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<front>
<journal-meta>
<journal-id journal-id-type="publisher-id">Front. Earth Sci.</journal-id>
<journal-title>Frontiers in Earth Science</journal-title>
<abbrev-journal-title abbrev-type="pubmed">Front. Earth Sci.</abbrev-journal-title>
<issn pub-type="epub">2296-6463</issn>
<publisher>
<publisher-name>Frontiers Media S.A.</publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="publisher-id">1099848</article-id>
<article-id pub-id-type="doi">10.3389/feart.2022.1099848</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Earth Science</subject>
<subj-group>
<subject>Original Research</subject>
</subj-group>
</subj-group>
</article-categories>
<title-group>
<article-title>Resistivity correction and water saturation evaluation for calcareous tight sandstone reservoir: A case study of G oil field in Sichuan Basin</article-title>
<alt-title alt-title-type="left-running-head">Yu et al.</alt-title>
<alt-title alt-title-type="right-running-head">
<ext-link ext-link-type="uri" xlink:href="https://doi.org/10.3389/feart.2022.1099848">10.3389/feart.2022.1099848</ext-link>
</alt-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname>Yu</surname>
<given-names>Zhang</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
</contrib>
<contrib contrib-type="author" corresp="yes">
<name>
<surname>Jun</surname>
<given-names>Jia</given-names>
</name>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
<xref ref-type="corresp" rid="c001">&#x2a;</xref>
<uri xlink:href="https://loop.frontiersin.org/people/2068562/overview"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Hua</surname>
<given-names>Hu</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Yao</surname>
<given-names>Du</given-names>
</name>
<xref ref-type="aff" rid="aff3">
<sup>3</sup>
</xref>
<xref ref-type="aff" rid="aff4">
<sup>4</sup>
</xref>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Hongyi</surname>
<given-names>An</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Shi</surname>
<given-names>Fang</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
</contrib>
</contrib-group>
<aff id="aff1">
<sup>1</sup>
<institution>Exploration Business Department of PetroChina Southwest Oil and Gas Field Company</institution>, <addr-line>Chengdu</addr-line>, <country>China</country>
</aff>
<aff id="aff2">
<sup>2</sup>
<institution>College of Resource and Environmental Engineering</institution>, <institution>Mianyang Normal University</institution>, <addr-line>Mianyang</addr-line>, <country>China</country>
</aff>
<aff id="aff3">
<sup>3</sup>
<institution>State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation</institution>, <institution>Southwest Petroleum University</institution>, <addr-line>Chengdu</addr-line>, <country>China</country>
</aff>
<aff id="aff4">
<sup>4</sup>
<institution>School of Geoscience and Technology</institution>, <institution>Southwest Petroleum University</institution>, <addr-line>Chengdu</addr-line>, <country>China</country>
</aff>
<author-notes>
<fn fn-type="edited-by">
<p>
<bold>Edited by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/1582636/overview">Qiaomu Qi</ext-link>, Chengdu University of Technology, China</p>
</fn>
<fn fn-type="edited-by">
<p>
<bold>Reviewed by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/2104474/overview">Hongtao Wang</ext-link>, Chengdu University of Technology, China</p>
<p>
<ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/2106966/overview">Xiaobin Li</ext-link>, China National Petroleum Corporation, China</p>
</fn>
<corresp id="c001">&#x2a;Correspondence: Jia Jun, <email>e.cruiser@163.com</email>
</corresp>
<fn fn-type="other">
<p>This article was submitted to Structural Geology and Tectonics, a section of the journal Frontiers in Earth Science</p>
</fn>
</author-notes>
<pub-date pub-type="epub">
<day>04</day>
<month>01</month>
<year>2023</year>
</pub-date>
<pub-date pub-type="collection">
<year>2022</year>
</pub-date>
<volume>10</volume>
<elocation-id>1099848</elocation-id>
<history>
<date date-type="received">
<day>16</day>
<month>11</month>
<year>2022</year>
</date>
<date date-type="accepted">
<day>05</day>
<month>12</month>
<year>2022</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#xa9; 2023 Yu, Jun, Hua, Yao, Hongyi and Shi.</copyright-statement>
<copyright-year>2023</copyright-year>
<copyright-holder>Yu, Jun, Hua, Yao, Hongyi and Shi</copyright-holder>
<license xlink:href="http://creativecommons.org/licenses/by/4.0/">
<p>This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.</p>
</license>
</permissions>
<abstract>
<p>The calcareous tight sandstone reservoir of the Triassic Shaximiao Formation in the G oil field of the central Sichuan Basin has high calcium content and abnormally high resistivity, making it difficult to reveal the oil-bearing property, evaluate water saturation, and calculate geological reserves. In this work, a petrophysical volume model of calcareous tight sandstone was established through systematic petrophysics experiments and the analysis of the main control factors of oil bearing grade. A method of using conventional logging data to calculate the calcium content of the reservoir and correct the calcium content of resistivity was proposed. After resistivity correction, the water saturation of the tight calcareous sandstone reservoir was more accurately calculated based on variable rock-electro parameters. The results indicated that with the decrease in calcium content and the increase in feldspar content, the reconstructive effect of corrosion was enhanced, the physical properties and pore structure of the reservoir were improved, and the oil bearing grade increased. The calcium content of the reservoir can be continuously calculated by the volume model and the crossplot of logRt<sub>n</sub>/AC<sub>n</sub> and V<sub>ca</sub>/POR. The resistivity of the reservoir with a high calcium content can be corrected using the resistivity index of calcium content (I<sub>ca</sub>). In conjunction with the water saturation calculation model using variable parameters, the accuracy of calculated water saturation was 14% and 5.8% higher than the calculation results without resistivity correction and using fixed rock-electro parameters, which can satisfy the requirements for reservoir evaluation and the calculation accuracy of hydrocarbon reserves.</p>
</abstract>
<kwd-group>
<kwd>Sichuan Basin</kwd>
<kwd>calcareous tight sandstone</kwd>
<kwd>petrophysics</kwd>
<kwd>resistivity correction</kwd>
<kwd>water saturation</kwd>
</kwd-group>
<contract-sponsor id="cn001">National Natural Science Foundation of China<named-content content-type="fundref-id">10.13039/501100001809</named-content>
</contract-sponsor>
<contract-sponsor id="cn002">Sichuan Province Science and Technology Support Program<named-content content-type="fundref-id">10.13039/100012542</named-content>
</contract-sponsor>
</article-meta>
</front>
<body>
<sec id="s1">
<title>1 Introduction</title>
