Taking into consideration the difficulties in predicting the properties of liquid production and evaluating the irreducible water saturation of low-porosity and ultra-low-permeability sandstone reservoirs, the relationships between the irreducible water saturation and logging reservoir evaluation parameters are explored based on a large number of core mercury injection experiment. When the permeability cumulative contribution value reaches 99.9%, the lower limit of pore throat radius is determined as 0.025 μm and the corresponding irreducible water saturation is more accurate. The experimental results of 77 samples in the research area showed that the irreducible water saturation has a good correlation with the median pore throat radius which has a good correlation with the porosity. The irreducible water saturation is consistent with the nuclear magnetic experiment results. Therefore, a new method to determine the irreducible water saturation based on logging data is established. The application results of this method in tight sandstone reservoirs in the Keshen area show that the fluid types identified by the relationship between the calculated irreducible water saturation and total water saturation are consistent with the actual test results, which confirms the accuracy and feasibility of this method. This method solves the problem of irreducible water saturation evaluation in low-porosity and ultra-low-permeability sandstone reservoirs. In the field or other situations where core testing is lacking, accurate irreducible water saturation can be obtained based on only porosity. It also lays a foundation for further improving the prediction accuracy of fluid properties, which has broad application prospects.
Since the 1970s, more than 70 basins with low-porosity and low-permeability gas reservoirs have been discovered or evaluated. These basins were mainly located in North America, Latin America, the former Soviet Union, Central Asia, and China, as well as the Middle East and North Africa. The resources from the aforementioned accounted for one-seventh of the total natural gas production in the world. Furthermore, it has become an important field of natural gas exploration and development [1,2]. The United States and Canada have the highest percentage of exploration and development of low-porosity and low-permeability sandstone gas reservoirs. In China, low-porosity and low-permeability sandstone gas reservoirs are in the early stage of large-scale development, but rapid progress occurred in recent years. The prospective resources of low-porosity and low-permeability sandstone gas in China exceed 10 × 1012 m3, accounting for about one-fifth of the total natural gas resources in China. These resources are mainly distributed in the Ordos, Turpan-Hami, Tarim, Sichuan, and Songliao Basins [1,3–5].
For ultra-low porosity and low-permeability gas reservoirs, irreducible water saturation is one of the key parameters to identify fluid properties (pure gas layer or gas-water layer), and it is also an important parameter to calculate gas saturation and recoverable reserves of ultra-low porosity and low-permeability gas reservoirs [6–8]. To conduct a more accurate evaluation of oil and gas reservoirs, reserve calculation, and productivity prediction, it is necessary to study the evaluation method of irreducible water saturation which is a key parameter .
Scholars all over the world have done a lot of research related to the evaluation of irreducible water saturation. The principal methods utilized to obtain the saturation of irreducible water are the core test method and the logging prediction method [10–18]. The core test is a direct measurement method, which can obtain more accurate irreducible water saturation. However, its cost is relatively high and it is difficult to obtain the irreducible water saturation value of the whole reservoir with this method. The logging prediction method can make up for this deficiency; nevertheless, its accuracy is relatively low. Gao et al.  explored the irreducible water saturation and micropore structure, rock particle size, porosity, permeability, and the relationship between gas columns. A large number of experimental data showed that for the low-porosity low-permeability sandstone reservoirs, irreducible water saturation and porosity have a good correlation. In the aforementioned study, it is also believed that pure atmospheric irreducible water saturation is related to gas column height. Therefore, the regional empirical relation between irreducible water saturation, porosity, and gas column height was established. Huang et al.  studied the method of estimating irreducible water saturation by using conventional and nuclear magnetic logging data. The results show that for clastic reservoirs with variable lithology and complex pore structure, it is difficult to determine the irreducible water saturation accurately by conventional logging method and nuclear magnetic logging method based on the T2 cut-off value. However, the calculation formula of irreducible water saturation obtained by using the nuclear magnetic resonance (NMR) logging T2 spectrum determination of pore composition combined with neutron-density porosity difference and regression method has achieved a good application effect in Hailar Basin. Yang et al.  used NMR technology to measure the “irreducible water saturation” of six core samples (average porosity 12.1% and average permeability 1.96 mD) in Sulige low-permeability