Based on the analysis of geological experiments from multiple samples across the study area, the following characteristics of the reservoir rock were identified: (1) the target reservoir lithology is mainly composed of quartz, feldspar, and lithic fragments, with well-developed mica flakes; (2) the dominant grain size ranges from 0.25 to 0.5 mm, showing good sorting and sub-rounded to sub-angular shapes (Wu, 2014; Gao, 2016; Li, 2006). As shown in Figure 2 and Figure 3. The cementation is primarily pore-type, and the grains are mostly in linear contact.

Based on the geological experimental results from multiple samples across the study area, the target reservoir exhibits a high relative content of stress-sensitive minerals. The illite–smectite mixed-layer clays account for up to 61%, while the rapidly swelling mineral kaolinite represents approximately 20.75%. As shown in Figure 4 and Table 1. The content of these sensitive minerals shows minimal variation across different permeability levels.

Based on the analysis of geological experimental results from multiple samples across the study area, the reservoir is dominated by intergranular dissolution pores and feldspar dissolution pores, followed by intergranular pores. Porosity increases with the permeability level. For secondary pores, intergranular dissolution pores are commonly developed, and the proportion of feldspar dissolution pores gradually increases with permeability, reaching a maximum of 1%. For primary pores, intergranular pores account for 0.3% in reservoirs with permeability greater than 1.0 mD, but their proportion is relatively small compared to other pore types at the same permeability level, only about 15% (Guthrie and Greenberger, 2003). As shown in Figure 5 and Table 2. In ultra-low permeability reservoirs, secondary porosity formed by dissolution plays a major role in enhancing permeability.

Nuclear magnetic resonance (NMR) experiments indicate that after water injection-induced damage, the proportion of large pore throats in the reservoir significantly decreases. This is attributed to the blockage of pore throats by stress-sensitive minerals. As shown in Figure 6 and Table 3. High-pressure mercury intrusion (HPMI) tests further show a decline in mercury withdrawal efficiency and an increase in residual mercury saturation, suggesting that the oil displacement efficiency after water flooding is notably reduced.

Analysis of the petrographic composition and pore-throat structure reveals that the target reservoir is mainly composed of quartz and feldspar, with pore-type cementation dominating (He et al., 2022). Locally, microfractures and intergranular dissolution pores are developed, resulting in an overall fragile structure with poor compressive strength. Notably, the clay mineral content is high, with illite–smectite mixed-layer minerals accounting for up to 61%, distributed evenly across different permeability levels, indicating a strong potential for structural deformation.

Furthermore, nuclear magnetic resonance (NMR) and high-pressure mercury intrusion (HPMI) experiments show a significant reduction in the proportion of large pore throats after water flooding, along with increased residual mercury saturation and decreased mercury withdrawal efficiency. These results further confirm measurable physical deformation of the reservoir structure under increased effective stress.

Combining these petrographic and pore-throat characteristics, it can be preliminarily concluded that stress sensitivity is the primary reservoir damage mechanism, providing a solid material basis for conducting quantitative stress sensitivity experiments.

Samples with higher clay content and smaller pore throats exhibit stronger stress sensitivity. NMR results show a significant reduction in large pore volumes after stress loading. SEM images confirm pore collapse and throat narrowing under increased effective stress.

The experimental samples were obtained from the L reservoir and consist of cylindrical cores with lithology characterized as tight sandstone. To achieve the research objectives, two groups of carefully selected core samples were used to conduct stress sensitivity experiments. As shown in Table 4. The basic physical properties of the samples are listed as follows:

Stress sensitivity experiments were conducted by selecting core samples with two different permeability levels. As shown in Table 5. The confining pressure was gradually increased while maintaining a constant injection rate to investigate the effect of varying confining pressures on reservoir permeability.

The experimental procedures follow the SY/T5358-2010 standard, titled “Evaluation Method for Reservoir Sensitivity Flow Experiments.” All experiments were conducted at a constant temperature of 60 °C to simulate the actual reservoir temperature conditions.

In the stress sensitivity experiment, formation water is injected into the core samples under varying confining pressures. According to Darcy’s law, the permeability of the rock is measured during the pressure increase process to calculate the permeability damage rate. As shown in Table 6. The permeability variation rate of the rock samples under different effective stresses during the increase of effective stress is expressed as: D s t n = K i − K n K i × 100 % where,

Dstn—permeability variation rate during the increase of effective stress;

Kn—permeability of the core sample during the pressure increase process, in mD;

Ki—initial permeability of the core sample under initial effective stress, in mD.

