Viscosity of Alaska Heavy Oil Saturated with Methane - Energy & Fuels

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Viscosity of Alaska heavy oil saturated with methane Ala Bazyleva, Babajide Akeredolu, and Matthew W. Liberatore Energy Fuels, Just Accepted Manuscript • Publication Date (Web): 08 Jan 2013 Downloaded from http://pubs.acs.org on January 17, 2013

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Viscosity of Alaska heavy oil saturated with methane Ala Bazyleva, Babajide Akeredolu, Matthew W. Liberatore*

Department of Chemical and Biological Engineering, Colorado School of Mines, Golden, CO 80401

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ABSTRACT

Viscosity, µ, of Ugnu heavy oil (North Slope of Alaska, USA) saturated with methane was measured at temperature from 0 oC to 60 oC, pressure from 15 psi to 1800 psi, and shear rate of 0.1 s-1 to 500 s-1 using a high-pressure rheology apparatus constructed for this work. Under all saturated conditions, the oil behaves as a Newtonian fluid. The influence of temperature, pressure, and methane concentration was analyzed, and important regularities in the viscosity were established. A two-variable Antoine-type correlation, µ=f(T,p), with 6 fitting parameters was developed using 48 points on a p,T,µ-diagram for Ugnu oil. Since produced oil is accompanied by sand and water, their influence on the viscosity of Ugnu oil saturated with methane at 1500 psi was also studied. The relative viscosity of the Ugnu oil + water emulsions at temperatures from 2 oC to 60 oC increased linearly with increasing water concentration from 0 to 20 wt.% following the Einstein viscosity model for dilute suspensions. Although possible in the timescale of days, hydrate formation at temperatures below 13 oC (thermodynamic hydrate formation temperature at 1500 psi) did not interfere with the rheological measurements for the emulsions. Due to rapid sand particle sedimentation in methane-saturated Ugnu oil during experimental stages, the impact of sand concentration on the live oil viscosity could not be evaluated. Overall, the viscosity of Ugnu oil as a function of pressure and temperature can be used to simulate the oil’s behavior during production.

KEYWORDS: Heavy oil; Viscosity; High-pressure rheology; Oil/water mixtures; Viscosity correlation


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1. Introduction The production of unconventional oil/bitumen has grown continuously in recent years. Estimates of more than 80 % of the total world oil reserves are heavy oil, extra-heavy oil, and bitumen (5.5 trillion barrels vs 1.02 trillion barrels of conventional crude oil).1-3 One heavy oil reserve is located on the North Slope of Alaska (United States).4 Although the Alaskan heavy oil reserves are enormous (approximately 20 to 25 billion barrels of original oil in place)5, difficult technical and economic aspects are involved in producing the oil. Challenges include high viscosity and asphlatene content from biodegradation, low reservoir temperatures due to the high northern latitude, the presence of 1800 ft (550 m) of permafrost, and relatively shallow burial depth. The Ugnu formation on the North Slope contains the most viscous, biodegraded oils (7 to 10 billion barrels of oil in place). The Ugnu formation is quite cold with temperature of 45 to 65 °F (7 to 18 oC) and shallow with 2400 to 3000 ft (730 to 910 m) depth and 1300 psi (8.96 MPa) reservoir pressure. Some pertinent properties of Ugnu oil are: specific gravity of 7 to 12 °API (density 0.99 to 1.02 g·cm-3 at 15.6 oC), viscosity from 60 to 10000 Pa·s, gas-to-oil ratio (GOR) from 120 to 130 scf/stb (21.4 to 23.2 m3/m3) at 15.6 oC and 1330 psi (9.17 MPa).6-7 The oil reservoir is located in an unconsolidated sandstone formation with porosity of 34 to 37 % and oil saturation of 66 to 72 %.6-7 Unconsolidated sands of the Ugnu formation creates potential problems of sand control, handling and disposal. Thus, standard production methods will be ineffective and an enhanced oil recovery (EOR) technology will be required. Therefore, accurate oil and rock properties are required for the development of efficient oil production and transportation on the North Slope. High temperature properties are extremely important for future development of thermal oil recovery, which may be an efficient production scheme in the arctic environment. Although the Ugnu formation was discovered more than 40 years ago, the database of oil and rock properties is extremely limited,6-9 especially for temperatures above ambient conditions (i.e., 40 °C). Frequently, the literature data are not attributed to any specific conditions, such as temperature or saturation pressure. One report8 provides a brief analysis of the viscosity of dead oils from three ACS Paragon Plus Environment

