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Diffusion coefficients and oil swelling factors of carbon dioxide, methane, ethane, propane, and their mixtures in heavy oil
Fluid Phase Equilibria 243 (2006) 64–73
Diffusion coefficients and oil swelling factors of carbon dioxide, methane, ethane, propane, and their mixtures in heavy oil Chaodong Yang, Yongan Gu ∗ Petroleum Technology Research Centre (PTRC), Faculty of Engineering, University of Regina, Regina, Saskatchewan, Canada S4S 0A2 Received 10 January 2006; received in revised form 13 February 2006; accepted 18 February 2006 Available online 6 March 2006
Abstract In this paper, a newly developed dynamic pendant drop volume analysis (DPDVA) method is applied to measure the diffusion coefficients and oil swelling factors of four pure solvents (carbon dioxide, methane, ethane, and propane) and three solvent mixtures (mixture #1: 70 mole% carbon dioxide + 30 mole% propane, mixture #2: 70 mole% methane + 30 mole% propane, and mixture #3: 70 mole% ethane + 30 mole% propane) in Lloydminster heavy oil in the pressure range of 0.4–14.0 MPa and at T = 23.9 ◦ C. The experimental results show that both the diffusion coefficient and the oil swelling factor of a heavy oil–solvent system increase with pressure. In particular, the diffusion coefficients and oil swelling factors of propane and ethane in heavy oil at pressures slightly lower than their respective vapour pressures are relatively large (D ≥ 0.680 × 10−9 m2 /s, fsw ≥ 1.314). It is also found that the apparent diffusion coefficients and the apparent oil swelling factors of the three solvent mixtures at pressures slightly below their respective dew-point pressures are large (Da ≥ 0.706 × 10−9 m2 /s, fsw ≥ 1.351). The experimental results clearly indicate that there exist certain correlations among the diffusion coefficient, oil swelling factor, solubility, and viscosity of a heavy oil–solvent system. Further experimental and theoretical studies are needed to determine these correlations. © 2006 Elsevier B.V. All rights reserved. Keywords: Diffusion coefficient; Oil swelling factor; Heavy oil; Solvent; Vapour extraction (VAPEX) process
1. Introduction With the depletion of conventional crude oil reserves in the world, heavy oil and bitumen resources have great potential to meet the future demand for petroleum products. However, oil recovery from heavy oil and bitumen reservoirs is much more difficult than that from conventional oil reservoirs. This is mainly because heavy oil or bitumen is partially or completely immobile under reservoir conditions due to its extremely high viscosity. The vapour extraction (VAPEX) process, which employs hydrocarbon or non-hydrocarbon solvents to recover heavy oil or bitumen, has attracted more attention in recent years [1–3]. In the VAPEX process, a pure solvent, such as carbon dioxide, methane, ethane, propane, butane, or a solvent mixture, is injected from an upper horizontal well into a heavy oil reservoir at a pressure slightly below its vapour pressure or dew-point pressure. The solvent dissolves into heavy oil and reduces its viscosity. The diluted oil drains by gravity to a lower horizontal
∗
Corresponding author. Tel.: +1 306 585 4630; fax: +1 306 585 4855. E-mail address: [email protected] (Y. Gu).
0378-3812/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.fluid.2006.02.020
production well. The production rate of VAPEX is strongly dependent on the oil viscosity reduction, which in turn depends on the dissolution of the solvent into heavy oil mainly through molecular diffusion. Previous studies have shown that molecular diffusion of the injected solvent in heavy oil plays a vital role in the VAPEX process [4–7]. Thus the diffusion coefficient of a solvent in heavy oil under the practical reservoir conditions becomes an important parameter for the reservoir simulation and field design of the VAPEX process. A large database of the diffusion coefficients of various heavy oil–solvent systems can be further used in the optimization of solvent composition and in the determination of injection pressure in the VAPEX process. Swelling of crude oil due to solvent dissolution is a wellknown phenomenon [8–11]. Oil swelling has two benefits to oil recovery [8,12]. First, oil swelling can mobile some of the residual oil so that it can be recovered. Flow visualization studies in two-dimensional micro-models qualitatively confirmed the oil swelling effect on mobilizing residual oil [13]. Second, oil swelling also increases oil saturation and consequently the relative permeability of oil. Therefore, accurate measurement of the oil swelling factor of a heavy oil–solvent system will help
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to achieve a better understanding of oil recovery mechanisms involved in the VAPEX process. In the literature, there are limited data of solvent diffusion coefficients and oil swelling factors of heavy oil–solvent systems. The purpose of this study is to measure the solvent diffusion coefficients and oil swelling factors of carbon dioxide, methane, ethane, propane, and their mixtures in heavy oil in a broad range of solvent injection pressure. The experimental measurements are conducted by applying the newly developed dynamic pendant drop volume analysis (DPDVA) method [14,15]. It is worthwhile to point out that the DPDVA method has several distinct advantages over the other existing methods. For example, with the DPDVA method, a single experimental test can be completed within 2 h and both the solvent diffusion coefficient and the oil swelling factor of a heavy oil–solvent system can be measured simultaneously. Second, this method allows the measurement of solvent diffusion coefficient and oil swelling factor at a high pressure and a constant temperature. Furthermore, the DPDVA method is applicable for measuring the apparent diffusion coefficient and the apparent oil swelling factor of a heavy oil–solvent mixture system. 2. Dynamic pendant drop volume analysis method The DPDVA method determines the solvent diffusion coefficient and the oil swelling factor of a heavy oil–solvent system at the same time. In the experiment, a see-through windowed highpressure cell is filled with a test solvent at pre-specified pressure and temperature. Then a heavy oil sample is introduced to form a pendant oil drop inside the pressure cell. Subsequent solvent dissolution into the pendant oil drop causes its volume to increase until it is completely saturated with the solvent. The sequential digital images of the dynamic pendant oil drop are acquired and analyzed to measure the oil drop volumes at different times. Theoretically, a mass transfer model is formulated to describe the diffusion process of the solvent in the pendant oil drop. This model is solved numerically by applying the semi-discrete Galerkin finite element method. Thus the volume of the dynamic pendant oil drop at any time is calculated from the predicted transient solvent concentration distribution inside the pendant oil drop. Mathematically, an objective function is constructed to express the discrepancy between the theoretically calculated and experimentally measured volumes of the dynamic pendant oil drop at different times. The solvent diffusion coefficient and the oil swelling factor of the heavy oil–solvent system are used as adjustable parameters and thus determined once the objective function is minimized. A brief description of the DPDVA method is given below and its technical details can be found elsewhere [14,15]. 2.1. Mass transfer model Fig. 1 shows an axisymmetric pendant oil drop surrounded by a test solvent. The outer radius of the syringe needle is rn , the wall thickness of the needle is εn , and the height of the syringe needle is hn . The heavy oil inside the pendant drop, including the heavy oil inside the syringe needle, is chosen as the computational
Fig. 1. Schematic diagram of an axisymmetric pendant oil drop surrounded by a solvent depicted in the cylindrical coordinate system (r, z).
domain, which is denoted by Ω. The boundaries formed between the syringe needle and the heavy oil together with the cutting plane at the top of the syringe needle are expressed by Φn . In this study, the cutting plane is chosen far above the tip of the syringe needle so that solvent diffusion cannot reach it during the diffusion test. The surface of the pendant oil drop, i.e., the heavy oil–solvent interface, is represented by Φint . In the cylindrical coordinate system as shown in Fig. 1, the diffusion equation for describing the solvent concentration distribution inside the computational domain Ω can be expressed in the following dimensionless form [16]: ∂C 1 ∂ ∂C ∂2 C = R + , (R, Z) ∈ Ω, τ > 0, (1) ∂τ R ∂R ∂R ∂Z2 with the following initial and boundary conditions: C(R, Z, τ)|τ=0 = 0, C(R, Z, τ) = 1,
(R, Z) ∈ Ω,
(2)
(R, Z) ∈ Φint , τ > 0,
(3)
∂C ∂C nR + nZ = 0, ∂R ∂Z
(R, Z) ∈ Φn , τ > 0,
where the dimensionless variables are defined as: c r z t C= , R= , Z= , τ= 2 . csat rn rn rn /D
(4)
(5)
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Here, c is the molar concentration of the solvent in heavy oil, i.e., the number of moles of solvent dissolved into per unit volume of heavy oil, csat the solvent concentration in the solvent-saturated heavy oil at the experimental pressure and temperature, r the radial coordinate, z the axial coordinate, t time, D the diffusion coefficient of the solvent in heavy oil, and nR and nz are the direction cosines, i.e., R and Z components of the outward unit vectors normal to the boundaries. By applying the semi-discrete Galerkin finite element method [17], Eq. (1) subject to Eqs. (2)–(4) is solved numerically to obtain the dimensionless solvent concentration distribution, C(R,Z,τ), (R,Z) ∈ Ω. The detailed mathematical formulations of the Galerkin finite element method for solving the diffusion Eq. (1) inside the computational domain can be found in the literature [18].
