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Fractal characteristics of an asphaltene deposited heterogeneous surface
Applied Surface Science 256 (2009) 67–75
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Fractal characteristics of an asphaltene deposited heterogeneous surface J. Sayyad Amin, Sh. Ayatollahi *, A. Alamdari EOR Research Center, School of Chemical and Petroleum Engineering, Shiraz University, Zand Street, Shiraz 713451719, Iran
A R T I C L E I N F O
A B S T R A C T
Article history: Received 17 May 2009 Received in revised form 19 July 2009 Accepted 19 July 2009 Available online 28 July 2009
Several methods have been employed in recent years to investigate homogeneous surface topography based on image analysis, such as AFM (atomic force microscopy) and SEM (scanning electron microscopy). Fractal analysis of the images provides fractal dimension of the surface which is used as one of the most common surface indices. Surface topography has generally been considered to be monofractal. On the other hand, precipitation of organic materials on a rough surface and its irregular growth result in morphology alteration and converts a homogeneous surface to a heterogeneous one. In this case a mono-fractal description of the surface does not completely describe the nature of the altered surface. This work aims to investigate the topography alteration of a glass surface as a result of asphaltene precipitation and its growth at various pressures using a bi-fractal approach. The experimental results of the deposited surfaces were clearly indicating two regions of micro- and macro-asperities namely, surface types I and II, respectively. The fractal plots were indicative of bi-fractal behavior and for each surface type one fractal dimension was calculated. The topography information of the surfaces was obtained by two image analyses, AFM and SEM imaging techniques. Results of the bi-fractal analysis demonstrated that topography alteration in surface type II (macro-asperities) is more evident than that in surface type I (micro-asperities). Compared to surface type II, a better correlation was observed between the fractal dimensions inferred from the AFM images (DA) and those of the SEM images (DS) in surface type I. ß 2009 Elsevier B.V. All rights reserved.
Keywords: Bi-fractal Surface roughness AFM SEM Wettability alteration
1. Introduction Determination of roughness and surface topography for aggregated, porous and amorphous materials has been investigated in various application areas such as the polymer industry, drug delivery systems and enhanced oil recovery techniques. Some of the major properties of materials such as tendency of fluids to stick to the surface, known as wettability, can be determined by the characteristics of the surface structure. The roughness topography is considered an intensive property for the surface which changes dramatically in the precipitation process on the surface. If the mineral surface is homogeneous before the precipitation process, the deposition of the organic material will convert it to a heterogeneous one. Asphaltene precipitation on solid surfaces provides an example of a heterogeneous surface which is observed in the oil industry both in upstream and downstream. This phenomenon leads to surface topography changes which cause the wettability of the rock to be changed, known as wettability alteration. Wettability alteration is a major phenomenon that affects the oil recovery
* Corresponding author. Tel.: +98 711 6474602; fax: +98 711 6473575. E-mail address: [email protected] (S. Ayatollahi). 0169-4332/$ – see front matter ß 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.apsusc.2009.07.071
during oil production processes including enhanced oil recovery [1–4]. Being an appropriate representative for topography information, fractal dimension can describe intricate surfaces [5–9]. The concept of surface self-similarity at different scales makes fractal dimension a favorable representative of surfaces [10]. It has recently been proved that the fractal dimension is the most significant parameter for characterization of surface topography. It can be correlated with the other surface roughness parameters [11–13]. In almost all of the surface researches previously performed based on fractal theory, the dominant approach has been to tackle the problem by one fractal dimension, [14,15]. However, in the study of heterogeneous surfaces, in addition to the traditional fractal approach, bi-fractal could be a more efficient approach. No uniform status throughout the surface could be detected because of the precipitation or detachment of the second phase on the surface. Hence, a bi-fractal approach would describe the heterogeneous surface better than a mono-fractal one. The simplest way to capture the surface roughness is to divide the surface into two different surface types. This includes regions of macro- and microasperities. A bi-fractal approach utilizes two different fractal dimensions for the two distinct regions of scale. There are different methods for analysis and description of the surface topography [16–20]. Some of these methods are
J.S. Amin et al. / Applied Surface Science 256 (2009) 67–75
68 Table 1 SARA analysis of crude oila. No.
Test name
Test method
Result (wt%)
1 2 3 4 5
Total acid no. Saturates content Aromatic content Asphaltene content Resins content
ASTM D 664 SARA test SARA test SARA test SARA test
3.94 48.02 34.15 5.3 8.5
a
SP.GR at 15.56/15.56 8C: 0.8793–29.42 8API.
established based on the analysis of the surface images. Information obtained from digital images of the surface structure is used to determine fractal dimensions. The imaging techniques can be provided through different methods such as X-ray, SEM, AFM, and other surface imaging tests. AFM as an advanced browsing technique and SEM as a common method to detect the alteration of the surface are used in this study which be described, respectively. Recently, AFM has emerged as a powerful and important tool in the analysis of structure characterization and heterogeneous properties of surface. In the AFM method, the information of surface roughness such as root-mean-square (RMS) and mean roughness are often considered to be a criterion for surface topography. Quantitative measurement of surface roughness is considered to be a valuable characteristic of the AFM technique [21–23]. Therefore, the examination of surface alteration by the
Fig. 1. Schematic diagram of experimental apparatus at high pressure (1) peristaltic pump, (2) distillation water reservoir, (3) computer, (4) CCD camera, (5) microscope, (6) sight glass, (7) piston-cylinder, (8) cold light source, (9) heater, (10) magnetic mixer, (11) high pressure vessel, (12) rotator, (13) metal disk and (14) fan.
materials that adhere to the surface is usually monitored by this method [23–29]. Moreover, it has occasionally been observed that a good correlation between the obtained fractal dimension from this method and fractal dimensions resulting from the other methods exist [17].
