# A Laboratory Approach Considering Salinity to Investigate Archie’s Parameters in Deep Shale: A Case Study in Longmaxi Formation, Southern Sichuan

Authors: Yanran Li; Xiangui Liu; Changhong Cai; Zhiming Hu; Bo Wu; Ying Mu; Xianggang Duan; Qingxiu Zhang; Shuti Zeng; Jingshu Guo; Zhijin Pu
Journal: Geofluids
 (2022)

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## Abstract

Archie’s parameters are substantial to be investigated in the evaluation of water saturation. Many researchers adhered to the opinion that Archie’s equation can still be applied to water saturation calculation in shale if the accuracy of relative parameters could be improved. External conditions, such as temperature, confining pressure, water salinity, wettability, and displacement, may influence the determination of Archie’s parameters. The aim of the study is to investigate the effect of salinity on Archie’s parameters and their correlation with mineral composition and pore structure. The mineral contents and petrophysical properties were firstly acquired through X-ray diffraction (XRD) and basic measurements. Rock-electric experiments under different salinity were conducted on deep shale samples taken from Longmaxi (LMX) Formation in Luzhou (LZ). The results indicate that Archie’s parameters of “a,” “b,” “m,” and “n” under actual brine salinity are assigned to 1.47, 1, 1.26, and 1.6, respectively. Our cementation factor is lower than that in other studies including (shaly) sandstones, carbonates, and shales, probably due to the extremely low porosity in study area. Salinity has a positive effect on cementation factor (m) and saturation exponent (n), suggesting the traditional assignment to Archie’s parameters is inappropriate. It was concluded that the complicated pore structure and high porosity mainly associated with clay mineral may trigger the increased cementation factor. Further mathematical derivations confirmed that the rock resistivity is inextricable from pore system and establish a physical model. The paper provides a solid evidence base for further understanding and evaluation of water saturation in unconventional shale reservoirs, more significantly, innovatively unveils the research into Archie formula in deep shale reservoirs of southern Sichuan basin.


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## Body

## 1. Introduction

Since Archie proposed his representative equation in 1942, the barrier between fluid saturation calculation and resistivity logging data has been broken, sparking a scientific sensation throughout the entire energy industry [1–4]. Despite several alternative models, Archie formula is still popular for determining water saturation in shale [5–7]. These researchers were convinced that Archie’s model was superior to other approaches if the accuracy of relative parameters could be improved. In conventional practice, the Archie parameters (a,b,m,n) were acquired under ambient conditions. Nevertheless, there are signs from recent studies that “m” and “n” may vary due to external conditions. For instance, under different confining pressure, the rock pore structure and fracture aperture are bound to alter, leading to the redistribution of pore fluid and variation of Archie’s parameters. Meanwhile, recently, the deep shale reservoirs at depths of 3500-4500 m possess splendid hydrocarbon generation potential, allowing them to gradually become a vital developing field for further exploration [8–10]. Therefore, the accuracy of Archie parameters considering external conditions in deep shale should be systematically investigated [11].The laboratory conditions (temperature, confining pressure, mineralization, wettability, and displacement) in rock-electric experiments have a substantial influence on Archie’s parameters [12]. Richening literatures with many trails are browsed to improve the understanding of external factors affecting Archie parameters. Some researchers believed that “m” and “n” in Archie’s formula were not only related to pore structure and lithology of formation but also dominated by confining pressure, temperature, and brine salinity [13, 14]. They observed “m” and “n” values in sandstones ascended with the increase of temperature and confining pressure whereas they had a negative correlation with salinity. Chen et al. studied the impact of confining pressure on resistivity in carbonate rocks and revealed the results can be divided into two stages with the increase of water content [15]. Based on high temperature and pressure, Huang et al. applied Simandoux model with varied “m” values to effectively calculate the fluid content in complex reservoirs of low permeability [16]. By conducting resistivity experiments under normal and overburden pressure, Jiang argued that the effect of pressure on “a” and “m” is not as significant as “b” and “n” [17]. Zou stated that “n” corresponded to a lower value when the temperature elevated and pressure declined, but “b” varied slightly [18]. Zhao et al. proposed a positive correlation between salinity and “m” and “n” in sandstone and gravel [19]. Kazak et al. supported variable salinities rendered Archie saturation calculations questionable [20]. Despite considerable research being devoted to the evaluation of water saturation, little if any empirical work has been done to consider the influence of external conditions on Archie’s parameters. The existing cases for parameter study are being encountered for a variety of rocks, such as clean sandstones, shaly sandstones, tight stone, and carbonates, but none for deep shale. Moreover, the previous literatures mainly focused on the qualitative analysis rather than quantitative analysis. Hence, the research on Archie’s parameters by considering external conditions will innovatively improve the calculating accuracy of water and hydrocarbon saturation in deep shale.The aim of this study is to investigate the effect of salinity on Archie parameters and the correlation thereof with rock minerals and pore system in deep shale, expecting to assist in the evaluation of water content in deep shale. Furthermore, the relationship among water saturation, resistivity, and pore system was induced by integrating the Archie and empirical models.


## 2. Archie’s Equation

Archie’s equation is an inevitable equation in the field of petrophysics when the term of water is involved. From empirical observations, Archie mentioned that the ratio of the resistivity of a completely brine-saturated rock (R0) to the contained formation water resistivity (Rw) referred to a proportionality constant [1]. This constant, known as formation factor (F), was expressed in terms of porosity (φ) as follows:
(1)F=R0Rw=1ϕm.This was the initial presentation of resistivity-porosity correlation for clean sandstones. Then, it was developed by numbers of researchers. Humble Oil Company and Winsauer analyzed 30 samples (28 sandstones, 1 unconsolidated sandstone, and 1 limestone) and observed that the most appropriate regression fit forF vs. φ plot may intersect the abscissa at the spot unequal to 1 [21]. Carothers obtained another generalized equation from 793 sandstone sample points [22]. Shell Oil Company applied the initial form to unfractured carbonate rocks with low porosity (9%), but “m” was treated as a variable value. The corresponding equations are displayed below:
(2)F=0.62ϕ2.15Humbleoilcompanyformula;Winsaueretal.,1952,F=1.45ϕ1.54Carothers,1968,F=1ϕm,m=1.87+0.019ϕShellOilCompany.Thus, it is recommended to generalize the numerator from 1 to the term “a,” so that a more general form can be employed in other rock formations:
(3)F=R0Rw=aϕm.For the electrical study of partially saturated rocks, Archie mainly adopted the data derived from already published experiments, such as Wyckoff, Leveret, Kogan, and Jakosky experiments [23]. After plotting these experimental data in double logarithmic coordinate, it was found that the resistivity ratio of partially saturated rock (Rt) to completely saturated rock (R0) was a constant called resistivity factor, I. Additionally, the resistivity factor had a correlation with water saturation (Sw), and their modern equation can be expressed as:
(4)I=RtR0=bSwn.Integrating these equations above led to what is now known as the Archie equation:(5)Sw=abRwRtϕmn.When estimating accurate water saturation from resistivity logs, the first obstacle confronted was the determination of suitable Archie’s parameters (a, m, and n). Opinion about these exponents of Archie’s law has been sharply divided by the physical significance (Table 1) or the lack thereof. For those who ascribed a physical meaning to the term “a,” it was often known as the “tortuosity index” describing the geometrical characterization of porous rocks [21]. Wyllie observed the formation factors in two formations with the same porosity and salinity were not identical, which may be attributed to the varied pore geometries and rock textures [24]. Adisoemarta et al. proposed that “a” depended on the tortuosity of current flow path with a value constrained to 1.0~1.4 [25]. Kamel and Mabrouk assigned the value of 0.6 for unconsolidated sandstones, 0.8 for consolidated sandstones, and 1 for carbonates [26]. Moreover, the tortuosity was defined as the ratio of the practical path length (La) to the linear length of porous medium (L) [27]:
(6)a=LaL.Table 1
The petrophysical meaning of Archie parameters.
Archie parameterpetrophysical meaningaTortuosity indexDescribe the geometrical characterization of current flow pathmCementation factor or porosity exponentModel 1: pore space is composed of capillary tubes with identical cross-sectional areaIndicate pore channel tortuosityModel 2: pore space is subdivided into conductive channels and nonconductive trapsA relative partition between conductive and nonconductive partsModel 3: a more realistic system of pore bodies connected by pore throatsAn effective area ratio of pore-throat to pore-body in logarithmsm expresses the degree of pore connectivity and consolidationnSaturation exponentn was linked to many factors such as wettability, lithology, fluid properties, and pore structureOn the contrary, some researchers regarded “a” as a weak-fitting exponent with no physical significance. Doveton reported that when the cementation factor was constrained to a fixed value in heterogeneous sandstones, “a” was merely viewed as a slippage element to compensate the variation in “m” [28]. Maute et al. (1992) set “a” to unity in addition to other fixed values in equations forementioned [29]. Ransom insisted that this factor had no defined purpose, and it was not sensible to fix “a” with a constant. Exponent “b” is rarely discussed with a possible meaning related to rock wettability [30].Compared with “a” and “b,” “m” and “n” are more critical parameters that have aroused extensive interest. In an early model, the pore space was composed of a bundle of capillary tubes with identical cross-sectional area. The resistivity was controlled by tube length and the cementation factor indicating pore channel tortuosity. Afterwards, Perez-Rosales proposed a model subdividing the pore space into conductive channels and nonconductive traps, where “m” became a measure of the relative partition between them [31]. Later, Etris et al. introduced a more realistic system of pore bodies connected by pore throats [32]. Ehrlich et al. expanded this model and believed that “m” was an effective area ratio of pore-throat to pore-body in logarithms [33]. Thus, “m” was conferred an informal name as “cementation factor” or “porosity exponent,” which expressed the degree of pore connectivity (shape, shape distribution, and orientation) and consolidation [34, 35]. In respect of “n,” named as saturation exponent, it is derived from the discharging process of water in rocks. An extensive experiment and theoretical analysis showed that “n” was linked to many factors such as wettability, lithology, fluid properties, and pore structure [18]. Knackstedt et al. stated that the saturation exponent for oil-wet samples was significantly higher than water-wet rocks (n>5) [36]. Abdassah et al. held the same opinion and reported that the saturation exponent was lowest to 1.8 for strongly water-wet rocks and highest to 5.3 for strongly oil-wet rocks [37]. Montaron observed that the I-Sw curve behaved nonlinearly in various bending degrees at low water saturation [38].


