Quantitative Study of Residual Oil Distribution during Water Flooding through Digital Core Analysis

School of Mechanical and Electrical Engineering, Xi’an University of Architecture and Technology, Xi’an 710000, China Engineering Research Center of Development and Management for Low to Ultra-Low Permeability Oil & Gas Reservoirs in West China, Ministry of Education, Xi’an Shiyou University, Xi’an 710000, China Research Institute of Petroleum Exploration and Development, PetroChina Changqing Oilfield Company, Xi’an 710018, China Drilling and Production Technology Research Institute, CNPC Chuanqing Drilling Engineering Company Limited, Xi’an 710021, China


Introduction
Crude oil is one of the most important energy sources. Nowadays, more and more advanced and low-cost development technologies are needed to enhance reservoir recovery [1]. Water flooding and other enhanced oil recovery techniques are based on the common methodology aimed at increasing oil production; however, it is usually with high cost [2,3]. Therefore, petroleum engineering methods and numerical simulation are needed to understand oil mobility and distribution characteristics, which are also needed to simulate reservoir history and predict future performance [4,5]. It would make the development process more rational. However, due to reservoir characteristics, both the pore structure and oil distribution are complicated. Besides, the conventional microscope observation method is not enough to analyze the real core, so that other techniques, like X-ray computed tomography, are needed for quantitative and detailed description on the microscale. In 1991, X-ray computed tomography (X-CT) technology was introduced for porous media analysis. It can provide lossless images at micrometer or even nanometer scale, which makes microscale analysis possible and has become one of the effective means in oil reservoir studies [6][7][8][9][10].
In recent years, researchers have performed X-CT scans on real cores to obtain images and reconstruct the pore structure to analyze reservoir characteristics [11][12][13][14], seepage simulation, and enhanced oil recovery [15,16]. Combining with the image processing method, X-CT scanning technology also extracts the distribution of different fluids in a core, so as to study pore structure and fluid motion [17][18][19]. Using this technique, some researchers have further studied the pattern and quantity of liquid clustering in real core samples [20]. For reservoir studies, some researchers have observed the distribution of remaining oil in different flow states (including oil-water system and immiscible CO 2 brine system) [21][22][23][24]. With in situ displacement, An et al. have found volume of residual oil can also be quantitatively calculated and classified with shape factor [25]. In addition, other researchers have found different patterns of residual water and their effect on permeability through digital core analysis [26].
However, there are few researches that focus on the relationship between oil distribution and pore size in the process of displacement based on digital core analysis. In this paper, we studied the relationship between oil distribution and pore radius during the process of water flooding by using in situ displacement scanning technique for tight sandstone. We take the Chang 7 tight sandstone reservoir in Ordos Basin as the research object and use in situ displacement scanning technology to deeply analyze dynamic change characteristics of oil in different pore sizes during water flooding.

Experiment
The research object is from Chang 7 reservoir in Huaqing oilfield, Ordos Basin, China, with a length of 5 mm and a diameter of 3 mm. The device comprises a low-rate fluid injection system and in situ displacement system equipped with X-CT scanning system (510 VERSA, made by Carl Zeiss Optics Co. Ltd.). We set the resolution of the scanning equipment at 3.32 μm per pixel, and the 3D reconstruction volume comprised 1004 × 1004 × 1005 pixels. Confining pressure was configured at 2.0 MPa, displacement pressure was constant at 0.02 MPa, and the room temperature was 25°C. The 10% potassium iodide solution was used as saturated fluid to improve the imaging ability of water. The experimental steps are as follows: (1) Clean oil and salt from the core with distilled water, then conduct porosity and permeability tests (2) Scan the core in dry situation for 14 hours (3) Saturate the core with potassium iodide solution to get a saturated water situation and scan for 14 hours (4) Saturate the core with oil to get a saturated oil situation and scan for 14 hours (5) Saturate the core with potassium iodide solution to get a residual oil situation and scan for 14 hours (6) Extract and process data acquired from X-CT scanning results