be seen from Eq. (6) that the above-defined objective function E is merely dependent on two to-be-determined parameters, i.e., the diffusion coefficient D and the oil swelling factor fsw of the heavy oil–solvent system. Therefore, D and fsw can be used as the adjustable parameters to minimize the objective function E [21]. Once the global minimum objective function is found, the corresponding global optimum values of D and fsw are considered as the measured solvent diffusion coefficient and oil swelling factor, respectively. Two previous articles [14,15] presented the detailed numerical procedure for simultaneously determining the solvent diffusion coefficient and the oil swelling factor by minimizing the objective function. 3. Experimental 3.1. Materials
2.2. Theoretical prediction of the dynamic pendant oil drop volume In the phase behavior studies, oil swelling factor is often used to quantify the oil swelling effect when a solvent dissolves into heavy oil [8,19,20]. In this paper, symbol fsw is used to represent the oil swelling factor, which is defined as the ratio of the volume of the solvent-saturated heavy oil to the volume of the original heavy oil without any solvent dissolution. The volume of the dynamic pendant oil drop at any time t is equal to the sum of the initial heavy oil drop volume and the volume change due to the solvent dissolution into the heavy oil [15]: D(t + tf ) 3 Vc (t) = V0 + (fsw − 1)rn C R, Z, rn2 −C R, Z,
(R,Z) ∈ Ω
Dtf rn2
πR dR dZ.
(6)
where Vc (t) is the calculated volume of the dynamic pendant oil drop at any time t, V0 the measured initial volume of the dynamic pendant oil drop at t = 0, and tf is the time needed to form a well-shaped pendant heavy oil drop inside the pressure cell. 2.3. Objective function and its minimization Let Vm (t) be the measured volume of the dynamic pendant oil drop and Vc (t) be the calculated volume of the dynamic pendant oil drop at any time t, 0 ≤ t ≤ tm , where tm is the total duration of the diffusion test. In this study, the root-mean-squared relative error between the theoretically calculated and experimentally measured volumes of the dynamic pendant oil drop is used to define the objective function E: 1 tm Vm (t) − Vc (t) 2 dt × 100%. (7) E= tm 0 Vm (t) Once the volumes of the dynamic pendant oil drop at different times are measured, the objective function depends on the theoretically calculated volumes only. Furthermore, it can
The heavy oil sample is collected from the Lloydminster area, Canada. Prior to usage, the heavy oil sample is cleaned to remove brine, fine solids, and any solution gas. The density of the cleaned heavy oil sample is 988 kg/m3 and its viscosity is 23,000 mPa s at T = 23.9 ◦ C. The asphaltene content of the heavy oil is 11.5 wt.% (n-heptane insoluble). The heavy-ends of C50+ for this heavy oil are 47.5 wt.%. Carbon dioxide, methane, ethane, and propane are purchased from Praxair Canada with stated purity of 99.99%, 99.97%, 99.0%, and 99.5%, respectively. Theses four solvents are used to prepare solvent mixture #1 (70 mole% carbon dioxide + 30 mole% propane), solvent mixture #2 (70 mole% methane + 30 mole% propane), and solvent mixture #3 (70 mole% ethane + 30 mole% propane). The vapour pressures of carbon dioxide, methane, ethane, and propane are found to be Pv = 6.28, 31.38, 4.12, and 0.93 MPa at T = 23.9 ◦ C [14], respectively. The CMG WinProp (Version 2004.12, Computer Modelling Group Ltd., Canada) software is used to determine the phase diagrams of three solvent mixtures. It is found that the dew-point pressures of solvent mixture #1, solvent mixture #2, and solvent mixture #3 are equal to Pdew = 3.27, 4.79, and 2.19 MPa at T = 23.9 ◦ C, respectively. In this study, the solvent diffusion coefficients and the oil swelling factors of the four heavy oil–pure solvent systems and the apparent diffusion coefficients and the apparent oil swelling factors of three heavy oil–solvent mixture systems are measured at T = 23.9 ◦ C. This temperature is chosen as it is the same as that of the actual heavy oil reservoir from which the oil sample is collected and used in this study. The experimental pressures are selected to cover most practical cases of interest for the VAPEX process, which requires the solvent injection pressure to be slightly lower than the vapor pressure of a pure solvent or the dew-point pressure of a solvent mixture at the temperature of interest. 3.2. Apparatus Fig. 2 shows the schematic diagram of the experimental setup used in this study. The major component of the setup is a seethrough windowed high-pressure cell (IFT-10, Temco, USA).
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Fig. 2. Schematic diagram of the experimental setup used for measuring the solvent diffusion coefficient and the oil swelling factor of a heavy oil–solvent system by applying the dynamic pendant drop volume analysis (DPDVA).
The pressure cell has a chamber volume of 41.5 cm3 and can sustain pressures up to 69 MPa. The maximum working temperature of the pressure cell is 177 ◦ C. The syringe needle used to form the pendant oil drop is made of stainless steel. Its outer radius is rn = 0.79 mm, wall thickness is εn = 0.59 mm, and height is hn = 2.40 mm. Heavy oil is introduced from a heavy oil sample cylinder to the syringe needle by using a programmable syringe pump (100DX, ISCO Inc., USA). A heated waterbath (DC10, Thermo Hakke, USA) is used to control the temperature of the pressure cell by circulating water at a constant temperature of T = 23.9 ◦ C. Meanwhile, the room temperature is also set at the same constant temperature to minimize the temperature fluctuations. It is found in the experiments that temperature variations are within ±0.2 ◦ C. The pressure inside the high-pressure cell is measured by using a digital pressure gauge (DTG-6000, 3D Instruments, USA). The accuracy of the pressure gauge is 0.007 MPa in the pressure range of 0–6.89 MPa, and 0.007–0.034 MPa in the pressure range of 6.89–34.5 MPa, respectively. A light source and a Teflon diffuser are used to provide uniform illumination for the pendant oil drop inside the pressure cell. A microscope camera (MZ6, Leica, Germany) is used to acquire the sequential digital images of the dynamic pendant oil drop. The high-pressure cell is placed between the light source and the microscope camera. The high-pressure cell, light source, diffuser, and microscope camera are placed on a vibration-free table (RS4000, Newport, USA). The digital images of the dynamic pendant oil drop at different times are acquired sequentially in tagged image file format (TIFF) with resolution of 640 × 480 pixels by using a digital frame grabber (Ultra II, Coreco Imaging, Canada). A DELL desktop computer is used to store the digital images and perform subsequent image analyses. This PC-based optical system can be used to grab the sequential digital drop images at a speed of three images per second.
3.3. Experimental procedure Prior to the diffusion test for a heavy oil–solvent system, the high-pressure cell is thoroughly cleaned with kerosene and acetone, flushed with nitrogen, and finally purged with a test solvent at least five times. Then the solvent is introduced into the high-pressure cell from a solvent cylinder. After the solvent is injected, it usually takes less than 30 min for the pressure and temperature inside the pressure cell to reach their stable values. A heavy oil sample is introduced by using the syringe pump to form a pendant oil drop at the tip of the syringe needle, which is installed at the top of the high-pressure cell. Once the pendant oil drop is formed, a digital image acquisition program (TciPro, Coreco Imaging, Canada) is executed to acquire its sequential images during the diffusion test. The time intervals for the sequential image acquisition are preset properly so that they are smaller at the beginning and larger at the end of the diffusion test. These digital drop images are automatically stored in the computer in TIFF file format. For each acquired digital drop image, a digital image processing and analysis program [14] is executed to determine the volume of the dynamic pendant oil drop at any time. After all the digital drop images are analyzed, the experimentally measured volumes of the dynamic pendant oil drop at different times, Vm (t), 0 ≤ t ≤ tm , are obtained. Here, tm represents the total duration of the diffusion test. 4. Results and discussion 4.1. Heavy oil–pure solvent systems 4.1.1. Measured volumes of the dynamic pendant oil drops The measured relative pendant oil drop volumes, i.e., Vm (t)/V0 , versus time curves for the heavy oil–carbon dioxide, heavy oil–methane, heavy oil–ethane, and heavy oil–propane systems are shown in Fig. 3a–d, respectively. Here, the rel-
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Fig. 3. Comparison between the calculated and measured relative volumes of the dynamic pendant oil drops at T = 23.9 ◦ C with drop formation time tf = 8 s. The empty symbols represent the measured relative drop volumes, whereas the lines represent the calculated relative drop volumes with the determined diffusion coefficient and oil swelling factor. (a) Heavy oil-carbon dioxide system, P = 2.00, 3.00, 4.00, 5.00, and 6.00 MPa. (b) Heavy oil-methane system, P = 6.00, 8.00, 10.00, 12.00, and 14.00 MPa. (c) Heavy oil-ethane system, P = 1.50, 2.00, 2.50, 3.00, and 3.50 MPa. (d) Heavy oil-propane system, P = 0.40, 0.50, 0.60, 0.70, 0.80, and 0.90 MPa.
ative drop volume is chosen and plotted in these figures for graphical reason. These figures clearly show that the volume of the dynamic pendant heavy oil drop increases quickly at the beginning and then it approaches a constant value at the end of each diffusion test. More and more solvent dissolves into the pendant oil drop as the molecular diffusion process proceeds. Finally, the pendant heavy oil drop is completely saturated with the solvent and its volume reaches a maximum value asymptotically.
