Measurement and Prediction of Density for the Mixture of Athabasca

Article pubs.acs.org/EF

Measurement and Prediction of Density for the Mixture of Athabasca Bitumen and Pentane at Temperatures up to 200 °C Hossein Nourozieh, Mohammad Kariznovi, and Jalal Abedi* Department of Chemical & Petroleum Engineering, University of Calgary, 2500 University Dr., NW, Calgary, Alberta, T2N 1N4 Canada ABSTRACT: The main recovery mechanism in the solvent-based bitumen recovery processes is gravity drainage. The density of heated bitumen or diluted bitumen at operational conditions is required to predict the production rate and cumulative oil recovery. In this manuscript, the densities of bitumen, pentane, and their mixtures at different pentane weight fractions (0.05, 0.1, 0.2, 0.3, 0.4, and 0.5) have accurately been measured. The measurements were conducted under conditions applicable for both in situ recovery methods and pipeline transportation of heavy oil. The experiments were taken using Athabasca bitumen at temperatures varying from ambient up to 200 °C and at pressures up to 10 MPa. The volume change upon mixing for the mixtures is evaluated from the experimental results, and the influence of pressure, temperature, and solvent weight fraction on the volume change upon mixing and density is studied. The density data are also represented with three different approaches considering no volume change, excess volume, effective liquid densities, and equation of state. The results indicated that the mixture data are well-predicted using equation of state and effective liquid densities with average absolute relative deviations (AARD) of 0.55% and 0.57%, respectively.

1. INTRODUCTION The Alberta oil sands are Canada’s most important oil producing region. The oil sands (tar sands) are saturated with solid or semisolid petroleum called bitumen. Unconventional techniques are required to produce this type of oil, and as a result, the production cost for heavy oil and bitumen is considerably higher than for conventional oil. For this reason, considerable attention and investment have been focused on developing more effective and less expensive recovery methods for viscous reserves. The two most promising methods are open pit mining and in situ production. Open pit or surface mining, the principal method of oil sand production, is expected to decline in the future because more than 80% of oil sands are too deep to access with this method. In situ extraction is an alternative for production from deep reservoirs. Steam-assisted gravity drainage (SAGD) is promising method for producing heavy oil and bitumen in Alberta; however, it has been criticized from high water consumption and significant greenhouse gas (GHG) emissions. SAGD has limited applications in thin reservoirs and or reservoirs with active aquifers because of high heat loss. Vapor extraction (VAPEX) and solvent-based processes represent an alternative to steam-based processes, but they have their own drawbacks. The main problem with solvent-based processes is a relatively low production rate. Solvent-based recovery relies on diffusion and dispersion mechanisms, which are very slow processes. To overcome the limitations of steam and solvent processes, researchers proposed a hybrid process in which steam and solvent are coinjected. Several researchers including Farouq-Ali and Abad,1 Redford and McKay,2 Redford,3 Shu and Hartman,4 Sarma et al.,5 Nasr et al.,6 Nasr and Ayodele,7 Ayodele et al.,8,9 Gates and Chakrabarty,10 Ivory et al.,11 Ardali et al.,12,13 Mohammadzadeh et al.,14 Ezeuko et al.,15 and Yazdani et al.16 investigated the advantages of solvent coinjection processes using both experimental and simulation studies. They showed that steam © 2014 American Chemical Society

solvent coinjection produces promising results in most situations and reservoir conditions. Pentane and its mixtures with other hydrocarbons are potential additives to steam-based processes for bitumen or heavy oil recovery. It can also be used as an agent to precipitate asphaltene from bitumen for oil upgrading or performing saturate-aromatic-resin-asphaltene (SARA) analysis in the lab. Several lab-scale experiments have considered pentane as a solvent to be coinjected with steam for heavy oil and bitumen recovery.2,3,6 Additional lab-scale and field-scale simulations were conducted to predict the performance of pentane in a solvent−steam hybrid process.4,17−20 These studies indicated that the coinjection of pentane results in an improved steamoil-ratio (SOR) proportional to the solvent concentration. The above discussions support the consideration of pentane as a potential solvent candidate for heavy oil and bitumen in situ recovery. The main mechanism in the in situ recovery processes is gravity drainage in which arises from the difference between the oil and the solvent/steam densities. Thus, to design and optimize these processes, the density of oil and its mixtures with solvent at high-temperature conditions are required. Limited phase behavior data for pentane/bitumen was reported by Zou et al.21 and Argüelles-Vivas et al.22 Pentane can be used to precipitate asphaltene from oil and is frequently applied in petroleum research studies of asphaltene precipitation. Zou et al.21 evaluated the phase behavior of Athabasca vacuum bottoms (ABVB) with n-alkanes, particularly n-pentane. The authors reported multiphase equilibrium (L1V, L1L2V, L1L2L3V, L2L3V, and L2V) for a 40% ABVB and n-pentane mixture over a wide range of pressures and temperatures. Argüelles-Vivas et al.22 reported the density and viscosity of Received: November 19, 2013 Revised: April 2, 2014 Published: April 3, 2014 2874

dx.doi.org/10.1021/ef4022784 | Energy Fuels 2014, 28, 2874−2885

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pentane/Athabasca bitumen mixtures up to 15% pentane concentrations by weight at a constant pressure of 1 MPa and temperatures up to 448 K. In this study, the density of bitumen and the pentane-diluted bitumen was measured at different proportions of pentane. Four different temperatures (50, 100, 150, and 190 °C) and five pressures (2, 4, 6, 8, and 10 MPa) were considered in the experiments. The proportions were varied from 0.05 to 0.5% weight fraction. Then, the volume change on the mixing for the mixture was calculated from the experimental data, and different approaches were evaluated to predict and correlate density data.

