Polymer Flooding at an Adverse Mobility Ratio: Acceleration of Oil

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Polymer Flooding at Adverse Mobility Ratio – Acceleration of Oil Production by Crossflow into Water Channels Iselin Cecilie Salmo, Øystein Pettersen, and Arne Skauge Energy Fuels, Just Accepted Manuscript • Publication Date (Web): 19 May 2017 Downloaded from http://pubs.acs.org on May 23, 2017

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Polymer Flooding at Adverse Mobility Ratio – Acceleration of Oil Production by Crossflow into Water Channels Iselin C. Salmo†,‡*, Øystein Pettersen† and Arne Skauge† †

Uni Research CIPR, Bergen, Norway, ‡ University of Bergen, Bergen, Norway

Uni Research CIPR, Allégaten 41, 5007 Bergen, Norway KEYWORDS: Polymer flooding, Crossflow, Enhanced Oil Recovery, Heavy Oil

ABSTRACT: Water channels are formed in high permeable thief zones or in situations with strong adverse mobility ratio, like waterflood in heavy oil reservoirs. This paper discusses the effect of tertiary polymer injection on oil mobilization in already established water channels generated by viscous unstable flow in apparent homogenous rock material. Polymers may accelerate oil production by moving oil into water channels, known as crossflow. The conditions for crossflow to occur are discussed and quantified by key parameters for maximizing crossflow.

Crossflow in layered rock with permeability contrast has been studied extensively.1-7 We have also studied permeability contrast in conventional thief zones for comparison. Recently

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published experimental studies including in-situ saturation maps have proved acceleration of heavy oil production by injection of polymer in rather homogeneous sandstones.8-10

The simulation study involves computation of saturation induced crossflow, in particular with respect to wettability, relative permeability hysteresis, capillary pressure, oil viscosity, mobility ratio and polymer viscosity. In order to have a realistic representation of channeling, the water channels are constructed from waterflooding saturation data at adverse mobility. Saturation induced crossflow into water channels at homogenous permeability is found to be strongly affected by wettability, viscosity ratio (oil/water) and width of water channels.

1. INTRODUCTION Polymer injection is a well-known chemical enhanced oil recovery method. Screening criteria 3 recommend polymer to be used for reservoirs with oil viscosities below 100 cP. Injection of polymer in heavy and extra-heavy oil reservoirs has gained increasing attention and promising results during the last years.11 Results from East Bodo (Canada) and Pelican Lake (Canada) have shown accelerated displacement efficiency and a rapid response to polymer flooding.12-13 This paper aims to understand the reasons behind the early response of polymer flooding and accelerated oil production. Several studies on the effect of crossflow (extra oil recovery by moving oil from low permeability to high permeability layers) in heterogeneous layered models have been conducted, focusing on vertical and horizontal permeability, layer thickness and fluid mobility. From crossflow studies in layered models it was observed, both experimentally and by simulation, that the sweep efficiency is improved when crossflow is present.4-7,

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The ordering of layers is


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important due to the gravity effect which will interact with viscous forces.4,

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It was also

observed that the amount of crossflow was higher when the permeability contrast was lower.3 Several laboratory studies and field applications have shown that waterflooding and polymer flooding can potentially increase oil recovery significantly, even in extra heavy oil.8-10, 12-13, 15-16 The better experimental insight especially by in-situ saturation measurement has encouraged more detailed understanding of polymer in-situ rheological properties and modelling of characteristics of viscous fingering and development of water channeling. Viscous fingers develop during heavy-oil waterflooding and leads to water channels being established.9 Viscous fingering results in early water breakthrough and lower oil recovery, and has been observed even at rather low oil viscosities.16 The accelerated oil production during tertiary polymer flooding and the early response to polymer injection is coupled to the crossflow of mobilized oil into established water channels and transport of oil in these channels. Polymer flooding has a remarkably efficiency at high adverse mobility, and an increase from 30 % after waterflooding to 60 % after polymer flooding has been observed.8,

16

Skauge et al. (2014)16

concluded that it was sufficient with a viscosity ratio with a fraction of 20 to 30 to obtain an efficient oil recovery by polymers. Reproducing viscous fingering by simulations has however turned out to be problematic. Lumped finger model presented by Doorwar et al. (2016)17 related fingering to pseudo-relative permeability functions for unstable displacements. An instability number correlates the waterwet porous media to viscous fingering and was confirmed by experiments on pore scale, in micromodels and core floods. This method gave a good match on experimental oil recovery and differential pressure. Luo et al. (2016)18 included this method for upscaling of viscous fingering. The upscaling was conducted by dividing the flow into three flow zones. This model showed


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improved effect of polymer rheology on oil recovery. They showed that classical relative permeability curves obtain by history matching waterflood may lead to incorrect oil recovery and pressure drop. Most multiphase experiments have been simulated (history matched) by two phase models. The simulation match of experiments guides both polymer rheological properties and relative permeability representation. Simulating and history matching both polymer pilots and heavy oil laboratory experiments have been attempted,19-23 focusing on relative permeability. Most history match studies have shown that Corey-type of relative permeability curves is not sufficient to history match polymer flooding.13, 19, 22 The normal way of estimating the potential of polymer flooding is to use the same set of relative permeability curves obtained for history matched waterflooding, and also include polymer properties.13 However, polymer may alter the fluid flow characteristics, and will therefore need a second set of relative permeability curves.21-22 Other approaches to improve the history match of tertiary polymer flood have been to include hysteresis21 and divide the polymer flow model into two initial flow regions, one swept and one unswept.22 Previous studies have shown that crossflow of oil into established water channels acts against both capillary forces and relative permeability, but is favorable with respect to viscous forces.9 This crossflow phenomenon is an important factor for heavy oil recovery during polymer flooding. The main objective with this paper is to better understand the mechanisms behind extra oil recovery using tertiary polymer flooding at adverse mobility ratio. This involves analysis of crossflow phenomenon and quantification of crossflow with respect to mobility ratio, wettability, relative permeability hysteresis, capillary pressure, number and width of water channels and thief zones. The crossflow phenomenon has been analyzed for homogeneous permeability, thus


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saturation induced crossflow.

