Monitoring and Characterizing the Finger Patterns Developed by

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Monitoring and Characterizing the Finger Patterns Developed by Miscible Displacement in Fractured Heavy Oil Systems Amin Shokrollahi, Seyed Mohammad Javad Majidi, and Mohammad Hossein Ghazanfari Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/ie4013908 • Publication Date (Web): 11 Jul 2013 Downloaded from http://pubs.acs.org on July 13, 2013

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Industrial & Engineering Chemistry Research

Monitoring and Characterizing the Finger Patterns Developed by Miscible Displacement in Fractured Heavy Oil Systems Amin Shokrollahi, Seyed Mohammad Javad Majidi , Mohammad Hossein Ghazanfari∗ Chemical and Petroleum Engineering Department, Sharif University of Technology, Tehran, Iran

Abstract This work concerns with experimentally quantifying the finger behavior during miscible displacements in fractured porous media. A series of miscible tests performed on five-spot fractured micromodels which are initially saturated with heavy crude oil, and the developed finger patterns were quantified using image analysis technique. The results revealed that the numbers of macro fingers formed is well correlated with the square root of dimensionless time, while the rate of finger initiation is independent to fracture characteristics. The level of bypassed oil linearly decreases with dimensionless distance traveled by front precisely. The transient fractal dimension behavior experience a minimum due to advancement of front in fractures, and subsequently, growth of side fingers. Variable transient behavior of fingers fractal dimension may suggest that miscible injection in fractured media does not obey from fractal theory. Therefore, more care is required for up scaling of miscible displacements in fractured media using fractal characteristics. Key Words: Finger patterns characterizing, Miscible displacement, Heavy oil, Fractal Dimension, Fractured micromodel, Five-spot systems

∗

Corresponding author, email:[email protected], Sharif University of Technology, Chemical and Petroleum Engineering Department, Azadi Ave., Tel: +98-21-66166413, Fax: +98-21-6622853.

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1

Background Viscous fingering is a complex phenomenon which controls the efficiency of miscible

floods. Despite numerous studies, experimentally quantifying the finger behavior, e.g. minimum/maximum finger length, the rate of finger initiation, transient fractal dimension of fingers and local level of oil bypassing by the fingers in fractured media remains a topic of debate in the literature, especially in five-spot systems. Although heavy oil and bitumen reserves represent a substantial fraction of worldwide energy, the maximum primary recovery of these types of reservoirs is about 10% 1. On the other hand, miscible flooding as a candidate for enhanced oil recovery from these types of reservoirs suffer from insufficient efficiency induced by adverse mobility ratio which causes an unstable displacement front. Thus, fundamental understanding and characterizing the unstable nature of finger patterns during miscible displacements, obtained from experimental experiences might be unavoidable. Engelberts and Klinenberg

2

introduced viscous fingering term for the first time in 1951.

They showed that with an increase in mobility ratio greater than unity, the length of transition zone increases. In 1957, van Meurs 3 by using transparent three dimensional models showed that viscous fingering did not occur at a viscosity ratio of unity but did occur at a viscosity ratio of 80. After that in 1958,van Meurs and van der Poel

4

developed formulas that relate the

cumulative water injection and oil-water viscosity ratio to the oil production and pressure drop across the formation. The role of capillary pressure on the length of fingers were studied by Chuoke et al. 5. They stated that in high oil viscosity or low interfacial tension condition, fingers wane.


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In 1960, Sheldon

6

proposed a theory to determine the transient behavior of fingers with

large amplitudes. Outmans

7

analytically demonstrated that no linear relation can be observed

between pressure difference and curvature at the interface. Benham and Olson8 conducted a series of complex experiments and finally confirmed the results that were reported by van Meurs 3

in 1963. In 1969, Perkins and Johnston 9 showed that in the early stages of displacements, the

presence of connate water results in breaking up the fingers into a graded saturation zone. The research on behavior of viscous fingering continued in the 1970s. In 1971, Gupta et al. 10

reported that fingering is a macroscopic process which depends on the local macroscopic

irregularity in the porous medium. After that, Gupta and Greenkorn

11

showed that several

fingers occur at the early stage of displacement can be degenerate into a single finger. Also they showed that, the rate of finger growth behaves linearly with time. In 1981, Peters and Flock

12

introduced a dimensionless number and its critical value to

predict the onset of instability during immiscible displacement. Paterson et al. 13 reported that in the oil-wet media the structure of fingers significantly changes for a specific range of capillary number. Vossoughi et al.

14

derived a general form of convection-dispersion equation that

encompasses viscous fingering. Furthermore , Vossoughi and Seyer 15 extended the Darcy’s law to predict the oil recovery and saturation profiles in immiscible displacement in absence of capillary and gravity forces. Mui and Miller

16

presented a theoretical analysis for growth of a

single, large elliptical finger in a porous medium. They found that elliptical finger model is capable of predicting the width and speed of growth of the fastest growing finger. Ni et al.

17

performed a series of immiscible displacement experiments in consolidated porous media and observed a good agreement with the previous findings of the breakthrough recovery in the case of linear displacement. Stokes et al.

