Calculation of Water Saturation of Dolomite Reservoir Based on Multi-Pore Structure Model Open Access

Carbonate salt oil reservoirs are rich in reserves, and as one of the important carriers for oil and gas storage, it has always been an important research object for petroleum exploration workers. However, due to the complex pore structure, poor porosity-permeability relationship, and strong heterogeneity of dolomite reservoirs [1, 2], the calculation accuracy of water saturation is low, which brings significant difficulties to reservoir evaluation. The commonly used methods for determining saturation can be divided into the following categories: (1) the method of closed coring [3], the core is protected by the synthetic base sealing fluid to avoid the pollution of the drilling fluid, so as to obtain the important physical parameters such as porosity and permeability in the formation more accurately, and finally complete the calculation of saturation. However, the high cost of coring in this method limits its large-scale application in saturation measurement. (2) The method of the Archie equation [4], which links water saturation with formation resistivity and calculates the water saturation by fitting the values of parameters a, b, m, and n using rock electrical experimental data. To improve the accuracy of saturation calculation, many scholars [5, 6] have continuously explored suitable parameter values. For sandstone reservoirs, the Archie parameters are not fixed and need to be determined based on specific geological conditions. The variation of resistivity and resistivity increase factor was analyzed through rock physics experiments by Zhao et al. [7], and an exponential saturation calculation model was proposed. An acoustic-electric joint inversion method for saturation was proposed by Luo et al. [8], which combines the Wood correction equation for calculating clay content and the exponential model for calculating resistivity. The factors affecting the cementation index were analyzed by Hu et al. [9] based on the rock physics experiment method, and a variable cementation index calculation model was proposed. Although the above method can obtain better prediction accuracy, the applicable conditions of the Archie formula are only applicable to pure sandstone with relatively uniform porosity and consistent formation water salinity. The above method does not consider the strong heterogeneity of carbonate reservoirs, and it does not take into account the effect of rock clay content on conductivity. (3) The method of combining the capillary pressure curve [10]. The empirical J function was proposed by Leverett [11], with an attempt to standardize the capillary pressure curve by combining the absolute permeability and porosity in the form of hydraulic radius. The capillary pressure data of mercury injection were analyzed by Thomeer et al. [12], and a function method was proposed to estimate the capillary pressure based on the volume percentage of mercury injection. Although the aforementioned methods each have their own advantages in saturation calculation, they are generally characterized by poor applicability, high costs, making it difficult to meet the demands for high precision and practical applications in complex reservoir environments.

In view of the limitations of the above methods in the application process, especially in the context of the changing reservoir properties during the geological evolution process, the applicability of the traditional Archie formula in the calculation of water saturation gradually decreases. Therefore, many scholars [13, 14] have proposed saturation calculation models that are more suitable for the characteristics of different reservoir types, based on experimental studies and theoretical derivations, in an effort to improve the prediction accuracy in complex reservoir environments. A W-S model based on cation exchange capacity was proposed by Waxman et al. [15] to address the additional conductivity of clay minerals. The Equivalent Rock Component saturation model was proposed by Shang et al. [16], in which the pores and throats forming the pore space are divided into parallel and series pores, effectively improving the accuracy of saturation calculations for reservoirs with complex pore structures. Considering the effect of rock clay minerals on conductivity, the Simandoux model was proposed by Simandoux et al. [17], in which it is assumed that the sand and clay in the rock are uniformly mixed, achieving a correction of the formation resistivity. The method for calculating carbonate rock oil and gas saturation for fracture-type reservoirs was proposed by Fraser et al. [18], distinguishing conductive components from the perspective of pore structure. A method for determining shale reservoir rock electrical parameters and oil saturation was proposed by Li et al. [19], which involved constructing a four-dimensional digital core framework and using finite-element simulation to determine the electrical parameters of shale rocks. A new calculation model was proposed by Hu et al. [20], which considered the trapezoidal pore structure and divided the tight sandstone pore structure into two types: straight pores with a constant cross-section and trapezoidal pores with a variable cross-section. An improved dual-porosity reservoir rock physics analysis model was proposed by Aguilera et al. [21], which takes into account the effects of pore structure and conductive volume on rock electrical properties. It has been demonstrated to be applicable to all combinations of matrix porosity and disconnected porosity. For complex dolomite reservoirs, the gas probability volume of dolomite reservoirs was calculated by Cai et al. [22] through rock physics analysis and prestack inversion. A method for determining critical connectivity and conductivity model parameters based on the physical properties, rock electrical properties, CT scanning, nuclear magnetic resonance, and thin section analysis data of dolomite reservoirs was proposed by Xie et al. [23]. The “new three-water saturation model” with a variable exponent, considering the effects of clay and calcium content, was proposed by Wang et al. [24], and production capacity prediction was completed.

