Experimental Investigation of the E ﬀ ects of Water and Polymer Flooding on Geometric and Multifractal Characteristics of Pore Structures

: During water and polymer flooding for enhanced oil recovery, pore structures may vary because of the fluid–rock interactions, which can lead to variations in petrophysical properties and affect oil field production. To investigate the effects of fluid flooding on pore structures, six samples were subjected to brine water, dual-system, and alkaline–surfactant–polymer (ASP) polymer displacement experiments. Before and after experiments, samples were scanned by X-ray CT. Thin sections, X-ray diffraction, and high pressure mercury injection tests were also carried out to characterize mineralogy and fractal dimension of pore systems before experiments. Experiment results show that water flooding with low injection pore volume ratio (IPVR) can improve reservoir quality since total porosity and connected porosity of samples rise after the flooding and the proportion of large pores also increases and heterogeneity of pore structure decreases. However, water flooding with high IPVR has reverse effects on pore structures. Polymer flooding reduces the total porosity, connected porosity, the percentage of small pores and enhances the heterogeneity of pore structures. It can be found that pore structures will change in fluid flooding and appropriate water injection can improve reservoir quality while excessive water injection may destroy the reservoir. Meanwhile, injected polymer may block throats and destroy reservoirs. The experimental results can be used as the basis for oil field development. observation and multifractal analysis of images of thin section are performed to characterize pore structures. Oil-bearing conditions of the samples are analyzed with ﬂuorescent thin sections.


Introduction
Certain physical properties of a rock, for instance, porosity and permeability, are a function of the pore system within the rock [1]. The analysis of pore structures for reservoir characterization is of great significance, since it can be used not only for evaluation of the heterogeneity of rocks and reservoir classification, but also for the prediction of rock properties and estimation of the resource potential [2]. Thus, a large number of studies have been made to characterize the pore structures of conventional and unconventional reservoirs [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. The geometric, topological, and fractal characteristics of pore systems have been analyzed using various techniques, e.g., scanning electron microscopy (SEM), mercury injection capillary pressure (MICP), nuclear magnetic resonance spectroscopy (NMR), X-ray computed tomography (X-ray CT), small-angle neutron scattering (SANS), and gas (i.e., N2 and CO2) Basin, eastern China, and is one of the four major oil-bearing depressions in the basin [35,36]. It is a long and narrow depression running southwest to northeast ( Figure 1A). Yangsanmu Field lies between the Kongdian Uplift and Qinan Sag in the depression ( Figure 1B) and has produced petroleum for about 50 years. The field is geologically located at a faulted-anticline whose long axis points runs southwest-northeast. The anticline is separated by a northeastern normal fault which is sealing ( Figure 1B). In the past 40 years, there have been four wells drilled in the area and the latest, well Y11A, was drilled in October 2018 and is at the center of the anticline ( Figure 1C). The well Y11A penetrated a braided bar sandstone reservoir, the size of which is approximately 0.5 × 1 km in area ( Figure 1D) [37].   Above basement rocks, there are Paleogene, Neogene, and Quaternary sediments in the Huanghua Depression (see Figure 2). The Paleogene is subdivided into three formations including Kongdian (Ek), Shahejie (Es), and Dongying (Ed) while the Neogene includes the Guantao (Ng) and Minghuazhen (Nm) Formations. There is a regional unconformity between Dongying (Ed) and the Guantao Formation [37]. There are three members in Ng and the target reservoir for this study is the second member (Ng2) (Figure 2). During the Ng2 stage, the climate of the Bohai Bay Basin was mid-subtropical warm and humid and the basin was structurally at a stage of slow subsidence [37,38].
Energies 2020, 13, 5288 4 of 19 second member (Ng2) (Figure 2). During the Ng2 stage, the climate of the Bohai Bay Basin was midsubtropical warm and humid and the basin was structurally at a stage of slow subsidence [37,38].

