With dramatically increasing global energy demands, the unconventional hydrocarbon resources have been regarded as a necessary alternative for the oil and gas resources exploration and development ^[1⇓-3]. The natural gas stored in low-permeability (tight) sandstone reservoirs is an important target for exploration and development of unconventional petroleum resources ^[4-5] and also serves as the national stratagic energy resource in China for reserve and production increase^[6-7]. Evident differences have been reported in the accumulation characteristics and mechanisms of low-permeability (tight) sandstone gas reservoirs in comparison with conventional reservoirs ^[8⇓-10], of which primary gas migration from source rock to reservoir, namely, the charging process, is key for the accumultion of low-permeability (tight) sandstone gas reservoirs. The reasons for the differences lay in the space configuration of the interbedded source and reservoir rocks and the nano- to micro-meter pore system in these reserovirs ^{[11⇓⇓-14]}. The fluid flow mechanism in the charging process determines the charging behaviors, fluid occurrence states, and accumulation degree in low-permeability (tight) sandstone reservoir, which is critial for understanding the natural gas charging mechanism ^{[11,15⇓ -17]}.

Numerous investigations, involving physical simulation, numerical simulation, and theoretical derivation, have been conducted to probe the fluid flow mechanisms in low-permeability (tight) sandstone reservoirs ^{[15,18⇓⇓⇓ -22]}. Sand box model, core flooding experiment, and pore-scale fluid flow physcial simulation are three major techniques employed in physical simulaiton ^{[23⇓⇓⇓⇓⇓-29]}. The fluid flow in hydrocarbon charging process has been investigated through the sand box model macroscopically in lab, but the results can hardly be used to describe the actual multiphase flow in the charging process in low-permeability (tight) reservoirs. Therefore, the core flooding experiments were introduced and performed on the actual low-permeability (tight) sandstone samples in China and abroad ^{[16-17,29 -30]}, in which the non-Darcy flow behaviors with an evident threshold pressure gradient (TPG) were identified in hydrocarbon flow ^{[15,26 -27]}. Qiao et al. and Zeng et al. have reported a low-velocity non-linear flow in the charging and migration process during the hydrocarbon accumulation in low-permeability (tight) sandstone reservoirs ^[14,27,31]. The governing equations describing the low-velocity non-Darcy flow have been obtained by theoretical derivation. However, differences presented in these equations due to different influencing factors taken into account in the fluid flow ^[32⇓-34]. Recently, pore-scale visualized microscopic physical simulation for the multiphase flow in reservoirs has been widely performed by combining the fluid flow flux apparatus and micrometer X-ray computed tomography (X-μCT). The popular investigations tend to focus on the water flooding or imbibition process in the hydrocarbon development of conventional sandstone or carbonate rocks ^{[35⇓⇓⇓⇓-40]}. The multiphase flow for oil/gas displacing water in charging process of the hydrocarbon accumulation remains poorly investigated although Lin et al. have noticed the multiphase flow behaviors during the capillary drainage procedure of gas displacement in heterogeneous sandstones ^[38]. Based on the pore-scale research, other scholars have observed and studied the dynamic multiphase fluid flow in low-permeability (tight) reservoirs by Lattice Boltzmann, Monte Carlo, and other multi-field fluid flow numerical simulation methods ^[41].