<p>In the past decade, unconventional hydrocarbon resources represented by tight oil/gas and shale oil/gas, have played an increasingly important role in world energy structures (<xref ref-type="bibr" rid="B36">Roberto, 2013</xref>; <xref ref-type="bibr" rid="B53">Zou et al., 2014</xref>). Unconventional oil and gas accounted for 25% of global oil production in 2018 (<xref ref-type="bibr" rid="B41">US EIA, 2018</xref>), with tight oil contributing significantly. The tight oil production in the United States alone reached 3.29 &#xd7; 10<sup>8</sup> t, pushing the oil production in the U.S. to the second-highest level (<xref ref-type="bibr" rid="B42">US EIA, 2019</xref>). Unlike conventional oil and gas exploitation, the exploitation in tight reservoirs has been a challenge due to the complex lithology and pore structure (<xref ref-type="bibr" rid="B9">Clarkson et al., 2012</xref>), strong heterogeneity (<xref ref-type="bibr" rid="B30">Liu, 2021</xref>), and difficulty in determining the controlling factors of oil bearing grade (<xref ref-type="bibr" rid="B10">Dai et al., 2012</xref>) and characterizing reservoir parameters (<xref ref-type="bibr" rid="B27">Li and Zhu, 2020</xref>).</p>
<p>Lithology identification is the foundation for tight reservoir evaluation and hydrocarbon exploitation (<xref ref-type="bibr" rid="B51">Zhang C. S. et al., 2019</xref>; <xref ref-type="bibr" rid="B35">Mateen et al., 2022</xref>). Mineral composition, structure, and cementation mode are directly related to the physical properties (<xref ref-type="bibr" rid="B16">Enkin et al., 2020</xref>; <xref ref-type="bibr" rid="B4">Bai et al., 2021</xref>), pore structure (<xref ref-type="bibr" rid="B39">Slatt and O&#x2019;Neal, 2011</xref>), and wettability of reservoirs (<xref ref-type="bibr" rid="B17">Esfahani and Haghighi, 2004</xref>; <xref ref-type="bibr" rid="B37">Sauerer et al., 2020</xref>), and affect the distribution of reservoir fluid (<xref ref-type="bibr" rid="B44">Wu et al., 2016</xref>) and the evaluation accuracy of reservoir parameters (<xref ref-type="bibr" rid="B1">Agbasi et al., 2018</xref>). Lithology can be identified by experimental test techniques, such as Scanning Electron Microscope (SEM) (<xref ref-type="bibr" rid="B21">Quaid et al., 2016</xref>; <xref ref-type="bibr" rid="B28">Li et al., 2017</xref>), Cast Thin Section (CTS) (<xref ref-type="bibr" rid="B6">Borazjani et al., 2016</xref>; <xref ref-type="bibr" rid="B14">Dong et al., 2019</xref>), X-Ray Diffraction (XRD) (<xref ref-type="bibr" rid="B22">Kahle et al., 2002</xref>), and Computed Tomography Scan (CT) (<xref ref-type="bibr" rid="B25">Kyle and Ketcham, 2015</xref>; <xref ref-type="bibr" rid="B33">Ma et al., 2017</xref>). However, the experimental results are discrete, and it is difficult to obtain the continuous lithological characterization along the Well shaft. In addition, the above techniques cannot be widely used due to the excessive cost. In recent years, statistical analysis techniques have been applied to lithology identification, such as Gradient Boosting Decision Trees (<xref ref-type="bibr" rid="B52">Zhang G. et al., 2019</xref>; <xref ref-type="bibr" rid="B12">Dev and Eden, 2019</xref>), Neural Networks (<xref ref-type="bibr" rid="B19">Gu et al., 2018</xref>; <xref ref-type="bibr" rid="B2">Ahmed et al., 2021</xref>), and Machine Learning techniques (<xref ref-type="bibr" rid="B40">Thinesh et al., 2022</xref>). However, the identification accuracy of the above statistics methods depends on the number and significance of samples, and their application is regionally restricted. Economical, efficient, and continuous logging data with high vertical resolution have become a crucial means for lithology identification. Previous studies plotted the crosslet by lithology-sensitive logging curves (<xref ref-type="bibr" rid="B5">Benoit et al., 1980</xref>; <xref ref-type="bibr" rid="B31">Liu et al., 2016</xref>) and identified the logging lithology using Elemental Capture Spectroscopy (ECS) logging (<xref ref-type="bibr" rid="B43">Wu et al., 2013</xref>), imaging logging (<xref ref-type="bibr" rid="B26">Lai et al., 2019</xref>), and multi-mineral model (<xref ref-type="bibr" rid="B7">Butt and Naseem, 2022</xref>). Crossplot has been widely used to identify the lithology of conventional reservoirs; however, it is less effective in identifying the complex lithology of tight sandstone reservoirs due to the similar logging response of complicated lithological components. Therefore, it is beneficial to refine the crossplot technique and improve its performance in identifying complex lithology in tight reservoirs.</p>
<p>Some calcareous tight sandstone reservoirs in the Triassic Shaximiao Formation in the G oil field of the central Sichuan Basin are characterized by high calcium content (&#x2265; 20%) and large variation in calcium content, which, together with the random distribution of calcium, complicates the lithology identification. The calcareous sandstone reservoir contains quartz and calcite, and the mineral content ratios are variables. As a result, the rock matrix value cannot be easily determined by logging evaluation. In addition, logging response characteristics are influenced by the change in calcium content, leading to large errors in lithology identification and reservoir parameters evaluation. At the same time, calcium will reduce the travel time of acoustic waves, increase the compensated density, and abnormally increase the resistivity of the sandstone reservoir (<xref ref-type="bibr" rid="B13">Djebbar and Erle, 2012</xref>). Consequently, the logging response characteristics between tight dry and oil reservoirs are easily confused, which further adversely affects fluid identification and hydrocarbon reserves calculation.</p>
<p>To address these problems, this paper analyzed the controlling factors of oil-bearing property in the calcareous tight sandstone reservoir through systematic petrophysical experiments, established the petrophysical volume model of calcareous tight sandstone, and uses optimized crossplot to extract lithology-sensitive logging curves to calculate the calcium content of the reservoir. On this basis, the resistivity index caused by calcium content (I<sub>ca</sub>) was proposed to correct the resistivity, then the water saturation of the calcareous tight sandstone reservoir was calculated by variable rock-electro parameters to eliminate the influence of calcium and improve the evaluation accuracy of the calcareous tight sandstone reservoir.</p>
</sec>
<sec id="s2">
<title>2 Geological setting</title>
<p>G oilfield is located in the north-central Sichuan Basin, with hilly terrain and an altitude of 300&#x2013;500&#xa0;m (<xref ref-type="fig" rid="F1">Figure 1</xref>). The northern part is higher than the southern part, and the exploration area is 1700&#xa0;km<sup>2</sup> (<xref ref-type="bibr" rid="B48">Yang et al., 2016</xref>). The regional geological structure is formed in Yanshanian, which is a long stripe-shaped anticline extending in an east-west direction with NE-EW stress orientation, and its main fault lies parallel to the tectonic axis. The targeted formation, Shaximiao Formation in the Middle Jurassic, is the main productive zone of the oilfield and is widely spread in this area, with a formation thickness of 600&#x2013;2200&#xa0;m and a buried depth of 2100&#x2013;2700&#xa0;m. The sedimentary type is inland freshwater lacustrine facies clastic sediment, dividing into S<sub>1</sub> and S<sub>2</sub> sub segments from the bottom up, and the lithology is mainly aubergine and grey-green mudstone interbedded with pale grey-green and grey-green sandstone (<xref ref-type="bibr" rid="B20">Huang et al., 2017</xref>). In recent years, tight sandstone oil/gas reservoirs in this region have proven reserves of over 100 million tons, making it one of the hot spots for unconventional hydrocarbon exploitation in China (<xref ref-type="bibr" rid="B49">Yang et al., 2022</xref>).</p>
