Introduction

Wettability is one of the critical parameters for reservoir rocks in oil and gas fields. It influences distribution of pore fluids, determines the microscale displacement efficiency of rocks, and plays a significant role in formulating and implementing recovery strategies, as well as evaluating parameters such as permeability and saturation (He and Tang 2011; Anderson 1986; Tiab and Donaldson 2004; AL-Dujaili et al. 2023a, b). Currently, shale oil development in Ordos Basin relies on natural energy development, that is the imbibition-displacement process of fracturing fluids, to develop crude oil (Zhiyu et al. 2021). Therefore, identifying the wettability of shale oil reservoirs provides a foundation for understanding the fluid flow mechanisms and development approaches.

Common methods for determining wettability include the contact angle method, centrifugation (USBM), spontaneous imbibition (Amott), automatic imbibition, and the Amott-USBM combination method (Bobek et al. 1958; Sutanto et al. 1990; Anderson 1986; Donaldson et al. 1969; Yan 2001). Among these, the Amott spontaneous imbibition method is widely used for wettability assessment in laboratory experiments. It relies on the differences in interfacial energy between rock, water, and oil (Brown and Fatt, 1956). One liquid is more likely to wet the rock surface than the other does and can spontaneously displace the other. By comparing quantities of capillary imbibition of oil (spontaneous imbibition of water) at the presence of residual oil (bound water), the relative wettability index is calculated (Minh et al. 2015; Chen et al. 2020; Huang et al. 2021). The wettability is determined based on the distribution range of the relative wettability index (Borgia et al. 1991; Howard 1998; Zhong et al. 2013; Wang et al. 2018; AL-Dujaili et al. 2023a, b). However, this method shows several limitations: (1) precision of the experiment relies on the volume measurement of oil and water imbibed, and the graduated tube hardly meet the required precision. (2) The Amott spontaneous imbibition method primarily focuses on the relative sizes of capillary imbibition of oil and water under the influence of capillary forces, neglecting the imbibition effects during water and oil displacement processes, leading to overestimation of wettability. (3) The Amott spontaneous imbibition method is more suitable for evaluating the macroscopic wettability of rock samples, i.e., whether they are oil-wet or water-wet, but cannot assess the wettability of different pore-scale spaces.

With continuous development of nuclear magnetic resonance (NMR) technology, low-field NMR has become a vital geophysical logging method. Due to its unique ability to identify fluid properties, it has been widely used in wettability characterization (Wang et al. 2016, 2018; Xing et al. 2021; Zhao et al. 2021; Xiao 2023).

Petrophysical characterization of shale formations also interested researcher in the USA, due to the increasingly importance of the unconventional resources. They found that acyclic pore model is the one that can most describe spatial distribution of throat sizes (Sakhaee-Pour, and Bryant 2012, 2015; Zapata, and Sakhaee-Pour 2016; Tran, and Sakhaee-Pour 2018a, b, 2019; Yu et al. 2018), among which tree-like pore model is the most applicable to the core-scale measurements(Tran and Sakhaee-Pour 2019), because this model was able to account for the non-plateau-like trend of the drainage during capillary pressure measurement of the shale cores (Sakhaee-Pour and Bryant 2015). Sakhaee-Pour and Li (2016) analyzed drainage experiments conducted on cores and found that the fractal dimension is on the order of 3.1–5.3 for the different shales, reflecting the complexity pore space structure of shale cores. Alessa et al. (2021) explored the pore-throat size and pore-body size distributions of Midra shale in Qatar by measuring capillary pressure and found that unlike the nonplateau-like trend in US shales, Midra shale showed a plateau-like trend, and the pore-throat size has a narrow distribution with an average of close to 22 nm. Machine learning was also adapted by Kasha et al. (2022) to narrow the gap between J curves and allowed an accurate scaling of capillary pressure, providing a very useful way to evaluate the capillary pressure when experiment data are unavailable.

This study proposes a new approach for Amott wettability assessment based on NMR technology to address the limitations of the Amott method. It combines traditional Amott spontaneous imbibition with NMR technology, calculating the extent of fluid extraction at different pore throat scales during the imbibition and the displacement processes relying on capillary imbibition. This calculates the water wetness index, oil wetness index, and relative wettability index for various pore throats. The wettability of different pore throat levels in rock samples is determined based on the relative wettability index. This approach aims to establish a quantitative wettability characterization method for shale oil reservoirs with complex mineral compositions and pore structures, providing guidance for the formulation of shale oil development policies.