The displacement experiments were conducted using the DLY-III multi-scale multifunctional high-temperature and high-pressure fracture fluid transport integrated experimental system. As shown in Figure 7. This equipment mainly comprises a constant-speed constant-pressure pump, annular pressure tracking pump, piston container, high-temperature and high-pressure core holder, thermostatic chamber, precision pressure gauges, digital pressure gauges, valves, six-way valves, backpressure valves, and high-precision oil-water metering devices (Yan et al., 2018).

Evacuate the core samples and saturate them with formation water;

Exponential Decay Model as shown in Equation 1: k = k 0 e − α σ − σ 0 (1)

k 0 : Permeability at the reference effective stress

σ : Current effective stress

α : Stress sensitivity coefficient

This exponential decay model is one of the most commonly used stress-dependent permeability models and is particularly applicable to tight sandstone reservoirs.

Power-Law Model as shown in Equation 2: k = k 0 σ 0 σ β (2) where β is the power-law exponent, reflecting the degree of stress sensitivity.

This model is suitable for cases where the permeability variation with effective stress is non-linear and more complex.

Linear Model as shown in Equation 3: k = k 0 · 1 − β σ − σ 0 (3)

This model is appropriate for formations with weak stress sensitivity or in stress ranges where permeability changes approximately linearly.

Fracture Closure Model (Porosity-Coupled) as shown in Equation 4: w = w 0 · e − α σ − σ 0 (4)

w is the current fracture aperture,

w 0 is the initial aperture at the reference effective stress σ 0 ,

α is the stress sensitivity coefficient.

This model is used when natural fractures are present in the reservoir and their closure behavior dominates permeability reduction.

Under higher differential stress conditions, deformation bands and shear fractures may develop around the wellbore. Previous studies suggest that deformation bands generally reduce permeability, whereas shear fractures may locally enhance permeability if well connected. However, the stress levels investigated in this study are below the shear failure threshold; therefore, permeability evolution is dominated by elastic compaction mechanisms.

At higher effective stresses, permeability variation with stress tends to appear linear, which can be interpreted as a local linear approximation of the exponential stress-sensitive permeability model.

Based on the experimental data from Chapter 3 and the stress sensitivity characterization model established in Chapter 4, combined with reservoir characteristics and field data of the L oilfield, the key model parameters are determined.

Using the production rate formula as shown in Equation 25: q = 2 π h k i μ α ⁡ ln r e r w e − α p i − p w − e − α p i − p e (25)

To maximize the production rate qqq, the bottom-hole flowing pressure pwp_wpw should be controlled to weaken the stress sensitivity effect.

Let: C = 2 π h k i μ α ⁡ ln ⁡ r e r w

The production can be expressed as shown in Equation 26: q p w = C e − α p i − p w − e − α p i − p e (26)

Where the formation pressure pe is fixed, and the bottom-hole pressure pw is adjusted to maximize q.

It is seen that as shown in Equation 27: q p w = C e − α p i − p w − constant (27)

Taking the derivative yields as shown in Equation 28: q ′ p w = C · α · e − α p i − p w > 0 (28)

Since the derivative is always positive, the production rate q monotonically increases with the bottom-hole pressure pw.

When pw approaches pi (i.e., pressure drawdown approaches zero), the production approaches its maximum; however, the pressure differential (pi−pw) is very small, resulting in insufficient driving force and production approaching zero.

The corrected analysis shows: Increasing the pressure drawdown enhances the driving force, benefiting production; Excessive drawdown increases effective stress, reduces permeability, and diminishes productivity.

Therefore, an optimal drawdown Δp exists that balances the driving force and stress sensitivity to maximize production.

Further defining the pressure drawdown as a variable x = Δp = pi-pw, the production rate can be written as shown in Equation 29: q x = C e − α x − e − α p i − p e (29)

Taking the derivative: d q d x = − C α e − α x

Since the derivative is always negative, this expression decreases monotonically with x, representing only the negative impact of permeability loss on production.

To comprehensively evaluate the dual effect of pressure drawdown on production—both permeability degradation and pressure-driven flow—Darcy’s law is considered: q = k p i − p w μ

Substituting the stress-sensitive permeability model k = k i e − α p i − p w gives as shown in Equation 30: q p w = k i p i − p w e − α p i − p w μ (30)

Letting x = pi-pw, we obtain: q x = A x e − α x ,where A = ki/ μ

Taking the derivative: d q d x = A e − α x 1 − α x

Setting the derivative to zero: 1−αx = 0⇒x = α1.

Hence, the optimal pressure drawdown is: x = 1 α

At this value, the production reaches a maximum, representing the most favorable drawdown under stress-sensitive conditions.