Energy Fuels 2011, 25, 782–790 Published on Web 01/14/2011
: DOI:10.1021/ef101435r
Forced and Diffusive Mass Transfer between Pentane and Athabasca Bitumen Fractions Ardalan Sadighian, Mildred Becerra, Ala Bazyleva, and John M. Shaw* Department of Chemical and Materials Engineering, University of Alberta, Edmonton, Alberta T6G 2G6, Canada Received October 20, 2010. Revised Manuscript Received December 23, 2010
Forced and diffusive mass transfer between pentane and Athabasca bitumen fractions was investigated at 297 K. Mutual diffusion coefficients were obtained using a free diffusion technique, where time-dependent composition profiles were jointly fit to obtain composition-dependent values. Because the density difference between pentane and Athabasca bitumen is significant, the density gradient was accounted for explicitly in the data analysis. Forced mass-transfer measurements were made by placing a high shear impeller in the pentane-rich phase adjacent to the pentane-feedstock interface. Mass-transfer coefficients were evaluated independently on the basis of the movement of the interface with time and changes in the bulk composition of the well-mixed pentane-rich phase above the interface. Because bitumen fractions are only partially soluble in pentane, the impact of the asymptotic assumptions, complete miscibility and complete immiscibility, on mass-transfer coefficient values obtained was assessed and found to fall within experimental error. The dependence of mass-transfer coefficients upon the shear rate and impeller-interface distance was also evaluated. Mass-transfer rates are shown to range from the diffusion limit at low shear rates and large impeller-interface distances to values consistent with those obtained from pertinent correlations for forced mass transfer under turbulent conditions at higher shear rates. The results suggest that bitumenpentane mass transfer in reservoirs and surface facilities is likely to be diffusion-limited.
feedstock þ light hydrocarbon mixtures.4-10 However, the validity of some of these measurement and data analysis methods has been challenged because variations in the apparent mutual diffusion coefficients for gases in oils of up to 3 orders of magnitude have been reported on the basis of the same primary data.9 Further, failure to account for density gradients with composition in such mixtures during data analysis leads to artifacts,4,5 including mutual diffusion coefficients that appear to be time-dependent and overestimated by orders of magnitude and may have maxima at intermediate compositions. Values of the mutual diffusion coefficient for Peace River bitumen þ propane as high as 10-7 m2 s-1 have been reported.6 Such values are larger than the liquid- and
1. Introduction The hydrocarbon energy industry is increasingly focused on the production of heavy feedstocks, where improving recovery rates and yields from reservoirs 1,2 and facilitating the separation of mined bitumen from sand3 are illustrative of the diversity of research and development topics. The success of proposed and modified process designs for heavy feedstocks will rely on accurate thermophysical and transport property knowledge. For example, production rates of heavy feedstocks from a reservoir where light hydrocarbons are injected depend upon how rapidly the light hydrocarbons penetrate into the feedstock. Consequently, knowledge related to mutual diffusion coefficients and hydrodynamic conditions at the boundary between the undisturbed feedstock and the added light hydrocarbon (liquid or vapor) is crucial. For surface operations, diverse hydrodynamic conditions arise in separation vessels, where separation efficiency may rely on mass transfer within a phase or between phases. Mutual diffusion coefficients are not measured directly but are derived from concentration profiles or other data. A number of measurement and data analysis techniques have been used to assess mutual diffusion coefficients in heavy