As channels, the geometrical and topological features of pores in porous media govern the fluid flow and distribution characteristics ^{[23-24,42⇓ -44]}. The micro- to nano-meter pore system in low-permeability (tight) sandstone is responsible for the complex fluid flow and distribution law^[22]. With progresses in pore-throat analysis techniques, especially the applications of scanning electron microscope (SEM), nuclear magnetic resonance (NMR), and X-μCT, explorations on the controlling factors for the fluid flow and distribution in the hydrocarbon reservoirs have emerged ^{[14,29,45 -46]}. Qiao et al. have discovered that the pore-throat configuration controls the fluid flow behaviors in tight gas charging process through X-μCT and core flooding experiments. Gong et al. have reported that the non-Darcy gas flow in low-permeability (tight) sandstone falls into four models, including composite, concave-up, concave-down, and linear models, under the control of the microscopic pore structures ^[29]. However, these results cannot directly reflect the fluid flow and distribution in the micro-nanometer pore system since they were based on the simple coupling of core flooding experiment and pore structure characterization. The statistically averaging of fluid flow and pore structure, and cross-scale coupling would result in more systematic errors ^[31], resulting in uncertainties in the fluid flow, distribution, and their controlling factors. As indicated, the key to uncovering the hydrocarbon charging mechanism in low-permeability (tight) sandstone lies in revealing the characteristics, law, and controlling factors of the fluid flow and distribution in the micro-nanometer pore system, which must rely on high-resolution pore-scale flow simulation ^[23⇓-25].

In this study, a three-dimensional (3D) visualized real- time micro-nanometer pore-scale physical simulation of natural gas charging experiment is conducted on the low-permeability (tight) sandstone, combined with a systematic micro-nanometer pore-throat structure description integrating casting thin section (CTS) and SEM. The apparent permeability evaluation, in-situ pore-scale computation, and pore network modelling (PNM) are incorporated to describe the law and distribution of fluid flow, and explore the microscopic controlling factors. This work tries to throw a light on the low-permeability (tight) sandstone gas charging mechanism and to provide guidance for its exploration and development.

The core samples in this study were collected in the second member of the Shahejie Formation (Es₂) in the Palaeogene tight sandstone gas reservoir located in the Qibei slope of Qikou Sag in middle Huanghua Depression, the Bohai Bay Basin. The Es₂ interval is characterized by interbedded source rocks and reservoirs ^[47⇓-49]. The sample was taken at 3790.49 m in Well BS35 drilled in Banqiao slope belt on the Qibei Slope, which is located at the interface of source rocks and low-permeability (tight) sandstone reservoirs where natural gas charging happens. The lithology is medium grained, the core length, diameter is 6.56 and 2.51 cm, the gas porosity is 11.42%, the permeability is 3.94×10^-3 μm² and the contact angle is 51.90°.

The experimental method and work flow are shown in Fig. 1, of which the procedure of the 3D visualized real-time pore-scale gas charging physical simulation will be introduced in details in the following.

The experiment was conducted on a physical simulation instrument designed for hydrocarbon migration and accumulation in unconventional reservoirs, which is developed in the hydrocarbon accumulation physical simulation laboratory of the State Key Laboratory of Petroleum Resources and Prospecting in China University of Petroleum, Beijing (Fig. 2a). The instrument is consisted of a Zeiss Xradia Versa 510 X-μCT apparatus with the highest resolution of 650 nm; a Core Flooding System (CFS) with the maximum axis pressure and maximum confining pressure of 70 MPa, maximum temperature of 120 °C, and fluid flow measuring accuracy of 0.001 μL/min; and a Peek core holder system with compressive strength greater than 45 MPa and outer diameter of 2 cm that guarantees the highest scanning resolution of 2 μm (Fig. 2a, 2b). The system can monitor, image, and analyze the pore-scale fluid flow in low-permeability (tight) sandstone reservoir in real-time at actual formation pressure and temperature.

The simulation was performed employing the steady- state fluid flow method, which was kept real-time in the whole process in order to realize the in-situ scanning (Fig. 2c). The detailed experiment procedure is introduced as follows.

(1) The residual salt and oil in the sample were removed before the experiment. A sub-sample with diameter of 5 mm and length of 22 mm was drilled from the core and put into a special rubber sleeve before loading to the Peek core holder system. The core holder was then loaded into the objective table of the X-CT instrument and linked with CFS using the pipelines. The sealing capacity of the system was checked before starting the experiment.

(2) A proper confining pressure of 2 MPa was loaded via the CFS in the core holder. Then a first-time X-CT scanning was conducted on the sample under the original dry state with a scanning resolution of 2.00 μm, aiming to obtain the original pore-throat structure data.