Geological setting

Geological overview

Shale oil in the Triassic Chang 7 member of the Mesozoic era in Ordos Basin is primarily controlled by the semi-deep lake to deep lake gravity flow sedimentary system (Fig. 1). The co-genetic pattern of fine-grained sandstone and mud shale, widely distributed, is influenced by ancient climate, topography, and water depth, controlled by gravity flow deposits developed in the steep slope belts and central basin, and deltaic deposits in the gentle slope belts. The sweet spots of shale oil are controlled by ultra-rich organic matter supplying hydrocarbons, large-scale rich sand in deep water, co-storage in micro and nanometer pores and throats, and high-intensity continuous injections. The medium-thin layers of silt-fine sandstone held within thick mud shale layers are the primary targets for cost-effective shale oil development (Yang et al. 2021; Fu et al. 2018, 2019, 2021) (Fig. 2). The pressure coefficient of the Chang 7 stratum in the Ordos Basin ranges from 0.7 to 0.8, making it a typical low-pressure basin. The crude oil has characteristics of low density (0.73–0.78 g/cm3), low viscosity (1.36–1.47 mPa·s), low freezing point (15.68–16.33 °C), and lack of sulfur. Overall, it is considered light crude oil. The initial gas-oil ratio ranges from 90 to 110 m3/t, and the high gas-oil ratio reduces the viscosity and density of shale oil, which is key to the cost-effective development of low-pressure shale oil in the Chang 7 member.

Fig. 1
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Shale oil exploration results in the Ordos Basin (modified from Fu, 2022)

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Fig. 2
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Shale oil profile of Chang 7 Member in Qingcheng Oilfield (modified from Fu, 2022)

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Development status

Before 2011, the Chang 7 section was primarily studied as a source rock. Sparse exploration had identified several oil-rich areas. However, after direct well fracturing, poor trial pumping and rapid production decline made it economically unviable for extraction. From 2011 to 2017, Changqing Oilfield made a significant paradigm shift in the understanding of the Chang 7 shale layer system, transitioning from viewing it as "solely a source rock" to an integrated "source and reservoir." Drawing from North American shale oil exploration and development concepts, with "horizontal drilling + volume fracturing" as the breakthrough, trials were carried out in the West 233 well area, Zhuang 183 well area, and Ning 89 well area. The initial daily production of the trial area was 12.8 tons, with a yearly production of 3,970 tons in the first year. Currently, the average daily production is 4.7 tons per well, with a cumulative production of 23,000 tons, marking a breakthrough in daily and cumulative production. This proves that refining horizontal drilling with volume fracturing can further enhance production, proving crucial for efficient extraction of interbedded shale oil. Since 2018, it has entered a phase of large-scale development with dense well deployments and factory-like operations. Since 2018, a total of 511 horizontal wells have been put into production in Qingcheng Oilfield, with an average horizontal section length of 1679 m, an average oil layer encounter rate of 77.0%, an average of 24 fracturing stages per well, an injected fluid volume of 27,000 cubic meters, and a sand addition volume of 2975 cubic meters. For the 350 horizontal wells that have been in production for three months, the initial daily oil production is 13.6 tons, with a water cut of 35.2%, reaching a daily production of 12.3 tons in the year of production. The first-year average cumulative production is 4430 tons, with a forecasted 20-year EUR value of 26,000 tons.

Data and method

Experimental samples

Samples were selected from shale oil reservoirs of Chang7 member in Huachi and Heshui areas of the Longdong region in Ordos basin. Porosity range of the samples is from 8.26% to 9.26% and permeability between 0.195 and 0.237 mD (Table 1). Wettability experiments based on the NMR technology using a simulated formation water with a 20,000 ppm concentration of MnCl2 solution. The oil used in the experiment is crude oil from the same member.

Table 1 Basic physical properties of experimental rock samples
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Observation of core cast thin sections (CTS) and scanning electron microscope (SEM) found that the lithology of the reservoir in the study area includes very fine to fine-grained feldspar lithic sandstone, and fine-grained lithic sandstone. Clastic rock composition is primarily dominated by quartz and feldspar, with a certain amount of rock fragments and other clasts. It exhibits a high quartz and low feldspar characteristic, with pore-filling materials mainly composed of illite, calcite, and dolomite. The overall porosity of the region is moderately developed, predominantly consisting of dissolution pores, including feldspar dissolution pores and residual pores (Fig. 3a, b). The overall porosity of the rock samples ranges from 4.6% to 7% (Fig. 3c). SEM analysis reveals a widespread distribution of clay minerals on the reservoir pore and throat surfaces, with illite being the primary component, and relatively fewer water-sensitive minerals.

