Experimental and Numerical Investigations of Low-Permeability Sandstone Under Water Injection–Induced Dilation in West Oilfield, South China Sea

Abstract

With the development of offshore oil fields, the reservoirs of X oilfield in the west of the South China Sea are poor in physical property, serious in pollution, and increasingly prominent in interlayer contradictions. Water injection dilation technology has strongly affected the development of loose sandstone reservoirs. To explore whether this technology applies to the low-permeability sandstone of X oilfield in the west of the South China Sea and the dilation effect and radius of water injection dilation technology on the target reservoir, low confining pressure rock mechanics experiments and numerical simulation of water injection in this reservoir section are carried out. The triaxial shear experiment of low confining pressure shows that the target reservoir sandstone with low-permeability can have a shear strength of 45 MPa when the effective confining pressure is 0.5 MPa, and the target reservoir core can have dilatancy. When the axial strain is 2.5%, the core dilatancy is 1%, and the permeability changes by 1.17 times. It was found that the core volume dilation was obviously under low effective confining pressure, and the permeability is 2 orders higher than in the initial condition. The numerical simulation of the target reservoir shows that the bottom-hole pressure reaches 47.12 MPa at the end of water injection in typical wells. The reservoir was deformed to different degrees around the well, and the top layer was raised by 5.58 mm. This paper characterizes the rock expansion potential and expansion flow capacity of low-permeability sandstone reservoirs from multiple perspectives and establishes a three-dimensional, full-size wellbore formation crustal stress strict matching geological model for offshore expansion wells. We have provided theoretical guidance for on-site construction.

1. Introduction

With the research on unconventional oil fields, the conventional production of medium- and low-permeability sandstone oil fields is relatively low. Therefore, reservoir modification technology is needed to improve its recovery rate. The commonly used techniques for improving oil recovery in medium- and low-permeability sandstone reservoirs include conventional fracturing [1,2,3,4,5] and acid fracturing [6,7,8]. However, currently, offshore platform resources are precious, and the use of large-volume equipment should be reduced. Therefore, whether small-volume equipment can be used for reservoir modification of low-permeability sandstone at sea has become a research question.

X oilfield in the west of the South China Sea is rich in low-permeability reserves. Still, the reservoir has poor physical property, severe pollution, and prominent interlayer contradictions. To release the production capacity of low-permeability reservoirs, most oilfields in Weizhou are mainly developed by waterflooding, with complex water source types and a high proportion of clean and mixed injection. With the continuous development of Weizhou Oilfield, water injection well pressure increases year by year due to microparticle blockage near wells [9]. The offshore oil field adopts different ways to remove plugging to solve the high water injection pressure. At present, the most commonly used plugging removal technology is acid plugging.

With the increase of acidification times, the effect of reservoir injection worsens, and the validity period becomes shorter, which seriously affects the difficulty and economy of reservoir development. Finding a new injection technology with low cost, long validity, and convenient operation is urgent. Inspired by “SAGD (Steam Assisted Gravity Drainage) capacity dilation technology of oil sands [10,11,12,13]” at home and abroad, a new water injection capacity dilation technology of low-permeability sandstone at sea is proposed. This technology reduces the effective stress of the target reservoir by controlling the wellhead displacement and bottom-hole pressure of the injection well, promotes the formation of the shear dilation zone and tension dilation zone of the reservoir rock, increases the porosity and permeability of the reservoir near the injection well, and improves the production efficiency.

In the early stage, water injection capacity dilation technology was applied in SAGD technology of oil sand mining to solve the problems of long preheating periods and uneven heat receiving in SAGD technology [13,14]. With the increase of successful cases abroad, SAGD technology was adopted for oil sands exploitation in the Xinjiang oilfield in 2013, and a pilot test was conducted in Fengcheng Oilfield [15,16,17,18]. For capacity dilation technology, domestic and foreign scholars have carried out corresponding theoretical, laboratory experiments, and numerical simulation research [15,16,17,18,19,20,21]. Rowe et al. [22] proposed a theoretical model of sand strength and dilation. Bolton et al. [23] summarized the dilatancy angle of sandstone and proposed the theoretical relationship between dilatancy performance and critical strength angle. Lin [24,25,26,27] et al. conducted a rock mechanics experiment and numerical simulation analysis for SAGD capacity dilation in Fengcheng oil field, Xinjiang, and explained the mechanism of oil sand reservoir capacity dilation and the numerical simulation results of SAGD reservoir in oil sand reservoir, respectively. Chen et al. [28]. Conducted water injection simulation experiments and numerical simulation analysis for offshore unconsolidated sandstone water injection wells and expounded that water injection capacity expansion technology has a good prospect for application for offshore low-permeability sandstone.

In developing offshore low-permeability sandstone reservoirs, the plugging near the injection well is similar to the connectivity between two horizontal wells in the oil sand. However, the target oil reservoir is low-permeability sandstone, and the degree of influence of water-injection dilation technology on low-permeability sandstone needs to be studied in the early stage. The development and distribution of reservoir fracture zones are closely related to rock mechanical properties and geo-stress characteristics of reservoirs [29,30,31]. Therefore, it is necessary to conduct mechanical experiments to explore whether the rock of the target reservoir has the capacity for water injection and how much capacity it has before water injection dilation of the low-permeability reservoir.

The effect of low-permeability sandstone on water injection dilation (shear dilation and tensile dilation) in X oilfield is studied by numerical simulation of a primary water injection well in this oilfield. The area affected by the water injection dilation process is determined according to the dilation radius simulated by numerical simulation, and guiding opinions are provided for on-site construction.

This paper uses the effective confining pressure triaxial test to determine whether the low-permeability sandstone of X oilfield in the west of the South China Sea has the capacity for water injection expansion. According to the axial and radial sensor values in the triaxial test, whether the experimental core has shear dilatancy is determined. Inspired by G. M. Lomize et al.’s [32,33,34,35] study on rocks’ shear and seepage coupling characteristics, seepage testing was carried out in the triaxial experiment of stones. The expansion effect of low-permeability sandstone cores under low confining pressure is further judged by seepage capacity.

Numerical simulation was born in 1953 by experts Bruce G. H. and Peaceman D.W. to simulate one-dimensional gas phase unstable radial and linear flows. In 1955, Peaceman and Rachford developed the Alternate Implicit Solution (ADI), which applied numerical simulation to petroleum, nuclear physics, heat conduction, and other fields. In 1959, Douglas Jim and Peaceman D. W. performed the first 2D two-phase simulation, which marked the beginning of modern numerical simulation techniques. The simulator adds the effects of relative permeability, viscosity, density, gravity, and capillary pressure. Stone published the three-phase relative permeability model in the 1970s, which calculated the relative permeability of oil, gas, and water in a three-phase flow from the two-phase relative permeability of oil, water, and oil.

By simulating the reservoir, the numerical simulation technology can predict the feasibility verification and development benefits of different reservoir technologies. In this paper, the historical fitting of the typical well and the numerical simulation of water injection expansion were carried out to obtain the reservoir volume deformation, permeability variation, and pore pressure at monitoring points after using water injection dilation technology.