Fig. 2. Three-dimensional AFM images of asphaltene precipitation on glass surface: (a) p = 35 bar, (b) p = 90 bar and (c) p = 135 bar.
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Fig. 3. Two dimensional AFM images of asphaltene precipitation on glass surface: (a) p = 35 bar and (b) p = 135 bar.
It has also been common to use SEM images to determine fractal features. In SEM imaging, a high depth of focus provides more qualitative information about the surface topography. In the interpretation of SEM images, the surface topography can be inferred from variations in the image intensity. Quantitative information can be obtained through image fractal analysis. The fractal information obtained by this method is more preferable than other methods such as electrochemical impedance spectroscopy [30,31]. Such comparison between fractal dimensions obtained from AFM and SEM images has been the subject of this study. Remarkable achievement could be found by using a bifractal analysis compared to a simple mono-fractal method when it is used for heterogonous surfaces. 2. Theory A number of methods have been used to calculate fractal features of the surface, one of which is difference statistics
method [32–34]. In this study, the difference statistics method, which relies on establishing the difference function Df(e) (also called structural function) as a function of spatial scale was used: D
D f ðeÞ ¼ ½ f ðx; yÞ f ðx0 ; y0 Þ2
E1=2
(1)
where f(x0,y0) is the value of the considered attribute of the image at a reference point and f(x,y) is its value at a point at distance (lag space) e from the reference point. The difference is averaged over the spatial extent of the considered surface image. For a e z [30,31]:
D f ðeÞ ¼ eH
(2)
where z is the lateral correlation length, and H = d D is the Hurst also called Ho¨lder exponent of roughness, D is the fractal dimension of the surface and d is the embedding Euclidian dimension. Therefore, it is evident that fractal dimension of a
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Fig. 5. Histogram of image roughness height based on AFM image information: (a) p = 35 bar and (b) p = 135 bar.
3. Experimental work 3.1. Materials Asphaltene used in this study was extracted from a sample of an oil reservoir located in the south of Iran according to the procedure of ASTM-D86 [35]. The SARA (saturate, aromatic, resin, and asphaltene) analysis of the crude oil is listed in Table 1. To prepare the synthetic oil, toluene and normal heptane with a high performance liquid chromatography grade supplied by the Merck Company were used. Glass substrates were utilized as the solid surface to mimic the sandstone [3] while representing the original homogeneous surface. This homogeneous surface would be altered into a heterogeneous one through asphaltene precipitation. 3.2. Sample preparation
Fig. 4. Representative SEM micrographs showing asphaltene precipitated on glass surface: (a) p = 35 bar, (b) p = 90 bar and (c) p = 135 bar.
rough surface is in the interval of 2 and 3. Correlation length is defined as the distance from a point beyond which there is no further correlation of a physical property associated with that point. Eq. (3) can be used to obtain fractal dimension as follows [32]: log D f ðeÞ D ¼ lim d logðeÞ e!0
(3)
In order to create a heterogeneous surface, asphaltene was precipitated on glass substrate at different pressures. Fig. 1 shows the schematic diagram of the apparatus designed for this purpose in the Shiraz University EOR Research Center. The main part of the apparatus includes a high pressure cell with a working pressure up to 200 bar. Glass substrates were inserted into the cell as they were placed on a metallic rotating disk adjusted to be seen under the ¨ SS, microscope. The use of a high resolution microscope (KRU MBL2000) enabled us to monitor the surface changes of the substrates used in the cell. A clod light source was designed to illuminate the scene of the microscope and prevent adding extra heat into the system. The glass substrate was located between the cold light source and the microscope. To take the required pictures, a charge coupled device (CCD) Camera (iDS, UI-1485LE-C-HQ, 5.7 megapixels) was used. The resulting digitized pictures were then
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Fig. 8. Schematic mechanism proposed for topography alteration of glass surface at three different states: (a) pure glass, (b) asphaltene precipitated on surface at p = 35 bar and (c) asphaltene precipitated on surface at p = 135 bar, colorful surfaces represent different layers of asphaltene deposit. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
Fig. 6. 3D plot of asphaltene precipitation height of heterogeneous glass surface based on AFM image information: (a) p = 35 bar and (b) p = 135 bar.