Digital Core Results and Analysis
3.1. Scanning Results. Scanning slices of the core in the water flooding procedure are shown in Figure 1. According to Xray attenuation when penetrating different materials, the dark gray range below the low threshold indicates pores and oil, and the light gray range above the high threshold indicates water. In Figure 1(b), bound water fills in small pores of the core, while existing in the corners or similar membranes in large-scale pores. In Figure 1(c), after water flooding, bound water fills most of pores, and large-size pores are filled with oil and water. From these scanning slices, the pore and water phase can be extracted by image processing. Before image segmentation, nonlocal mean algorithm was used to filter noise [27,28]. Then, a watershed algorithm was employed to segment the rock matrix, water phase, and gas phase based on different thresholds. By logical operation, we reconstructed the oil and water volume from the pore structure in a dry situation and the water phase in a saturated situation, as shown in Figure 2. Compared with saturated oil, the water content in the core of the residual oil state extremely increased, but residual oil also exists.
A local core, with a central position of (356, 125, 228) and a size of 420 * 270 * 154 μm, is extracted as shown in Figure 3. We can observe more detail about the oil-water distribution changing during water flooding.
In Figure 3(a), the local core contains large-size and small-size pores with narrow throats. After water flooding in Figure 3(e), there is a large amount of residual oil in the large pores, while the small pores are filled with water. The reason is that the internal pore throat is narrow due to heterogeneity. That results in oil flow truncation and the residual oil enrichment in macropores. At the same time, a fingering phenomenon also occurs and makes it difficult for the oil to flow in the macropore, so that only part of the oil in the outermost layer of the oil phase is driven away. Figure 4 shows the composition of porosity, oil saturation, and water saturation extracted from the digital core, which are consistent with the experimental measurements. In the saturated oil situation, oil saturation is lower than water saturation, mainly because there are narrow throats and part of the pore space cannot be filled by oil during saturation of the core with oil. However, after water flooding, oil saturation substantially reduces. Oil displacement efficiency is 66.28%, indicating that the oil displacement is efficient. Combined with Figure 3, the reason is that oil in small-size pores of the core is driven out efficiently.

Displacement Evaluation Based on Curve Similarity
With the digital core, we use curve similarity to calculate difference of the distribution between the pore and every stage during water flooding and describe the dynamic distribution character. Figure 5 describes the probability accumulation distribution of the radius for the porosity and oil phase in different states. These three curves have the same trend, but their difference reflected in the influence on oil distribution is caused by the pore structure.

Evaluation Model.
Similarity is a research hotspot in the data mining field. By measuring the similarity degree and analyzing the association between the objects, it provides guidance for research in different fields [29,30]. In this paper, the displacement evaluation system based on similarity is established which 2 Geofluids includes three indicator-overall trend, translation, and retractility, as shown in Figure 6. Firstly, the radius of the porosity and oil phase in the saturated oil situation and residual situation is extracted. Secondly, frequency cumulative distribution curve of parameters is constructed after parameter normalization. Finally, the curve similarity is analyzed with three indicators based on evaluation results of displacement. The overall trend should be combined with saturation to analyze displacement efficiency and oil movement features in pores. The retractility  3 Geofluids describes the relation between different pore radii and oil changing rates. The translation reflects relative distribution of residual oil in pore space.

Evaluation Index
The heterogeneity leads to diversity of the pore structure in the core. Therefore, only by standardizing parameters can the evaluation index have generalization ability. The normalization equation can be expressed as follows: where x i is data to be normalized and i ∈ ð1, nÞ, n is number of samples, y i is the normalized data, X min and X max are the actual radius range, and max 1<j≤n fy j g and min 1<j≤n fy j g are the data range after normalization. In the water flooding procedure, the radius range of the oil phase changes under different states, so the porosity parameter in the dry situation is taken as the standard reference. In this study, the pore radius range of the core in a dry situation is 3.38 μm-810 μm. Hence, X min and X max are set to 3.38 μm and 810 μm, min 1<j≤n fy j g is set to 1, and max 1<j≤n fy j g is set to 1000.

Overall
Trend. Since cumulative distributions are similar in different core situations, the overall trend is calculated by absolute value difference between the evaluated curve and the reference curve. Ideally, pores in the core should be filled with oil and the oil should be completely displaced. Therefore, the reference curve in this paper is the distribution curves of the core in the dry situation. The overall trend is defined as follows: where i is the sampling point of the pore radius, n is the total number of sampling points, y S i is the value of the cumulative distribution corresponding to the i sampling point in the reference curve, y D i is the value of the cumulative distribution corresponding to the i sampling point in the evaluated curve, and y ir is the aperture coordinate.