This paper attempts to solve the problem of the low injectivity of injection wells and the low recovery of production wells in the offshore low-permeability sandstone oil fields. To improve injectivity and recovery, a new reservoir stimulation technology named water injection–induced dilation is more suitable for offshore oil fields than common reservoir stimulation methods such as hydraulic fracking. The current production is relatively low, with the long-term development of unconventional low-permeability sandstone oil fields. Therefore, a proper reservoir stimulation technology should be employed to improve its recovery. Common techniques for improving oil recovery in low-permeability sandstone reservoirs include conventional hydraulic fracking and acid treatment. However, the space of offshore platforms is limited, so the large equipment for fracking is not suitable. In this regard, inspired by a new reservoir stimulation method applied in the development of oil sands and offshore loose sandstone reservoirs, the water injection–induced dilation technology is adopted for offshore low-permeability sandstone reservoirs by increasing the porosity, permeability, and micro-fractures in the near-wellbore region. This paper will study core-scale triaxial compression experiments’ deformation and permeability evolution and oil field-scale numerical stimulation.

The novelty of this paper embodies the first attempt at the acquirement of the elastoplastic mechanical parameters such as elastic modulus, Posson’s ratio, cohesion, internal friction angle, and dilation angle using shear dilation and tensile parting dilation experiments for the low-permeability sandstone reservoirs in the west oil field of the South China Sea. Additionally, the permeability evolution with the effective stress and volumetric strain under shear dilation and tensile parting dilation is studied. The CT shows the fracture morphology and the difference between the shear dilation and tensile parting dilation. At last, the 3D full-size geological model considering wellbore trajectory, layers, and geo-stress is established, and a case study is conducted by numerical simulation, which shows good accuracy for predicting the bottom-hole pressure (BHP) compared with field test data.

This paper experimentally achieved in situ permeability testing under shear and tensile dilation paths, innovatively determined the quantitative relationship between volumetric strain and permeability, and proposed a partitioned permeability model based on differential crack development. The workflow of this study is shown in Figure 1.

2. Experimental Material and Experimental Scheme

The dilation of rock water injection mainly depends on the rock’s shear and tensile deformation. Shear deformation, also known as “dilatancy”, refers to the overturning and tumbling of sand particles of rock under shear action, increasing the rock mass volume [36,37]. Tensile deformation mainly increases rock mass volume by increasing pore pressure. When the pore pressure exceeds the tensile strength, tension occurs between rock and sand grains, resulting in microcracks.

2.1. Experimental Instrument

The instrument used in this experiment is the RTX-3000 rock triaxial test system produced by GCTS (Geotechnical Consulting and Testing Systems) Company (Tempe, AZ, USA). The RTX-3000 is shown in Figure 2. This test system is a closed-loop digital servo control device used for simple and rapid triaxial tests of rock samples. It can carry out a variety of rock mechanical experiments and permeability tests under low, effective confining pressure. The test system has four main modules: SCON (Serial Control Register)/data acquisition and control module, axial control module, HPVC cell pressure controller, and steam injection control module. The experiment adopts the standard GB/T 24107.1-2009 [38].

SCON/data acquisition module: SCON is the data and control center, connected to the central control machine, PID control, mainly integrated temperature module, pressure module, displacement control module, and wave speed module, and can collect the indoor confining pressure, temperature, axial pressure, sample radial displacement, and axial displacement in real time for three weeks.

The axial control module has two control modes: displacement control axial strain and stress control axial strain. Two LVDT sensors measure the axial displacement control, and the internal stress sensor in the module measures the axial stress control. The measured data of the module are fed back to the SCON/data acquisition module and then applied to the sample according to the program settings in the control module.

The confining pressure control module also has two control modes: displacement-controlled radial strain and stress-controlled radial strain. Radial displacement control is measured by a chain LVDT (Linear Variable Differential Transformer) sensor, and a module internal stress sensor measures stress control. The measured data of the module are fed back to the SCON/data acquisition module and then applied to the sample according to the program settings in the control module.

The gas injection control module has two gas injection tanks and two gas-filling tanks. The gas injection tanks are injected into the upper and lower ends of the sample, respectively, and the gas-filling tank is filled to ensure that the gas injection tank can be carried out at high pore pressure according to the requirements of the experimental scheme.

2.2. Experimental Material

The experimental cores were taken from the reservoir segment of X oilfield in the west of the South China Sea, and the cores were taken from two positions in well A, with depths of 3176.73 m. Due to the non-standard size of the core provided on-site, to obtain the 25 mm × 50 mm standard size core, it is necessary to take the core machine and other tools for the secondary core. The methods of obtaining standard core in this paper are as follows:

• -. Measuring the length and diameter of two cores;

• -. Take the core into a cylinder of 50 mm in length with a high-speed cutting machine;

• -. Using a coring machine, take out the standard core column with a diameter of 25 mm;

• -. Use the cutting machine to make the two ends of the core column flat, and the flatness of the end face does not exceed 0.1 mm to obtain the core for experimental use. The 25 mm × 50 mm core is shown in Figure 3.

Before conducting mechanical parameter tests on rocks, three sets of samples were subjected to original condition tests. The test results are shown in Table 1.

2.3. Shear Triaxial Experiment

The standard cylindrical core with a diameter of 25 mm for the triaxial experiment was prepared using the underground sandstone core of the target oilfield. The triaxial compression experiment was carried out under the temperature of 20 °C and the low effective confining pressure (0.2 MPa and 5 MPa) by the triaxial press. The shear and dilatation phenomenon of the offshore sandstone during the liquid injection process at different temperatures was simulated by the square model loaded with axial strain. The curves of axial strain–deviating stress and axial strain–volume strain are obtained. The triaxial compression experiment stops when the residual stress is stable. The rock’s corresponding average effective and deviator stress (i.e., critical stress state point) at yield is plotted in the mean effective stress–deviator coordinate system. The critical stress state point is fitted to obtain the yield surface curve. The D–P model describes offshore sandstone’s dilatancy during water flooding. According to the above experimental content, the axial strain–deviating stress curve, axial strain–volume strain curve, elastic modulus, Poisson’s ratio, cohesion force, internal friction angle, dilatancy angle, and other shear dilatancy mechanical parameters can be obtained. The core stress diagram is shown in Figure 4.

The specific process of the shear dilation experiment is as follows: The particular operation steps of the experiment are as follows:

First, start the data acquisition control system, signal regulation controller, and axial compression system; load the standard core into the pressure chamber of the axial compression system; and install the radial and circumaural displacement sensors.

Start the heating belt in the pressure chamber to heat the sample to the set temperature of 20 °C (temperature loading rate is 10 °C/h), and cover the pressure chamber with a glass fiber insulation sleeve for heat preservation. The specimen loading is shown in Figure 5.

Start the hydraulic control station to inject hydraulic oil into the pressure chamber to apply confining pressure to simulate the on-site formation pressure environment.

Start the pore pressure control station to apply 5 MPa pore pressure to the core to simulate the increase in pore pressure caused by water injection.

Connect the instantaneous pulse permeability meter to measure the permeability of the sample before compression.

The axial pressure is applied by loading the upper in-pressure head with a constant strain (0.03 mm/min) and stops when the axial strain reaches 2.5%. This model simulates the deformation characteristics of the oil sand under deviatoric stress after water injection.

The instantaneous pulse permeability meter is connected to measure the permeability change of the sample after compression.

Observe the data changes in the acquisition control system and output the data.

The data acquisition window (real-time monitoring platform) of the GCTS RTX-3000 large-scale high-temperature and high-pressure triaxial experiment used in this study can display and record in real-time many stress–strain and environmental parameters such as confining pressure, pore pressure, axial strain, radial strain, volume strain, temperature, etc., and display the change process of these parameters in real-time. The data acquisition are shown in Figure 6.

2.4. Tensile Triaxial Experiment

The tensile dilatancy mechanics experiment is the isotropic compression experiment or the hydrostatic pressure experiment, mainly used to describe the deformation characteristics of rock under a spherical stress state. The standard cylindrical core (25 mm × 50 mm) with a diameter of 25 mm for the triaxial experiment was prepared using the underground sandstone core of the target oilfield, and the triaxial isotropic compression at 20 °C was tested by the triaxial press.