gas reservoir under different displacement conditions but did not study the determination method of the true irreducible water saturation under reservoir conditions. Liang et al.  proposed a new irreducible water saturation calculation model that does not need to calculate T2 cut-off value in combination with Timur and SDR model. This model was aiming at the influence of diffusion relaxation on irreducible water saturation calculation of tight gas sandstone reservoir by using NMR logging data. The field application of tight gas sandstone reservoirs shows that the irreducible water saturation calculated by this model is in good agreement with the core analysis results. Chen et al.  established a porosity model, multiple linear regression models, and a pore structure index model for Sulige tight sandstone gas reservoir to calculate the irreducible water saturation. The results showed that the irreducible water saturation model established by pore structure index had the highest accuracy. Zhu et al.  conducted studies and proposed a method using NMR logging data to construct pseudo-capillary pressure curves. This method utilized the Purcell formula to determine the lower limit of flowing pore throat of rock samples and then determined the irreducible water saturation according to the lower limit of flowing pore throat. Zhang et al.  selected 18 representative tight sandstone samples (average porosity 7.9% and average permeability 0.37 mD) and carried out semi-permeable diaphragm, NMR, and mercury injection experimental measurements. The analysis of the irreducible water saturation was determined by the experiment. The analysis results show that when the threshold pressure of the semi-permeable diaphragm method is 3 MPa and the centrifugal force of the nuclear magnetic experiment method and the capillary pressure of the mercury injection method are 1.379 MPa, the irreducible water saturation is more reliable [23–26]. Yuan et al.  studied and established a calculation model of irreducible water saturation based on the capillary model and the fractal theory for hydrophilic low-permeability tight sandstone. The purpose of this model was the calculation of irreducible water saturation of low-permeability tight sandstone reservoirs. The feasibility of this method was verified by using the test results of 10 core samples (average porosity 12.0% and average permeability 2.1 mD). Yang et al.  obtained a power function relationship between the resistivity of sandstone samples and water saturation through electrical experiments, from which irreducible water saturation can be determined. Several scholars such as Corbelleri et al., Coates et al., Kleinberg and Boyd, Chen et al., Su et al., and Peng et al. (2019) [20,29–34] studied the method of determination of irreducible water saturation by using NMR logging data and different models.
Most of the above methods for the determination of irreducible water saturation are applied to non-low permeability or general low-permeability reservoirs. There are few studies on irreducible water saturation of tight sandstone with ultra-low porosity and permeability, and their application scope has regional limitations. In addition, most of the previous studies rely on core experiments or mathematical calculation models under laboratory conditions, which have not contributed much in the fieldwork. Aiming at the actual situation of low-porosity and ultra-low-permeability sandstone gas reservoirs in the study area, this article explores the methods and models for the calculation of irreducible water saturation by using logging data. These methods and models were applied in the oilfield and achieved a good application effect. In the absence of partial logging data or core experiments, the irreducible water saturation can be accurately calculated as long as there is porosity, which provides a new method and idea for the determination of irreducible water saturation, and greatly improves the accuracy of the irreducible water saturation of ultra-low porosity and permeability sandstone. The structure of this article is as follows: first, the general situation of the study area is introduced; then, the determination methods and models of irreducible water saturation are proposed; next, some application examples are given and analyzed; and finally, the article is summarized with conclusions drawn according to the results of this study.
2 Overview of the study area
In the study area, the Keshen gas field is located in the Keshen zone of the Kelasu structural belt in the Kuqa Depression, northern margin of the Tarim Basin . The Kuqa Depression is a typical superimposed foreland basin with the southern foot of the Tianshan Mountains in the north and the Tabei uplift in the south. The Kuqa Depression can be divided from north to south as follows: the Kelasu thrust belt, the Baicheng depression, and the Qiulitage thrust belt. The Kelasu thrust belt is the first row of thrust structures at the southern foot of the South Tianshan Mountains. The thrust belt consists of two secondary structural units the northern monoclinic belt and the Kelasu structural belt. The Kelasu structural belt can be further divided into two zones, namely the Kela zone in the north and the Keshen zone in the south. The Keshen zone mainly develops north-dipping thrust faults, which are composed of multiple fragments controlled by the wedge-shaped thrust imbricated fault blocks sandwiched by the Kelasu fault and the Baicheng fault.