In addition, we have studied crossflow due to permeability

contrasts present in reservoirs.

2. EXPERIMENTAL BACKGROUND AND HISTORY MATCHING The experimental setup has been extensively described in previous papers.8-10 The 2D imaging slab experiment, with dimensions of 30 cm × 30 cm × 2 cm has been conducted at the Centre of Integrated Petroleum Research (Uni Research CIPR), Bergen, Norway. The rock material of the experiment was homogeneous Bentheimer sandstone. Other characteristics of the experiment can be found in table 1. The slab was installed vertically in an X-Ray scanner. The density of oil and water was approximately identical during the experiment, so the displacement was not gravity influenced. The X-Ray scanner provided detailed information on internal saturations at different times during the experiment. Effluent were collected and quantified by X-Ray. The X-Ray images from waterflooding are shown in figure 1 (a). The large contrast in water and oil viscosity results in very unstable waterflooding with strong viscous fingering, see figure 1 (a). Fractal type fingers were observed early and they later collapsed into water channels. After 5.1 PVs of injected water, the total recovery was at 26.4 % OOIP. Neither the fractal type of fingers nor any kind of instabilities were observed by simulation of heavy oil waterflood in a commercial compositional reservoir simulator when anchoring the history match on oil production and differential pressure. This is shown in figure 1 (b). The finger growth and establishment has proven difficult to reproduce during simulation.24-29 Due to problems with reproducing the viscous fingering the crossflow phenomenon is studied after waterflooding when water channels has developed and polymer is injected. The initial


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saturation for polymer flooding in the simulations is a simplified model of the water channel observed at 1.2 PV of water injected during experiment (figure 1 (a)). Polymer was then injected for 3.2 PV and resulted in a total recovery of 63.1 % OOIP. Early water breakthrough (0.04 PV) was observed during waterflooding. Quick water cut rise (90 % after 0.6 PV) and a long production period at high and stable water cut were also observed. The injection of polymer led to a fast response and quick increase in oil fractional flow. The experimental data and history match of water and polymer flooding anchoring on oil production and differential pressure is shown in figure 2. Two sets of relative permeability curves were implemented in the simulation model, one for waterflooding and one for polymer flooding. Previous work has shown that the water relative permeability curves is not sufficient to history match the polymer flood at adverse mobility ratio.21-22 In figure 3, the extent of the light blue area show a good sweep by polymer compared to waterflood. The polymer breakthrough was calculated to be at about 0.4 PV after start of the polymer injection. The mobilized oil is following the water channels established during the waterflood, and oil is quickly being transported to the production well (see figure 3 at 0.15 PV polymer injected). The oil bank ahead of the polymer front can either miscible displace heavy oil in front or displace water from the established water channels. The latter seems to be the dominant process,9 as seen in figure 3. Polymer displaces oil that again displaces water in the channels. The oil displacing water process acts against capillarity, but the low viscosity of water makes oil displacing favorable, and especially favorable compared to miscible displacement of high viscous oil. Thus, the crossflow of oil into established water channels is favorable with respect to viscous forces, but acts against capillarity and relative permeability. The rock wettability was not


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measured directly, but capillary pressure and other experimental observations, such as no capillary end effects seen on the X-ray maps and clear fingering pattern observed during waterflooding, indicates that the porous media was intermediate-wet.

3. SIMULATION MODEL The simulation model was created as a simplified 2D model of the experiment presented in experimental background. The reservoir simulator STARS by Computer Modelling Group was used for the simulation study. Three components were present: water, polymer and oil. Characteristics of the simulation can be found in table 1. A horizontal injection well and a horizontal production well perforated from head to toe, thus all cells are active, which gives a uniform pressure, were included. Polymer was injected from the bottom of the model and production from the top. The density of water and oil was approximately equal, thus no gravity effects. The capillary pressure was neglected during most simulations since 2D immiscible displacements10, 30 have shown that capillarity may override the instability at adverse mobility ratio, especially for waterfloods performed at water-wet conditions. Capillary pressure was included as a sensitivity parameter in section 4.4, in order to analyze effect on oil recovery and oil crossflow. The capillary pressure curves are shown in figure 19. Figure 4 shows the simulation model. A water channel which covers approximately 30 % of the total volume has been included in the middle of the model. This is a simplified description of established water channels seen during experiment after waterflooding (figure 1 (a) at 1.2 PV). The water saturation outside the water channel was set to 0.1 and to 0.5 inside the water channel, in the water swept area, as a base case.


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The relative permeability curves used in the base case are shown in figure 5. The curves are Corey-type31 relative permeability curves with exponent to water and oil equal to 4 for waterflooding and exponent to polymer and oil equal to 2 for polymer flooding (see table 2). The endpoint relative permeability to water/polymer and oil indicates a water-wet state, with end point to oil of 1 and end point to water/polymer of 0.2. An interpolation scheme between the relative permeability curves for water and polymer flooding is used, where the set of relative permeability curves for polymer flooding is activated at very low polymer concentration. Polymer rheology was not included in these sensitivity studies. The polymer was injected at constant injection rate with a horizontal injection well and a horizontal production well, giving a uniform pressure. Thus, the velocity is well defined around Darcy velocity of 0.001 ml/min. The in-situ viscosity curve for the polymer used during the experiment is shown in figure 6. The curve is measured during a single-phase polymer injection experiment. The viscosity at u = 0.001 ml/min is close to the constant viscosity used in the base case, which is measured at γ = 10 s-1 (see table 1). Due to the continuous displacement process with uniform pressure, including insitu viscosity results in approximately equal results as constant polymer viscosity, shown in figure 7. Adsorption of polymer was set to 50 µg/g. RRF and inaccessible pore volume was not included.

