Study on the Flow Behavior of Gas and Water in Fractured Tight Gas Reservoirs Considering Matrix Imbibition Using the Digital Core Method

Abstract

Tight gas reservoirs possess unique pore structures and fluid flow mechanisms. Delving into the flow and imbibition mechanisms of water in fractured tight gas reservoirs is crucial for understanding and enhancing the development efficiency of such reservoirs. The flow of water in fractured tight gas reservoirs encompasses the flow within fractures and the imbibition flow within the matrix. However, conventional methods typically separate these two types of flow for study, failing to accurately reflect the true flow characteristics of water. In this study, micro-CT imaging techniques were utilized to evaluate the impact of matrix absorption and to examine water movement in fractured tight gas deposits. Water flooding experiments were conducted on tight sandstone cores with different fracture morphologies. Micro-CT scanning was performed on the cores after water injection and subsequent static conditions, simulating the process of water displacement gas in fractures and the displacement of gas in matrix pores by water through imbibition under reservoir conditions. Changes in gas–water distribution within fractures were observed, and the impact of fracture morphology on water displacement recovery was analyzed. Additionally, the recovery rates of fractures and matrix imbibition at different displacement stages were studied, along with the depth of water infiltration into the matrix along fracture walls. The insights gained from this investigation enhance our comprehension of the dynamics of fluid movement within tight gas deposits, laying a scientific foundation for crafting targeted development plans and boosting operational efficiency in such environments.

1. Introduction

Traditional natural gas reserves are progressively being exhausted; the large-scale development of tight gas resources has become an important approach to supplementing traditional gas sources [1,2,3]. Their notable low permeability and intricate pore formations characterize these reservoirs; tight gas reservoirs exhibit poor gas mobility, resulting in the low efficiency of traditional oil and gas extraction techniques in tight reservoir development [4,5,6,7]. Hydraulic fracturing technology, which fractures reservoir rocks with high-pressure fluids to increase rock permeability, enabling gas to flow and be effectively extracted, is a key technology for developing tight gas reservoirs [8,9,10,11]. Inherent water saturation exists within tight sandstone deposits, and the process of fracturing introduces substantial water volumes into these deposits. This alters the typical single-phase flow in the matrix to a more complex two-phase flow of gas and water within both fractures and the matrix [12,13]. The dynamics between gas and water in such tight environments significantly surpass the complexity found in standard reservoirs, underlining the importance of a thorough grasp of gas and water movement patterns for strategic development and efficiency enhancement.

A considerable amount of research has been conducted on the flow patterns of gas and water in sandstone reservoirs. For the flow in the matrix of sandstone reservoirs, predecessors have studied the effects of factors such as pressure gradient, stress, and water saturation on the flow patterns of gas and water through numerical simulation methods [14,15,16,17,18,19,20]. For fluid flow in the fractures of tight reservoirs, scholars have conducted numerous studies using numerical simulation and experimental methods. Saboorian-Jooybari, H. and Wu et al. [17] proposed an innovative analytical approach to accurately determine gas–liquid relative permeability within fractures. Liu et al. [21] crafted a mathematical formulation for modeling water and gas flow within the natural fracture–shale matrix setup, triggered by hydraulic fracturing activities, which encompass aspects like hydraulic, capillary, and permeation convection, along with gas adsorption and the sealing of natural fractures. Utilizing the volume of the fluid model, Huang et al. [22] applied CFD (computational fluid dynamics) software for the delineation of the gas–liquid two-phase flow interface within micro-fracture networks, exploring gas flow traits at the micro-level and the influence of fluidic parameters on flow regimes. Wang [23] and his team’s visual experiments revealed diverse gas–water two-phase flow patterns in fractures, identifying several flow typologies like bubble, stratified, slug, wave, annular-mist, and mist flows, influenced by various gas and liquid rate combinations. Chen et al. [24] adopted a method that combines large-scale physical simulation with discrete fracture numerical simulation to study the patterns of water invasion and customize water control strategies based on the water invasion patterns.