The main producing layer of the Keshen Gas Field is the cretaceous Bashijiqike Formation reservoir, which is an ultra-deep fractured low-porosity sandstone reservoir with burial depths over 6,500 m. The cretaceous Bashijiqike Formation reservoir is a set of terrigenous clastic rocks deposited by fan delta-braided river delta facies. The fan delta is formed by the alluvial fan from the distant Wenzhu uplift advancing to the lake basin in the study area. Only front subfacies are developed in the cretaceous Bashijiqike formation. The braided river delta is developed by plain and front subfacies. Cretaceous Bashijiqike Formation reservoir is mainly composed of feldspar lithic sandstone and lithic feldspar sandstone, partially intercalated with thin or medium-thick mudstone. The composition maturity is low to medium and the structure maturity is medium. The cement is mainly calcite, and can be divided into four types of diagenetic facies, in particular, strong compaction facies, unstable component dissolution facies, calcareous cementation facies, and structural fracture facies (Figure 1). In Figure 1, F1–F5 represent two secondary fault zones. A1–A7 represent seven wells in the field. The analysis of physical data shows that the sandstone matrix porosity of the cretaceous Bashijiqike Formation in the Keshen two-well area is mainly distributed between 2 and 7%, with an average value of 4.1%. The matrix permeability is mainly distributed between 0.01 and 0.5 mD, with a median value of 0.055 mD (Figure 2), generally belonging to the ultra-low porosity, low permeability, and ultra-low-permeability reservoir. The analysis of the high-pressure mercury intrusion experiment data of 56 representative core samples shows that the average pore throat radius of the reservoirs in the Keshen area is mainly distributed in the range of 0.02–0.07 μm, and the overall average pore throat radius is 0.0345 μm (Figure 3). The pore throat sorting is poor, which is generally characterized by pore structure with fine pores and small throats. In general, the current gas reservoirs in the Keshen area are generally characterized by deep burial, high temperature, high pressure, tight lithology, small pores, thin throats, poor connectivity, and strong heterogeneity [35–37].
3 Determination method and model of irreducible water saturation
Given the complex characteristics of low-porosity and ultra-low-permeability sandstone reservoirs in the study area, to more accurately predict the liquid production properties and formulate a reasonable and efficient development plan, it is necessary to determine the irreducible water saturation parameters of the reservoir as accurately as possible. Therefore, the method of determining the irreducible water saturation using the core mercury intrusion experimental data was selected after research and analysis. In addition, the relationship between the experimental analysis of irreducible water saturation and the evaluation parameters of the conventional logging data was explored and established, and then the conventional logging data was proposed. A method for evaluating irreducible water saturation from well data was also advanced.
3.1 Basic principles
The formation process of oil and gas reservoirs is a process in which the driving force of oil and gas migration constantly overcomes the capillary pressure and water is displaced to reach a balance . Water in underground reservoirs that cannot be displaced by high-pressure oil and gas can be considered as irreducible water. For reservoir rock samples, there must be a pore throat radius value that can distinguish movable fluid from the irreducible fluid. The pore throat larger than that value will store movable fluid, and the pore throat smaller than that value will not store movable fluid. The irreducible fluid is stored and cannot be discharged under formation conditions; this critical pore throat radius is also called the lower limit of the flow pore throat. The ratio of the amount of irreducible fluid to the total amount of fluid in the reservoir pores is the irreducible water saturation . The cumulative mercury injection saturation in the capillary pressure curve obtained by the mercury intrusion experiment method, when the pore throat radius is at the lower limit value of the flow pore throat, can be regarded as the movable fluid saturation [10,38,39]. As a result, the irreducible fluid saturation is further obtained.