4. RESULTS AND DISCUSSION 4.1. Numerical Dispersion. Three models with different number of grid cells, but same bulk volume, was used in a sensitivity study of grid size. The three models included 10 000 cells, 2500 cells and 100 cells. It is shown in figure 8 that the two finer models (10 000 and 2500 cells) gives approximately equal result in oil recovery and only a small deviation in water cut.


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A coarser grid refinement, with 100 cells deviates from the other models, therefore the model with 2500 cells was used as base case, based on computational time. The approximately equal oil recovery and water cut for 2500 cells and 10 000 cells is due to low numerical dispersion, see figure 9 (a). The numerical dispersion for 100 cells is quite large. The time step sizes are low. Material balance for the water channel was checked for oil viscosity of 7000 cP. The difference in liquid produced and liquid injected in the channel should be equal to the influx into/out of the water channel. This is shown in figure 9 (b). Although the coarse grid resolution has little impact on oil recovery, there are substantial differences in water cut (figure 8) and internal oil saturation (figure 10) compared to finer gird resolution. This is in accordance with previous work.32-33 Figure 10 shows the internal oil saturation at 0.1 PV polymer injected at different grid resolutions. (b) 2500 cells and (c) 10 000 cells has approximately equal oil saturation distribution and the saturation is converging, while (a) 100 cells has too large numerical dispersion and the crossflow mechanisms are poorly captured. 4.2. Oil Viscosity. Oil viscosity of 7000 cP, the same viscosity as the experiment presented in experimental background, was set as base case. Two arbitrary viscosities were included in the sensitivity study of oil viscosity. 30 cP is lower than the injected polymer viscosity (58 cP) and 1000 cP is higher, however still much lower than the 7000 cP oil. Polymer and water viscosity was constant, with viscosity of 58 cP and 1 cP, respectfully. The oil viscosities have the same initial oil distribution. Viscous fingering is observed from low oil viscosities to extra heavy oil.16 The fractal finger development observed during heavy oil waterflooding is not observed at low oil viscosities, however viscous instabilities at front is observed and wide water channels are observed for lower oil viscosities. Keeping the initial


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saturation distribution constant will help in evaluating the amount of crossflow as a function of viscosity ratio. The simulation is dependent on the relative values of water, polymer and oil viscosity and not the absolute viscosity values. Figure 11 shows the oil recovery factor given in percentage of original oil in place for 3 pore volumes of water injected and for 3 pore volumes of polymer injected. Oil production from polymer flooding alone may be a poor indicator of polymer injection impact. The oil production by comparing polymer flooding to waterflooding is therefore shown. Polymer flooding increases the oil recovery, for the one water channel model, significantly, compared to waterflooding. The oil is increased from an oil recovery of 56% after waterflooding to 85% after polymer flooding in the 30 cP case. The recovery increases from 33% to 66% in the 1000 cP case. The recovery of the 7000 cP oil is 18% after waterflood, while after polymer flooding it is 43%. There are 3 significant time intervals for changes in oil production and differential pressure during polymer injection. The first is before polymer breakthrough. From start of polymer injection to polymer breakthrough the mobility is higher outside (0.2 for 7000 cP oil) of the water channel compared to inside (0.013 for 7000 cP oil) for the heavier oils. Due to higher pressure outside of the channel, oil is then being displaced into the water channel, and it is in this interval the crossflow of oil occurs. This is also shown in figure 14 where the influx of oil during polymer injection is strongly reduced after 0.2 PV injected polymer. As polymer breaks through the production increases and the water cut stabilizes at a constant level. At this point the crossflow is low and the lateral pressure deviation is reduced, but remains due to the advancement of the polymer front in the margin regions and an oil “bank” builds up before breakthrough. After continuous injection the pressure difference is negligible and mobility inside and outside of the channel is approximately equal.


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The internal oil saturation during polymer flooding for (a) 7000 cP, (b) 1000 cP and (c) 30 cP is shown in figure 12. From the simulation pictures it appears to be more oil being pushed into the water channel with higher oil viscosity. This is seen as an early narrowing of the water channel. This is not observed for the 30 cP oil. There is also an oil bank in front of the polymer front outside of the channel for the higher oil viscosities, not observed for the lighter oil. The internal pressure is shown in figure 11 for (a) 7000 cP, (b) 1000 cP and (c) 30 cP. For the 30 cP case, the pressure outside the channel is slightly lower than inside the channel. This will lead to some oil being pushed out of the water channel and result in a more piston like displacement as the polymer front advances. For the two more viscous oils, the pressure is higher on the outside of the channel than inside. This should lead to crossflow of oil into the water channel. There is positive flux from the bulk into the channel for the 1000 cP and 7000 cP oils early during polymer flooding, which is seen in figure 14. The positive oil flow rate is due to higher pressure on the outside of the water channel, thus driving forces is pushing fluids into the channel, observed in figure 13 (a) and (b). For the 30 cP oil, oil flow rate is negative, thus oil is flowing from the water channel to the bulk. The pressure is slightly higher inside the water channel, shown in figure 13 (c), which results in small fluid flow from water channel. Water influx is small compared to oil influx in all cases. 4.3. Wettability. The wettability was changed from water wet to intermediate and oil wet, for both water and polymer relative permeability curves. The end point values are given in table 2. Corey exponent to oil and water was kept constant, for water and polymer respectively. Residual saturations were the same, given in table 1. When the wettability goes from water wet towards oil wet, the mobility of oil decreases, thus λo,ww > λo,iw > λo,ow. The opposite occurs for the


