Oil displacement through pores plays a critical role in increasing the efficiency of oil recovery. Injecting water into the reservoir is one available method. During water flooding, the force responsible for displacing oil is a viscous force. The displacement behavior between the displacing and displaced fluid is not piston-like, in which water pushes all of the oil from the pores to the displacement front (Buckley & Leverett, 1942). Rather, the difference in viscosity between water and oil forms viscous fingers, which result in both early breakthrough and reduced sweep efficiency. Therefore, the use of a more viscous liquid than water is beneficial in improving the sweep efficiency in water flooding.
In a laboratory setting, Detling (1944) tested different types of materials for viscous water flooding. Barens (1962) used sugar and zinc chloride to improve water sweep in reservoirs partially invaded by aquiver water. The results indicated that the use of viscous water can increase the ultimate oil recovery. However, the use of materials such as sugar and glycerin to increase water viscosity is not economically feasible. Water-soluble polymers work more efficiently as thickening agents. Sandiford (1964) added partially hydrolyzed polyacrylamide during water flooding to reduce water mobility and increase oil recovery. According to Pye (1964), certain high molecular weight synthetic polymers in very dilute solutions can decrease the water mobility in porous media 5 to 20 times more than brine solution at the same viscosity.
The oil recovery efficiency (overall displacement efficiency, E) of any EOR technique is the amount of hydrocarbon displaced divided by the volume of hydrocarbon at the beginning of the EOR process; it also can be defined as the product of the microscopic efficiency (ED) and the macroscopic efficiency (EV), as expressed in Equation below.
Microscopic displacement efficiency, ED
ED is reflected in the magnitude of the residual oil saturation, Sor, in the area that the displacing fluid contacts. The microscopic efficiency also can be expressed in terms of saturation using Equation below.
where Soi is the oil saturation at the beginning of the EOR process (displacing agent) and Sor is the residual oil saturation in the pore volume after being swept during the EOR process (displacing agent).
Factors affecting microscopic displacement behavior:
The microscopic efficiency plays a significant role in the successful application of EOR techniques because it reflects the extent to which a certain displacement process can reduce the residual oil saturation. The residual oil can be recovered if the displacing agent causes a viscous force that exceeds the retention or capillary force (Abrams, 1975; Chatzis & Morrow, 1984). The viscous force refers to the viscous pressure gradient (ѵµ), while the retention force or capillary force is related to the interfacial tension (σ) between the displacing and displaced fluids (Wang et al., 2007). The ratio of viscous to capillary forces is called the "capillary number," which can be defined as the ratio of the viscous pressure gradient (viscous force) to the interfacial tension.
where ѵ is the interstitial velocity, µ is the viscosity of the displacing fluid, and σ is the interfacial tension between oil and the displacing fluid.
The capillary number has been reported in the range of 10-6 to 10-7 for water flooding processes (Donaldson et al., 1989). The capillary number increases as the viscous force increases and the interfacial tension decreases. Many researchers have conducted laboratory tests and field applications to improve the displacement efficiency by increasing the capillary number.
The first step of any displacement process is to mobilize residual oil and form an oil bank that can be mobilized by increasing the capillary number above the critical capillary number (Ncc). Laboratory studies have shown that the Ncc is affected by wettability (Melrose & Brandner, 1974; Ramakrishnan & Wasan, 1984; Lake, 1989). If oil is the non-wetting phase, the residual oil saturation decreases as the Ncc increases with an order of magnitude of 10-5 (Melrose & Brandner, 1974). However, the Ncc for the wetting phase is two orders of magnitude higher than the Ncc for the non-wetting phase (Ramakrishnan & Wasan, 1984). Some studies have found that the minimum critical value of the capillary number is approximately 10-4 (Leferbre du Prey, 1973; Moore & Slobod, 1956). However, other studies (Melrose & Brander, 1974; Ng et al., 1978; Chatzis & Morrow, 1984) have suggested that the minimum value of Ncc is 10-5. Figure p11 shows the effect of the capillary number on the residual oil according to different studies. The maximum Ncc is of the order of 10-2 to 10-1 for 100% displacement oil from the reservoir (Donaldson et al., 1989), as shown in Figure p12.