As the water injection progresses, the injected liquid spreads from the wellbore to the surrounding area. As the injection amount increases, the effective stress of the rock sample near the wellbore gradually decreases.

The main steps of the experiment process are as follows:

As in the triaxial shear experiment, do all the preparatory work, such as sample handling, sample holding, and sensor installation.

Set the loading rate of confining pressure and pore pressure, control confining pressure and pore pressure synchronously, and try to make the confining pressure and pore pressure reach 10 MPa and 5 MPa, respectively, at similar times so that the effective stress of the sample reaches 5 Mpa.

Set the temperature of the pressure chamber to the experimental value (20 °C).

The triaxial isostatic pressure of 5.5 MPa was applied to the sample. The pore pressure was gradually increased from 0.5 MPa to 5 MPa at the loading speed of 0.1 MPa/min and the pressure interval of 0.5 MPa to simulate increasing progressively injection pressure. The stress–strain curve was recorded at the same time.

After loading 0.5 MPa pore pressure every time, observe the volume strain until it becomes stable, conduct one or two permeability tests, and then load the next step.

The unloading pore pressure was reduced from 5 MPa to 0.5 MPa, and the stress–strain curve at the unloading stage of the pore pressure was recorded.

The tension dilation pressure loading curve is shown in Figure 7.

2.5. Permeability Test

There are two standard permeability experiment methods: the steady flow method and the transient pressure pulse method. Steady-state flow method: steady-state flow is a simple and commonly used method for rock permeability measurement. The technique is to form a certain pressure difference at both ends of the specimen. Under pressure difference, the test fluid flows toward the pressure gradient. After the flow rate stabilized, the sample’s permeability was calculated according to Darcy’s law.

When the test medium is liquid, the permeability calculation formula is as follows:

(1)$K={\displaystyle \frac{\mathrm{q}\mu L}{A\left(P_{\mathrm{u}}-P_{\mathrm{d}}\right)}}$

When the test medium is gas, the permeability calculation formula is as follows [39]:

(2)$K={\displaystyle \frac{{2\mathrm{Q}}_0{\mathrm{P}}_{ 0}\mu L}{A\left({P_{\mathrm{u}}}^2-{P_{\mathrm{d}}}^2\right)}}$

where K is the sample permeability, m₂; Q₀ is the gas flow volume, m³/s, under standard conditions; q is liquid volume flow, m³/s; μ is viscosity, Pa·s; P₀ is the standard atmospheric pressure, Pa; P_u is the upstream fluid pressure, Pa; P_d is the downstream fluid pressure, Pa; A is the cross-sectional area of the sample, m²; L is the sample length, m.

Transient pulse method: the transient pulse method changes the upper and lower end pressure from balance to imbalance, forming a pressure difference and producing a pressure gradient. With the fluid pressure gradient migration, the pressure on both ends of the sample gradually recovered balance.

(3)$K=\mu \beta V\left({\displaystyle \frac{\ln \left[\frac{\Delta P_i}{\Delta P_f\left(1+V\right)}\right]}{2\Delta t\frac{A}{L}}}\right)$

where β is the volume compression coefficient of fluid, -; V is the volume of the gas storage tank, m³; ΔP_i is the initial pressure difference, Pa; ΔP_f is the initial pressure difference, Pa; Δt is the test time, s.

This experiment used the transient pulse method to measure the sample’s permeability. Multiple sets of permeability tests were conducted using 2 samples from the above shear dilatancy mechanical experiments and tensile dilatancy mechanical experiments to quantitatively characterize the influence of shear dilatancy (dilatancy) and tensile dilatancy on the permeability of sandstone rocks at sea under different effective confining pressures. The transient pulse permeability test is carried out simultaneously with the triaxial compression test. It can be stopped when the load is loaded to any stress or volume strain state. In this experiment, a permeability test was carried out after the samples were loaded in the triaxial experiment. By default, the permeability test result of this permeability test was the initial permeability (volume strain was 0). The sample’s permeability under arbitrary volume strain was measured in the triaxial experiment. The permeability test is carried out using a rock permeameter, using the RTX-3000 (triaxial) rock permeability test system, which is still produced by the GCTS (Geo) company in the United States. This part of the experiment can provide data for establishing a quantitative relationship between rock deformation porosity and permeability. The pore parameter test experiment is to be carried out.

In the 0.2 MPa low effective confining pressure shear experiment, the permeability test was carried out for the sample’s volume strain of 0%, 0.49%, −0.59%, −3.68%, −9.21%, and −12% successively, and the transverse comparison was made. In the tensile dilatation experiment, the effective confining pressures of 5 MPa, 1.9 MPa, 0.92 MPa, 0.57 MPa, and 0.33 MPa were tested and compared horizontally.

3. Experimental Result

3.1. Shear Triaxial Experiment

The temperature is 20 °C, the effective confining pressure is 0.2 MPa (confining pressure is 5.2 MPa, pore pressure is 5 MPa), and the axial strain is constant (0.03 mm/min). The axial pressure is applied when the axial strain reaches 2.5%. The low-permeability sandstone of X oilfield in the West South China Sea is stopped.

Under effective confining pressure of 0.2 MPa, low-permeability sandstone has undergone 6 stages: elastic deformation, local microcracking of natural weak surfaces (microcracks and bedding), local cracking of natural weak surfaces with strain softening (2 sub-stages), strain strengthening, strain softening, and residual stress. Different degrees of stress drop accompany local microcracking and local cracking of naturally weak surfaces.

It can be seen from Figure 8 that obvious dilatancy occurs at one end of the rock, indicating that the offshore low-permeability sandstone of the target well can undergo shear dilatancy.

The shear strength of the core is 45 MPa, and the dilatancy starts from the second sub-stage when the naturally weak surface is locally broken and accompanied by strain softening. The dilatancy reaches 4% when the axial strain is 13%.

Dilatancy mainly occurs in strain softening and residual stress; the corresponding dilatancy capacity is the largest when the stress falls. In contrast, the strain strengthening inhibits the dilatancy phenomenon, as shown in Figure 9.

This is the stress–strain curve under an effective confining pressure of 0.2 MPa. According to the effective confining pressure stress–strain curve, it can be seen that there are many small peaks generated throughout the entire stage of partial stress rise (elastic stage, local micro rupture stage, and stress softening stage), indicating that low-permeability sandstone at sea has undergone natural weak plane local micro rupture. However, the core did not experience widespread rupture at this time, and the rock’s deviatoric stress continued to rise after falling. This conclusion indicates that the pressure of the target reservoir may continue to increase after a decrease. According to the strain curve, it can be seen that when the axial strain is less than 1%, the core begins to experience shear dilation, with a maximum volumetric strain of 13%. During water injection dilation, rocks with high pore pressure will experience strong volume dilation, consistent with many scholars’ findings [12,13,14,15,16].

This is the stress–strain curve under an effective confining pressure of 0.2 MPa. According to the effective confining pressure stress–strain curve, it can be seen that there are many small peaks generated throughout the entire stage of partial stress rise (elastic stage, local micro rupture stage, and stress softening stage), indicating that low-permeability sandstone at sea has undergone natural weak plane local micro rupture. Nevertheless, the core did not experience widespread rupture at this time, and the rock’s deviatoric stress rose after falling. This conclusion indicates that the pressure of the target reservoir may continue to increase after a decrease.