Samples
The samples used in this study are from the well Y11A which was drilled in October 2018 in Yangsanmu oil field. Fifty-six meters of continuous core in the Ng Formation (including 30 m in the Ng2 Member) was recovered from the well. Six samples from three depth sections were collected as listing in Table 1. These samples can be divided into 3 groups based on their depths and samples whose depth difference is 1-2 cm belong to the same group. Samples within the same group have the same lithofacies, petrological characteristics, and similar porosity and permeability (see Table 1). The lithofacies of samples 6-003 and 7-008 are parallel bedded sandstones, while that of sample 10-010 is massive sandstone. For the investigation of the effects of both water and polymer flooding on rock properties, six experiments are carried out.

Samples
The samples used in this study are from the well Y11A which was drilled in October 2018 in Yangsanmu oil field. Fifty-six meters of continuous core in the Ng Formation (including 30 m in the Ng2 Member) was recovered from the well. Six samples from three depth sections were collected as listing in Table 1. These samples can be divided into 3 groups based on their depths and samples whose depth difference is 1-2 cm belong to the same group. Samples within the same group have the same lithofacies, Energies 2020, 13, 5288 5 of 19 petrological characteristics, and similar porosity and permeability (see Table 1). The lithofacies of samples 6-003 and 7-008 are parallel bedded sandstones, while that of sample 10-010 is massive sandstone. For the investigation of the effects of both water and polymer flooding on rock properties, six experiments are carried out.

Water and Polymer Flooding Experiments
The multiphase flow experiments were carried out on six samples, three groups of two taken at adjacent depths, to study the influence of displacement by different fluid media on pore structures, which can improve our understanding of the advantages and disadvantages of water and polymer flooding approaches, and provide useful guidance for designing new protocols for enhanced oil recovery (EOR).
Types of the tested injection fluid including brine, polymer-surfactant dual-compound polymer/ surfactant system, and triple-compound alkali/surfactant/polymer system (abbreviated as ASP). Components of the polymer, surfactant, and alkali are partially hydrolyzed polyacrylamide (HPAM), iodate surfactant, and sodium carbonate respectively, which are commonly used in EOR in the oil field ( Table 2).
The experiment was carried out under 20 • C at test center of Energy Development Co., CNOOC. The injection pressure varied and is listed in Table 1. The schematic of the experiment process is presented in Figure 3 and the key processes in the experiments were as follows.
(1) Step 1: sample preparation and dry scan. The six water-wetting core plug samples were packed into carbon fiber holders which are transparent to X rays. After that, each of the dry samples was scanned by X ray CT for 4 h and 57 min. (2) Step 2: oil-saturated sample preparation. All the samples were vacuumed for 2 h with Castable Vacuum System (CVS). After that, all the six samples were saturated with brine of 2343 mg/L in salinity which was the same as that of the formation water in the study area. The injection velocity of brine was 0.05 mL/min and saturation took 1.5 h. Then, oil was injected at a rate of 0.02 mL/min for 1.5 h at which time the samples were completely saturated with oil. Viscosity of the simulated oil was 5 mPa·S at 20 • C. In order to recognize oil in the CT images, 7 vol% Diiodomethane (CH2I2) was added to the oil as indicator to improve the response to X-rays in the CT scan after flooding. (3) Step 3: water flooding experiments. Experiment nos.1, 2, 3 and 5, were carried out according to the experimental plan in Table 1. After the experiments, each sample was scanned by X ray CT for 4 h and 57 min. (4) Step 4: multiphase flooding and scan. Dual-system polymer/surfactant (Experiment no. 4) and ASP (Experiment no. 6) were injected to displace the oil. The injection pressures were 0.15 MPa and 0.23 MPa, respectively. The injection velocity was 0.05 mL/min. Samples were scanned by X ray CT after the experiments, as described above.
In the experiment plan, the injected volume of fluids was measured with injection pore volume ratio (abbreviated as IPVR). It is the ratio of injected fluid volume to pore volume. In the study of displacement effect, this measurement method is more reasonable.
Before and after the displacement experiment, all the samples were scanned using X ray CT twice. Three-dimension digital images of these samples were built. Based on these digital rocks, the geometric and fractal properties were analyzed. For the processing of X ray CT data, a traditional workflow was implemented including 3D reconstruction, median filtering, and binarization process, pore-network extraction, and calculation of pore-throat diameter distributions statistics and analysis [17].   Note: the core plug is a cylinder which is 3 cm in length and 2.5 cm in diameter. IPVR: injection pore volume ratio. ASP: triple-compound alkali/surfactant/polymer system