In the mercury intrusion experiment, the rock samples are first dried, and then the mercury in the non-wetting phase is pressurized, so that the mercury can overcome the capillary pressure in the pore system to enter the pores. This process of the experiment is realized to obtain the capillary pressure . Different pressures (corresponding to different pore throat radii) are provided in the experiment, and different mercury injection saturations can be obtained accordingly. By connecting the measurement points, a capillary pressure curve is obtained .
3.2 Method and steps of determination of irreducible water saturation based on mercury intrusion experiment
The method flow of determining irreducible water saturation using mercury intrusion experiment data of cores is shown in Figure 4. This method can be realized in five steps as follows: first, carry out core porosity and permeability experiments to analyze the porosity and permeability parameters of cores; second, select core samples with porosity and permeability within the target porosity and permeability parameters, and carry out mercury intrusion experiments; third, determine the lower limit value of flowing pore throats; fourth, according to the capillary pressure curve obtained from mercury intrusion experiments and combined with flowing pore throats, the lower limit value determines the movable fluid saturation; and finally, the irreducible fluid saturation is determined according to the movable fluid saturation.
Since the porosity and permeability of cores at some depths may be extremely low and less than the lower limit of porosity and permeability in the study area, the strata in these depths are not effective reservoirs of particular concern. For that reason, it is not necessary to evaluate the porosity of these reservoirs. Therefore, before carrying out the mercury intrusion experiment, it is necessary to analyze the porosity and permeability of the core and select the core samples which are within the target porosity and permeability parameters.
Determining the lower limit of the flow pore throat is a key step in the method of determining irreducible water saturation using mercury intrusion experimental data. Its precision determines the accuracy of irreducible water saturation evaluation. For conventional reservoirs, the lower limit of flow pore throat is a certain value. For tight sandstone, due to its complex pore structure and strong microscopic heterogeneity, the lower limit of flow pore throat is not a certain value. The statistical results of mercury intrusion experiment data of a large number of core samples show that although the lower limit of flow pore throats of different rock samples is not the same, the contribution of pores with a radius larger than the lower limit of flow pore throats to the cumulative permeability of the rock samples is about 99.9%. That is to say, the contribution of the irreducible pore system to the permeability is roughly 0.1% [10,41]. This shows that the contribution of pore throats with different radii to permeability is different, and the fluid stored in the pore throats which contributes to the permeability is too low in irreducible fluid. So, the pore throat radius corresponding to the cumulative permeability contribution of 99.9% can be used as the lower limit of the flow pore throat. The cumulative permeability contribution value can be calculated using the Purcell formula , which is:
In formula (1), P i and P i+1 are the mercury injection pressure at the i and i + 1 measurement points on the capillary pressure curve. ΔS Hg is the mercury injection amount in the interval from i to i + 1 (the mercury injection pressure increases from P i to P i+1). ΣK is the cumulative penetration contribution.
Through the above method for determining the lower limit value of the pore throat radius for fluid flow in tight sandstone, the core mercury injection experiment data of eight wells in the study area were processed and analyzed. The mean of the lower limit value of the pore throat radii for fluid flow of each well was obtained, and the productivity data and core experiments of each well were calculated. The average pore throat radius obtained from the analysis is shown in Table 1. The histogram of the mean of the lower limit value of the pore throat radii for fluid flow, the cross graph between the average pore throat radius, and the productivity index of eight wells are further drawn as shown in Figures 5 and 6.
|Well no.||Test interval (m)||Gas layer thickness (m)||Productivity index (m3/D/MPa/m)||Average pore throat radius (μm)||The mean of the lower limit value of the pore throat radii for fluid flow (μm)|
It can be seen from Table 1 and Figure 5 that the average value of the lower limit value of the flow pore throat radius of the eight wells in the study area is between 0.022 and 0.034 μm and the overall average value is 0.025 μm. Therefore, the lower limit value of the flow pore throat radius in the work area can be approximately determined as 0.025 μm. It can be seen from Figure 6 that the average pore throat radius of the cores of the wells with effective productivity is greater than or approximately equal to 0.025 μm, which further confirms that the lower limit of the flow pore throat radius in the research area determined above is reasonable.