Fig. 3
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CTS and SEM Images, and Statistics for Huachi and Heshui Areas a Sample-1 for sandstone lithoclast dissolution pores; b Sample-3 for quartz filling, feldspar dissolution; c Statistics of Porosity Type

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Experimental instruments

Amott spontaneous imbibition experiments combined with nuclear magnetic resonance (NMR) technology were conducted using deuterium oxide (heavy water) and reservoir crude oil. This allowed for an accurate determination of imbibition oil (water) volumes and displacement oil (water) volumes from NMR spectra at different stages. It characterized the wettability features within different pores. By comparing the volume ratio of self-imbibed water displacing oil (or self-imbibed oil displacing water) to the total displaced oil (or oil–water), wettability of the samples was determined (Fig. 4).

Fig. 4
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Experimental Setup by Amott Method Combined with NMR (1)High pressure displacement pump; (2) Oil and water container; (3)Confining pressure pump;(4) Core holder; (5) Fluid collector; (6) NMR instrument

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Experimental procedures

The experimental procedures for this study, as shown in Fig. 5, were as follows:

  1. 1.

    A cylindrical rock core with a length of 7–8 cm from the shale oil reservoir was selected, cleaned, and dried. The dry weight (m0), porosity (φHe), and permeability (k) of the core were measured. It was then cut into three sections: Sections I and II were 1–2 cm in length, while Section III was 4–5 cm.

  2. 2.

    High-pressure mercury injection experiments were conducted on the Section II, following the national standard GB/T 29171-2012 "Determination of Mercury Intrusion Porosimetry Curve of Rocks" to obtain pore throat radius and distribution data.

  3. 3.

    Section III of the core underwent a vacuum pressure saturation experiment using formation water. Initially, the core was evacuated to 133 Pa, and then it was pressurized with a 20 MPa formation water for 48 h. Mass of Section III was measured (m1), and effective pore volume (Veff) and effective porosity (φeff) were calculated. When the relative difference between φeff and φHe was less than 2%, the core was considered fully saturated. Otherwise, the saturation process was repeated following the above steps. Simultaneously, the NMR instrument was initiated, and parameters were set to measure the NMR T2 spectra of the saturated water in Section III.

  4. 4.

    Section III, saturated with water, was placed in a core holder, and the displacement process was initiated. Deuterium oxide (heavy water) was used to displace the saturated water in Section III. The NMR T2 spectra during the displacement process were monitored until there were no signal responses.

  5. 5.

    Formation crude oil was used to displace the heavy water-saturated Section III to establish a bound water saturation. Subsequently, the core was aged for one week under formation temperature, and the NMR T2 spectra were measured after aging.

  6. 6.

    The aged Section III was placed in a water uptake apparatus filled with deuterium oxide, and self-imbibition of water and oil displacement were conducted. The self-imbibition experiment was considered complete when the water uptake and oil displacement remained stable for 24 consecutive hours. The water uptake and oil displacement volumes (Vo1), and the T2 spectra of the sample were measured.

  7. 7.

    Section III, after self-imbibition, was placed in a core holder, and heavy water was used to displace the core until the exit end reached a water saturation of 99.95%. This marked the end of the water-flooding experiment, and water displacement volumes (Vo2) and the T2 spectra of the sample were recorded.

  8. 8.

    Crude oil was filled in an oil uptake apparatus, and the oil-saturated Section III was placed in a bottle for self-imbibition and oil drainage experiments. The self-imbibition experiment was considered complete when the self-imbibition and oil drainage remained stable for 24 consecutive hours. The self-imbibition oil drainage volume (Vw1) and the T2 spectra of the rock sample were measured.

  9. 9.

    Section III, after self-imbibition, was placed in a core holder, and formation oil was used to displace the core until the oil saturation at the exit end reached 99.95%. This marked the end of the displacement experiment, and the oil displacement volume (Vw2) and the T2 spectra of the sample were recorded.

  10. 10.

    The pore throat distribution curve obtained from high-pressure mercury injection and the NMR T2 spectra under complete water saturation were plotted on the same coordinate system for scale comparison. This allowed the conversion coefficient between NMR T2 time and pore throat radius to be determined, enabling the transformation of the NMR T2 spectrum into the corresponding pore throat distribution curve.