Additionally, water imbibition in tight gas reservoirs is also a critically important issue of concern. Water imbibition can affect the flow behavior of gas in reservoirs, thus impacting the productivity of gas reservoirs [25,26]. For water-bearing tight sandstone gas reservoirs, water imbibition may serve as a potential mechanism for enhanced production [27]. By thoroughly studying the laws of water imbibition, water flooding techniques can be explored to increase the recovery rate of gas reservoirs, facilitating the efficient development of oil and gas resources. Scholars both domestically and abroad have conducted extensive and in-depth experimental research as well as numerical simulation studies, gradually revealing the mechanisms and influencing factors of water imbibition in tight gas reservoirs [28,29,30,31].

In the context of fractured tight sandstone gas deposits, water traverses through fractures and simultaneously seeps into the matrix via imbibition. However, most scholars tend to separate these two phenomena for research, which fails to accurately reflect water movement patterns within these reservoirs. In this study, the digital core method was employed to conduct water displacement gas experiments on tight sandstone cores with different fracture morphologies. By performing CT scans on the cores after displacement at different displacement nodes and after static conditions, the water displacement gas process in fractures and the water imbibition process in the matrix under reservoir conditions were simulated separately. Monitoring the spatial distribution of gas and water within fracture systems offers valuable insights. The impact of fracture morphology on water displacement recovery rate was analyzed. The water displacement gas recovery rate in fractures and the imbibition recovery rate in the matrix at different displacement stages were studied, and the depth of water infiltration into the matrix along the fracture walls was determined. This research approach provides a new perspective for studying the flow patterns of gas and water in fractures and the matrix in fractured gas reservoirs, and the results of the study provide data support for the evaluation of reservoir productivity and reserve estimation.

2. Methodology

2.1. Core Preparation

The research specimens were sourced from the tight sandstone formations within the Keshen sector of the Tarim Oilfield, situated in China. The reservoir burial depth is greater than 6000 m, with a pressure coefficient of about 1.8. The porosity is usually less than 8%, and the permeability is generally lower than 0.1 × 10⁻³ μm. Using six cylindrical core samples of tight sandstone with a diameter of 25 mm as the research objects, artificial fractures were created to conduct water flooding gas displacement experiments. To simulate different types of fractures found in real reservoirs, the artificially created fractures included transverse fractures (TF), conjugate fractures (CF), and longitudinal fractures (LF). CT scans were performed on the fractured cores at a resolution of 17 μm, as shown in Figure 1. The basic information of the cores is presented in

Table 1. Experimental core sample information.

Number	Length, mm	Matrix Permeability of Dry Sample, 10−3 μm3	Matrix Porosity of Dry Sample, %	Fracture Porosity of Dry Samples, %	Type of Fracture
No. 1	38.42	0.089	7.08	0.21	TF
No. 2	35.22	0.079	6.30	1.88	CF
No. 3	33.12	0.038	5.08	1.57	CF
No. 4	36.68	0.068	4.79	1.88	LF
No. 5	31.23	0.083	8.06	0.75	LF
No. 6	38.49	0.097	5.44	1.14	LF

, where it is noteworthy that the fracture porosity in Table 1 represents the dry sample porosity observed under 15 MPa confining pressure in subsequent displacement experiments.

2.2. Experimental Plan

Conduct water flooding displacement experiments on the above six artificially fractured core samples. To enhance the contrast of gas–water phases during displacement, the displacement solution is a water solution containing an added contrast agent. The primary steps involved in the experiment are as follows:

(1) Secure the core samples within the clamp, adjust the confining pressure to 15 MPa, the outlet pressure to 12 MPa, and set the temperature to 90 °C. Once equilibrium is achieved, execute micro-CT scans on both the top and bottom sections of the dry core samples, achieving a resolution of 17 μm.