The above research shows that by introducing various factors such as pore structure, rock composition, and conductive mechanisms, a saturation calculation model considering multiple porosities is proposed, which also accounts for the impact of fractures on the oil-bearing properties of dolomite reservoirs to some extent. Further studies have found that factors such as wettability and pore throat structure have a significant effect on rock resistivity, and under certain conditions, the relationship between resistivity and water saturation shows a “nonArchie phenomenon.” Therefore, based on the determination of the controlling factors of saturation in complex carbonate reservoirs, a saturation calculation method was proposed, in which the influence of small pore throat matrix pores, connected pores, fracture pores, and clay content on resistivity was considered, along with the effect of clay content on formation conductivity. For low-porosity, low-permeability carbonate reservoirs, high-temperature, high-pressure rock electrical experiments were conducted to obtain the rock electrical parameters of the reservoir under actual formation conditions. A saturation model based on pore structure was established using the rock electrical experiment fitting formula, and the parameters calculated by the model were applied to validate the M-area reservoir. In addition, the bound water saturation was determined based on its relationship with porosity and oil column height. A comparison with the results from the pore model showed minimal differences, confirming the reliability of the saturation results calculated using the pore structure model. Therefore, in the treatment of water saturation for the dolomite reservoir in M-area, the water saturation calculated by the pore structure model is more accurate.

Resistivity logging has been widely used in the identification of liquid and compound properties in oil and gas reservoirs and in the qualitative evaluation of reservoir response characteristics. Until the Archie formula was put forward, people gradually applied resistivity logging technology to the calculation of water saturation in reservoirs. The water saturation calculated by Archie’s formula consists of two parts: formation factor and resistivity increase index.

However, through further research conducted by some scholars [25-27], it was found that due to the heterogeneity and varying degrees of cementation in sandstone, the values of a and b in the Archie equation are not simply equal to 1. As a result, the Archie equation is modified to:

Therefore, the formula for quantitative evaluation of saturation by resistivity logging can be obtained by combining the (3) and (4) formula:

where F represents the formation factor; R₀ is the resistivity of the rock in a pure water-bearing zone, Ω·m; R_t is the resistivity of the reservoir rock, Ω·m; R_w is the resistivity of the formation water in the reservoir, Ω·m; ϕ is the porosity of the reservoir rock, expressed as a percentage; %; S_w is the water saturation of the reservoir rock, %; a, m, b, and n are regression coefficients obtained from rock-electric experiments. Among them: a is related to the properties of the rock, m is the cementation exponent, b is a coefficient related to lithology, n is the saturation exponent, which is related to the distribution of oil, gas, and water within the pores.

The introduction of Archie’s formula remains an important method for calculating reservoir oil saturation. However, the Archie’s formula is only applicable to pore-type and void-type reservoirs with relatively weak heterogeneity. In dolomite reservoirs, due to the complexity of rock composition, pore structure, and the diversity of storage space, as well as highly irregular random distribution, strong heterogeneity is exhibited by the reservoir. Therefore, based on the controlling factors of saturation in complex carbonate reservoirs and considering the conductive effects of multiple pores in the rock, the use of a multi-pore structure model is proposed for calculating water saturation. The components in the strata are shown in Figure 1. And the total electrical conductivity of the simulated rock is shown in Figure 2.

In this equation, R_t represents the rock resistivity, R_j represents the resistivity of small throat matrix pores, R_l represents the resistivity of connected matrix pores, R_f represents the resistivity of fractures, and R_sh represents the resistivity of clay.