Table 2. Compositional Analysis of Bitumen Sample

2. EXPERIMENTAL SECTION 2.1. Materials. The n-pentane was supplied by Spectrum Chemical Mfg. Corp. with a minimum assay of 0.99. The bitumen sample was provided by ConocoPhillips oil company operating a SAGD project (Surmont project) southeast of Fort McMurray. The sample was processed to remove sand and water. The density of the bitumen sample was measured with an Anton Paar density measuring cell and was 1009 kg/m3 at 23 °C and atmospheric pressure. The molecular weight of bitumen sample was measured using a cryoscopy method which is based on freezing point depression; benzene was used as the solvent. The solutions were prepared to have 0.15 molal concentrations. This value is within the range recommended by the factory for the molecular weight measurements. The average molecular weight of bitumen based on four different measurements is 539.2 ± 7.9 g/mol. The SARA analysis was conducted on the sample to separate different fractions (saturates, aromatics, resins, and asphaltenes) using a n-paraffin solvent and the adsorption of fractions on clay or silica gel. The asphaltene fraction of bitumen is precipitated with n-heptane. The resin fraction is adsorbed on attapulgus clay, while the aromatic fraction is adsorbed on silica gel. The SARA compositional analysis of bitumen was completed using the American Society for Testing and Materials (ASTM) D2007 method, and the results are presented in Table 1.

Table 1. SARA Analysis for Bitumen Sample fraction

mass percent

saturates aromatics resins asphaltenes

12.26 40.08 36.53 11.13

The bitumen sample was also subjected to compositional analyses to obtain carbon number distributions up to C100 using the standard test method, ASTM D7169. This test method was used to determine the boiling point distribution through a temperature of 720 °C, which corresponds to the elution of n-C100. The boiling point distribution for bitumen sample is given in Table 2. 2.2. Experimental Apparatus. The details of experimental apparatus and its validation were presented elsewhere.23 The schematic diagram of the apparatus is shown in Figure 1. It consists of feeding cells, an equilibration cell, four sampling cells, a density measuring cell, and two Quizix automated pressure activated pumps. The Quizix pumps charge and discharge water to displace the fluids or maintain constant pressure. The equilibration, sampling, and feeding cells are equipped with pistons to prevent the contamination of the mixture with water. The pistons are sealed with Viton O-rings supported by Teflon backup rings. The equilibration and sampling cells and the density measuring cell are placed in a temperature-controlled Blue M oven. The oven (DCW1406-E-PM-GOP) was equipped with a temperature controller capable of maintaining the temperature within ± 0.1 °C. The temperature range of the oven was 15 °C above ambient to 350 °C. Two Quizix pumps control the pressure of the system. The rocking action of the equilibration cell with the rolling ball expedites the mixing process and reduces the time required to reach the equilibrium condition. The

% off

temperature (°C)

% off

temperature (°C)

IBP 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42

192.4 213.2 236.1 252.7 265.7 277.6 288.4 297.1 305.2 312.8 320.1 327.2 334.1 341.0 347.5 353.8 360.1 366.3 372.5 378.8 385.1 391.3 397.5 403.5 409.4 415.0 420.3 425.6 431.0 436.4 441.9 447.7 453.2 458.8 464.6 470.3 476.1 482.0 488.2 494.6 500.4 506.2 512.1

43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84

518.1 524.4 531.2 537.7 544.1 550.9 557.8 564.7 571.2 577.7 584.2 590.4 596.3 602.1 607.8 613.2 618.5 623.7 628.5 633.0 637.3 641.7 645.9 649.9 653.7 657.1 661.4 665.9 670.5 674.6 679.9 684.7 689.5 693.8 698.8 703.5 708.0 713.3 718.4 723.8 729.5 735.4

Anton Paar custom densitometer has been used to measure fluid density. The measuring cell is equipped with a U-shaped Hastelloy tube into which the fluid is transferred. The tube is vibrated electronically at its characteristic frequency which is dependent on the density of the fluid. The characteristic frequency was precisely determined and converted into the period of oscillation, which was displayed on the evaluation unit. The densitometer was calibrated with nitrogen and water using a wide range calibration method. The pressure inside the apparatus was measured and controlled by three different pressure transducers. An inline pressure transducer was installed as shown by equipment #5 in Figure 1. The transducer is a Rosemount 3051CG5A capable of measuring pressure between −0.1 to 13.8 MPa (−14.2 to 2000 psig) with an accuracy of 0.04%. The Quizix pumps were also equipped with pressure transducers. 2.3. Experimental Procedure. Prior to each experiment, the entire system was thoroughly cleaned to remove any potential contaminants including oil and solid particles. Toluene, acetone, and similar solvents were used to clean and remove bitumen, water, and 2875


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Figure 1. Apparatus for the phase behavior study of solvent/bitumen systems. any contaminants from the cells. To ensure that contaminants are not left inside the system, the cells and lines are successively evacuated and flushed with dry helium. Bitumen is charged into the equilibration cell using two Quizix pumps. The mass of the bitumen inside the equilibration cell is obtained by measuring its volume and density at a constant temperature and pressure. Next, n-pentane is charged into the cell following the same procedure. In this way, the mass fraction of the injected fluids is calculated. The Quizix pump maintains a constant pressure with an error of less than ±5 kPa. The equilibration cell is rocked to improve mixing for the solvent/ bitumen system. During the mixing period, we record the volume of water that is charged or discharged to maintain a constant pressure in the equilibration cell. Equilibrium is achieved when there is no recorded change in the cumulative volume of the water. To discharge the diluted bitumen from the top of the rocking cell, the equilibration cell is kept in a vertical position. Following this, the equilibrium fluid is discharged through the density measuring cell, maintaining a constant temperature and pressure. Both the in-line and Quizix pump pressure transducers measure the pressure. The value reported by the in-line pressure transducer, which is the exact system pressure, is reported as the equilibrium pressure. The phase sample is collected with steady readings of the density measuring cell, and the volume of saturated phase is measured by monitoring the volume of water charged into the equilibration cell.