For each heavy oil–solvent system, the relative drop volume at a higher pressure is larger than that at a lower pressure. For example, for the heavy oil–carbon dioxide system at pressures of P = 2.00, 3.00, 4.00, 5.00, and 6.00 MPa, the relative oil drop volume is equal to 1.021, 1.038, 1.058, 1.079, and 1.103 at t = 600 s (see Fig. 3a), respectively. Also the saturation time for the pendant oil drop is shorter at a higher pressure. These two observed phenomena are attributed to the following three reasons. First, the drop volume of the dynamic pendant heavy oil drop depends
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on the amount of solvent dissolved into the heavy oil as shown in Eq. (6), which is higher at a higher pressure [22]. Secondly, the initial volume of the dynamic pendant heavy oil drop is smaller at a higher pressure because the interfacial tension between heavy oil and a solvent is lower. This means that the specific surface area of the pendant oil drop is larger at a higher pressure and that the oil drop can be saturated with the solvent more quickly. Thirdly, it is speculated that the diffusion coefficient of a solvent in heavy oil increases with pressure, which is verified after the solvent diffusion coefficients at different pressures are determined in this study. Comparison of Fig. 3d for the heavy oil–propane system with Fig. 3a–c for the other three heavy oil–pure solvent systems shows that the volume increase of the dynamic pendant heavy oil drop surrounded by propane is the largest among the four heavy oil–pure solvent systems tested, even though the test pressure for propane is much lower than those for carbon dioxide, methane, and ethane. This indicates that propane has the strongest oil swelling effect because it has the largest solubility in heavy oil among the four pure solvents tested in this study [22]. 4.1.2. Determination of solvent diffusion coefficient and oil swelling factor With the measured drop volume versus time data, the objective function in Eq. (7) can be minimized to determine the solvent diffusion coefficient D and the oil swelling factor fsw of a heavy oil–solvent system at each pressure. With the determined solvent diffusion coefficient and oil swelling factor, the volumes of the dynamic pendant oil drops at different times can be calculated by using Eq. (6) at each pressure. Fig. 3a–d show the comparisons of the calculated relative pendant oil drop volumes (lines), i.e., Vc (t)/V0 , with the measured relative pendant oil drop volumes (empty symbols), i.e., Vm (t)/V0 . In general, the numerically calculated relative pendant drop volumes at different times are in excellent agreement with the experimentally measured data for the four heavy oil–pure solvent systems tested.
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Fig. 4. The measured diffusion coefficients of carbon dioxide, methane, ethane, and propane in Lloydminster heavy oil vs. the dimensionless pressure at T = 23.9 ◦ C.
P/Pv . This figure clearly shows that the oil swelling factors of the four heavy oil–pure solvent systems increase with pressure. This is because the oil swelling factor is proportional to the solubility of a solvent in heavy oil, which increases with pressure [20,22,26,27]. It can also be seen from Fig. 5 that, at the same dimensionless pressure, the oil swelling factors of ethane and propane are large and close to each other, whereas the oil swelling factors of carbon dioxide and methane are much smaller. 4.1.5. Comparison with the literature data Table 1 compares the solvent diffusion coefficients measured in this study with those published in the literature [25,26,28,29]. The comparison shows that the solvent diffusion coefficients measured in this study agree well with those reported by Tharanivasan [26], who measured the diffusion coefficients of carbon dioxide, methane, and propane in the Lloydminster heavy oil by using the pressure decay method [28–30]. Furthermore, it can
4.1.3. Effect of pressure on the solvent diffusion coefficient Fig. 4 shows the measured diffusion coefficients of carbon dioxide, methane, ethane, and propane in Lloydminster heavy oil as a function of the dimensionless pressure, which is defined as P/Pv . It can be seen from this figure that the solvent diffusion coefficients of the four heavy oil–pure solvent systems increase with pressure. This is because, as pressure increases, the solubility of a solvent in the heavy oil increases and the viscosity of the solvent-saturated heavy oil decreases [22]. The viscosity reduction results in the increase of the diffusivity of the solvent in the heavy oil [23–26]. Fig. 4 also shows that the diffusivities of ethane and propane increase with the dimensionless pressure faster than those of carbon dioxide and methane. 4.1.4. Effect of pressure on the oil swelling factor The measured oil swelling factors of carbon dioxide, methane, ethane, and propane in Lloydminster heavy oil are plotted in Fig. 5 as a function of the dimensionless pressure,
Fig. 5. The measured oil swelling factors of carbon dioxide, methane, ethane, and propane in Lloydminster heavy oil vs. the dimensionless pressure at T = 23.9 ◦ C.
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Table 1 Comparison of measured solvent diffusion coefficients in different crude oils Solvent
Crude oil
Pressure (MPa)
Temperature (◦ C)
Viscosity (mPa s)
Diffusivity (10−9 m2 /s)
CO2
Lloydminster heavy oil (this study) Lloydminster heavy oil [26] Athabasca bitumen [25] Athabasca bitumen [28] Athabasca bitumen [29]
2.0–6.0 3.5–4.2 5.0 3.1–4.1 4.0
23.9 23.9 20 25 25
23,000 at 23.9 ◦ C 20,267 at 23.9 ◦ C 361,700 at 20 ◦ C 767 at 80 ◦ C 821,000 at 25 ◦ C
0.20–0.55 0.46–0.53 0.28 0.16–0.22 0.12–0.20
CH4
Lloydminster heavy oil (this study) Lloydminster heavy oil [26] Athabasca bitumen [29] Athabasca bitumen [29]
6.0–14.0 4.9–5.0 4.0 4.0–8.0
23.9 23.9 25 25
23,000 at 23.9 ◦ C 20,267 at 23.9 ◦ C 224,500 at 25 ◦ C 821,000 at 25 ◦ C
0.12–0.19 0.21–0.22 0.08–0.11 0.06–0.08
C2 H6
Lloydminster heavy oil (this study) Athabasca bitumen [29]
1.5–3.5 4.0
23.9 25
23,000 at 23.9 ◦ C 821,000 at 25 ◦ C
0.13–0.77 0.21–0.38
C3 H8
Lloydminster heavy oil (this study) Lloydminster heavy oil [26]
0.4–0.9 0.4–0.8
23.9 23.9
23,000 at 23.9 ◦ C 20,267 at 23.9 ◦ C
0.09–0.68 0.49–0.79
be seen from Table 1 that solvent diffusion coefficients in Lloydminster heavy oil are larger than those in Athabasca bitumen because the viscosity of Lloydminster heavy oil is much lower than that of Athabasca bitumen. The comparison of the measured oil swelling factors of the heavy oil–carbon dioxide system by using the dynamic pendant drop volume analysis method with the literature data was made and presented elsewhere [15]. 4.2. Heavy oil–solvent mixture systems For a solvent mixture with different components, it can be roughly treated as a pseudo-component. Thus the molecular diffusion process of the pseudo-component in heavy oil can be described by using an apparent diffusion coefficient Da . In this study, the DPDVA method is applied to measure the apparent diffusion coefficients and the apparent oil swelling factors of three heavy oil–solvent mixture systems. These solvent mixtures are mixture #1 (70 mole% carbon dioxide + 30 mole% propane), mixture #2 (70 mole% methane + 30 mole% propane), and mixture #3 (70 mole% ethane + 30 mole% propane). 4.2.1. Measured volumes of the dynamic pendant oil drops Fig. 6a–c show the measured relative pendant oil drop volume, i.e., Vm (t)/V0 , versus time curves for the heavy oil–solvent mixture #1, heavy oil–solvent mixture #2, and heavy oil–solvent mixture #3 systems, respectively. It is shown in these figures that the dynamic pendant heavy oil drop surrounded by a solvent mixture swells as the solvent mixture dissolves into it at each pressure. Finally, the pendant heavy oil drop is completely saturated with the solvent mixture and its volume reaches a maximum value. For each heavy oil–solvent mixture system, the relative drop volume at a higher pressure is larger than that at a lower pressure. Also the higher the pressure is, the shorter time is needed for the pendant oil drop to be completely saturated with the solvent mixture. These two phenomena are quite similar to those observed for the heavy oil–pure solvent systems [14,15]. Comparison of Fig. 6c with Fig. 6a and b indicates that, at the same pressure and temperature, the volume increase of the
dynamic pendant oil drop for the heavy oil–solvent mixture #3 system is the largest among the three heavy oil–solvent mixture systems tested. This is because, as shown in Fig. 5, ethane has the largest oil swelling factor in the heavy oil among the three pure solvents (carbon dioxide, methane, and ethane). 4.2.2. Determination of the apparent diffusion coefficient and apparent oil swelling factor With the measured drop volume versus time data, the objective function in Eq. (7) can be minimized to determine the apparent diffusion coefficient Da and the apparent oil swelling factor fsw of a heavy oil–solvent mixture system at each pressure. With the determined apparent diffusion coefficient and apparent oil swelling factor, the volumes of the dynamic pendant oil drop at different times can be calculated from Eq. (6) for each heavy oil–solvent mixture system at each pressure. Fig. 6a–c show the comparisons of the calculated relative pendant oil drop volumes (lines), i.e., Vc (t)/V0 , with the measured relative pendant oil drop volumes (empty symbols), i.e., Vm (t)/V0 . It can be seen from these figures that the numerically calculated relative pendant oil drop volumes are in good agreement with the experimentally measured data for the three heavy oil–solvent mixture systems tested. 4.2.3. Effect of pressure on the apparent diffusion coefficient Fig. 7 shows the measured apparent diffusion coefficients of solvent mixture #1, solvent mixture #2, and solvent mixture #3 in Lloydminster heavy oil at different dimensionless pressures, P/Pdew , and T = 23.9 ◦ C. This figure clearly shows that the apparent diffusion coefficients of the three heavy oil–solvent mixture systems are close to each other and increase with pressure. This is probably because propane dominates the behavior of the solvent mixtures due to its largest solubility in heavy oil. It can be seen from Fig. 7 that the apparent diffusion coefficients of the three solvent mixtures at the pressures close to their respective dew-point pressures are large (Da ≥ 0.706 × 10−9 m2 /s). This indicates that, at pressures close to the dew-point pressures of the three solvent mixtures, the
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Fig. 6. Comparison between the calculated and measured relative volumes of the dynamic pendant oil drops at T = 23.9 ◦ C with drop formation time tf = 8 s. The empty symbols represent the measured relative drop volumes, whereas the lines represent the calculated relative drop volumes with the determined apparent diffusion coefficient and apparent oil swelling factor. (a) Heavy oil-solvent mixture #1 system, P = 1.00, 1.40, 1.80, 2.20, 2.60, and 3.00 MPa. (b) Heavy oil-solvent mixture #2 system, P = 2.00, 2.50, 3.00, 3.50, 4.00, and 4.50 MPa. (c) Heavy oil-solvent mixture #3 system, P = 0.75, 1.00, 1.25, 1.50, 1.75, and 2.00 MPa.
