Experimental and Modeling Study of Residual Liquid Recovery from

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Experimental and Modeling Study of Residual Liquid Recovery from Spent Sand in Bitumen Extraction Processes from Oil Sands Moosa Rabiei Faradonbeh, Mingzhe Dong,* Thomas G. Harding, and Jalal Abedi Department of Chemical and Petroleum Engineering, University of Calgary, Calgary, Alberta T2N 1N4, Canada S Supporting Information *

ABSTRACT: Disposing solid residue with high liquid content into the environment may impact the immediate ecosystem and its surroundings. In bitumen recovery process from oil sands, it is environmentally and economically desirable to effectively recover as much of the liquid trapped in the spent solids as possible, prior to releasing it into the environment. An experiment was designed to investigate the effect of capillary force to enhance liquid recovery by using a thin, semipermeable layer as the membrane. The results indicate that by employing a membrane at the outlet, and pressurizing the air above the sand bed, the average liquid saturation can be decreased by 50%; however, the maximum pressure applied is restricted by the physical characteristics of the membrane. A mathematical model is developed to predict the liquid saturation profile along the sand pack during transient and steady-state conditions, and results are validated against measured average saturation using two different sand types. Results suggest that more liquid can be recovered from the spent sand bed by increasing the height of the bed; however, the required time to achieve the maximum recovery is increased as well. This method can be applied to reduce the liquid content of spent sand from any process before it is disposed of, thereby reducing possible hazards which may affect the environment.

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INTRODUCTION Trillions of barrels of bitumen are contained in the Cretaceous sands of northern Alberta; about 18% of the deposit can be recovered by surface mining.1 The hot water extraction process,2 the only successful commercial process for extracting bitumen from surface-mineable oil sands, has encountered serious problems including: high energy and water consumption; greenhouse gas emissions; and accumulation of considerable volumes of tailings, which impact the surrounding environment. Recycling tailing pond water allows for a reduction in the need for freshwater withdrawals, and also promotes bioremediaion through the removal of pollutants that contribute to acute and chronic toxicity in aquatic biota, ensuring that downstream sites meet water guidelines for the protection of aquatic ecosystems.1 In a solvent extraction process, oil sand is mixed with a lowboiling-point solvent, followed by the separation of the bitumen-solvent mixture from the spent sands. This method has been tested by numerous experimental studies, reported in the literature. Cormack et al.3 extracted bitumen form Athabasca oil sands using various solvents in a batch, stirred vessel. They identified the solvent type, solid concentration, stirrer speed, and contact time as important factors in the extraction process. They found that solvents with a higher fraction of aromatic compounds have a higher solvating power in the dissolution of bitumen. In another study, Meadus et al. 4 © 2013 American Chemical Society

employed bitumen-derived hydrocarbon fractions, such as naphtha and kerosene, to extract bitumen from oil sands in a rotating contactor. They observed a higher solvency of bitumen in naphtha than in kerosene, which they attributed to the higher aromatic content. For either of these processes, there is an urgent need to find a new processing method which will reduce the environmental footprint caused by tailing ponds, and make the operation sustainable. Screening is the simplest method for solid−liquid separation, in which gravity is the major desaturating force. In this method, the liquid retention forces will be governed by particle size distribution, liquid viscosity, surface tension, and the wettability of the solids by the saturating fluid.5 In the screening method, higher fines content ( 0 ⎨ ⎪ dPcD ∂SwD − 1 = 0 z D = 1, t D > 0 ⎪ ⎩ dSwD ∂z D

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Case 1: Without Membrane. Under this condition, capillary pressure at the production tube is zero, which, based on the capillary continuity concept, implies that the liquid saturation at the bottom of the core is equal to unity. In this case, the corresponding boundary condition at z = 0 will be as follows:

(8)

SwD = 1

Having the saturation distribution at each time, it is possible to calculate the average saturation of the column by integrating over the total length, and determining the recovery versus time during free gravity drainage. As mentioned earlier, the nature of eq 1 is diffusive, and it is expected to attain a steady state saturation profile after a long time. The corresponding recovery at later times would be the maximum recovery achievable without pressurizing the air at the top of the column. It can be shown that the fractional recovery at the end of the free gravity drainage can be expressed by the following relation: r = 1 − BwD(1 − e−1/ BwD)