## 3. Materials and Methods

### 3.1. Geological Context

Luzhou block, situated in the low-steep structural belt of Southern Sichuan, is one of the principal targets for shale gas exploration and development in the Sichuan Basin. It is surrounded by Qiyueshan fault belt on the east and Huayingshan fault belt on the west. Geologically, the folding structures, generally distributed in the shape of straight line or arc belt, are developed in LZ block, which are mainly concentrated from center to southern part along with some in northern part. The syncline zone is gentle and wide, but the two wings of the anticline zone are steep with a low angle. Overall, the study area is dominated by reverse faults accompanied by strata uplift locally [39] (Figure 1).Figure 1
The geological location of Luzhou area in Southern Sichuan Basin (modified from Pan et al. [42]).It is demonstrated that the LZ block in Southern Sichuan has gradually developed after a long geological evolution process, in which the high temperature and overpressure are conductive to the accumulation and preservation of shale gas [40]. Thus, the section from Wufeng Formation in Upper Ordovician to Longmaxi Formation in Lower Silurian is the primary gas-producing layer, especially LMX Formation buried at depth of 3500-4500 m, and gradually deepens from north to south. The enrichment of hydrocarbon potential in LZ block can enable it to become a crucial successive field after Changning-Weiyuan block [41–43].


### 3.2. Sample Preparation

#### 3.2.1. Core Selection

To select suitable samples for rock-electric experiment, some criteria need to be satisfied. Based on the logging data, the cores should be quantitatively sufficient and representative to manifest the petrophysical features in the target region. Subsequently, the porosity of samples is recommended to cover a certain range of values in case of an awfulF vs. φ diagram with concentrated spots. Ultimately, it should be noted that shale samples are very prone to failure and as such cautions must be paid to ensure the core plugs are prepared without initial cracks.Following these principles, ten appropriate deep shale samples taken from the Longmaxi Formation in Luzhou area are utilized in this study. These core plugs were cut oversize and trimmed down to 2.5 cm in diameter and 3-5 cm in length using a diamond saw. All experiments, including petrophysical parameters, chlorine content, and XRD were performed in Shale Gas Research Institute of Southwest Oil & Gas Field Branch. The porosity is calculated by liquid saturation method that subtracts the dry weight from water-saturated weight, then divides by the core plug volume. The permeability is measured by the pulse method. Table2 shows that the porosities of samples are distributed in a range of 1.03%~6.24% with permeability constrained to 0.0039~0.0301 mD. Besides, no crack is visible on the surface.Table 2
The petrophysical information of target samples in LZ region (U and L represent samples from Upper and Lower Longmaxi Formation, respectively).
Sample numberDepth (m)Porosity (%)Permeability (10-3μm2)U33894.45-3894.482.820.009U243916.31-3916.364.050.026U353927.18-3927.233.270.026U373929.28-3929.332.090.030L43976.69-3976.744.820.008L233994.74-3994.791.510.004L524024.82-4024.875.990.014L534025.81-4025.866.240.009L604033.03-4033.085.230.008L664039.30-4039.351.030.007


#### 3.2.2. Salinity of Brine Water

The salinity of formation water is determined by analyzing the relative chemical data. During the flowback and production period in Fushun-Yongchuan area, 65 water samples were collected from 17 wells and evaluated. It is suggested that in the beginning, the chloride content of different wells varied significantly but ultimately reached a stable level around 20000 ppm. Furthermore, the mixed liquid was analyzed from a well in adjacent area where the flowback ratio exceeded 100%, and the average salinity approached 22500 ppm. Eventually, based on the production and drainage data, the salinity of formation water in target well approximates to 22500 ppm (Figure2).Figure 2
Variation of chlorine content with flowback ratio in produced water of adjacent wells.


### 3.3. XRD

Mineral composition is characterized as a basis in the study of shale reservoirs. On one hand, shale gas exists primarily in two states, where adsorbed gas is stored on clay and organic matter surfaces, and free gas is preserved on matrix surface [44]. Irreducible water is mainly divided into clay-bound water and capillary-bound water. The interaction between gas and water plays an important role in some basic properties, such as resistivity. On the other hand, the mechanical features of reservoir can be affected by minerals of different types, content, combinations, and interactions. As such, XRD technique was implemented to obtain the mineral contents of all samples, which is favorable for subsequent study of resistivity and pore system.In this paper, XRD was performed to quantitatively analyze the mineral composition of specimens. The test was conducted in an ambient environment at a temperature of 25°C and humidity of 30%. Based on suggested practices [45], the samples were prepared. Rock chips weighing 2-4 g were crushed in an agate mortar and pulverized to 200 mesh. Subsequently, the powder was packed in a measuring cell and measured by X pertPowder, an X-ray Diffractometer, with Cu-Kα radioactive source at scanning angle of 25°. Finally, the relevant diffractograms were interpreted to identify the whole rock and clay minerals, where the peaks of maximal intensity delivered a semiquantitative abundance of mineral phases. The results were analyzed in line with the protocol of the Chinese Oil and Gas Industry Standard (SY/T) 5163-2018.