<fig id="F1" position="float">
<label>FIGURE 1</label>
<caption>
<p>Geographical and structural location of G oilfield.</p>
</caption>
<graphic xlink:href="feart-10-1099848-g001.tif"/>
</fig>
</sec>
<sec id="s3">
<title>3 Methodologies</title>
<p>We collected core samples from 11 Wells with a high coring recovery rate and representative reservoir characteristics, prepared rock plug samples with diameters ranging from 25 to 80&#xa0;mm, and performed the petrophysical experiment in steps (<xref ref-type="fig" rid="F2">Figure 2</xref>).</p>
<fig id="F2" position="float">
<label>FIGURE 2</label>
<caption>
<p>Experiment and research flow chart.</p>
</caption>
<graphic xlink:href="feart-10-1099848-g002.tif"/>
</fig>
<p>X&#x2019;Pert MPD PRO was used in the X-ray diffraction (XRD) analysis. AniMR-Hole Core was used in the nuclear magnetic resonance (NMR) experiment (maximum sample size: 150mm &#xd7; 150mm &#xd7; 150&#xa0;mm). The automated mercury porosimeter Poremaster60&#xa0;GT was applied in the High-Pressure Mercury Injection (HPMI) experiment (pore-size distribution: 0.0036&#x2013;950um). The ion chromatography instrument ICS-5000 was employed in Anion Test (AT). The above experiments were completed in strict accordance with industry standards. The core samples used for the petroelectric test and conventional physical properties were pretreated beforehand by washing oil and salt using the carbon dioxide displacement method. Considering the influence of crystal water of clay minerals on pore structure, samples were dried at constant temperature and humidity (T&#x26;H: 70&#xb0;C, 40%).</p>
</sec>
<sec id="s4">
<title>4 Phenomena and results</title>
<sec id="s4-1">
<title>4.1 Lithologic characteristics</title>
<p>XRD results showed that the lithology of the Shaximiao Formation was mainly feldspar lithic sandstone and detritus feldspar sandstone (<xref ref-type="fig" rid="F3">Figure 3A</xref>). The mass fraction of quartz (w<sub>Q</sub>) and feldspar (w<sub>R</sub>) ranged from 22% to 72% and 4%&#x2013;48%, respectively, and their average values were 45.95% and 20.4%, respectively. The composition of debris was complicated, including sedimentary rock debris, igneous rock debris, metamorphics debris, and little mica (<xref ref-type="fig" rid="F3">Figure 3B</xref>). Laumontite was also found in some wells.</p>
<fig id="F3" position="float">
<label>FIGURE 3</label>
<caption>
<p>Lithology <bold>(A)</bold> and debris <bold>(B)</bold>.</p>
</caption>
<graphic xlink:href="feart-10-1099848-g003.tif"/>
</fig>
<p>Laumontite is a porous silicate mineral with a water frame structure formed by the alteration of intermediate basic pyroclastic and alkaline minerals in an environment of low temperature and alkaline water medium. It has a large number of micropores and cavities (<xref ref-type="bibr" rid="B32">Lu et al., 2004</xref>; <xref ref-type="bibr" rid="B8">Chipera et al., 2008</xref>).</p>
<p>Compared with common porous minerals, laumontite is much less dense than quartz, plagioclase, and calcite, with an average density of 2.3&#xa0;g/cm<sup>3</sup>. At the same time, due to its high specific surface area (SSA), laumontite can adsorb large amounts of water and has large neutron porosity (CNL&#x3e;31.3&#x2013;35.3%). In terms of electrochemistry, the hydrous cation in laumontite cannot migrate through the zeolite skeleton cavity, resulting in poor conductivity. Therefore, laumontite strata generally have high resistivity (<xref ref-type="bibr" rid="B47">Yang and Qiu, 2002</xref>).</p>
</sec>
<sec id="s4-2">
<title>4.2 Physical properties</title>
<p>The analysis of physical properties showed that Shaximiao Formation was a tight sandstone reservoir with low porosity and permeability. The porosity and permeability of the reservoir ranged from 2% to 10% and 0.01 mD to 0.5 mD, respectively. The means of porosity and permeability were 5.5% and 0.12 mD, respectively. Porosity less than 6% and permeability less than 0.1 mD contributed up to 77.8% and 79.3% to the core physical properties, respectively. In general, core porosity had a good correlation with permeability.</p>
</sec>
<sec id="s4-3">
<title>4.3 Pore structure characteristics</title>
<p>The analysis of rock thin section indicated that the pore types of the Shaximiao tight sandstone reservoir were dominated by residual intergranular pore (43.18%) (<xref ref-type="fig" rid="F4">Figure 4A</xref>), feldspar dissolution pore (23.35%) (<xref ref-type="fig" rid="F4">Figure 4B</xref>), and debris dissolution pore (21.28%) (<xref ref-type="fig" rid="F4">Figure 4C</xref>), followed by intergranular dissolution pore (<xref ref-type="fig" rid="F4">Figures 4D, E</xref>) and moldic pore (<xref ref-type="fig" rid="F4">Figure 4F</xref>). No microfractures appeared. According to statistical analysis, the more developed the residual intergranular pores and secondary dissolution pores, the better the reservoir pores, and the higher the areal porosity and core porosity.</p>
<fig id="F4" position="float">
<label>FIGURE 4</label>
<caption>
<p>Pore types of reservoir. <bold>(A)</bold> Residual intergranular pore. <bold>(B)</bold> Feldspar dissolution pore. <bold>(C)</bold> Debris dissolution pore. <bold>(D)</bold> Intergranular dissolution pore. <bold>(E)</bold> Intragranular dissolution pore. <bold>(F)</bold> Moldic pore.</p>
</caption>
<graphic xlink:href="feart-10-1099848-g004.tif"/>
</fig>
</sec>
</sec>
<sec id="s5">
<title>5 Analysis and discussions</title>
<sec id="s5-1">
<title>5.1 Influencing factors of oil-bearing grade</title>
<p>Oil bearing grade was synthetically influenced by generating, reservoiring and capping conditions, hydrocarbon charging degree, and reservoir characteristics (<xref ref-type="bibr" rid="B50">Zhang et al., 2017</xref>). To study the controlling factors of the oil-bearing grade of calcareous tight sandstone, this paper analyzed the interrelationships between oil bearing grade, lithology, physical properties, and pore types from the perspective of reservoir characteristics.</p>
<sec id="s5-1-1">
<title>5.1.1 Influence of lithology on physical properties</title>
<p>The analysis results on the correlation between physical properties and XRD experimental results demonstrated that calcium and feldspar had a greater influence on the physical properties of the reservoir in the Shaximiao Formation. Overall, as the calcium content decreased and the feldspar content increased, the porosity and permeability continued to rise, while the correlation between the content of quartz, clay, and physical properties was not significant (<xref ref-type="fig" rid="F5">Figure 5</xref>). However, a few samples with a high feldspar content but a low calcium content (g21-3-2, g46-1, g46-2) still had poor physical properties. The rock thin section analysis revealed that their residual intergranular pores and secondary dissolution pores were underdeveloped, and part of the pore space was filled by asphalt.</p>
<fig id="F5" position="float">
<label>FIGURE 5</label>
<caption>