viscosities of solvent-saturated heavy oils may be significantly reduced mainly because of the presence of propane in the three solvent mixtures. 4.2.4. Effect of pressure on the apparent oil swelling factor The measured apparent oil swelling factors of solvent mixture #1, solvent mixture #2, and solvent mixture #3 in Lloydminster heavy oil are plotted in Fig. 8 as a function of the dimensionless pressure, P/Pdew . It can be seen from this figure that the apparent oil swelling factors of the three heavy oil–solvent mixture systems are similar and increase with pressure. This is prob-
ably because the effect of propane in the solvent mixtures is so dominant that there are no appreciable differences among the measured apparent oil swelling factors for the three heavy oil–solvent mixture systems. Fig. 8 also shows that, when the heavy oil is saturated with solvent mixture #1, solvent mixture #2, and solvent mixture #3 at the pressures close to their dewpoint pressures, the apparent oil swelling factors are equal to 1.478, 1.351, and 1.369, respectively. These large oil swelling factors indicate that significant amounts of solvent mixtures are dissolved into the heavy oil at their respective dew-point pressures.
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reduced significantly because of the presence of propane in the three solvent mixtures. The oil swelling factors of the four heavy oil–pure solvent systems and three heavy oil–solvent mixture systems increase with pressure. Among the four pure solvents (carbon dioxide, methane, ethane, and propane), propane has the largest oil swelling effect (fsw = 1.502 at P = 0.90 MPa). When the heavy oil is saturated with solvent mixture #1, solvent mixture #2, and solvent mixture #3 at the pressures close to their dew-point pressures, the oil swelling factors are relatively large (fsw ≥ 1.351). The large oil swelling factors indicate that significant amounts of solvent mixtures are dissolved into the heavy oil at the pressures close to their dew-point pressures. Acknowledgments Fig. 7. The measured apparent diffusion coefficients of solvent mixture #1 (70 mole% carbon dioxide + 30 mole% propane), solvent mixture #2 (70 mole% methane + 30 mole% propane), and solvent mixture #3 (70 mole% ethane + 30 mole% propane) in Lloydminster heavy oil at different dimensionless pressures and T = 23.9 ◦ C.
The authors acknowledge the discovery grant from the Natural Sciences and Engineering Research Council (NSERC) of Canada and the Innovation Fund from the Petroleum Technology Research Centre (PTRC) to Y. Gu. References
Fig. 8. The measured apparent oil swelling factors of solvent mixture #1 (70 mole% carbon dioxide + 30 mole% propane), solvent mixture #2 (70 mole% methane = 30 mole% propane), and solvent mixture #3 (70 mole% ethane + 30 mole% propane) in Lloydminster heavy oil at different dimensionless pressures and T = 23.9 ◦ C.
5. Conclusions The diffusion coefficients and oil swelling factors of carbon dioxide, methane, ethane, propane, and their three mixtures in Lloydminster heavy oil are measured by applying the newly developed dynamic pendant drop volume analysis method. The experimental results show that the diffusion coefficients of the four pure solvents and three solvent mixtures in Lloydminster heavy oil increase with pressure. It is found that the apparent diffusion coefficients of the three solvent mixtures at the pressures close to their dew-point pressures are large (Da ≥ 0.706 × 10−9 m2 /s). This implies that, at the pressures close to the dew-point pressures of the three solvent mixtures, the viscosities of solvent mixture-saturated heavy oils may be
[1] R.M. Butler, I.J. Mokrys, Solvent analog model of steam-assisted gravity drainage, AOSTRA J. Res. 5 (1989) 17–32. [2] S.K. Das, R.M. Butler, Mechanism of the vapor extraction process for heavy oil and bitumen, J. Pet. Sci. Eng. 21 (1998) 43–59. [3] R.M. Butler, Q. Jiang, Improved recovery of heavy oil by VAPEX with widely spaced horizontal injectors and producers, J. Can. Pet. Technol. 39 (1) (2000) 48–56. [4] S.K. Das, R.M. Butler, Diffusion coefficients of propane and butane in Peace River bitumen, Can. J. Chem. Eng. 74 (1996) 985–992. [5] L.X. Nghiem, B.F. Kohse, P.H. Sammon, Compositional simulation of the VAPEX process, J. Can. Pet. Technol. 40 (8) (2001) 54–61. [6] A. Boustani, B.B. Maini, The role of diffusion and convective dispersion in vapour extraction process, J. Can. Pet. Technol. 40 (4) (2001) 68–77. [7] D. Cuthiell, C. McCarthy, T. Frauenfeld, S. Cameron, G. Kissel, Investigation of the VAPEX process using CT scanning and numerical simulation, J. Can. Pet. Technol. 42 (2) (2003) 41–48. [8] K.N. Jha, A laboratory study of heavy oil recovery with carbon dioxide, J. Can. Pet. Technol. 25 (2) (1986) 54–63. [9] H.D. Do, W.V. Pinczewski, Diffusion controlled swelling of reservoir oil by direct contact with injection gas, Chem. Eng. Sci. 46 (1991) 1259–1270. [10] L. Avaullee, E. Neau, J.N. Jaubert, Thermodynamic modelling for petroleum fluid III. Reservoir fluid saturation pressures. A complete PVT property estimation, application to swelling test, Fluid Phase Equilib. 141 (1997) 87–104. [11] B. Bijeljic, A.H. Muggeridge, M.J. Blunt, Multicomponent mass transfer across water films during hydrocarbon gas injection, Chem. Eng. Sci. 58 (2003) 2377–2388. [12] P. Jarrell, C. Fox, M. Stein, S. Webb, Practical Aspects of CO2 Flooding, Society of Petroleum Engineers (SPE), Richardson, Texas, 2002. [13] B.T. Campbell, Flow Visualization of CO2 –Crude Oil Mixtures, Master Thesis, Department of Petroleum and Natural Gas Engineering, New Mexico Institute of Mining and Technology, Socorro, New Mexico, 1983. [14] C. Yang, A New Method for Measuring Solvent Diffusion Coefficients and Oil Swelling Factors of Heavy Oil–Solvent Systems, Ph.D. Dissertation, Petroleum Systems Engineering, Faculty of Engineering, University of Regina, 2005.