Applying the relationships for the relative permeability and capillary pressure (eqs 5 and 6), eq 10 along with the boundary conditions (eqs 11 and 12), has an analytical solution in the following form (see the Appendix): ⎛ 1 − e−n w (1 +ΔPgD)/ BwD ⎞ ⎟⎟(1 − e−n w z D/ BwD) [SwD(z D)]n w = 1 − ⎜⎜ 1 − e−n w / BwD ⎝ ⎠ (13)

As eq 13 shows, the liquid saturation at each height decreases by increasing the pressure difference at the top of the sand pack. The average saturation and corresponding fractional recovery at the given pressure, in steady state conditions, can be calculated by numerical integration of the saturation distribution obtained in eq 13, along the length of the column. Case 2: With Membrane. The membrane is a thin, porous layer used at the bottom face of the sand pack, which is 100% saturated with the wetting liquid phase during the liquid recovery by forced drainage. Since the membrane is impermeable to gas, the liquid will be a continuous phase, and its pressure is equal to the atmospheric pressure. Just above the membrane, on the bottom face of the sand core, the liquid saturation is less than unity because some liquid has been produced by pressurized air, which has overcome the capillary pressure. Using definition of the capillary pressure, we have the following:

(9)

It can be inferred from the above equation that the final recovery is only a function of BwD, which in turn depends on the capillary pressure constant (Bw), density of the liquid and height of the column. For example, the recovery factor decreases by increasing the value of Bw, which corresponds to a higher fraction of fine sand particles. Forced Drainage. In the case of the forced drainage, the air at the inlet face of the core is pressurized and held constant. Higher air pressure overcomes the capillary pressure, and more fluid is expelled from the sand pack. After an adequate amount of time, when no more liquid is produced at the prevailing condition, pressure is increased to a higher level, and the procedure is repeated until air breaks through from the outlet face. The equation for the forced gravity drainage is the same as the previous one, except we need to consider the saturation profile at the end of each pressure step, where no more liquid is produced at the given air pressure on the top. Therefore, we have the following: ⎛ dP ∂S ⎞⎤ ∂ ⎡ ⎢ −k rw ⎜ − cD wD + 1⎟⎥ = 0 ∂z D ⎢⎣ ⎝ dSwD ∂z D ⎠⎥⎦

Pc = Pg − Pw = Pg − Pa = ΔPg

(14)

and, therefore, the dimensionless boundary condition at zD = 0 is found to be as follows: SwD = e−ΔPgD/ BwD

(15)

The solution of eq 10, along with the boundary conditions (eqs 11 and 15), in this case is as follows:

(10)

The upper boundary condition for the above differential equation is found by using the steady state assumption, where there is no liquid production at a given pressure. Since the flow rate of the wetting phase is zero, the flow potential at the top and bottom of the column should be the same. By equating the flow potentials at both sides, the dimensionless liquid saturation at the upper boundary is found to be (see the Appendix): ⎛ ΔPgD + 1 ⎞ SwD = exp⎜ − ⎟at z D = 1 BwD ⎠ ⎝

(12)

SwD(z D) = e−z D+ΔPgD/ BwD

(16)

This equation is another representation of the hydrostatic equilibrium along the column, when it is incorporated with the capillary pressure equation and assumption of negligible pressure gradient in the gas (air) phase. Integration of eq 16 over the total length of the core gives the average saturation as function of air pressure, expressed in dimensionless form as follows:

(11)

−ΔP / B −1/ BwD SwD ) ̅ (ΔPgD) = BwDe gD wD(1 − e

where ΔPgD is normalized pressure difference of the air at the upper and lower face of the sand pack. By specifying the other boundary condition at the production face, the solution of eq 10 is complete. The boundary condition at the outlet face depends on whether or not a membrane is used at the bottom of the column. At the outlet face, liquid is produced through a U-shape tube, which is used to ensure contact with 100% of the liquid. Since the solution of eq 10 depends on the second boundary condition as well, we have two cases, depending on presence of a membrane at the lower end of the core.

(17)

The above relation shows that by increasing the gas phase pressure, the average wetting phase saturation decreases exponentially; however, there is a limiting value for the gas pressure above which gas breaks through. This pressure depends on the physical property of the membrane used. Equation 17 can be used to calculate fractional recovery at each pressure level. For example, in the case of the zero pressure difference (free gravity drainage), the recovery factor using above relation can be simplified to eq 9 for free gravity drainage process. 2112

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Figure 2. Profile of liquid saturation versus height for a sand column with BwD = 0.5 and (a) at different time steps during free gravity drainage; (c) at different pressures during forced drainage and without membrane at the outlet (Case 1); (e) at different pressures during forced drainage and with membrane at the outlet (Case 2). Fractional liquid recovery for a column with different sand types for (b) case a; (d) case c; and (f) case e.