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different Ugnu locations in a narrow temperature interval from 60 to 100 oF (16 to 38 oC). However, no information on the influence of shear rate, water and gas content on Ugnu oil viscosity is available in the literature. More detailed rheological characterization including dilution with light hydrocarbons and water-based emulsification was conducted on West Sak heavy oil (adjacent location to the Ugnu formation)10-11 as well as a heavy oil from an unspecified Alaskan location.12-13 A large database has been recently compiled by Bergman and Sutton14 for dead oil viscosity ranging 6·10-5 to 109 Pa·s for more than 3000 oil samples from different places of the world. They also reviewed existing dead oil viscosity correlations (most correlations were valid for light and medium oils only) and developed a more universal correlation for temperatures from -40 to 500 oF (-40 to 260 oC). The average absolute deviation of these correlations was 2 to 60 times smaller than that of traditional correlations. However, in order to simulate the reservoir conditions, live oil data are crucial. Dissolved gases (methane, ethane, carbon dioxide, nitrogen, etc.) are known to significantly reduce the viscosity of oils and bitumen by several orders of magnitude depending on the saturation pressure.15-19 Bergman and Sutton20 have also collected available data on gas-saturated oils (1850 samples) covering a limited viscosity range from 5·10-5 to 3.3 Pa·s with GOR from 3 to 6500 scf/stb (0.5 to 1160 m3/m3) and bubble pressure from 66 to 10300 psi (0.46 to 71.02 MPa), which they used for creation of an improved live-oil viscosity correlation. This comprehensive study demonstrates the absence of a live-oil viscosity correlation for heavy oils with higher viscosities, which can be used to predict their fluid transport characteristics. Moreover, heavy oil and bitumen are likely to have the non-Newtonian behavior (dependence on the applied shear rate) and thixotropy (time-dependent viscosity),21-23 not normally accounted for in such databases and common correlations. In addition, water naturally present in hydrocarbon resources can form stable water-in-oil emulsions, whose viscosities are higher than that of parental oil,24 and can also induce shear thinning and thixotropy in the oil due to fluid structuring including gel formation,24-26 which requires special attention. Only a few rheological studies have been done on gas saturated water-in-oil emulsions.27,28


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In this work, we present viscosity measurements for Ugnu oil saturated with methane across a wide range of pressures and temperatures. Since the produced oil is always accompanied by sand and water, their influence on the high-pressure viscosity of Ugnu oil is also evaluated. The presented research is important for simulating realistic behavior of the Ugnu oil in situ.

2. Experimental 2.1 Materials Oil. Ugnu heavy oil (abbreviation MPS-41) with specific gravity of 12.9 °API (0.9788 g·cm-3 density at 15.6 oC) was donated by BP. The oil sample was separated from sand and collected in August 2011 from the S pad in the Milne Point field at around 3500 ft (1070 m) depth with a temperature around 52 oF (11 oC). The volatile plus solubility fractions of the oil are the following: Volatiles – 5 wt.%, Saturates – 38 wt.%, Aromatics – 40 wt.%, Resins – 10 wt.%, Asphaltenes – 7 wt.% (VSARA analysis). The volatile fraction is obtained by passing nitrogen for 24 h before the saturate, aromatic, resin, and asphaltene fractions are determined using open column liquid chromatography.29 The age of oil samples can be important for characterization over months and years. Therefore, oil samples were labeled as different subsamples by the date. The samples were taken from a single, master container in batches. Two subsamples were used: Aliquot 1 and Aliquot 2 were sampled on April 10, 2012 and June 13, 2012, respectively. Aliquot 1 was used for the rheology study of methane-saturated and non-saturated pure oil measurements. Aliquot 2 was mixed with deionized water or sand in different proportions to study the high-pressure viscosity of emulsion or suspension systems. The water content in both samples was measured with a Mettler Toledo V20 volumetric Karl Fisher titrator and was determined to be statistically identical and averaged to 0.62 ± 0.14 wt.%. Both oil samples were stored at room temperature. Sand. In order to correctly reproduce the oil + sand mixture, sand was separated from Ugnu oil sands (donated by BP) obtained from the produced Ugnu oil after recovery. Goo Gone (The Homax Group, Inc), a commercial cleaner, was applied to remove residual oil. Rinsing the clean sands in ethanol and ACS Paragon Plus Environment

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drying completed the cleaning process. The average particle diameter measurements were performed using an Olympus IX81 Motorized Inverted Microscope. For the optical measurements, sand grains were suspended in mineral oil to ensure the particles were well dispersed.

2.2 High-pressure rheology Apparatus. A high-pressure rheology apparatus combines a stand-alone mixing reactor, a highpressure pump, and a commercial rheometer (Figure 1). The system operates at pressures from ambient to 2000 psi and temperatures from -10 to 150 oC. The experimental setup is very similar to another apparatus developed previously in our laboratory.30-31 The major difference from the other apparatus, which is used to study gas hydrates, is an improved mixing reactor suitable for effective, rapid saturation of high viscosity oils. The components of the new high-pressure rheometer are briefly described below.

Figure 1. Schematic of the high pressure rheometer system: (1) rheometer; (2) syringe pump; (3) mixing reactor; (4) gas cylinder