(5) Zhang, X. H.; Fulem, M.; Shaw, J. M. Liquid-phase mutual diffusion coefficients for Athabasca bitumen plus pentane mixtures. J. Chem. Eng. Data 2007, 52 (3), 691–694. (6) Das, S. K.; Butler, R. M. Diffusion coefficients of propane and butane in Peace River bitumen. Can. J. Chem. Eng. 1996, 74 (6), 985–992. (7) Wen, Y.; Bryan, J.; Kantzas, A. Estimation of diffusion coefficients in bitumen solvent mixtures as derived from low field NMR spectra. J. Can. Pet. Technol. 2005, 44 (4), 29–35. (8) Wen, Y. W.; Kantzas, A. Monitoring bitumen-solvent interactions with low-field nuclear magnetic resonance and X-ray computerassisted tomography. Energy Fuels 2005, 19, 1319–1326. (9) Tharanivasan, A. K.; Yang, C.; Gu, Y. Comparison of three different interface mass transfer models used in the experimental measurement of solvent diffusivity in heavy oil. J. Pet. Sci. Eng. 2004, 44 (3-4), 269–282. (10) Riazi, M. R. A new method for experimental measurement of diffusion coefficients in reservoir fluids. J. Pet. Sci. Eng. 1996, 14 (3-4), 235–250. (11) Robinson, R. C.; Stewart, W. E. Self-diffusion in liquid carbon dioxide and propane. Ind. Eng. Chem. Fundam. 1968, 7 (1), 90–95. (12) Woessner, D. E.; Snowden, B. S., Jr.; George, R. A.; Melrose, J. C. Dense gas diffusion coefficients for the methane-propane system. Ind. Eng. Chem. Fundam. 1969, 8 (4), 779–786. (13) Greiner-Schmid, A.; Wappmann, S.; Has, M.; L€ udemann, H.-D. Self-diffusion in the compressed fluid lower alkanes: Methane, ethane, and propane. J. Chem. Phys. 1991, 94, 5643–5649.
*To whom correspondence should be addressed. Telephone: þ1-780492-8236. E-mail:
[email protected]. (1) Speight, J. G. The Chemistry and Technology of Petroleum, 4th ed.; CRC Press (Taylor and Francis Group): Boca Raton, FL, 2006. (2) Boak, J.; Palmgren, C. Preliminary numerical analysis for a naphtha co-injection test during SAGD. J. Can. Pet. Technol. 2007, 46 (1), 13–19. (3) Sparks, B. D.; Meadus, F. W. A study of some factors affecting solvent losses in the solvent extraction;Spherical agglomoration of oil sands. Fuel Process. Technol. 1981, 4 (4), 251–264. (4) Zhang, X.; Shaw, J. M. Liquid-phase mutual diffusion coefficients for heavy oil plus light hydrocarbon mixtures. Pet. Sci. Technol. 2007, 25 (5-6), 773–790. r 2011 American Chemical Society
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: DOI:10.1021/ef101435r
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gas-phase self-diffusion coefficients for propane under similar experimental conditions11-13 and are clearly too high. Time-dependent mutual diffusion coefficient values have been reported for mixtures of Cold Lake bitumen with heptane.8 More recently, Zhang et al.4,5 reported time- and composition-independent values for liquid-phase mutual diffusion coefficients of 1.7 ( 0.4 10-10 m2 s-1 for Athabasca bitumen þ pentane at 295 K in the composition range from 0.1 to 0.9 pentane mass fraction. They also reprocessed data from Wen and Kantzas,8 accounting explicitly for density gradients, and reported time- and composition-independent mutual diffusion coefficients of 1.6 ( 0.6 10-10 m2 s-1 for Cold Lake bitumen þ heptane mixtures at 295 K over a similar composition range. While these latter values would appear to be reliable, it is important to note that the orientation of phases, with respect to one another and with respect to the gravitational field, are both fixed in these measurements. The interface between the feedstock and the light hydrocarbons is horizontal. The lower density n-alkane-rich phase is on top, and the higher density feedstock phase is on the bottom. Because the hydrocarbon resources and their mixtures with n-alkanes are multiphase,14 artifacts may be introduced. For example, if asphaltenes or other organic or inorganic matter accumulate at the interface, diffusion and mass transfer rates may be reduced over time. This possible artifact, if present, is masked by the error inherent in the measurements at least over the duration of the experiments from 30 min to 1 day.4,5 However, these mutual diffusion coefficient values may well be conservative vis- a-vis field experience, in either reservoirs or agitated vessels, where interface orientations are random relative to the gravitational field and where thermal gradients, opposed density and composition gradients, convection, and other effects are likely to augment mass-transfer rates. Forced mass-transfer coefficient data do not appear to be available in the literature for bitumen or bitumen fractions þ light hydrocarbons. Such measurements are complex because these mixtures exhibit up to four phases in equilibrium.14 To evaluate mass-transfer coefficients, assumptions regarding mutual solubility of constituents must be made. Asymptotic cases, complete miscibility of bitumen fractions in pentane, and complete immiscibility provide upper and lower extrema for mass-transfer coefficient values and their dependence upon composition. Data treatment and analysis of forced mass-transfer measurements reported here follow established approaches applied to diverse mixtures in stirred vessels,15-20 where the focus is on the identification of the transition from diffusion-controlled mass transfer (lower bound for mass-