Analytical Methods
In this study, the 3D CT scan was carried out using a BRUKER Micro-CT SkyScan 1173. The main scan parameters and data reconstruction parameters are listed in Table 3. The image matrix of the scan result is 2240 × 2240 pixels. Scan resolution is 13.84 μm. The vertical interval of CT slices is 10 μm.
Porosity and permeability were measured using routine helium test methods. Size of the plunger sample was 2.5 cm in diameter and 3 cm in length. X-ray diffraction (XRD) of common minerals, clay minerals, and their relative contents were conducted using D/max-2500 X-ray diffractometer. The test condition was 25 °C and 40% of air humidity. Grain size was analyzed with laser particle sizer MS2000 manufactured by Malvern PANalytical. High-pressure mercury intrusion porosimetry (HPMI) for pore structure was performed under 20 °C using Autopore IV 9500 mercury intrusion tester. The test pore scale ranges from 0.003 to 1000 μm. Direct observation and multifractal analysis of images of thin section are performed to characterize pore structures. Oil-bearing conditions of the samples are analyzed with fluorescent thin sections.

Analytical Methods
In this study, the 3D CT scan was carried out using a BRUKER Micro-CT SkyScan 1173. The main scan parameters and data reconstruction parameters are listed in Table 3. The image matrix of the scan result is 2240 × 2240 pixels. Scan resolution is 13.84 µm. The vertical interval of CT slices is 10 µm.
Porosity and permeability were measured using routine helium test methods. Size of the plunger sample was 2.5 cm in diameter and 3 cm in length. X-ray diffraction (XRD) of common minerals, clay minerals, and their relative contents were conducted using D/max-2500 X-ray diffractometer. The test condition was 25 • C and 40% of air humidity. Grain size was analyzed with laser particle sizer MS2000 manufactured by Malvern PANalytical. High-pressure mercury intrusion porosimetry (HPMI) for pore structure was performed under 20 • C using Autopore IV 9500 mercury intrusion tester. The test pore scale ranges from 0.003 to 1000 µm. Direct observation and multifractal analysis of images of thin section are performed to characterize pore structures. Oil-bearing conditions of the samples are analyzed with fluorescent thin sections. Table 3. CT scan and data reconstruction parameters.

Fractal Analysis of HPMI Results
Fractal geometry dates from the 1970s. It is a useful tool in the description of irregularity and randomness of objects and can be used to characterize complex structures [20,27,[39][40][41]. Distribution and geometrical structures of pores in rocks have fractal characteristics [27,32,42].
The cumulative volume of pores is the integral of pore radius distribution density function to pore radius [16,43]. The cumulative volume of pores whose radius is larger than r (N r ) can be presented as follows: where r max is the maximum radius of pores in µm; f (r) is the pore radius distribution density function; a is a constant and D is the fractal dimension of the pore structure. From Equation (1) and the sphere model of pores, the cumulative volume of pores (V r− ) whose radius is smaller than r can be presented as follows: where r min is the minimum radius of pores in µm and α is a scale factor constant related to pore structure. So, the volume proportion of pores (S) whose radius is smaller than r is: where V is the total pore volume of the rock in µm. For reservoirs with complex pore structures, the maximum pore radius is far greater than the minimum pore radius. Hence, Equation (3) can be simplified to: In sandstones, the r max of rocks is commonly far greater than r min and meets the simplification condition of Formula (4) [44].
In capillary pressure analysis using the mercury intrusion method, the capillary pressure P c is inversely proportional to pore radius and the relationship is presented as: Energies 2020, 13, 5288 where P c is capillary pressure in MPa; σ is interfacial tension and θ is wetting angle. In a mercury injection test, the pressure corresponding to r max , the maximum pore throat radius, is the initial capillary pressure (P min ). From Equations (4) and (5), it can be deduced that In Formula (7), S can be calculated by injected mercury saturation and P min can be read from the mercury injection curve. The fractal dimension (D) of pore structures can be determined by linear regression analysis of the mercury injection curve.