The various material components can be expressed through the basic principles of the Archie equation. “Small throat matrix pores” refer to the matrix pores where oil and gas cannot enter, so their water saturation is 100%, S_wj = 100%. Their resistivity can be expressed as follows:

Second, the resistivity of the pores of the connected block, the resistivity of the fracture, and the resistivity of the mud are expressed as follows:

Equations (4), (5), (6), (7), and (8) can be combined to yield:

where ϕ_j and m_j represent the small throat matrix porosity and the corresponding porosity index, %; ϕ_j and m_l represent the porosity and corresponding porosity index of the connected matrix pores, %; ϕ_f and m_f represent the fracture porosity and fracture porosity index, %; V_sh represents the clay content; R_tsh represents the resistivity of pure mudstone; S_wj represents the water saturation of small throat matrix pores. For the small throat matrix pores, which are inaccessible to oil and gas, the water saturation is 100%. S_wl represents the water saturation in the connected matrix pores. α is a regional empirical parameter, with a value typically between 1 and 2, commonly taken as 1.5.

Using the above equations, the value of S_wl can be calculated, and then the total water saturation of the rock can be calculated using the following equation:

In equation (10), S_wf represents the fracture water saturation. Generally, in oil zones, it can be taken as 0.1, and in water zones, it can be taken as 1.

The bound water in a reservoir refers to the “nonmovable water” within the pores under formation pressure conditions. Its volume ratio relative to the total porosity is called the bound water saturation. Bound water saturation [28] is one of the key parameters for reservoir oil and gas evaluation, production capacity prediction, and reserve calculation. The value of bound water saturation depends on the rock porosity structure, grain size, and clay content. However, these parameters cannot be directly measured through logging techniques and can only be indirectly reflected through logging data. Therefore, only by finding the quantitative relationship between logging information that reflects the bound water content can the formation’s bound water saturation be evaluated using logging data.

1. Relationship between Bound Water Saturation and Porosity. Porosity and permeability are rock physical parameters that can indirectly reflect the size of the bound water saturation. Rocks with low porosity generally have more complex pore structures, smaller pore spaces, and narrower pore throats, which can hold more bound water. Rocks with larger pore spaces, simpler structures, and larger pore throats have stronger fluid permeability. Therefore, there is a correlation between porosity and bound water saturation. Accurate porosity can be obtained from logging data, and this physical parameter can be used to adequately reflect the bound water saturation. As shown in the figure, with the increase in porosity, the bound water saturation decreases significantly.

2. The relationship between bound water saturation and free water height. During the process of oil and gas accumulation, as the pressure differential from oil and gas injection increases, the water in the formation pores will gradually be displaced. However, when the pressure differential reaches a certain level, although the oil saturation continues to increase, its increment becomes very small. At this point, the formation becomes a pure oil zone, and the remaining water is bound pore water. By using the capillary pressure curve to obtain the corresponding mercury injection saturation, the bound water saturation can be determined by subtracting the mercury injection saturation from 100.

To convert the capillary pressure curve obtained in the laboratory to the reservoir conditions, the following formula is used:

The relationship between the height above the free water interface and the capillary pressure under reservoir conditions [29] is as follows:

Thus, the relationship between the height above the free water interface and the laboratory capillary pressure curve is as follows:

where P_CL represents the laboratory capillary pressure, σ_L is the interfacial tension between mercury and air in the laboratory, σ_R is the interfacial tension between formation water and oil, θ_L is the contact angle for the mercury-air system in the laboratory, θ_R is the wetting angle for the formation water-oil system, P_W is the density of water, P₀ is the density of oil, and h is the height of free water.

According to Table 1, the crude oil density in the M reservoir formation is 0.81 g/cm³, and the density of water is 1 g/cm³. By substituting into formula (15), the relationship between the height of the free water interface and water saturation is obtained as:

From the above analysis, it can be concluded that the bound water saturation is related.

Dolostone is a sedimentary carbonate rock primarily composed of dolomite, quartz, and calcite, and it appears grayish-white with high hardness. Dolostone reservoirs are the most important reservoir type in deep carbonate oil and gas fields. Their pores are generally well-developed, manifested as needle-shaped dissolution pores, superfine crystalline pores, intercrystalline pores, and others. These pores provide excellent reservoir space for oil and gas. The formation of dolostone reservoirs is controlled by various geological factors, including sedimentary environment, diagenesis, and tectonic movements, which result in the formation of high-quality reservoir rock. Dolostone reservoirs, which are widely developed in the M area, also serve as the main production zones in this region.