Figure p11. Capillary number versus residual oil saturation (Fulcher et al., 1985)
Figure p12. Microscopic displacement efficiency versus capillary number(Donaldson et al., 1989)
When viscoelastic fluid flows through the pores, the molecules continuously stretch and recoil in porous media, thereby improving the sweep efficiency (Urbissinova & Kuru, 2010), as shown in Figure p13.
Figure p13. Schematic of viscoelastic polymer solution flow in porous media (Urbissinova & Kuru, 2010)
Previous laboratory studies of polymer flooding ignored the effect of polymer viscoelasticity on the capillary number and the microscopic displacement efficiency (Smith, 1970; Hirasaki & Pope, 1974). Recently, numerous studies have shown that viscoelastic polymer helps to improve the microscopic displacement efficiency more than water flooding (Demin et al., 2000; Huh & Pope, 2008; Jiang et al., 2008; Kamaraj et al., 2011; Urbissinova & Kuru, 2010; Wang et al., 2007; Demin et al., 2001; Wenxiang et al., 2007; Xi et al., 2004; Yin et al., 2012; Yin et al., 2006).
Wenxiang et al. (2007) studied the relationship between the capillary number, the displacement efficiency, and the residual oil saturation during polymer flooding in weak oil-wet cores. They found that when the capillary number was small, the recovery efficiency increased slowly, and the residual oil saturation decreased slowly as the capillary number increased; however, when the capillary number reached between 10-3 and 10-2, the increase in the oil recovery efficiency and the reduction in the residual oil saturation was marked (Wenxiang et al., 2007), as shown in Figure p14. The results also revealed that at the same polymer solution elasticity, the higher the capillary number, the higher the recovery efficiency and the lower the residual oil saturation. They concluded that the capillary number and the elasticity of the polymer solution are important to the improvement of polymer flooding oil recovery.
Figure p14. Capillary number at different elasticities (Wenxiang et al., 2007)
Recent laboratory and numerical studies have shown that the capillary number theory accurately explains the results of Newtonian fluid flooding, but the macro pressure gradient cannot explain the increase in the microscopic displacement efficiency in viscoelastic polymer flooding (Jiang et al., 2008). Wang (2007) and Jiang (2008) showed that the displacement efficiency increases due to the micro force during polymer flooding, which is caused by the change in both the direction and magnitude of the fluid velocity. The magnitude of force is proportional to the mass and the change of flow velocity:
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Macroscopic (sweep) displacement of fluid in a reservoir, EV
Volumetric efficiency or sweep efficiency is defined as the fraction of the reservoir (pore volume) that is swept or invaded by displacing fluid. The estimation of volumetric sweep efficiency is very important to know which portion of reservoir is swept by the invaded fluid.The volumetric sweep efficiency can be estimated using material balance concepts. The oil recovery can be calculated using the following equation:
The volumetric sweep efficiency is expressed as follows:
where Np is the displaced oil, Vp is the reservoir pore volume, and So1 and So2 are the oil saturation at the beginning and end of the displacement process, respectively.
The volumetric sweep efficiency is commonly estimated using areal and vertical sweep efficiencies, as follows:
where EA is the areal sweep efficiency and EI is the vertical sweep efficiency.
Vertical sweep efficiency (EI)
EI is defined as the ratio of pore space invaded by the displacing fluid to the total pore space. A vertical sweep efficiency schematic appears in Figure p15. The vertical sweep efficiency is affected by gravity segregation effects and permeability variation.
Figure p15. Vertical sweep efficiency schematic (Green & Willhite, 1998)
The gravity segregation effects occur due to the differences between the displacing and displaced fluids. The displacing fluid moves toward either the top or bottom of the formation, as shown in Figure p16. When the displacing fluid is denser than the displaced fluid, the former moves underneath the latter, as shown in Figure (p16a). This gravity segregation underride effect occurs during water flooding. Figure (p16b) shows the effect of gravity segregation when the displacing fluid is less dense than the displaced fluid. This gravity override effect occurs in steam displacement, in-situ combustion, Co2 flooding, and solvent flooding processes. Gravity segregation leads to a vertical sweep efficiency reduction due to the early breakthrough of the displacing fluid.