After determining the lower limit value of the flow pore throat, we found that the cumulative mercury injection saturation corresponds to the pore throat radius and to the lower limit value of the flow pore throat on the capillary pressure curve obtained by the mercury intrusion experiment. It can be regarded as the movable fluid saturation (S fm), and then the irreducible fluid saturation can be calculated as follows:
In formula (2), S firr is the irreducible fluid saturation and S fm is the movable fluid saturation.
3.3 Determination method of irreducible water saturation based on conventional logging data
The core experimental data are often limited. In order to directly use the logging data to evaluate the irreducible water saturation in the oil field, the irreducible water saturation and conventional logging data were studied. This investigation was done by using the core mercury intrusion experimental data to determine the irreducible water saturation. The relationship between the evaluation parameters was established, and an evaluation method of irreducible water saturation based on conventional logging data was established.
The irreducible water saturation of 77 core samples in the research area was determined by the above-mentioned method for the determination of the irreducible water saturation based on the mercury intrusion experiment. At the same time, the NMR experiment was carried out on the NMR irreducible water saturation data of 31 core samples. The results of this experiment were collected and then plotted. The intersection diagram of irreducible water saturation acquired by mercury intrusion and nuclear magnetic experimental data is shown in Figure 7. It can be seen from Figure 7 that all the intersection pattern points fall near the black dotted line with a slope of 1 and an intercept of 0. This indicates that the mercury intrusion irreducible water saturation is in good agreement with the NMR irreducible water saturation, which confirms the evaluation of the irreducible water saturation and therefore shows the accuracy of the results.
The irreducible water saturation was determined by the mercury intrusion experiment data of the core. The relationship between the irreducible water saturation of 77 core samples and other parameters of the core and the evaluation parameters of the logging data was further studied and analyzed. A large number of analysis results show that the irreducible water saturation has a good correlation with the median pore throat radius in the core (as shown in Figure 8a), and the median pore throat radius has a good correlation with the porosity (as shown in Figure 8b). Therefore, conventional logging data can be used to evaluate the reservoir porosity. The irreducible water saturation can be calculated according to the relationships between the median pore throat radius and porosity, as well as between the irreducible water saturation and median pore throat radius. The specific calculation formula is as follows:
In formula (3), S wirr is the irreducible water saturation, r mth is the median pore throat radius, and ϕ is the porosity.
According to the above analysis, it is easy to draw the method and steps of using logging data to evaluate irreducible water saturation by first, using logging data to evaluate the reservoir porosity; second, carrying out core mercury intrusion experiments, analyzing experimental data, and establishing quantitative relationships between irreducible water saturation, median pore throat radius, and porosity (for old work areas, this step can be omitted if this relationship is established); third, the median pore throat radius is calculated from the porosity according to the relationship between the median pore throat radius and the porosity; and finally, according to the relationship between the irreducible water saturation and the median pore throat radius, the irreducible water saturation of the reservoir can be calculated. The specific method flow is shown in Figure 9.
4 Field application and analysis
The measured data of several wells in the study area were processed and analyzed by using the above-established method for evaluating irreducible water saturation based on conventional logging data. Figure 10 shows the results of the comprehensive processing of logging data in the X605–X680 m depth section of Well X1. It can be seen from the saturation trace (trace 8) in the figure that the irreducible water saturation is in good agreement with the total water saturation. This indicates that the depth section is also in favorable agreement. There is no movable water, which is comprehensively interpreted as a pure gas layer. The fracturing production test results show that the daily gas production at this depth interval is 910,728 m3, which is a pure gas layer. This proves that the interpretation and conclusion are accurate. Figure 11 shows the result of the comprehensive processing of logging data in the depth section of X310–X400 m in Well X2. It can be seen from the saturation trace (trace 8) in the figure that the irreducible water saturation is in good agreement with the total water saturation in some depth sections. However, the irreducible water saturation is significantly lower than the total water saturation in some depths. This indicates that there is a certain amount of movable water in these depths, which is comprehensively interpreted as a water-bearing gas layer. The fracturing production test results show that the daily gas production at this depth interval is 343,770 m3 and the daily water production is 25.2 m3, which is an aquifer. This proves that the interpretation and conclusion are accurate. Figure 12 is the result of the comprehensive processing of logging data in the depth section of X210–X300 m in Well X3. From the saturation trace (trace 8) in the figure, it can be seen that the irreducible water saturation in this depth section is significantly lower than the total water saturation. This indicates that there is a large amount of movable water in the depth section, which is comprehensively interpreted as a gas-bearing water layer. The fracturing production test results show that the daily production of gas in this depth section is small, and the daily production of water is 108 m3. This demonstrates that it is a gas-bearing water layer, which proves the accuracy of the interpretation and conclusion.