Fig. 5
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Schematic of the wettability experiment based on nmr Amott spontaneous imbibition method

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Results and discussion

Qualitative evaluation of wettability

Spontaneous imbibition method

Under the influence of capillary pressure, wetting fluids possess the characteristic of spontaneously imbibed into the rock pores and displacing non-wetting fluids. By measuring and comparing the quantities of capillary imbibition of oil (or spontaneous imbibition of water) in the presence of residual oil (or bound water) in reservoir rocks and the displacement of oil by water (or displacement of water by oil), the wettability of reservoir rocks to oil (or water) can be determined (Brown, 1956). The wettability was evaluated using the spontaneous imbibition method for 13 samples from the Huachi area and 12 samples from the Heshui area in Ordos Basin. The results indicate that reservoirs of Huachi area are oil-wet, while that in Heshui area show weakly oil-wet, and the overall basin exhibits weakly oil-wet characteristics (Table 2) (standards refer to “Appendix”).

Table 2 Wettability results of reservoirs in the Longdong region using the spontaneous imbibition method
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Contact angle method

At three-phase junction of a water–oil–solid system, equilibrium relationship of surface energies follows the Young–Laplace equation, and the size of the contact angle is related to the wetting degree of the solid by oil and water (Washburn 1921; Al-Dujaili et al 2023a, b). Therefore, measuring the contact angle of the oil–water-reservoir rock system provides insights into the wettability of oil and water on the reservoir rock surface. During this contact angle test, actual reservoir rock samples provides a more realistic representation of the reservoir. Three modes were set up: (1) dry samples (without oil washing); (2) samples 100% saturated with water; (3) samples saturated with oil and water (oil saturation between 55 and 70%). Oil and water were dropped onto the rock surface, and the contact angles of the oil droplets and water droplets on the rock surface were measured. Results showed that in all states, the contact angle of oil is < 10°, and that of water ranges from 37.3° to 73.6°, indicating that the Chang 7 reservoir exhibits an oil wet (Fig. 6) (National Development and Reform Commission, 2007).

Fig. 6
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Contact Angle Tests by Young–Laplace equation for Shale Oil Reservoirs in the Ordos Basin

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Quantitative evaluation of wettability using NMR-based Amott spontaneous imbibition method

Wettability calculation

Conversion coefficient between NMR T2 time and pore throat radius is calculated using Eq. (1) (Yang et al. 2013):

$$T_{2} = Cr$$
(1)

where T2 is the transverse relaxation time (ms), C is the conversion coefficient (ms/μm), and r is the pore throat radius (μm).

During the experiment, heavy water was used to shield the NMR signal of the water. Therefore, the obtained T2 spectrum represents only the signal from oil. Changes in T2 spectrum reflect variations in the oil phase within the experimental core. Hence, extent of extraction for various pore throat levels during self-imbibition of water and self-imbibition of oil drainage processes can be calculated using Eqs. (2) to (3) (modified from Yang et al. 2023):

$$E_{ws - ri} = \frac{{\int_{{ri_{\min } }}^{{ri_{\max } }} {m(r_{i} )_{bw} {\text{d}}r_{i} } - \int_{{ri_{\min } }}^{{ri_{\max } }} {m(r_{i} )_{aw} {\text{d}}r_{i} } }}{{\int_{{r_{\min } }}^{{r_{\max } }} {m(r_{i} )_{bw} {\text{d}}r_{i} } }}$$
(2)
$$E_{os - ri} = \frac{{\int_{{ri_{\min } }}^{{ri_{\max } }} {m(r_{i} )_{ao} {\text{d}}r_{i} } - \int_{{ri_{\min } }}^{{ri_{\max } }} {m(r_{i} )_{bo} {\text{d}}r_{i} } }}{{\int_{{r_{\min } }}^{{r_{\max } }} {m(r_{i} )_{ao} {\text{d}}r_{i} } }}$$
(3)

where Ews-ri is the extraction extent of oil after water self-imbibition for the i-th pore throat, Eos-ri is the extraction extent of water after oil self-imbibition for the i-th pore throat, rimin is the minimum radius of the i-th pore throat (μm), Rimax is the maximum radius of the i-th pore throat, μm, rmin is the minimum pore throat radius of the rock sample (μm), rmax is the maximum pore throat radius of the rock sample(μm), m(ri)bw is the signal amplitude before self-imbibition of water for the i-th pore throat, m(ri)aw is the signal amplitude after self-imbibition of water for the i-th pore throat, m(ri)bo is the signal amplitude before self-imbibition of oil for the i-th pore throat and m(ri)ao is the signal amplitude after self-imbibition of oil for the i-th pore throat.