used for post processing calculations. The cell was also equipped with a heater and its controller to maintain the system temperature. The cell pressure was supplied by a high pressure liquid chromatography (HPLC) pump (Agilent Technologies 1200 series) and a piston-cylinder. The required solution to prepare the synthetic oil used in this experiment consists of toluene and normal heptane with a ratio of 3:1. Temperature was fixed at 100 8C during this process. In the first step, the cell pressure was gradually increased up to the point that asphaltene formation is observed. The onset pressure for asphaltene precipitation was found to be 35 bar at this condition. After 2 h, when the entire asphaltene was precipitated, the solution was quickly drained and the glass substrates were taken out of the cell. The treated glass substrates were utilized to perform AFM (DualscopeTM DS95-200) test and SEM (S360 Oxford-Cambridge) imaging. In order to analyze the AFM image, the information from the image topography was converted into ASCII data. Two more experiments were subsequently performed at 90 and 135 bar to check the effects of pressure on the asphaltene precipitation. To ensure the repeatability, each experiment was repeated at the specified condition. 4. Results and discussion
Fig. 7. Cumulative curve of pixels of heterogeneous glass surface vs. roughness height: (a) heterogeneous 1, p = 35 bar and (b) heterogeneous 2, p = 135 bar.
Previous investigations [36–38] showed that most of the asphaltene in the mixture was precipitated at the onset pressure. The precipitated asphaltene was observed to be detached from the surface as the pressure increases, below the bubble pressure [38]. The same results of precipitation behavior were observed in this work. Figs. 2 and 3 which show the 5 mm 5 mm scans of the treated glass surface illustrate the heterogeneity of the surfaces. As observed in these results, at the onset pressure, the glass substrate surface is covered by precipitated asphaltene creating tall peaks, transforming to shorter peaks as the pressure increases
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Fig. 9. Main window of the coded software while analyzing AFM image of a glass surface on which asphaltene is deposited.
(Fig. 3). The sole cause of this phenomenon is the asphaltene solubility reduction in the solution because of the pressure effects as it is discussed in other research work [36]. The deposited asphaltene on the glass is categorized into two different groups. The first group consists of precipitants placed on the higher peaks and the second deposited on the shorter ones. The precipitants belonging to the first group are more easily detached from the surface because of the weak molecular binding between the accumulated asphaltene. This phenomenon was also shown in 2D images shown in Fig. 3a–c as the deposited organic material, light color (For interpretation of the references to color in this sentence, the reader is referred to the web version of the article)spots, become smaller in size. Glass substrate micrographs at different pressures are also obtained by SEM technique, shown in Fig. 4. Reduction of
precipitation as a result of pressure increase is demonstrated by a reduction in the size of the white spots. Fig. 5 shows histograms of roughness height for the asphaltene deposited heterogeneous surface at two different pressures of 35 and 135 bar (the onset and maximum pressure used in this work). The histogram has been obtained based on the AFM images. The number of pixels having a certain height, clearly indicate the topography alteration during the asphaltene precipitation. The results also verify the pressure effects as the number of pixels having the taller height has been reduced while the number of pixels corresponding to shorter height values has been increased. The 3D plot topography of asphaltene precipitated on the glass surface at two different conditions (35 and 135 bar) is shown in Fig. 6. The Z-axis represents the height of the deposited material, while the X- and Y-axis represent the area scanned by the AFM
Fig. 10. Main window of the coded software while analyzing SEM image of a glass surface on which asphaltene is deposited.
J.S. Amin et al. / Applied Surface Science 256 (2009) 67–75
Fig. 11. AFM and SEM macro-asperity fractal dimension of samples at different pressure, No. 1 at 35 bar, No. 2 at 90 bar, and No. 3 at 135 bar. Error bars show the corresponding standard deviation.
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Fig. 13. Correlation between the fractal dimensions obtained from the AFM and SEM method for micro-asperity roughness.