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The mixing cell is a Parr Instruments 4560 Mini Stirred Reactor with a vessel volume of ~500 mL and a Series 4848 Controller for temperature control. The reactor with a PTFE sealing gasket is rated for a maximum working pressure of 3000 psi and up to 350 °C. A magnetically driven impeller was developed based on a pitched blade impeller (basic configuration of the reactor) and an additional anchor impeller for rapid saturation of a fluid. A variable speed motor provides stirring speeds adjustable from 0 to 1700 rpm. If necessary, the vessel can be inserted into a heating jacket to heat the mixture and accelerate saturation of gas into the liquid. The pressure is controlled using an Omega PX309-3KG5V general purpose pressure transducer up to 3000 psi gauge pressure (NIST traceable calibration) with the uncertainty of ±7.5 psi including linearity, hysteresis and repeatability. During the saturation process, pressure in the closed vessel decreased with time at constant temperature until a plateau was reached, indicating that the oil was fully saturated. After saturation, the oil was transferred to the rheometer cell via a syringe pump through steel tubing. The sample was piped from about 1 cm from the bottom of the mixing reactor. The syringe pump is a Teledyne IS 260D model with a pressure rating of 7500 psi (±40 psi uncertainty), operation temperature from 5 to 40 oC, a maximum volume of 266 mL. An additional Omega PX309-3KG5V general purpose pressure transducer is attached to the pump for more precise pressure control. Although the maximum flow rate through the pump is 107 mL·min-1, only 5 mL·min-1 rate was applied to avoid bubble formation upon pumping the saturated oil. The commercial rheometer is an AR G2 (TA Instruments, New Castle, DE). Briefly, the high pressure geometry is a Peltier controlled concentric cylinder system (cup-and-bob, rotor radius of 13 mm, stator radius of 14 mm) with a 1 mm gap, which can be pressurized to 2000 psi and operate in a temperature range from -10 to 150 °C (temperature uncertainty of ±0.1 °C, maximum heating/cooling rate of 2 °C·min-1). The sample volume used in an experiment is 9.5 mL. The inner bob is driven with the use of a magnetic coupling: an inner four-pole magnet couples with an outer magnet, which is attached to the rheometer spindle. This system has a maximum torque of 200 mN·m, and maximum angular velocity of 50 rad·s-1. According to the rheometer specification, the magnetic coupling driving the bob ACS Paragon Plus Environment

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can operate to the maximum torque limit of the equipment without slipping in the magnetic coupling. Three ports access the cup: one for a rupture disk with a 2500 psi (gauge) limit, one for entering liquid from the pump, one for entering and exiting gas with an attached Omega PX303-3KG5V pressure transducer rated for up to 3000 psi absolute pressure (±7.5 psi uncertainty including linearity, hysteresis and repeatability). A full description of this apparatus is shown elsewhere.30-32 The uncertainty of viscosity measurements using the pressure cell was estimated by measuring the viscosity of the Cannon certified viscosity standards N350 and S8000 (polybutenes, from CANNON Instrument Company, USA), whose viscosities are close to those of the Ugnu oil. The agreement with the standards in the certified temperature range 20 to 80 oC was better than ±10 %. The repeatability of the rheological measurements was better than 1 %. Experimental procedure. Due to the unique nature of the rheology experiments, the procedure is included in detail. The experimental procedure consists of a number of steps depending on the type of studied system: Step 1 (for emulsions and suspensions): weigh mixture components and homogenize the mixture inside the reactor for 30 min at ~1000 rpm at room temperature (the impeller setup in the mixing cell gives superior mixing compared to a stand-alone homogenizer). Step 2 (for saturated oil, emulsions, and suspensions): saturation of oil (or emulsions, or suspensions) with methane in the reactor at 25 to 30 oC under desired pressure for at least 24 h at ~500 rpm. The consumption of methane into the oil primarily occurs in the first 2 h of mixing at ambient temperatures. Step 3 (for saturated oil, emulsions, and suspensions): fill the flow lines with the saturated fluid under a pressure about 50 psi higher than the desired pressure (the impeller must be stopped before additional pressurizing). The higher pressure is necessary to avoid bubble formation upon pumping the fluid into the syringe pump. Step 4 (all samples): calibrate the rheometer, including instrument inertia calibration, zeroing the gap, bearing friction calibration (removes inaccuracies due to residual friction), rotational mapping (ensures


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accurate torque control over the 360o range of rotation and uniformity of instant viscosity values throughout each revolution). Step 5a (for saturated oil, emulsions, and suspensions): transfer the saturated fluid to the rheometer pressure cell under a pressure higher than the desired pressure (the impeller must be stopped before additional pressurizing), which is necessary to avoid bubble formation upon pumping the fluid into the rheometer; after the transfer is complete, the pressure is reduced to the desired value. This step takes up to 5 min. The transfer of excess methane from the gas phase into the liquid is expected to be negligible during this step due to fluid viscosities above 1 Pa·s, no mixing in the reactor or rheometer, and little or no liquid-gas interface in the syringe pump. Step 5b (for dead oil): load dead oil into the pressure cell with a graduated 10 mL syringe. Step 6 (for saturated oil, emulsions, and suspensions): stir the fluid at 100 s-1, 25 oC, and the desired pressure to remove excess of methane. In all cases, the pressure plateaus, indicating that excess methane has been removed. Step 7 (for all samples): measure the isothermal steady state viscosity at temperatures 0 oC (or 2 oC for water + oil emulsions to prevent ice formation), 10 oC, 20 oC, 30 oC, 40 oC, 60 oC under the isochoric conditions; measurements at 20 oC are repeated after the whole cycle to ensure that no changes (e.g., phase separation) occurred during the heating cycle. The shear rate range (ߛሶ ) was from 0.01 s-1 to either 500 s-1 or the shear rate produced by the torque up to 100 mN·m to avoid significant viscous shear heating of the sample, which will be discussed in Section 3.1. The sampling period was set to 10 s with 3 consecutive points to agree within 3%, i.e., at least a 30 s collection period for each viscosity value at each shear rate, and data is collected for up to 2 min or until steady state is reached. The rotational mapping in Step 4 allows using such sampling periods even for low shear rates providing reliable viscosity values irrespective of bob revolution.