18

illustrated that, if the displaced fluid preferentially wets 3

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the medium, the finger width is analogous to the pore size and independent to other parameters. In 1987, Peters and Khataniar

19

proved that with an increase in the instability, the oil relative

permeability wanes and the water relative permeability upsurges. A comprehensive review of viscous fingering behavior in porous media was presented by Homsy

20

. Huang and Gryte

21

investigated the fingering behavior within a thin slab of porous medium using gamma-cameraimaging system. Odeh

22

showed that in one-dimensional oil-water displacement, the

macroscopic effect of viscous fingering can be captured when its behavior is modeled with a reservoir simulator. In the early 1990s, Brock and Orr

23

stated that in homogenous models, the only effective

factor on the fingering patterns is the mobility ratio, while in heterogeneous systems, patterns of heterogeneity significantly affect the fingering patterns. Pavone

24

showed that in 3D, natural

unconsolidated porous samples, stable displacements exist behind the unstable front and instabilities are in the form of fingers. Tchelepi and Orr

25

demonstrated that the existence of

heterogeneities lowers the range of viscous-to-gravity ratio in 2D or 3D flow. A great deal of research on viscous fingering also exists in the past decade. Cuthiell et al. 26 showed that for the case of solvent floods, the fingering behavior is characterized by a single dominant finger that breaks through first, and secondary fingers that grow only very slowly after breakthrough. Islam and Azaiez

27

suggested it is possible to simulate the thermo-viscous

fingering instability in miscible displacement using highly accurate Hartley transform based on pseudo-spectral method. Ghesmat and Azaiez

28

numerically proved that there is a completely

different behavior between reactive and non-reactive systems such that more complex finger structures are observed in the case of reactive systems. Behrooz et al. 29 investigated the Miscible displacements of heavy oil in 1D homogeneous micromodel. Yadali Jamaloei and Kharrat 4 ACS Paragon Plus Environment

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illustrated that in Low Tension Polymer Flooding (LTPF), the geometry (size and shape) of the pores have a tremendous effect on the number of fingers formed. After that, Yadali Jamaloei et al.

31

reported the existence of fingers with many tiny branches during the dilute surfactant

flooding in a mix wet micromodel containing heavy oil and connate water. Farzaneh et al.

32

reported the results of solvent injection in fractured five-spot micromodels, and discussed the role of fracture geometrical characteristics on oil recovery. A series of miscible flood experiments in fractured five-spot systems were conducted by Saidian et al.

33

. Their results

showed that the existence of fractures enhance the finger development. Sajjadi and Azaiez

34

proposed that due to the faster fluid velocity in permeable layers, mechanism of fingering is more complex in heterogeneous media. Yadali Jamaloei et al.

35

experimentally showed that

viscous instability effect in evaluation of the low-IFT viscous-modified flow is important and plays a key role. However, a little attention has been paid on correlating of finger behavior in miscible displacements, especially in fractured porous media. Also, how the level of bypassed oil changes by distance traveled by front in these systems may be attractive. In recent decades, fractal theory is applied to characterize irregular and fragmented objects in numerous areas in engineering and scientific phenomena. Mandelbrot36 introduced the concept of fractal theory for the first time. Recently, it has been applied for characterizing viscous fingering as a complex nature phenomenon. For instance, Van Damme et al.37 proposed that combination of high viscosity contrast and low interfacial tension results in occurrence of fractal morphology. In 1986, Fanchi and Christiansen

38

showed that except in the vicinity of the

injector port and the production groove, viscous finger development obeys from fractal theory with an average fractal dimension of 1.7. Later, Peters and Cavalero

39

illustrated that injection

rate and mobility ratios slightly influenced the fractal nature of induced fingers in first contact 5 ACS Paragon Plus Environment


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miscible displacements. Ferer et al.

40

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noted that if fractal flows dominate viscous fingering,

saturation will not be a function of fractional flow. Zhang and Liu 41 interpreted that the effective fractal dimension of fingers decreases by an increase of viscosity ratio, and also, low fractal dimension corresponds to severely ramified viscous fingering fractal structure and short breakthrough time. In 2000, Gharbi et al.

42

stated that the fractal dimension decreases with

decreasing gravity number and increasing viscosity ratio. Stevenson et al. 43 illustrated that both heterogeneities and viscosity ratios have great importance in determining the flow characteristics in miscible, two-phase flow within a 2D porous media. Recently, Doorwar and Mohanty

44

showed that when viscosity ratio increases, the number of growing fingers before breakthrough decreases. Also, they noted that at high viscosity ratios the fingers formed follow a fractal behavior. However, it is still an open question that how the fractal behavior of the front influenced by possible fracture characteristics. Also it might be attractive to see the transient behavior of fractal dimension in fractured models. The previous reported experiences believed that there is a great wealth of studies dealing with viscous fingering. However, few researchers tried to characterize the finger behavior in fractured systems as a kind of heterogeneity in porous media, and how it depends on flow dynamic in miscible displacements.


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2 2.1

Experimental Set-up Description A detailed description of experimental setup and its components can be found elsewhere 33.

To investigate the effect of medium characteristics on fingering behavior, three different types of fracture pattern were designed and used in the experiments (Figure 1). A detailed procedure for constructing micromodels is presented in ref.

45

. One of the most attracting oil-field patterns is

five-spot well pattern. Therefore, the micromodels used in this study were prepared in the form of one-quarter five-spot patterns. In conventional five-spot pattern (one injector at center- four producers at each corner) the overlapping of fingering pattern between injector and producers is possible. This overlapping makes it difficult to analyze the individual fingering pattern associated with each producer and injector. Thus, to overcome this problem, one-quarter fivespot pattern has been chosen. Furthermore, the objective of this study is to merely analyzing the behavior of viscous fingering not the combine effect of the capillary and viscous fingering. Therefore, the patterns utilized in this study have uniform pore body and pore throat size. Physical properties of the micromodels are given in Table 1. 2.2

Materials Fluids used in the experiments are kerosene as the displacing fluid (solvent), and Sarvak

crude oil as the oil sample. The solvent fluid used in our experiments was provided from Merck products. The crude oil has been taken from Azadegan oil-field located in the south-western Iran. Characteristics of the oil sample and solvent are given in Table 2.