Figure p16. Gravity segregation in displacement process (Green & Willhite, 1998)
Vertical variation in permeability reduces the vertical sweep efficiency resulting from the displacement process. Figure p17 shows layers of vertical cross-section with different thicknesses and permeabilities.
Figure p17. Vertical variation in permeability (Green & Willhite, 1998)
Areal sweep efficiency (EA)
The areal sweep efficiency is the fraction of the area that is swept by the displacing fluid. An areal sweep efficiency schematic appears in Figure p18.
Figure p18. Areal sweep efficiency schematic (Green & Willhite, 1998)
The areal sweep efficiency is affected by the flood pattern, and reservoir permeability variation, but most strongly by the mobility ratio.
Mobility ratio
The objective of mobility is to improve the volumetric sweep efficiency of a displacement process. Mobility is defined as the ratio of the permeability of a particular petroleum fluid (either water or oil) to its apparent viscosity (kfluid/µfluid). In polymer flooding, the polymer is added to water to increase the viscosity of the water therefore decreasing the mobility of the water phase. In addition, the polymer reduces the relative permeability of the water phase in porous media. The mobility ratio (M) is defined as the ratio of displacing fluid mobility to displaced fluid mobility:
where λw is the mobility of water at the residual oil saturation; λo is the mobility of oil at the irreducible water saturation; kw and µw are the permeability and viscosity of the water phase, respectively; and ko and µo are the permeability and viscosity of the oil phase, respectively.
A favorable value of M is one or less. Figure p19 shows the displacement at a favorable mobility ratio. The polymer solution sweeps evenly out from the injection well to the producer, which increases the sweep efficiency.
Figure p19. Diaplacement by polymer flooding at a favorable mobility ratio (Aluhwal, 2008)
A mobility ratio greater than one typically causes viscous fingers in the displacement, as shown in Figure p20. This viscous fingering will increase the production of water and decrease the production of oil.
Figure p20. Displacement by polymer flooding at an unfavorable mobility ratio (Aluhwal, 2008)
Fractional flow. The fractional flow curve is important determining the amount of oil recovery expected from a polymer flooding method. Figure p21 illustrates the fractional flow curve derived from relative permeability experiments as a function of saturation (Patton et al., 1971).
Figure p21. Typical fractional flow curve (Patton, 1971)
Leverett (1941) developed fractional flow equations for two immiscible fluids (oil and water). The fractional flow of oil is given by Equation (3.9):
When the mobility ratio decreases the fraction flow of oil (oil cut) and the displacement efficiency will increase, as shown in Figure p22. This figure depicts a typical fractional flow curve for both high and low oil viscosity. When the curve shifts to the right, this indicates that the oil’s fractional flow has increased.
Figure p22. Effect of mobility ratio on fractional flow
When the oil viscosity is high, the fractional flow of water will increase, and both the fractional flow of oil and the oil mobility will decrease. Moreover, an increase in the fractional flow of water will cause early water breakthrough. The fractional flow of water is defined as
Figure p23 illustrates two fractional flow curves for water flooding, one for which µw = 1 cp (normal water) and the other for which µw = 5 cp (polymer water) (Patton et al., 1971). Two saturation shocks form during the flooding method, the first when the water saturation increases from connate saturation, and the second saturation when the polymer solution contacts connate water saturation. Additionally, the fractional flow for water flooding increases very steeply as the mobile water saturation increases. The connate (irreducible) water saturation was 16.8 %. On the other hand, due to the reduction in the water cut percentage, the fractional flow curve shifts to the right when the polymer solution is injected. This increase in the flood’s front saturation indicates good performance for the polymer flooding. Pope (1980) concluded that the size of the shock front in a linear flow can be determined from the water and polymer fractional flow curves.
Figure p23. Fractional flow curves for water and polymer solution (Patton et al., 1971)
Water mobility decreases as its phase permeability decreases due to polymer retention (Gogarty, 1967). Polymer retention may result from a mechanical blockage at pores with smaller openings or adsorption of polymer on the surface of the rock (Ershaghi & Handy, 1971; Mungan et al., 1966). Figure p24 illustrates how the polymer adsorbs on the surface of the rock, thereby reducing the diameter of the pores.
Figure p24. Polymer adsorption on the surface of the rock
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