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3. Results and Discussion 3.1. Saturated Ugnu Oil The raw viscosity measurements for methane-saturated Ugnu oil (Aliquot 1) at different temperatures, pressures, and shear rates are listed in Table S1 (Supporting Information). The shear rate range applied in each experiment depended on the viscosity of the sample: the lower limit is dictated by the sensitivity of the instrument and the higher limit is determined by energy dissipation due to viscous shear heating,33-36 i.e., frictional heating. Macosko34 presented a formula to estimate the shear rate when the viscous heating becomes noticeable: n +1   b µ 0 (R1Ω ) µ  b Br    = 1−   = 1−  n −1  µ0 12 n    12n k T T0 (R0 − R1 )  , n

n

(1)

where µ and µ0 are the viscosities with and without viscous heating, Br is the Brinkman number, n is the flow behavior index (n = 1 for Newtonian fluids, n < 1 for shear-thinning fluids, and n > 1 for shearthickening fluids), R0 and R1 are the radii of outer (stator) and inner (rotor) cylinders, Ω is the angular velocity, kT is the thermal conductivity of the fluid, T0 is the temperature of the outer cylinder, b is the dimensionless coefficient in the following exponential viscosity-temperature relation:

 T − T0  µ (T )  = exp − b µ (T0 ) T 0  

(2)

.

Eqs. 1–2 are applied in Figure 2 for dead and live Ugnu oil (and in Figure S1 in Supporting Information for Newtonian certified Cannon standards). The equations qualitatively predict the onset of viscosity decrease due to frictional heating for samples with different viscosities. However, this equation does not account for other phenomena, such as destabilization of the flow due to viscous heating, secondary flows, rod climbing, etc. Thus, the equation cannot quantitatively capture the measured shear rate dependence of viscosity before and after the onset of viscous heating.


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viscosity (Pa⋅s)

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10 9 8 7 6 5 4 3 2 10

100 -1 shear rate (s )

1000

Figure 2. Effect of viscous heating on viscosity of Ugnu oil: , Ugnu oil saturated with methane at o 1405 psi and 0 C (b = 30.1 for Eq. 2); , dead Ugnu oil at 40 oC (b = 27.7 for Eq. 2); solid line,

viscosity calculated by Eqs. 1–2 accounting for viscous heating (for both fluids kT = 0.13 W·m-1·K-1 taken from Ref. 35 and n = 1).

Slight shear thinning accounting for less than 5 – 7 % viscosity decrease, which is smaller than the experimental uncertainty, is observed in the flow curves for both Newtonian Cannon standards, dead and live Ugnu oil at shear rates below the frictional heating onset (Figures 2 and S1). This is likely to be an instrument artifact, which can be ignored due to its small magnitude. In addition, Figure S2 in Supporting Information compares the flow curves for dead Ugnu oil at 40 oC obtained in the concentric cylinder pressure cell and with the use of 40 mm Peltier plate (1 mm gap in both cases), which confirms the Newtonian behavior of the oil and eliminates the wall slip effect as a significant artifact in the pressure cell. All these facts allowed us to consider both dead and methane saturated Ugnu oils as Newtonian fluids and average the apparent viscosity values. The viscosity data are summarized in Table 1 and in Figure 3.


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Table 1. Viscosity of Ugnu oil non-saturated and 100% saturated with methane at different pressures and temperatures t, o C

p, psi

Isopleth 1 0 1405 10 1460 20 1510 30 1555 40 1600 60 1685 Isopleth 2 0 955 10 980 20 1010 30 1040 40 1065 60 1115

µ, a Pa·s

t, C

o

p, psi

16.9 (0.2) 5.23 (0.07) 1.92 (0.03) 0.813 (0.010) 0.385 (0.004) 0.111 (0.001)

Isopleth 4 0 1510 10 1570 20 1625 30 1675 40 1725 60 1810

35.0 (0.5) 9.66 (0.12) 3.26 (0.05) 1.27 (0.02) 0.566 (0.007) 0.150 (0.001)

Isopleth 5 0 1315 10 1360 20 1405 30 1445 40 1485 60 1560

Isopleth 3 Isopleth 6 0 480 112.5 (0.9) 0 740 10 495 26.0 (0.3) 10 760 20 505 7.51 (0.10) 20 780 30 515 2.61 (0.04) 30 800 40 530 1.06 (0.01) 40 815 60 550 0.244 (0.001) 60 850 a The standard deviation is in the parentheses

µ, a Pa·s

t, C

o

p, psi

µ, a Pa·s

15.1 (0.2) 4.83 (0.06) 1.73 (0.02) 0.747 (0.010) 0.356 (0.004) 0.105 (0.001)

Isopleth 7 0 250 10 255 20 265 30 270 40 275 60 285

239 (1) 48.3 (0.4) 12.7 (0.2) 4.09 (0.06) 1.56 (0.03) 0.328 (0.004)