The temperature is 20 °C, the effective confining pressure is 5 MPa (confining pressure is 5.2 MPa, pore pressure is 5 MPa), and the axial strain is constant (0.03 mm/min). The loading method is to apply axial pressure and stop until the axial strain is 4%. The low-permeability sandstone of X oilfield in the West South China Sea is stopped.

Under the effective confining pressure of 5 MPa, ductile failure occurs in the marine low-permeability sandstone, which goes through 2 stages, pre-peak and post-peak. There are 2 sub-stages (different elastic moduli) before the peak, and the post-peak stress decreases rapidly. After failure, the sample cannot bear the stress (shear failure is divided into two parts), the shear strength is 70 MPa, no obvious dilatancy occurs, and the rock volume is compressed.

It is obvious from Figure 10 that no obvious dilatation occurs in the rock, indicating that the offshore low-permeability sandstone of the target well has a shear phenomenon under the effective confining pressure of 5 MPa.

Dilatancy mainly occurs in strain softening and residual stress; the corresponding dilatancy capacity is the largest when the stress falls. In contrast, strain strengthening inhibits the phenomenon of dilatancy, as shown in Figure 11.

The mechanical parameters of low-permeability sandstone are one of the key factors affecting the applicability of water injection capacity dilation technology. Among them, the elastic modulus, Poisson’s ratio, cohesion force, internal friction angle, and dilatancy angle are all important parameters that affect reservoir reconstruction technology. They are also the input parameters of the subsequent numerical simulation.

This is the stress–strain curve under an effective confining pressure of 5 MPa. According to the stress curve, it can be seen that the effective confining pressure of low-permeability sandstone at sea has undergone ductile failure, which has gone through 2 stages: pre-peak and post-peak. There are 2 sub-stages before the peak of deviatoric stress is reached, each with a different elastic modulus. The deviatoric stress rapidly decreases after reaching its peak. This phenomenon indicates that the rock cannot withstand the stress and undergoes shear failure. According to the strain curve, it can be observed that the rock is continuously subjected to high-strength compression before the peak stress is reached; after the rock stress reaches its peak, the rock is subjected to lower-strength compression. The rock continues to shear and shrink without experiencing shear dilation, which is consistent with the findings of many scholars [12,13,14,15,16].

The elastic modulus is the degree to which the elastic body deforms when an external force is applied. According to Hooke’s law, the stress and stress of an elastic body should become directly proportional, and the proportional coefficient is the elastic modulus. The elastic modulus is an important parameter in engineering. The larger the elastic modulus is, the more difficult the elastic deformation of the rock is; that is, it is not easy to dilate.

(4)$E={\displaystyle \frac{\sigma }{\epsilon }}$

where E is the elastic modulus of the sample, Pa; σ is the specimen stress, Pa; ε is the sample strain, %.

Poisson’s ratio is a constant that reflects the elastic properties of rock. Poisson’s ratio is the absolute value of the ratio of lateral positive strain to axial positive strain under unidirectional compression of rock; that is, Poisson’s ratio ν mathematical model is as follows:

(5)$\nu =-{\displaystyle \frac{{\epsilon }_x}{{\epsilon }_y}}$

where ν is Poisson’s ratio, and ε_x is the radial deformation of rock, %; ε_y is the axial deformation of the rock, %.

The shear dilation angle is a physical quantity used to represent a material’s volume change rate during the shearing process. It describes a material’s volume change when subjected to shear force. The shear dilation angle is an important parameter in the mechanical properties of materials. For rocks with an internal friction angle greater than 30 degrees, the shear dilation angle is the internal friction angle minus 30 degrees [40]. The calculation formula for the shear dilation angle is shown in Formula (6).

(6)$\psi =\beta -{30}^{°}$

where β is the internal friction angle and ψ is the shear dilation angle.

Cohesion is the mutual attraction between adjacent parts of the same substance. Under effective stress, the total shear strength of rock mass is the cohesive force after subtracting the friction strength.

The internal friction Angle is the index of the shear strength of rock. Internal friction angle includes sliding and occlusal friction, an important parameter in engineering design.

Taking X oilfield in the west of the South China Sea as an example, the triaxial shear test of cores extracted from drilling reveals the following parameters for Sample 1. Under low effective confining pressure (0.2 MPa), the elastic modulus of the core is 11.67 GPa, the Posson ratio is 0.17, the cohesion is 6.45 MPa, the internal friction angle is 48.85°, and the dilatation angle is 18.85°. Under a low effective confining pressure (5 MPa), the elastic modulus of the core is 5.00 GPa, the Posson ratio is 0.18, the cohesion is 6.54 MPa, the internal friction angle is 48.85°, and the dilatation angle is 18.85°. The rock mechanical parameters of the samples are shown in Table 2.

According to the rock mechanics parameters in Table 2, this reservoir’s rock mechanics parameters belong to low-permeability sandstone rock parameters. Obtaining parameters can provide parameter support for subsequent numerical simulations.

To further explore the dilatation phenomenon of low-permeability sandstone at sea under effective confining pressure, a 3D X-ray microscope was used to scan the samples after the experiment.

X-ray three-dimensional microscope is an analytical instrument used in mechanical engineering. X-ray three-dimensional microscope uses X-ray as a means of detection, uses perspective projection imaging from different angles, and combines 3D digital imaging construction technology of a computer to build a three-dimensional transmission imaging model of the object to be tested. In the form of images, the internal structure characteristics of the object to be tested, the density of the material, the presence or absence of defects, the location and size of defects, and other information are clearly, accurately, and visually displayed. It can observe the sample’s internal structure in the non-destructive state of the tested object, provide detailed image information, and provide new scientific research and engineering means for digital manufacturing technology’s modeling and simulation process.

The CT scan of the rock core shows that after shearing under an effective confining pressure of 0.2 MPa (Figure 12), the shear dilation under low effective confining pressure will cause the specimen to produce non-closed shear microcracks. The results indicate that using water injection technology can produce a strong dilation phenomenon in reservoirs with low effective confining pressure, permanently expanding the reservoir volume, which is more conducive to developing oil and gas production technology.

The CT scan of the rock core after high effective confining pressure (5 MPa) (Figure 13) shear shows that the effective confining pressure shear compression under this condition will cause penetrating cracks in the rock core without causing shear dilation of the specimen. The results indicate that using low effective confining pressure water injection technology for reservoir transformation will increase the reservoir volume and be more conducive to developing oil and gas production technology.

3.2. Tensile Triaxial Experiment

The temperature is 20 °C, the confining pressure is 5.5 MPa, the pore pressure increases from 0.5 MPa, and the pore pressure is successively 0.5 MPa (effective confining pressure is 5 MPa), 3.5 MPa (effective confining pressure is 2 MPa), 4.5 MPa (effective confining pressure is 1 MPa), and 5 MPa (effective confining pressure is 0.5 MPa): x oilfield, west of South China Sea. By default, the effective confining pressure of 1 MPa is the near wellbore area, the effective confining pressure of 1~2 MPa is the middle position, and the effective confining pressure of more than 2 MPa is the far wellbore area.

In water injection dilation technology, pore pressure increases, effective stress decreases, and volume expands with the progress of water injection. The permeability test of different effective confining pressure stages shows that the volume strain does not increase significantly with the increase of pore pressure, but the permeability rises significantly. It shows that rock pores expand isotropically under tensile dilatation, which is more conducive to oil and gas production than the local dilation state. The effective confining–volume strain curve of 20 °C tensioned dilatation is shown in Figure 14.

According to the effective confining–volume strain curve of 20 °C tensioned dilation, it was found that tensional dilation also has a more significant volume dilation effect as the effective confining pressure decreases. However, compared with tensile dilation, under the same effective confining pressure conditions, tensile dilation causes less change in rock volume strain. This phenomenon indicates that the reservoir water injection dilation and transformation process results in relatively small-volume deformation caused by tensile dilation.