<p>Correlation between feldspar, calcium, and clay content with porosity and permeability. <bold>(A)</bold> Crossplot between core porosity and calcium content. <bold>(B)</bold> Crossplot between core permeability and calcium content. <bold>(C)</bold> Crossplot between core porosity and feldspar content. <bold>(D)</bold> Crossplot between core permeability and feldspar content. <bold>(E)</bold> Crossplot between core porosity and clay content. <bold>(F)</bold> Crossplot between core permeability and clay content.</p>
</caption>
<graphic xlink:href="feart-10-1099848-g005.tif"/>
</fig>
</sec>
<sec id="s5-1-2">
<title>5.1.2 Influence of lithology and dissolution on pore structure</title>
<p>Many studies have confirmed that there is a connection between T<sub>2</sub> spectrum distribution and pore radius (<xref ref-type="bibr" rid="B34">Mao and He, 2005</xref>). In this paper, the pore structure of the core was investigated by NMR T<sub>2</sub> spectra (<xref ref-type="bibr" rid="B45">Yan et al., 2017</xref>; <xref ref-type="bibr" rid="B46">Yan et al., 2020</xref>), and the relationship between the T<sub>2</sub> spectrum and calcium and feldspar content in the core was further analyzed.</p>
<p>From the test results, for the core samples with calcium content greater than 2%, the transverse relaxation time (T<sub>2</sub>) ranged from 0.01&#x2013;3&#xa0;ms, and the curve exhibited a unimodal distribution of the T<sub>2</sub> spectrum. For core samples with calcium content less than 2%, one part of the curve still showed a unimodal distribution and T<sub>2</sub> between 0.05&#x2013;6&#xa0;ms, while the other part exhibited bimodal characteristics and T<sub>2</sub> between 4&#x2013;200&#xa0;m after the peak (<xref ref-type="fig" rid="F6">Figure 6A</xref>). When the feldspar content of core samples was less than 30%, the curve exhibited a unimodal distribution, and T<sub>2</sub> ranged from 0.02 to 3&#xa0;m. When the content was greater than 30%, most of the distribution curve exhibited bimodal characteristics, and T<sub>2</sub> was in the range of 7&#x2013;200&#xa0;m after the first peak (<xref ref-type="fig" rid="F6">Figure 6B</xref>). In other words, low calcium content, high feldspar content, and good physical properties were the basis for high-quality reservoir space. However, the pore structure of some core samples which can meet the above conditions was still not ideal (<xref ref-type="fig" rid="F7">Figure 7A</xref>), and the reconstructive effect of corrosion of the pore space of such cores was weak. However, the pore structure gradually becomes better with the development of dissolution pores and the increase in secondary areal porosity (<xref ref-type="fig" rid="F7">Figures 7B, C</xref>).</p>
<fig id="F6" position="float">
<label>FIGURE 6</label>
<caption>
<p>NMR T<sub>2</sub> spectrum of core samples with different calcium <bold>(A)</bold> and feldspar <bold>(B)</bold> content.</p>
</caption>
<graphic xlink:href="feart-10-1099848-g006.tif"/>
</fig>
<fig id="F7" position="float">
<label>FIGURE 7</label>
<caption>
<p>NMR T<sub>2</sub> spectrum of core with different development degrees of dissolution pores. <bold>(A)</bold> No.G46-1, low calcium content (0.76%), high feldspar content (46%), undeveloped dissolution pores (secondary surface porosity &#x3d; 1.5%), poor pore structure. <bold>(B)</bold> No.G27-3-2, low calcium content (1.39%), high feldspar content (42.8%), dissolution pores developed (secondary areal porosity 3.5%), better pore structure. <bold>(C)</bold> No.G104-1-2, low calcium (0.76%), high feldspar content (46%), dissolution pores developed (secondary areal porosity 3.8%), good pore structure.</p>
</caption>
<graphic xlink:href="feart-10-1099848-g007.tif"/>
</fig>
</sec>
<sec id="s5-1-3">
<title>5.1.3 Influence of physical properties and pore structure on oil-bearing grade</title>
<p>The porosity, permeability, and NMR T<sub>2</sub> spectral characteristics of core samples in different oil-bearing grades indicated that the porosity of oily cores mainly ranged from 6% to 12% and the permeability was generally greater than 0.05 mD. Therefore, the physical properties of oily cores were better than those of oil-free cores (<xref ref-type="fig" rid="F8">Figure 8</xref>). Regarding the pore structure characteristics, the T<sub>2</sub> spectrum of oily cores showed a bimodal distribution (<xref ref-type="bibr" rid="B11">Daigle and Johnson, 2015</xref>; <xref ref-type="bibr" rid="B18">Gong and Liu, 2020</xref>), T<sub>2</sub> ranged from 0.4 to 3&#xa0;m and 7&#x2013;200&#xa0;m. In addition to micropores, meso- and macropores were also developed in oily cores to some extent. The T<sub>2</sub> distribution curves of oil-free cores were almost unimodal and T<sub>2</sub> ranged from 0.3 to 1.5&#xa0;m. The samples were dominated by small- and micropores, with poor pore structure and weak permeability (<xref ref-type="bibr" rid="B38">Shao et al., 2017</xref>).</p>
<fig id="F8" position="float">
<label>FIGURE 8</label>
<caption>
<p>Variation of oil-bearing grade with physical properties and pore structure (Well G27)</p>
</caption>
<graphic xlink:href="feart-10-1099848-g008.tif"/>
</fig>
</sec>
</sec>
<sec id="s5-2">
<title>5.2 Resistivity correction for the effect of calcium content</title>
<p>In conventional sandstone reservoirs, resistivity logging curves were used to analyze the fluid properties and distribution features. Under similar reservoir conditions, the resistivity of the oil-bearing interval was greater than that of the oil-free interval. Based on classic <xref ref-type="bibr" rid="B3">Archie (1942)</xref>&#x2019;s formula, water saturation can be calculated by resistivity curves. However, due to the high calcium content in the tight reservoir in the study area, in the oil-free interval, the resistivity increased significantly and the calculated water saturation was low, resulting in an inaccurate reflection of the oil content of the reservoir. Therefore, in order to eliminate the influence of calcium on resistivity, the calcium of resistivity must be corrected before evaluating the saturation of calcareous tight sandstone reservoir with resistivity logging.</p>
<sec id="s5-2-1">
<title>5.2.1 Calculation of calcium content</title>
<p>XRD results were used to calibrate logging curves. The logging response of intervals with high calcium content (V<sub>ca</sub>) was characterized by short acoustic travel time (AC) and increased resistivity (Rt), and there was no significant correlation between other logging curves. By analyzing the crossplot of AC and logRt with V<sub>ca</sub> of corresponding reservoir intervals, it was found that their correlation was low, which indicated that apart from lithology (calcium content), AC was also influenced by porosity, and resistivity was influenced by porosity and the formation water salinity (R<sub>W</sub>).</p>
<p>Given that the study intervals belong to the same sedimentary type and their R<sub>W</sub> is close, the influence of R<sub>W</sub> on Rt could be ignored. As the calcium content increased, AC and POR decreased, logRt increased, and the variation trends of V<sub>ca</sub>/POR and logRt/AC were the same. Although the correlation between logRt/AC and V<sub>ca</sub>/POR (<xref ref-type="fig" rid="F9">Figure 9</xref>) was higher than that of AC, logRt, and V<sub>ca</sub> of corresponding intervals, it still did not satisfy the accuracy requirements for log evaluation. According to the analysis, the dimensional differences of data between logRt and AC might lead to a low correlation, and the difference of R<sub>W</sub> between Wells might also lead to the deviation of Rt.</p>