17.8 (0.2) 5.45 (0.08) 2.02 (0.03) 0.836 (0.012) 0.395 (0.005) 0.115 (0.001)

Isopleth 8 0 15 10 15 20 16 30 16 40 17 60 18

593 (6) 99.5 (0.5) 23.0 (0.3) 6.68 (0.08) 2.38 (0.04) 0.446 (0.005)

61.7 (0.7) 15.7 (0.2) 4.92 (0.09) 1.83 (0.04) 0.783 (0.014) 0.194 (0.002)

0% saturation 10 1560 197 (3) 10 1250 176 (3) 10 995 158 (2) 10 530 132 (1) 10 250 119 (1) 10 15 109 (1)


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Figure 3. Pressure and temperature dependence of methane saturated Ugnu oil: black lines, isotherms; grey lines, isopleths

As mentioned in the Experimental section, the oil is saturated at 25 to 30 oC and then measured from 0 to 60 oC and back at 20 oC (e.g., one series of measurements is shown in Figure 4). Since dissolution of gases in liquids is a slightly exothermic process, their solubility decreases with increasing temperatures at constant pressure. On the other hand, according to the Raoult’s law, the solubility of methane increases with increasing pressure at constant temperature. However, our measuring system is isochoric, i.e. both pressure and temperature changes codirectionally, which can lead to a full or partial compensation of these two effects. Hence, the amount of dissolved methane in the liquid phase during the isochoric measurements (isopleths conditions) is nearly constant. Specifically, estimation of the methane content change in the liquid phase caused by simultaneous temperature, pressure, and gas volume change (due to liquid expansion with increasing temperature) in one of the isochoric series from ACS Paragon Plus Environment

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Table 1 gave (0 ± 5) % from 0 to 60 oC. This supports the conclusion that the isochoric series are performed along corresponding isopleths (iso-compositional curves). The constant composition of the fluid along the isopleths is indirectly confirmed by the following experimental observations: (1) constant viscosity values upon repeated measurements at 60 oC, when diffusion of the gas dissolved in liquid is noticeable due to lower viscosity of the oil, and (2) repeatability of viscosity of Ugnu oil at 20 oC measured before and after high temperature experiments within 1 %.

o

t = 0 C, p = 1405 psi

10 o

t = 10 C, p = 1460 psi

viscosity (Pa⋅s)

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o

t = 20 C, p = 1510 psi o

t = 30 C, p = 1555 psi

1

o

t = 40 C, p = 1600 psi

o

t = 60 C, p = 1685 psi

0.1 10

100 -1 shear rate (s )

1000

Figure 4. Isopleth (constant liquid concentration) flow curves for methane saturated Ugnu oil

This observation allows us to estimate the enthalpy of solution of methane in the Ugnu oil combining Henry’s law, Eq. 3, and the van Hoff equation for the Henry constant, Eq. 4: K H = psat / x ,

∆ sol H = R

d ln K H , d (1 / T )

(3) .

(4)

where psat is the saturation pressure; KH is the Henry constant; x is the molar fraction of methane in the oil; ∆solH is the enthalpy of solution of methane in the oil; R is the gas constant, 8.31447 J·K-1·mol-1; T is ACS Paragon Plus Environment

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the temperature in K. Since there is no change in composition of the solution along an isopleth and if the enthalpy of solution is constant in the studied temperature range, one can convert Eq. 4 to:

ln psat =

∆ sol H + A, . RT

(5)

where A is a constant. If Eq. 5 is applied to pressure vs. temperature dependences for each isopleths in Table 1, the average enthalpy of solution of methane in the Ugnu oil is estimated to be -2.0 ± 0.3 kJ·mol1

. This value is in close agreement with ∆solH determined from the solubility of methane in hexane (-2.9

kJ·mol-1) and decane (-2.2 kJ·mol-1).37 Both temperature and pressure have a drastic impact on the Ugnu oil viscosity (Figure 3). In order to separate the effects of pressure and dissolved methane, a series of experiments with pressurized Ugnu oil with no saturation with methane was conducted at 10 oC (Table 1). The low temperature was selected to prevent dissolution of methane in the high-viscosity oil during the time scale of rheological experiments (due to slow diffusion). Repeatability of viscosity values at atmospheric pressure before and after the measurement series proved the absence of any methane dissolution. The viscosity of 0 % gas-saturated oil slowly increases with pressure, almost linearly on semi-log coordinates (Figure 5). The viscosity increases only 2 times when p rises from atmospheric pressure to ≈1600 psi. Conversely, dissolution of methane across the same pressure range leads to a drastic decrease in oil viscosity – about a 40-times decrease from 0 to 100 % saturation at p ≈ 1600 psi. Hence, methane serves as an efficient thinning agent. The increase of viscosity of non-saturated oil with pressure is consistent with literature viscosity data on pure organic compounds (e.g., dodecane, octadecane, cis-bicyclo[4.4.0]decane, glycerol, etc.), where similar linearity in ln µ vs pressure exists up to at least 500 atm (7350 psi).38-43 However, the slope depends on the compound nature and temperature. Since the reservoir pressure is unlikely to reach more than 500 atm, this linear trend could be a good basis for a correlation of viscosity of under-saturated oil with pressure above its bubble pressure.