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mobility of water which increases when the wettability goes towards more oil wet state, thus λw,ww < λw,iw < λw,ow. This change in mobility was implemented in the relative permeability endpoints even though the Corey exponent was equal in all wettability cases. This is in accordance with work presented by Anderson (1987)34 stating that the relative permeability of a fluid is higher when it is the non-wetting phase. The reduction/increase in mobility might be slightly overestimated by not changing the curvature of the curves; however the exponent to water and oil was kept constant for the simplicity of the model. Figure 15 shows the oil recovery from water and polymer flooding for the three wettability cases. It is clear that oil recovery decreases the more oil wet the model becomes. This is due to oil being less mobile at lower water saturation when wettability is changing from water to intermediate to oil wet. The water wet model responds faster to the polymer injection and gives a significant increase in oil recovery compared to waterflood. In the water wet case a rapid increase in oil flow rate into the channel occurs, observed in figure 16. For the intermediate case, there is also positive crossflow of oil into the water channel; however the first peak is almost less than one third than that of the water wet case. The oil wet case has some influx early; however after the first peak in flow rate, the flow rate is slowly increasing. Oil is being produced slowly in the oil wet case, thus both production rate and influx oil rate is still increasing after the water wet influx goes towards zero. 4.4. Relative Permeability Hysteresis. From experimental data it is observed a hysteresis effect during polymer flooding in water channels.8-9, 35 The residual oil saturation after polymer flooding in the water channel is higher than after waterflooding, thus oil is “trapped” in the system. A simple hysteresis model based on Killough’s non wetting phase model36 is applied to


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the polymer relative permeability curve and it assumes that the oil relative permeability curve is reversible. An additional input curve corresponding to secondary drainage mode is included and given in figure 5, denoted as hysteresis. Two parameters are necessary to describe the drainage polymer relative permeability curve: the saturation at which polymer becomes immobile, which in this case is set to 0.5, and curvature of the Corey curve is set to 4. The oil recovery with hysteresis on the polymer relative permeability curve is shown in figure 17. Hysteresis on the polymer relative permeability curve alone has no impact on the recovery. The polymer saturation is not increasing than decreasing; hence will it not experience hysteresis. Figure 18 shows the oil crossflow into the channel. The crossflow rate is also equal, as expected due to the equal oil recovery. 4.5. Capillary Pressure. The capillary pressure curves included in the sensitivity analysis is given in figure 19. The primary drainage curve is obtained from de Loubens et al. (2017)37. The forced imbibition curves for water and polymer is obtained from unpublished laboratory work conducted at UniResearch CIPR, Norway. Figure 20 shows the oil recovery without capillary pressure and both water and polymer flooding. There is only a small deviation in the oil recovery curves, thus the effect of capillary pressure is not significant for the oil recovery. The oil crossflow rate into the channel is shown in figure 21. The capillary pressure results in lower oil cross flow into the channel, with a lower peak in oil crossflow rate. 4.6. Permeability Change. As most reservoirs have some degree of heterogeneity, crossflow was also studied as a function of permeability contrast. In the base case a homogeneous permeability of 2500 mD was used, shown in figure 22 together with three other permeability


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contrasts. Permeability field (b) has a contrast of 4 with permeability outside of the water channel of 2500 mD and permeability inside the water channel of 10 000 mD. (c) has a permeability contrast of 10, lowering the permeability outside of the water channel to 1000 mD, but keeping the permeability inside of the channel at 10 000 mD. The last permeability field (d) has a contrast of 100 with permeability outside of 100 mD and inside at 10 000 mD. The water channel is still present in the model. Water flows more easily in the water channel due to the high permeability thief zone present. This results in lower recovery with thief zone. This is shown in figure 23, where the oil recovery decreases with higher permeability contrast. The response to polymer flooding is approximately equal for polymer injection with and without thief zone permeability. The results are in accordance with previous results reported by Clifford and co-workers.2-3 Zhou et al. (2015) have shown that there is a decrease in recovery factor when the permeability contrast increases for high viscosity ratios. They showed that polymer injection increased oil recovery compared to waterflooding as long as the oil-water viscosity ratio was equal to or higher than 10. For lower oil-water viscosity ratios the incremental oil recovery varied nonmonotonically with the permeability contrast. The incremental oil recovery was much less for low permeability contrast and high permeability contrast, than what would be obtained for oil viscosity greater than 10.14 The simulated influx of oil into the channel is reduced as the permeability contrast is increased, observed in figure 24. The influx is much lower than the homogeneous permeability case. Early influx of oil into the water channel result in a small area in front of the polymer front with higher oil saturation. Permeability contrast of 100 result in approximately zero crossflow of oil as the


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mobility is much higher inside of the channel compared to outside. The oil production outside the channel is low due to low resistance to water in the channel. 4.7. Number of Water Channels. The crossflow effect as a result of number of water channels was studied. During heavy oil experiments the finger propagation is unpredictable and may result in many narrow or a few broad channels. Knowing the number of water channels may be important if the simulation analysis result in unequal oil recovery and polymer induced crossflow. Figure 25 shows (a) one, (b) three and (c) five water channels. The total volume of the channels are equal (30 %), thus oil in place is equal; however the initial saturation distribution is different. The oil recovery curve for polymer flooding with different number of water channels is approximately equal, however looking at the oil recovery from waterflooding the recovery decreases with less water channels, given in figure 26. The number of water channels is important for waterflooding compared to polymer injection. Figure 27 shows the oil flow rate into the water channels for one, three and five channels. As the model with five channels has more interfaces between high and low oil saturation there is slightly higher flow of oil into the channels earlier in the narrower channels. The amount of crossflow increases when the number of channel increases giving rise to the importance of knowing the shape of the channels and not only the volume. 4.8. Width of Water Channel. Three different widths of the water channel was analyzed; thin (8 %), base case (30 %) and wide (50 %), shown in figure 28. The initial oil saturation was not constant. Oil saturation inside the channel was 0.5, while it was set to 0.9 outside.