Retractility.
The coordinate of the pore radius is divided into sections, and the maximum difference is used to describe the horizontal retractility for every section with the help of the deviation standardization idea. It is defined via the following equation: where y S j max and y S j min are the max value and min value in  4 Geofluids section j of the reference curve, y D j max and y D j min are the max value and min value in section j of the evaluated curve, and k is number of sections. We add 0.01 to the denominator to prevent the denominator from being 0.
During flooding, when movable oil in the pore moves, the radius of the oil space changes, following the corresponding statistical distribution curve change, which reflects retractility. The greater the absolute value of retractility, the more the variation of the movable oil in the space range.
We also need to set an appropriate step size to accurately reflect the relationship between the pore radius and movable oil. If the step size is too large, it is impossible to obtain accurate calculation results; if the step size is too small, the results cannot be calculated. In this paper, the step size is 10 μm.

Translation Measurement.
There are two aspects to translation, the horizontal and vertical differences. Since the longitudinal range of the curve is constant between 0% and 100%, horizontal differences are mainly evaluated.
The formula is shown in Equation (4), where m is the sampling number of the pore radius in the sublevel interval, N is the number of segments, y D max ji is the ith big radius in the j section for the curve to be evaluated, and y S max ji is the i th big radius in the j section for reference curve. In this paper, 10% is taken as the step size and then N = 10.

Water Flooding Analysis
Based on Similarity. The calculation results of the overall trend, retractility, and translation based on curve similarity are shown in Figure 7. The dry situation porosity is the reference curve in "dry samplesaturated oil" and "dry sample-residual oil." In Figure 7(a), the overall trend difference of the oil phase between the dry situation and the saturated oil is valued at 33, showing that oil in the saturated oil state accounts for more in the macrospore space. Combined with Figure 5, it again indicates that the pore space is not filled by oil due to the pore end or narrow throat when that is  In Figure 7(b), the minimum retractility value is obtained within the aperture range of 60 μm-70 μm (actual core aperture is 51 μm-59 μm). According to the inverse process of Equation (1), it indicates that the oil moved greatly with the pore radius in this range during water flooding, while, in those pores with a radius greater than 210 μm (real size is 172 μm) or less than 10 μm (real size is 10.64 μm), the retractility result tends to be 0, showing that little oil changed in those areas. It also reflects that oil in pores with a large size in our study sample is not easy to move, and pores with a small size cannot be filled.
In Figure 7(c), compared with the dry sample, saturated oil gets a translation degree at -17.55 and curve has shifted to the right corresponding to the oil moving in large pores. The displacement degree of the residual oil is -12.55, absolutely less than 17.55, also indicating oil moving in large pores.
The conclusions of these three indexes are consistent and quantitatively show microscopic movement of oil in pores during water flooding.

Conclusion
In this paper, we take the tight sandstone in Ordos Basin as the research object, use in situ displacement scanning technology to conduct a water flooding experiment and employ image processing to extract digital cores. Then, a water flooding evaluation model is established by curve similarity analysis.
(1) We extract the digital core based on an in situ displacement scan and observe the dynamic distribution of oil during water flooding. And then, we calculate the oil saturation, water saturation, and probability cumulative distribution of the core aperture (2) Based on the curve similarity, the displacement evaluation model is established: the displacement efficiency is analyzed by the overall trend, the relation between the oil momentum and the pore diameter is described by the retractility degree, and the distribution characteristic of oil is reflected by the translation degree. At the same time, the normalization method is given to improve the generalization (3) According to the calculated results, we describe the difference of fluid distribution in the pore space of the core under different states during displacement. This model further explains the dynamic change rule of oil occurring in the process of displacement, provides a quantifiable comparative analysis for reservoir study in the same area, and gives theoretical guidance for reservoir development by water driving

Data Availability
The experimental data belongs to the laboratory, Engineering Research Center of Development and Management for Low to Ultra-Low Permeability Oil & Gas Reservoirs in West China, Ministry of Education, Xi'an Shiyou University. The readers can obtain the data if permitted.

Conflicts of Interest
The authors declare that no conflicts of interest exit regarding the submission of this paper.   Geofluids