C. Yang, Y. Gu / Fluid Phase Equilibria 243 (2006) 64–73 [15] C. Yang, Y. Gu, A new experimental method for measuring gas diffusivity in heavy oil by the dynamic pendant drop volume analysis (DPDVA), Ind. Eng. Chem. Res. 44 (2005) 4474–4483. [16] R. Ghez, Diffusion Phenomena, second ed., Kluwer Academic/Plenum Publishers, New York, 2001. [17] D.S. Burnett, Finite Element Analysis: From Concepts to Applications, Addison-Wesley Publishing Company, Reading, MA, 1987. [18] C. Yang, Y. Gu, Modeling of the adsorption kinetics of surfactants at the liquid–fluid interface of a pendant drop, Langmuir 20 (2004) 2503–2511. [19] L.W. Lake, Enhanced Oil Recovery, Prentice-Hall, Upper Saddle River, NJ, 1989. [20] T.A. Nguyen, S.M. Farouq Ali, Effect of nitrogen on the solubility and diffusivity of carbon dioxide into oil and oil recovery by the immiscible WAG process, J. Can. Pet. Technol. 37 (2) (1998) 24–31. [21] L. Cooper, D. Steinberg, Introduction to Methods of Optimization, W.B. Saunders Company, Philadelphia, PA, 1970. [22] A.K. Mehrotra, W.Y. Svrcek, Viscosity, density and gas solubility data for oil sand bitumens, Part III: Wabasca bitumen saturated with N2 , CO, CH4 , CO2 and C2 H6 , AOSTRA J. Res. 2 (2) (1985) 83–93. [23] W. Hayduk, S.C. Cheng, Review of relation between diffusivity and solvent viscosity in dilute liquid solutions, Chem. Eng. Sci. 26 (1971) 635–646.
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[24] N.O. Umesi, R.P. Danner, Predicting diffusion coefficients in nonpolar solvents, Ind. Eng. Chem. Process Des. Dev. 20 (1981) 662– 665. [25] T. Schmidt, Mass transfer by diffusion, in: AOSTRA Technical Handbook on Oil Sands, Bitumens and Heavy Oils, Alberta Oil Sands Technology and Research Authority (AOSTRA), Edmonton, Alberta, 1989. [26] A.K. Tharanivasan, Measurements of Molecular Diffusion Coefficients of Carbon Dioxide, Methane and Propane in Heavy Oil Under Reservoir Conditions, Master Thesis, Petroleum Systems Engineering, Faculty of Engineering, University of Regina, 2004. [27] J.R. Welker, D.D. Dunlop, Physical properties of carbonated oils, J. Pet. Technol. 15 (1963) 873–876. [28] S.R. Upreti, A.K. Mehrotra, Experimental measurement of gas diffusivity in bitumen: results for carbon dioxide, Ind. Eng. Chem. Res. 39 (2000) 1080–1087. [29] S.R. Upreti, A.K. Mehrotra, Diffusivity of CO2 , CH4 , C2 H6 , and N2 in Athabasca bitumen, Can. J. Chem. Eng. 80 (2002) 116–125. [30] A.K. Tharanivasan, C. Yang, Y. Gu, Comparison of three different interface mass transfer models used in the experimental measurement of solvent diffusivity in heavy oil, J. Pet. Sci. Eng. 44 (2004) 269– 282.
Diffusion coefficients and oil swelling factors of carbon dioxide, methane, ethane, propane, and their mixtures in heavy oil Chaodong Yang, Yongan Gu ∗ Petroleum Technology Research Centre (PTRC), Faculty of Engineering, University of Regina, Regina, Saskatchewan, Canada S4S 0A2 Received 10 January 2006; received in revised form 13 February 2006; accepted 18 February 2006 Available online 6 March 2006
Abstract In this paper, a newly developed dynamic pendant drop volume analysis (DPDVA) method is applied to measure the diffusion coefficients and oil swelling factors of four pure solvents (carbon dioxide, methane, ethane, and propane) and three solvent mixtures (mixture #1: 70 mole% carbon dioxide + 30 mole% propane, mixture #2: 70 mole% methane + 30 mole% propane, and mixture #3: 70 mole% ethane + 30 mole% propane) in Lloydminster heavy oil in the pressure range of 0.4–14.0 MPa and at T = 23.9 ◦ C. The experimental results show that both the diffusion coefficient and the oil swelling factor of a heavy oil–solvent system increase with pressure. In particular, the diffusion coefficients and oil swelling factors of propane and ethane in heavy oil at pressures slightly lower than their respective vapour pressures are relatively large (D ≥ 0.680 × 10−9 m2 /s, fsw ≥ 1.314). It is also found that the apparent diffusion coefficients and the apparent oil swelling factors of the three solvent mixtures at pressures slightly below their respective dew-point pressures are large (Da ≥ 0.706 × 10−9 m2 /s, fsw ≥ 1.351). The experimental results clearly indicate that there exist certain correlations among the diffusion coefficient, oil swelling factor, solubility, and viscosity of a heavy oil–solvent system. Further experimental and theoretical studies are needed to determine these correlations. © 2006 Elsevier B.V. All rights reserved. Keywords: Diffusion coefficient; Oil swelling factor; Heavy oil; Solvent; Vapour extraction (VAPEX) process
1. Introduction With the depletion of conventional crude oil reserves in the world, heavy oil and bitumen resources have great potential to meet the future demand for petroleum products. However, oil recovery from heavy oil and bitumen reservoirs is much more difficult than that from conventional oil reservoirs. This is mainly because heavy oil or bitumen is partially or completely immobile under reservoir conditions due to its extremely high viscosity. The vapour extraction (VAPEX) process, which employs hydrocarbon or non-hydrocarbon solvents to recover heavy oil or bitumen, has attracted more attention in recent years [1–3]. In the VAPEX process, a pure solvent, such as carbon dioxide, methane, ethane, propane, butane, or a solvent mixture, is injected from an upper horizontal well into a heavy oil reservoir at a pressure slightly below its vapour pressure or dew-point pressure. The solvent dissolves into heavy oil and reduces its viscosity. The diluted oil drains by gravity to a lower horizontal
∗
Corresponding author. Tel.: +1 306 585 4630; fax: +1 306 585 4855. E-mail address: [email protected] (Y. Gu).
0378-3812/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.fluid.2006.02.020
production well. The production rate of VAPEX is strongly dependent on the oil viscosity reduction, which in turn depends on the dissolution of the solvent into heavy oil mainly through molecular diffusion. Previous studies have shown that molecular diffusion of the injected solvent in heavy oil plays a vital role in the VAPEX process [4–7]. Thus the diffusion coefficient of a solvent in heavy oil under the practical reservoir conditions becomes an important parameter for the reservoir simulation and field design of the VAPEX process. A large database of the diffusion coefficients of various heavy oil–solvent systems can be further used in the optimization of solvent composition and in the determination of injection pressure in the VAPEX process. Swelling of crude oil due to solvent dissolution is a wellknown phenomenon [8–11]. Oil swelling has two benefits to oil recovery [8,12]. First, oil swelling can mobile some of the residual oil so that it can be recovered. Flow visualization studies in two-dimensional micro-models qualitatively confirmed the oil swelling effect on mobilizing residual oil [13]. Second, oil swelling also increases oil saturation and consequently the relative permeability of oil. Therefore, accurate measurement of the oil swelling factor of a heavy oil–solvent system will help
C. Yang, Y. Gu / Fluid Phase Equilibria 243 (2006) 64–73
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to achieve a better understanding of oil recovery mechanisms involved in the VAPEX process. In the literature, there are limited data of solvent diffusion coefficients and oil swelling factors of heavy oil–solvent systems. The purpose of this study is to measure the solvent diffusion coefficients and oil swelling factors of carbon dioxide, methane, ethane, propane, and their mixtures in heavy oil in a broad range of solvent injection pressure. The experimental measurements are conducted by applying the newly developed dynamic pendant drop volume analysis (DPDVA) method [14,15]. It is worthwhile to point out that the DPDVA method has several distinct advantages over the other existing methods. For example, with the DPDVA method, a single experimental test can be completed within 2 h and both the solvent diffusion coefficient and the oil swelling factor of a heavy oil–solvent system can be measured simultaneously. Second, this method allows the measurement of solvent diffusion coefficient and oil swelling factor at a high pressure and a constant temperature. Furthermore, the DPDVA method is applicable for measuring the apparent diffusion coefficient and the apparent oil swelling factor of a heavy oil–solvent mixture system. 2. Dynamic pendant drop volume analysis method The DPDVA method determines the solvent diffusion coefficient and the oil swelling factor of a heavy oil–solvent system at the same time. In the experiment, a see-through windowed highpressure cell is filled with a test solvent at pre-specified pressure and temperature. Then a heavy oil sample is introduced to form a pendant oil drop inside the pressure cell. Subsequent solvent dissolution into the pendant oil drop causes its volume to increase until it is completely saturated with the solvent. The sequential digital images of the dynamic pendant oil drop are acquired and analyzed to measure the oil drop volumes at different times. Theoretically, a mass transfer model is formulated to describe the diffusion process of the solvent in the pendant oil drop. This model is solved numerically by applying the semi-discrete Galerkin finite element method. Thus the volume of the dynamic pendant oil drop at any time is calculated from the predicted transient solvent concentration distribution inside the pendant oil drop. Mathematically, an objective function is constructed to express the discrepancy between the theoretically calculated and experimentally measured volumes of the dynamic pendant oil drop at different times. The solvent diffusion coefficient and the oil swelling factor of the heavy oil–solvent system are used as adjustable parameters and thus determined once the objective function is minimized. A brief description of the DPDVA method is given below and its technical details can be found elsewhere [14,15]. 2.1. Mass transfer model Fig. 1 shows an axisymmetric pendant oil drop surrounded by a test solvent. The outer radius of the syringe needle is rn , the wall thickness of the needle is εn , and the height of the syringe needle is hn . The heavy oil inside the pendant drop, including the heavy oil inside the syringe needle, is chosen as the computational
Fig. 1. Schematic diagram of an axisymmetric pendant oil drop surrounded by a solvent depicted in the cylindrical coordinate system (r, z).