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2.3

Experimental procedure To perform the experiments, the glass micromodels were initially cleaned by injection of

o toluene acetone, and distillated water and then dried in an oven up to 140 C for 30 min. After

that, patterns were saturated with the heavy oil using a syringe pump. To study the effect of injection rate on fingering behavior, the solvent was injected into the models with two different flow rates of 0.0008 and 0.004 (cc/min) by using a high-accuracy Quizix injection pump . High resolution Nikon camera was used to capture high-quality images during the course of displacement. The resulting images were loaded into Adobe Photoshop CS6 and ImageJ FracLac software, which will analyze the images and gives out the quantitative features at different times of the displacement. All experiments were carried out at ambient temperature and pressure at horizontal mounting. 3

Results and Discussions To investigate the effect of fracture characteristics and the rate of solvent injection, the

experiments were performed on all patterns A, B, and C with two different flow rates of 0.0008 and 0.004 (cc/min). Figures 2 to 7 show the fingering patterns during the displacement front at different times before breakthrough of injected solvent. Quantitative features of displacement front and fingering patterns at different times of the displacement up to breakthrough time are presented in figures 8-12. Furthermore, accurate values of data points are provided in supporting information as Tables S-1 to S-6 for the readers who are interested to know more details about the quantitative analysis of finger behavior. It should be mentioned that, this work only focused on monitoring and characterizing of finger behavior including the rate of finger initiation, dimensionless minimum/maximum finger 8 ACS Paragon Plus Environment

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length, and etc. in heterogeneous systems which can be obtained with a reasonable confidence level through experiments. Contribution to the flow theory and prediction of onset of instability may be a topic for future works. It is obvious that the medium heterogeneity and flow rate affect the breakthrough time of the injected solvent. Decreasing trend of breakthrough time with the injection flow is expected, but it would be very difficult to predict how it varies by heterogeneity, especially for scattered fractures in the media. This compels a need to a re-scale time, dimensionless breakthrough time, which changes between zero and one for all patterns and injection rates. This re-scale time allows us to characterize the developed fingers at same fractions of total breakthrough time. Also, it would be beneficial to use a dimension distance traveled by front changes between zero and one for all patterns and injection rates. Therefore, characterizing and correlating of the finger behavior are based on dimensionless time and dimensionless distance. The dimensionless parameters used here are similar those applied by Yadali Jamaloei et al.45. Here we seek the location as well as corresponding time of traveled front, so the required dimensionless parameters are fundamentally different from the famous dimensionless numbers e.g. Reynolds and capillary. Details of definitions are as follows: The dimensionless time is the elapsed time of displacement divided by the breakthrough time. The distance traveled by the front is the distance between injection port and tips of front at any time, and dimensionless distance traveled by the front is the distance traveled by the front divided by the distance between the injection and production port. The level of bypassing of initial oil saturation is the average oil saturation that is bypassed via the displacement front at any time. The number of macro fingers formed at any time is the number of distinct macro fingers



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that exist at the time of displacement. Dimensionless minimum/maximum finger length is the length of minimum/maximum finger at any time divided by the length of minimum/maximum finger at breakthrough time 45. Figure 8 depicts the relationship between number of macro fingers with the square root of dimensionless time for all patterns A, B, and C at two different injection rates of 0.0008 and 0.004 cc/min. According to these figures it is evident that there is good relation between the numbers of macro fingers with the square root of the dimensionless time. These observations are in contrast to the results presented by Moissis et al.46 in the case of miscible displacement and Gupta and Greenkorn

11

in the case of immiscible displacement. They showed that the finger

growth experience a linear behavior with the time but our results suggested that finger growth behave linearly with square root of the dimensionless time. Furthermore, these results are in agreement with results that demonstrated by Yadali Jamaloei et al.

45

but at different miscibility

condition, in the case of LTPF. They showed that in the homogenous micromodel, the number of distinct fingers formed at any time is well correlated with square root of displacement time, not with the displacement time. Also, the results in figure 8 illustrates that the ultimate number of macro fingers formed at breakthrough time (Td =1) in all patterns is lower for injection rate of 0.004 (cc/min) than injection rate of 0.0008 (cc/min). It is clear that in high injection rate, the injected solvent reaches to the production port rapidly (early breakthrough) and do not have sufficient time to make finger in the media. On the contrary, at low injection rate, the injected solvent has more time to make finger before breakthrough to the production port. These results are not in agreement to the results presented by Amiell47 in the case of immiscible displacement. He stated that in the absence of surfactant and polymer in the injected solution, the number of


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fingers formed at any time is independent of injection rate but the shape of the finger was rate dependent. Figure 9 exhibits the comparison between number of fingers formed in all patterns A, B, and C at two injection rates. A glance at the figure 9 reveals that the rate of finger generation versus square root of the dimensionless time (i.e.