cantilever, 5 mm 5 mm of the glass substrate equivalent to 125 125 pixels. Fig. 6 also indicates that the number of short heights increases while the number of tall summits decreases as the pressure increases from 35 to 135 bar. Histograms shown in Fig. 5 as well as 3D plots in Fig. 6 indicated the existence of two different surface types of the micro- and macro-roughness. Surface type I consists of short summits and wide shallow valleys, while surface type II refers to the tall summits and deep valleys. As it is indicated in the results both surface types are randomly distributed on the surface. Fig. 7 clearly indicates the cumulative height distribution of the roughness for the glass surface at three different conditions, pure glass and two heterogeneous altered surfaces obtained from AFM images. Two different surface types are generated on the pure glass surface during the precipitation process, indicated as surface types I and II. As the pressure increases from the onset condition, more precipitated materials are detached and the number of the taller peaks corresponds to surface type II reduces. The margin between the two surface types for the cumulative number of pixels with respect to the height is obtained graphically in Fig. 7. This would indicate that 13,000 pixels corresponding to heights shorter than 4 108 m would belong to surface type I and the rest applies to surface type II. The same number of pixels was obtained as the pressure increased from case 1 to case 2, indicating that the altered surface could be transformed to the condition of fresh glass when the pressure increased from 35 to 135 bar. A proposed mechanism for this phenomenon is presented in Fig. 8. According to this proposed scheme, the onset pressure causes the asphaltene to precipitate on the surface rendering smooth micro-asperities and sharp macro-asperities (Fig. 8b). Increasing the pressure leads to the detachment of precipitates
from the macro-asperities, decreasing their heights, and increasing in the number of micro-asperities (Fig. 8c). Considering the existence of two surface types with different roughness, a fractal number is calculated for each one to represent the distinct roughness of the surface type. The fractal dimensions of surface types I and II were calculated according to the principles explained in the theoretical section. Two separate softwares were developed here to analyze the AFM and SEM images. User interfaces were designed for both codes to show the topography changes and calculated parameters from AFM and SEM images as shown in Figs. 9 and 10. Figs. 11 and 12 compare the fractal dimensions obtained from AFM and SEM images for macro- and micro-asperities, respectively. The bi-fractality observed in these two figures further proves the formation of macro- and micro-asperities previously interpreted from the histogram and the curve of cumulative number of pixels versus height. Increasing the pressure results in decreasing the DA and DS of the macro-asperities and increases those of micro-asperities. Diminished asphaltene agglomeration is the major cause of this phenomenon. Trends for the increase and decrease in D for micro- and macroasperities are evident for both AFM and SEM images, respectively. The only difference is in the values of fractal dimensions. Figs. 13 and 14 examine possible correlations between DA and DS, fractal dimensions for AFM and SEM, respectively, for surface type I (micro-asperity) and surface type II (macro-asperity). Surface type I exhibits a better correlation with a cross- correlation coefficient (R2) of 0.996 compared to 0.503 for surface type II. This could be explained by shading (non-uniform illumination) and random noise problems during SEM tests [20]. The shading occurs when an object is illuminated from a source which leads to a non-
Fig. 12. AFM and SEM micro-asperity fractal dimension of samples at different pressure, No. 1 at 35 bar, No. 2 at 90 bar, and No. 3 at 135 bar. Error bars show the corresponding standard deviation.
Fig. 14. Correlation between the fractal dimensions obtained from the AFM and SEM method for macro-asperity roughness.
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uniform background image. In SEM method, the electron intensity to the detector or viewer is a function of surface orientation considering the electron source leads to the reduction of topographical contrasts. The more heterogeneous surface is the lesser topographical contrasts can be observed [20]. The random noise during SEM tests received by the image detectors caused by incident electrons and/or by the quantization devices makes the pixels brighter or darker [20]. Heterogeneity of surface type II is more than that of surface type I which is represented by brighter pixels in the produced images. Hence, the problems of random noise and shading are more apparent in this surface type. Electron intensity and random noise, however, play no role in AFM images; therefore, the fractal dimensions obtained from these images are more accurate. This accuracy makes AFM images more favorable for fractal analysis. The results of this study postulate the bi-fractal characteristic of heterogeneous surfaces. It is apparent that two fractal dimensions can represent heterogeneous surfaces more accurately. In other words, for surfaces composed of two distinct materials, bi-fractal analysis can better characterize the changes in surface microasperities (that depend on the topography of the original surface) and surface macro-asperities (that depend on the topography of the precipitated material). 5. Summary and conclusions The asperities observed on the heterogeneous surface were categorized into micro- (surface type I) and macro- (surface type II) asperities. Surface type I includes short peaks and shallow valleys, where surface type II includes tall peaks and deep valleys. These two categories were proposed according to the roughness information obtained from the AFM tests. The boundary between the two surface types was determined graphically and shows that the roughness of surface type I approaches that of the pure glass as the pressure increases. The fractal dimension of each surface type was calculated by two distinct codes prepared for AFM and SEM. Changes in fractal dimensions observed for surface types I and II based on AFM and SEM images were found to follow similar trends. A better correlation was observed between the SEM fractal dimension (DS) and AFM fractal dimension (DA) for surface type I as this surface type was less sensitive to the intensity of the light. Heterogeneous surfaces composed of two different asperities appear to be proper subjects for bi-fractal analysis as the two fractal dimensions can describe changes in the topography of each surface type with reasonable accuracy. Acknowledgments The authors would like to express their sincere gratitude to Navid Pazhuhesh Farda (NPF) Co. for their kind collaboration and help during the installation and set up of the instruments. They also greatly appreciate Mahar Fanabzar Co. for their support and help in performing AFM tests. Financial support from NIOC-RTD is also appreciated. The authors are thankful to Ehsan Nikooee from the Department of Civil Engineering, Shiraz University, for his valuable comments and help in performing fractal analyses on SEM and AFM images. Last but not least, intellectual help and constructive remarks from the members of the EOR Research Center are gratefully acknowledged. References [1] R.A. Salathiel, Oil recovery by surface film drainage in mixed wettability rocks, J. Petrol. Technol. 25 (1973) 1216–1224. [2] L. Cuiec, Evaluation of reservoir wettability and its effects on oil recovery, in: N.R. Morrow (Ed.), Interfacial Phenomena in Oil Recovery, Marcel Dekker Inc., New York City, 1991, pp. 319–375.