domain, which is denoted by Ω. The boundaries formed between the syringe needle and the heavy oil together with the cutting plane at the top of the syringe needle are expressed by Φn . In this study, the cutting plane is chosen far above the tip of the syringe needle so that solvent diffusion cannot reach it during the diffusion test. The surface of the pendant oil drop, i.e., the heavy oil–solvent interface, is represented by Φint . In the cylindrical coordinate system as shown in Fig. 1, the diffusion equation for describing the solvent concentration distribution inside the computational domain Ω can be expressed in the following dimensionless form [16]: ∂C 1 ∂ ∂C ∂2 C = R + , (R, Z) ∈ Ω, τ > 0, (1) ∂τ R ∂R ∂R ∂Z2 with the following initial and boundary conditions: C(R, Z, τ)|τ=0 = 0, C(R, Z, τ) = 1,
(R, Z) ∈ Ω,
(2)
(R, Z) ∈ Φint , τ > 0,
(3)
∂C ∂C nR + nZ = 0, ∂R ∂Z
(R, Z) ∈ Φn , τ > 0,
where the dimensionless variables are defined as: c r z t C= , R= , Z= , τ= 2 . csat rn rn rn /D
(4)
(5)
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Here, c is the molar concentration of the solvent in heavy oil, i.e., the number of moles of solvent dissolved into per unit volume of heavy oil, csat the solvent concentration in the solvent-saturated heavy oil at the experimental pressure and temperature, r the radial coordinate, z the axial coordinate, t time, D the diffusion coefficient of the solvent in heavy oil, and nR and nz are the direction cosines, i.e., R and Z components of the outward unit vectors normal to the boundaries. By applying the semi-discrete Galerkin finite element method [17], Eq. (1) subject to Eqs. (2)–(4) is solved numerically to obtain the dimensionless solvent concentration distribution, C(R,Z,τ), (R,Z) ∈ Ω. The detailed mathematical formulations of the Galerkin finite element method for solving the diffusion Eq. (1) inside the computational domain can be found in the literature [18].
be seen from Eq. (6) that the above-defined objective function E is merely dependent on two to-be-determined parameters, i.e., the diffusion coefficient D and the oil swelling factor fsw of the heavy oil–solvent system. Therefore, D and fsw can be used as the adjustable parameters to minimize the objective function E [21]. Once the global minimum objective function is found, the corresponding global optimum values of D and fsw are considered as the measured solvent diffusion coefficient and oil swelling factor, respectively. Two previous articles [14,15] presented the detailed numerical procedure for simultaneously determining the solvent diffusion coefficient and the oil swelling factor by minimizing the objective function. 3. Experimental 3.1. Materials
2.2. Theoretical prediction of the dynamic pendant oil drop volume In the phase behavior studies, oil swelling factor is often used to quantify the oil swelling effect when a solvent dissolves into heavy oil [8,19,20]. In this paper, symbol fsw is used to represent the oil swelling factor, which is defined as the ratio of the volume of the solvent-saturated heavy oil to the volume of the original heavy oil without any solvent dissolution. The volume of the dynamic pendant oil drop at any time t is equal to the sum of the initial heavy oil drop volume and the volume change due to the solvent dissolution into the heavy oil [15]: D(t + tf ) 3 Vc (t) = V0 + (fsw − 1)rn C R, Z, rn2 −C R, Z,
(R,Z) ∈ Ω
Dtf rn2
πR dR dZ.
(6)
where Vc (t) is the calculated volume of the dynamic pendant oil drop at any time t, V0 the measured initial volume of the dynamic pendant oil drop at t = 0, and tf is the time needed to form a well-shaped pendant heavy oil drop inside the pressure cell. 2.3. Objective function and its minimization Let Vm (t) be the measured volume of the dynamic pendant oil drop and Vc (t) be the calculated volume of the dynamic pendant oil drop at any time t, 0 ≤ t ≤ tm , where tm is the total duration of the diffusion test. In this study, the root-mean-squared relative error between the theoretically calculated and experimentally measured volumes of the dynamic pendant oil drop is used to define the objective function E: 1 tm Vm (t) − Vc (t) 2 dt × 100%. (7) E= tm 0 Vm (t) Once the volumes of the dynamic pendant oil drop at different times are measured, the objective function depends on the theoretically calculated volumes only. Furthermore, it can
The heavy oil sample is collected from the Lloydminster area, Canada. Prior to usage, the heavy oil sample is cleaned to remove brine, fine solids, and any solution gas. The density of the cleaned heavy oil sample is 988 kg/m3 and its viscosity is 23,000 mPa s at T = 23.9 ◦ C. The asphaltene content of the heavy oil is 11.5 wt.% (n-heptane insoluble). The heavy-ends of C50+ for this heavy oil are 47.5 wt.%. Carbon dioxide, methane, ethane, and propane are purchased from Praxair Canada with stated purity of 99.99%, 99.97%, 99.0%, and 99.5%, respectively. Theses four solvents are used to prepare solvent mixture #1 (70 mole% carbon dioxide + 30 mole% propane), solvent mixture #2 (70 mole% methane + 30 mole% propane), and solvent mixture #3 (70 mole% ethane + 30 mole% propane). The vapour pressures of carbon dioxide, methane, ethane, and propane are found to be Pv = 6.28, 31.38, 4.12, and 0.93 MPa at T = 23.9 ◦ C [14], respectively. The CMG WinProp (Version 2004.12, Computer Modelling Group Ltd., Canada) software is used to determine the phase diagrams of three solvent mixtures. It is found that the dew-point pressures of solvent mixture #1, solvent mixture #2, and solvent mixture #3 are equal to Pdew = 3.27, 4.79, and 2.19 MPa at T = 23.9 ◦ C, respectively. In this study, the solvent diffusion coefficients and the oil swelling factors of the four heavy oil–pure solvent systems and the apparent diffusion coefficients and the apparent oil swelling factors of three heavy oil–solvent mixture systems are measured at T = 23.9 ◦ C. This temperature is chosen as it is the same as that of the actual heavy oil reservoir from which the oil sample is collected and used in this study. The experimental pressures are selected to cover most practical cases of interest for the VAPEX process, which requires the solvent injection pressure to be slightly lower than the vapor pressure of a pure solvent or the dew-point pressure of a solvent mixture at the temperature of interest. 3.2. Apparatus Fig. 2 shows the schematic diagram of the experimental setup used in this study. The major component of the setup is a seethrough windowed high-pressure cell (IFT-10, Temco, USA).
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Fig. 2. Schematic diagram of the experimental setup used for measuring the solvent diffusion coefficient and the oil swelling factor of a heavy oil–solvent system by applying the dynamic pendant drop volume analysis (DPDVA).
The pressure cell has a chamber volume of 41.5 cm3 and can sustain pressures up to 69 MPa. The maximum working temperature of the pressure cell is 177 ◦ C. The syringe needle used to form the pendant oil drop is made of stainless steel. Its outer radius is rn = 0.79 mm, wall thickness is εn = 0.59 mm, and height is hn = 2.40 mm. Heavy oil is introduced from a heavy oil sample cylinder to the syringe needle by using a programmable syringe pump (100DX, ISCO Inc., USA). A heated waterbath (DC10, Thermo Hakke, USA) is used to control the temperature of the pressure cell by circulating water at a constant temperature of T = 23.9 ◦ C. Meanwhile, the room temperature is also set at the same constant temperature to minimize the temperature fluctuations. It is found in the experiments that temperature variations are within ±0.2 ◦ C. The pressure inside the high-pressure cell is measured by using a digital pressure gauge (DTG-6000, 3D Instruments, USA). The accuracy of the pressure gauge is 0.007 MPa in the pressure range of 0–6.89 MPa, and 0.007–0.034 MPa in the pressure range of 6.89–34.5 MPa, respectively. A light source and a Teflon diffuser are used to provide uniform illumination for the pendant oil drop inside the pressure cell. A microscope camera (MZ6, Leica, Germany) is used to acquire the sequential digital images of the dynamic pendant oil drop. The high-pressure cell is placed between the light source and the microscope camera. The high-pressure cell, light source, diffuser, and microscope camera are placed on a vibration-free table (RS4000, Newport, USA). The digital images of the dynamic pendant oil drop at different times are acquired sequentially in tagged image file format (TIFF) with resolution of 640 × 480 pixels by using a digital frame grabber (Ultra II, Coreco Imaging, Canada). A DELL desktop computer is used to store the digital images and perform subsequent image analyses. This PC-based optical system can be used to grab the sequential digital drop images at a speed of three images per second.