dN ) is independent on the medium characteristics d ( Td )

and depends on the injection rate and fluids presents in media. It should be mentioned that in miscible solvent flooding, the number of fingers formed at any time depend on the medium characteristics and injection rate. Also, figure 9 illustrates that for patterns B and C, which have similar medium characteristics the number of fingers formed at any square root of dimensionless time are close together. Figure 10 shows the correlation between the level of bypassed oil with dimensionless distance traveled by front for all the patterns A, B, and C at two different injection rates. As shown in figure 10, the level of bypassed oil decreases linearly with increase in dimensionless distance traveled by front with a good precision for all patterns. In the case of immiscible displacement, Pavone24 inferred that for drainage type water flooding process in 3D consolidated media at high IFT flow, the oil saturation profiles are linear along the sample. Furthermore, Yadali Jamaloei et al.45 proved that in the LTPF process, the mean local oil saturation has a decreasing linear relationship with dimensionless distance traveled by front in the homogenous micromodel. Our observation supports the view that the results obtained by Pavone24 and Yadali Jamaloei et al.

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in the case of immiscible displacement, are valid for the solvent flooding

process in fractured heterogonous media. It is worth stating that for any pattern used in this study, the level of bypassed oil by the front increases with an increase in injection rate (figure 11 ACS Paragon Plus Environment


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10). This is due to early breakthrough of injected solvent to the production port at higher injection rate compared to the lower injection rate. Figures 11-12 demonstrate the trend of transient dimensionless maximum and minimum finger length for all patterns A, B, and C for two injection rates of 0.0008 and 0.004 (cc/min), respectively. According to the figures 11-12, the dimensionless maximum finger length increases with an increase in dimension less time. In contrast, the dimensionless minimum finger length decreases as the dimensionless time increases. These trends have been shown for all patterns at different injection rates (figure 11-12). Figure 11 also shows a sharp change in dimensionless minimum finger length versus dimensionless time at early times of displacement for all patterns A, B, and C. After that, the change in dimensionless minimum finger length versus dimensionless time of displacement becomes relatively slow. On the other hand, we can observe that (Figure 12) with an increase in injection rate, the change in dimensionless minimum finger length versus dimensionless time becomes uniform during all the stages of displacement. This observation is in agreement with the result obtained by Yadali Jamaloei et al.45 in the case of LTPF at injection rate of 0.0008 (cc/min) in the homogenous micromodel. Moreover, figures 11 and 12 reveal that the dimensionless maximum finger length versus dimensionless time of displacement changes uniformly during all the stages of displacement at two injection rates of 0.0008 and 0.004 (cc/min) for all patterns utilized in this study. This result is in contrast with the result demonstrated by Yadali Jamaloei et al.45. They showed a sharp change in dimensionless maximum finger length versus dimensionless time during the early stages of the displacement in the case of LTPF at injection rate of 0.0008 (cc/min) in homogeneous micromodel.


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3.1

Fractal analysis The traditional nature of fractal is a non-Euclidean relationship between mass and size (i.e.

Mass∝ Volume)38. As an example for a sphere, mass is proportional to R 3 , but for a fractal D

object the mass is proportional to R , where D is fractal dimension of the object and R is the radius of gyration. Fractal dimension is a non-integer number and always less than Euclidean dimension of the object44. Viscous fingering is an example of chaotic motion which indicates a hydrodynamic instability. This chaotic motion causes a complex nature for viscos fingering patterns. Also, chaotic processes are very sensitive to initial conditions. Therefore, it is hard to reproduce it experimentally because of the unavoidable errors that exist in any experimental setup. Chaotic nature of viscos fingering causes different results when repeating an experiment several times39. There is a close relationship between chaos and fractals. Hence the use of fractal dimension to characterize viscous fingering is a good idea. One of the prevalent methods to calculate the fractal dimension is “box counting” method48-50. This method is based on the fact that fractal objects show self-similarity and can be split into parts, that each part is a reduced-size copy of the whole. According to box counting method, the number N(R) of boxes of size R needed to cover a fractal set follows a power-law,

N = N0 × R - D

(1)

Where D is fractal dimension of the object and N0 is the proportionality constant. Thus,

D=−

ln( N ) ln(R)

(2)



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To investigate the fractal behavior of fingering pattern in fractured heterogeneous media, we analyzed the fractal dimension of viscous fingering versus dimensionless time in all patterns. The open source ImageJ plug-in FracLac V.2.5 was used to compute the fractal dimension of captured images during displacement. Figure 13 exhibits the relationship between fractal dimension and dimensionless time for all patterns at two injection rates of 0.0008 and 0.004 (cc/min). As shown in figure 13, the fractal dimension of front varies with time. Therefore, this displacement process does not follow the fractal behavior; thus, up scaling of this displacement process by using fractal characteristics is not possible. Also, figure 13 reveals that the fractal dimension decreases during the early stages of displacement and then increases. The decrease in fractal dimension represents advancement of front in fractures and when front meets all the fractures in direction of displacement, the side fingers begin to growth, then fractal dimension increases continuously until breakthrough time. Moreover, as can be seen in figure 13, it is obvious that with an increase in injection rate, the fractal dimension decreases at any dimensionless time. Because of high pressure difference between injection and production ports, at high injection rate the front reaches to the production port rapidly, and does not have enough time to make branches in the media. This causes a pseudo linear frontal movement before breakthrough time. But, at low injection rate, the front has enough time to propagate in media and make more side fingers (see figures 2-7). For this reason, the fractal dimension at low injection rate is higher than the fractal dimension at high injection rate. Considering fractal dimension with its corresponding recovery factor during displacement for each pattern, it can be seen that at any dimensionless time, the recovery factor is related to fractal dimension in a manner that the greater fractal dimension results in greater 14 ACS Paragon Plus Environment