<fig id="F9" position="float">
<label>FIGURE 9</label>
<caption>
<p>Crossplot between logRt/AC and V<sub>ca</sub>/POR.</p>
</caption>
<graphic xlink:href="feart-10-1099848-g009.tif"/>
</fig>
<p>The crossplot of logRtn/ACn and Vca/POR (<xref ref-type="fig" rid="F10">Figure 10</xref>) was plotted to weaken the influence of the above factors, that is, the relationship between logging response characteristics and calcium content (Vca) was analyzed with relative variation trends of logRt and AC, instead of their concrete values (<xref ref-type="bibr" rid="B29">Li et al., 2022</xref>). After normalization, the values of logRt and AC ranged from 0 to 1. When Vca increased, Rt increased, and AC decreased. The variation trends of Rt and AC were opposite. The normalized ratios could effectively reflect the variation features of logging-sensitive curves caused by Vca change. In addition, the normalized logRt attenuated the influence of the different resistivity of formation water among Wells. The results indicated that logRtn/ACn was highly correlated with Vca/POR, and the model to calculate Vca was derived (Eq. <xref ref-type="disp-formula" rid="e1">1</xref>):<disp-formula id="e1">
<mml:math id="m1">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">V</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">c</mml:mi>
<mml:mi mathvariant="normal">a</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>2.676</mml:mn>
<mml:mo>&#xd7;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="normal">l</mml:mi>
<mml:mi mathvariant="normal">o</mml:mi>
<mml:mi mathvariant="normal">g</mml:mi>
<mml:mi mathvariant="normal">R</mml:mi>
<mml:mi mathvariant="normal">t</mml:mi>
</mml:mrow>
<mml:mi mathvariant="normal">n</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="normal">A</mml:mi>
<mml:mi mathvariant="normal">C</mml:mi>
</mml:mrow>
<mml:mi mathvariant="normal">n</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>0.367</mml:mn>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#xd7;</mml:mo>
<mml:mo>&#x3a6;</mml:mo>
</mml:mrow>
</mml:math>
<label>(1)</label>
</disp-formula>where V<sub>ca</sub> is the calcium content, %; logRt<sub>n</sub> is the normalized logRt, fraction; AC<sub>n</sub> is the normalized AC, f; and &#x3a6; is the porosity, %.</p>
<fig id="F10" position="float">
<label>FIGURE 10</label>
<caption>
<p>Crossplot between logRt<sub>n</sub>/AC<sub>n</sub> and V<sub>ca</sub>/POR.</p>
</caption>
<graphic xlink:href="feart-10-1099848-g010.tif"/>
</fig>
<p>The above model of V<sub>ca</sub> indicates that obtaining reliable porosity is the prerequisite for the accurate calculation of V<sub>ca</sub>. To this end, we proposed the petrophysical volume model that considers calcareous content (<xref ref-type="fig" rid="F11">Figure 11</xref>) and established logging response equations (Eqs. <xref ref-type="disp-formula" rid="e2">2</xref>, <xref ref-type="disp-formula" rid="e3">3</xref>).<disp-formula id="e2">
<mml:math id="m2">
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x3d;</mml:mo>
<mml:mo>&#x3a6;</mml:mo>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi mathvariant="normal">V</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">c</mml:mi>
<mml:mi mathvariant="normal">a</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi mathvariant="normal">V</mml:mi>
<mml:mi mathvariant="normal">m</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
<label>(2)</label>
</disp-formula>
<disp-formula id="e3">
<mml:math id="m3">
<mml:mrow>
<mml:mi mathvariant="normal">A</mml:mi>
<mml:mi mathvariant="normal">C</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="normal">D</mml:mi>
<mml:mi mathvariant="normal">T</mml:mi>
</mml:mrow>
<mml:mi mathvariant="normal">f</mml:mi>
</mml:msub>
<mml:mo>&#xd7;</mml:mo>
<mml:mo>&#x3a6;</mml:mo>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="normal">D</mml:mi>
<mml:mi mathvariant="normal">T</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="normal">c</mml:mi>
<mml:mi mathvariant="normal">a</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#xd7;</mml:mo>
<mml:msub>
<mml:mi mathvariant="normal">V</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">c</mml:mi>
<mml:mi mathvariant="normal">a</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="normal">D</mml:mi>
<mml:mi mathvariant="normal">T</mml:mi>
</mml:mrow>
<mml:mi mathvariant="normal">m</mml:mi>
</mml:msub>
<mml:mo>&#xd7;</mml:mo>
<mml:msub>
<mml:mi mathvariant="normal">V</mml:mi>
<mml:mi mathvariant="normal">m</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
<label>(3)</label>
</disp-formula>where &#x3a6; is the porosity, %; DT<sub>f</sub> is the travel time of fluid, 189&#xa0;&#x3bc;s/ft; and DT<sub>ca</sub> is the travel time of calcium, 47.5&#xa0;&#x3bc;s/ft. DT<sub>m</sub> is the travel time of the matrix, DT<sub>m</sub> is in the range of 51&#x2013;58&#xa0;&#x3bc;s/ft, V<sub>ca</sub> is the calcium content, %; and V<sub>m</sub> is the matrix volume, %.</p>
<fig id="F11" position="float">
<label>FIGURE 11</label>
<caption>
<p>Petrophysical volume model of calcareous sandstone.</p>
</caption>
<graphic xlink:href="feart-10-1099848-g011.tif"/>
</fig>
<p>By combining Eqs. <xref ref-type="disp-formula" rid="e1">1</xref>&#x2013;<xref ref-type="disp-formula" rid="e3">3</xref>, the calculation model of porosity was obtained (Eq. <xref ref-type="disp-formula" rid="e4">4</xref>):<disp-formula id="e4">
<mml:math id="m4">
<mml:mrow>
<mml:mo>&#x3a6;</mml:mo>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mi mathvariant="normal">A</mml:mi>
<mml:mi mathvariant="normal">C</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="normal">D</mml:mi>
<mml:mi mathvariant="normal">T</mml:mi>
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<mml:mi mathvariant="normal">m</mml:mi>
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</mml:mrow>
<mml:mrow>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="normal">D</mml:mi>
<mml:mi mathvariant="normal">T</mml:mi>
</mml:mrow>
<mml:mi mathvariant="normal">f</mml:mi>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="normal">D</mml:mi>
<mml:mi mathvariant="normal">T</mml:mi>
</mml:mrow>
<mml:mi mathvariant="normal">m</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x2b;</mml:mo>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="normal">D</mml:mi>
<mml:mi mathvariant="normal">T</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="normal">c</mml:mi>
<mml:mi mathvariant="normal">a</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="normal">D</mml:mi>
<mml:mi mathvariant="normal">T</mml:mi>
</mml:mrow>
<mml:mi mathvariant="normal">m</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#xd7;</mml:mo>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>2.676</mml:mn>
<mml:mo>&#xd7;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="normal">l</mml:mi>
<mml:mi mathvariant="normal">o</mml:mi>
<mml:mi mathvariant="normal">g</mml:mi>
<mml:mi mathvariant="normal">R</mml:mi>
<mml:mi mathvariant="normal">t</mml:mi>
</mml:mrow>
<mml:mi mathvariant="normal">n</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="normal">A</mml:mi>
<mml:mi mathvariant="normal">C</mml:mi>
</mml:mrow>
<mml:mi mathvariant="normal">n</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>0.367</mml:mn>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:math>