3.3. Experimental procedure Prior to the diffusion test for a heavy oil–solvent system, the high-pressure cell is thoroughly cleaned with kerosene and acetone, flushed with nitrogen, and finally purged with a test solvent at least five times. Then the solvent is introduced into the high-pressure cell from a solvent cylinder. After the solvent is injected, it usually takes less than 30 min for the pressure and temperature inside the pressure cell to reach their stable values. A heavy oil sample is introduced by using the syringe pump to form a pendant oil drop at the tip of the syringe needle, which is installed at the top of the high-pressure cell. Once the pendant oil drop is formed, a digital image acquisition program (TciPro, Coreco Imaging, Canada) is executed to acquire its sequential images during the diffusion test. The time intervals for the sequential image acquisition are preset properly so that they are smaller at the beginning and larger at the end of the diffusion test. These digital drop images are automatically stored in the computer in TIFF file format. For each acquired digital drop image, a digital image processing and analysis program [14] is executed to determine the volume of the dynamic pendant oil drop at any time. After all the digital drop images are analyzed, the experimentally measured volumes of the dynamic pendant oil drop at different times, Vm (t), 0 ≤ t ≤ tm , are obtained. Here, tm represents the total duration of the diffusion test. 4. Results and discussion 4.1. Heavy oil–pure solvent systems 4.1.1. Measured volumes of the dynamic pendant oil drops The measured relative pendant oil drop volumes, i.e., Vm (t)/V0 , versus time curves for the heavy oil–carbon dioxide, heavy oil–methane, heavy oil–ethane, and heavy oil–propane systems are shown in Fig. 3a–d, respectively. Here, the rel-
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C. Yang, Y. Gu / Fluid Phase Equilibria 243 (2006) 64–73
Fig. 3. Comparison between the calculated and measured relative volumes of the dynamic pendant oil drops at T = 23.9 ◦ C with drop formation time tf = 8 s. The empty symbols represent the measured relative drop volumes, whereas the lines represent the calculated relative drop volumes with the determined diffusion coefficient and oil swelling factor. (a) Heavy oil-carbon dioxide system, P = 2.00, 3.00, 4.00, 5.00, and 6.00 MPa. (b) Heavy oil-methane system, P = 6.00, 8.00, 10.00, 12.00, and 14.00 MPa. (c) Heavy oil-ethane system, P = 1.50, 2.00, 2.50, 3.00, and 3.50 MPa. (d) Heavy oil-propane system, P = 0.40, 0.50, 0.60, 0.70, 0.80, and 0.90 MPa.
ative drop volume is chosen and plotted in these figures for graphical reason. These figures clearly show that the volume of the dynamic pendant heavy oil drop increases quickly at the beginning and then it approaches a constant value at the end of each diffusion test. More and more solvent dissolves into the pendant oil drop as the molecular diffusion process proceeds. Finally, the pendant heavy oil drop is completely saturated with the solvent and its volume reaches a maximum value asymptotically.
For each heavy oil–solvent system, the relative drop volume at a higher pressure is larger than that at a lower pressure. For example, for the heavy oil–carbon dioxide system at pressures of P = 2.00, 3.00, 4.00, 5.00, and 6.00 MPa, the relative oil drop volume is equal to 1.021, 1.038, 1.058, 1.079, and 1.103 at t = 600 s (see Fig. 3a), respectively. Also the saturation time for the pendant oil drop is shorter at a higher pressure. These two observed phenomena are attributed to the following three reasons. First, the drop volume of the dynamic pendant heavy oil drop depends
C. Yang, Y. Gu / Fluid Phase Equilibria 243 (2006) 64–73
on the amount of solvent dissolved into the heavy oil as shown in Eq. (6), which is higher at a higher pressure [22]. Secondly, the initial volume of the dynamic pendant heavy oil drop is smaller at a higher pressure because the interfacial tension between heavy oil and a solvent is lower. This means that the specific surface area of the pendant oil drop is larger at a higher pressure and that the oil drop can be saturated with the solvent more quickly. Thirdly, it is speculated that the diffusion coefficient of a solvent in heavy oil increases with pressure, which is verified after the solvent diffusion coefficients at different pressures are determined in this study. Comparison of Fig. 3d for the heavy oil–propane system with Fig. 3a–c for the other three heavy oil–pure solvent systems shows that the volume increase of the dynamic pendant heavy oil drop surrounded by propane is the largest among the four heavy oil–pure solvent systems tested, even though the test pressure for propane is much lower than those for carbon dioxide, methane, and ethane. This indicates that propane has the strongest oil swelling effect because it has the largest solubility in heavy oil among the four pure solvents tested in this study [22]. 4.1.2. Determination of solvent diffusion coefficient and oil swelling factor With the measured drop volume versus time data, the objective function in Eq. (7) can be minimized to determine the solvent diffusion coefficient D and the oil swelling factor fsw of a heavy oil–solvent system at each pressure. With the determined solvent diffusion coefficient and oil swelling factor, the volumes of the dynamic pendant oil drops at different times can be calculated by using Eq. (6) at each pressure. Fig. 3a–d show the comparisons of the calculated relative pendant oil drop volumes (lines), i.e., Vc (t)/V0 , with the measured relative pendant oil drop volumes (empty symbols), i.e., Vm (t)/V0 . In general, the numerically calculated relative pendant drop volumes at different times are in excellent agreement with the experimentally measured data for the four heavy oil–pure solvent systems tested.
69
Fig. 4. The measured diffusion coefficients of carbon dioxide, methane, ethane, and propane in Lloydminster heavy oil vs. the dimensionless pressure at T = 23.9 ◦ C.
P/Pv . This figure clearly shows that the oil swelling factors of the four heavy oil–pure solvent systems increase with pressure. This is because the oil swelling factor is proportional to the solubility of a solvent in heavy oil, which increases with pressure [20,22,26,27]. It can also be seen from Fig. 5 that, at the same dimensionless pressure, the oil swelling factors of ethane and propane are large and close to each other, whereas the oil swelling factors of carbon dioxide and methane are much smaller. 4.1.5. Comparison with the literature data Table 1 compares the solvent diffusion coefficients measured in this study with those published in the literature [25,26,28,29]. The comparison shows that the solvent diffusion coefficients measured in this study agree well with those reported by Tharanivasan [26], who measured the diffusion coefficients of carbon dioxide, methane, and propane in the Lloydminster heavy oil by using the pressure decay method [28–30]. Furthermore, it can
4.1.3. Effect of pressure on the solvent diffusion coefficient Fig. 4 shows the measured diffusion coefficients of carbon dioxide, methane, ethane, and propane in Lloydminster heavy oil as a function of the dimensionless pressure, which is defined as P/Pv . It can be seen from this figure that the solvent diffusion coefficients of the four heavy oil–pure solvent systems increase with pressure. This is because, as pressure increases, the solubility of a solvent in the heavy oil increases and the viscosity of the solvent-saturated heavy oil decreases [22]. The viscosity reduction results in the increase of the diffusivity of the solvent in the heavy oil [23–26]. Fig. 4 also shows that the diffusivities of ethane and propane increase with the dimensionless pressure faster than those of carbon dioxide and methane. 4.1.4. Effect of pressure on the oil swelling factor The measured oil swelling factors of carbon dioxide, methane, ethane, and propane in Lloydminster heavy oil are plotted in Fig. 5 as a function of the dimensionless pressure,
Fig. 5. The measured oil swelling factors of carbon dioxide, methane, ethane, and propane in Lloydminster heavy oil vs. the dimensionless pressure at T = 23.9 ◦ C.