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recovery factor. At any dimensionless time for each pattern at higher injection rate, the displacement has lower fractal dimension and subsequently a lower recovery factor. 3.2

Practical Implication Miscible displacements occur in different industrial applications, e.g. miscible enhanced

oil recovery methods. Theoretical modeling of flow behavior in these systems normally faces with different challenges, especially in heterogeneous systems, e.g. fractured media. Finger characterizing including the rate of finger initiation; number of fingers, fractal dimension, and level of bypassed oil as a function of time/traveled distance, can be utilized as an alternative method for predicting of displacement efficiency in fractured porous media. The flow dynamics and heterogeneity control the number of developed fingers. For example the rate of finger initiation is higher at lower injection rate. Also, the level of bypassed oil (residual) at lower injection rate is lower. This showed that in a larger scale, e.g. oil reservoirs lower injection rates should be considered as it possible. One of important practical point should be considered in reservoir simulators is confident of fractal behavior of the fingers in heterogeneous media, which this work showed it is in doubt. So one could recommend more care is required when up scaling of the fingering pattern in heterogeneous media is under consideration. Although the flow behavior thorough the reservoir rock cannot be expected to be exactly represented by that in glass micromodels, but characterizing the finger behavior in miscible displacements of heterogeneous systems could be a spotlight to better understanding the issues in miscible injections.



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4

Conclusion In this study fundamental understanding how medium characteristics and flow dynamics

affect the behavior of developed fingers in fractured porous media has been examined. The following are the conclusions drawn from the observations: •

The numbers of macro fingers formed is well correlated with the square root of the dimensionless time in fractured media.

•

The rate of finger initiation versus square root of the dimensionless time is independent to fracture characteristics. It only depends on the flow dynamic. For the case of high flow rate, the numbers of fingers are the same for media with similar fracture characteristics.

•

The level of bypassed oil linearly decreases with dimensionless distance traveled by front with a good precision.

•

The dimensionless minimum finger length decreases continuously, while the dimensionless maximum finger length increases monotonically as the dimensionless time increases.

•

At early times, the dimensionless minimum finger length changes sharply at low injection rate, while it changes smoothly for the case of high flow rate.

•

The fractal dimension is decreasing with the injection rate, also at same dimensionless time the more fractal dimension results in more oil recovery.

•

The transient fractal dimension behavior experiences a minimum value which decreases by injection rate. This might be due to advancement of front in fractures at first, and when fingers meet all the fractures in direction of displacement, the side fingers begin to growth, thus, fractal dimension increases continuously before breakthrough.


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•

Variable transient behavior of fractal dimension of fingers might suggest that the miscible injection in fractured media does not obey from fractal theory. Therefore, more care is required for up scaling of miscible displacement processes in fractured media using fractal characteristics.

References 1. Butler, R. M.; Mokrys, I. J., Recovery of Heavy Oils Using Vapourized Hydrocarbon Solvents: Further Development of the Vapex Process. Journal of Canadian Petroleum Technology 1993, 32, (6). 2. Engelberts, W.; Klinkenberg, L. t., Laboratory Experiments on the Displacement of Oil by Water from Packs of Granular Material. In Proceedings 3rd World Petroleum Congress, The Hague, 1951; Vol. 2, pp 544-554. 3. Meurs, P. V., The Use of Transparent Three-Dimensional Models for Studying the Mechanism of Flow Processes in Oil Reservoirs. Trans. AIME 1957, 210, 295-301. 4. Meurs, P. v.; Poel, C. v. d., A Theoretical Description of Water-Drive Processes Involving Viscous Fingering. 1958. 5. Chuoke, R. L.; Meurs, P. v.; Poel, C. v. d., The Instability of Slow, Immiscible, Viscous LiquidLiquid Displacements in Permeable Media. Trans. AIME 1959, 216, 188-194. 6. Sheldon, J. W., On the Fingering of Slow Immiscible, Viscous Liquid-Liquid Displacements. In Fall Meeting of the Society of Petroleum Engineers of AIME, Denver, Colorado, 1960. 7. Outmans, H. D., Nonlinear Theory for Frontal Stability and Viscous Fingering in Porous Media. Old SPE Journal 1962, 2, (2), 165 - 176. 8. Benham, A. L.; Olson, R. W., A Model Study of Viscous Fingering. SPE Journal 1963, 3, (2). 9. Perkins, T. K.; Johnston, O. C., A Study of Immiscible Fingering in Linear Models. 1969. 10. Gupta, H. P.; Varnon, J. E.; Greenkorn, R. A., A Mechanistic Study of Viscous Finger Wavelengths. In Society of Petroleum Engineers: 1971. 11. Gupta, S. P.; Greenkorn, R. A., An experimental study of immiscible displacement with an unfavorable mobility ratio in porous media. Water Resour. Res. 1974, 10, (2), 371-374. 12. Peters, E. J.; Flock, D. L., The Onset of Instability During Two-Phase Immiscible Displacement in Porous Media. Society of Petroleum Engineers Journal 1981, 21, (2), 249-258. 13. Paterson, L.; Hornof, V.; Neale, G., Visualization of a Surfactant Flood of an Oil-Saturated Porous Medium. Society of Petroleum Engineers Journal 1984, 24, (3), 325-327. 14. Vossoughi, S.; Smith, J. E.; Green, D. W.; Willhite, G. P., A New Method To Simulate the Effects of Viscous Fingering on Miscible Displacement Processes in Porous Media. Society of Petroleum Engineers Journal 1984, 24, (1), 56-64. 15. Vossoughi, S.; Seyer, F. A., Prediction of recovery and water saturation distribution during an unstable immiscible displacement of oil from a porous medium. Industrial & Engineering Chemistry Fundamentals 1984, 23, (1), 64-74. 16. Mui, K. C.; Miller, C. A., Stability of Displacement Fronts in Porous Media Growth of Large Elliptical Fingers. Society of Petroleum Engineers Journal 1985, 25, (2), 255-267. 17. Ni, L. W.; Hornof, V.; Neale, G., Radial fingering in a porous medium. Oil & Gas Science and Technology 1986, 41, (2), 217-228.