<label>(4)</label>
</disp-formula>
</p>
</sec>
<sec id="s5-2-2">
<title>5.2.2 Resistivity correction for the effect of calcium content</title>
<p>In reservoir intervals with high calcium content, calcium will significantly increase the deep lateral resistivity, up to 1000&#xa0;&#x3a9;&#xa0;m. The influence of calcium on resistivity is greater than the effect of fluid properties on resistivity. In accordance with the principle of resistivity logging, the existence of calcium is equivalent to the addition of a heterogeneous and stochastically varying resistivity to the homogeneous sandstone reservoir. In addition, its influence on formation resistivity is closely related to the degree of homogeneity. When the calcium is homogeneously distributed, it is equivalent to high resistance in parallel in the formation, and the influence is limited. When the distribution of calcium is heterogeneous, the formation is equivalent to a high resistance sometimes in series and sometimes in parallel, which will have a significant impact on the formation resistivity. In this case, the water saturation calculation by Archie&#x2019;s formula based on resistivity logging will be greatly affected. The followings are two common scenarios: (1) The water or dry layers with high calcium content are mistaken for oil-water or oil layers. (2) Low-resistivity oil zones with low calcium content are mistaken for water layers.</p>
<p>In order to eliminate the influence of calcium content on water saturation calculation, it is necessary to correct the calcium content of resistivity. In the classic <xref ref-type="bibr" rid="B3">Archie (1942)</xref>&#x2019;s formula, the contribution of oil and gas to resistivity is manifested by the resistivity index, I (I&#x3d;Rt/Rw). Based on the above principle, in this study, the resistivity index caused by calcium content was defined as Ica, which is the ratio of the resistivity of calcareous formation (logRtca) to that of sandstone formation (logRt). The regression analysis on calcium content (Vca) and Ica showed that they had a good linear relationship, and the correlation coefficient was 0.93 (<xref ref-type="fig" rid="F12">Figure 12</xref>).<disp-formula id="e5">
<mml:math id="m5">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">I</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">c</mml:mi>
<mml:mi mathvariant="normal">a</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mi mathvariant="normal">l</mml:mi>
<mml:mi mathvariant="normal">o</mml:mi>
<mml:mi mathvariant="normal">g</mml:mi>
<mml:mi mathvariant="normal">R</mml:mi>
<mml:msub>
<mml:mi mathvariant="normal">t</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">c</mml:mi>
<mml:mi mathvariant="normal">a</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="normal">l</mml:mi>
<mml:mi mathvariant="normal">o</mml:mi>
<mml:mi mathvariant="normal">g</mml:mi>
<mml:mi mathvariant="normal">R</mml:mi>
<mml:mi mathvariant="normal">t</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>0.0257</mml:mn>
<mml:mo>&#xd7;</mml:mo>
<mml:msub>
<mml:mi mathvariant="normal">V</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">c</mml:mi>
<mml:mi mathvariant="normal">a</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:mn>0.98</mml:mn>
</mml:mrow>
</mml:math>
<label>(5)</label>
</disp-formula>
</p>
<fig id="F12" position="float">
<label>FIGURE 12</label>
<caption>
<p>Crossplot between I<sub>ca</sub> and V<sub>ca</sub>.</p>
</caption>
<graphic xlink:href="feart-10-1099848-g012.tif"/>
</fig>
<p>Then, the correction model for calcium content of resistivity was obtained as follows:<disp-formula id="e6">
<mml:math id="m6">
<mml:mrow>
<mml:mi mathvariant="normal">R</mml:mi>
<mml:mi mathvariant="normal">t</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mi mathvariant="normal">R</mml:mi>
<mml:msub>
<mml:mi mathvariant="normal">t</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">c</mml:mi>
<mml:mi mathvariant="normal">a</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#xd7;</mml:mo>
<mml:msup>
<mml:msub>
<mml:mi mathvariant="normal">I</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">c</mml:mi>
<mml:mi mathvariant="normal">a</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msup>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mi mathvariant="normal">R</mml:mi>
<mml:msub>
<mml:mi mathvariant="normal">t</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">c</mml:mi>
<mml:mi mathvariant="normal">a</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:mn>0.0257</mml:mn>
<mml:mo>&#xd7;</mml:mo>
<mml:msub>
<mml:mi mathvariant="normal">V</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">c</mml:mi>
<mml:mi mathvariant="normal">a</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:mn>0.98</mml:mn>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:math>
<label>(6)</label>
</disp-formula>
</p>
<p>The above method was used to correct the calcium content of resistivity in Well G30. The resistivity of the calcium-free interval (2510&#x2013;2530&#xa0;m) did not change before and after correction, while that of intervals with a high calcium content (2546&#x2013;2550m, 2554&#x2013;2560m) decreased significantly after correction (<xref ref-type="fig" rid="F13">Figure 13</xref>). The calculated calcium content and porosity were in good accordance with those from the core analysis. The calcium content and porosity of Wells G21, G27, G30, G36, and G104 were calculated and compared with analyzed calcium content and porosity. Both calculation and analyzed results were in high agreement. The average absolute errors of porosity and calcium content were 3.8% (<xref ref-type="fig" rid="F14">Figure 14</xref>) and 4.2% (<xref ref-type="fig" rid="F15">Figure 15</xref>), respectively.</p>
<fig id="F13" position="float">
<label>FIGURE 13</label>
<caption>
<p>Resistivity correction of Well G30.</p>
</caption>
<graphic xlink:href="feart-10-1099848-g013.tif"/>
</fig>
<fig id="F14" position="float">
<label>FIGURE 14</label>
<caption>
<p>Crossplot between core analysis and calculated porosity.</p>
</caption>
<graphic xlink:href="feart-10-1099848-g014.tif"/>
</fig>
<fig id="F15" position="float">
<label>FIGURE 15</label>
<caption>
<p>Crossplot between core analysis and calculated calcium content.</p>
</caption>
<graphic xlink:href="feart-10-1099848-g015.tif"/>
</fig>
</sec>
</sec>
<sec id="s5-3">
<title>5.3 Water-saturation calculation of calcareous tight sandstone</title>
<p>Based on resistivity correction, the water saturation of the calcareous sandstone reservoir could be calculated by Archie&#x2019;s formula. As the key parameters in Archie&#x2019;s formula, rock-electro parameters have a direct impact on the calculation accuracy of water saturation and are usually obtained by rock electricity experiments at high pressure and temperature.</p>
<sec id="s5-3-1">
<title>5.3.1 Archie parameters</title>
<sec id="s5-3-1-1">
<title>5.3.1.1 Fixed Archie parameters</title>