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Applied Surface Science journal homepage: www.elsevier.com/locate/apsusc
Fractal characteristics of an asphaltene deposited heterogeneous surface J. Sayyad Amin, Sh. Ayatollahi *, A. Alamdari EOR Research Center, School of Chemical and Petroleum Engineering, Shiraz University, Zand Street, Shiraz 713451719, Iran
A R T I C L E I N F O
A B S T R A C T
Article history: Received 17 May 2009 Received in revised form 19 July 2009 Accepted 19 July 2009 Available online 28 July 2009
Several methods have been employed in recent years to investigate homogeneous surface topography based on image analysis, such as AFM (atomic force microscopy) and SEM (scanning electron microscopy). Fractal analysis of the images provides fractal dimension of the surface which is used as one of the most common surface indices. Surface topography has generally been considered to be monofractal. On the other hand, precipitation of organic materials on a rough surface and its irregular growth result in morphology alteration and converts a homogeneous surface to a heterogeneous one. In this case a mono-fractal description of the surface does not completely describe the nature of the altered surface. This work aims to investigate the topography alteration of a glass surface as a result of asphaltene precipitation and its growth at various pressures using a bi-fractal approach. The experimental results of the deposited surfaces were clearly indicating two regions of micro- and macro-asperities namely, surface types I and II, respectively. The fractal plots were indicative of bi-fractal behavior and for each surface type one fractal dimension was calculated. The topography information of the surfaces was obtained by two image analyses, AFM and SEM imaging techniques. Results of the bi-fractal analysis demonstrated that topography alteration in surface type II (macro-asperities) is more evident than that in surface type I (micro-asperities). Compared to surface type II, a better correlation was observed between the fractal dimensions inferred from the AFM images (DA) and those of the SEM images (DS) in surface type I. ß 2009 Elsevier B.V. All rights reserved.
Keywords: Bi-fractal Surface roughness AFM SEM Wettability alteration
1. Introduction Determination of roughness and surface topography for aggregated, porous and amorphous materials has been investigated in various application areas such as the polymer industry, drug delivery systems and enhanced oil recovery techniques. Some of the major properties of materials such as tendency of fluids to stick to the surface, known as wettability, can be determined by the characteristics of the surface structure. The roughness topography is considered an intensive property for the surface which changes dramatically in the precipitation process on the surface. If the mineral surface is homogeneous before the precipitation process, the deposition of the organic material will convert it to a heterogeneous one. Asphaltene precipitation on solid surfaces provides an example of a heterogeneous surface which is observed in the oil industry both in upstream and downstream. This phenomenon leads to surface topography changes which cause the wettability of the rock to be changed, known as wettability alteration. Wettability alteration is a major phenomenon that affects the oil recovery
* Corresponding author. Tel.: +98 711 6474602; fax: +98 711 6473575. E-mail address: [email protected] (S. Ayatollahi). 0169-4332/$ – see front matter ß 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.apsusc.2009.07.071
during oil production processes including enhanced oil recovery [1–4]. Being an appropriate representative for topography information, fractal dimension can describe intricate surfaces [5–9]. The concept of surface self-similarity at different scales makes fractal dimension a favorable representative of surfaces [10]. It has recently been proved that the fractal dimension is the most significant parameter for characterization of surface topography. It can be correlated with the other surface roughness parameters [11–13]. In almost all of the surface researches previously performed based on fractal theory, the dominant approach has been to tackle the problem by one fractal dimension, [14,15]. However, in the study of heterogeneous surfaces, in addition to the traditional fractal approach, bi-fractal could be a more efficient approach. No uniform status throughout the surface could be detected because of the precipitation or detachment of the second phase on the surface. Hence, a bi-fractal approach would describe the heterogeneous surface better than a mono-fractal one. The simplest way to capture the surface roughness is to divide the surface into two different surface types. This includes regions of macro- and microasperities. A bi-fractal approach utilizes two different fractal dimensions for the two distinct regions of scale. There are different methods for analysis and description of the surface topography [16–20]. Some of these methods are
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68 Table 1 SARA analysis of crude oila. No.
Test name
Test method
Result (wt%)
1 2 3 4 5
Total acid no. Saturates content Aromatic content Asphaltene content Resins content
ASTM D 664 SARA test SARA test SARA test SARA test
3.94 48.02 34.15 5.3 8.5
a
SP.GR at 15.56/15.56 8C: 0.8793–29.42 8API.
established based on the analysis of the surface images. Information obtained from digital images of the surface structure is used to determine fractal dimensions. The imaging techniques can be provided through different methods such as X-ray, SEM, AFM, and other surface imaging tests. AFM as an advanced browsing technique and SEM as a common method to detect the alteration of the surface are used in this study which be described, respectively. Recently, AFM has emerged as a powerful and important tool in the analysis of structure characterization and heterogeneous properties of surface. In the AFM method, the information of surface roughness such as root-mean-square (RMS) and mean roughness are often considered to be a criterion for surface topography. Quantitative measurement of surface roughness is considered to be a valuable characteristic of the AFM technique [21–23]. Therefore, the examination of surface alteration by the
Fig. 1. Schematic diagram of experimental apparatus at high pressure (1) peristaltic pump, (2) distillation water reservoir, (3) computer, (4) CCD camera, (5) microscope, (6) sight glass, (7) piston-cylinder, (8) cold light source, (9) heater, (10) magnetic mixer, (11) high pressure vessel, (12) rotator, (13) metal disk and (14) fan.
materials that adhere to the surface is usually monitored by this method [23–29]. Moreover, it has occasionally been observed that a good correlation between the obtained fractal dimension from this method and fractal dimensions resulting from the other methods exist [17].