(3) The air in the core holder system was evacuated by CFS before the KI solution with mass fraction of 25% was continuously injected. KI solution was chosen as it shows great absorption capacity for X-ray, resulting in higher grayscales in solution-saturated pores than rock matrix and gas-saturated pores on images and guaranteeing reliable separation of rock matrix and gas and water in pores. Following X-CT scanning was conducted on the brine-saturated sample after the injection had lasted at least 72 h.

(4) Gas charging followed the last scanning under the brine-saturated state, which started at a low stable injection pressure of 0.1 MPa. According to the steady-state experimental principle, X-CT scanning was performed after the stable gas flow was captured at the outlet, as well as flow equilibrium was established until the gas flow rate and gas injection rate equaled.

(5) The injection pressure was gradually increased after the stable flow equilibrium was established under each pressure node. Corresponding X-CT scanning was separately conducted at different injection pressure nodes. The experiment ceased when there was no more water flow out from the outlet and flow equilibrium kept stable.

(6) The fluid flow data in the gas charging physical simulation process were recorded in details and X-CT scanning data derived from different injection pressure nodes was analyzed.

To acquire the two-phase gas-water fluid flow and occurrence at different charging stages, the scanning data at different injection pressures was processed employing the FEI AVIZO 9.0.1 graphic software for in-situ pore-scale computation and PNM. The detailed procedure is given in the following.

(1) Image reconstruction was performed on the original scanning data using the Zeiss Reconstruction Software to calibrate the center shift, to eliminate the X-ray beam harding, and to reconstruct the grayscale tomography images. Smoothing was done by using the 3D Non Local Median Filter in AVIZO, which is based on the pixel grayscale weighted averaging of the self-similar structure on the images, to remove the image noises. This procedure was repeated until the surfaces of grains were smooth and interfaces between grains, pores, gas, and water were clear enough in order to guarantee the accuracy of the following grayscale threshold segmentation (Fig. 3a-3c).

(2) Image registration module in Avzio was invoked to calibrate the micrometer spatial displacement by identifying the characteristic minerals among the different image sequences obtained at the adjacent charging pressure nodes. The calibration guarantees the grayscale images at different charging pressure nodes are spatially in-situ. Accordingly, in-situ computation can be performed after registering all image sequences (Fig. 3a-3c).

(3) Interactive threshold segmentation, taking the gas porosity as standard, was preferentially performed on the original dry grayscale images to extract the pore space from the rock matrix. The binary pore-throat network image was obtained under the condition that the X-CT porosity calculated by the Material Statistics module in Avizo approximately equals to the gas porosity. The connected 3D pore-throat network was derived by pore connectivity separation. PNM was then processed on the connected system to construct the 3D pore-throat skeleton model, by which the original pore structure parameters can be acquired.

(4) In-situ digital core computation was performed on the calibrated grayscale images. The KI solution-saturated stage was set as the original state, and the illustrated calculation was processed on the grayscale images at the charging pressures of 0.15 and 0.10 MPa by employing the Arithmetic module of Avizo (Fig. 3d-3e). The distribution of the KI solution (bright white) at the charging pressure 0.15 MPa minus that at 0.10 MPa gives the binary image of the water phase displaced by the gas phase at the charging pressure of 0.15 MPa, namely, the gas phase charged at 0.15 MPa (Fig. 3f). An accurate binary image of the gas phase in pore-throat at 0.15 MPa can be obtained by adding the binary image of the charged gas phase at 0.15 MPa to that of the gas phase at 0.10 MPa. The binary image of the water phase can be derived by segmenting the bright white zones (KI solution) on the image of 0.15 MPa. The 3D gas-water distribution was constructed at certain charging pressure by superimposing the spatial distributions of gas and water phases (Fig. 3g). According to the above computation method, the gas and water occurrence states and distribution at different charging pressures can be accessed. On the basis of the threshold segmentation of water and gas phases, the volume fraction of the water phase at KI solution-saturated state and that of the gas phase at different pressures can be calculated by utilizing the Volume Fraction module, thus, the gas saturation can be calculated by employing Eq. (1). The parameters of the gas-bearing pores and throats were obtained by applying the PNM to the binary images of the gas phase at different charging pressures.