<p>In the rock electricity experiment, it was found that some cores were oversaturated, that is, the actual water inflow exceeded the theoretical water inflow of pores by 22%. By comparing XRD and CTS results for this type of core, it was found that the oversaturation was caused by laumontite cementation in cores. The crystal structure of laumontite contains a lot of cavities and canals and is in the shape of a porous sponge (<xref ref-type="bibr" rid="B24">Koporulin, 2013</xref>). After a long time of pressure saturation, water flows into laumontite to form zeolitic water, which can conduct electricity, similar to bound water. In addition, due to the unbalanced electrovalence generated by the displacement of silicon by aluminum, alkali metal ions and water molecules can move between the crystal lattice of laumontite, making the laumontite itself conductive and affecting the accurate calculation of rock-electro parameters.</p>
<p>Due to the above factors, the resistivity of the oversaturated rock decreased significantly, resulting in small F values of samples. By comparison, the n parameter was unrelated to saturation, therefore, oversaturation did not affect n values. After excluding the oversaturated core samples, the parameters of Archie&#x2019;s formula were determined as a &#x3d; 1, b &#x3d; 1, m &#x3d; 1.798, and <italic>n</italic> &#x3d; 2.904 (<xref ref-type="fig" rid="F16">Figure 16</xref>). However, the influence of the reservoir heterogeneity (lithology, physical property) was not considered in the saturation calculation using fixed rock-electro parameters.</p>
<fig id="F16" position="float">
<label>FIGURE 16</label>
<caption>
<p>Rock-electro parameters. <bold>(A)</bold> Crossplot between F and&#x3c6;. <bold>(B)</bold> Crossplot between I and S<sub>w</sub>. <bold>(C)</bold> Crossplot between m and &#x3a6;. <bold>(D)</bold> Crossplot between n and S<sub>w</sub>.</p>
</caption>
<graphic xlink:href="feart-10-1099848-g016.tif"/>
</fig>
</sec>
<sec id="s5-3-1-2">
<title>5.3.1.2 Variable Archie parameters</title>
<p>The analysis of the relationship between m, n, and porosity revealed that there was a piecewise functional relationship between m and porosity, and a linear functional relationship between n and porosity. In addition, m and n of calcic samples were greater than those of calcium-free samples. When m and n were fixed, the calculation of S<sub>w</sub> must have errors. Therefore, considering the relationship between porosity, m, and n, a statistical regression model was proposed to calculate m and n by porosity. The calculation model for n is as follows (Eq. <xref ref-type="disp-formula" rid="e7">7</xref>):<disp-formula id="e7">
<mml:math id="m7">
<mml:mrow>
<mml:mi mathvariant="normal">n</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>0.2562</mml:mn>
<mml:mo>&#xd7;</mml:mo>
<mml:mo>&#x3a6;</mml:mo>
<mml:mo>&#x2b;</mml:mo>
<mml:mn>4.5575</mml:mn>
</mml:mrow>
</mml:math>
<label>(7)</label>
</disp-formula>
</p>
<p>Taking porosity of 6.5% as the boundary value, the piecewise calculation model of m was obtained (Eqs. <xref ref-type="disp-formula" rid="e8">8</xref>, <xref ref-type="disp-formula" rid="e9">9</xref>):<disp-formula id="e8">
<mml:math id="m8">
<mml:mrow>
<mml:mo>&#x3a6;</mml:mo>
<mml:mo>&#x3e;</mml:mo>
<mml:mn>6.5</mml:mn>
<mml:mo>%</mml:mo>
<mml:mo>,</mml:mo>
<mml:mi mathvariant="normal">m</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:math>
<label>(8)</label>
</disp-formula>
<disp-formula id="e9">
<mml:math id="m9">
<mml:mrow>
<mml:mo>&#x3a6;</mml:mo>
<mml:mo>&#x3c;</mml:mo>
<mml:mn>6.5</mml:mn>
<mml:mo>%</mml:mo>
<mml:mo>,</mml:mo>
<mml:mi mathvariant="normal">m</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>0.1281</mml:mn>
<mml:mo>&#xd7;</mml:mo>
<mml:mo>&#x3a6;</mml:mo>
<mml:mo>&#x2b;</mml:mo>
<mml:mn>1.2</mml:mn>
</mml:mrow>
</mml:math>
<label>(9)</label>
</disp-formula>
</p>
</sec>
</sec>
<sec id="s5-3-2">
<title>5.3.2 <italic>In-situ</italic> application</title>
<p>Archie&#x2019;s formula with fixed and variable parameters was used to calculate S<sub>w</sub> of Well G21 (<xref ref-type="fig" rid="F17">Figure 17</xref>).</p>
<fig id="F17" position="float">
<label>FIGURE 17</label>
<caption>
<p>Comprehensive interpretation of Well G21.</p>
</caption>
<graphic xlink:href="feart-10-1099848-g017.tif"/>
</fig>
<p>The core analysis showed that V<sub>ca</sub> and S<sub>w</sub> of intervals between 2211.8&#x2013;2213.3 m, 2228.9&#x2013;2230.8 m, 2236.2&#x2013;2238.3 m, and 2252.7&#x2013;2255.3&#xa0;m ranged in 2.7&#x2013;34.7% and 62&#x2013;84.5%, respectively. The logging curves were characterized by abnormally low GR and high resistivity responses due to the influence of calcium on the above intervals. In previous studies, S<sub>w</sub> measured by the classic Archie&#x2019;s formula without calcium correction for resistivity ranged from 20.5% to 54%, obviously lower than the results from the core analysis. Logging interpretation misidentified intervals as productive strata. After calcium correction, S<sub>w</sub> calculated by the model with fixed and variable parameters ranged from 56.5&#x2013;79% and 60&#x2013;83%, respectively, close to the results from the core analysis. Logging interpretation corrected intervals as unproductive strata, and hydraulic fracturing tests confirmed that no industrial oil flowed in the above intervals.</p>
<p>The above methods were adopted to measure the S<sub>w</sub> of Wells in the study area, and the results were compared with calculations and core irreducible water saturation (S<sub>wir</sub>) in previous studies (<xref ref-type="table" rid="T1">Table 1</xref>). The mean absolute error of S<sub>w</sub> in previous research was 18.5%. After calcium correction of resistivity, the mean absolute error of S<sub>w</sub> measured by Archie&#x2019;s model with fixed and variable parameters was 10.3% and 4.5%, respectively. The errors were significantly reduced and met the accuracy requirements of reservoir evaluation and oil reserves calculation.</p>
<table-wrap id="T1" position="float">
<label>TABLE 1</label>
<caption>
<p>Water saturation calculation results with different methods.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th rowspan="3" align="center">Core no.</th>
<th rowspan="3" align="center">Core analysis water saturation (%)</th>
<th rowspan="2" colspan="2" align="center">Previous calculation resultsact (%)</th>
<th colspan="4" align="center">Correcting resistivity</th>
</tr>
<tr>
<th colspan="2" align="center">Fixed rock-electro parameters (%)</th>
<th colspan="2" align="center">Variable rock-electro parameters (%)</th>
</tr>
<tr>
<th align="center">Calculated value</th>
<th align="center">Absolute error</th>
<th align="center">Calculated value</th>
<th align="center">Absolute error</th>
<th align="center">Calculated value</th>
<th align="center">Absolute error</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">1</td>
<td align="center">39.5</td>
<td align="center">14.5</td>
<td align="center">25.0</td>
<td align="center">25.0</td>
<td align="center">14.5</td>
<td align="center">35.5</td>
<td align="center">4.0</td>
</tr>
<tr>
<td align="center">2</td>
<td align="center">38.0</td>
<td align="center">20.0</td>
<td align="center">18.0</td>
<td align="center">27.0</td>
<td align="center">11.0</td>
<td align="center">35.0</td>
<td align="center">3.0</td>
</tr>
<tr>
<td align="center">3</td>
<td align="center">37.5</td>
<td align="center">25.0</td>
<td align="center">12.5</td>
<td align="center">26.0</td>
<td align="center">11.5</td>
<td align="center">34.5</td>
<td align="center">3.0</td>
</tr>
<tr>
<td align="center">4</td>
<td align="center">52.0</td>
<td align="center">16.5</td>
<td align="center">35.5</td>
<td align="center">34.5</td>
<td align="center">17.5</td>