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Wider channel results in later osil production for both water and polymer flooding, as seen in figure 29. The oil recovery is higher for the 8 % water channel. This is due to water starting to mobilize outside of the channel during waterflooding early. The oil recovery after polymer flooding results in reduction in oil recovery when the water channel increases and also initial oil in place is reduced. The thin water channel has influx of oil rapidly after start of polymer injection; however it decreases to around zero fast, shown in figure 30. The flow of oil into the water channel last longer when the width of the channel increases; however the peak in rate is lower. This is a result of a larger volume for water to flow inside the water channels.

5. CONCLUSION Simulation of tertiary polymer flooding may underestimate acceleration of oil production and total oil recovery for heavy oil due to water saturation gradients induced by adverse mobility ratio. The key element is water channeling and it is important to understand the mechanisms of crossflow and impact on oil recovery. We have utilized knowledge from obtained experimental results in our simulation of crossflow phenomenon. In this paper, the relative importance of oil viscosity, wettability, relative permeability hysteresis, capillary pressure and thief zone crossflow versus saturation induced crossflow on tertiary polymer flooding were investigated. Saturation induced crossflow increased with increase in oil viscosity, but seems to level off, in our cases, for extra heavy oils (μo > 1000 cP). There is thus an optimal oil-polymer viscosity ratio for maximizing crossflow and oil recovery for polymer flooding in heavy oils. The wettability of the reservoir strongly influenced the potential of saturation induced crossflow. Water wet condition gave strong crossflow at start of polymer flooding and also


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increased total oil recovery by crossflow. Crossflow decreased in the order: water wet > intermediate wet > oil wet. Introducing heterogeneity (permeability thief zones) resulted in lower incremental oil recovery compared to a homogenous model. This is due to the high permeable thief zone being the path of least resistance for water, thus leading to water flowing more easily and rapidly in this region which will reduce amount of crossflow. Higher number of water channels at constant total volume of channel, accelerated crossflow but had negligible effect on total oil recovery. Thinner water channels were found to have crossflow of oil rapidly after start of injection; however the amount of crossflow was rather low. We found that higher amount of crossflow resulted in higher incremental oil recovery for polymer injection at adverse mobility ratio.

AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]

ACKNOWLEDGMENTS The authors would like to thank Foundation CMG for funding the simulation work.

NOMENCLATURE 2D

two-dimensional

BHP

bottom hole pressure

C

concentration


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C0

initial concentration

IPV

inaccessible pore volume

IW

intermediate wet

kr

relative permeability

n

Corey exponent

o

oil

OOIP

original oil in place

OW

oil wet

p

polymer

PF

polymer flooding

PV

pore volume

RRF

residual resistance factor

Sor

residual oil saturation

Swi

initial water saturation

w

water

WF

waterflooding

WW

water wet

μ

viscosity

λ

mobility

γ

shear rate

Page 18 of 38


18

Page 19 of 38

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Energy & Fuels

REFERENCES (1)

Cinar, Y.; Jessen, K.; Berenblyum, R.; Juanes, R.; Orr, F. M. An Experimental and

Numerical Investigation of Crossflow Effects in Two-Phase Displacements. SPEJ 2006, 11 (02), 216-226. (2)

Clifford, P.; Sorbie, K. Polymer Flooding in Stratified Systems: Recovery Mechanisms

and the Effects of Chemical Degradation, IEA Collaborative Project on EOR, Trondheim, Norway, 1984. (3)

Sorbie, K. S., Polymer-Improved Oil Recovery. Blackie and Son Ltd: Glasgow, 1991.

(4)

Zapata, V. J.; Lake, L. W. A Theoretical Analysis of Viscous Crossflow, SPE Annual

Technical Conference and Exhibition, San Antonio, Texas, USA, 4-7 October, 1981; Society of Petroleum Engineers: 1981. (5)

Sorbie, K. S.; Walker, D. J. A Study of the Mechanism of Oil Displacement Using Water

and Polymer in Stratified Laboratory Core Systems, SPE Enhanced Oil Recovery Symposium, Tulsa, Oklahoma, USA, 16-21 April, 1988; Society of Petroleum Engineers: 1988. (6)

Sorbie, K. S.; Wat, R. M. S.; Rowe, T.; Clifford, P. J. Core Flooding in Well-

Characterized Heterogeneous Systems: An Experimental and Simulation Study, SPE International Symposium on Oilfield Chemistry, San Antonio, Texas, 4-6 February, 1987; Society of Petroleum Engineers: 1987. (7)

Sorbie, K. S.; Wat, R. M. S.; Rowe, T. C. Oil Displacement Experiments in

Heterogeneous Cores: Analysis of Recovery Mechanisms, SPE Annual Technical Conference and Exhibition, Dallas, Texas, USA, 27-30 September, 1987; Society of Petroleum Engineers: 1987.