Multifractal Analysis of CT and Thin Section Images
In the HPMI test, the result is a one-dimensional curve corresponding to the overall response of the pore structure of the sample with x-axis of mercury saturation and y-axis of displacement pressure. It can be treated as distribution of pores and throats which have different radiuses. Pore features reflected in the capillary pressure curve have one simple fractal dimension [44]. But in the X ray CT image, geometry of every pore and throat can be imaged. Heterogeneity of pore structures is more detailed, and multifractal analysis is used to describe the heterogeneity of pores [32]. Grassberger (1990) proposed the theory and an optimized box-assisted method of multi-fractal analysis [45]. Multifractal analysis has been used widely in image processing and can provide a continuous spectrum of fractal dimensions [40]. In this paper, an optimized box-assisted method is employed. According to multifractal theory, where ε is a small measure scale; N(ε) is the number of boxes in the subset; α is an index which reflects the singular degree of a small range and is related to its position in the image; f (α) is a singular spectrum and it presents density of parameter α with a continuous function. The density distribution function of α can be further weighted summed as: where X(q, ε) is the partition function of q with scale ε; q is moment order of distribution; τ(q) is mass exponent function, which is expressed as: In the description of multi-fractal with q-D q parameters, the generalized Renyi dimension D q is given by: Using the Legendre transformation, the above two descriptions of multi-fractal parameters can be correlated as [32]: Energies 2020, 13, 5288 9 of 19

Mineral and Pore Features of the Samples
As mentioned above, the six samples used in the displacement experiment were collected from three depths. It means that there were two parallel samples whose features were more or less the same at each depth. Mineral components of the three groups of samples are listed in Table 4. The samples of the three groups had very similar contents of quartz, potash feldspar, plagioclase, calcite, dolomite, and total clay minerals. The microscopic oil-bearing condition and plane porosity of the three sample groups were similar (Figure 4).
Apart from the mineral characteristics of the samples, the geometric and fractal properties of pore structures of the samples were characterized using HPMI data. There is a wide "platform" in the mercury injection curve of each sample in Figure 4. The "platform" has a wide range of mercury saturation which indicates a wide range of pore and throat size. The injection pressure of the "platform" is low and this indicates that the pore and throat size of the "platform" is large. Stated thus, the geometry of capillary pressure curves of these samples indicate distribution of pores are relatively homogeneous ( Figure 4). In addition, it can be also concluded that sample 7-008 has a more homogeneous pore distribution and larger total connected pore volume than the other two. This can be also verified quantitatively from the HPMI parameters, such as maximum mercury injection saturation of the samples (Table 5).