From the CT scan results in Figure 15, it can be seen that there are still many microcrack groups present after the experiment. Compared to shear dilation, tensile dilation did not produce large-scale cracks. Tensional dilation is equivalent to isotropic dilation, and significant changes in permeability can also occur under small-volume strains. When the sample is repeatedly expanded after dilation, the crack group opens faster, and the pore throat channels of the sample are significantly improved. At the same time, it was found that under the condition of no pore pressure, tensile dilation does not have a self-supporting ability, and the crack group is easily closed.

3.3. Permeability Test

In geology and petroleum engineering, permeability describes the energy a rock allows fluids (such as oil, gas, water, etc.) to pass through. This ability is affected by the pore structure inside the rock, including the size and shape of the pores and how they are connected. Absolute permeability refers to the permeability measured in the presence of a single fluid (such as water or oil), while effective permeability and relative permeability relate to multiphase fluids (such as oil and water), and these concepts are particularly important in the study of oil extraction and groundwater flow.

According to the triaxial experiment, both the shear and tensile dilatancy experiments can improve the fluid flow capacity in the rock. At the same time, both shear and tensile dilatancy change the volume of rock, but the way of changing the volume is different. Shear dilation is a large dilation of the local scope, and tensile dilation is a uniform dilation of the overall scope. To quantitatively analyze the influence of two kinds of dilatation on rock flow capacity, this paper quantitatively investigates the permeability.

3.3.1. Triaxial Shear Dilatation Permeability Test

The Kozeny–Poiseuille formula is used in this paper to judge the variation trend of rock permeability under different volume strains [41]. By comparing the measured rock permeability with the theoretical value of the Kozeny–Poiseuille formula, it is found that the permeability measured after rock dilation is the same as the theoretical value under the effective confining pressure of 0.5 MPa, while the permeability measured under rock compression is less than the theoretical value.

(7)${\displaystyle \frac{k}{k_0}}={\displaystyle \frac{{\left(1-\frac{{\epsilon }_{\mathrm{v}}}{\varphi }\right)}^3}{\left(1-{\epsilon }_{\mathrm{v}}\right)}}$

where k is the real-time permeability under different volume strains, m²; k₀ is the permeability when the volume strain is 0, m², ε_v is the volume strain, %; ϕ is rock porosity, %.

In this paper, the transient pulse method is used to measure permeability. According to the triaxial shear dilatation experiment, the permeability test of the shear dilatation sample is carried out at the sample volume strain of 0%, 0.49, −0.59%, −3.68%, −9.21%, and −12%, respectively (positive volume strain indicates the rock compression state, negative volume strain indicates the rock dilation state). When the volume strain of the sample is 0% (the rock’s initial permeability), the rock’s permeability is 2.05 mD. When the volume strain of the sample is 0.49%, the permeability of the rock is 1.84 mD. When the volume strain of the sample is −0.59%, the rock permeability is 2.08 mD. The rock permeability is 4.09 mD when the volume strain is −3.68%. When the volume strain of the sample is −9.21%, the rock permeability is 4.23 mD. When the volume strain of the sample is −12.00%, the rock permeability is 7.90 mD. The 0.2 MPa effective confining pressure underbody strain–permeability (measured vs theory) is shown in Figure 16 and Table 3.

The red dashed line in Figure 16 represents the calculation data of the K–P(Kozeny-Poiseuille) equation. The gray point represents the measured strain change of the rock sample when the effective confining pressure is 0.2 MPa. According to the measured curve, when the volumetric strain is positive (the rock is in a compressed state), the permeability value is lower than the initial permeability value of the sample. When the volumetric strain is negative (the rock is expanding), the permeability value is greater than the initial value. The permeability test points in Figure 16 are shown in Table 3.

For the results shown in Figure 16 and Table 3: According to Figure 16 and Table 3, it is found that the permeability change caused by shear dilation follows the K–P equation law. Low effective confining pressure (0.2 MPa) can cause a permeability change of approximately 4 times. Therefore, the K–P equation can be used to approximately predict the permeability changes caused by rock water injection dilation in low-permeability sandstone reservoirs.

In this paper, the transient pulse method is used to measure permeability. According to the triaxial shear dilatation experiment, the permeability test of the shear dilatation sample is carried out at the sample volume strain of 0%, 0.77%, 1.54%, 1.81%, 2.57%, and 3.28%, respectively (positive volume strain indicates the rock compression state, negative volume strain indicates the rock expansion state). When the volume strain of the sample is 0% (the initial permeability of the rock), the rock permeability is 8.60 mD. When the volume strain of the sample is 0.77%, the rock permeability is 6.46 mD. When the volume strain of the sample is 1.54%, the rock permeability is 6.08 mD. When the volume strain of the sample is 1.81%, the rock permeability is 5.91 mD. When the volume strain of the sample is 2.57%, the rock permeability is 5.81 mD. When the volume strain of the sample is 3.28%, the rock permeability is 5.13 mD. The 5 MPa effective confining pressure underbody strain–permeability (measured vs theory) is shown in Figure 17 and Table 4.

The red dashed line in Figure 17 represents the calculation data of the K–P equation. The gray point represents the measured strain change of the rock sample when the effective confining pressure is 5 MPa. According to the measured curve, when the volumetric strain is positive (the rock is in a compressed state), the permeability value is lower than the initial permeability value of the sample. When the volumetric strain is negative (the rock is expanding), the permeability value is greater than the initial value. The permeability test points in Figure 17 are shown in Table 4.

For the results shown in Figure 17 and Table 4, the permeability change caused by high shear dilation (5 MPa) also conforms to the K–P equation law. Due to the high effective confining pressure (5 MPa), the rock has been in a state of shear shrinkage, and the permeability at the test points is lower than the initial sample permeability. Therefore, when using the water injection dilation process on-site, a large range of rocks should be placed under low effective confining pressure conditions, that is, high pore pressure.

3.3.2. Triaxial Tensile Dilatation Permeability Test

According to the triaxial tensioning dilatation experiment, the permeability of the tensioning dilatation sample was tested at the effective confining pressure of 5 MPa, 1.9 MPa, 0.92 MPa, and 0.57 MPa at the temperature of 20 °C. When the effective confining pressure of the sample is 5 MPa, the permeability of the rock is 6.62 mD. When the effective confining pressure of the sample is 1.90 MPa, the permeability of the rock is 76.62 mD when the volume strain becomes −0.025%. When the effective confining pressure is 0.92 MPa and the volume strain is −0.042%, the permeability of the rock is 119.44 mD. When the sample is 0.57 MPa and the volume strain is −0.061%, the permeability of the rock is 190.67 mD.

According to the experimental results of permeability measurement, the change in volume strain is small. Still, the change of permeability multiple is large during the process of tensile dilation. When the effective confining pressure is 5 MPa and 0.57 MPa, the permeability only changes by −0.061%, but the permeability increases by two orders of magnitude. At low effective confining pressure, the permeability increases more, indicating that the original ground stress level is lower, which is more conducive to tensile dilation. The transient gas permeability measurement under stress–isotropic dilation and deformation coupling is shown in Figure 18 and Table 5.

Figure 18 shows the trend of permeability changes in rock samples during tensile dilation. From the horizontal and vertical axes of the curve, it can be seen that the permeability of the rock sample increases under high pore pressure (low effective confining pressure) conditions while it decreases under low pore pressure (high effective confining pressure) conditions. Therefore, in the technology of reservoir transformation by water injection dilation, the permeability improvement brought by tensile dilation near the wellbore area (high pore pressure zone) is more significant. The permeability test points in Figure 18 are shown in Table 5.