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RESULTS AND DISCUSSION

the saturation profile reaches an equilibrium state after a sufficient amount of time. At early times, there is an abrupt change in liquid saturation at the top of the column; however, the rate of the saturation change decreases at later times. This can be explained by the fact that in the early stages, the top portion has a high liquid saturation, and there is a higher potential to flow, whereas during the later stages, air has replaced the drained area, and the potential for moveable liquid is small; therefore, according to the Darcy’s law, the rate decreases with time.

Free Gravity Drainage. Figure 2(a) displays the profile of liquid saturation in the sand column during free gravity drainage, at different time steps predicted by eq 1, and corresponding the boundary conditions of eq 8. Equation 1 is a diffusion equation in terms of saturation, with a variable diffusion coefficient. As characteristic of the nature of diffusion, saturation would propagate along the length of the sand column, in order to remove sharp gradients. It is expected that 2113

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Having the membrane at the outlet of the sand pack means the liquid saturation at the production end also decreases, and since this portion has high saturations after free gravity process, more liquid can be removed by pressurizing the air at the top. Also, the process can perform with higher pressure levels since the membrane will restrict the air flow, to some extent. As shown in Figure 2(e), even a small pressure difference is very effective in lowering the saturation at the production face; however, there is a limitation in the maximum pressure applied. The membrane is a very thin, porous layer which allows the liquid to pass through it and prevents the passage of air. For each membrane, there is a maximum pressure beyond which air can pass through, and this pressure depends on the pore size of the membrane. When this pressure is exceeded, air can flow across the membrane and bypasses the liquid phase. As a result, no more liquid will be produced since its phase become discontinues. Figure 2(f) illustrates the fractional recovery during forced drainage using membrane at steady state condition. It is revealed form the graph that, for the systems with smaller values of BwD, a small pressure difference can significantly increase the liquid recovery. Also, for those with larger values of the dimensionless capillary constant, a very high pressure is needed to achieve a high recovery factor, which may not be practical as there is a limit to the pressure for a given membrane. Theoretically, all systems (with different BwD) can achieve the recovery of 100% at infinite pressure. This graph can offer a practical application in recovery of liquid from the spent sand. Assume the value of BwD = 2 for a given sand type and column height, the recovery factor at dimensionless pressure of unity would be equal to 0.52. Now if the height of the column doubles, the corresponding recovery factor for the new system at the same value of air pressure would be 0.62, which corresponds to 10% increase in liquid recovery. Experimental Results. The size distribution of both the clean sand and the extracted sand (obtained by dry-sieving method) are plotted in Figure 3. It is evident that the extracted

It is interesting to note that the curvature of the saturation distribution also changes throughout the gravity drainage process. This phenomenon can be described by the interaction of gravitational and capillary forces, which contribute to the fluid flow in the system. Initially, the saturation is very high and capillary forces are small, whereby the liquid at high elevation has more potential (gravitational force) to flow downward. As more liquid is drained, its saturation decreases and, consequently, capillary forces increases, while the magnitude of the gravitational forces becomes smaller by decreasing the liquid height. Finally, the saturation profile reaches a steady state condition (shown by red color), where both capillary and gravitational forces are at equilibrium. The distribution profile, shown in Figure 2(a), is for the system with a dimensionless capillary pressure constant (BwD) of 0.5. For systems with larger values of BwD, the curve would be steeper, due to either a higher capillary pressure constant, Bw, or a smaller liquid height, H (see eq 7). The fractional recovery versus time in the free gravity drainage process is illustrated in Figure 2(b) for different rock types and drainage height systems. It can be inferred from the graph that, for a given type of sand, fractional recovery increases by increasing the height of the liquid column. However, the time required for achieving the maximum recovery will be longer. The reason for this is, simply, because the gravity drainage is a slow process, and it would take more time to complete for longer column heights. For a sand pack with the same height, lower recovery factors will be obtained for sands with high fractions of fine particles, corresponding to larger capillary constants; however, the process is faster and more liquid is left behind. Forced Drainage. The recovery of liquid by free gravity drainage process is stopped once it reaches equilibrium between gravity and capillary forces. Pressurizing the air at the top of the sand column can drain more liquid from the sand pack, to some extent, depending on the methodology employed. Figure 2(c) represents the steady state distribution of liquid saturation at different dimensionless pressure differences, when no membrane is employed at the outlet. The curve with PgD = 0 corresponds to the profile at the end of the free gravity drainage. As a constant saturation boundary condition is used at the outlet (eq 12) for forced drainage, the high liquid saturation near the outlet of the sand pack does not change much, and the applied air pressure can only reduce the saturation in the upper sector of the sand pack. Lower saturations at the top cannot have a major contribution to the liquid production, even at very high air pressures, as shown in Figure 2(c). Additionally, air breaks through at much lower pressure levels, as there is no restriction on air flow at the production face. Figure 2(d) shows the fractional recovery as function of pressure for different dimensionless capillary pressure constants. Generally, raising the air pressure does not improve the recovery factor significantly, particularly for smaller values of BwD. Similar to the free gravity drainage, increasing the height of the liquid column for a given sand type would increase the fractional recovery factor, which is almost the same as the free gravity drainage recovery. However, for a fixed height of sand pack, higher pressures would increase the recovery factor for sands with larger capillary pressure constants (or sand with a higher proportion of fine particles), but the maximum applied pressure is very limited. In this case, the high liquid saturation in the top segment of the column will contribute in liquid production.