Primary and secondary pores are two major pore types in the tight sandstone samples ^[50], of which the primary residual intergranular pores dominate the primary pores, exhibiting regular appearances with sizes between dozens and hundreds of microns (Fig. 4a). Intergranular dissolution pores, dissolution intragranular pores, intercrystalline pores, and micro fractures are secondary pores. The dissolution intergranular pores are the results of dissolution along dissolvable grain edges (feldspar and rock fragment), showing irregular pore shapes with widths between dozens and hundreds of microns (Fig. 4a, 4b). The dissolution intragranular pores form inside the dissolvable grains, exhibiting irregular outlines and sizes ranging from several to dozens of microns (Fig. 4b). The intercrystalline pores are located between the clay aggregates, ranging from several hundred nanometers to several microns (Fig. 4c). The micro fractures are slits running through the rock grains with long extensions, providing connections for disconnected pores (Fig. 4a). Section observation suggests the sample shares similar pore genesis to typical tight sandstone ^[50], in which the intergranular pores account for 80%. The primary intergranular pores are comparable with the dissolution intergranular pores in proportions. Dissolution intragranular pores in rock fragments and feldspars account for about 15%, and a few amount of micro fractures and intercrystalline pores exists in the pore system (Fig. 4a).

The analysis on X-μCT scanning suggests the connected large-sized pores with regular shape construct the major structure of the pore-throat system in low-permeability (tight) sandstone, while small-sized, irregular, and poorly connected pores are generally distributed along the major structure. The spherical tiny pores exhibit disperse distributions, which can locate inside the major structure, bridging the large-sized and small-sized pores, or distribute away from the main body, showing isolated spatial distributions (Fig. 5a-5d). The radius distribution of pores and throats derived from the PNM developed by Dong and Blunt ^[51] indicates wide distribution range of low-permeability (tight) sandstone (Fig. 5d). The pore radius ranges from 10 to 120 μm, with main peak in 20-60 μm (avg. 12.34 μm) (Fig. 5e). The throats are 2-120 μm, mainly in 10-30 μm (avg. 9.67 μm) (Fig. 5f). The average pore-throat ratio and average coordination number are 1.28 and 1.31, respectively, indicating a relative good connectivity (Fig. 5d).

Non-linear natural gas flow was identified in the charging process of low-permeability (tight) sandstone, which is quite similar to the single-phase non-Darcy flow in low-permeability (tight) sandstone and exhibiting evident “threshold pressure square gradient”, namely, the critical pressure square gradient (CPSG) for natural gas charging. The CPSG is 0.01 MPa²/cm. The gas flow velocity increases with the pressure square gradient, firstly increases and then becomes stable. The gas flow plot can be divided into two segments, including a concave-up part and a linear one (Fig. 6a). The gas saturation shows a two-stage growth pattern along with the pressure gradient, increases rapidly before the pressure gradient lower than 0.29 MPa/cm, and becomes stable afterward (Fig. 6b).

Gas phase apparent permeability, widely employed to describe the flow regime variation of the gas phase in two-phase fluid flow ^[14,27], can be calculated using Eq. (2). The gas apparent permeability variation in the charging process agrees with the changing patterns of gas flow and gas saturation, firstly increasing and then becoming stable

with the increase of the pressure square gradient (Fig. 6c).