instability in the system. Our experimental results indicated that, at 0.6 weight fraction of pentane, two phases (liquid−liquid or liquid−solid) formed at the equilibrium condition. The density of raw bitumen was measured over the specified pressure and temperature range in our previous study, and the data are listed in Table A1 (Appendix A). Tables 3 to 5 summarize the experimental density values of the pseudobinary mixture of bitumen and n-pentane at different temperatures, pressures, and n-pentane weight fractions. The uncertainty of pressure measurement was 0.01 MPa, and density measurements are with a 0.5 kg/m3 uncertainty. As the tables show, the density of the binary mixture decreases with increasing temperature at a constant pressure and increases with increasing pressure at a constant temperature. The density of the pseudobinary mixture is significantly decreased when the n-pentane weight fraction is increased at a constant temperature and pressure. The saturation pressure of n-pentane at temperature of 190 °C is 3.05 MPa. The mixtures with concentrations greater than 0.05 weight fraction of pentane form a vapor−liquid equilibrium at a constant temperature of 190 °C and a constant pressure of 2 MPa. Thus, no single phase was observed for a pressure less than 3 MPa and n-pentane concentration higher than 0.05 weight fraction. The impact of pressure on the density of pure n-pentane is more pronounced at high-temperature conditions (i.e., 150 and 190 °C). The critical temperature of n-pentane is 196.6 °C, and as the experimental temperature increased toward the critical point, the change in n-pentane density with the pressure became more significant. The same trend was also observed for the raw bitumen. That is, at higher temperatures (i.e., 150 and

3. RESULTS AND DISCUSSION As mentioned previously, the density of pentane-diluted bitumen was measured with different proportions of pentane at a constant temperature. Four different temperatures (50, 100, 150, and 190 °C) were used, and the pentane proportions were varied from 0.05 to 0.5 weight fractions including 0.05, 0.1, 0.2, 0.3, 0.4, and 0.5 fractions. A single liquid phase was observed for these experiments. The mixtures with a pentane concentration of higher than 0.5 weight fraction show asphaltene 2876


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Table 3. Experimental Liquid Densities of Pentane/Bitumen Mixtures at 0.05 and 0.1 Weight Fractions of Pentane; T, Temperature; P, Pressure; ρm, Density of Mixture w = 0.05

Table 4. Experimental Liquid Densities of Pentane/Bitumen Mixtures at 0.2 and 0.3 Weight Fractions of Pentane; T, Temperature; P, Pressure; ρm, Density of Mixture

w = 0.1

w = 0.2

w = 0.3

T/(°C)

P/MPa

ρm/(kg/m )

T/(°C)

P/MPa

ρm/(kg/m )

T/(°C)

P/MPa

ρm/(kg/m )

T/(°C)

P/MPa

ρm/(kg/m3)

189.8 189.8 189.8 189.8 189.8 150.3 150.3 150.3 150.3 150.3 100.7 100.7 100.7 100.7 100.7 50.3 50.3 50.3 50.3 50.3 22.6 22.6 22.6 22.6 22.6

1.99 4.03 6.03 8.00 9.98 2.02 4.00 6.01 8.02 10.00 2.01 4.04 5.98 7.98 9.93 2.02 4.02 6.01 8.03 10.01 2.01 3.97 6.01 7.96 9.92

876.1 878.2 880.4 882.5 884.5 902.5 904.4 906.2 907.9 909.6 934.0 935.5 936.9 938.2 939.6 964.8 966.0 967.3 968.2 969.7 982.2 983.0 984.2 985.2 986.2

190.3 190.3 190.3 190.3 190.3 150.6 150.6 150.6 150.6 150.6 100.5 100.5 100.5 100.5 100.5 50.0 50.0 50.0 50.0 50.0 23.1 23.1 23.1 23.1 23.1

2.01 4.03 6.04 8.01 9.99 1.97 4.01 6.00 7.99 10.01 2.02 4.03 6.04 7.98 10.02 2.01 4.02 6.05 8.09 10.00 2.01 4.03 5.98 7.99 9.97

845.3 848.1 850.5 852.8 871.2 873.2 875.2 877.2 879.1 904.5 906.2 907.7 909.2 910.8 937.4 938.6 940.0 941.2 942.5 954.7 955.8 956.9 958.1 959.2

190.0 189.8 189.8 189.8 189.8 150.9 150.9 150.9 150.9 150.9 99.7 99.7 99.7 99.7 99.7 49.5 49.5 49.5 49.5 49.5 22.3 22.3 22.3 22.3 22.3

2.00 4.04 6.10 7.92 9.93 2.04 3.99 5.93 8.01 10.02 2.03 4.01 6.02 8.02 10.04 2.00 4.00 6.01 8.00 10.03 2.02 4.04 6.01 7.99 10.00

787.1 790.6 793.3 796.4 814.6 817.3 819.9 822.6 825.1 852.5 854.4 856.3 858.0 859.8 887.8 888.9 890.2 891.5 892.9 905.0 906.9 908.3 909.7 911.0