(2) Set the injection rate to 0.005 mL/min, injecting from bottom to top. Measure the injected volume at the inlet of the core samples. Inject 0.15 pore volume (PV), 0.3 PV, 0.5 PV, 1 PV cumulative pore volume of water. After each injection, perform CT scans on the upper and lower sections of the core samples, then allow them to stand for 12 h before performing another set of CT scans. Repeat the process for each volume multiple. The experimental process involves injecting the predetermined volume of water, performing CT scans, allowing for a 12 h static period, and conducting another CT scan. It should be noted that there are differences in the water injection nodes for each sample. Sample 6# does not undergo a 12 h static period after each water injection before injecting the next volume multiple directly.

2.3. CT Scan Image Processing

The images from CT scans at different water injection nodes were reconstructed, filtered, and denoised [32,33], followed by segmentation of the three phases: gas, water, and rock matrix. In this study, WEKA software was used for image threshold segmentation. The image threshold segmentation function in WEKA software [34,35] is mainly based on machine learning algorithms. Image segmentation progresses through stages including the extraction of grayscale features, preparation of data, creation of labeled datasets, choice of classifiers, training of the segmentation model, evaluation of the model’s performance, segmentation of additional images, and their subsequent refinement, all facilitated by advanced algorithms and machine learning techniques; manual intervention is greatly reduced, thereby enhancing the accuracy and consistency of image segmentation.

2.4. Analysis of Water Flooding Flow Patterns

Based on the gas–water–rock images at different displacement stages, the process of water infiltration can be intuitively observed. Due to the limitation of scanning resolution (17 μm) and the small pore size of the tight rock matrix, CT imaging primarily reveals alterations in gas and water distribution within fractures, with changes within the matrix pores being less discernible. The post-displacement static period is the process where water infiltrates into the matrix through imbibition. The difference between the water volume in the fractures after a certain displacement node injection and the water volume in the fractures after 12 h of a static period represents the amount of water infiltrated into the matrix. At any given stage, displacement efficiency is determined by the ratio of the cumulative water volume within the fractures post-static period plus the water volume absorbed by the matrix against the core’s total pore volume. It is important to note that prior to fracturing, the core’s bound water saturation was established between 30% and 40%. The core pore volume used in calculations excludes the volume of bound water. By statistically analyzing the gas and water content during the water flooding process, changes in water saturation can be analyzed, thus obtaining the water flooding recovery curve.

By separately counting the water volume entering the fractures and the water volume infiltrating into the matrix during the displacement process, we can determine the contributions of fractures and matrix to the water flooding recovery. The recovery contribution from fractures is calculated as the ratio of the total water volume in the fractures after each displacement node’s static period to the total volume of core pores. The matrix’s contribution to recovery is quantified by the proportion of the total water volume that permeates the matrix during each displacement node’s static period to the total volume of core pores.

2.5. Calculation of Water Imbibition Depth into the Matrix

During the water injection (WI) stabilization process (i.e., static period), a reduction in water volume within the fractures is indicative of water seeping into the matrix pores via imbibition. Assuming that water ingresses into the matrix uniformly along the fracture pore walls observed by micro-CT scanning, the infiltration depth of water into the matrix is calculated as the ratio of the water volume entering the matrix against the combined product of the fracture surface area and the matrix’s porosity(see Equation (1)), derived by aggregating the fracture surface area, water volume entering the matrix, and matrix porosity. The depth of water infiltration into the matrix along the fracture surface can be calculated as follows:

$$h=\frac{V_w}{S_f\times {\varnothing }_m}$$

(1)

In the above equation: h represents the depth of water infiltration into the matrix along the fracture surface, m; V_w is the metric for the water volume entering the matrix, m³; S_f represents the fracture surface area, m²; $\varnothing$m indicates the core matrix’s porosity.

3. Results and Discussion

3.1. Distribution of Fluids at Different Displacement Stages

3.1.1. Observation of Gas and Water Distribution Images

By conducting threshold segmentation of gas, water, and rock skeleton phases on the CT scan images at different displacement nodes, observations reveal variations in gas and water distributions within fractures throughout the displacement activity, with samples 1#, 3#, and 5# illustrating these changes, as shown in Figure 2, Figure 3 and Figure 4. In these illustrations, water is depicted in blue, gas in red, and the rock matrix in gray.