Mineral and Pore Features of the Samples
As mentioned above, the six samples used in the displacement experiment were collected from three depths. It means that there were two parallel samples whose features were more or less the same at each depth. Mineral components of the three groups of samples are listed in Table 4. The samples of the three groups had very similar contents of quartz, potash feldspar, plagioclase, calcite, dolomite, and total clay minerals. The microscopic oil-bearing condition and plane porosity of the three sample groups were similar (Figure 4).
Apart from the mineral characteristics of the samples, the geometric and fractal properties of pore structures of the samples were characterized using HPMI data. There is a wide "platform" in the mercury injection curve of each sample in Figure 4. The "platform" has a wide range of mercury saturation which indicates a wide range of pore and throat size. The injection pressure of the "platform" is low and this indicates that the pore and throat size of the "platform" is large. Stated thus, the geometry of capillary pressure curves of these samples indicate distribution of pores are relatively homogeneous (Figure 4). In addition, it can be also concluded that sample 7-008 has a more homogeneous pore distribution and larger total connected pore volume than the other two. This can be also verified quantitatively from the HPMI parameters, such as maximum mercury injection saturation of the samples (Table 5). Table 4. Quantitative analysis of mineral components of rock and clay with X-ray diffraction.    The relationship of displacement pressure (Pc) and water saturation (Sw) has segmented characteristics and presents as four straight lines with the different gradients in the lgPc-lgSw scatter diagram ( Figure 5). According to Formula (7), fractal geometry parameters are derived from Figure 5. The three samples have similar fractal parameters ( Table 6). From the fractal geometry parameters listed in Table 6, four characteristics can be indicated: (1) Since parameters Pc and Sw, which are derived from HPMI test, are a response to pore radius and its distribution, the heterogeneity of pore radius distribution has segmented characteristics in the study area. (2) Pores in the same radius range of the three samples have similar fractal dimension. Distribution of pores with a radius within the range of 9.704-23.68 µm, which have a lower fractal dimension, are more homogeneous than that of pores with a radius larger than 23.68 µm or smaller than 9.704 µm. (3) In Figure 5, the second part (segment 2 ) of the four segmented lines which has a high gradient has the smallest fractal dimension of HPMI curve (Table 6). It corresponds to the level part of capillary pressure curve whose mercury saturation ranges from about 10% to 60% (Figure 4). Pores in this range make up more than 45% pore volume in the samples (Figure 4 and Table 6). (4) Fractal dimension of pore radius distribution of large pores (with a radius larger than 23 µm and 17.75 µm for sample 10-010) and small pores (with a radius smaller than about 0.021 µm) is very high and larger than 2.9. It means pore radius distribution of large pores and small pores mentioned above are very heterogeneous (Table 6).
Energies 2020, 13, 5288 10 of 19 The relationship of displacement pressure (Pc) and water saturation (Sw) has segmented characteristics and presents as four straight lines with the different gradients in the lgPc-lgSw scatter diagram ( Figure 5). According to Formula (7), fractal geometry parameters are derived from Figure  5. The three samples have similar fractal parameters ( Table 6). From the fractal geometry parameters listed in Table 6, four characteristics can be indicated: (1) Since parameters Pc and Sw, which are derived from HPMI test, are a response to pore radius and its distribution, the heterogeneity of pore radius distribution has segmented characteristics in the study area. (2) Pores in the same radius range of the three samples have similar fractal dimension. Distribution of pores with a radius within the range of 9.704-23.68 μm, which have a lower fractal dimension, are more homogeneous than that of pores with a radius larger than 23.68 μm or smaller than 9.704 μm. (3) In Figure 5, the second part (segment ②) of the four segmented lines which has a high gradient has the smallest fractal dimension of HPMI curve (Table 6). It corresponds to the level part of capillary pressure curve whose mercury saturation ranges from about 10% to 60% (Figure 4). Pores in this range make up more than 45% pore volume in the samples (Figure 4 and Table 6). (4) Fractal dimension of pore radius distribution of large pores (with a radius larger than 23 μm and 17.75 μm for sample 10-010) and small pores (with a radius smaller than about 0.021 μm) is very high and larger than 2.9. It means pore radius distribution of large pores and small pores mentioned above are very heterogeneous (Table 6).