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dead oil 100 viscosity (Pa⋅s)

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10 o

live oil

10 C 0

300

600

900 1200 pressure (psi)

1500

1800

Figure 5. Comparison of pressure dependences of viscosity for Ugnu oil with 0% () and 100% () saturation with methane at 10 oC and specified pressures; solid lines are for visual purposes only

The effect of temperature is more dramatic than methane saturation. Specifically, the viscosity drop for dead Ugnu oil from 0 to 60 oC accounts for three orders of magnitude (Figure 6) while the viscosity change with saturation at the reservoir pressure and temperature (≈1400 psi and 10 oC) is about one order of magnitude (Figure 5). The curvature of the temperature dependence for the viscosity isopleths in Figure 3 is more pronounced than that predicted by the simple Arrhenuis equation: ln µ = A + B / T ,

(6)

Thus, an Antoine-type equation accounted for the change in the activation energy:

ln µ = A + B / (T + C ) ,

(7)

where A, B, C are the fitting parameters, T is the temperature in K. A comparison of Eqs. 6 and 7 for dead Ugnu oil is shown in Figure 6.


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3.7

3.6

1000 / T (K) 3.4 3.3 3.2

3.5

3.1

3.0

50

60

1000

100 viscosity (Pa⋅s)

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10

1

0.1 0

10

20 30 o 40 temperature ( C)

70

Figure 6. Temperature dependence of viscosity for dead Ugnu oil at atmospheric pressure (isopleths 8 in Table 1): , experimental values; solid line, fitting using the Antoine-type equation Eq. 7; dashed line, fitting using the Arrhenius equation Eq. 6

When all isopleths for Ugnu oil are plotted in a single µ vs T graph (Figure 7a), the viscosity follows a single master curve (Figure 7b) when appropriate shifts along the T axis (∆Tshift) are accounted for. Since pressure is changing with temperature along an isopleth (according to Eq. 5), the pressure at 20 oC was selected as a reference pressure (pref) for each isopleth. A preliminary estimate showed that the dependence of ∆Tshift on pref is quadratic. Thus, the following set of equations can be applied to simultaneously fit µ=f(T,p) for methane saturated Ugnu oil: ln µ = A + B (T + ∆Tshift + C ) ,

(8)

∆Tshift = D ( pref − 15) + E ( pref − 15) ,

(9)

 ∆ H 1 1  pref = p ⋅ exp − sol  −  , R  T 293.15  

(10)

2


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1000 (a)

viscosity (Pa⋅s)

100

10

1

0.1 270

280

290

300 310 T (K)

320

330

340

1000 (b) 100 viscosity (Pa⋅s)

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10

1

0.1 270 280 290 300 310 320 330 340 350 360 370 T (K) + ∆Tshift Figure 7. Temperature dependences of viscosity of Ugnu oil along isopleths with the following pref: , 15 psi; , 265 psi; , 505 psi; , 780 psi; , 1010 psi; , 1405 psi; , 1510 psi; , 1625 psi; solid line, fitting using Eqs. 8-10 with the parameters from Table 2. Plot (a) – for original experimental isopleths; plot (b) – for the isopleths shifted by ∆Tshift along the temperature axis ACS Paragon Plus Environment

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where A, B, C, D, E are the fitting parameters; ∆solH = -2000 ± 300 J·mol-1 for dissolution of methane in Ugnu oil; p is the saturation pressure in psi; T is the temperature in K. Parameters A, B, C, D, E were obtained by a joint non-linear least-squares fitting of the experimental data (100% saturation from Table 1). The results of the fitting are shown in Table 2 and Figure 7b. The deviations of calculated values from experimental ones as a function of pressure and temperature are shown in Figure S3 (Supporting Information). The average relative deviation is 2.4 %, the maximum relative deviation is 7.9 %, which is within the uncertainty of the method.

Table 2. Parameters for the viscosity-temperature-pressure correlation (Eqs. 8-10) Parameter A B C D E ∆solH

Value -11.7 ± 0.3 1650 ± 80 -182 ± 3 (2.02 ± 0.06)·10-2 -(3.39 ± 0.35)·10-6 -2000 ± 300

Unit K K K·psi-1 K·psi-2 J·mol-1

The uniformity of temperature dependences of viscosity for dead and live Ugnu oil is a crucial observation. If a uniform temperature-viscosity correlation is valid for other heavy oils, then uniform correlations that predict live oil viscosities, using easily measurable viscosity data for the corresponding dead oil and gas solubility parameters (Henry constant and enthalpy of solution), are possible. Since the enthalpy of solution of methane in different oils is expected to be similar, prediction of live oils’ viscosity may require only two steps to obtain parameters of the correlation (Eqs. 8–10): (1) detailed analysis of the temperature dependence of viscosity of dead oil over a wide temperature range, and (2) detailed analysis of the saturation pressure dependence of the corresponding live oil at a single temperature, preferably in the middle of the studied temperature interval.