The next step is to create contribution diagrams for the imbibition and displacement processes during water and oil flooding. To do that, we first calculate extraction extent under the influence of imbibition at different pore throat sizes during water flooding and oil flooding. When both oil and water phases exist in the pore space, fluid velocity of the displacing phase can be calculated using Eq. (4). Equation (4) obtains the fluid velocity under imbibition and displacement processes. Then, contributions of imbibition and displacement at different pore throat radii can be calculated using Eqs. (4) to (6) (modified from He, 2011) using contact angle of the sample and the displacement pressure applied in the displacement experiment.

$$v_{s} { = }\frac{{r^{2} \left( {\frac{2\sigma \cos \theta }{r}} \right)}}{{8\mu_{w} \sqrt {L^{2} - \frac{{r^{2} }}{{4\mu_{o} }}\left( {1 - \frac{{\mu_{w} }}{{\mu_{o} }}} \right)\left( {\frac{2\sigma \cos \theta }{r}} \right)t} }}$$
(4)
$$v_{s} { = }\frac{{r^{2} \left( {\frac{2\sigma \cos \theta }{r}} \right)}}{{8\mu_{w} \sqrt {L^{2} - \frac{{r^{2} }}{{4\mu_{o} }}\left( {1 - \frac{{\mu_{w} }}{{\mu_{o} }}} \right)\left( {\frac{2\sigma \cos \theta }{r}} \right)t} }}$$
(5)
$$v_{d} { = }\frac{{r^{2} \Delta p}}{{8\mu_{w} \sqrt {L^{2} - \frac{{r^{2} }}{{4\mu_{o} }}\left( {1 - \frac{{\mu_{w} }}{{\mu_{o} }}} \right)\Delta pt} }}$$
(6)

And the last step is to create diagrams showing the contribution rates versus pore throat radius (Eqs. (7) to (8)).

$$\eta_{s} { = }\frac{{\frac{2\sigma \cos \theta }{r}}}{{\left( {\Delta p + \frac{2\sigma \cos \theta }{r}} \right)}}$$
(7)
$$\eta_{d} { = }\frac{\Delta p}{{\left( {\Delta p + \frac{2\sigma \cos \theta }{r}} \right)}}$$
(8)

where ηd is the percentage of displacement contribution, and Ηs is the percentage of imbibition contribution, as a decimal.

Based on the contribution diagrams formed above, choose a radius point where the imbibition contribution rate is greater than 0.9 to calculate the extraction extent of various pore throats using NMR T2 spectrum curves during water and oil flooding processes. The formulas for this calculation are as follows:

$$E_{wd - rj} = \frac{{\int_{{rj_{\min } }}^{{rj_{\max } }} {m(r_{j} )_{bd} {\text{d}}r_{j} } - \int_{{rj_{\min } }}^{{rj_{\max } }} {m(r_{j} )_{ad} {\text{d}}r_{j} } }}{{\int_{{r_{\min } }}^{{r_{\max } }} {m(r_{j} )_{b} {\text{d}}r_{j} } }}$$
(9)
$$E_{od - rj} = \frac{{\int_{{rj_{\min } }}^{{rj_{\max } }} {m(r_{j} )_{ad} {\text{d}}r_{j} } - \int_{{rj_{\min } }}^{{rj_{\max } }} {m(r_{j} )_{bd} {\text{d}}r_{j} } }}{{\int_{{r_{\min } }}^{{r_{\max } }} {m(r_{j} )_{a} {\text{d}}r_{j} } }}$$
(10)

where:

Ewd-rj is the extraction extent of oil under water-flooding for the j-th pore throat under imbibition,, Eod-rj is the extraction extent of water under oil-flooding for the j-th pore throat under imbibition, rjmin is the minimum radius of the j-th pore throat under imbibition (μm), rjmax is the maximum radius of the j-th pore throat under imbibition (μm), m(rj)bd is the signal amplitude before self-imbibition of water-flooding for the j-th pore throat under imbibition, m(rj)ad is the signal amplitude after self-imbibition of water-flooding for the j-th pore throat under imbibition, m(rj)bo is the signal amplitude before self-imbibition of oil-flooding for the j-th pore throat under imbibition, m(rj)ao is the signal amplitude after self-imbibition of oil-flooding for the j-th pore throat under imbibition, m(rj)b is the signal amplitude before self-imbibition of water-flooding for the j-th pore throat, and m(rj)a is the signal amplitude after self-imbibition of oil-flooding for the j-th pore throat.