Fig. 2. Three-dimensional AFM images of asphaltene precipitation on glass surface: (a) p = 35 bar, (b) p = 90 bar and (c) p = 135 bar.
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Fig. 3. Two dimensional AFM images of asphaltene precipitation on glass surface: (a) p = 35 bar and (b) p = 135 bar.
It has also been common to use SEM images to determine fractal features. In SEM imaging, a high depth of focus provides more qualitative information about the surface topography. In the interpretation of SEM images, the surface topography can be inferred from variations in the image intensity. Quantitative information can be obtained through image fractal analysis. The fractal information obtained by this method is more preferable than other methods such as electrochemical impedance spectroscopy [30,31]. Such comparison between fractal dimensions obtained from AFM and SEM images has been the subject of this study. Remarkable achievement could be found by using a bifractal analysis compared to a simple mono-fractal method when it is used for heterogonous surfaces. 2. Theory A number of methods have been used to calculate fractal features of the surface, one of which is difference statistics
method [32–34]. In this study, the difference statistics method, which relies on establishing the difference function Df(e) (also called structural function) as a function of spatial scale was used: D
D f ðeÞ ¼ ½ f ðx; yÞ f ðx0 ; y0 Þ2
E1=2
(1)
where f(x0,y0) is the value of the considered attribute of the image at a reference point and f(x,y) is its value at a point at distance (lag space) e from the reference point. The difference is averaged over the spatial extent of the considered surface image. For a e z [30,31]:
D f ðeÞ ¼ eH
(2)
where z is the lateral correlation length, and H = d D is the Hurst also called Ho¨lder exponent of roughness, D is the fractal dimension of the surface and d is the embedding Euclidian dimension. Therefore, it is evident that fractal dimension of a
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Fig. 5. Histogram of image roughness height based on AFM image information: (a) p = 35 bar and (b) p = 135 bar.
3. Experimental work 3.1. Materials Asphaltene used in this study was extracted from a sample of an oil reservoir located in the south of Iran according to the procedure of ASTM-D86 [35]. The SARA (saturate, aromatic, resin, and asphaltene) analysis of the crude oil is listed in Table 1. To prepare the synthetic oil, toluene and normal heptane with a high performance liquid chromatography grade supplied by the Merck Company were used. Glass substrates were utilized as the solid surface to mimic the sandstone [3] while representing the original homogeneous surface. This homogeneous surface would be altered into a heterogeneous one through asphaltene precipitation. 3.2. Sample preparation
Fig. 4. Representative SEM micrographs showing asphaltene precipitated on glass surface: (a) p = 35 bar, (b) p = 90 bar and (c) p = 135 bar.
rough surface is in the interval of 2 and 3. Correlation length is defined as the distance from a point beyond which there is no further correlation of a physical property associated with that point. Eq. (3) can be used to obtain fractal dimension as follows [32]: log D f ðeÞ D ¼ lim d logðeÞ e!0
(3)
In order to create a heterogeneous surface, asphaltene was precipitated on glass substrate at different pressures. Fig. 1 shows the schematic diagram of the apparatus designed for this purpose in the Shiraz University EOR Research Center. The main part of the apparatus includes a high pressure cell with a working pressure up to 200 bar. Glass substrates were inserted into the cell as they were placed on a metallic rotating disk adjusted to be seen under the ¨ SS, microscope. The use of a high resolution microscope (KRU MBL2000) enabled us to monitor the surface changes of the substrates used in the cell. A clod light source was designed to illuminate the scene of the microscope and prevent adding extra heat into the system. The glass substrate was located between the cold light source and the microscope. To take the required pictures, a charge coupled device (CCD) Camera (iDS, UI-1485LE-C-HQ, 5.7 megapixels) was used. The resulting digitized pictures were then
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Fig. 8. Schematic mechanism proposed for topography alteration of glass surface at three different states: (a) pure glass, (b) asphaltene precipitated on surface at p = 35 bar and (c) asphaltene precipitated on surface at p = 135 bar, colorful surfaces represent different layers of asphaltene deposit. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
Fig. 6. 3D plot of asphaltene precipitation height of heterogeneous glass surface based on AFM image information: (a) p = 35 bar and (b) p = 135 bar.