### 3.4. Rock-Electric Experiment

The rock-electric experiment was carried out by ZL5 intelligent LCR apparatus housed at Southwest Oil & Gas Field Branch (Chengdu). A set of salinity values at regular intervals should be selected as variable to investigate the effect of salinity on rock conductivity and electrical parameters. Hence, according to the standard plot of NaCl solution resistivity versus its concentration and temperature, the salinity value was assigned to uniform values of 7000 ppm, 22500 ppm, and 60000 ppm, where 22500 ppm corresponded to the formation brine water.The rock-electric experiment was manipulated at room temperature and atmospheric pressure to exclude the ambient error. Figure3 shows a workflow chart of detailed steps taken to measure the rock resistivity. The first step includes the measurement of basic physical parameters and drying shale cores. Physical parameters include length, diameter, permeability, and porosity determined by the alcohol saturation method. After drying in the oven for 24 h, all samples were cooled down to room temperature in a desiccator and weighed on balance. Meanwhile, the brine water was prepared and measured three times to obtain the average resistivity. Comparing the measured resistivity with the standard value in NaCl plot, they were found to be closed so that the result was reliable. Then, the samples were vacuumed and fully saturated with NaCl solution. During this process, the cores were dispersed among glass beads, which could reduce the external surrounding volume and support the rocks against expansion. Seal the container to trap vacuum space and impose a confining pressure of 30 MPa for 72 h. Herein, the shale samples were believed to be completely saturated according to practical experience, or else saturated for too long time may lead to imbibition behavior creating cracks. Afterwards, we recorded the measured rock resistivity in different moisture content and converted them to standard. Finally, based on Equation (3) and Equation (4), double logarithmic plots of F-φ and I-Sw were utilized to determine Archie parameters. These equations are rewritten in conventional process as:
(7)logF=loga−mlogϕ,(8)logI=logb−nlogSW.Figure 3
Workflow of rock-electric experiment in shale samples of LZ region.From them, “a” and “b” can be obtained from the intercept of sloping best-fit line with the y-axis. “m” and “n” are the slope of the straight line. It should be noted that “m” can only be derived from fully saturated points (Sw=1), whereas “n” is obtained from decreasing water saturation spots.


## 3.1. Geological Context

Luzhou block, situated in the low-steep structural belt of Southern Sichuan, is one of the principal targets for shale gas exploration and development in the Sichuan Basin. It is surrounded by Qiyueshan fault belt on the east and Huayingshan fault belt on the west. Geologically, the folding structures, generally distributed in the shape of straight line or arc belt, are developed in LZ block, which are mainly concentrated from center to southern part along with some in northern part. The syncline zone is gentle and wide, but the two wings of the anticline zone are steep with a low angle. Overall, the study area is dominated by reverse faults accompanied by strata uplift locally [39] (Figure 1).Figure 1
The geological location of Luzhou area in Southern Sichuan Basin (modified from Pan et al. [42]).It is demonstrated that the LZ block in Southern Sichuan has gradually developed after a long geological evolution process, in which the high temperature and overpressure are conductive to the accumulation and preservation of shale gas [40]. Thus, the section from Wufeng Formation in Upper Ordovician to Longmaxi Formation in Lower Silurian is the primary gas-producing layer, especially LMX Formation buried at depth of 3500-4500 m, and gradually deepens from north to south. The enrichment of hydrocarbon potential in LZ block can enable it to become a crucial successive field after Changning-Weiyuan block [41–43].


## 3.2. Sample Preparation

### 3.2.1. Core Selection

To select suitable samples for rock-electric experiment, some criteria need to be satisfied. Based on the logging data, the cores should be quantitatively sufficient and representative to manifest the petrophysical features in the target region. Subsequently, the porosity of samples is recommended to cover a certain range of values in case of an awfulF vs. φ diagram with concentrated spots. Ultimately, it should be noted that shale samples are very prone to failure and as such cautions must be paid to ensure the core plugs are prepared without initial cracks.Following these principles, ten appropriate deep shale samples taken from the Longmaxi Formation in Luzhou area are utilized in this study. These core plugs were cut oversize and trimmed down to 2.5 cm in diameter and 3-5 cm in length using a diamond saw. All experiments, including petrophysical parameters, chlorine content, and XRD were performed in Shale Gas Research Institute of Southwest Oil & Gas Field Branch. The porosity is calculated by liquid saturation method that subtracts the dry weight from water-saturated weight, then divides by the core plug volume. The permeability is measured by the pulse method. Table2 shows that the porosities of samples are distributed in a range of 1.03%~6.24% with permeability constrained to 0.0039~0.0301 mD. Besides, no crack is visible on the surface.Table 2
The petrophysical information of target samples in LZ region (U and L represent samples from Upper and Lower Longmaxi Formation, respectively).
Sample numberDepth (m)Porosity (%)Permeability (10-3μm2)U33894.45-3894.482.820.009U243916.31-3916.364.050.026U353927.18-3927.233.270.026U373929.28-3929.332.090.030L43976.69-3976.744.820.008L233994.74-3994.791.510.004L524024.82-4024.875.990.014L534025.81-4025.866.240.009L604033.03-4033.085.230.008L664039.30-4039.351.030.007


### 3.2.2. Salinity of Brine Water

The salinity of formation water is determined by analyzing the relative chemical data. During the flowback and production period in Fushun-Yongchuan area, 65 water samples were collected from 17 wells and evaluated. It is suggested that in the beginning, the chloride content of different wells varied significantly but ultimately reached a stable level around 20000 ppm. Furthermore, the mixed liquid was analyzed from a well in adjacent area where the flowback ratio exceeded 100%, and the average salinity approached 22500 ppm. Eventually, based on the production and drainage data, the salinity of formation water in target well approximates to 22500 ppm (Figure2).Figure 2
Variation of chlorine content with flowback ratio in produced water of adjacent wells.


## 3.2.1. Core Selection

To select suitable samples for rock-electric experiment, some criteria need to be satisfied. Based on the logging data, the cores should be quantitatively sufficient and representative to manifest the petrophysical features in the target region. Subsequently, the porosity of samples is recommended to cover a certain range of values in case of an awfulF vs. φ diagram with concentrated spots. Ultimately, it should be noted that shale samples are very prone to failure and as such cautions must be paid to ensure the core plugs are prepared without initial cracks.Following these principles, ten appropriate deep shale samples taken from the Longmaxi Formation in Luzhou area are utilized in this study. These core plugs were cut oversize and trimmed down to 2.5 cm in diameter and 3-5 cm in length using a diamond saw. All experiments, including petrophysical parameters, chlorine content, and XRD were performed in Shale Gas Research Institute of Southwest Oil & Gas Field Branch. The porosity is calculated by liquid saturation method that subtracts the dry weight from water-saturated weight, then divides by the core plug volume. The permeability is measured by the pulse method. Table2 shows that the porosities of samples are distributed in a range of 1.03%~6.24% with permeability constrained to 0.0039~0.0301 mD. Besides, no crack is visible on the surface.Table 2
The petrophysical information of target samples in LZ region (U and L represent samples from Upper and Lower Longmaxi Formation, respectively).
Sample numberDepth (m)Porosity (%)Permeability (10-3μm2)U33894.45-3894.482.820.009U243916.31-3916.364.050.026U353927.18-3927.233.270.026U373929.28-3929.332.090.030L43976.69-3976.744.820.008L233994.74-3994.791.510.004L524024.82-4024.875.990.014L534025.81-4025.866.240.009L604033.03-4033.085.230.008L664039.30-4039.351.030.007


## 3.2.2. Salinity of Brine Water

The salinity of formation water is determined by analyzing the relative chemical data. During the flowback and production period in Fushun-Yongchuan area, 65 water samples were collected from 17 wells and evaluated. It is suggested that in the beginning, the chloride content of different wells varied significantly but ultimately reached a stable level around 20000 ppm. Furthermore, the mixed liquid was analyzed from a well in adjacent area where the flowback ratio exceeded 100%, and the average salinity approached 22500 ppm. Eventually, based on the production and drainage data, the salinity of formation water in target well approximates to 22500 ppm (Figure2).Figure 2
Variation of chlorine content with flowback ratio in produced water of adjacent wells.


## 3.3. XRD

Mineral composition is characterized as a basis in the study of shale reservoirs. On one hand, shale gas exists primarily in two states, where adsorbed gas is stored on clay and organic matter surfaces, and free gas is preserved on matrix surface [44]. Irreducible water is mainly divided into clay-bound water and capillary-bound water. The interaction between gas and water plays an important role in some basic properties, such as resistivity. On the other hand, the mechanical features of reservoir can be affected by minerals of different types, content, combinations, and interactions. As such, XRD technique was implemented to obtain the mineral contents of all samples, which is favorable for subsequent study of resistivity and pore system.In this paper, XRD was performed to quantitatively analyze the mineral composition of specimens. The test was conducted in an ambient environment at a temperature of 25°C and humidity of 30%. Based on suggested practices [45], the samples were prepared. Rock chips weighing 2-4 g were crushed in an agate mortar and pulverized to 200 mesh. Subsequently, the powder was packed in a measuring cell and measured by X pertPowder, an X-ray Diffractometer, with Cu-Kα radioactive source at scanning angle of 25°. Finally, the relevant diffractograms were interpreted to identify the whole rock and clay minerals, where the peaks of maximal intensity delivered a semiquantitative abundance of mineral phases. The results were analyzed in line with the protocol of the Chinese Oil and Gas Industry Standard (SY/T) 5163-2018.