The 2D and 3D X-CT gray scale images under different charging pressures were acquired by choosing six featured nodes at four different charging states in the pore-scale gas charging physical simulation, including the original dry state, KI solution-saturated state, and states at charging pressures of 0.10, 0.15, 0.20, and 0.50 MPa (Fig. 7). On the grayscale images, the KI solution-saturated pores are bright white, the rock matrix is generally gray, while the part of pores will be complete black after gas intrusion. These imaging features are consistent with those in the pore-scale multiphase flow physical simulation conducted by Armstrong et al. and Khishvand et al. ^[23,36]. According to the grayscale differences among the rock matrix, gas, and aqueous solution, and considering the grayscale differences on the images of different nodes resulted from the gas-water distribution, the pore-scale spatial gas-water distributions at different charging pressures can be constructed by pore-scale in-situ computation and interactive threshold segmentation (Fig. 7g-7i). The pore-throat zones occupied by gas phase were extracted (Fig. 8a-8d), and then the pore- throat skeleton networks at different charging pressures were built by conducting PNM (Fig. 8e-8h). The pore structure parameters for the channels at corresponding nodes were calculated.

Observations on the 2D and 3D original grayscale images and 3D gas-water distribution graphs suggest that natural gas firstly displaced the water in the center of large- sized intergranular pores from the satu rated state to the pressure node of 0.10 MPa (Figs. 7c, 9a, 9d). The gas phase shows a concentrated occurrence at the center of the large-sized pores, while the water phase exhibits a thin-film occurrence and adheres to the pore edges. This is similar to the phenomenon that nitrogen firstly displaced water in the large-sized pores of the heterogeneous sandstone, observed during the capillary drainage process in the X-CT imaging experiment conducted by Lin et al. ^[38-39]. It also agrees with the phenomenon that CO₂ preferentially occupied the center of the pore-throats after precipitation during the carbonated water flooding in the X-CT imaging experiment performed by Alizadeh et al. ^[35]. However, there is still plenty of small-sized pores saturated with brine in this experiment. In space, both the gas phase and water phases are distributed as clusters in pore network (Fig. 7i), and the calculated gas saturation is 40%. The large intergranular pores filled with gas are connected by wide throats, constructing the primary framework of gas charging channels (Fig. 8a, 8e). The continuous gas flow and reduction of water saturation in the pore-throat system of primary framework resulted in an abrupt increase of apparent gas permeability (Fig. 6c).

As charging pressure increased to 0.15 MPa, KI solution adhering to the edges of large intergranular pores was displaced (Figs. 7d, 9b, 9e), making water films thinner and gas saturation higher. Simultaneously, aqueous solution in the center of the smaller intergranular pores was displaced, suggesting that the small-sized pores participate into fluid flow. The gas phase clusters spread, while the water phase turned to thin films (Fig. 7j, 7k). Along with the decrease of water saturation and gas saturation rising to 78% (Fig. 6d), the gas charging channels were expanding (Fig. 8b, 8c). The radii of the spheres and cylinders in the skeleton network increased, and more spheres and cylinders with smaller radii connected to the main body of the charging network (Fig. 8f, 8g). In this expanding process, the increasing gas flow velocity and decreasing water saturation are responsible for the increment of the gas apparent permeability.

The movable water in the connected pore-throat system was almost displaced when the charging pressure increased to 0.50 MPa (Fig. 7f), while the water in the tiny intragranular and intercrystalline pores or strongly absorbed to the edges of the connected pores can be hardly displaced by gas even the charging pressure was further raised (Fig. 9c, 9f), which preserved as bound water. The water phase distributes as disperse thin films, while the gas phase shows a concentrated cluster distribution with the maximum gas saturation reaching 95% (Fig. 7l, Fig. 6d), indicating that the gas charging channel expands to the limit and gas transports through stable channels. In this stage, the gas obeys linear flow and increment of the apparent gas permeability decreases before it stabilizes. During the steady-state charging procedure, the gas flow pathway is characterized by a stable and continuous variation, which differs from the intermitted variation of fluid flow channel in the transient flow reported by Spurn et al. through synchronous X-CT scanning during CO₂ injection procedure. But it is analogous to the flow channel variation in the steady-state flow in their experiment ^[52].