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3.2. Saturated Ugnu Oil + Water Emulsions The viscosity for methane saturated Ugnu oil (Aliquot 2) + water emulsions from 0.6 wt.% to 20.0 wt.% of water (water-in-oil type) at different temperatures and shear rates along the isopleth corresponding to 1525 psi at 20 oC are summarized in Table S2 (Supporting Information). It should be noted that the emulsions without methane were stable for several weeks at room temperature, i.e., no phase separation was visually observed. The size of water droplets was not established due to the opacity of the oil. Although methane hydrates can thermodynamically form at temperatures below 13 oC at pressure 1500 psi,44 the formation process is stochastic and requires significant supercooling. Since the lowest temperatures selected in this study for emulsions is 2 oC and the measurements at this temperature take less than 2 h, the formation of hydrates is not expected. Hydrate formation detected by a continuous increase in viscosity of several orders of magnitude was observed only once for the emulsion with 15 wt.% of water after several days of shearing at 2 oC. Similar to live Ugnu oil, these emulsions exhibit a Newtonian behavior and no wall slip effects were observed. The average viscosity values for the emulsions are listed in Table 3. Of note, the viscosity of Aliquots 1 and 2 at the same saturation pressure differ by not more than 7 %. Thus, differences between two oil subsamples are small, i.e., little change occurred in the oil with time.

Table 3. Viscosities of Ugnu oil + water emulsions saturated with methane at different temperatures with constant concentration of methane in the liquid phase a wwater, wt% 0 0.6 5.0 10.1 15.1 20.0 µ, Pa·s 2 1430 11.9 (0.1) 12.2 (0.1) 13.3 (0.1) 15.2 (0.2) 16.8 (0.2) 18.0 (0.3) 10 1470 4.74 (0.05) 4.88 (0.05) 5.35 (0.06) 5.99 (0.06) 6.73 (0.09) 7.37 (0.11) 20 1525 1.75 (0.02) 1.81 (0.02) 1.97 (0.02) 2.22 (0.03) 2.49 (0.03) 2.73 (0.04) 30 1570 0.742 (0.010) 0.768 (0.007) 0.834 (0.008) 0.947 (0.011) 1.07 (0.01) 1.17 (0.02) 40 1615 0.354 (0.005) 0.366 (0.002) 0.398 (0.003) 0.452 (0.005) 0.513 (0.006) 0.557 (0.008) 60 1700 0.105 (0.001) 0.108 (0.001) 0.118 (0.001) 0.132 (0.002) 0.148 (0.001) 0.158 (0.002) a The standard deviation is in the parentheses. b Obtained by a linear extrapolation of the experimental viscosities for Ugnu oil with different water content. p, t, C psi o

b


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In the studied concentration range, the viscosity of the Ugnu oil + water system increased linearly with water concentration, which is typical for other water-in-crude emulsions.45 This fact allowed us to make a linear extrapolation of viscosity to 0 wt.% of water, i.e., to obtain viscosity of dispersive media – µoil (Table 3). Relative viscosity of the water-in-oil emulsions, µemulsion / µoil, remains almost constant with temperature at constant composition, up to t = 40 oC (Figure 8), which indicates that the temperature dependence of the pure Ugnu oil is transferable to its emulsions with water. The deviation at higher temperatures may be attributed to some of the water phase separating. Indeed, the stability of the emulsions up to 40 oC was confirmed by repeatability within 1 % of viscosity values measured at 20 oC immediately after loading, after cooling to 2 oC and 10 oC, and after heating to 30 oC and 40 oC. On the other hand, the repetition of the viscosity measurements at 60oC for the emulsion with 20.0 wt.% of water shows 2 % decrease in viscosity within 20 min. Moreover, the viscosity values for that emulsion at 20 oC measured after high temperature experiments at 60 oC were about 5 % lower. In addition, large water droplets were observed at the bottom of the pressure cell upon cell disassembling after the exposure to 60 oC. This observation indicates noticeable phase separation of oil and water at temperature above 40 oC. In the studied range of water content up to 20 wt.%, the relative viscosity of the emulsions vs. water mass fraction at each studied temperature was found to follow the linear trend with an almost identical slope at different temperatures, (2.7 ± 0.3). The correlation coefficients of the fits were r > 0.997. Any other higher order equations (such as a Taylor series expansion) will not improve the fit. Due to the proximity of densities of water and Ugnu oil, the observed slope is similar in terms of mass and volume fractions.


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1.6 1.5 µemulsion / µoil

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1.4 1.3 1.2 1.1 1.0 0

10

20 30 40 o temperature ( C)

50

60

Figure 8. Temperature dependence of relative viscosity of Ugnu oil + water emulsions at different mass fractions of water along the isopleth characterized by p =1520 exp[-2280/R·(1/T – 1/293.15)] in psi:

, wwater = 0.6 wt.%; , wwater = 5.0 wt.%; , wwater = 10.1 wt.%; , wwater = 15.1 wt.%; , wwater = 20.0 wt.%. Error bars represent standard deviations.

The value of the slope agrees well with the Einstein equation, although it was developed for dilute suspensions of solid spheres:46

µ / µ 0 = 1 + 2.5ϕ ,

(11)

where µ and µ0 are the viscosities of suspension (emulsion) and dispersive media, respectively; φ is the volume fraction of solid spheres (droplets). This observation allows application of the Einstein viscosity model for the dilute water-in-oil emulsions.