For the results shown in Figure 18 and Table 5, low effective confining pressure dilation caused more significant changes in rock permeability. Under the effective confining pressure of 0.5 MPa, it can cause two orders of magnitude changes in the permeability of rocks. Based on the stronger dilation phenomenon observed under low effective confining pressure, it can be concluded that under the same conditions of tensile dilation, the seepage capacity is stronger than that of shear dilation, even if its volumetric strain is much smaller than that generated by shear dilation.

The permeability changes during shear and tensile dilation were compared. The volume strain changes more obviously in the process of shear dilatation. However, the permeability change caused by tensile dilatation under small-volume strain is much greater than that caused by shear dilatation. It may be because the tensile microcracks run through the two sections of the sample, the dilation zone is uniform, and the pore roar is amplified simultaneously. The dilation effect of this amplification is huge.

4. Numerical Simulation

This part establishes the physical and numerical models of rock mechanics dilatancy in the target oilfield. The rock mechanics parameters of the target reservoir were obtained through the rock triaxial mechanics laboratory test. The finite element method simulates the typical well rock mechanics dilation process. The influence of dilation on the later production was analyzed, providing a reference for improving the reservoir reconstruction effect.

During water injection and expansion, rocks mainly focus on changes in reservoir volume strain and permeability. Therefore, this paper adopts a fluid–solid coupling numerical model. This model mainly focuses on the width of rock fracture structure and the volume deformation of rock skeleton particles under the action of stress field, affecting rock permeability. Under the action of the seepage field, the static and dynamic water pressures of seepage will cause the expansion of rock fracture surfaces and also lead to changes in the permeability performance of the rock mass. The fluid–structure coupling model:

The fluid flow behaviors in the sandstone reservoir can be expressed as follows:

(8)${\partial }_{,i}\left[{\displaystyle \frac{{\rho }_{\mathrm{L}}{k}_{ij}^{\mathrm{L}}}{{\mu }_{\mathrm{L}}}}\left(p_{,j}+{\rho }_{\mathrm{L}}{g}_j\right)\right]=\varphi {\alpha }_{\mathrm{p}}{\displaystyle \frac{\partial p}{\partial t}}+{\displaystyle \frac{1-\varphi }{{\rho }_{\mathrm{fr}}}}{\displaystyle \frac{\mathrm{d}{\rho }_{\mathrm{fr}}}{\mathrm{d}t}}+\left(1-\varphi \right){\displaystyle \frac{\partial {\epsilon }_{\mathrm{v}}}{\partial t}}$

where

(9)${\alpha }_{\mathrm{p}}={\displaystyle \frac{1}{{\rho }_{\mathrm{L}}}}{\displaystyle \frac{\partial {\rho }_{\mathrm{L}}}{\partial p}}$

where ρ_L and ρ_fr are the densities of pore fluids and the framework, respectively; $k_{ij}^{\mathrm{L}}$ is the permeability coefficient of fluids; μ_L is the viscosity of fluids; p is pore pressure; g is the acceleration of gravity; $\varphi$ is the porosity; α_p is the compressibility of liquids; t is the time; ε_v is the volumetric strain.

Equations (8) and (9) describe the flows in sandstone reservoirs considering the hydro-mechanical coupled process. It is noted that the permeability evolution with the volumetric strain obeys Karman–Poiseuille’s law as described in Equation (10).

The total deformation can be calculated in two parts: elastic deformation and plastic deformation. If a change of the effective stress (dσ′) is given, the increase of the total deformation (dε) is as follows:

(10)$\mathrm{d}\epsilon =\mathrm{d}{\epsilon }^{\mathrm{e}}+\mathrm{d}{\epsilon }^{\mathrm{p}}$

where dε_e and dε_p are the elastic and plastic deformations, respectively.

Hook’s law can calculate the elastic strain, and the plastic law can determine the plastic deformation.

The poroelastic behavior can be obtained by generalized Hook’s law:

(11)${\sigma }_{ij}^{\prime }=\left(K_{\mathrm{fr}}-{\displaystyle \frac{2K_{\mathrm{fr}}{E}_{\mathrm{fr}}}{9K_{\mathrm{fr}}-E_{\mathrm{fr}}}}\right){\delta }_{ij}{\epsilon }_{kk}+{\displaystyle \frac{6K_{\mathrm{fr}}{E}_{\mathrm{fr}}}{9K_{\mathrm{fr}}-E_{\mathrm{fr}}}}{\epsilon }_{ij}$

where

(12)${\sigma }_{ij}^{\prime }={\sigma }_{ij}-{\alpha }_{\mathrm{b}}p{\delta }_{ij}$

(13)${\alpha }_{\mathrm{b}}=1-{\displaystyle \frac{K_{\mathrm{fr}}}{K_{\mathrm{s}}}}$

where ${\sigma }_{ij}^{\prime }$ is the effective stress; ${\sigma }_{ij}$ is the total stress; α_b is the Biot’s coefficient; K_fr and Ks are the bulk moduli of the framework and matrix, respectively; δ_ij is the Kronecker symbol; E_fr is Young’s modulus of the framework; ε_ij is the strain.

For the plastic deformation, the modified Drucker–Prager (D–P) model is used. The yield surface can be expressed as follows:

(14)$f\left(p^{\prime },q\right)=0$

where the function f can refer to the modified D–P model; p′ is the mean effective stress; q is the deviatoric stress.

The mean effective stress can be written as follows:

(15)$p^{\prime }={\displaystyle \frac{{\sigma }_1^{\prime }+{\sigma }_2^{\prime }+{\sigma }_3^{\prime }}{3}}$

where ${\sigma }_1^{\prime }$, ${\sigma }_2^{\prime }$, and ${\sigma }_3^{\prime }$ are maximum, intermediate, and minimum principal stresses, respectively.

The deviatory stress can be expressed as follows:

(16)$q=\sqrt{{\displaystyle \frac{1}{2}}\left[{\left({\sigma }_1-{\sigma }_2\right)}^2+{\left({\sigma }_2-{\sigma }_3\right)}^2+{\left({\sigma }_1-{\sigma }_3\right)}^2\right]}$

According to the different yield mechanisms, the field surfaces can be divided into three sections: the linear shear yield surface, the isotropic compression-induced (cap) yield surface, and a transition yield surface between the shear and cap yield surfaces.

The linear shear field surface fs can be expressed as follows:

(17)$f_{\mathrm{s}}=q-p^{\prime }\tan \beta -d=0$

where β is the D–P internal friction angle; d is the D–P cohesion.

The cap field surface fc can be written as follows:

(18)$f_{\mathrm{c}}=\sqrt{{\left(p^{\prime }-p_a\right)}^2+{\left[{\displaystyle \frac{Rq}{1+\alpha -\alpha /\cos \beta }}\right]}^2}-R\left[d+p_a\tan \beta \right]=0$

where R is a material parameter that controls the shape of the cap; α is a parameter that defines the smooth transition yield surface; p_a is an evolution parameter that controls the strain hardening or softening behaviors.

The transition surface ft can be expressed as follows:

(19)$f_t=\sqrt{{\left(p^{\prime }-p_a\right)}^2+{\left[q-\left(1-{\displaystyle \frac{\alpha }{\cos \beta }}\right)\left(d+p_a\tan \beta \right)\right]}^2}-\alpha \left[d+p_a\tan \beta \right]=0$

In general, the strain hardening/softening behavior can be determined by an empirical relation between the mean effective (yield) stress pb and volumetric plastic strain ${\epsilon }_{\mathrm{v}}^{\mathrm{pl}}$.