Equations (11) to (12) are to calculate the both the oil and water extraction extent by imbibition for each pore throat level during self-imbibition of water and water-flooding processes, and during self-imbibition of oil and oil-flooding.

$$E_{wi} = E_{ws - ri} + E_{wd - rj}$$
(11)
$$E_{oi} = E_{os - ri} + E_{od - rj}$$
(12)

where Ewi is the oil extraction extent at the i-th pore throat under water imbibition and water-flooding, and Eoi is the water extraction extent at the i-th pore throat under oil imbibition and oil-flooding.

Total extraction extent during both self-imbibition of water and water-flooding, as well as self-imbibition of oil and oil-flooding, are calculated using Eqs. (13) to (14):

$$E_{w} = \frac{{\int_{{r_{\min } }}^{{r_{\max } }} {m(r_{i} )_{bsw} {\text{d}}r_{i} } - \int_{{r_{\min } }}^{{r_{\max } }} {m(r_{i} )_{adw} {\text{d}}r_{i} } }}{{\int_{{r_{\min } }}^{{r_{\max } }} {m(r_{i} )_{bsw} {\text{d}}r_{i} } }}$$
(13)
$$E_{o} = \frac{{\int_{{r_{\min } }}^{{r_{\max } }} {m(r_{i} )_{ado} {\text{d}}r_{i} } - \int_{{r_{\min } }}^{{r_{\max } }} {m(r_{i} )_{bso} {\text{d}}r_{i} } }}{{\int_{{r_{\min } }}^{{r_{\max } }} {m(r_{i} )_{ado} {\text{d}}r_{i} } }}$$
(14)

where Ew is the total extraction extent during self-imbibition of water and water-flooding, and Eo is the total extraction extent during self-imbibition of oil and oil-flooding, as a decimal.

Water wettability index, oil wettability index, and relative wettability index for each pore throat level are calculated using Eqs. (11) to (14), and wettability of different pore throats in the samples are determined based on the wettability index in industry standards. And then the wettability index is modified based on the contribution diagrams of imbibition and flooding processes (Eqs. (17) to (18)) (modified from Anderson 1986; Morrow 1990). And in the end, the proportion of oil-wet pores and water-wet pores in the rock sample are calculated.

$${W}_{wi}=\frac{{E}_{wi}}{{E}_{w}}$$
(15)
$${W}_{oi}=\frac{{E}_{oi}}{{E}_{o}}$$
(16)
$${W}_{w}=\frac{{V}_{wso1}+{V}_{wso2}}{{V}_{wso1}+{V}_{wso2}+{V}_{wfo2}}$$
(17)
$${W}_{{\text{o}}}=\frac{{V}_{osw1}+{V}_{osw2}}{{V}_{osw1}+{V}_{osw2}+{V}_{ofw2}}$$
(18)
$${I}_{i}={W}_{w}-{W}_{o}$$
(19)

where Wwi is the water wettability index at each pore throat level, Woi: is the oil wettability index at each pore throat level, Ww is the water wettability index after modification at each pore throat level, Wo is the oil wettability index after modification at each pore throat level, Vwso1 and Vosw1 are the volumes of extracted oil or water during self-imbibition of water or self-imbibition of oil (mL), Vwso2, and Vosw2 are the volumes of extracted oil or water during water or oil flooding (mL), Vwfo2 and Vofw2 are the volumes of self-imbibed water and oil after modification based on contribution diagrams (mL), and Ii is the relative wettability index for each pore throat level.

Wetting characteristics of different pore throats

Based on the proposed new evaluation processes describing wetting characteristics in different pore spaces, significant variations were observed in T2 spectrum curves before and after water and oil self-imbibition (Fig. 7). This indicates that samples exhibit mixed wetting characteristics. Since capillary imbibition still occurs during displacement processes (Figs. 8, 9) (taking Sample 1 as an example), contribution diagrams for flooding and imbibition were plotted using the formula (Fig. 10). By considering the imbibition recovery during flooding process and modifying the wettability index accordingly, the modified water and oil wettability index were calculated for different pore spaces in the four samples, and corresponding distribution diagrams were generated (Figs. 11, 12, 13, 14, 15).