190.0 189.6 189.6 189.6 189.6 150.5 150.5 150.5 150.5 150.5 101.0 101.0 101.0 101.0 101.0 49.8 49.8 49.8 49.8 49.8 22.4 22.4 22.4 22.4 22.4

2.00 4.01 5.98 7.95 9.96 2.01 4.03 6.02 8.01 10.00 2.03 4.00 6.03 8.00 10.03 1.99 4.04 6.03 8.02 10.03 2.02 4.03 6.01 8.00 10.03

730.5 735.0 738.9 742.7 761.5 765.0 768.2 771.2 774.2 802.1 804.4 806.8 809.0 811.2 840.0 841.9 843.6 845.3 846.9 860.5 861.9 863.4 864.8 866.3

3

3

figure, the density is plotted as a function of n-pentane weight fraction at different temperatures and at a constant pressure of 10 MPa. The symbols are the experimental data, and the lines are the predictions using equation 1. An examination of Figure 2 demonstrates that the mixture densities change significantly with the n-pentane weight fractions over the studied concentrations. The predictions are in good agreement with the measured data at the lowest temperature (23 °C). At a constant temperature of 190 °C and a constant pressure of 2 MPa, no single phase was observed at n-pentane concentrations greater than 0.05 weight fraction. The n-pentane is in a gaseous state at temperature of 190 °C and 2 MPa. To predict the mixture densities at this condition, the density of saturated liquid at temperature of 190 °C was used in the calculations. As the temperature increased, the deviation between the predicted densities and the measured values increased. It is not possible to present all of the data, but the same trends were observed at other pressures. For instance, the AARD at a temperature of 23 °C is higher than that of temperature 190 °C. It should be mentioned that the calculated AARD for all of the temperatures is in the acceptable range (2.50%) but its value, 6.00%, at high temperature (190 °C) is relatively high compared to 0.64% at low temperature (22 °C). Figure 3 illustrates the impact of pressure on the density of the mixture at different solvent weight fractions and at temperatures of 23 °C. The figure illustrates a linear relationship between the mixture density and pressure at a constant solvent weight fraction at the low temperature (23 °C). At the higher temperature condition (190 °C), a nonlinear trend is observed which is more pronounced at higher solvent concentrations.

190 °C), the impact of pressure on the density of bitumen was more significant than at lower temperatures (i.e., 23 °C). Although the density of bitumen is also reduced with temperature, its variation is not as significant as pure n-pentane. Variations of the mixture density with temperature and pressure are highly dependent on the n-pentane weight fraction. At low solvent concentrations (i.e., 0.05 weight fraction), the behavior of the mixture is similar to bitumen, whereas at high npentane weight fraction (i.e., 0.5), the mixture behavior is more similar to n-pentane. Thus, the variation of density with pressure is very low at the n-pentane weight fraction of the 0.05 compared to the n-pentane weight fraction of 0.5. 3.1. Prediction of Mixture Density. The measured density data of n-pentane/bitumen mixtures are predicted using the following equation, 1 ρm = w 1−w s + ρ s ρ s

B

3

(1)

where ws is the weight fraction of n-pentane, and ρs and ρB are the densities of n-pentane and bitumen, respectively. This equation was developed with the assumption that no volume change occurs upon mixing. The density values were predicted using the above equation, and the results were in agreement with the measured data, within a 2.50% average absolute relative deviation (AARD). The density of pure n-pentane was taken from the NIST database and that of raw bitumen at each temperature and pressure given in Table A1 of Appendix A were used for the calculations. Figure 2 displays the measured density data for the mixtures of n-pentane/bitumen along with the predicted values. In this 2877


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Table 5. Experimental Liquid Densities of Pentane/Bitumen Mixtures at 0.4 and 0.5 Weight Fractions of Pentane; T, Temperature; P, Pressure; ρm, Density of Mixture w = 0.4

w = 0.5

T/(°C)

P/MPa

ρm/(kg/m )

T/(°C)

P/MPa

ρm/(kg/m3)

190.0 190.2 190.2 190.2 190.2 150.6 150.6 150.6 150.6 150.6 100.3 100.3 100.3 100.3 100.3 50.4 50.4 50.4 50.4 50.4 22.5 22.5 22.5 22.5 22.5

2.00 4.01 6.04 8.01 9.98 2.01 4.00 6.00 8.00 10.01 1.98 4.00 6.01 7.99 9.96 2.04 4.06 6.05 8.02 10.04 1.97 4.04 5.95 8.00 10.01

675.1 681.6 686.9 692.1 710.1 714.7 719.1 723.0 726.1 756.4 759.3 762.1 764.5 767.0 796.2 798.3 800.3 802.2 804.1 817.5 819.3 820.8 822.5 824.1

190.0 189.8 189.8 189.8 189.8 150.6 150.6 150.6 150.6 150.6 100.5 100.5 100.5 100.5 100.5 50.0 50.0 50.0 50.0 50.0 22.7 22.7 22.7 22.7 22.7

2.00 4.02 5.99 8.07 9.99 1.98 3.99 5.99 8.00 10.00 2.02 4.05 6.04 8.02 10.03 2.00 4.00 6.03 8.02 10.00 1.99 3.97 5.99 7.99 9.98

613.2 622.3 629.3 635.7 659.8 665.7 671.0 675.7 681.8 714.4 717.8 720.8 723.7 726.6 757.7 760.0 762.2 764.3 766.3 779.8 781.6 783.4 785.1 786.9

3

Figure 3. Density of n-pentane/bitumen mixtures as a function of pressure at different n-pentane weight fractions and at the lowest temperature (23 °C); ○, ×, green ▲, blue ■, red ◆, +, experimental data; , ----, predicted values.