used for post processing calculations. The cell was also equipped with a heater and its controller to maintain the system temperature. The cell pressure was supplied by a high pressure liquid chromatography (HPLC) pump (Agilent Technologies 1200 series) and a piston-cylinder. The required solution to prepare the synthetic oil used in this experiment consists of toluene and normal heptane with a ratio of 3:1. Temperature was fixed at 100 8C during this process. In the first step, the cell pressure was gradually increased up to the point that asphaltene formation is observed. The onset pressure for asphaltene precipitation was found to be 35 bar at this condition. After 2 h, when the entire asphaltene was precipitated, the solution was quickly drained and the glass substrates were taken out of the cell. The treated glass substrates were utilized to perform AFM (DualscopeTM DS95-200) test and SEM (S360 Oxford-Cambridge) imaging. In order to analyze the AFM image, the information from the image topography was converted into ASCII data. Two more experiments were subsequently performed at 90 and 135 bar to check the effects of pressure on the asphaltene precipitation. To ensure the repeatability, each experiment was repeated at the specified condition. 4. Results and discussion
Fig. 7. Cumulative curve of pixels of heterogeneous glass surface vs. roughness height: (a) heterogeneous 1, p = 35 bar and (b) heterogeneous 2, p = 135 bar.
Previous investigations [36–38] showed that most of the asphaltene in the mixture was precipitated at the onset pressure. The precipitated asphaltene was observed to be detached from the surface as the pressure increases, below the bubble pressure [38]. The same results of precipitation behavior were observed in this work. Figs. 2 and 3 which show the 5 mm 5 mm scans of the treated glass surface illustrate the heterogeneity of the surfaces. As observed in these results, at the onset pressure, the glass substrate surface is covered by precipitated asphaltene creating tall peaks, transforming to shorter peaks as the pressure increases
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Fig. 9. Main window of the coded software while analyzing AFM image of a glass surface on which asphaltene is deposited.
(Fig. 3). The sole cause of this phenomenon is the asphaltene solubility reduction in the solution because of the pressure effects as it is discussed in other research work [36]. The deposited asphaltene on the glass is categorized into two different groups. The first group consists of precipitants placed on the higher peaks and the second deposited on the shorter ones. The precipitants belonging to the first group are more easily detached from the surface because of the weak molecular binding between the accumulated asphaltene. This phenomenon was also shown in 2D images shown in Fig. 3a–c as the deposited organic material, light color (For interpretation of the references to color in this sentence, the reader is referred to the web version of the article)spots, become smaller in size. Glass substrate micrographs at different pressures are also obtained by SEM technique, shown in Fig. 4. Reduction of
precipitation as a result of pressure increase is demonstrated by a reduction in the size of the white spots. Fig. 5 shows histograms of roughness height for the asphaltene deposited heterogeneous surface at two different pressures of 35 and 135 bar (the onset and maximum pressure used in this work). The histogram has been obtained based on the AFM images. The number of pixels having a certain height, clearly indicate the topography alteration during the asphaltene precipitation. The results also verify the pressure effects as the number of pixels having the taller height has been reduced while the number of pixels corresponding to shorter height values has been increased. The 3D plot topography of asphaltene precipitated on the glass surface at two different conditions (35 and 135 bar) is shown in Fig. 6. The Z-axis represents the height of the deposited material, while the X- and Y-axis represent the area scanned by the AFM
Fig. 10. Main window of the coded software while analyzing SEM image of a glass surface on which asphaltene is deposited.
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Fig. 11. AFM and SEM macro-asperity fractal dimension of samples at different pressure, No. 1 at 35 bar, No. 2 at 90 bar, and No. 3 at 135 bar. Error bars show the corresponding standard deviation.
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Fig. 13. Correlation between the fractal dimensions obtained from the AFM and SEM method for micro-asperity roughness.