19

Energy & Fuels

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(8)

Page 20 of 38

Bondino, I.; Nguyen, R.; Hamon, G.; Ormehaug, P.; Skauge, A.; Jouenne, S. Tertiary

Polymer Flooding in Extra-Heavy Oil: an investigation using 1D and 2D experiments, core scale simulation and pore-scale network models, Review Proceedings of the 25th International Symposium of the Society of Core Analysis Austin, Texas, USA, 2011. (9)

Skauge, A.; Ormehaug, P.; Gurholt, T.; Vik, B.; Bondino, I.; Hamon, G. 2-D

Visualisation of Unstable Waterflood and Polymer Flood for Displacement of Heavy Oil, SPE Improved Oil Recovery Symposium, Tulsa, Oklahoma, USA, 14-18 April, 2012; Society of Petroleum Engineers: 2012. (10) Skauge, A.; Sorbie, K.; Ormehaug, P.; Skauge, T. Experimental and Numerical Modeling Studies of Viscous Unstable Displacement, 15th European Symposium on Improved Oil Recovery, Paris, France, 27 April, 2009; EAGE: 2009. (11) Sheng, J. J.; Leonhardt, B.; Azri, N. Status of polymer-flooding technology. J. Can. Pet. Technol. 2015, 54 (02), 116-126. (12) Delamaide, E.; Zaitoun, A.; Renard, G.; Tabary, R. Pelican Lake Field: First Successful Application of Polymer Flooding in a Heavy Oil Reservoir, SPE Enhanced Oil Recovery Conference, Kuala Lumpur, Malaysia, 2-4 July, 2013; Society of Petroleum Engineers: 2013. (13) Wassmuth, F.; Arnold, W.; Green, K.; Cameron, N. Polymer Flood Application to Improve Heavy Oil Recovery at East Bodo. J. Can. Pet. Technol. 2009, 48 (2), 55-61. (14) Zhou, Y.; Muggeridge, A.; Berg, C.; King, P. Quantifying Viscous Cross-flow and its Impact on Tertiary Polymer Flooding in Heterogeneous Reservoirs, IOR 2015-18th European Symposium on Improved Oil Recovery, Dresden, Germany, 14-16 April, 2015; EAGE: 2015. (15) Fabbri, C.; Romero, C.; Aubertin, F.; Nguyen, M.; Hourcq, S.; Hamon, G. Secondary Polymer Flooding in Extra-Heavy Oil: Gaining Information on Polymer-Oil Relative


20

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

Permeabilities, SPE Enhanced Oil Recovery Conference, Kuala Lumpur, Malaysia, 2-4 July, 2013; Society of Petroleum Engineers: 2013. (16) Skauge, T.; Vik, B. F.; Ormehaug, P. A.; Jatten, B. K.; Kippe, V.; Skjevrak, I.; Standnes, D. C.; Uleberg, K.; Skauge, A. Polymer Flood at Adverse Mobility Ratio in 2D Flow by X-ray Visualization, SPE EOR Conference at Oil and Gas West Asia, Muscat, Oman, 31 March-2 April, 2014; Society of Petroleum Engineers: 2014. (17) Doorwar, S.; Mohanty, K. K. Viscous-Fingering Function for Unstable Immiscible Flows. SPEJ 2017, 22 (01), 19-31. (18) Luo, H.; Mohanty, K. K.; Delshad, M.; Pope, G. A. Modeling and Upscaling Unstable Water and Polymer Floods: Dynamic Characterization of the Effective Finger Zone, SPE Improved Oil Recovery Conference, Tulsa, Oklahoma, USA, 11-13 April, 2016; Society of Petroleum Engineers: 2016. (19) Delaplace, P.; Delamaide, E.; Roggero, F.; Renard, G. History Matching of a Successful Polymer Flood Pilot in the Pelican Lake Heavy Oil Field (Canada), SPE Annual Technical Conferance and Exhibition, New Orleans, Louisiana, USA, 30 September-2 October, 2013; Society of Petroleum Engineers: 2013. (20) Delaplace, P.; Euzen, T.; Roggero, F.; Kopecny, P.; Renard, G.; Delamaide, E. Reservoir Simulations of a Polymer Flood Pilot in the Pelican Lake Heavy Oil Field (Canada) : a Step Forward, SPE Reservoir Characterization and Simulation Conference and Exhibition, Abu Dhabi, UAE, 16-18 September, 2013; Society of Petroleum Engineers: 2013. (21) Fabbri, C.; de Loubens, R.; Skauge, A.; Ormehaug, P. A.; vik, B.; Bourgeois, M.; Morel, D.; Hamon, G. Comparison of History-Matched Water Flood, Tertiary Polymer Flood Realtive Permeabilities and Evidence of Hysteresis during Tertiary Polymer Flood in Very Viscous Oils,


21

Energy & Fuels

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SPE Asia Pacific Enhanced Oil Recovery, Kualu Lumpur, Malaysia, 11-13 August, 2015; Society of Petroleum Engineers: 2015. (22) Skauge, A.; Salmo, I. Relative Permeability Functions for Tertiary Polymer Flooding, IOR 2015-18th European Symposium on Improved Oil Recovery, Dresden, Germany, 14-16 April, 2015; EAGE: 2015. (23) Wassmuth, F.; Green, K.; Hodgins, L.; Turta, A. Polymer Flood Technology for Heavy Oil Recovery, Canadian International Petroleum Conference, Calgary, Alberta, Canada, 12-14 June, 2007; Petroleum Society of Canada: 2007. (24) Doorwar, S.; Mohanty, K. K. Extension of the Dielectric Breakdown Model for Simulation of Viscous Fingering at Finite Viscosity Ratios. Phys. Rev. E: 2014, 90 (1), 013028. (25) Doorwar, S.; Mohanty, K. K. Fingering Function for Unstable Immiscible Flows, SPE Reservoir Simulation Symposium, Houston, Texas, USA, 23-25 February, 2015; Society of Petroleum Engineers: 2015. (26) Hughes, D.; Murphy, P., An Analytical Model of Unstable Immiscible Flow. In Society of Petroleum Engineers, 1987. (27) Mostaghimi, P.; Kamali, F.; Jackson, M. D.; Muggeridge, A. H.; Pain, C. C. A Dynamic Mesh Approach for Simulation of Immiscible Viscous Fingering, SPE Reservoir Simulation Symposium, Houston, Texas, USA, 23-25 February, 2015; Society of Petroleum Engineers: 2015. (28) Riaz, A.; Tchelepi, H. A. Numerical Simulation of Immiscible Two-Phase Flow in Porous Media. Phys. Fluids 2006, 18 (1), 014104. (29) Salmo, I. C. Simulation of Enhanced Oil Recovery: Waterflooding and Polymer Injetion at Adverse Mobility Ratio. Master thesis, University of Bergen, Bergen, 2013.