Figure 4. Density of n-pentane/bitumen mixtures as a function of pressure at different temperatures and at the lowest solvent weight fraction (0.05); ○, ×, green ▲, blue ■, red ◆, experimental data; , ----, predicted values.

highest n-pentane weight fraction (0.5). As depicted in these figures, the mixture density increases in a linear relationship with the pressure at different temperatures except at the highest temperature (190 °C). A comparison of Figures 4 and 5 reveals that equation 1 predicts the experimental data better at higher pressures. The deviation between the predictions and the measured data is greater at the lower pressures. It is also worth mentioning that at higher n-pentane concentrations or higher temperatures, equation 1 under-predicts the measured values. We can conclude that the volume change on mixing is a significant factor for mixtures of bitumen and n-pentane. The volume change on mixing is more pronounced at low pressures, high temperatures, and large solvent weight fractions where larger deviations from the measured data were obtained. The density of raw bitumen changes linearly with temperature at a constant pressure. The variations of mixture density with temperature at two different pressures (2 and 10 MPa) were shown in Figures 6 and 7. As depicted in these figures, all of the prepared mixtures follow a linear decrease in density with

Figure 2. Density of n-pentane/bitumen mixtures as a function of the weight fraction of n-pentane at different temperatures and at a constant pressure of 10 MPa; ■, ▲, ○, ◆, ×, experimental data; , ----, predicted values.

A closer examination of results reveals that the predictions at highest temperature (190 °C) and highest solvent concentration (0.5 weight fraction) deviate from experimental data. The variation of mixture density with pressure at other temperatures (i.e., 50, 100, and 150 °C), as it is shown in Figures 4 and 5, is linear for all temperatures except 190 °C over the studied pressure. This trend was observed for all measured concentrations. Figure 4 shows the variation of the mixture density with pressure at the lowest n-pentane weight fraction (0.05), while Figure 5 displays the same results at the 2878


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Figure 7. Density of n-pentane/bitumen mixtures as a function of temperature at different n-pentane weight fractions and at the highest pressure (10 MPa); ○, ×, green ▲, blue ■, red ◆, +, experimental data; , ----, predicted values.

Figure 5. Density of n-pentane/bitumen mixtures as a function of pressure at different temperatures and at the highest solvent weight fraction (0.5); ○, ×, green ▲, blue ■, red ◆, experimental data; , ----, predicted values.

the materials and the co-operative accommodation of the molecules influence the volume change on mixing. Petroleum fluids contain molecules with different sizes and structures and different densities. For this reason, mixtures containing petroleum compounds almost show volume change upon mixing. The mixtures of bitumen and n-pentane were affected by volume change during mixing. Although the volume change is not significant for specific pressure and temperature ranges, its value varied with the operating parameters. As the modeling results in previous section illustrate, the assumption of no volume change in the calculation of the mixture densities resulted in under-prediction of the measured data. This indicates that mixtures of bitumen and n-pentane undergo a negative volume change upon mixing. That is, the total volume of the mixture is reduced during the process of mixing. The negative volume change was observed for all measured data at different temperatures, pressures, and solvent weight fractions. The volume change upon mixing is calculated with the following equation,

Figure 6. Density of n-pentane/bitumen mixtures as a function of temperature at different n-pentane weight fractions and at the lowest pressure (2 MPa); ○, ×, green ▲, blue ■, red ◆, experimental data; , ----, predicted values.

ΔVmixing = Vfinal,m − Vinitial,B − Vinitial,s

temperature up to 150 °C. In fact, when the temperature approaches the critical temperature of n-pentane, the variation of mixture densities with temperature deviates from the linear decreasing trend. A comparison of Figures 6 and 7 confirms that a linear decrease in the density of the mixture with temperature was observed for all measured pressures. The density data at the highest n-pentane weight fraction (0.5) deviate slightly from the linear trend due to the nonlinear trend of the density with temperature for n-pentane at a constant pressure. 3.2. Volume Change on Mixing. The properties of mixtures are often relatively dissimilar to the properties of the species comprising the mixtures. When two species or components are mixed, the volume of the mixture may be different than the sum of the volume of each component. This means that the total volume may increase or decrease during mixing. In chemically similar components with the same sizes such as toluene and benzene, volume change upon mixing is negligible; however, unlike components and/or similar molecules with different sizes, such as alcohols and water experience a significant change in volume during mixing. Thus, the structure of

(2)

The summation of the volumes of each component before mixing is called the ideal volume. If the volume change upon mixing is zero, the solution is known as an ideal solution, Videal,mix = Vinitial,B + Vinitial,s

(3)

As presented earlier, the value of volume change upon mixing varied with the operating parameters. To evaluate the impact of each different parameter on the volume change, the following dimensionless parameter is used, ΔVmixing Videal,mix

=

1 ρm,exp

− ws ρs

(

ws ρs

+

+

1 − ws ρB

1 − ws ρB

) (4)

where ws is the weight fraction of n-pentane, ρs and ρB are the densities of n-pentane and bitumen, respectively, and ρm,exp is the measured density of the mixture. The predicted densities in the previous section confirmed that, at a constant pressure and solvent weight fraction, the deviation between the measured data and the calculated values 2879