(20)$p_{\mathrm{b}}=p_{\mathrm{b}}\left({\epsilon }_{\mathrm{v}}^{\mathrm{pl}}\right)$

The relation between pa and pb can be shown as follows:

(21)$p_a={\displaystyle \frac{p_b-Rd}{1+R\tan \beta }}$

Equations (14)–(21) determine the stress conditions in which the plastic deformation occurs. Therefore, the next discussion will focus on how to determine the magnitude of the plastic strain increase.

When the stress states satisfy the yield surface function, the geomaterial will generate plastic deformation. The increase of the plastic strain can be calculated by the flow law.

(22)$\mathrm{d}{\epsilon }^{\mathrm{p}}=\mathrm{d}{\lambda }_{\mathrm{p}}{\displaystyle \frac{\mathrm{d}G}{\mathrm{d}{\sigma }^{\prime }}}$

where dλ_p is the plastic proportional multiplier; G is the plastic potential function.

For the shear yield and transition sections, a non-associated flow law is used, and the plastic potential function G_t is as follows:

(23)$G_{\mathrm{t}}=\sqrt{{\left[\left(p^{\prime }-p_a\right)\tan \beta \right]}^2+{\left[{\displaystyle \frac{q}{1+\alpha -\alpha /\cos \beta }}\right]}^2}$

For the cap section, an associated flow law is used to define the plastic potential function G_c as follows:

(24)$G_{\mathrm{c}}=\sqrt{{\left(p^{\prime }-p_a\right)}^2+{\left[{\displaystyle \frac{Rq}{1+\alpha -\alpha /\cos \beta }}\right]}^2}$

The numerical simulation method of typical well rock mechanics dilation determines whether the geological model and mechanical parameters are correct based on old well-water injection construction parameters. The effect of thermal fluid–solid coupling numerical simulation on water injection dilation was analyzed using the correct geological and numerical models.

The nonlinear thermal pore elastoplastic constitutive model and nonlinear percolation model are used in the numerical simulation of water injection dilation, and the effects of heat transfer and forced convection heat transfer are considered. In the numerical simulation analysis, the simulation results are compared, analyzed, verified, and optimized with the field test data. To build a numerical model, the field data required include the following:

Formation geological information: reservoir buried depth range, cover layer, and bottom buried depth range.

Drilling and completion data: well track, depth, length, and size of injection wells.

Physical and mechanical parameters of formation and downhole equipment: elastoplastic mechanical parameters of reservoir, cap/bottom layer, and downhole equipment, such as elastic modulus, Poisson ratio, cohesion force, internal friction angle, etc. Thermodynamic parameters include thermal conductivity, specific heat capacity, thermal diffusion coefficient, latent heat of phase change, etc. See page parameters, such as permeability, porosity, etc.; other physical properties, such as density. Anisotropy and heterogeneity are not considered in this part.

Formation environment: ground stress environment, temperature environment, pore pressure environment, etc.

Site construction parameters: injection liquid temperature of each well, time–displacement relationship, time–bottom-hole pressure relationship, etc.

Numerical simulation of dilation and injection of old wells in offshore oil fields: Based on the above test data, a coupled reservoir–geomechanics numerical model of injection wells in offshore oil fields is established, and the whole process of numerical simulation before and after dilation of injection wells is carried out according to the actual injection data of injection wells that have been implemented at sea. The following Figure shows the comparison between the measured bottom-hole pressure and the numerical simulation prediction of the target sandstone reservoir after water injection and dilation, which can verify the reliability of the model proposed above.

Figure 19 compares the predicted and measured bottom-hole pressure values of the numerical simulation of water injection dilation in an old well. According to the figure, it can be seen that the geological model and numerical model used in this paper approximate the actual reservoir on-site. This historical fitting can provide theoretical support for the numerical simulation results of the paper.

The model was constructed using the indoor triaxial mechanical experiment and on-site drilling and completion data. The numerical simulation modeling process includes 3D geological body construction, material attribute assignment, analysis step setting, load application, boundary conditions, grid division, Fortran secondary development, submission calculation, etc. This simulation uses Abaqus finite element software (2020) to establish a geological model of an offshore low-permeability sandstone oilfield and simulate the water injection simulation effect of the offshore low-permeability sandstone reservoir [40]. According to the on-site geological data, the model has a vertical depth of 2328–2770 m with an inclination of about 16.5 degrees. It is divided into 37 sublayers, including oil layers and dry layers. The mechanical and permeability parameters of each layer of rock are different and consistent with the field test data. A 147,186-unit grid was constructed with cell type C3D8P. This model adopts the D–P constitutive model and the compressive strength of the rock is 47.52 MPa.

The model assumes the following conditions (Figure 20):

• (1). There are 37 sublayers in the model, assuming that the rocks in each sub-layer are isotropic and uniform;

• (2). Assuming that rock deformation after water injection affects fluid pressure;

• (3). Permeability affects fluid pressure;

• (4). Assuming that changes in porosity affect permeability;

• (5). Assuming that fluid pressure affects the effective stress of the skeleton.

The parameters of the constructed model are set. There are two kinds of historical fittings for water injection dilation of old wells: By controlling the injection fluid amount and the field construction conditions to see whether the numerical simulation results match the field data, by controlling the bottom pressure of the well and the field construction conditions, the injected liquid quantity after numerical simulation is consistent with the field data. In this paper, the injection flow control is consistent with the construction conditions, and the numerical simulation is used to obtain the bottom-hole pressure.

For the results shown in Figure 21 and Figure 22: through numerical simulation calculations, the bottom-hole pressure after water injection is 47.12 MPa and hydraulic pressure spreads towards the near wellbore area and extends deeper, as shown in Figure 21. The reservoir around the well has undergone varying degrees of deformation, resulting in a 5.58 mm uplift at the top of the water injection target layer, as shown in Figure 22. According to the numerical simulation results, it was found that water injection expansion technology has significant reservoir transformation effects on low-permeability sandstone rocks at sea, not only causing changes in reservoir volume strain but also improving permeability.

5. Discussion

This paper assumes that the physical simulation did not consider the influence of ion components on water injection dilation. However, the formation water type of the target oilfield is NaHCO₃ type, with a low total mineralization of 8301 mg/L to 9678 mg/L and a specific gravity of 1.005 g/cm³ to 1.006 g/cm³, belonging to the semi-closed water type. Therefore, the target well-working fluid consists of nanofiltration water, 0.5% clay stabilizer, and 0.5% nanomicroemulsion drainage aid (surfactant). When injecting water into low-permeability sandstone rocks at sea for dilation, ionic components in the working fluid can cause scale precipitation during the expansion process, reduce rock permeability, and damage production equipment [42]. The impact of ions on water injection dilation needs further discussion.

6. Conclusions

In this paper, the low-permeability sandstone at sea is taken as the research object, and the rock mechanics parameters are obtained through the shear dilation triaxial experiment, tensile dilation triaxial experiment, and permeability test to analyze the water-injection dilation effect of low-permeability sandstone at sea. The geological and numerical models are obtained through historical fitting through numerical simulation. According to the geological and numerical models, the effect of water injection dilation of low-permeability sandstone at sea is obtained.