Analyses on the pore structure parameters of the gas charging channels at different charging pressure nodes suggest that the maximum pore and throat radii of the channels do not vary with the charging pressures, with an exception that the maximum pore radius increases slightly at the pressure of 0.15 MPa, in which the maximum pore and throat radii stabilize at approximately 116 μm and 78 μm, respectively. The results suggest that large-sized pores and throats completely participate into the fluid flow at the initial charging stage, whose contributions to the channel reach the maximum at the beginning (Fig. 9g). However, the decreases of average pore radius, throat radius, coordination number, and throat length along with the increasing pressure indicate that smaller pores and throats make more contributions to the gas charging with the expansion of the channel (Fig. 9h). The greatest reduction of average pore structure parameters was observed at 0.10-0.15 MPa, suggesting the greatest expansion of the gas charging channel and the dominant role of small-sized pores in the middle charging stage. It can be inferred that large intergranular pore-throats are dominant at the initial charging stage, while small intergranular pores and connected intragranular pores determine the expansion of the channel in the later charging stage, and also determine the expansion limit (Figs. 7-9).

The volume fractions of gas phase in the pores and throats with different radii at different charging nodes can be calculated using the Eq. (3), whereby the pore-scale gas-bearing variations during the charging process can be plotted (Fig. 10a, 10b).

The gas-bearing variation plots suggest that the gas volume in pores with radii greater than 20 μm account for 90.35% of the total gas volume in all of the pores, and that in throats with radii greater than 20 μm account for 76.90% of the total gas volume in all of the throats in the initial gas charging stage (charging pressure of 0.10 MPa). It should be noted that the gas volume fraction of pores with radii greater than 80 μm reaches the maximum in the initial stage, indicating that these pores act as an important controlling factor on the gas flow behaviors, gas and water occurrence states, and gas saturation growth pattern in the initial stage. When the charging pressure increases to 0.15 MPa, the increase of gas volume fraction mainly originates from the pores and throats with the sizes of 20-70 μm, accounting for 80.21% and 80.31% of their respective increments of total gas volume fraction (Fig. 10c, 10d). When the pressure increases to 0.20 MPa, the increase of gas volume fraction barely happens in the pores and throats with radii greater than 50 μm, but the pores and throats with radii of 20-50 μm dominate the increase, which account for 85.42% and 93.29% of their respective increments of total gas volume fraction (Fig. 10c, 10d). This variation suggests that the small-sized pores and throats serve as the main controls for the gas-water distribution variation and gas saturation growth with increasing charging pressure. The gas volume fraction increase mainly occurs in the pores and throats with the size of 3-50 μm when the charging pressure rose to 0.50 MPa, which account for 84.43% and 85.86% of their respective increments of total gas volume fraction (Fig. 10c, 10d). With the charging pressure rising from 0.15 to 0.50 MPa, the increments of gas volume fraction in the pores and throats with radii smaller than 20 μm rises from 0.224% to 0.428% and from 0.54% to 0.65%, respectively. It indicates that the pores and throats with radii smaller than 20 μm determine the variations in the gas-water distribution and growth in gas saturation in the late charging stage (Fig. 10).

The correlations between the pore structure parameters of the gas phase charging channel and gas apparent permeability at different charging pressure nodes show that the variation of the apparent permeability is negatively correlated to the average pore radius, throat radius, throat length, and coordination number, indicating that the change of fluid flow regime during gas charging is controlled by the overall structure of the connected pore-throat system (Fig. 11). Smaller pores and throats participate in gas flow with increasing charging degree, and play a dominant role in enhancing the gas apparent permeability.

These results suggest that the pores and throats with radii greater than 20 μm, especially those with radii greater than 80 μm, construct the primary framework of gas charging in low-permeability (tight) sandstone reservoir. They are responsible for the critical condition of gas charging, and also exert primary effects on the gas flow behavior, gas-water distribution, and gas saturation growth pattern at the initial stage. With charging pressure increasing, the pores and throats with radii of 20-50 μm and smaller than 20 μm successively dominate the expansion of the gas charging channel, and become the controlling factors on the variations in the gas flow regime, gas-water distribution, and gas saturation growth. Moreover, the pores and throats with radii smaller than 20 μm serve as the most important controls on the stable gas-water distribution and the maximum gas saturation in the late charging period (Figs. 10 and 11).