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(30) Skauge, A.; Horgen, T.; Noremark, B.; Vik, B. Experimental Studies of Unstable Displacement in Carbonate and Sandstone Material, IOR 2011 - 16th European Symposium on Improved Oil Recovery, Cambridge, UK, 12-14 April, 2011; EAGE: 2011. (31) Corey, A. T. The Interrelation between Gas and Oil Relative Permeabilities. Producers monthly 1954, 19 (1), 38-41. (32) Shotton, M.; Stephen, K.; Giddins, M. A. High-Resolution Studies of Polymer Flooding in Heterogeneous Layered Reservoirs, SPE EOR Conference at Oil and Gas West Asia, Muscat, Oman, 21-23 March, 2016; Society of Petroleum Engineers: 2016. (33) Clifford, P. J. Simulation of Small Chemical Slug Behavior in Heterogeneous Reservoirs, SPE Enhanced Oil Recovery Symposium, Tulsa, Oklahoma, USA, 16-21 April, 1988; Society of Petroleum Engineers: 1988. (34) Anderson, W. G. Wettability Literature Survey Part 5: The Effects of Wettability on Relative Permeability. J. Pet. Technol. 1987, 39 (11), 1453 - 1468. (35) Skauge, A.; Ormehaug, P.; Vik, B.; Fabbri, C.; Bondino, I.; Hamon, G. Polymer Flood Design for Displacement of Heavy Oil Analysed by 2D-imaging, IOR 2013 - 17th European Symposium on Improved Oil Recovery, St. Ptersburg, Russia, 16 April, 2013; EAGE: 2013. (36) Killough, J. E. Reservoir Simulation With History-Dependent Saturation Functions. SPEJ 1976, 16 (01), 37-48. (37) Loubens, R. d.; Vaillant, G.; Regaieg, M.; Yang, J.; Moncorgé, A.; Fabbri, C.; Darche, G. Numerical Modeling of Unstable Water Floods and Tertiary Polymer Floods into Highly Viscous Oils, SPE Reservoir Simulation Conference, Montgomery, Texas, USA, 20-22 February, 2017; Society of Petroleum Engineers: 2017.


23

Energy & Fuels

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Page 24 of 38

Table 1. Main Characteristics of Experiment and Simulation Model. Experiment

Simulation Model

Length [cm]

29.7

30

Width [cm]

29.9

30

Thickness [cm]

2.05

2

Grid [cells]

-

50 × 50 × 1

Porosity [-]

0.24

0.24

Pore volume [cc]

440

432

Permeability [D]

2.8

2.5

5.1 PV water Injected Fluid

3 PV Polymer 3.2 PV polymer

Polymer Concentration [ppm]

1650

1650

Injection Rate [ml/min]

0.05

0.05

BHPproduction well [kPa]

101.1

101.1

Water Viscosity [cP]

1

1

7000

7000

58 @ 10s-1

58

Oil Viscosity [cP] Polymer Viscosity [cP] Channel Volume [%]

30

Swi [frac.]

0.07

0.1

Sor[frac.]

0.25

0.1

Table 2. Relative Permeability End Point for Different Wettabilities. Wettability

krw,or kro,iw nw no np nop

Water wet

0.2

1

4

4

2

2

Intermediate wet

0.5

0.5

4

4

2

2

1

0.2

4

4

2

2

Oil wet


24

Page 25 of 38

Figure 1. 2D imaging of waterflood into Bentheimer (homogenous) rock with 7000 cP crude oil

80

1800 1500

60 1200 40

900 600

20 300 0

0 0

5

Differential Pressure [mbar]

for (a) experiment9 and (b) simulation.

Oil Recovery [% OOIP]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

10

PV inj. EXP Oil Recovery

SIM Oil Recovery

EXP Differential Pressure

SIM Differential Pressure

Figure 2. Experimental and history matched oil recovery and differential pressure for water- and polymer flood with oil viscosity of 7000 cP.


25

Energy & Fuels

Figure 3. Change in saturation during polymer injection. Blue: increase in water saturation and Red: increase in oil saturation9.

Figure 4. Internal oil saturation.

1 Relative Permeability

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 26 of 38

0.8 0.6 0.4 0.2 0 0

0.5

1

Water Saturation krw WF krw PF Hysteresis

kro WF kro PF

Figure 5. Relative permeability curves for water and polymer flooding.


26

Page 27 of 38

Viscosity [cP]

250 200 150 100 50 0 1.00E-05

1.00E-03

1.00E-01

Darcy Velcoity [ml/min]

Figure 6. Polymer viscosity as a function of Darcy velocity.

100 Oil Recovery [%]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

80 60 40 20 0 0

1

2

3

PV Polymer Injected 7000 cP Non-Newtonian 7000 cP Newtonian 1000 cP Non-Newtonian 1000 cP Newtonian 30 cP Non-Newtonian 30 cP Newtonian

Figure 7. Oil production for polymer flooding with constant viscosity and shear dependent viscosity for oil viscosity of 30 cP, 1000 cP and 7000 cP.


27

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Oil Recovery and Water Cut [%]

Energy & Fuels

Page 28 of 38

100 80 60 40 20 0 0

0.5

1

1.5

2

PV Polymer Injected Oil Recovery 10 000 cells

Water Cut 10 000 cells

Oil Recovery 2500 cells

Water Cut 2500 cells

Oil Recovery 100 cells

Water Cut 100 cells

Figure 8. Oil recovery and water cut for grid size sensitivity.