transfer rates) to another mass-transfer rate-limiting phenomenon (upper bound for mass transfer). This transition provides a basis for selecting operating conditions for industrial processes and informs the development of in-reservoir and surface-facility process models.21 2. Experimental Section 2.1. Materials. Two samples of Athabasca bitumen (Alberta, Canada) from different technological stages of bitumen production were obtained from Syncrude Canada, Ltd. Both samples are derived from mined bitumen subjected to warm-water extraction, naphtha dilution, and naphtha recovery but with a different extent of naphtha and light end removal. The sample with a density of 1000 kg m-3 and viscosity of 18 Pa s at 297 K is referred to as Athabasca bitumen and was previously characterized and used for diffusion coefficient measurements.4,5 The second more viscous sample from a later stage of naphtha removal, Athabasca atmospheric residue (coker feed), has a density of 1028 kg m-3 and viscosity of 2600 Pa s at 297 K. Its chemical composition is described elsewhere.22 The second sample has a significantly higher asphaltene and inorganic matter content, because more of the lighter components were removed by distillation. Anhydrous pentane (mass fraction purity not less than 0.99) was purchased from Fisher Scientific and used without additional purification. 2.2. Local Composition Measurements. Mutual diffusion coefficients and mass-transfer coefficients for Athabasca bitumen þ pentane and Athabasca atmospheric residue þ pentane mixtures at 297 K and atmospheric pressure were derived from local compositions and their spatial and time derivatives using a free diffusion method and a forced mass-transfer method, respectively, using an X-ray view-cell apparatus. The apparatus and experimental procedure for the free diffusion method were described previously.4,5,23 The apparatus consists of three principle parts: (1) a Phillips MCN-165 tungsten-target bremsstrahlung X-ray source with spectral end-point energies between 5 and 160 keV, (2) a cylindrical glass tube (internal diameter of 37 mm and length of 130 mm) filled with a sample, sealed, and placed on a holder, and (3) an X-ray video-capture system comprising of a Microphotonics X-ray imager LA 115 mn, with a spatial resolution of 150 μm/pixel and an image capture speed of 33 frames/s, Image-Pro Express, version 6.0 (from Media Cybernetics, Inc.), software for image processing and analysis. For forced mass-transfer experiments, a turbine impeller (Figure 1; 24 and 30 mm in diameter of upper and lower planes and 12 mm in height) was inserted in the glass tube. The rotational speed was controlled with an IKA RW 16 controller (Fisher Scientific), calibrated using an optical tachometer and having a rotation speed range from 0.67 to 20 Hz. Feedstock samples were placed in the bottom of a cylindrical glass tube, and pentane was added on top. If present, the base of the impeller was placed 22 mm above the initial liquid-liquid interface. Composition changes occurring with time along the vertical axis were obtained from transmitted X-ray video images. Intensities from 100 consecutive images, captured over a 3 s interval, were averaged across 1 pixel (150 μm) vertically and 38 pixels (5.7 mm) horizontally. Horizontal composition gradients parallel or perpendicular to the beam are not obtained. The averaged local intensities were normalized with respect to
(14) Zou, X.; Zhang, X.; Shaw, J. M. The phase behavior of Athabasca vacuum bottoms þ n-alkane mixtures. SPE Prod. Oper. 2007, 22 (2), 265–272. (15) Mamidi, S. S.; Meas, B.; Farhat, T. R. Rotational hydrodynamic diffusion system to study mass transport across boundaries. Anal. Chem. 2008, 80 (21), 8109–8114. (16) Gregory, D. P.; Riddiford, A. C. Dissolution of copper in sulfuric acid solutions. J. Electrochem. Soc. 1960, 107 (12), 950–956. (17) Gharehbagh, F. S.; Mousavian, S. M. A. Hydrodynamic characterization of mixer-settlers. J. Taiwan Inst. Chem. Eng. 2009, 40 (3), 302–312. (18) Tezura, S.; Kimura, A.; Yoshida, M.; Yamagiwa, K.; Ohkawa, A. Solid-liquid mass transfer characteristics of an unbaffled agitated vessel with an unsteadily forward-reverse rotating impeller. J. Chem. Technol. Biotechnol. 2008, 83 (5), 763–767. (19) Torab-Mostaedi, M.; Safdari, S. J.; Moosavian, M. A.; Ghannadi Maragheh, M. Mass transfer coefficients in a Hanson mixersettler extraction column. Braz. J. Chem. Eng. 2008, 25 (3), 473–481. (20) Tao, J. C.; Cussler, E. L.; Evans, D. F. Accelerating gallstone dissolution. Proc. Natl. Acad. Sci. U.S.A. 1974, 71 (10), 3917–3921.