## 3.4. Rock-Electric Experiment

The rock-electric experiment was carried out by ZL5 intelligent LCR apparatus housed at Southwest Oil & Gas Field Branch (Chengdu). A set of salinity values at regular intervals should be selected as variable to investigate the effect of salinity on rock conductivity and electrical parameters. Hence, according to the standard plot of NaCl solution resistivity versus its concentration and temperature, the salinity value was assigned to uniform values of 7000 ppm, 22500 ppm, and 60000 ppm, where 22500 ppm corresponded to the formation brine water.The rock-electric experiment was manipulated at room temperature and atmospheric pressure to exclude the ambient error. Figure3 shows a workflow chart of detailed steps taken to measure the rock resistivity. The first step includes the measurement of basic physical parameters and drying shale cores. Physical parameters include length, diameter, permeability, and porosity determined by the alcohol saturation method. After drying in the oven for 24 h, all samples were cooled down to room temperature in a desiccator and weighed on balance. Meanwhile, the brine water was prepared and measured three times to obtain the average resistivity. Comparing the measured resistivity with the standard value in NaCl plot, they were found to be closed so that the result was reliable. Then, the samples were vacuumed and fully saturated with NaCl solution. During this process, the cores were dispersed among glass beads, which could reduce the external surrounding volume and support the rocks against expansion. Seal the container to trap vacuum space and impose a confining pressure of 30 MPa for 72 h. Herein, the shale samples were believed to be completely saturated according to practical experience, or else saturated for too long time may lead to imbibition behavior creating cracks. Afterwards, we recorded the measured rock resistivity in different moisture content and converted them to standard. Finally, based on Equation (3) and Equation (4), double logarithmic plots of F-φ and I-Sw were utilized to determine Archie parameters. These equations are rewritten in conventional process as:
(7)logF=loga−mlogϕ,(8)logI=logb−nlogSW.Figure 3
Workflow of rock-electric experiment in shale samples of LZ region.From them, “a” and “b” can be obtained from the intercept of sloping best-fit line with the y-axis. “m” and “n” are the slope of the straight line. It should be noted that “m” can only be derived from fully saturated points (Sw=1), whereas “n” is obtained from decreasing water saturation spots.


## 4. Results

### 4.1. Mineral Composition

In the results of XRD measurement, the primary mineral composition of each sample was described in terms of mass fractions: quartz, feldspar (potassium feldspar and plagioclase), carbonate minerals (calcite and dolomite), pyrite, and clay minerals. In shale samples, quartz and clay minerals are dominant compositions accounting for 26%~60% (mean of 43.9%) and 5%~52% (mean of 36.3%), respectively. Carbonate minerals, including dolomite and calcite, also exist as a significant component in the range of 0%~31%. Overall, brittle minerals including quartz, feldspar, pyrite, and carbonate minerals occupy a higher content in the deeper formation below 4000 m whilst in the upper interval distributed more clay minerals (Figure4(a)).Figure 4
Mineral composition (a) and clay composition (b) of target shale samples in Longmaxi Formation.
(a)(b)Clay minerals will experience diagenesis in different burial depths and maturity, contributing to diverse groups of clay minerals [46]. During the process of diagenesis, clay minerals can be transformed into other types. For example, smectite and kaolinite are gradually converted into mixed-layer illite/smectite, chlorite, mixed-layer chlorite/smectite, and illite [47, 48]. As presented in Figure 4(b), the clay minerals in study area consist of illite (60%~96%, ave=71.8%), chlorite (0%~23%, mean of 16.1%), kaolinite (0%~8%, mean of 5%), and mixed-layer illite/smectite (5%~9%, mean of 7.1%). In brief, illite is more abundant in deeper formation and chlorite is opposite (Figure 4(b)).


### 4.2. The Effect of Salinity on Archie’s Parameters

According to Equation (3), mathematical curves relating formation factor with porosity of ten samples were plotted in double logarithm coordinate, where the slope and intercept represent “m” and “a,” respectively. As shown in Figure 5, the logarithmic correlation between F and φ is relatively awesome. The shape and varying trend of curves are closely resembled, indicating the formation factor depends on the rock itself. When the salinity is assigned to 7000 ppm, 22500 ppm, and 60000 ppm, tortuosity index (a) and cementation factor (m) are equal to 1.84, 1.47, 1.34, 1.1, 1.26, and 1.4, respectively (Figure 5(d)). Hence, as the salinity of brine water increases, “m” and “a” show a constrained and covariant relationship that increased “m” corresponds to a decreased “a,” and vice versa. The variation of “m” is not as significant as “a” and they tend to slow down at higher salinity. Moreover, the actual value of “a” and “m” in target shale samples are assigned to 1.47 and 1.26 when considering the real chlorine content in section 3.1.2.Figure 5
Determination ofm and a from log porosity versus log F under different salinities. (a) 7000 ppm; (b)22500 ppm; (c) 60000 ppm; (d) comparison of m and a.
(a)(b)(c)(d)To investigate the physical meaning of cementation factor in a narrow sense, a special method was proposed. Supposinga=1, Archie’s formula can be transformed into Equation (9). Then, by taking the logarithm on both sides, Equation (10) can be obtained to calculate “m” for every rock sample. Traditional treatment to obtain empirical coefficients from lines fitted to the F plotted against φ in a log-log chart is no longer valid due to the strong heterogeneity in shale. In other words, this special method with fixed “a” value can ignore the influence of lithology and concentrate pore structure information on “m.” Hence, it is possible to investigate the correlation between “m” and certain geological factors.
(9)F=ϕ−m,(10)m=lgR0/Rwlgϕ,where m is the cementation factor of single rock when a=1, R0 and RW represent the resistivity of completely saturated rock and brine water, Ω•m, and φ is the porosity of rock, %. Looking at Figure 6, it appears that the cementation factor of every single sample under a=1 also ascends slightly with the increasing salinity, except for sample L66. This abnormal point may be linked to laboratory operation. In Table 2, sample L66 has the lowest porosity at only 1.03% and may not be fully saturated, triggering the inappropriate results of larger R0, F, and n. The special method to assign “a” as unity provides another definition of cementation factor. Nevertheless, for those samples with F and φ measured, it is a more common and extensive manner to acquire “m” by calculating the negative gradient of the logF versus logφ plot.Figure 6
Comparative analysis results of cementation factor in each single sample under three assigned salinities (a=1).Unlike cementation factor, the saturation exponent (n) is acquired from resistivity measurements at different water saturation, inferring that “n” may depend on water displacement and indirectly reflect the wettability and pore structure of rocks. In this section, the relationship between water saturation (Sw) and resistivity index (I) was established in every shale sample. All logarithmic curves present as a negative straight line with a coefficient up to 0.95 or more (Figure 7).Figure 7
Resistivity index vs. water saturation in sample L4 (first row) and L53 (second row).Based onI vs. Sw curves, a series of “b” and “n” under assigned salinity were obtained and summarized in Figure 8. It can be seen that “n” in most samples exhibits a rising trend with the increase of salinity, whereas “b” generally varies around 1 without significant changes. Meanwhile, cementation factors are added to the same coordinate so as to compare with “n.” From Figure 8(a), “m” is smaller than “n” overall, but both present a consistent positive trend when salinity rises. The effect of mineralization on cementation factor is not as complicated and dramatic as saturation exponent. Specifically, the saturation exponent in core samples is affected by salinity in different degree, where some change significantly (such as sample L4, L23, and L52) and some vary slightly (sample U24 and L53), but the cementation factor ascends uniformly with the increase of salinity. In addition, when all data points are integrated, the saturation exponent in target area is believed to be 1.6 (Figure 8(c)). Therefore, it is extraordinarily unreasonable to adopt the conventional “m” and “n” as constants of 2, which should be varied with rock cores and regions. Studying Archie’s parameters is mainly biased towards cementation factor and saturation exponent.Figure 8
Comparative analysis results ofb and n in LZ shale samples under different salinity. (a) Saturation exponent in every sample; (b) lithologic parameter b; (c) saturation exponent obtained from all sample data under formation water of 22500 ppm.
(a)(b)(c)