cantilever, 5 mm 5 mm of the glass substrate equivalent to 125 125 pixels. Fig. 6 also indicates that the number of short heights increases while the number of tall summits decreases as the pressure increases from 35 to 135 bar. Histograms shown in Fig. 5 as well as 3D plots in Fig. 6 indicated the existence of two different surface types of the micro- and macro-roughness. Surface type I consists of short summits and wide shallow valleys, while surface type II refers to the tall summits and deep valleys. As it is indicated in the results both surface types are randomly distributed on the surface. Fig. 7 clearly indicates the cumulative height distribution of the roughness for the glass surface at three different conditions, pure glass and two heterogeneous altered surfaces obtained from AFM images. Two different surface types are generated on the pure glass surface during the precipitation process, indicated as surface types I and II. As the pressure increases from the onset condition, more precipitated materials are detached and the number of the taller peaks corresponds to surface type II reduces. The margin between the two surface types for the cumulative number of pixels with respect to the height is obtained graphically in Fig. 7. This would indicate that 13,000 pixels corresponding to heights shorter than 4 108 m would belong to surface type I and the rest applies to surface type II. The same number of pixels was obtained as the pressure increased from case 1 to case 2, indicating that the altered surface could be transformed to the condition of fresh glass when the pressure increased from 35 to 135 bar. A proposed mechanism for this phenomenon is presented in Fig. 8. According to this proposed scheme, the onset pressure causes the asphaltene to precipitate on the surface rendering smooth micro-asperities and sharp macro-asperities (Fig. 8b). Increasing the pressure leads to the detachment of precipitates
from the macro-asperities, decreasing their heights, and increasing in the number of micro-asperities (Fig. 8c). Considering the existence of two surface types with different roughness, a fractal number is calculated for each one to represent the distinct roughness of the surface type. The fractal dimensions of surface types I and II were calculated according to the principles explained in the theoretical section. Two separate softwares were developed here to analyze the AFM and SEM images. User interfaces were designed for both codes to show the topography changes and calculated parameters from AFM and SEM images as shown in Figs. 9 and 10. Figs. 11 and 12 compare the fractal dimensions obtained from AFM and SEM images for macro- and micro-asperities, respectively. The bi-fractality observed in these two figures further proves the formation of macro- and micro-asperities previously interpreted from the histogram and the curve of cumulative number of pixels versus height. Increasing the pressure results in decreasing the DA and DS of the macro-asperities and increases those of micro-asperities. Diminished asphaltene agglomeration is the major cause of this phenomenon. Trends for the increase and decrease in D for micro- and macroasperities are evident for both AFM and SEM images, respectively. The only difference is in the values of fractal dimensions. Figs. 13 and 14 examine possible correlations between DA and DS, fractal dimensions for AFM and SEM, respectively, for surface type I (micro-asperity) and surface type II (macro-asperity). Surface type I exhibits a better correlation with a cross- correlation coefficient (R2) of 0.996 compared to 0.503 for surface type II. This could be explained by shading (non-uniform illumination) and random noise problems during SEM tests [20]. The shading occurs when an object is illuminated from a source which leads to a non-
Fig. 12. AFM and SEM micro-asperity fractal dimension of samples at different pressure, No. 1 at 35 bar, No. 2 at 90 bar, and No. 3 at 135 bar. Error bars show the corresponding standard deviation.
Fig. 14. Correlation between the fractal dimensions obtained from the AFM and SEM method for macro-asperity roughness.
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uniform background image. In SEM method, the electron intensity to the detector or viewer is a function of surface orientation considering the electron source leads to the reduction of topographical contrasts. The more heterogeneous surface is the lesser topographical contrasts can be observed [20]. The random noise during SEM tests received by the image detectors caused by incident electrons and/or by the quantization devices makes the pixels brighter or darker [20]. Heterogeneity of surface type II is more than that of surface type I which is represented by brighter pixels in the produced images. Hence, the problems of random noise and shading are more apparent in this surface type. Electron intensity and random noise, however, play no role in AFM images; therefore, the fractal dimensions obtained from these images are more accurate. This accuracy makes AFM images more favorable for fractal analysis. The results of this study postulate the bi-fractal characteristic of heterogeneous surfaces. It is apparent that two fractal dimensions can represent heterogeneous surfaces more accurately. In other words, for surfaces composed of two distinct materials, bi-fractal analysis can better characterize the changes in surface microasperities (that depend on the topography of the original surface) and surface macro-asperities (that depend on the topography of the precipitated material). 5. Summary and conclusions The asperities observed on the heterogeneous surface were categorized into micro- (surface type I) and macro- (surface type II) asperities. Surface type I includes short peaks and shallow valleys, where surface type II includes tall peaks and deep valleys. These two categories were proposed according to the roughness information obtained from the AFM tests. The boundary between the two surface types was determined graphically and shows that the roughness of surface type I approaches that of the pure glass as the pressure increases. The fractal dimension of each surface type was calculated by two distinct codes prepared for AFM and SEM. Changes in fractal dimensions observed for surface types I and II based on AFM and SEM images were found to follow similar trends. A better correlation was observed between the SEM fractal dimension (DS) and AFM fractal dimension (DA) for surface type I as this surface type was less sensitive to the intensity of the light. Heterogeneous surfaces composed of two different asperities appear to be proper subjects for bi-fractal analysis as the two fractal dimensions can describe changes in the topography of each surface type with reasonable accuracy. Acknowledgments The authors would like to express their sincere gratitude to Navid Pazhuhesh Farda (NPF) Co. for their kind collaboration and help during the installation and set up of the instruments. They also greatly appreciate Mahar Fanabzar Co. for their support and help in performing AFM tests. Financial support from NIOC-RTD is also appreciated. The authors are thankful to Ehsan Nikooee from the Department of Civil Engineering, Shiraz University, for his valuable comments and help in performing fractal analyses on SEM and AFM images. Last but not least, intellectual help and constructive remarks from the members of the EOR Research Center are gratefully acknowledged. References [1] R.A. Salathiel, Oil recovery by surface film drainage in mixed wettability rocks, J. Petrol. Technol. 25 (1973) 1216–1224. [2] L. Cuiec, Evaluation of reservoir wettability and its effects on oil recovery, in: N.R. Morrow (Ed.), Interfacial Phenomena in Oil Recovery, Marcel Dekker Inc., New York City, 1991, pp. 319–375.
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