The M area covers approximately 460,000 square kilometers and is surrounded by faulted or folded mountain ranges. It has undergone four major tectonic evolutions, with oil and gas accumulation occurring after the formation of Ordovician carbonate fracture-cavity reservoirs, with burial depths exceeding 6000 meters. Dolostone is widely developed in the region, often manifesting as open sand-shale transitional facies deposits. Under the influence of weathering and karstification, high-quality reservoirs can form, offering great potential for oil exploration. However, the region’s geological structure is complex, with strong heterogeneity, unclear oil and gas distribution, and high exploration difficulty. By analyzing core experimental data, it can be observed that the porosity is less than 10%, indicating a low-permeability and low-porosity reservoir structure. The permeability is low, the clay content is high, and the pore structure is complex. Due to the complex pore structure, diverse reservoir types, the varying space combinations, pore-permeability conditions, and testing results of different fracture-cavity reservoirs, the calculation of oil saturation in the reservoirs is influenced.

In general, the cementation index m and saturation index n in the Archie formula are regarded as the description parameters of rock electrical properties, which are generally referred to as rock electrical parameters. The experiment to determine the rock electrical parameters is called the rock electrical experiment [30]. Rock electrical experiment is an important means to describe the electrical properties of rock. Rock electrical parameters have a great relationship with temperature, pressure, and formation water salinity. Therefore, the rock electricity experiment under the formation condition is very important to calculate the water saturation. In this article, the results of the rock electricity experiment are used to analyze the calculation of unknown parameters in the formula, and the calculated parameter values are brought into the calculation of porosity saturation, so as to realize the calculation of reservoir saturation.

For the multi-porosity saturation model, the calculation process of the various parameters involved is as follows, and the final parameters are obtained in Table 2:

(1) Fracture Porosity Index. For the fracture porosity index m_f, based on the physical meaning of the cementation exponent m, when fractures are regular and well-developed, m_f=1. However, in actual carbonate reservoirs, fractures are often complex, accompanied by dissolution cavities and other features. Therefore, the fracture porosity index is typically greater than 1, ranging between 1 and 1.5. In this study, a value of 1.2 is used.

(2) Micro-pore Throat Matrix Porosity. For the determination of micro-pore throat matrix porosity, it can be considered as the porosity value corresponding to formations with poor physical properties. There are two methods: one is to select the formation layer with the highest resistivity and relatively small porosity, assuming that the porosity here is primarily matrix porosity. The porosity value at this point can then be used as the micro-pore throat matrix porosity value ϕ_j, which is a fast method. Alternatively, based on the petrophysical analysis data of the study area, the average porosity value corresponding to low permeability can be used as the micro-pore throat matrix porosity value. In this study, the first method was adopted, and the matrix porosity of the area was calculated to be 0.8%.

(3) Selection of m_j, m_l and n. The samples selected for rock electrical experiments are typically rock blocks with undeveloped fractures, and the clay content in the samples can be ignored. In this case, equation (11) becomes equation (17). The small pore throat matrix porosity index m_j can be deduced from the rock electrical experiment data, and the values of m_l and n can be determined using multiple nonlinear regression with the experimental results.

Through the above multi-porosity model, the values of m_j,m_l and n can be obtained via multiple nonlinear regression. The corresponding values were determined under high-temperature and high-pressure experimental conditions.

The parameter values obtained from the model through multivariable nonlinear regression are to be substituted into the following equation to calculate the water saturation of the reservoir.

When the porosity structure is complex and the rock particles are poorly sorted (i.e. exhibiting low porosity), the water saturation of bound water is better reflected by both the porosity and the height above the free water interface. Through repeated research and trial calculations, the following equation can more effectively express the relationship between bound water saturation, porosity, and the height above the free water interface:

where S_wi represents the bound water saturation, %; ϕ represents porosity, %; h is the height above the free water interface, in meters; a, b, c, and d are regional parameters.

The values obtained from mercury injection data are as follows:

For oil reservoirs: a = 1.109, b = −35.981, c = −0.0899, d = 0.877, R² = 0.823

For oil-water reservoirs: a = 1.047, b = −4.915, c = −0.24, d = 0.214, R² = 0.872

From equation (19), the relationships between bound water saturation and height above the free water interface, as well as between bound water saturation and porosity, can be plotted. The following graph illustrates the relationship between bound water saturation and porosity, as well as the relationship between bound water saturation and height above the free water interface under different porosity conditions. The relationship between irreducible water saturation and free water height in well Y is shown in Figure 3. And the relationship between irreducible water saturation and porosity in Well Y is shown in Figure 4.