### 4.3. Water Saturation and Resistivity

There is a consensus that formation water affects rock resistivity. Herein, the resistivity and water saturation of rocks filled with actual brine water (22500 ppm) were portrayed in a coordinate system, expecting to observe more valuable details. As shown in Figure9, the resistivity is negatively correlated with water saturation and can be best expressed in power function. With the increase of water content, rock conductivity is improved. However, the correlation curves in different shale samples do not share the same morphological features, which can be classified into two categories due to the variation rate of resistivity. The first group (involve U3 and L23) is identified with the characterization that resistivity rises rapidly when water saturation decreases. The decrease in water saturation can trigger an increase in resistivity up to nearly 49%. The second group comprises the rest cores and is weakly affected by water saturation. Specifically, when the water content descends from 80% to 30%, the resistivity of shale rocks presents a similar ascending trend. Moreover, when the water content is constrained to a fixed value, the electrical property of the former type is obviously inferior to the latter one. Compared with the first category, the resistivity in the second group has a notably lower ascending rate with an inflection point of saturation at 70% approximately, which may be attributed to the relatively simple pore structure and better connectivity. The resistivity of water-bearing rock is primarily affected by capillary irreducible water, so the better connectivity of pore and throat is conductive to establishing a stable and wide-spread water network, making rock resistivity increase at a lower rate. Furthermore, the resistivity obtained at saturation below 35% accounts for 1/5 to 1/2 of that in the first type, reaching a maximum of nearly 150 Ω•m. Incidentally, since the shale resistivity was measured in laboratory, it was higher than that of underground logging. The experimentally determined resistivity of water-bearing cores can only reflect a certain trend, i.e., the resistivity and water content in shale underground and on the surface are not correlated uniformly.Figure 9
Relationship between rock resistivity and water saturation in deep shale samples.


## 4.1. Mineral Composition

In the results of XRD measurement, the primary mineral composition of each sample was described in terms of mass fractions: quartz, feldspar (potassium feldspar and plagioclase), carbonate minerals (calcite and dolomite), pyrite, and clay minerals. In shale samples, quartz and clay minerals are dominant compositions accounting for 26%~60% (mean of 43.9%) and 5%~52% (mean of 36.3%), respectively. Carbonate minerals, including dolomite and calcite, also exist as a significant component in the range of 0%~31%. Overall, brittle minerals including quartz, feldspar, pyrite, and carbonate minerals occupy a higher content in the deeper formation below 4000 m whilst in the upper interval distributed more clay minerals (Figure4(a)).Figure 4
Mineral composition (a) and clay composition (b) of target shale samples in Longmaxi Formation.
(a)(b)Clay minerals will experience diagenesis in different burial depths and maturity, contributing to diverse groups of clay minerals [46]. During the process of diagenesis, clay minerals can be transformed into other types. For example, smectite and kaolinite are gradually converted into mixed-layer illite/smectite, chlorite, mixed-layer chlorite/smectite, and illite [47, 48]. As presented in Figure 4(b), the clay minerals in study area consist of illite (60%~96%, ave=71.8%), chlorite (0%~23%, mean of 16.1%), kaolinite (0%~8%, mean of 5%), and mixed-layer illite/smectite (5%~9%, mean of 7.1%). In brief, illite is more abundant in deeper formation and chlorite is opposite (Figure 4(b)).


## 4.2. The Effect of Salinity on Archie’s Parameters

According to Equation (3), mathematical curves relating formation factor with porosity of ten samples were plotted in double logarithm coordinate, where the slope and intercept represent “m” and “a,” respectively. As shown in Figure 5, the logarithmic correlation between F and φ is relatively awesome. The shape and varying trend of curves are closely resembled, indicating the formation factor depends on the rock itself. When the salinity is assigned to 7000 ppm, 22500 ppm, and 60000 ppm, tortuosity index (a) and cementation factor (m) are equal to 1.84, 1.47, 1.34, 1.1, 1.26, and 1.4, respectively (Figure 5(d)). Hence, as the salinity of brine water increases, “m” and “a” show a constrained and covariant relationship that increased “m” corresponds to a decreased “a,” and vice versa. The variation of “m” is not as significant as “a” and they tend to slow down at higher salinity. Moreover, the actual value of “a” and “m” in target shale samples are assigned to 1.47 and 1.26 when considering the real chlorine content in section 3.1.2.Figure 5
Determination ofm and a from log porosity versus log F under different salinities. (a) 7000 ppm; (b)22500 ppm; (c) 60000 ppm; (d) comparison of m and a.
(a)(b)(c)(d)To investigate the physical meaning of cementation factor in a narrow sense, a special method was proposed. Supposinga=1, Archie’s formula can be transformed into Equation (9). Then, by taking the logarithm on both sides, Equation (10) can be obtained to calculate “m” for every rock sample. Traditional treatment to obtain empirical coefficients from lines fitted to the F plotted against φ in a log-log chart is no longer valid due to the strong heterogeneity in shale. In other words, this special method with fixed “a” value can ignore the influence of lithology and concentrate pore structure information on “m.” Hence, it is possible to investigate the correlation between “m” and certain geological factors.
(9)F=ϕ−m,(10)m=lgR0/Rwlgϕ,where m is the cementation factor of single rock when a=1, R0 and RW represent the resistivity of completely saturated rock and brine water, Ω•m, and φ is the porosity of rock, %. Looking at Figure 6, it appears that the cementation factor of every single sample under a=1 also ascends slightly with the increasing salinity, except for sample L66. This abnormal point may be linked to laboratory operation. In Table 2, sample L66 has the lowest porosity at only 1.03% and may not be fully saturated, triggering the inappropriate results of larger R0, F, and n. The special method to assign “a” as unity provides another definition of cementation factor. Nevertheless, for those samples with F and φ measured, it is a more common and extensive manner to acquire “m” by calculating the negative gradient of the logF versus logφ plot.Figure 6
Comparative analysis results of cementation factor in each single sample under three assigned salinities (a=1).Unlike cementation factor, the saturation exponent (n) is acquired from resistivity measurements at different water saturation, inferring that “n” may depend on water displacement and indirectly reflect the wettability and pore structure of rocks. In this section, the relationship between water saturation (Sw) and resistivity index (I) was established in every shale sample. All logarithmic curves present as a negative straight line with a coefficient up to 0.95 or more (Figure 7).Figure 7
Resistivity index vs. water saturation in sample L4 (first row) and L53 (second row).Based onI vs. Sw curves, a series of “b” and “n” under assigned salinity were obtained and summarized in Figure 8. It can be seen that “n” in most samples exhibits a rising trend with the increase of salinity, whereas “b” generally varies around 1 without significant changes. Meanwhile, cementation factors are added to the same coordinate so as to compare with “n.” From Figure 8(a), “m” is smaller than “n” overall, but both present a consistent positive trend when salinity rises. The effect of mineralization on cementation factor is not as complicated and dramatic as saturation exponent. Specifically, the saturation exponent in core samples is affected by salinity in different degree, where some change significantly (such as sample L4, L23, and L52) and some vary slightly (sample U24 and L53), but the cementation factor ascends uniformly with the increase of salinity. In addition, when all data points are integrated, the saturation exponent in target area is believed to be 1.6 (Figure 8(c)). Therefore, it is extraordinarily unreasonable to adopt the conventional “m” and “n” as constants of 2, which should be varied with rock cores and regions. Studying Archie’s parameters is mainly biased towards cementation factor and saturation exponent.Figure 8
Comparative analysis results ofb and n in LZ shale samples under different salinity. (a) Saturation exponent in every sample; (b) lithologic parameter b; (c) saturation exponent obtained from all sample data under formation water of 22500 ppm.
(a)(b)(c)