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components and their molecular behavior changes when the operating conditions are adjusted. The measured volume change on mixing reduced as the pressure was increased at a constant temperature. This is due to a more compact arrangement of the n-pentane molecules in the bitumen molecules. As the pressure increases at a constant temperature, the densities of the raw bitumen and pure n-pentane increased. The molecules of each component are forced closer together as the pressure increases, reducing their occupied volume. The same behavior occurs in the mixtures, where molecules of different sizes are forced into a tighter configuration. The effect of pressure on the volume change during mixing at the lowest temperature (23 °C) is negligible for all solvent weight fractions. As the temperature increases, the volume change on mixing with pressure becomes significant. At two of the high-temperature conditions (150 and 190 °C), a substantial change in volume on mixing is observed and the variations can be described as a nonlinear function of pressure. Figure 10 illustrates the change in the volume during the

became significant when the temperature was increased. This is an indirect representation of the increase in volume change on the mixing with temperature. However, when the calculated values from equation 4 are plotted with respect to the temperature at a constant pressure and constant solvent weight fraction, we found that the volume change upon mixing is directly affected by the temperature. Figures 8 and 9 illustrate

Figure 8. Effect of temperature on the volume change on mixing for n-pentane/bitumen mixtures with different solvent weight fractions at a constant pressure of 2 MPa.

Figure 10. Effect of pressure on the volume change on mixing for n-pentane/bitumen mixtures with different solvent weight fractions at 190 °C.

mixing process for n-pentane/bitumen mixtures at the highest temperature (190 °C). The decreasing trend of the volume change on mixing with the pressure was observed at five different temperatures and six n-pentane weight fractions. The mixture of n-pentane/bitumen with 0.05 weight fraction of solvent exhibits a lesser pressure dependence than that of a 0.5 weight fraction of solvent where a larger decrease in the volume change on mixing is measured for each pressure change. To evaluate the impact of temperature and pressure on the volume change on mixing, the volume change can be plotted as a function of pressure at different temperatures and at a constant weight fraction of pentane. At 0.05 pentane weight fraction, the impact of pressure is insignificant. However, when the solvent weight fraction is increased to 0.1 or 0.2, the variation of the volume change on mixing with pressure becomes important. Figure 11 demonstrates the volume change on mixing as a function of pressure at the highest solvent weight fraction (0.5). As anticipated from the figure, the volume change on mixing at the ambient temperature (23 °C) even at high solvent weight fractions is negligible. We conclude that, at ambient temperature, the volume change on mixing for mixtures of n-pentane/bitumen over the entire concentration

Figure 9. Effect of temperature on the volume change on mixing for n-pentane/bitumen mixtures with different solvent weight fractions at a constant pressure of 10 MPa.

the dimensionless volume change as a function of temperature at a constant pressure. The figures illustrate that the volume change upon mixing increases with the temperature. Although the magnitude of the increase in the volume change on mixing is not the same at different pressures, the increasing trend was observed for all measured pressures. The effect of the solvent weight fraction on the volume change upon mixing is depicted in Figures 8 and 9. Increasing the solvent weight fraction enhances the volume change on mixing for the mixtures. We were able to accurately predict this trend because the mixture of two components has zero volume change on mixing at infinite dilution of each component. The density of raw bitumen and pure n-pentane is a function of temperature and pressure. Thus, the volume of the 2880


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Figure 11. Effect of pressure on the volume change on mixing for n-pentane/bitumen mixtures at a constant solvent weight fraction of 0.5 and at different temperatures.

Figure 13. Volume change on mixing for n-pentane/bitumen mixtures as a function of the weight fraction of pentane at different temperatures and at a constant pressure of 10 MPa.

range is insignificant, and equation 1 can adequately predict the density of mixture. The volume change on mixing increases as the solvent weight fraction in the mixture increases. In the binary systems such as (n-hexane + n-decane), the volume change on mixing reaches a minimum or maximum value at a specific concentration. For the bitumen/n-pentane mixtures, the volume change on mixing increases with the n-pentane weight fraction over the entire concentration range considered in this study. As previously mentioned, the mixtures show a negative volume change during mixing. A negative volume change on mixing over the entire concentration range indicates that the mixture forms a more compact molecular structure than the pure species. Figures 12 and 13 illustrate the volume change on mixing for the n-pentane/bitumen mixture as a function of the solvent

mixing at a constant temperature. Similar to the binary hydrocarbon systems, the pressure reduced the maximum value of the volume change on the mixing and forced the concave curve toward a zero value. As expected from the binary hydrocarbon mixtures, the volume change on mixing should increase with the increasing solvent weight fraction to a maximum and then begin to decrease toward zero. However, as depicted in Figure 12 for the bitumen/n-pentane mixtures for the solvent concentrations considered in this study, the volume change on mixing flatten off after the n-pentane weight fraction of 0.3. 3.3. Improvement in the Calculation of Mixture Density. The densities calculated using equation 1 resulted in an under-prediction of the measured data. As discussed earlier, the volume change on mixing for the n-pentane/ bitumen mixtures is significant especially at high temperatures. This section presents three approaches to improve the calculation of the densities. The first approach considers the excess volume in the prediction of the densities, and the second approach applies the concept of effective liquid densities to represent the measured densities. The third approach shows the application of equation of state for density predictions. 3.3.1. Excess Volume Mixing Rule. The measured density data for the n-pentane/bitumen mixtures are correlated with the following equation,24 ⎡1 w 1 − ws 1 1⎤ ⎥β = s + − ws(1 − ws)⎢ + ⎢⎣ ρs ρm ρs ρB ρB ⎥⎦ ij

(5)

where ws is the weight fraction of n-pentane, and ρs and ρB are the densities of n-pentane and bitumen, respectively. The last term accounts for the volume change on mixing, and βij is the binary interaction parameter between n-pentane and bitumen obtained by the regression of the measured densities. The density values were correlated using the above equation, and the results were in agreement with the measured data. The best-fitted binary interaction parameter (βij) was 0.0556, which gave the lowest average absolute relative deviation (1.58%). 3.3.2. Effective Liquid Densities. The density of the mixtures with a dissolved gas can be predicted by equation 1 using the effective liquid density for the gas. Tharanivasan et al.25 proposed a method based on the extrapolated molar volume of liquid normal alkanes to obtain the effective liquid molar volumes of light normal alkanes present in the gaseous state in