For the transverse fracture (Figure 2), even after injecting 0.15 PV of water and allowing for a static period, there is still no water phase observed in the fracture; this indicates the water front has yet to penetrate the fracture, necessitating additional water injections to detect the presence of water within the fracture, particularly in scenarios involving longitudinal fractures (Figure 3) and conjugate fractures (Figure 4). Water enters the fractures from the beginning of injection (0.15 PV) and gradually fills the fractures. During the static period after water injection, the water in the fractures decreases, infiltrating into the matrix of the core.

3.1.2. Water Saturation Changes

Data on the water content within fractures are gathered post-displacement across various stages and the water content in fractures after the static period is shown in Figure 5.

Compared to the artificially fractured cores where fractures do not completely penetrate longitudinally (Figure 5a,b), for cores where fractures fully penetrate longitudinally (Figure 5c–f), the water flooding front arrives at the fractures earlier. With increased volumes of the water injected, the imbibition effect transfers water from fractures into the surrounding matrix, although the extent of the water absorbed by the matrix through imbibition diminishes progressively. For the 6 tight sandstone cores in the experiment, at the moment of injecting 0.5 PV of water, over 90% of the fracture volume is filled with water, and, thereafter, there is no significant change in fracture water saturation with continued water injection.

3.2. Displacement Efficiency

The water flooding efficiency for each sample is shown in Figure 6. Before injecting 0.3 PV of water, the water flooding recovery rate increases linearly with the increasing water injection volume. At 0.5 PV of water injection, a turning point appears in the water flooding recovery rate, where the increase slows down, and the continued water injection has little effect on enhanced recovery. This indicates that, before injecting 0.5 PV of water, it is the main stage of water flooding for gas recovery. The water flooding efficiency is higher for samples 2#, 3# (CF), and 4# (LF), exceeding 50%; samples 5# and 6# (LF) have intermediate water flooding efficiency, ranging from 20% to 30%; sample 1# (TF) has the lowest water flooding efficiency, less than 10%. Therefore, conjugate fractures are most conducive to water flooding gas recovery, followed by longitudinal fractures, while transverse fractures exhibit the poorest water flooding effect. Sample 6# did not undergo a static period after water injection, thus failing to utilize the capillary action of matrix pores through imbibition. Therefore, water saturation within the fractures rapidly attains its maximum capacity, leading to negligible increases in the rate of recovery from water flooding and, ultimately, a significantly reduced efficiency in water flooding recovery.

Weighing the core samples before and after the flooding experiment allows for the calculation of water absorption by comparing their mass difference, which represents the amount of water that penetrated the core. Then, based on the core volume and porosity, the water flooding recovery rate could be calculated. The water flooding recovery rate obtained through weighing was compared with the water flooding recovery rate obtained through CT scanning using digital core technology, as shown in Figure 7.

The similarity in recovery rates determined through digital core analysis and traditional weighing methods underscores the efficacy of employing CT scanning to monitor and quantify changes in water saturation within fractures across different stages of water flooding. For instance, in sample 1# with transverse fractures, the initial water phase enters the matrix at the onset of injection, reaching the fractures only after achieving a certain level of saturation in the matrix. Given the limitations in resolution, this process is less observable in the matrix, leading to a discrepancy in recovery rates measured by CT scanning and those determined through experimental weighing.

The recovery rates through imbibition in the matrix and water flooding in the fractures are examined separately, as shown in Figure 8. It should be noted that since sample 6# did not undergo a static period after water injection, the recovery rate through imbibition is not considered.