## 4.3. Water Saturation and Resistivity

There is a consensus that formation water affects rock resistivity. Herein, the resistivity and water saturation of rocks filled with actual brine water (22500 ppm) were portrayed in a coordinate system, expecting to observe more valuable details. As shown in Figure9, the resistivity is negatively correlated with water saturation and can be best expressed in power function. With the increase of water content, rock conductivity is improved. However, the correlation curves in different shale samples do not share the same morphological features, which can be classified into two categories due to the variation rate of resistivity. The first group (involve U3 and L23) is identified with the characterization that resistivity rises rapidly when water saturation decreases. The decrease in water saturation can trigger an increase in resistivity up to nearly 49%. The second group comprises the rest cores and is weakly affected by water saturation. Specifically, when the water content descends from 80% to 30%, the resistivity of shale rocks presents a similar ascending trend. Moreover, when the water content is constrained to a fixed value, the electrical property of the former type is obviously inferior to the latter one. Compared with the first category, the resistivity in the second group has a notably lower ascending rate with an inflection point of saturation at 70% approximately, which may be attributed to the relatively simple pore structure and better connectivity. The resistivity of water-bearing rock is primarily affected by capillary irreducible water, so the better connectivity of pore and throat is conductive to establishing a stable and wide-spread water network, making rock resistivity increase at a lower rate. Furthermore, the resistivity obtained at saturation below 35% accounts for 1/5 to 1/2 of that in the first type, reaching a maximum of nearly 150 Ω•m. Incidentally, since the shale resistivity was measured in laboratory, it was higher than that of underground logging. The experimentally determined resistivity of water-bearing cores can only reflect a certain trend, i.e., the resistivity and water content in shale underground and on the surface are not correlated uniformly.Figure 9
Relationship between rock resistivity and water saturation in deep shale samples.


## 5. Discussions

### 5.1. Comparison of Archie’s Parameters

It has been demonstrated that “m” increases slightly with the rise of water salinity, and “a” is opposite, which may be induced by pore structure changes related to clay content. When the solution is more concentrated, the number of movable ions rises, and the cation exchange capacity enhances, leading to a better additional conductivity in diffusion layer and free water layer. In the crystal structure of clay (especially smectite), more movable ions enter the crystal interlayer and join with the edge bonds to expand the interlayer distance, causing a slight variation in the pore structure of clay. Expanded clay can also fill the pores in other minerals such as quartz to some extent. Thus, the additional conductivity caused by abundant mud content can result in low “a,” and the interlayer reaction in clay crystals can trigger a very slight variation in “m.” Moreover, we find that the fitting lines of φ vs. F in deep shale are not as eximious as those in sandstone and carbonate rock. On one hand, shale is characterized as a heterogeneous rock that contains considerable amounts of clay minerals and organic matter [49, 50], but Archie’s formula was originally designed for pure sandstone. Hence, the presence of clay, considered as a conductive medium, complicates the interpretation and may lead to unsatisfactory results when Archie’s equation is applied. On the other hand, completely saturating the rock cores with brine water is an obstacle in shale reservoirs due to low porosity and permeability. Therefore, it is difficult to obtain the formation factor F accurately, then affecting the cementation factor (m) and lithology coefficient (a). A new technique or method is in essential need to improve the application of cementation factor in shale reservoirs.In this paper, the cementation factor and lithology coefficient are determined to be 1.26 and 1.47 in deep shale when considering the real salinity in brine water. Herein, a comparison with other authors that used Archie’s equation in various rocks, such as sandstone, shaly sandstone, carbonate rock, and shale, is of great significance and can promote the understanding of Archie parameters. Initially, the theoretical value of “a” and “m” equaled to 1 and 2 [1, 37]. Afterwards, they were assigned different values in literatures based on the best fitting of specific experimental results. Archie stated that “m” varied in the range of 1.3-2.0. In unconsolidated pure sandstones, “m” approximated to 1.3, while in some well-consolidated sandstones from Gulf Coast region of America, “m” was between 1.8 and 2.0. Kamel and Mabrouk believed “a” generally varied from 0 to 1, where the widely used value of “a” was 0.6 for unconsolidated sandstones, 0.8 for consolidated sandstones, and 1.0 for carbonates [26]. They also insisted that “m” ranged in 1.4~2. Glover proposed “m” lay in 1.5~2.5 for most porous sandy sediments and can rise from 2.5 up to 5 in carbonate rocks with poor pore space connectivity [51]. Likewise, some researchers stated “m” varied in a range of 1.0~3.0 according to lithology (1~1.5 in fractured hard rocks, 1.6~2.3 in sandstone, 2.28 in shaly sandstone, and 2.3~3.0 in carbonate) [3, 49, 52, 53]. In terms of shale, the cementation factor m in gas shale reservoirs was around 1.6 to 1.7, below 2 in oil shale reservoirs, between 1.31 and 1.86 in Cauvery basin, and was around 1.6 in laboratory experiment [7, 54–57]. Recently, several relatively high m values of 2.9–3.6 under different salinity and 2.70 accounting for stress in Ordovician Goldwyer Formation from the Canning Basin are derived, together with 2.2 in Eagle Ford [58, 59]. The observed m values from previous literatures and our findings are listed in Table 3 for convenient comparison. It seems that Archie’s parameters in shale are obviously different from shaly sand and carbonate rock. The results obtained from other authors demonstrate that, on the whole, Archie’s cementation factor obeys the law of msandstone<mshalysandstone<mcarbonaterock whilst “a” is much less than “m.” The relatively low value of “m” in shales is similar to that of sandstones, and relatively high value corresponds to that of carbonate rocks, indicating “m” in shales can cover a large span of values. In contrast, the cementation factor in our study is nearly twice as small as 2, and when compared with other rocks, “a” is higher, and “m” is the opposite. Meanwhile, “a” and “m” values are similar without huge gap, which may be related to the layer-distributed clay minerals and additional conductivity of pyrite. The phenomenon that our cementation factor is not as much as that of other shales may be mainly attributed to the extremely low porosity in LZ shales. The complicated pore structure with low porosity and permeability affects the cementation factor. Additionally, the experimental condition only taking account of salinity without reservoir pressure may be another reason. Therefore, the traditional method to take “a” as 1 and “m” as 2 is inappropriate and will neglect some critical features in formation, such as textural changes with depth and presence of vugs and fractures. Cementation factor and saturation exponent, especially “m,” play a pivotal role in determining water saturation with Archie’s equation.Table 3
Comparative analysis results of Archie’s parameters in different rocks [1, 3, 7, 26, 37, 49–59].
LithologyamPorositySandstonePure sandstone (in Archie)1210~55%Unconsolidated sandstone0.61.3Weak-cemented sandstone0.71.9Medium-cemented sandstone0.52.2Sandstone1.6-2.3Shaly sandstone<1.52.28Carbonate rockUnconsolidated Shell limestone and dolomite0.551.85Medium-tight coarse crystalline limestone and dolomite0.62.5Tight fine crystalline limestone and dolomite0.82.3Carbonate rock12.5-5/2.3-3.0ShaleShale (relatively low values)\Gas shale reservoirs: 1.6-1.7Oil shale reservoirs: <2\Cauvery basin: 1.31-1.8610%~33%Laboratory experiment: 1.69.7%~20.1%Shale (relatively high values)\Canning Basin: 2.9–3.6 (different salinity); 2.70 (reservoir stress)7.9%~8.5%Eagle Ford: 2.22.1%Shale (in our paper)1.47LZ area: 1.261.0%~6.2%


### 5.2. Effect of Clay Content on Archie’s Parameters

As for the relationship between “m” and clay mineral, Sliner-Saner et al. proposed a mud-corrected method for Archie’s formula. They believed that more abundant shale content corresponded to the lower cementation factor, which was shown as a linear relationship of m=kVsh+d (Vsh: shale content; k, d: undetermined coefficient) [18]. In our research, it is found that shale content does have an impact on cementation factor but not a linear equation. Cementation factor presents a negative relationship with clay content and decreases rapidly at high clay content (Figure 10). This may be attributed to the mineral distribution, additional conductivity of shale, and its influence on tortuosity. Moreover, there is no correlation between saturation factor and clay content.Figure 10
The correlation between cementation factor and clay content (a=1).