Figure 12. Volume change on mixing for n-pentane/bitumen mixtures as a function of the weight fraction of pentane at different temperatures and at a constant pressure of 2 MPa.

weight fraction at a constant pressure. Figure 12 shows the results at a pressure of 2 MPa, and Figure 13 demonstrates the measurements at a pressure of 10 MPa. As depicted in Figures 12 and 13, increasing the solvent weight fraction results in a larger volume change on mixing. Additionally, the pressure reduces the volume change on the 2881


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pure form. The authors plotted the molar volume of liquid normal alkanes with respect to the molecular weight and extrapolated the curve to determine the effective liquid molar volumes of light normal alkanes. Tharanivasan et al.25 reported the effective liquid densities for normal alkanes at pressures above 10 MPa. Recently, Saryazdi26 found that the correlation proposed by Tharanivasan et al.25 resulted in higher values for the molar volumes of the lightest liquid n-alkanes. Saryazdi26 explained this overprediction by the proximity of the n-alkanes to their critical points and proposed a plot of the molar volumes of only the higher n-alkanes. Saryazdi26 found a linear molar volume trend for the higher n-alkanes. The author redeveloped the effective density correlation using the molar volumes of the higher liquid n-alkanes whose molar volumes were linearly related to their molecular weight. Thus, the higher n-alkane molar volumes at fixed temperatures and pressures were extrapolated linearly to determine new effective molar volumes for the lighter n-alkanes. The effective molar volumes were then converted to density and plotted versus pressure at fixed temperatures. Saryazdi et al.27 proposed the following equation for the effective densities of n-pentane,

Table 6. Properties of Pseudo-Components for the Peng− Robinson Equation of State; MW, Molecular Weight; Tc, Critical Temperature; Pc, Critical Pressure; w, Acentric Factor; SG, Specific Gravity MW (g/mol)

Tc (°C)

Pc (MPa)

w

SG

PC1 PC2 PC3 PC4

209.9 379.0 886.5 2140.0

450.2 587.7 756.3 961.1

2.34 1.50 0.81 0.55

0.547 0.869 1.308 1.584

0.888 0.955 1.027 1.156

Table 7. Deviations of Different Models for the Calculation of n-Pentane/Bitumen Mixture Densities calculation method

AARDa (%)

AADb (kg/m3)

MADc (kg/m3)

no volume change excess volume effective density Peng−Robinson

2.50 1.58 0.57 0.55

19.2 12.3 4.4 4.4

86.0 68.4 31.4 13.0

a

AARD: average absolute relative deviation. bAAD: average absolute deviation. cMAD: maximum absolute deviation.

The density of n-pentane/bitumen was then predicted with the tuned equation-of-state model. Table 7 summarizes the calculated deviations of the models for predicting the mixture densities. As the deviations show, the best results are obtained using the Peng-Robinson equation of state and the effective liquid densities approach, followed by the excess volume mixing rule, and then the no volume change assumption. Figures 14 to 17 are the dispersion plots of the calculated densities versus the measured values for the mixtures of

ρ = 878.006 − 0.82817T + ( − 0.0923 + 2.6481 × 10−3T )P

component

(6)

where ρ is the density in kg/m3, T is the temperature in Kelvin, and P is pressure in MPa. The measured densities of the n-pentane/bitumen were predicted using equation 1 along with the effective densities of n-pentane obtained using equation 6. The results are accurately predicted with this approach. The densities of raw bitumen at each temperature and pressure are given in Table A1 of Appendix A. 3.3.3. Equation-of-State Modeling. The density of the mixtures was also predicted with Peng−Robinson28 equation of state. The compositional analysis data for the bitumen sample was used for the characterization. The characterization method developed in the previous studies29,30 was applied. On the basis of the distillation data, 94 hydrocarbon components were assigned to the distillable fraction (C100), and one pseudocomponent was defined for the nondistillable fraction. The defined components adequately represent the molecular weight and specific gravity of bitumen as well as the distillation curve of bitumen. The critical properties and eccentric factor were obtained from the correlation proposed by Kesler and Lee.31 The critical volumes of components were calculated from Twu’s correlation.32 The pressure-temperature two-phase envelope was obtained with the Peng−Robinson equation of state using a full number of components. All components were then lumped into four pseudocomponents, while the pressure−temperature diagram was generated and compared with full characterization scheme. To improve the volumetric results, a volume translation according to Peneloux et al.33 was considered for Peng−Robinson equation of state. Linear temperature-dependent volume shifts based on Pedersen et al.34 study were applied to pseudocomponents to match the density of raw bitumen over the studied temperature and pressure ranges. The model predicted the density of bitumen with MAD, AAD, and AARD values of 0.8, 0.4, and 0.04%, respectively. Table 6 summarizes the properties of pseudocomponents.

Figure 14. Calculated densities of n-pentane/bitumen mixtures using no volume change on the mixing assumption versus the measured values.

n-pentane/bitumen using four different approaches. The excess volume mixing rule slightly improves the accuracy of the predictions when compared with the method that assumes no volume change on mixing. Considering the effective liquid densities for n-pentane significantly improves the predictions. The density values are well-predicted by the Peng−Robinson equation of state. Figures 18 and 19 display the measured densities for the mixtures of n-pentane/bitumen along with the calculated values. In Figure 18, the density is plotted as a function of 2882


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Figure 15. Calculated densities of n-pentane/bitumen mixtures using the excess volume mixing rule versus the measured values.