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18. Stokes, J. P.; Weitz, D. A.; Gollub, J. P.; Dougherty, A.; Robbins, M. O.; Chaikin, P. M.; Lindsay, H. M., Interfacial Stability of Immiscible Displacement in a Porous Medium. Physical Review Letters 1986, 57, (14), 1718-1721. 19. Peters, E. J.; Khataniar, S., The Effect of Instability on Relative Permeability Curves Obtained by the Dynamic-Displacement Method. SPE Formation Evaluation 1987, 2, (4), 469-474. 20. Homsy, G., Viscous fingering in porous media. Annual Review of Fluid Mechanics 1987, 19, (1), 271-311. 21. Huang, Y.-B.; Gryte, C. C., Gamma-Camera Imaging of Oil Displacement in Thin Slabs of Porous Media. SPE Journal of Petroleum Technology 1988, 40, (10), 1355-1360. 22. Odeh, A. S., A Proposed Technique for Simulation of Viscous Fingering in One-Dimensional Immiscible Flow SPE Reservoir Engineering 1989, 4, (3), 304-308. 23. Brock, D. C.; Orr Jr., F. M., Flow Visualization of Viscous Fingering in Heterogeneous Porous Media. In SPE Annual Technical Conference and Exhibition, 1991 , Society of Petroleum Engineers, Inc.: Dallas, Texas, 1991. 24. Pavone, D., Observations and Correlations for Immiscible Viscous-Fingering Experiments. SPE Reservoir Engineering 1992, 7, (2), 187-194. 25. Tchelepi, H. A.; Jr., F. M. O., Interaction of Viscous Fingering, Permeability Heterogeneity, and Gravity Segregation in Three Dimensions. SPE Reservoir Engineering 1994, 9, (4), 266-271. 26. Cuthiell, D.; Kissel, G.; Jackson, C.; Frauenfeld, T.; Fisher, D.; Rispler, K., Viscous Fingering Effects in Solvent Displacement of Heavy Oil. In Canadian International Petroleum Conference, Petroleum Society of Canada: Calgary, Alberta, 2004. 27. Islam, M. N.; Azaiez, J., Nonlinear Simulation of Thermo-Viscous Fingering in Nonisothermal Miscible Displacements in Porous Media. In SPE Annual Technical Conference and Exhibition, Society of Petroleum Engineers: San Antonio, Texas, USA, 2006. 28. Ghesmat, K.; Azaiez, J., Interfacial Instability in Reactive Miscible-Flow Displacements. In SPE Annual Technical Conference and Exhibition, Society of Petroleum Engineers: San Antonio, Texas, USA, 2006. 29. Behrouz, T.; Kharrat, R.; Ghazanfari, M. H., Experimental Study of Factors Affecting Heavy Oil Recovery in Solvent Floods. In Canadian International Petroleum Conference, Petroleum Society of Canada: Calgary, Alberta, 2007. 30. Yadali Jamaloei, B.; Kharrat, R., Fundamental Study of Pore Morphology Effect in Low Tension Polymer Flooding or Polymer–Assisted Dilute Surfactant Flooding. Transport in Porous Media 2009, 76, (2), 199-218. 31. Yadali Jamaloei, B.; Asghari, K.; Kharrat, R., Pore-scale flow characterization of low-interfacial tension flow through mixed-wet porous media with different pore geometries. Experimental Thermal and Fluid Science 2011, 35, (1), 253-264. 32. Farzaneh, S. A.; Kharrat, R.; Ghazanfari, M. H., Experimental Study of Solvent Flooding to Heavy Oil in Fractured Five-Spot Micro-Models: The Role of Fracture Geometrical Characteristics. Journal of Canadian Petroleum Technology 2010, 49, (3), 36-43. 33. Saidian, M.; Ghazanfari, M. H.; Masihi, M.; Kharrat, R., Five-Spot Injection/Production Well Location Design Based on Fracture Geometrical Characteristics in Heavy Oil Fractured Reservoirs during Miscible Displacement: An Experimental Approach. Chemical Engineering Communications 2011, 199, (2), 306-320. 34. Sajjadi, M.; Azaiez, J., Thermo-Viscous Fingering in Heterogeneous Media. In SPE Heavy Oil Conference Canada, Society of Petroleum Engineers: Calgary, Alberta, Canada, 2012. 35. Yadali Jamaloei, B.; Kharrat, R.; Asghari, K., The influence of salinity on the viscous instability in viscous-modified low-interfacial tension flow during surfactant–polymer flooding in heavy oil reservoirs. Fuel 2012, 97, (0), 174-185. 36. Mandelbrot, B. B., The fractal geometry of nature. Times Books: New York, 1983. 37. Van Damme, H.; Obrecht, F.; Levitz, P.; Gatineau, L.; Laroche, C., Fractal viscous fingering in clay slurries. Nature 1986, 320, (6064), 731-733. 18 ACS Paragon Plus Environment