### 5.3. Effect of Pore Structure on Archie’s Parameters and Resistivity

It is universally known that the parameter “m” is a comprehensive reflection of rock structure or skeleton structure. The first attempt to understand the meaning of “m” was conducted by Archie who referred to “m” as cementation index (factor or exponent) due to the relation with cementation degree of rock fabric. He qualitatively proved that “m” was linked to the connectivity of rocks, which was widely used in transport channels. In this study, a comprehensive physical parameter method is briefly applied to explore the effect of porosity and pore structure (characterized with KP=K/ϕ) on “m.” Low KP always implies complicated pore structure. From the plot of “m” versus KP (Figure 11(a), the curves are fitted well with high coefficients except salinity at 60000 ppm. Overall, “m” diminishes with the rise of KP under a certain salinity, indicating complicated pore structure corresponds to high “m” value. Likewise, “m” generally presents a positive linear correlation with porosity (Figure 11(b). This is because as the clay being more abundant, “m” has been proved to be reduced by a quadratic polynomial function. Clay fills the pore and throat in other mineral composition and is prone to be condensed, impairing the development of porosity. As such, high clay content contributes to the positive correlation between “m” and φ. Complicated pore structure and high porosity could trigger increased cementation factor. In terms of saturation exponent, it is revealed that “n” shows a positive correlation with porosity (Figure 11(c)).Figure 11
The correlation between Archie’s parameters and pore system. (a) Pore structure parameter vs cementation factor; (b) porosity vs. cementation factor; (c) saturation exponent vs. porosity.
(a)(b)(c)Theoretically, the developed porosity implies more water contained in homogeneous rock and corresponds to superior conductivity. Nevertheless, this is not always the case in fact. Based on theSw-Rt plot (Figure 9), the porosity of each core is marked sequentially on the right, where the resistivity has no conspicuous functional relationship with porosity. High porosity can still be accompanied by poor conductivity. In this section, attempts are implemented to explain this phenomenon from a mathematical aspect. Based on the existing results, water saturation and resistivity can be expressed as an exponential function of Rt=cedSw, where c and d are coefficients of exponential function and are not identical in different cores. When Sw is fixed, c and d are regarded to be decided by rock resistivity. Afterwards, the exponential function and Archie’s formula in Equation (5) are integrated to gain some fresh comments:
(11)Rt=abRWSWnϕm=RWSWnϕm=cedSW.In this derivation, “a” and “b” are assigned as 1. Rw represents the resistivity of formation brine water and equals to 0.3060 Ω•m in study area (22500 ppm). “m” becomes a variable reflecting the pore structure information. In Subsections 4.2 and 4.3, it is observed that m and n are linearly correlated with porosity, i.e., m=11.34φ+0.94 and n=18.48φ+1.11. Substitute m and n and take logarithm on both sides of Equation (11):
(12)−1.18−18.48ϕlnSW−1.11lnSW−11.34ϕlnϕ−0.94lnϕ=lnc+dSW.In mathematical point of view, the coefficients (c,d) and relevant resistivity are dependent on porosity at the same water saturation, yet not a simple functional relationship. Thus, it is unreasonable to judge the resistivity by porosity. From a physical perspective, it is indicated that resistivity is not only inseparable from porosity, but affected by other elements, such as pore structure (connectivity of pore throat and cementation of pores, etc.), which is also in line with the common perception. For further analysis, suppose Sw=1, then:
(13)Rt=0.306ϕ11.34ϕ+0.936.From Equation (13), if the porosity approaches zero, the denominator containing only φ is derived by taking the limit as follows:
(14)limϕ⟶0ϕ11.34ϕ+0.936=limϕ⟶0e11.34ϕ+0.936lnϕ=elimϕ⟶011.34ϕlnϕ+lim/x⟶00.936lnϕ=elimϕ⟶0lnϕ/1/11.34ϕ+lim/x⟶00.936lnϕ=elimϕ⟶01/ϕ/−1/11.34ϕ2+lim/ϕ⟶00.936lnϕ=elimϕ⟶0−11.34ϕ+lim/ϕ⟶00.936lnϕ=e0+0.936lim/ϕ⟶0lnϕ=limϕ⟶0ϕ0.936=0.Consequently, if the porosity approaches zero, the rock is absolutely insulated with infinite resistivity. Conversely, the resistivity of rock is equivalent to that of formation water when porosity approaches 1, and the rock core can be regarded as a cylindrical container fully filled with water.In conclusion, shale reservoirs are characterized by high clay content, complex pore structure, low porosity, and poor permeability. It is believed that irreducible water plays a predominant role in rocks with rare or irrespective movable water. Hence, the variation in formation resistivity chiefly relies on the conductive network composed of high salt-bearing bound water.


## 5.1. Comparison of Archie’s Parameters

It has been demonstrated that “m” increases slightly with the rise of water salinity, and “a” is opposite, which may be induced by pore structure changes related to clay content. When the solution is more concentrated, the number of movable ions rises, and the cation exchange capacity enhances, leading to a better additional conductivity in diffusion layer and free water layer. In the crystal structure of clay (especially smectite), more movable ions enter the crystal interlayer and join with the edge bonds to expand the interlayer distance, causing a slight variation in the pore structure of clay. Expanded clay can also fill the pores in other minerals such as quartz to some extent. Thus, the additional conductivity caused by abundant mud content can result in low “a,” and the interlayer reaction in clay crystals can trigger a very slight variation in “m.” Moreover, we find that the fitting lines of φ vs. F in deep shale are not as eximious as those in sandstone and carbonate rock. On one hand, shale is characterized as a heterogeneous rock that contains considerable amounts of clay minerals and organic matter [49, 50], but Archie’s formula was originally designed for pure sandstone. Hence, the presence of clay, considered as a conductive medium, complicates the interpretation and may lead to unsatisfactory results when Archie’s equation is applied. On the other hand, completely saturating the rock cores with brine water is an obstacle in shale reservoirs due to low porosity and permeability. Therefore, it is difficult to obtain the formation factor F accurately, then affecting the cementation factor (m) and lithology coefficient (a). A new technique or method is in essential need to improve the application of cementation factor in shale reservoirs.In this paper, the cementation factor and lithology coefficient are determined to be 1.26 and 1.47 in deep shale when considering the real salinity in brine water. Herein, a comparison with other authors that used Archie’s equation in various rocks, such as sandstone, shaly sandstone, carbonate rock, and shale, is of great significance and can promote the understanding of Archie parameters. Initially, the theoretical value of “a” and “m” equaled to 1 and 2 [1, 37]. Afterwards, they were assigned different values in literatures based on the best fitting of specific experimental results. Archie stated that “m” varied in the range of 1.3-2.0. In unconsolidated pure sandstones, “m” approximated to 1.3, while in some well-consolidated sandstones from Gulf Coast region of America, “m” was between 1.8 and 2.0. Kamel and Mabrouk believed “a” generally varied from 0 to 1, where the widely used value of “a” was 0.6 for unconsolidated sandstones, 0.8 for consolidated sandstones, and 1.0 for carbonates [26]. They also insisted that “m” ranged in 1.4~2. Glover proposed “m” lay in 1.5~2.5 for most porous sandy sediments and can rise from 2.5 up to 5 in carbonate rocks with poor pore space connectivity [51]. Likewise, some researchers stated “m” varied in a range of 1.0~3.0 according to lithology (1~1.5 in fractured hard rocks, 1.6~2.3 in sandstone, 2.28 in shaly sandstone, and 2.3~3.0 in carbonate) [3, 49, 52, 53]. In terms of shale, the cementation factor m in gas shale reservoirs was around 1.6 to 1.7, below 2 in oil shale reservoirs, between 1.31 and 1.86 in Cauvery basin, and was around 1.6 in laboratory experiment [7, 54–57]. Recently, several relatively high m values of 2.9–3.6 under different salinity and 2.70 accounting for stress in Ordovician Goldwyer Formation from the Canning Basin are derived, together with 2.2 in Eagle Ford [58, 59]. The observed m values from previous literatures and our findings are listed in Table 3 for convenient comparison. It seems that Archie’s parameters in shale are obviously different from shaly sand and carbonate rock. The results obtained from other authors demonstrate that, on the whole, Archie’s cementation factor obeys the law of msandstone<mshalysandstone<mcarbonaterock whilst “a” is much less than “m.” The relatively low value of “m” in shales is similar to that of sandstones, and relatively high value corresponds to that of carbonate rocks, indicating “m” in shales can cover a large span of values. In contrast, the cementation factor in our study is nearly twice as small as 2, and when compared with other rocks, “a” is higher, and “m” is the opposite. Meanwhile, “a” and “m” values are similar without huge gap, which may be related to the layer-distributed clay minerals and additional conductivity of pyrite. The phenomenon that our cementation factor is not as much as that of other shales may be mainly attributed to the extremely low porosity in LZ shales. The complicated pore structure with low porosity and permeability affects the cementation factor. Additionally, the experimental condition only taking account of salinity without reservoir pressure may be another reason. Therefore, the traditional method to take “a” as 1 and “m” as 2 is inappropriate and will neglect some critical features in formation, such as textural changes with depth and presence of vugs and fractures. Cementation factor and saturation exponent, especially “m,” play a pivotal role in determining water saturation with Archie’s equation.Table 3
Comparative analysis results of Archie’s parameters in different rocks [1, 3, 7, 26, 37, 49–59].
LithologyamPorositySandstonePure sandstone (in Archie)1210~55%Unconsolidated sandstone0.61.3Weak-cemented sandstone0.71.9Medium-cemented sandstone0.52.2Sandstone1.6-2.3Shaly sandstone<1.52.28Carbonate rockUnconsolidated Shell limestone and dolomite0.551.85Medium-tight coarse crystalline limestone and dolomite0.62.5Tight fine crystalline limestone and dolomite0.82.3Carbonate rock12.5-5/2.3-3.0ShaleShale (relatively low values)\Gas shale reservoirs: 1.6-1.7Oil shale reservoirs: <2\Cauvery basin: 1.31-1.8610%~33%Laboratory experiment: 1.69.7%~20.1%Shale (relatively high values)\Canning Basin: 2.9–3.6 (different salinity); 2.70 (reservoir stress)7.9%~8.5%Eagle Ford: 2.22.1%Shale (in our paper)1.47LZ area: 1.261.0%~6.2%