Figure 18. Density of n-pentane/bitumen mixtures as a function of the weight fraction of n-pentane at different temperatures and at a constant pressure of 4 MPa; blue ■, green ▲, ○, red ◆, pink ×, experimental data; ----, excess volume mixing rule; , effective liquid densities; , Peng−Robinson equation of state.

Figure 16. Calculated densities of n-pentane/bitumen mixtures using effective liquid densities versus the measured values. Figure 19. Density of n-pentane/bitumen mixtures as a function of pressure at different n-pentane weight fractions and at the highest temperature (190 °C); ○, pink ×, green ▲, blue ■, red ◆, +, experimental data; ----, excess volume mixing rule; , effective liquid densities; , Peng−Robinson equation of state.

from the figures, the application of the effective liquid densities and equation of state for the prediction of mixture densities resulted in close agreement between the measured and the calculated data. Although the excess volume mixing rule with one adjustable parameter slightly improved the correlations, the calculated values show large deviations from the experimental data at high temperatures and at high solvent weight fractions.

4. CONCLUSION The experimental results in this study indicated that, at higher temperatures (i.e., 150 and 190 °C), the impact of pressure on the density of pentane and raw bitumen was more significant than at lower temperatures (i.e., 23 °C). Variations of the mixture density with temperature and pressure are highly dependent on the n-pentane weight fraction. At low n-pentane concentrations (i.e., 0.05 weight fraction), the behavior of the mixture is similar to bitumen, whereas at high n-pentane weight fraction (i.e., 0.5), the mixture behavior is more similar to

Figure 17. Calculated densities of n-pentane/bitumen mixtures using the Peng−Robinson equation of state versus the measured values.

n-pentane weight fraction at different temperatures and a constant pressure (4 MPa). Figure 19 illustrates the impact of pressure on the density of the mixture at different solvent weight fractions at a temperature of 190 °C. As anticipated 2883


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n-pentane. Thus, the variation of density with pressure is very low at the n-pentane weight fraction of the 0.05 compared to n-pentane weight fraction of 0.5. There is a negative volume change upon mixing for the pentane/ bitumen system, which should be considered for predicting the density of the mixture especially at high temperatures or solvent concentrations. The measured volume change on mixing increases with temperature and solvent weight fraction and reduces with pressure. Although the assumption of no volume change on mixing leads to large deviations from the experimental data, it can reasonably predict the data at low temperatures (22 and 50 °C). The excess volume mixing rule slightly improves the density predictions over the entire range. However, the modeling results show that the mixture densities are well-predicted with considering the effective liquid density for n-pentane or using the Peng−Robinson equation of state.

■

H.N.: Computer Modelling Group Ltd., Calgary, AB, Canada. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS The authors wish to express their appreciation for the financial support of all member companies of the SHARP consortium: Alberta Innovates Energy and Environment Solutions, Athabasca Oil Sands, Brion Energy, Chevron Energy Technology Co., Computer Modelling Group Ltd., ConocoPhillips Canada, Devon Canada Co, Foundation CMG, Husky Energy, Japan Canada Oil Sands Limited, Nexen Energy ULC, Laricina Energy Ltd., Natural Sciences and Engineering Research Council of Canada (NSERC-CRD), OSUM Oil Sands Co., PennWest Energy, Statoil Canada Ltd., Suncor Energy, and Total E&P Canada. The Department of Chemical and Petroleum Engineering at the University of Calgary is also acknowledged.

APPENDIX A

■

Table A1 is shown here. Table A1. Experimental Density ρ of Bitumen at Temperatures T and Pressures P Tc/(°C)

P/MPa

ρ/(kg/m3)

Tc/(°C)

P/MPa

ρ/(kg/m3)

190.0 174.6 150.3 125.0 100.6 89.8 79.9 69.9 20.1 49.9 23.0 190.0 174.6 150.3 125.0 100.6 89.8 79.9 69.9 60.1 49.9 23.0 190.0 174.6 150.3 125.0 100.6 89.8 79.9 69.9 60.1 49.9 23.0

2.01 2.01 2.02 1.99 2.02 2.00 2.01 2.01 2.00 2.01 1.99 4.00 4.06 4.01 4.00 4.06 3.99 3.99 4.00 4.01 4.00 4.02 6.00 6.01 5.98 6.00 6.02 6.01 5.99 6.01 6.01 6.01 6.00

907.6 917.3 932.7 947.9 962.6 969.1 974.9 980.9 986.7 992.9 1009.3 909.5 918.6 934.3 949.4 964.0 970.3 976.1 982.0 987.8 994.0 1010.1 911.5 920.8 935.9 950.8 965.3 971.6 977.2 983.2 989.0 995.0 1011.0

190.0 174.6 150.3 125.0 100.6 89.8 79.9 69.9 60.1 49.9 23.0 190.0 174.6 150.3 125.0 100.6 89.8 79.9 69.9 60.1 49.9 23.0

8.00 8.00 8.02 8.01 8.01 8.00 8.01 8.00 8.01 8.01 8.00 10.01 10.01 10.00 10.01 10.01 10.00 9.99 10.01 10.01 10.00 10.01

913.3 922.5 937.5 952.3 966.6 972.8 978.5 984.4 990.1 996.1 1012.0 915.2 924.1 939.0 953.7 967.8 974.1 979.6 985.5 991.3 997.2 1012.9

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AUTHOR INFORMATION

Corresponding Author

*J.A.: E-mail: [email protected]; Tel.: 403-220-5594. 2884


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