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38. Fanchi, J. R.; Christiansen, R. L., Applicability of Fractals to the Description of Viscous Fingering. In SPE Annual Technical Conference and Exhibition, Society of Petroleum Engineers, Inc.: San Antonio, Texas, 1989. 39. Peters, E. J.; Cavalero, S. R., The Fractal Nature of Viscous Fingering in Porous Media. In SPE Annual Technical Conference and Exhibition, 1990: New Orleans, Louisiana, 1990. 40. Ferer, M. V.; Sams, W. N.; Geisbrecht, R. A.; Smith, D. H., The Fractal Nature of Viscous Fingering: Saturation Profiles and Fractional Flows From Modeling of Miscible, Two-Component Flows in Two-Dimensional Pore Level Models. In SPE Symposium on Reservoir Simulation, Not subject to copyright. This document was prepared by government employees or with government funding that places it in the public domain.: New Orleans, Louisiana, 1993. 41. Zhang, J. H.; Liu, Z. H., Study of the relationship between fractal dimension and viscosity ratio for viscous fingering with a modified DLA model. Journal of Petroleum Science and Engineering 1998, 21, (1–2), 123-128. 42. Gharbi, R. B.; Qasem, F.; Peters, E. J., A Relationship Between the Fractal Dimension and Scaling Groups of Unstable Miscible Displacements. In SPE Annual Technical Conference and Exhibition, Copyright 2000, Society of Petroleum Engineers Inc.: Dallas, Texas, 2000. 43. Stevenson, K.; Ferer, M.; Bromhal, G. S.; Gump, J.; Wilder, J.; Smith, D. H., 2-D network model simulations of miscible two-phase flow displacements in porous media: Effects of heterogeneity and viscosity. Physica A: Statistical Mechanics and its Applications 2006, 367, (0), 7-24. 44. Doorwar, S.; Mohanty, K. K., Viscous Fingering during Non-Thermal Heavy Oil Recovery. In SPE Annual Technical Conference and Exhibition, Society of Petroleum Engineers: Denver, Colorado, USA, 2011. 45. Yadali Jamaloei, B.; Kharrat, R.; Torabi, F., Analysis and Correlations of Viscous Fingering in Low-Tension Polymer Flooding in Heavy Oil Reservoirs. Energy & Fuels 2010, 24, (12), 6384-6392. 46. Moissis, D. E.; Wheeler, M. F.; Miller, C. A., Simulation of Miscible Viscous Fingering Using a Modified Method of Characteristics: Effects of Gravity and Heterogeneity. SPE Advanced Technology Series 1993, 1, (1), 62-70. 47. Amiell, P. Ecoulements Diphasiques Gaz-Liquid en Milieu Poreux. Ph.D. Dissertation Ecole Natl. Sup. des Mines des Paris Paris, France, 1988. 48. Liebovitch, L. S.; Toth, T., A fast algorithm to determine fractal dimensions by box counting. Physics Letters A 1989, 141, (8–9), 386-390. 49. Foroutan-pour, K.; Dutilleul, P.; Smith, D. L., Advances in the implementation of the boxcounting method of fractal dimension estimation. Applied Mathematics and Computation 1999, 105, (2– 3), 195-210. 50. Sarkar, N.; Chaudhuri, B. B., An efficient differential box-counting approach to compute fractal dimension of image. Systems, Man and Cybernetics, IEEE Transactions on 1994, 24, (1), 115-120.



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

Figures Captions: Figure 1: Different patterns designed for micromodel experiments. Figure 2: Displacement fronts and fingering patterns for pattern A at different displacement time (Injection rate of 0.0008 (cc/min)). Figure 3: Displacement fronts and fingering patterns for pattern B at different displacement time (Injection rate of 0.0008 (cc/min)). Figure 4: Displacement fronts and fingering patterns for pattern C at different displacement time (Injection rate of 0.0008 (cc/min)). Figure 5: Displacement fronts and fingering patterns for pattern A at different displacement time (Injection rate of 0.004 (cc/min)). Figure 6: Displacement fronts and fingering patterns for pattern B at different displacement time (Injection rate of 0.004 (cc/min)). Figure 7: Displacement fronts and fingering patterns for pattern C at different displacement time (Injection rate of 0.004 (cc/min)). Figure 8: Correlation of the number of fingers formed with the square root of the dimensionless time for (a) Pattern A, (b) Pattern B, and (c) Pattern C. Figure 9: Comparison between number of fingers formed in all patterns at two injection rates (a) 0.0008 (cc/min) and (b) 0.004 (cc/min).


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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


Figure 10: Correlation of the level of bypassing of initial oil saturation with dimensionless distance traveled by front for (a) Pattern A, (b) Pattern B and (c) Pattern C. Figure 11: Trend of change in the dimensionless maximum and minimum finger length versus dimensionless time for (a) Pattern A ,(b) Pattern B and (c) Pattern C at injection rate of 0.0008 (cc/min). Figure 12: Trend of change in the dimensionless maximum and minimum finger length versus dimensionless time for (a) Pattern A ,(b) Pattern B and (c) Pattern C at injection rate of 0.004 (cc/min). Figure 13: Correlation between fractal dimension and dimensionless time for (a) Pattern A ,(b) Pattern B and (c) Pattern C at two injection rates of 0.0008 and 0.004 (cc/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

Figure 1


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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


Figure 2



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

Figure 3


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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


Figure 4



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

Figure 5


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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


Figure 6



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

Figure 7


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Pattern A 14 Injection Rate of 0.0008 (cc/min.) 12

Injection Rate of 0.004 (cc/min.)