<td align="center">48.5</td>
<td align="center">3.5</td>
</tr>
<tr>
<td align="center">5</td>
<td align="center">51.5</td>
<td align="center">25.0</td>
<td align="center">26.5</td>
<td align="center">43.0</td>
<td align="center">8.5</td>
<td align="center">49.0</td>
<td align="center">2.5</td>
</tr>
<tr>
<td align="center">6</td>
<td align="center">48.5</td>
<td align="center">35.0</td>
<td align="center">13.5</td>
<td align="center">40.0</td>
<td align="center">8.5</td>
<td align="center">41.0</td>
<td align="center">7.5</td>
</tr>
<tr>
<td align="center">7</td>
<td align="center">62.5</td>
<td align="center">28.0</td>
<td align="center">34.5</td>
<td align="center">42.0</td>
<td align="center">20.5</td>
<td align="center">50.5</td>
<td align="center">12.0</td>
</tr>
<tr>
<td align="center">8</td>
<td align="center">53.5</td>
<td align="center">44.0</td>
<td align="center">9.5</td>
<td align="center">63.0</td>
<td align="center">9.5</td>
<td align="center">60.0</td>
<td align="center">6.5</td>
</tr>
<tr>
<td align="center">9</td>
<td align="center">67.0</td>
<td align="center">37.5</td>
<td align="center">29.5</td>
<td align="center">60.0</td>
<td align="center">7.0</td>
<td align="center">61.6</td>
<td align="center">5.4</td>
</tr>
<tr>
<td align="center">10</td>
<td align="center">65.0</td>
<td align="center">31.0</td>
<td align="center">34.0</td>
<td align="center">54.0</td>
<td align="center">11.0</td>
<td align="center">58.0</td>
<td align="center">7.0</td>
</tr>
<tr>
<td align="center">11</td>
<td align="center">70.0</td>
<td align="center">34.0</td>
<td align="center">36.0</td>
<td align="center">78.5</td>
<td align="center">8.5</td>
<td align="center">72.5</td>
<td align="center">2.5</td>
</tr>
<tr>
<td align="center">12</td>
<td align="center">71.0</td>
<td align="center">45.5</td>
<td align="center">25.5</td>
<td align="center">78.0</td>
<td align="center">7.0</td>
<td align="center">76.0</td>
<td align="center">5.0</td>
</tr>
<tr>
<td align="center">13</td>
<td align="center">64.5</td>
<td align="center">47.0</td>
<td align="center">17.5</td>
<td align="center">55.0</td>
<td align="center">9.5</td>
<td align="center">60.5</td>
<td align="center">4.0</td>
</tr>
<tr>
<td align="center">14</td>
<td align="center">62.0</td>
<td align="center">51.0</td>
<td align="center">11.0</td>
<td align="center">57.0</td>
<td align="center">5.0</td>
<td align="center">53.0</td>
<td align="center">9.0</td>
</tr>
<tr>
<td align="center">15</td>
<td align="center">64.0</td>
<td align="center">56.5</td>
<td align="center">7.5</td>
<td align="center">56.0</td>
<td align="center">8.0</td>
<td align="center">60.5</td>
<td align="center">3.5</td>
</tr>
<tr>
<td align="center">16</td>
<td align="center">64.0</td>
<td align="center">61.0</td>
<td align="center">3.0</td>
<td align="center">69.5</td>
<td align="center">5.5</td>
<td align="center">67.0</td>
<td align="center">3.0</td>
</tr>
<tr>
<td align="center">17</td>
<td align="center">62.0</td>
<td align="center">60.0</td>
<td align="center">2.0</td>
<td align="center">55.0</td>
<td align="center">7.0</td>
<td align="center">56.0</td>
<td align="center">6.0</td>
</tr>
<tr>
<td align="center">18</td>
<td align="center">70.0</td>
<td align="center">75.0</td>
<td align="center">5.0</td>
<td align="center">90.0</td>
<td align="center">20.0</td>
<td align="center">71.5</td>
<td align="center">1.5</td>
</tr>
<tr>
<td align="center">19</td>
<td align="center">65.5</td>
<td align="center">82.0</td>
<td align="center">16.5</td>
<td align="center">56.0</td>
<td align="center">9.5</td>
<td align="center">65.0</td>
<td align="center">0.5</td>
</tr>
<tr>
<td align="center">20</td>
<td align="center">69.0</td>
<td align="center">85.0</td>
<td align="center">16.0</td>
<td align="center">80.0</td>
<td align="center">11.0</td>
<td align="center">70.5</td>
<td align="center">1.5</td>
</tr>
<tr>
<td align="center">21</td>
<td align="center">77.0</td>
<td align="center">87.0</td>
<td align="center">10.0</td>
<td align="center">83.0</td>
<td align="center">6.0</td>
<td align="center">80.0</td>
<td align="center">3.0</td>
</tr>
<tr>
<td colspan="3" align="center">Mean absolute error (%)</td>
<td colspan="2" align="center">18.5</td>
<td align="center">10.3</td>
<td colspan="2" align="center">4.5</td>
</tr>
</tbody>
</table>
</table-wrap>
</sec>
</sec>
</sec>
<sec sec-type="conclusion" id="s6">
<title>6 Conclusion</title>
<p>
<list list-type="simple">
<list-item>
<p>(1) Calcium and feldspar are the main minerals controlling the physical properties of the calcareous tight sandstone reservoir in the Shaximiao Formation. Corrosion further improves the porosity and pore structure of the reservoir. In addition, lithology and pore structure jointly control the oil bearing grade of the reservoir.</p>
</list-item>
<list-item>
<p>(2) By using the improved crossplot of logRt<sub>n</sub>/AC<sub>n</sub> and V<sub>ca</sub>/POR, the influence of different R<sub>w</sub> among Wells and dimensional differences of logging curves was weakened, and the difference in logging response of calcium content was effectively reflected. Based on the calcareous petrophysical volume model, a calculation model of calcium content and porosity of the calcareous sandstone reservoir with high accuracy was proposed.</p>
</list-item>
<list-item>
<p>(3) By introducing the I<sub>ca</sub> index, the regression relation between V<sub>ca</sub> and I<sub>ca</sub> was established, and the resistivity in reservoir intervals with high calcium content was effectively corrected.</p>
</list-item>
<list-item>
<p>(4) The calculation accuracy of S<sub>w</sub> in calcareous tight sandstone obtained by putting the resistivity after calcium correction into Archie&#x2019;s formula with variable parameters was significantly better than that of the formula with fixed parameters and previous results. The absolute error was less than 5% compared with water saturation through sealed coring, which met the accuracy requirements of reservoir evaluation and oil and gas reserves calculation.</p>
</list-item>
</list>
</p>
</sec>
</body>
<back>
<sec sec-type="data-availability" id="s7">
<title>Data availability statement</title>
<p>The original contributions presented in the study are included in the article/Supplementary Material; further inquiries can be directed to the corresponding author.</p>
</sec>
<sec id="s8">
<title>Author contributions</title>
<p>ZY: Writing&#x2014;Original Draft, FS: Data Curation, Investigation. JJ: Conceptualization, Writing&#x2014;Review and Editing, Investigation. HH: Resources and Editing. DY: Visualization. AH: Editing.</p>
</sec>
<sec id="s9">
<title>Funding</title>
<p>This research was jointly supported by the National Natural Science Foundation of China (Grant No. U2003102) and Natural Science Foundation of Science and Technology Department in Sichuan Province (Declaration No. 23NSFSC1626).</p>
</sec>
<sec sec-type="COI-statement" id="s10">
<title>Conflict of interest</title>
<p>Authors ZY, HH, and AH were employed by the company of Exploration Business Department of PetroChina Southwest Oil and Gas Field Company.</p>
<p>The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.</p>
</sec>
<sec sec-type="disclaimer" id="s11">
<title>Publisher&#x2019;s note</title>
<p>All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.</p>
</sec>
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