Fig. 7
figure 7

Nuclear magnetic resonance (NMR) spectra during the spontaneous imbibition process a Core-1 self-imbibition process NMR spectrum; b Core-2 self-imbibition process NMR spectrum; c Core-3 self-imbibition process NMR spectrum; d Core-4 self-imbibition process NMR spectrum

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Fig. 8
figure 8

Extraction extent of different pore spaces in sample 1 during spontaneous water imbibition and spontaneous oil imbibition

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Fig. 9
figure 9

Imbibition extent during water and oil flooding in sample 1

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Fig. 10
figure 10

Imbibition and displacement chart

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Fig. 11
figure 11

Wettability evaluation results for different pore spaces in sample 1 after modification

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Fig. 12
figure 12

Wettability evaluation results for different pore spaces in sample 2 after modification

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Fig. 13
figure 13

Wettability evaluation results for different pore spaces in sample 3 after modification

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Fig. 14
figure 14

Wettability evaluation results for different pore spaces in sample 4 after modification

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Fig. 15
figure 15

Flow of oil and water in shale oil reservoir during PFSIS

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Figures show that the wetting characteristics in different pore spaces of the studied area's rock exhibit significant variations. In relatively larger pores, water wettability index is generally higher than the oil wettability index, and for some samples, the water wettability index even reaches 1, indicating a strongly water-wet characteristic in these pores. As the pore radius decreases, the oil wettability index increases and gradually surpasses the water wettability index (Samples 1 and 3). Some samples exhibit a "double-peak" feature in their oil wettability index (2 and 4), with oil wettability index peaks at different pore spaces. Overall, oil-wet pores are mainly distributed in the pore radius with a range of 0.1 to 4 μm. Pores with a radius larger than approximately 4–5 μm and smaller than 0.1 μm exhibit significantly lower oil wettability index and are mostly show a water wetting behavior.

Table 3 provides statistics of the proportions of water-wet and oil-wet pores in the micro-pores, meso-pores, and macro-pores within the four rock samples. For samples from the Huachi area (Samples 1 and 2), oil-wet characteristics are relative stronger than oil-wet in the micro-pores, with water-wet pores accounting for approximately 38.25% and oil-wet pores for 61.75%. In contrast, samples from Heshui area (Samples 3 and 4) exhibit stronger water-wet characteristics in the micro-pores, with water-wet pores accounting for 43.95% and oil-wet pores 56.05%. Based on the statistical results, the Chang7 reservoir overall exhibits a more oil-wet characteristic( with oil wet pores accounting for 58.9%).

Table 3 Summary of the proportions of water-wet and oil-wet pores in samples
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Mechanism of imbibition processes in the reservoir

After years of practices in shale oil development in Ordos Basin, a development approach has gradually emerged, known as "long horizontal wells—large-scale volume fracturing—post-fracturing shut-in—backflow" (Jiao 2021). During PFSIS, crude oil is extracted by the imbibition and displacement of fracturing fluid and reservoir fluid in the pore spaces (Zhiyu et al. 2021). During fracturing and PFSIS, pressure around the near-wellbore zone is much higher than the formation pressure. Some fracturing fluid enters large pores under this pressure differences (displacement), while some enters small pores due to capillary pressure (imbibition) (Wan et al. 2023). As pressure propagate and water saturation changes, the displacement process gradually weakens, and imbibition becomes relatively strong (Fig. 15).

Physical simulation of oil production characteristics during the PFSIS of shale oil wells

To investigate oil production characteristics in different pore throat sizes during PFSIS, samples from Longdong region were used to simulate dynamic imbibition under reservoir conditions at different injection pressures during PFSIS.

During the experiment, real-time data were collected, including NMR T2 spectra, injection pressure, and imbibition time. T2 figures were drawn before and during the experiment. The rock sample properties and experimental recovery rates are shown in Table 4, and the NMR T2 spectra during the imbibition process are displayed in Fig. 14.

Table 4 Basic parameters of the samples used in dynamic imbibition experiment
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T2 spectra peaks of the small and large pores gradually decrease with increasing imbibition time, and the relaxation times corresponding to pore sizes in the range of 1–10 ms only show small fluctuations, indicating that during the imbibition process, the small and large pores are effectively active. Pore size with the relaxation times corresponding to 1–10 ms are acting as channels connecting the small and large pores (Xiao et al. 2021). Taking sample 7 as an example (Fig. 16), NMR T2 spectrum of the core in bound water state exhibits a “double-peak” feature, with the signal amplitude peak of the short relaxation time (T2 between 0.01 and 5.94 ms) being smaller than that of the long relaxation time (T2 between 5.94 and 219 ms). On the one hand, this indicates that the distribution of crude oil in the reservoir core exhibits strong non-uniformity, and on the other, crude oil is primarily located in the medium to large pores. After 16 h of imbibition, decrease of NMR signal in the core mainly comes from pores corresponding to T2 values greater than 10 ms, and with the increase of imbibition time, crude oil in pores corresponding to relaxation times less than 10 ms start to flow.