10 Number of fingers

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

R² = 0.9812

6 4

R² = 0.9864

2 0 0.4

0.5

0.6 0.7 0.8 Square roote of dimensionless time

(a)


0.9

1


Pattern B 14 Injection Rate of 0.0008 (cc/min.) 12

Injection Rate of 0.004 (cc/min.)

10 Number of fingers

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

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8

6

R² = 0.9937

4 R² = 0.9985 2

0 0.4

0.5


(b)


0.9

1

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Pattern C 14 Injection rate of 0.0008 (cc/min.)

12

Injection rate of 0.004 (cc/min.) 10 Number of fingers

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 6

R² = 0.9937

4 R² = 0.9977 2 0 0.4

0.5


(c) Figure 8


0.9

1


16 Pattern A

14

Pattern B 12 Number of fingers

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

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Pattern C

10 8 R² = 0.9812 6 R² = 0.9985 4 R² = 0.9977

2 0 0.4

0.5


(a)


0.9

1

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16 Pattern A

14

Pattern B 12 Number of fingers

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


Pattern C R² = 0.9937

10 8 6

R² = 0.9937

4 R² = 0.9864

2 0 0.4

0.5


(b) Figure 9


0.9

1


Pattern A 100 95 R² = 0.9340 Level of bypassed oil

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

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90 85 80

R² = 0.9665 Injection rate of 0.0008 (cc/min.)

75

Injection rate of 0.004 (cc/min.) 70 0.2

0.3

0.4

0.5 0.6 0.7 Dimensionless distance

(a)


0.8

0.9

1

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Pattern B 99 R² = 0.9443

97 Level of bypassed oil

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


95 93 91 R² = 0.8210

89 Injection rate of 0.0008 (cc/min.) 87

Injection rate of 0.004 (cc/min.)

85 0.2

0.3

0.4


(b)


0.8

0.9

1


Pattern C 100

95 Level of bypassed oil

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

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R² = 0.9765

90

85

80 Injection rate of 0.0008 (cc/min.)

75

R² = 0.9389

Injection rate of 0.004 (cc/min.) 70 0

0.1

0.2

0.3


(c) Figure 10


0.7

0.8

0.9

1

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Pattern A 10 9 Dimensionless finger length

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


Dimensionless minimum finger length

8

Dimensionless maximum finger length

7 6 5 4 3 2 1 0 0

0.1

0.2

0.3

0.4 0.5 0.6 Dimensionless time

0.7

(a)


0.8

0.9

1


Pattern B 3 Dimensionless minimum finger length Dimensionless maximum finger length Dimensionless finger length

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

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2

1

0 0

0.1

0.2

0.3


(b)


0.7

0.8

0.9

1

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Pattern C 3 Dimensionless minimum finger length Dimensionless finger length

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


Dimensionless maximum finger length 2

1

0 0

0.1

0.2

0.3


(c) Figure 11


0.7

0.8

0.9

1


Pattern A 4 Dimensionless minimum finger length Dimensionless maximum finger length Dimensionless finger length

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

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3

2

1

0 0

0.1

0.2

0.3


(a)


0.7

0.8

0.9

1

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Pattern B 2 Dimensionless minimum finger length Dimensionless maximum finger length Dimensionless finger length

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


1

0 0

0.1

0.2

0.3


(b)


0.7

0.8

0.9

1


Pattern C 3 Dimensionless minimum finger length Dimensionless finger length

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

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Dimensionless maximum finger length 2

1

0 0

0.1

0.2

0.3


(c) Figure 12


0.7

0.8

0.9

1

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Pattern A 1.74

1.72 Fractal Dimension

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


1.7

1.68

1.66 Injection rate of 0.004 (cc/min.)

1.64

Injection rate of 0.0008 (cc/min.) 1.62 0

0.1

0.2

0.3


(a)


0.7

0.8

0.9

1


Pattern B 1.74


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

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1.7

1.68

1.66

1.64

Injection rate of 0.004 (cc/min.) Injection rate of 0.0008 (cc/min.)

1.62 0

0.1

0.2

0.3


(b)


0.7

0.8

0.9

1

Page 45 of 46

Pattern C 1.74


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


1.7

1.68

1.66

1.64

Injection rate of 0.004 (cc/min.) Injection rate of 0.0008 (cc/min.)

1.62 0

0.1

0.2

0.3


(c) Figure 13


0.7

0.8

0.9

1


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 46 of 46

Table 1: physical properties of micromodels used in the experiments Pattern

Coordination Number

Porosity (%)

A B C

4 4 4

52.29 52.29 52.33

Absolute Permeability (md) 2100 2000 2200

Number of Fracture 3 3 2

Fracture Length (cm) 2 2 2.5

Fracture Aperture ( µm ) 700 700 700

*Fracture orientation is measured with respect to average flow direction.

Table 2: Properties of oil and solvent used in experiments 3

Density ( Kg/m ) Viscosity (cP)

Oil 920

Solvent 795

92

1.64


Fracture Orientation (Degree)* 45 45 45

Monitoring and Characterizing the Finger Patterns Developed by

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