That is, at the same porosity, the bound water saturation decreases as the gas column height increases. Under the same free water height conditions, the bound water saturation decreases as the porosity increases.

The following figure shows a comparison between the water saturation calculated using the multi-porosity structure model and the bound water saturation calculation results. The blue line represents the calculation results using the multi-porosity structure model, while the green line represents the bound water saturation calculation results.

From the above figure, the blue represents the water saturation calculated using the multi-porosity structure model (as shown in Figure 5), while the green represents the bound water saturation. By comparing the bound water saturation and the multi-porosity structure saturation model, it can be observed that the difference between the two calculations is small, indicating that there is no mobile water in this section of the well, and it is likely a pure oil layer. Therefore, both models can mutually validate each other, confirming the reliability of the water saturation calculated using the multi-porosity structure model. In addition, the results of the multi-porosity saturation model are evaluated using the Root Mean Square Error (RMSE). Its RMSE value is 3.693, indicating that the model’s results are reliable.

From the above figure, it can be observed that at the depth of 6800-6825 m (as shown in Figure 6), the water saturation value calculated by the multi-porosity saturation model is separated from the value calculated by bound water saturation, indicating that movable water exists in this section of the well, and it is likely an oil-water interface. Meanwhile, the water saturation results calculated by the Archie model in the oil-water coexistence layer are still underestimated and do not match the actual situation.

As shown in the figure above, the trend of bound water saturation values is consistent with the water saturation values calculated by the multi-porosity model (as shown in the Figure 7). Compared to the results from the Archie formula, it is found that the water saturation calculated by the Archie formula is overestimated in the intervals of 6903–6908 m and 6915–6920 m. The results of the multi-porosity saturation model are significantly better than those of the Archie equation. Each model was evaluated separately using RMSE and Mean Absolute Error (MAE), as shown in Table 3. The RMSE value of the multi-porosity saturation model is 6.58%, while the RMSE of the Archie equation is 20.1%, which is 13.52% lower than Archie. The MAE value of the multi-porosity saturation model is 5.05%, while the MAE of the Archie equation is 14.91%, which is 9.86% lower than Archie.

In summary, the multi-porosity model for reservoir water saturation calculation fully considers the effects of different porosity types, such as clay content, matrix porosity, connected porosity, and fracture porosity, on the calculated reservoir water saturation. Therefore, the calculated water saturation obtained by this method is more accurate compared to the actual interpretation results of the region, demonstrating that the multi-porosity saturation model provides a better method for calculating water saturation.

The evaluation accuracy of the multi-porosity structure model is mainly influenced by model parameters, porosity, and other factors. When these parameters are accurately obtained, the Archie model, which does not consider the impact of pore structure on rock conductivity, produces less accurate saturation calculations. In contrast, the water saturation calculated using the multi-porosity structure model aligns more closely with actual conditions and provides higher accuracy and broader applicability in the quantitative evaluation of dolostone reservoirs.

In response to the suboptimal performance of using the conventional Archie model for water saturation calculation in the complex geological conditions of the M region, this study proposes a multi-porosity structure saturation model for calculating water saturation in the M region. This model accounts for the influence of various media in the formation of the total electrical conductivity, including small pore throat matrix pores, connected matrix pores, fracture pores, and clay content. Results from the rock electrical experiment show that the water saturation calculated using the multi-porosity structure model is in close agreement with the bound water saturation results, indirectly confirming the reliability of the saturation calculation. This indicates that the water saturation calculated using the multi-porosity structure model is more accurate and better reflects the true oil saturation in the formation, making the model’s results more reasonable and applicable.

The multi-porosity saturation model comprehensively accounts for the influences of matrix porosity, connected pore systems, fractures, and clay conductivity. Although it enables a more thorough characterization of complex reservoirs, the model involves numerous input parameters and a relatively intricate computational process, which may constrain its practical application in certain scenarios.

Data are unavailable due to ethical restrictions.

The authors declare no conflict of interest.

This research is funded by the Major Science and Technology Project of China National Petroleum Corporation Limited - Research and application of Geophysical Key technologies for Ultra-deep Exploration and Development [2023ZZ14YJ05]