• (1). Through shear triaxial mechanics experiments, it is found that when the effective confining pressure of the core is 0.2 MPa, the low-permeability sandstone goes through 6 stages: elastic deformation, local micro-fracture of the natural weak surface, large-scale fracture of the natural weak surface, accompanied by strain softening, strain strengthening, strain softening, and residual stress dilation. Under low effective confining pressure, the core is mainly a shear failure controlled by weak surfaces such as microcracks and bedding in the rock. The experiment characterized the rock dilation capacity of low-permeability sandstone reservoirs in the target oilfield through triaxial mechanical tests, revealing the geomechanical conditions for shear dilation. It was found that under an effective confining pressure of 0.2 MPa, the rock can achieve a maximum volume dilation of 13% at an axial strain of 4%.

• (2). It is found through the tensile triaxial mechanics experiment that the core confining pressure remains unchanged, and a certain volume dilation occurs with the increase of pore pressure. At the end of the experiment, CT scans revealed many microcrack groups in the rock. The crack group will open more rapidly when the dilation is repeated, and the pore throat channel of the sample will be significantly improved. At the same time, it is found that under the condition of no pore pressure, the tensile dilation capacity is not self-supporting, and the fracture group is easy to close. It has been proven that low-permeability sandstone at sea can undergo plastic deformation recovery, and it is concluded that using water injection dilation reservoir modification technology will generate many tensile plastic fracture groups around the wellbore.

• (3). The permeability test showed that the improvement of the dilatation/shear-induced permeability under an effective confining pressure of 0.2 MPa was linearly related to the bulk strain. In the process of tensor dilatation, water injection leads to isotropic dilation of the reservoir. It significantly improves the induced permeability, which is inconsistent with the rule of the Kozeny–Poiseuille model. The permeability experiment of tensor dilatation is carried out to establish a transient gas permeability measurement model under the coupling effect of stress–isotropic dilatation and deformation. The impact of different effective confining pressure and volume strains on permeability and permeability improvement multiples were characterized. Prove that water injection dilation and reservoir transformation technology can enhance the pore permeability of low-permeability sandstone reservoirs at sea, providing technical, and theoretical support for the dilation and injection technology of low-permeability sandstone.

• (4). The numerical simulation results found that the bottom-hole pressure reached 47.12 MPa at the end of water injection by the geological and numerical models after historical fitting, and the hydraulic power spread to the near-well area and extended to the deep. The reservoir around the well is deformed to different degrees, resulting in the top of the target layer of water injection uplifting 5.58 mm. In this typical well, water injection dilation technology is adopted, and obvious dilation of the reservoir can occur. The simulation conclusion forms an evaluation of the water injection dilation effect of low-permeability sandstone reservoirs at sea. It obtains a three-dimensional full-size wellbore formation geo-stress geological model of offshore dilation wells, providing technical guidance for on-site construction.

The research in this paper strongly supports the subsequent development of target reservoir blocks by water injection dilation technology and guides field construction.

Author Contributions

Conceptualization, S.W. and Y.G.; methodology, H.Y. and Y.G.; validation, S.W.; formal analysis, S.W., Y.G. and D.L.; investigation, S.W., H.Y., H.C., X.C., Y.C. and D.L.; resources, S.W., H.Y., H.C. and W.L.; data curation, Y.G.; writing—original draft, D.L; writing—review and editing, D.L.; visualization, S.W.; supervision, S.W., H.Y., H.C., X.C., Y.C. and W.L.; project administration, S.W., H.Y., H.C. and Y.C.; funding acquisition, S.W., H.Y., H.C., Y.C., W.L. and Y.G. All authors have read and agreed to the published version of the manuscript.

Data Availability Statement

The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding authors.

Acknowledgments

Thank CNOOC Research Institute Co., Ltd. for providing technical support for marine low-permeability sandstone rock expansion. Thank the Department of Geology, Northwest University, for providing us with an indoor test site, experimental technology, and numerical simulation technology support. Thanks for Hailong Jiang’s guidance during the revision stage.

Conflicts of Interest

Authors Shaowei Wu, Hui Yuan, Xiao Chen and Wentao Lao were employed by the company China National Offshore Oil Corporation (CNOOC) Limited. Authors Huan Chen and Yanfeng Cao were employed by the company CNOOC Research Institute Ltd. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. The China National Offshore Oil Corporation (CNOOC) Limited and CNOOC Research Institute Ltd. had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.

Footnotes

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Figures and Tables

Figure 1. Research workflow diagram.

Figure 2. RTX-3000.

Figure 3. 25 mm × 50 mm core.

Figure 4. Core stress diagram.

Figure 5. Specimen loading.

Figure 6. Data acquisition.

Figure 7. Tension dilation pressure loading curve.

Figure 8. Appearance of the sample after the test under effective confining pressure of 0.2 MPa.

Figure 9. Stress–axial strain curves of rock shear dilation (top) and bulk strain–axial stress curves (bottom) under an effective confining pressure of 0.2 MPa.

Figure 10. Appearance of the sample after the test under an effective confining pressure of 5 MPa.

Figure 11. Stress–axial strain curves of rock shear dilation (top) and bulk strain–axial stress curves (bottom) under an effective confining pressure of 5 MPa.

Figure 12. The CT scan of the rock core after effective confining pressure (0.2 MPa).

Figure 13. The CT scan of the rock core after high effective confining pressure (5 MPa).

Figure 14. Effective confining–volume strain curve of 20 °C tensioned dilatation.

Figure 15. The C.T. scan of Effective confining–volume strain curve of 20 °C tensioned dilatation.

Figure 16. 0.2 MPa effective confining pressure underbody strain–permeability (measured vs. theory).

Figure 17. 5 MPa effective confining pressure underbody strain–permeability (measured vs. theory).

Figure 18. Evolution of permeability under stress.

Figure 19. Bottom-hole pressure history fitting.

Figure 20. Schematic diagram of the modeling process.

Figure 21. Pore pressure distribution (left) and deformation distribution (right) in typical wells.

Figure 22. Expansion radius in typical wells.

Table 1

Original parameter testing of rock samples.

Mechanical Parameter	Length (mm)	Diameter (mm)	Weight (g)	Density (g/cm3)	Initial Porosity (%)	Initial Permeability (mD)
Sample 1	49.91	25.26	60.01	2.40	7.67	2.05
Sample 2	49.98	25.21	60.40	2.42	8.25	8.60
Sample 3	49.87	25.25	59.91	2.40	8.12	2.91

Table 2

Rock mechanical parameters of samples.

Mechanical Parameter	Elasticity Modulus	Poisson Ratio	Cohesive Force	Angle of Internal Friction	Dilation Angle
Sample 1	11.67 GPa	0.17	6.45 MPa	48.85°	18.85°
Sample 2	5.00 GPa	0.18	6.54 MPa	48.85°	18.85°

Table 3

The gas permeability values correspond to different body strains at 0.2 MPa effective confining pressure and the calculated values of the K–P model.

Experiment Number	Volumetric Strain/%	Test Permeability/mD	Theoretical Permeability/mD
1	0	2.05	2.05
2	0.49	1.84	1.86
3	−0.59	2.08	2.28
4	−3.68	4.09	3.82
5	−9.21	4.23	7.89
6	−12.00	7.90	10.67

Table 4

The gas permeability values correspond to different body strains at 5 MPa effective confining pressure and the calculated values of the K–P model.

Experiment Number	Volumetric Strain/%	Test Permeability/mD	Theoretical Permeability/mD
1	0	8.60	8.60
2	0.77	6.46	7.40
3	1.54	6.08	6.31
4	1.81	5.91	5.95
5	2.57	5.81	5.02
6	3.28	5.13	4.24

Table 5

Transient gas permeability measurement under stress–isotropic dilation and deformation coupling.

Experiment Number	Effective Confining Pressure/MPa	Test Permeability/mD
1	5	6.62
2	1.90	76.62
3	0.92	119.44
4	0.57	190.67
5	0.33	267.98

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