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Table 1 Comparison of measured solvent diffusion coefficients in different crude oils Solvent
Crude oil
Pressure (MPa)
Temperature (◦ C)
Viscosity (mPa s)
Diffusivity (10−9 m2 /s)
CO2
Lloydminster heavy oil (this study) Lloydminster heavy oil [26] Athabasca bitumen [25] Athabasca bitumen [28] Athabasca bitumen [29]
2.0–6.0 3.5–4.2 5.0 3.1–4.1 4.0
23.9 23.9 20 25 25
23,000 at 23.9 ◦ C 20,267 at 23.9 ◦ C 361,700 at 20 ◦ C 767 at 80 ◦ C 821,000 at 25 ◦ C
0.20–0.55 0.46–0.53 0.28 0.16–0.22 0.12–0.20
CH4
Lloydminster heavy oil (this study) Lloydminster heavy oil [26] Athabasca bitumen [29] Athabasca bitumen [29]
6.0–14.0 4.9–5.0 4.0 4.0–8.0
23.9 23.9 25 25
23,000 at 23.9 ◦ C 20,267 at 23.9 ◦ C 224,500 at 25 ◦ C 821,000 at 25 ◦ C
0.12–0.19 0.21–0.22 0.08–0.11 0.06–0.08
C2 H6
Lloydminster heavy oil (this study) Athabasca bitumen [29]
1.5–3.5 4.0
23.9 25
23,000 at 23.9 ◦ C 821,000 at 25 ◦ C
0.13–0.77 0.21–0.38
C3 H8
Lloydminster heavy oil (this study) Lloydminster heavy oil [26]
0.4–0.9 0.4–0.8
23.9 23.9
23,000 at 23.9 ◦ C 20,267 at 23.9 ◦ C
0.09–0.68 0.49–0.79
be seen from Table 1 that solvent diffusion coefficients in Lloydminster heavy oil are larger than those in Athabasca bitumen because the viscosity of Lloydminster heavy oil is much lower than that of Athabasca bitumen. The comparison of the measured oil swelling factors of the heavy oil–carbon dioxide system by using the dynamic pendant drop volume analysis method with the literature data was made and presented elsewhere [15]. 4.2. Heavy oil–solvent mixture systems For a solvent mixture with different components, it can be roughly treated as a pseudo-component. Thus the molecular diffusion process of the pseudo-component in heavy oil can be described by using an apparent diffusion coefficient Da . In this study, the DPDVA method is applied to measure the apparent diffusion coefficients and the apparent oil swelling factors of three heavy oil–solvent mixture systems. These solvent mixtures are mixture #1 (70 mole% carbon dioxide + 30 mole% propane), mixture #2 (70 mole% methane + 30 mole% propane), and mixture #3 (70 mole% ethane + 30 mole% propane). 4.2.1. Measured volumes of the dynamic pendant oil drops Fig. 6a–c show the measured relative pendant oil drop volume, i.e., Vm (t)/V0 , versus time curves for the heavy oil–solvent mixture #1, heavy oil–solvent mixture #2, and heavy oil–solvent mixture #3 systems, respectively. It is shown in these figures that the dynamic pendant heavy oil drop surrounded by a solvent mixture swells as the solvent mixture dissolves into it at each pressure. Finally, the pendant heavy oil drop is completely saturated with the solvent mixture and its volume reaches a maximum value. For each heavy oil–solvent mixture system, the relative drop volume at a higher pressure is larger than that at a lower pressure. Also the higher the pressure is, the shorter time is needed for the pendant oil drop to be completely saturated with the solvent mixture. These two phenomena are quite similar to those observed for the heavy oil–pure solvent systems [14,15]. Comparison of Fig. 6c with Fig. 6a and b indicates that, at the same pressure and temperature, the volume increase of the
dynamic pendant oil drop for the heavy oil–solvent mixture #3 system is the largest among the three heavy oil–solvent mixture systems tested. This is because, as shown in Fig. 5, ethane has the largest oil swelling factor in the heavy oil among the three pure solvents (carbon dioxide, methane, and ethane). 4.2.2. Determination of the apparent diffusion coefficient and apparent oil swelling factor With the measured drop volume versus time data, the objective function in Eq. (7) can be minimized to determine the apparent diffusion coefficient Da and the apparent oil swelling factor fsw of a heavy oil–solvent mixture system at each pressure. With the determined apparent diffusion coefficient and apparent oil swelling factor, the volumes of the dynamic pendant oil drop at different times can be calculated from Eq. (6) for each heavy oil–solvent mixture system at each pressure. Fig. 6a–c show the comparisons of the calculated relative pendant oil drop volumes (lines), i.e., Vc (t)/V0 , with the measured relative pendant oil drop volumes (empty symbols), i.e., Vm (t)/V0 . It can be seen from these figures that the numerically calculated relative pendant oil drop volumes are in good agreement with the experimentally measured data for the three heavy oil–solvent mixture systems tested. 4.2.3. Effect of pressure on the apparent diffusion coefficient Fig. 7 shows the measured apparent diffusion coefficients of solvent mixture #1, solvent mixture #2, and solvent mixture #3 in Lloydminster heavy oil at different dimensionless pressures, P/Pdew , and T = 23.9 ◦ C. This figure clearly shows that the apparent diffusion coefficients of the three heavy oil–solvent mixture systems are close to each other and increase with pressure. This is probably because propane dominates the behavior of the solvent mixtures due to its largest solubility in heavy oil. It can be seen from Fig. 7 that the apparent diffusion coefficients of the three solvent mixtures at the pressures close to their respective dew-point pressures are large (Da ≥ 0.706 × 10−9 m2 /s). This indicates that, at pressures close to the dew-point pressures of the three solvent mixtures, the
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Fig. 6. Comparison between the calculated and measured relative volumes of the dynamic pendant oil drops at T = 23.9 ◦ C with drop formation time tf = 8 s. The empty symbols represent the measured relative drop volumes, whereas the lines represent the calculated relative drop volumes with the determined apparent diffusion coefficient and apparent oil swelling factor. (a) Heavy oil-solvent mixture #1 system, P = 1.00, 1.40, 1.80, 2.20, 2.60, and 3.00 MPa. (b) Heavy oil-solvent mixture #2 system, P = 2.00, 2.50, 3.00, 3.50, 4.00, and 4.50 MPa. (c) Heavy oil-solvent mixture #3 system, P = 0.75, 1.00, 1.25, 1.50, 1.75, and 2.00 MPa.
viscosities of solvent-saturated heavy oils may be significantly reduced mainly because of the presence of propane in the three solvent mixtures. 4.2.4. Effect of pressure on the apparent oil swelling factor The measured apparent oil swelling factors of solvent mixture #1, solvent mixture #2, and solvent mixture #3 in Lloydminster heavy oil are plotted in Fig. 8 as a function of the dimensionless pressure, P/Pdew . It can be seen from this figure that the apparent oil swelling factors of the three heavy oil–solvent mixture systems are similar and increase with pressure. This is prob-
ably because the effect of propane in the solvent mixtures is so dominant that there are no appreciable differences among the measured apparent oil swelling factors for the three heavy oil–solvent mixture systems. Fig. 8 also shows that, when the heavy oil is saturated with solvent mixture #1, solvent mixture #2, and solvent mixture #3 at the pressures close to their dewpoint pressures, the apparent oil swelling factors are equal to 1.478, 1.351, and 1.369, respectively. These large oil swelling factors indicate that significant amounts of solvent mixtures are dissolved into the heavy oil at their respective dew-point pressures.
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reduced significantly because of the presence of propane in the three solvent mixtures. The oil swelling factors of the four heavy oil–pure solvent systems and three heavy oil–solvent mixture systems increase with pressure. Among the four pure solvents (carbon dioxide, methane, ethane, and propane), propane has the largest oil swelling effect (fsw = 1.502 at P = 0.90 MPa). When the heavy oil is saturated with solvent mixture #1, solvent mixture #2, and solvent mixture #3 at the pressures close to their dew-point pressures, the oil swelling factors are relatively large (fsw ≥ 1.351). The large oil swelling factors indicate that significant amounts of solvent mixtures are dissolved into the heavy oil at the pressures close to their dew-point pressures. Acknowledgments Fig. 7. The measured apparent diffusion coefficients of solvent mixture #1 (70 mole% carbon dioxide + 30 mole% propane), solvent mixture #2 (70 mole% methane + 30 mole% propane), and solvent mixture #3 (70 mole% ethane + 30 mole% propane) in Lloydminster heavy oil at different dimensionless pressures and T = 23.9 ◦ C.
The authors acknowledge the discovery grant from the Natural Sciences and Engineering Research Council (NSERC) of Canada and the Innovation Fund from the Petroleum Technology Research Centre (PTRC) to Y. Gu. References
Fig. 8. The measured apparent oil swelling factors of solvent mixture #1 (70 mole% carbon dioxide + 30 mole% propane), solvent mixture #2 (70 mole% methane = 30 mole% propane), and solvent mixture #3 (70 mole% ethane + 30 mole% propane) in Lloydminster heavy oil at different dimensionless pressures and T = 23.9 ◦ C.
5. Conclusions The diffusion coefficients and oil swelling factors of carbon dioxide, methane, ethane, propane, and their three mixtures in Lloydminster heavy oil are measured by applying the newly developed dynamic pendant drop volume analysis method. The experimental results show that the diffusion coefficients of the four pure solvents and three solvent mixtures in Lloydminster heavy oil increase with pressure. It is found that the apparent diffusion coefficients of the three solvent mixtures at the pressures close to their dew-point pressures are large (Da ≥ 0.706 × 10−9 m2 /s). This implies that, at the pressures close to the dew-point pressures of the three solvent mixtures, the viscosities of solvent mixture-saturated heavy oils may be
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