Figure 3. Size distribution of sand particles used for residual liquid recovery.

sand contains a higher fraction of fine particles than the clean sand; however, the exact fine fraction is expected to be higher due to lower accuracy of the dry-sieve method for fine particles. More liquid would be trapped in sand with a higher proportion of fine particles because of the small pores formed by the fine minerals. As such, it requires higher pressure levels to overcome 2114

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Figure 4. Variation of the average liquid saturation with pressure for the column packed with (a) clean sand with measured parameter of Bw = 3.6 KPa; (b) extracted sand with measured parameter of Bw = 4.1 KPa.

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the capillary pressure and recover the residual liquid. Therefore, this graph can represent the sand type and can be used to compare some characteristics of the sand type, such as capillary pressure constant (Bw). Figure 4 illustrates the variation of average liquid saturation left behind, at different applied air pressures, for the column packed with clean and extracted sand. This figure clearly shows that employing a membrane at the outlet face and gradually pressurizing the air at the top has the potential to significantly reduce the trapped liquid saturation and improve the total recovery of the trapped liquid by about 50%, in both types of sand; however, there is a limitation to the maximum pressure applied, which depends on the physical specification of the membrane used. In the analytical modeling of free gravity drainage and forced drainage, the measured values of Bw are used. Predictions are in good agreement with the experimental results for both cases. Referring to Figure 3, the extracted sand has a higher fraction of fine particles, which holds more liquid inside the small pores and therefore results in higher saturations at the end of both the free and forced gravity drainage processes shown in Figure 4. It implies that the grain size distribution of the sand has a major effect on the amount of liquid trapped in the sand bed. The trends for situations with and without a membrane are similar for both types of sands and the predicted values follow the experimentally measured saturations. It has to be noted that the experimental measurements have to be obtained in a steady state condition, where there will be no more production at the given air pressure. Therefore, it would take longer if the height of the sand pack is increased. The experimental measurements in Figure 4(a),(b) confirm the validity of the assumptions used and mathematical model developed for the liquid recovery using a membrane. The findings can be applied in the recovery of liquid trapped in spent sand during hot water or solvent extraction of bitumen from oil sands or removing contaminants from soil in any other processes, and will ultimately help reduce potential hazards to the environment.

ASSOCIATED CONTENT

* Supporting Information S

Appendix showing unsteady state equation of saturation profile. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Phone: (403)210-7642; fax: (403) 284-4852; e-mail: mingzhe. [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Acknowledgment is gratefully extended to Syncrude Canada Ltd. and the University of Calgary Department of Chemical and Petroleum Engineering for their financial support of the project. The authors are also thankful to Syncrude Canada Ltd. for providing oil sands and naphtha samples to this study.

■ Bw g H K kri kr0 n P r t V z

NOMENCLATURE capillary pressure constant, ML−1T−2 gravitational acceleration, LT−2 height of the sand pack, L absolute permeability, L2 relative permeability to phase i coefficient of relative permeability correlation exponent of relative permeability correlation pessure, ML−1T−2 recovery factor time, T velocity, LT−1 vertical coordinate direction

Greek Letters

Φ μ ρ ϕ Δ

flow potential, ML−1T−2 dynamic viscosity, ML−1T−1 density, ML−3 porosity difference

Subscripts

a 2115

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capillary dimensionless gas phase wetting phase connate wetting phase

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