Figure 9. (a) polymer concentration profile for the three grid resolutions (initial fluid is water) and (b) material balance during polymer injection for 2500 cells.

Figure 10. Oil Saturation at 0.1 PV polymer injected for (a) 100 cells, (b) 2500 cells and (c) 10 000 cells.


28

Page 29 of 38

100 Oil Recovery [%]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

80 60 40 20 0 0

1

2

3

PV Injected 7000 cP WF

7000 cP PF

1000 cP WF

1000 cP PF

30 cP WF

30 cP PF

Figure 11. Oil production for waterflooding and polymer flooding for oil viscosity of 30 cP, 1000 cP and 7000 cP.

Figure 12. Oil saturation development during polymer injection at 0.01 PV, 0.07 PV, 0.14 PV and 0.23 PV for (a) 7000 cP oil, (b) 1000 cP oil and (c) 30 cP oil.


29

Energy & Fuels

Figure 13. Pressure development during polymer injection at 0.01 PV, 0.07 PV, 0.14 PV and 0.23 PV for (a) 7000 cP oil, (b) 1000 cP oil and (c) 30 cP oil.

0.025 Oil Crossflow Rate [ml/min]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 30 of 38

0.02 0.015 0.01 0.005 0 -0.005

0

7000 cP

0.5

1

1.5

PV Polymer Injected

1000 cP

30 cP

Figure 14. Oil crossflow rate into the channel for oil viscosity of 30 cP, 1000 cP and 7000 cP.


30

Page 31 of 38

Oil Recovery [%]

60

40

20

0 0

1

2

3

PV Injected WW WF IW WF OW WF

WW PF IW PF OW PF

Figure 15. Oil recovery for waterflooding and polymer flooding for water wet (WW), intermediate wet (IW) and oil wet (OW) wettability.


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

0.012 0.008 0.004 0 0 -0.004

0.5

1

1.5

PV Polymer Injected Water Wet Intermediate Wet Oil Wet

Figure 16. Oil crossflow rate into the channel for water wet, intermediate wet and oil wet model.


31

Energy & Fuels

Oil Recovery [%]

60 50 40 30 20 10 0 0

1

2

3

PV Polymer Injected No Hysteresis Hysteresis on Polymer RelPerm

Figure 17. Oil Recovery for polymer flooding of oil with viscosity of 7000 cP with hysteresis on polymer relative permeability.

0.016 Oil Crossflow Rate[ml/min]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 32 of 38

0.012 0.008 0.004 0 0 -0.004

0.5

1

1.5

PV Polymer Injected No Hysteresis Hysteresis on Polymer RelPerm

Figure 18. Oil crossflow rate into the channel for relative permeability curves including hysteresis.


32

Page 33 of 38

Capillary Pressure [kPa]

60 30 0 0

0.2

0.4

0.6

0.8

1

-30 -60 -90

Water Saturation Primary Drainage

Imbibition Water

Imbibition Polymer

Figure 19. Experimentally measured capillary pressure curves for primary drainage, imbibition of water and imbibition of polymer.

60 Oil Recovery [%]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

50 40 30 20 10 0 0

1

2

3

PV Polymer Injected Without Capillary Pressure With Capillary Pressure

Figure 20. Oil Recovery for polymer flooding of oil with viscosity of 7000 cP including capillary pressure.


33

Energy & Fuels


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 34 of 38

0.02 0.015 0.01 0.005 0 0 -0.005

0.5

1

1.5

PV Polymer inj. Without Capillary Pressure With Capillary Pressure

Figure 21. Oil crossflow rate into the channel for relative permeability curves including capillary pressure.

Figure 22. Permeability contrasts of (a) 1, (b) 4, (c) 10 and (d) 100.


34

Page 35 of 38

Oil Recovery [%]

60

40

20

0 0

1

2

3

PV Injected WF Ratio = 1

PF Ratio = 1

WF Ratio = 4 WF Ratio = 10 WF Ratio = 100

PF Ratio = 4 PF Ratio = 10 PF Ratio = 100

Figure 23. Oil recovery for waterflooding and polymer injection for permeability change.

2.00E-02 Oil Crossflow Rate [ml/min]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

1.50E-02 1.00E-02 5.00E-03 0.00E+00 0 -5.00E-03

0.5

1

1.5

PV Polymer Injected

Perm Ratio = 1

Perm Ratio = 4

Perm Ratio = 10

Perm Ratio = 100

Figure 24. Oil crossflow rate into the channel for permeability change.


35

Energy & Fuels

Figure 25. (a) one, (b) three and (c) five water channels.

60

Oil Recovery [%]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 36 of 38

40

20

0 0

1

2

3

PV Injected WF One Channel PF One Channel WF Three Channels PF Three Channels WF Five Channels PF Five Channels

Figure 26. Oil recovery for waterflooding and polymer injection for one, three and five water channels.


36

Page 37 of 38


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

0.02 0.015 0.01 0.005 0 0 -0.005

0.5

1

1.5

PV Polymer inj. One Channel Three Channels Five Channels

Figure 27. Oil crossflow rate into water channels for one, three and five channels.

Figure 28. (a) thin water channel (8 %), (b) base case water channel (30 %) and (c) wide water channel (50 %).


37

Energy & Fuels

Oil Recovery [%]

60

40

20

0 0

1

2

3

PV Injected WF 8 %

PF 8 %

WF 30 %

PF 30 %

WF 50 %

PF 50 %

Figure 29. Oil recovery for waterflooding and polymer injection for 8 %, 30 % and 50 % water channel.


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 38 of 38

0.025

0.015

0.005

-0.005

0

0.5 1 PV Polymer Injected 8%

30 %

1.5

50 %

Figure 30. Oil crossflow rate into the channel for 8 %, 30 % and 50 % water channel.


38

Polymer Flooding at an Adverse Mobility Ratio: Acceleration of Oil

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