(21) Moghadam, S.; Nobakht, M.; Gu, Y. Theoretical and physical modeling of a solvent vapour extraction (VAPEX) process for heavy oil recovery. J. Pet. Sci. Eng. 2009, 65 (1-2), 93–104. (22) Bazyleva, A. B.; Hasan, M. A.; Fulem, M.; Becerra, M.; Shaw, J. M. Bitumen and heavy oil rheological properties: reconciliation with viscosity measurements. J. Chem. Eng. Data 2010, 55 (3), 1389–1397. (23) Abedi, S. J.; Cai, H. Y.; Seyfaie, S.; Shaw, J. M. Simultaneous phase behaviour, elemental composition and density measurement using X-ray imaging. Fluid Phase Equilib. 1999, 158-160, 775–781.
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Figure 1. Turbine impeller: (a) side view, (b) front view, and (c) position in the view cell.
available,25-28 and derivations of the equations employed here are available elsewhere.4,5 Key points are rehearsed for clarity and completeness. 3.1. Mutual Diffusion Coefficients. The one-dimensional equation of continuity for a binary mixture in the absence of a chemical reaction and bulk flow is expressed as ∂fFðw2 Þw2 ðx, tÞg ∂ ∂w2 ðx, tÞ ¼ Fðw2 ÞD12 ðw2 Þ ð2Þ ∂t ∂x ∂x
transmitted intensities for pentane and feedstock at the same elevation to obtain composition profiles. From standard X-ray optics, the intensity of a transmitted X-ray beam I is I ¼ I0 expð- FλΔxÞ
ð1aÞ
where the incident beam intensity is I0, the density of a sample is F, the thickness of a sample is Δx, and the mass absorption coefficient of the sample is λ.23,24 Because the incident beam intensity and sample thickness at each elevation are invariant and the variation of the absorption coefficient, dependent upon elemental composition, is small, the mass fraction of pentane, w2, at each elevation can be approximated as h i ln II1 F - F1 ð1bÞ w2 h i I2 F 2 - F1 ln
where x is the spatial coordinate, t is the time, D12(w2) is the mutual diffusion coefficient, w2(x,t) is the composition of component 2 (pentane in this work), and F(w2) is the mass density. Equation 2 can be transformed to eq 3, which is more suitable for treatment of experimental concentration profiles, by completing the indicated differentiations 9 8 > > w2 ∂F ∂w2 2 > > ∂ w > > 2 = 1 þ F ∂w ∂t < ∂F 1 2 2 ∂D12 þ ∂x 2 ¼ þ D12 ð3Þ 2 > > ∂w F ∂w2 > ∂w2 > ∂w2 > > 2 ; : ∂x ∂x
I1
where I1 and I2 are the local transmitted X-ray intensities of the feedstock and pentane, respectively. The ln of intensity is proportional to density. Explicit assumptions in the derivation of eq 1b include that the volume of mixing is negligible and that X-ray absorbance is composition-invariant. The repeatability of composition and interface position measurements is (0.25 wt % and (75 μm, respectively.