Geometric Characteristics
After water flooding at low water IPVR, the quality of relative good reservoirs, that have high porosity and relatively homogeneous pore radius distribution, can be further improved. For example, samples 6-003 and 7-008 have high porosity (>29%) and relatively homogeneous pore radius distribution as discussed in Section 4.1 of this paper. After 1.25 PV water flooding (Experiment no.2), porosity of sample 6-003G increased from 29.2% to 32.5%. Connected pores (connected porosity), as measured by 3D CT model, increased from 29.1% to 32.4% (Table 7) and the relative proportion of large pores whose radius was greater than 124.58 µm increased ( Figure 6B). It means pore connectivity becomes better. The range of ∆α, which is defined as the difference between the maximum and minimum value of α, decreased from 0.7574 to 0.7528 ( Figure 7E). Since heterogeneity decrease with the range of ∆α [32], the above decreasing of ∆α range indicates the heterogeneity of reservoir pore structure is weakened. Similar changes happened for the sample 7-008F ( Figure 8E, Table 7).
Water flooding at high water IPVR decreases both connected porosity and total porosity of reservoirs. In Experiment no.1, with sample 6-003F, connected porosity and total porosity decrease by 3.1% and 3.0%, respectively ( Table 7). Statistics of pore radius distribution in Figure 6A show the increase in small pores and decrease in large pores with a pore diameter threshold of 96.89 µm. The increase in ∆α from 0.7661 to 0.8714 indicates that distribution of pore radius becomes more heterogeneous after 50 PV flooding ( Figure 7F). Water flooding of at high water IPVR may decrease the pore connectivity ( Figure 8C,D). Comparing results of Experiment nos.1 and 2, it can be concluded that volume of injected water controls the influence of water flooding on pore structures. It is inferred that at the early stage of water flooding, matrix and small grains began to move and some of the fine-grained components were washed away. Large pores which are main channel of flooding water can expand and the average pore radius increase. Meanwhile, pore structures become more homogeneous than that before water flooding. As more and more water was injected into the pores, water injection pore volume ratios increased and the average radius of movable grains in flooding also increased. This means larger grains move with flooding water in the pore network. The possibility that small pores and throats are blocked by these moving particles will increase greatly. The connectivity of pores will decrease and pore radius distribution will become more heterogeneous.
Polymer-surfactant dual-compound system and the triple compound ASP system are commonly used displacement fluids in EOR. The influence of the two systems on pore structures was tested and the results were compared with that of water. Controlled Experiments nos.3 and 4 used water and the polymer-surfactant dual-compound system (abbreviated to dual-system). The dual-system caused the total porosity of sample 7-008G to decrease from 28.6% to 22.0% and connected porosity to decrease from 28.5% to 21.7%. Pore connectivity became poor and the relative proportion of isolated porosity increased to 3× the original ( Table 7). The proportion of small pores whose diameters were under 96.89 µm increased while that of large pores decreased ( Figure 6D).  Water flooding at high water IPVR decreases both connected porosity and total porosity of reservoirs. In Experiment no.1, with sample 6-003F, connected porosity and total porosity decrease by 3.1% and 3.0%, respectively ( Table 7). Statistics of pore radius distribution in Figure 6A show the increase in small pores and decrease in large pores with a pore diameter threshold of 96.89 μm. The increase in Δα from 0.7661 to 0.8714 indicates that distribution of pore radius becomes more heterogeneous after 50 PV flooding ( Figure 7F). Water flooding of at high water IPVR may decrease the pore connectivity ( Figure 8C,D). Comparing results of Experiment nos.1 and 2, it can be concluded that volume of injected water controls the influence of water flooding on pore structures.    Tables 1 and 2.  In the controlled Experiment no.6, ASP injection caused total porosity to decrease significantly from 20.9% to 13.4%, and connected porosity decreased from 20.3% to 11.5%. The relative proportion of isolated porosity increased from 3.0% to 14.3% (Table 7). The proportion of pores with a diameter larger than 96.89 µm decreased while the proportion of small pores with a diameter under 69.21 µm increased ( Figure 6F). In the multifractal analysis of the CT image, ∆α increased from 0.7233 to 0.7615 and indicated that the distribution of pore radius became more heterogeneous after the ASP flooding ( Figure 9F).
Overall, chemical flooding decreased porosity and increased the heterogeneity of pore structures. In Figure 10A, the distribution of retained polymer in the space can be visualized in the digital core model. Some narrow "neck" connecting adjacent pores is blocked such as (a) in Figure 10C. Large pores can be partially filled and divided into small pores just like (b) in Figure 10B,C. Small pores around the large pore are wholly or partially filled as (c-e) in Figure 10B,C. It can be concluded that the mechanism of chemical flooding's influence on pore structures is the blocking and filling of the residual polymer. Considering the above mechanism, choosing polymers that have suitable molecular size and structure is very important in EOR.
Polymer-surfactant dual-compound system and the triple compound ASP system are commonly used displacement fluids in EOR. The influence of the two systems on pore structures was tested and the results were compared with that of water. Controlled Experiments nos.3 and 4 used water and the polymer-surfactant dual-compound system (abbreviated to dual-system). The dualsystem caused the total porosity of sample 7-008G to decrease from 28.6% to 22.0% and connected porosity to decrease from 28.5% to 21.7%. Pore connectivity became poor and the relative proportion of isolated porosity increased to 3× the original ( Table 7). The proportion of small pores whose diameters were under 96.89 μm increased while that of large pores decreased ( Figure 6D).
In the controlled Experiment no.6, ASP injection caused total porosity to decrease significantly from 20.9% to 13.4%, and connected porosity decreased from 20.3% to 11.5%. The relative proportion of isolated porosity increased from 3.0% to 14.3% (Table 7). The proportion of pores with a diameter larger than 96.89 μm decreased while the proportion of small pores with a diameter under 69.21 μm increased ( Figure 6F). In the multifractal analysis of the CT image, Δα increased from 0.7233 to 0.7615 and indicated that the distribution of pore radius became more heterogeneous after the ASP flooding ( Figure 9F).
Overall, chemical flooding decreased porosity and increased the heterogeneity of pore structures. In Figure 10A, the distribution of retained polymer in the space can be visualized in the digital core model. Some narrow "neck" connecting adjacent pores is blocked such as (a) in Figure  10C. Large pores can be partially filled and divided into small pores just like (b) in Figure 10B,C. Small pores around the large pore are wholly or partially filled as (c-e) in Figure 10B,C. It can be concluded that the mechanism of chemical flooding's influence on pore structures is the blocking and filling of the residual polymer. Considering the above mechanism, choosing polymers that have suitable molecular size and structure is very important in EOR.