The gas saturation viewed on the vertical slices of the core image sequences at different charging pressure nodes (Fig. 12a) shows that the gas saturation on the vertical slice sequence at 0.10 MPa is almost even, and fluctuates slightly at the gas saturation axis of 40%. With the increase of charging pressuring, evident differences appear in gas saturation in the middle stage. When the pressure increases to 0.15 MPa, the gas saturation on the slice increases on the whole, but is different in different zones. The gas saturation increase in zones # 175-400 is much greater than the other zones owing to the presence of connected larger pores (Fig. 12b). The overall gas saturation shows a small increase when the charging pressure reaches 0.20 MPa, indicating that gas is mainly charged into smaller pores and accumulates in local. As the charging pressure increases to 0.50 MPa, there is a certain degree of increment in the gas saturation on the slice, and the differences in the gas saturation of vertical slice reduce comparing with those of the middle stages since the movable water is almost displaced. The gas saturation reaches the maximum and overall distribution of gas saturation is even, with exception that the gas saturation in zones # 50-150 stays low (Fig. 12a, 12b). It can be discovered that the gas saturation in the zones dominated by large connected pores and throats exhibits a two-stage growth pattern, increasing rapidly before becoming stable, while the variation in the zones dominated by small connected pores and throats is complex (Fig. 12a, 12b). The heterogeneity of the pore structure exerts an evident impact on the dynamic variations in the gas-water occurrences and gas saturation during the charging process, which further leads to the gas-bearing heterogeneity in low-permeability (tight) sandstone reservoirs.

The gas charging in the low-permeability (tight) sandstone can be divided into two stages, including charging channel expansion stage and stabilized stage. In the expanding stage, gas displaces water from large-sized intergranular pores prior to small-sized intergranular pores and from the center of pores prior to the edge. With increasing charging pressure, the gas charging channel expands, and water in the center of small-sized pores and absorbing to the edge of large-sized pores is displaced. The gas phase is distributed as clusters, while water phase is dispersed as thin films. The expansion brings reductions to the pore radius, throat radius, throat length, and coordination number of the charging channel, which is also the main stage for gas saturation growth. At the stable stage, the gas charging channel expands to the limit, in which the pore structure parameters keep stable, and gas transports continuously along the stable channel, resulting in stable gas-water occurrence state and making gas saturation reach the maximum.

The pores and throats with radii greater than 20 μm construct the basic framework of gas charging channel in the initial gas charging stage, which govern the fluid flow regimes. The pores and throats with radii of 30-50 μm are dominant storage spaces for gas, influencing the gas-water occurrence and distribution and gas saturation growth pattern. With increasing charging pressure, the pores and throats with radii of 20-50 μm and smaller than 20 μm successively dominate the expansion of the gas charging channel, controlling the later variations in the gas-water distribution and gas saturation growth. Especially, the connected pores and throats with radii smaller than 20 μm determine the expansion limit of the gas charging channel, and control the formation of the stable gas-water distribution and the maximum gas saturation.

The heterogeneity of the micro-nanometer pore-throat system exerts a great impact on the dynamic gas-water distribution in the gas charging process. Zones dominated by large-sized connected pores and throats exhibit greater gas saturation increments. The heterogeneity of connected pores and throats will further influence the gas-bearing heterogeneity in low-permeability (tight) sandstone reservoirs.

A—cross-section area of the core, cm²;

K_a—gas apparent permeability, 10^-3 μm²;

L—core length, cm;

p₀—standard atmosphere pressure, MPa;

Δp—charging pressure, MPa;

Q—gas flow rate, mL/s;

S_gi—the gas saturation at the ith charging pressure node, %;

μ—gas viscosity, mPa·s;

ϕ—total porosity, %;

ϕ_g—volume fraction of gas in pore-throats with different sizes, %;

ϕ_gi—total volume fraction of gas at the ith charging pressure node, %;

ϕ_p—volume fraction of pore-throats with different sizes, %;

ϕ_wo—total volume fraction of pore water at the KI solution-saturated stage, %.