Direct analysis of the composition profiles in free diffusion experiments yields composition derivatives with time at fixed position and with space at fixed time. Density is assumed to vary linearly with composition in the construction of the composition profiles. The density derivative with composition is thus F2 - F1. In the absence of a general theory for the variation of diffusion coefficients with composition, one can express the mutual diffusion coefficient and its derivative with composition as a Taylor series expansion
3. Computation of Mutual Diffusion Coefficients and Forced Mass-Transfer Coefficients Diffusive and forced mass transfer is treated in numerous references. Pertinent standard reference texts are readily (24) Kaelble, E. F. Handbook of X-rays: For Diffraction, Emission, Absorption, and Microscopy; McGraw-Hill: New York, 1967. (25) Bird, R. B.; Stewart, W. E.; Lightfoot, E. N. Transport Phenomena; Wiley: New York, 2002. (26) Poling, B. E.; Prausnitz, J. M.; O’Connell, J. P. The Properties of Gases and Liquids; McGraw-Hill: New York, 2001. (27) Basmadjian, D. Mass Transfer Principles and Applications; CRC Press (Taylor and Francis Group): Boca Raton, FL, 2004. (28) Geankoplis, C. J. Transport Processes and Separation Process Principles, 4th ed.; Prentice Hall: Upper Saddle River, NJ, 2003.
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D12 ¼ R þ βðw2 Þ þ εðw2 Þ2 þ γðw2 Þ3 þ :::
ð4Þ
∂D12 ¼ β þ 2εðw2 Þ þ 3γðw2 Þ2 þ ::: ∂w2
ð5Þ
Energy Fuels 2011, 25, 782–790
: DOI:10.1021/ef101435r
Sadighian et al. Table 1. Liquid-Phase Mutual Diffusion Coefficients, D12, for Mixtures of Athabasca Bitumen þ Pentane and Athabasca Atmospheric Residue þ Pentane at 297 Ka Athabasca bitumen þ pentane w2
1010D12 (m2 s-1)
1010σb (m2 s-1)
0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9
1.45 1.46 1.48 1.50 1.52 1.54 1.56 1.59 1.61 1.64 1.67 1.70 1.73 1.76 1.80 1.84 1.88
0.09 0.10 0.19 0.20 0.18 0.14 0.17 0.16 0.08 0.06 0.02 0.01 0.01 0.003 0.004 0.02 0.6
Athabasca atmospheric residue þ pentane w2
1010D12 (m2 s-1)
1010σb (m2 s-1)
0.66 0.67 0.68 0.69 0.7 0.71 0.72 0.73 0.74 0.75 0.76 0.77
0.50 0.51 0.52 0.54 0.55 0.56 0.57 0.58 0.60 0.61 0.62 0.64
0.06 0.03 0.01 0.007 0.004 0.002 0.004 0.02 0.04 0.09 0.15 0.22
a Reported values were averaged over all composition profiles. b Error evaluated from extremes obtained from sets of three profiles, the minimum needed to evaluate time derivatives.
Figure 2. Pentane mass fraction profiles for the free diffusion experiments: (a) mixture of 30 mL of Athabasca bitumen and 70 mL of pentane and (b) mixture of 20 mL of Athabasca atmospheric residue and 80 mL of pentane.
Equations 4 and 5 can be substituted into the objective function (OF) 0 9 8 > > > ∂2 w2 > > > B = < ∂F 1 n B∂D12 2 1X ∂x þ OF ¼ absB þ D 12 h i B 2 > > n 1 ∂w2 F @ ∂w2 > ∂w2 > > > ; : ∂x
1 w2 ∂F ∂w2 1 þ F ∂w ∂t C 2 C C 2 A ∂w2 ∂x
Figure 3. Mutual diffusion coefficients averaged over all concentration profiles measured for (9) Athabasca bitumen þ pentane (this work), (b) Athabasca bitumen þ pentane (reported in ref 4), and (2) Athabasca atmospheric residue þ pentane (this work).