## 5.2. Effect of Clay Content on Archie’s Parameters

As for the relationship between “m” and clay mineral, Sliner-Saner et al. proposed a mud-corrected method for Archie’s formula. They believed that more abundant shale content corresponded to the lower cementation factor, which was shown as a linear relationship of m=kVsh+d (Vsh: shale content; k, d: undetermined coefficient) [18]. In our research, it is found that shale content does have an impact on cementation factor but not a linear equation. Cementation factor presents a negative relationship with clay content and decreases rapidly at high clay content (Figure 10). This may be attributed to the mineral distribution, additional conductivity of shale, and its influence on tortuosity. Moreover, there is no correlation between saturation factor and clay content.Figure 10
The correlation between cementation factor and clay content (a=1).


## 5.3. Effect of Pore Structure on Archie’s Parameters and Resistivity

It is universally known that the parameter “m” is a comprehensive reflection of rock structure or skeleton structure. The first attempt to understand the meaning of “m” was conducted by Archie who referred to “m” as cementation index (factor or exponent) due to the relation with cementation degree of rock fabric. He qualitatively proved that “m” was linked to the connectivity of rocks, which was widely used in transport channels. In this study, a comprehensive physical parameter method is briefly applied to explore the effect of porosity and pore structure (characterized with KP=K/ϕ) on “m.” Low KP always implies complicated pore structure. From the plot of “m” versus KP (Figure 11(a), the curves are fitted well with high coefficients except salinity at 60000 ppm. Overall, “m” diminishes with the rise of KP under a certain salinity, indicating complicated pore structure corresponds to high “m” value. Likewise, “m” generally presents a positive linear correlation with porosity (Figure 11(b). This is because as the clay being more abundant, “m” has been proved to be reduced by a quadratic polynomial function. Clay fills the pore and throat in other mineral composition and is prone to be condensed, impairing the development of porosity. As such, high clay content contributes to the positive correlation between “m” and φ. Complicated pore structure and high porosity could trigger increased cementation factor. In terms of saturation exponent, it is revealed that “n” shows a positive correlation with porosity (Figure 11(c)).Figure 11
The correlation between Archie’s parameters and pore system. (a) Pore structure parameter vs cementation factor; (b) porosity vs. cementation factor; (c) saturation exponent vs. porosity.
(a)(b)(c)Theoretically, the developed porosity implies more water contained in homogeneous rock and corresponds to superior conductivity. Nevertheless, this is not always the case in fact. Based on theSw-Rt plot (Figure 9), the porosity of each core is marked sequentially on the right, where the resistivity has no conspicuous functional relationship with porosity. High porosity can still be accompanied by poor conductivity. In this section, attempts are implemented to explain this phenomenon from a mathematical aspect. Based on the existing results, water saturation and resistivity can be expressed as an exponential function of Rt=cedSw, where c and d are coefficients of exponential function and are not identical in different cores. When Sw is fixed, c and d are regarded to be decided by rock resistivity. Afterwards, the exponential function and Archie’s formula in Equation (5) are integrated to gain some fresh comments:
(11)Rt=abRWSWnϕm=RWSWnϕm=cedSW.In this derivation, “a” and “b” are assigned as 1. Rw represents the resistivity of formation brine water and equals to 0.3060 Ω•m in study area (22500 ppm). “m” becomes a variable reflecting the pore structure information. In Subsections 4.2 and 4.3, it is observed that m and n are linearly correlated with porosity, i.e., m=11.34φ+0.94 and n=18.48φ+1.11. Substitute m and n and take logarithm on both sides of Equation (11):
(12)−1.18−18.48ϕlnSW−1.11lnSW−11.34ϕlnϕ−0.94lnϕ=lnc+dSW.In mathematical point of view, the coefficients (c,d) and relevant resistivity are dependent on porosity at the same water saturation, yet not a simple functional relationship. Thus, it is unreasonable to judge the resistivity by porosity. From a physical perspective, it is indicated that resistivity is not only inseparable from porosity, but affected by other elements, such as pore structure (connectivity of pore throat and cementation of pores, etc.), which is also in line with the common perception. For further analysis, suppose Sw=1, then:
(13)Rt=0.306ϕ11.34ϕ+0.936.From Equation (13), if the porosity approaches zero, the denominator containing only φ is derived by taking the limit as follows:
(14)limϕ⟶0ϕ11.34ϕ+0.936=limϕ⟶0e11.34ϕ+0.936lnϕ=elimϕ⟶011.34ϕlnϕ+lim/x⟶00.936lnϕ=elimϕ⟶0lnϕ/1/11.34ϕ+lim/x⟶00.936lnϕ=elimϕ⟶01/ϕ/−1/11.34ϕ2+lim/ϕ⟶00.936lnϕ=elimϕ⟶0−11.34ϕ+lim/ϕ⟶00.936lnϕ=e0+0.936lim/ϕ⟶0lnϕ=limϕ⟶0ϕ0.936=0.Consequently, if the porosity approaches zero, the rock is absolutely insulated with infinite resistivity. Conversely, the resistivity of rock is equivalent to that of formation water when porosity approaches 1, and the rock core can be regarded as a cylindrical container fully filled with water.In conclusion, shale reservoirs are characterized by high clay content, complex pore structure, low porosity, and poor permeability. It is believed that irreducible water plays a predominant role in rocks with rare or irrespective movable water. Hence, the variation in formation resistivity chiefly relies on the conductive network composed of high salt-bearing bound water.


## 6. Conclusions

The rock-electric experiments in deep shale samples under different salinity were conducted to determine Archie’s parameters and investigate the correlation with mineral composition and pore structure. The results obtained reveal that Archie’s parameters of “a,” “b,” “m,” and “n” under the actual brine salinity in study area are assigned to 1.47, 1, 1.26, and 1.6, respectively. By comparison, our cementation factor is not as large as that of shales in other papers probably due to the extremely low porosity in LZ shales. A steady increase in “m” (a=1 and a≠1) and “n” is observed as the water salinity increases. Hence, the traditional assignment to Archie parameters is inappropriate as it ignores the effects of external conditions. Moreover, the cementation factor is also found to be associated with pore system, which is principally influenced by clay minerals. It is concluded that complicated pore structure and high porosity contribute to an increased cementation factor. Subsequently, a mathematical derivation is implemented to investigate how porosity influences the rock resistivity and establish a physical model.In regard to the research method, it needs to be acknowledged that we merely explore the effect of salinity on shale samples. Further research could also be conducted to determine the effectiveness of reservoir pressure and temperature on Archie’s parameters and rock resistivity. To conclude, the acquisition of Archie parameters accounting for external factors is critical, but we are still far from achieving it.



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