Multifractal Parameters before and after Multiphase Flooding
Multifractal analysis is used in 2D image analysis of both thin sections and CT images to describe microscopic heterogeneity of pores before and after multiphase flooding. The "heterogeneity of pores" we discussed with analysis of 2D pictures here is mainly the geometrical heterogeneity of pores and statistical heterogeneity of pore radius distribution.

Multifractal Parameters before and after Multiphase Flooding
Multifractal analysis is used in 2D image analysis of both thin sections and CT images to describe microscopic heterogeneity of pores before and after multiphase flooding. The "heterogeneity of pores" we discussed with analysis of 2D pictures here is mainly the geometrical heterogeneity of pores and statistical heterogeneity of pore radius distribution.
Firstly, multifractal analysis of the 2D thin section image was made to describe the geometrical heterogeneity of pores before flooding. The f(α)-α crossplots and multifractal parameters in Figure 11 indicate the difference in pore structure heterogeneity of the reservoir sands. In f(α)-α crossplot, the geometry of f(α)-α curves of the samples 10-010 and 6-003 are similar while that of sample 7-008 is obviously different (Figure 11). Quantitatively, the width and height of the curves are different. The width of α (range of αmax−αmin) and maximum f(α) of the samples all decrease in the order of samples 10-010, 6-003, and 7-008 ( Figure 11). Firstly, multifractal analysis of the 2D thin section image was made to describe the geometrical heterogeneity of pores before flooding. The f (α)-α crossplots and multifractal parameters in Figure 11 indicate the difference in pore structure heterogeneity of the reservoir sands. In f (α)-α crossplot, the geometry of f (α)-α curves of the samples 10-010 and 6-003 are similar while that of sample 7-008 is obviously different (Figure 11). Quantitatively, the width and height of the curves are different. The width of α (range of α max− α min ) and maximum f (α) of the samples all decrease in the order of samples 10-010, 6-003, and 7-008 ( Figure 11).