Displacement efficiency within the matrix can be categorized into three phases in Figure 8a. Initially, a rapid linear increase in imbibition recovery rate is observed until 0.3 PV. This is followed by a deceleration in recovery rate growth between 0.3 PV and 0.5 PV. The third stage is the late stage of imbibition, where the imbibition recovery rate basically remains unchanged over time, indicating that the imbibition process is essentially completed. The segmentation of the imbibition process into distinct stages arises from the interplay of multiple forces, including capillary, viscous, and gravitational forces, which dominate at different phases of the imbibition, especially noticeable during the initial stage; although there are viscous and gravitational forces, the capillary force predominates, and the resistance can be ignored, resulting in a strong driving force for imbibition and, thus, a rapid imbibition rate. After a period of imbibition, as gravity gradually increases and cannot be ignored, the combined force of the three forces decreases, resulting in a slower imbibition rate. In the late stage of imbibition, the resistance becomes increasingly significant, and the capillary force cannot overcome the resistance to drive the imbibition process effectively, resulting in an insignificant imbibition effect.

Figure 9 shows the correlation between matrix and fracture recovery rates and fracture porosity. It can be observed that both matrix and fracture recovery rates are positively correlated with fracture porosity. Except for sample 5#, the overall matrix recovery rate of the other samples is either equal to or slightly lower than the fracture recovery rate. Notably, sample 5# demonstrates a matrix recovery rate that markedly surpasses the recovery rate from fractures, while the porosity of fractures in sample 5# is relatively low. This indicates that, in reservoirs with small fracture volumes, it may be beneficial to extend the soaking time appropriately to fully utilize the imbibition effect of matrix porosity, thereby increasing reservoir recovery.

3.3. The Depth of Water Invasion into the Matrix Due to Water Imbibition

The depth of water infiltration into the matrix for the rock core samples is presented in

Table 2. The depth of water invasion into the matrix.

Core Number	Depth of Invasion (10−2 m)
1#	1.569
2#	0.408
3#	0.343
4#	0.691
5#	0.193

. During the static phase after water injection, the average depth of water infiltration into the matrix is 0.674 cm. Sample 1#, characterized by a very small fracture area, exhibits the greatest infiltration depth, while sample 5#, owing to its higher matrix porosity, shows a relatively smaller infiltration depth.

4. Conclusions

This study conducted water flooding experiments on tight sandstone cores with different fracture morphologies under reservoir conditions. Micro-CT scans were performed to observe the gas displacement process in the fractures and the process of gas displacement by imbibition. Changes in gas–water distribution in the fractures during displacement were observed, and the study closely examined how the shape and structure of fractures impact the efficacy of water flooding recovery. Moreover, the recovery rates of matrix imbibition and fracture flooding at different displacement stages were investigated, and the depth of water infiltration into the matrix along the fracture walls was calculated. Through these comparisons, the following understandings were obtained:

(1) A comparison between the water flooding recovery rates obtained using digital rock CT scanning technology and those obtained traditionally through core weighing showed good consistency, verifying the reliability of studying the water flooding process using digital rock technology.

(2) For the artificial fractured tight sandstone cores used in the experiments, the period before injecting 0.5 PV of water was the main stage of gas displacement by water flooding. Conjugate fractures were most favorable for gas displacement by water flooding, followed by longitudinal fractures, while transverse fractures showed the poorest water flooding effectiveness due to the lack of effective flow channels.

(3) Water flooding recovery rates were significantly positively correlated with fracture volume. For reservoirs with small fracture volumes, the subsequent static period after water injection (soaking period), which allowed the capillary action of the matrix pores to come into play, can significantly increase the overall water flooding recovery rates.

(4) The process of water being absorbed into the matrix is systematically divided into three distinct phases. In the initial stage, the dominate capillary forces will result in linear growth in imbibition recovery rates. During the mid-stage of imbibition (0.3 PV~0.5 PV), as the imbibition advances, the acceleration in recovery rates observed initially tends to decrease. In the late stage of imbibition (after 0.3 PV), the capillary forces are unable to overcome the resistance to drive the imbibition process, resulting in imbibition recovery rates essentially no longer changing over time.

(5) The average depth of water infiltration into the matrix along the fracture surface in this study was 0.674 cm, providing data support for guiding the evaluation of reservoir productivity and reserves and formulating production strategies for this type of gas reservoir.