Fig. 16
figure 16

Nuclear magnetic resonance (NMR) T2 spectrum during the dynamic imbibition process of Sample 7

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Figure 17 shows the recovery curves of different pores as a function of imbibition time. It shows that the recovery rate in the large pores, mainly in water-wet pores, increases rapidly initially, while the recovery rate in the medium and small pores, mainly oil-wet pores, increases relatively slowly. With a longer imbibition time, the recovery rate in the large pores stabilizes, while the recovery rate in the medium and small pores, especially the small pores, increases rapidly.

Fig. 17
figure 17

Imbibition curves for different pore spaces at different imbibition stages

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Optimization of post-fracturing shut-in duration (PFSID) among different areas

Pressure characteristics during the PFSIS in the Chang 7 shale oil reservoir and its relationship with reservoir wettability

Extensive field development practices have revealed that a very short PFSID leads to unstable reservoir pressure diffusion and increased sand production, while an overly PFSID results in an increased viscosity of crude oil, wellbore scaling, and other issues that can impact well productivity. It has been observed that the bottom hole pressure stabilizes after approximately 30 to 40 days. In the case of Chang 7 shale oil reservoir in Ordos Basin, wellhead pressure change undergoes two distinct phases during PFSIS (Fig. 18): a rapid decline phase (with a pressure drop rate greater than 0.5 MPa/day) and a slow decline phase (with a pressure drop rate ranging from 0.1 to 0.5 MPa/day) (Wan et al., 2023). These phases correspond to rapid and slow stages of imbibition, respectively. When the pressure drop rate exceeds 0.5 MPa/day, it indicates that PFSIS is in the pressure expansion phase. When the pressure drop rate ranges from 0.1 to 0.5 MPa/day, it suggests that the PFSIS is in the oil–water displacement phase (Wan et al. 2023). The PFSIS is considered to be ended when the pressure curve stabilizes, with a continuous pressure drop rate less than 0.1 MPa/day for three consecutive days (Wan et al. 2023).

Fig. 18
figure 18

Relationship between wellhead pressure decline curve and time during the shut-in process of intermittent horizontal shale oil wells (Wan, 2023)

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The PFSID, water-cut decline curves, pressure drop rates, and water-cut decline rates were analyzed for different wettability indices in the Chang 7 reservoirs of the Ordos Basin. Results showed a consistent pattern: neutral wettability > weak oil-wet > oil-wet (Figs. 19, 20.).

Fig. 19
figure 19

Relationship between PFSID and pressure decline curve under different Wettability

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Fig. 20
figure 20

Decline curves of water saturation in daily production for different wettability

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The relationship between PFSID and fracturing parameters

As indicated in the previous evaluation of reservoir wettability, the overall wettability of the shale oil reservoirs in Longdong region exhibit a mixed characteristic, with a greater prevalence of oil-wet pores in Huachi area compared to Heshui area. This suggests that Heshui area is more favorable for fracturing fluid imbibition displacement. Numerical simulations have shown a nonlinear positive correlation between PFSID and the average volume of injected fluid for a single stage (Fig. 21). By considering both the injected fluid and reservoir parameters, the PFSID for Heshui and Huachi regions were optimized (Table 5).

Fig. 21
figure 21

Numerical simulation of the relationship between PFSID and injection volume

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Table 5 Optimization of shut-in time for Huachi and Heshui areas
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Conclusions

  1. 1.

    This study provided a quantitative way to estimate reservoir wettability in shale oil formation, and determines post-fracture shut-in duration (PFSID) of a horizontal well based on the wettability and fracturing parameters. It showed that shale oil reservoirs in the Longdong region generally exhibit mixed wettability, with large pores being predominantly water-wet and small pores being mainly oil-wet.

  2. 2.

    Combining the Amott method with nuclear magnetic resonance (NMR), we calculated the volume of water and oil both by imbibition and flooding at every step of NMR experiment in four samples from Longdong region in Ordos basin. With the fixed equation for wettability index calculation, the study gave both quantitative oil and water wettability in every pore throat scale and found that Huachi and Heshui areas in Longdong region show a slight different wettabilty, and this leads to a difference in the PFSID in two areas.

  3. 3.

    Four samples from Longdong region showed that because of the difference in wettability among large, medium, and small pores, large pores are the space where crude oil are developed from at the first stage of production. Then, recovery rate in the medium and small pores, especially the small pores, increases rapidly with the production goes by.

  4. 4.

    Quantitative reservoir wettability and fracturing parameters of a horizontal well are the two most decisive factors that affect PFSID. Numerical simulations have shown a nonlinear positive correlation between PFSID and the average volume of injected fluid and the optimal PFSID in Huachi and Heshui areas are determined to be 36 and 43 days, respectively.