, rheological measurement results (from both thermal cycle and strain sweep tests) showed that the gap size required was larger than the gap size determined from the ten-to-one rule. The findings indicated that wax crystallization and gelation is a complex and random process which lead to random wax crystals interaction and aggregation. The results also showed strong indication that, in gel
The reliability of the yield strength measurements via oscillatory tests of gelled waxy crude oil has been proven to be highly dependent on the gap selection in the rheometer. Presence of large crystals encompassing the trapped oil forming a gel network could interfere with the rheology measurements. The ten-to-one ratio is not applicable for gelled waxy crude oils even with wax porosity greater than 80% and hence, care should be taken in deciding the suitable gap. Smaller gap measurements of gelled waxy crude oil are subjected to the wall effects which also subsequently reduce the measurement repeatability. The thermal cycle test as proposed by Marchesini et al. [12] could be a good start in deciding the gap parameter. Nevertheless a detailed analysis using a strain sweep test is a better option for greater accuracy while maintaining repeatability to be within 10% without the need to determine the crystals size under a microscope. It is also important to note that the gap selection is crude specific and highly dependent on the shear and cooling conditions as reported in the literature [19] and confirmed in this study. Under medium shear for instance, the wax crystals formed may be smaller than that formed under no shear condition. Even greater imposed shear may induce crystals aggregations changing the effective size of the wax crystals. Aggregates of wax crystals sizes as large as 74 lm at a cooling rate of 1 °C/min. (standard measurement cooling rate) has been observed in this study which would then require a minimum gap greater than that provided by the cone and plate system. However, very large gap within the parallel plate system also has limitations such as lack of temperature control and reduce surface adhesion by samples of low surface tension. Hence, a minimum gap can be selected through the proposed strain sweep procedure such that these limitations are not violated. Using a suitable gap setting ensures achieved prescribed strain, minimized instrument inertia effect where the ratio between raw phase and delta angles (i.e. the inertia correction) is maintained below 10, good measurement repeatability with gap-independent results and well respond from the sample to the applied load as seen from the sinusoidal waveforms. This study also confirms that the wax crystal size and aggregations are not the only indicator to be considered in determining the gap required especially when the testing protocol involves dynamic oscillatory shear measurements on gelled waxy crude oil. The strong interlocking and interactions between the wax crystals forming the gelled network complicate the gap analysis based on crystal size alone.
Acknowledgements The authors would like to thank PETRONAS Carigali Sdn Bhd (PCSB) for providing samples and the continuous information input extended throughout the project. Also to PETRONAS Research Sdn Bhd (PRSB) for letting us to use the Cross Polar Microscopy. We also wish to extend our gratitude to our technician, Mr. Hazri Shahpin and the personnel from PCSB and PRSB for their technical assistance. Last but not least, the Universiti Teknologi PETRONAS for providing the platform for the research to be conducted.
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Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.jnnfm.2015.02. 001. References [1] C. Bai, J. Zhang, Effect of carbon number distribution of wax on the yield stress of waxy oil gels, Ind. Eng. Chem. Res. 52 (2013) 2732–2739. [2] H.A. Barnes, A review of the slip (wall depletion) of polymer solutions, emulsions and particle suspensions in viscoemeters: its cause, character and cure, J. Nonnewton. Fluid Mech. 56 (1995) 221–251. [3] H.A. Barnes, Measuring the viscosity of large-particle (and flocculated) suspensions — a note on the necessary gap size of rotational viscometers, J. Nonnewton. Fluid Mech. 94 (2000) 213–217. [4] M. Bolourchifard, An Experimental Study of the In Situ Gelation of a Polyacrylamide-Chromium Acetate System in a Polymer-Treated Porous Medium (MSc Thesis), University of Kansas, 2006. [5] K.K. Botne, Modelling wax thickness in single phase turbulent flow (MSc Thesis), NTNU, 2012. [6] C. Chang, D.V. Boger, Q.D. Nguyen, The yielding of waxy crude oils, Ind. Eng. Chem. Res. 37 (1998) 1551–1559. [7] C. Chang, D.V. Boger, Q.D. Nguyen, Influence of thermal history on the waxy structure of statically cooled waxy crude oil, SPE J. 5 (2000) 148–157. [8] P.J. Flory, Principles of Polymer Chemistry, Cornell University Press, Ithaca, NY, 1953. pp. 347–398. [9] I. Henaut, O. Vincke, F. Brucy, Waxy crude oil restart: mechanical properties of gelled oils, in: Paper SPE 56771 presented at the SPE Annual Technical Conference and Exhibition Houston, 3–6 October, 1999.
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