Multifractal Parameters before and after Multiphase Flooding
Multifractal analysis is used in 2D image analysis of both thin sections and CT images to describe microscopic heterogeneity of pores before and after multiphase flooding. The "heterogeneity of pores" we discussed with analysis of 2D pictures here is mainly the geometrical heterogeneity of pores and statistical heterogeneity of pore radius distribution.
Firstly, multifractal analysis of the 2D thin section image was made to describe the geometrical heterogeneity of pores before flooding. The f(α)-α crossplots and multifractal parameters in Figure 11 indicate the difference in pore structure heterogeneity of the reservoir sands. In f(α)-α crossplot, the geometry of f(α)-α curves of the samples 10-010 and 6-003 are similar while that of sample 7-008 is obviously different (Figure 11). Quantitatively, the width and height of the curves are different. The width of α (range of αmax−αmin) and maximum f(α) of the samples all decrease in the order of samples 10-010, 6-003, and 7-008 ( Figure 11). Furthermore, multifractal analysis was made on the CT images of the samples before and after displacement experiments based on the multifractal theory in Section 3.4.2. According to the ranges of ∆α in Figure 11, heterogeneity of pore structures increase in the order of sample 7-008, 6-003 and 10-010. At the pore scale, multifractal features of CT images indicate heterogeneity of pore structures. The multifractal characteristics of six samples are demonstrated in Figures 7-9. According to the data and curves from Figure 7 to Figure 9, average ∆α of the three sample groups before displacement experiments are 0.76175, 0.6838, and 0.8011, respectively, in the order of sample 6-003, 7-008 and 10-010. So the pore structure of sample 7-008 is the most homogeneous while that of 10-010 is the most heterogeneous. From either fractal or multifractal features mentioned above, it can be observed that the original pore structure heterogeneity of the samples on a multi-scale increase in the sequence of 7-008, 6-003, and 10-010.
Multifractal parameters change after the displacement experiments. For Experiment no.2 with 1.25 PV water injection, although the geometry of curves and the maximum f (α) before and after the experiments are similar, the ∆α decreases slightly after water flooding ( Figure 7E). In Figure 7F, it can be observed the two curves coincide when α is in the range 1.80-2.30, and the curve before displacement is enclosed by that after displacement. It is obvious that ∆α increases after the experiment. The geometry of curves in the Figure 7F, Figure 8E,F and Figure 9F are similar such that the f (α)-α curves of samples after displacement are gentler and wider.

Conclusions
This study presents an experimental investigation of the effects of water flooding and polymer flooding on the characteristics of pore systems including the distribution of pore radius and geometrical features of pores based on six high-porosity rocks. Firstly, the lithofacies and mineral components were described based on the drilling core observation and X-ray diffraction, which provides the basic geological information for the samples. Subsequently, the fractal dimension of pore structures of these samples was analyzed using the HMPI data, revealing the heterogeneity of the pore systems. Finally, the multifractal and geometric characteristics of pore structures of samples before and after the water and polymer flooding were calculated and compared to CT images. The findings of the study are as follows.
(1) Although fractal analysis of HPMI, multifractal analysis of thin sections, and CT images are different in scale and information types, their results of heterogeneity analysis of pore structures are the same. (2) Water flooding changes petrophysics (e.g., porosity) and the distribution of the pore radius of reservoirs. For reservoirs with high porosity, water flooding of low water IPVR can improve reservoir quality slightly. Both total porosity and connected porosity increase somewhat after the flooding. The proportion of large pores increases and heterogeneity of pore radius distribution decreases. However, the water flooding of high water IPVR worsens the pore size and rock properties. The mechanism of the above phenomena in the study area is the change of matrix/grain moving during flooding. (3) On the other hand, polymer flooding has an adverse effect on the improvement of reservoir quality. First, total porosity and connected porosity decrease after the polymer flooding. Moreover, the relative proportion of small pores rises, and distribution of pore radius of reservoirs become more heterogeneous.