ð6Þ
pentane, M2, is constant. Differentiation of eq 7 with respect to time gives the mass flux of feedstock, component 1 1 ∂M1 M2 - 1 ∂w2 ð8Þ ¼ A ∂t A w2 2 ∂t
which is then minimized using available composition profiles to obtain values for the parameters R, β, ε, and γ. In eq 6, n is the number of measurements in a composition profile. Typically, n exceeds 100. Because time and spatial derivatives are required, a minimum of three and typically eight composition profiles are regressed simultaneously. 3.2. Forced Mass Transfer. The mass of feedstock transferred across the interface into the pentane-rich liquid is computed from two independent sets of experimental measurements. (1) From the composition of the pentane-rich liquid ð7Þ M1 ¼ M2 ð1 - w2 Þ=w2
where A is the interfacial area. (2) From the elevation of the interface 1 ∂M1 ∂h ¼ - F1 A ∂t ∂t
ð9Þ
where h is the interface elevation, defined as the elevation where w1 deviates from unity, and F1 is the density of the feedstock. The composition of the pentane-rich liquid and the interface elevation are obtained from the composition profiles. While the X-ray transmission measurements are insensitive to whether the feedstock is dispersed or soluble, expressions for mass-transfer coefficients are sensitive because the
where M1 and M2 are the masses of feedstock and pentane, respectively, in the pentane-rich liquid phase. The mass of 785
Energy Fuels 2011, 25, 782–790
: DOI:10.1021/ef101435r
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composition of the pentane-rich phase is a function of time in the experiments if the feedstock is soluble. Because the feedstocks are only partially soluble, asymptotic solutions for the mass-transfer coefficient (K), in terms of the pentane-
rich liquid composition and interface elevation, are presented without proof as eqs 10a and 10b, for miscible species, and eqs 11a and 11b, for immiscible species.
M2 - 1 ∂w2 K ¼ AF1 w2 3 ∂t - 1 ∂h K ¼ w2 ∂t M2 - 1 ∂w2 K ¼ AF1 w2 2 ∂t
ð10bÞ
∂h K ¼ ∂t
ð11bÞ
ð10aÞ
ð11aÞ
At a minimum, the asphaltene þ inorganic matter fractions comprising more than 15 wt % of the feedstocks are insoluble and remain dispersed in the pentane-rich liquid. Thus, the anticipated behavior falls between eqs 10a and 11a or, equivalently, between eqs 10b and 11b. While these four expressions for the mass-transfer coefficient appear to differ, the pentane composition of the pentane-rich phase remains close to unity during experiments. Measured variables (elevation, density, effective interface area, mass, and composition) also possess experimental uncertainty. Thus, the
Figure 4. Pentane mass fractions above and below the impeller as a function of distance from the Athabasca bitumen - pentane interface. Time is a parameter: (2) t = 0.3 h, (b) t = 1.1 h, (9) t = 3 h, and (|) impeller boundaries.
Figure 5. Pentane mass fraction profiles for the forced mass-transfer experiments for 20 mL of Athabasca bitumen þ 80 mL of pentane with the mixing rates: (a) 2.31 Hz, (b) 5.16 Hz, (c) 6.90 Hz, and (d) 9.75 Hz.
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impact of miscibility or miscibility differences on masstransfer coefficients is unlikely to be detected. 3.3. Interfacial Mass-Transfer Coefficient Correlations for Stirred Vessels. The boundary layer or film theory relates the mass-transfer coefficient (K) to the boundary layer thickness (δ) and the mutual diffusion coefficient (D12)27,28 D12 ð12Þ K ¼ δ where the boundary layer is assumed to be laminar and where only molecular diffusion occurs. Because interfacial mass transfer is a function of shear field intensity adjacent to an interface, vessel geometry, impeller geometry, the distance between the impeller and the interface, and other field variables play significant roles in interfacial mass transfer. Correlations, employing dimensionless groups, have been developed for specific geometries and applications, especially for turbulent mass transfer. Correlations for masstransfer coefficients in agitated vessels include eq 13 for solid-liquid mass transfer and eq 14 for liquid-liquid mass transfer.27 These equations are valid for 102 < Re = (di2NF)/ (μ)