3.3. Saturated Ugnu Oil + Sand Suspensions The hydraulic diameter distribution of sand particles (density of 2650 kg·m-3 from Ref. 47) measured using optical microscopy is presented in Figure 9. More than 1600 sand particles were counted. There ACS Paragon Plus Environment

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are two groups of particles: 1 to 40 µm (fine powder) and about 300 µm (visible sand grains). Although the number of particles in the first group is three orders of magnitude greater than that in the second group, the mass fraction of particles from the second group with the size of about 300 µm is 99.5 wt.%. 1000 800 600 400 200 100 80 60 40

Count

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0.5 wt%

20

99.5 wt%

10 8 6 4 2 0 0 5 10 15 20 25 30 35 40

280 290 300 310 320 330 340

Diameter (µm)

Figure 9. Size distribution of Ugnu sand grains determined using optical microscopy

Since the particulate suspensions of sand in Ugnu oil have a tendency to settle, the particle settling speed was estimated from the following equation:48

vsed

1 g D 2 (ρs − ρ f ) = , 18 µ

(12)

where vsed is the sedimentation speed; g is the gravitational acceleration; D is the diameter of settling particles; ρs and ρf are the densities of solid particles and dispersive fluid; µ is the viscosity of the fluid. It was estimated that 99.5 wt% of sand (with the size of about 300 µm) will settle in the rheometer (50 mm travel distance) within 30 min when Ugnu oil was saturated with methane at 1500 psi and 20 oC (µoil = 1.92 Pa·s). About 5 min are required for pumping the oil + sand mixture from the reactor to the


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Energy & Fuels

rheometer at room temperature. During this time and the following measurements, a significant fraction of sand was expected to settle. A test experiment with 35.7 wt.% suspension of sand in Ugnu oil saturated with methane at 20oC and at 1500 psi (µoil = 1.92 Pa·s) was conducted. Two successive shear sweep experiments lasting about 30 min each and separated by 30 minutes. The viscosity (Figure 10) decreased more than 30 % over this time period. Also, the viscosities in run 1 are below those expected for such concentrated suspension. In addition, sand sediment was observed at the bottom of the pressure cell after disassembling the cell. All these facts indicated sedimentation during the loading procedure and rheology measurements. This phenomenon prevents us from measuring the viscosity of the Ugnu oil + sand reconstituted fluids.

4.0

3.6 viscosity (Pa⋅s)

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3.2

2.8

2.4 10

-1

100

shear rate (s ) Figure 10. Influence of sand sedimentation on the apparent viscosity of Ugnu oil + sand (35.7 wt.%) mixture saturated with methane at 20oC and 1500 psi: , run 1; , run 2


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4. Conclusions A rheology apparatus allowing saturation of a fluid with pressurized gases and variable shear-rate rheological measurements was constructed. The viscosity of dead and live Ugnu oil (North Slope of Alaska, USA) was measured between 0.1 to 600 Pa·s in a wide range of reservoir and operational conditions, such as temperature of 0 to 60 oC, methane-saturation pressure from 15 to 1800 psi, shear rate of 0.1 to 500 s-1, water concentration from 0 to 20 wt.%. The oil was found to behave as a Newtonian fluid under all saturated conditions. Regularities in the viscosity change with varying saturation pressure, temperature, methane concentration, and water content of Ugnu oil have been quantified and are crucial for development of an effective oil recovery scheme on the North Slope (Alaska). The temperature-pressure dependence of dead and live Ugnu oil was described by a uniform two-variable Antoine-type correlation with 6 fitting parameters. The viscosity of the Ugnu oil + water emulsions with water concentration from 0 to 20 wt.% followed the Einstein viscosity model. Rapid sedimentation of sand in Ugnu oil did not allow for study of Ugnu oil + sand suspensions. Two promising directions of future study can be outlined: (1) dependence of viscosity of undersaturated oil on pressure above the bubble pressure can be used to predict the viscosity of the oil at different degrees of saturation, and (2) combination of mass spectroscopy and rheology to develop a correlation between a viscosity drop with saturation pressure and oil composition.

AUTHOR INFORMATION

Corresponding Author *To whom correspondence should be addressed: Matthew W. Liberatore, E-mail: [email protected], Telephone: +1-303-273-3531.


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ACKNOWLEDGMENT This work is supported by the U.S. Department of Energy, DE-NT0005663. The authors are grateful to Prof. Michael Batzle (Department of Geophysics, Colorado School of Mines) and Prof. Andrew M. Herring (Department of Chemical and Biological Engineering, Colorado School of Mines) for valuable discussion.

ASSOCIATED CONTENT

Supporting Information Tables S1 and S2 summarizes the raw viscosity values for Ugnu oil and Ugnu oi + water emulsions saturated with methane; Figure S1 represents the effect of viscous heating on viscosity of Newtonian Cannon certified standards in the concentric cylinder pressure cell; Figure S2 compares flow curves for dead Ugnu oil at 40 oC measured in the concentric cylinder pressure cell and with the use of a 40 mm Peltier plate; Figure S3 shows the percentage deviation of viscosities calculated by Eqs. 8-10 from the experimental ones for Ugnu oil. This material is available free of charge via the Internet at http://pubs.acs.org.

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Energy & Fuels

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Viscosity of Alaska Heavy Oil Saturated with Methane - Energy & Fuels

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