The processing and analysis results of the above-mentioned actual well data show that the fluid types identified according to the relationship between the calculated irreducible water saturation and the total water saturation are consistent with the actual test results. This indicates that the calculation results of reservoir irreducible water saturation are accurate, which confirms the proposed method. Consequently, showing the correctness and feasibility of the evaluation method of irreducible water saturation based on conventional logging data.
Previous studies have proved the correlation between irreducible water saturation and porosity, but only for non-low porosity and permeability clastic reservoirs. Tight sandstone is an ultra-low porosity and permeability reservoir, so it is more difficult to carry out physical experiments on rock samples. Therefore, researches on irreducible water saturation of tight sandstone are mostly based on mathematical and theoretical models, and few physical experiments are used. In order to accurately evaluate the irreducible water saturation of ultra-low porosity and permeability tight sandstone reservoirs, the quantitative relationship between irreducible water saturation and median pore throat radius and between median pore throat radius and porosity was determined by mercury injection experiments. Therefore, a method and model for evaluating irreducible water saturation in tight reservoirs using conventional logging data are established, which provides a new solution for the evaluation of irreducible water saturation in tight reservoirs. It should be noted that the accuracy of evaluating irreducible water saturation in this scheme depends on the accuracy of the above-mentioned irreducible water saturation evaluation model and the accuracy of porosity. In addition, this evaluation scheme of irreducible water saturation may have regional limitations. The above-mentioned irreducible water saturation evaluation model may not be directly applicable to other research areas, but the method and process established by the above-mentioned irreducible water saturation evaluation model can be applied to other research areas. This study is mainly carried out on ultra-low porosity and permeability tight sandstone reservoirs. For other lithologic reservoirs, the applicability of the above-mentioned methods for establishing the irreducible water saturation evaluation model still needs further investigation. Accurate evaluation methods of irreducible water saturation and median pore throat radius in tight reservoirs also need further study.
The main conclusions of this study are as follows:
The irreducible water saturation of low-porosity and ultra-low-permeability sandstones determined based on the cumulative permeability contribution of the core mercury injection experiment is reliable.
The irreducible water saturation has a good relationship with the core median pore throat radius, and the median pore throat radius has a good correlation with porosity.
A method and model for evaluating porosity and then irreducible water saturation based on conventional logging data was established and applied to oilfield data processing. The interpretation and conclusion are consistent with the production test results, which confirms the correctness and feasibility of the method and model.
The method proposed in this article can better solve the problem of irreducible water saturation evaluation of low-porosity and ultra-low-permeability sandstone reservoirs, as long as porosity data is available, accurate irreducible water saturation can be obtained, which lays a foundation for further improving the prediction accuracy of fluid properties. It can be applied to the evaluation of low-porosity and ultra-low-permeability sandstone reservoirs in other areas as well.
The authors thank all the reviewers and editors for valuable comments.
Funding information: This work was supported by National Natural Science Foundation of China (Grant No. 42104126, 41774116), Science and Technology Research Project of Department of Education of Hubei Province, China (Grant No. Q20211309), PetroChina Innovation Foundation (Grant No. 2019D-5007-0303).
Conflict of interest: Authors state no conflict of interest.
Data availability statement: Some or all data, models, or code generated or used during the study are proprietary or confidential in nature and may only be provided with restrictions.
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