Coupled Productivity Prediction Model for Multi-Stage Fractured Horizontal Wells in Low-Permeability Reservoirs Considering Threshold Pressure Gradient and Stress Sensitivity

Multi-stage fractured horizontal wells (MSFHWs) represent a crucial development approach for low-permeability reservoirs, where accurate productivity prediction is essential for production operations. However, existing models suffer from limitations such as inadequate characterization of complex flow mechanisms within the reservoir or computational complexity. This study subdivides the flow process into three segments: matrix, fracture, and wellbore. By employing discretization concepts, potential distribution theory, and the principle of potential superposition, a productivity prediction model tailored for MSFHWs in low-permeability reservoirs is established. Moreover, this model provides a clearer characterization of fluid seepage processes during horizontal well production, which aligns more closely with the actual production process. Validated against actual production data from an offshore oilfield and benchmarked against classical models, the proposed model demonstrates satisfactory accuracy and reliability. Sensitivity analysis reveals that a lower Threshold Pressure Gradient (TPG) corresponds to higher productivity; a production pressure differential of 10 MPa yields an average increase of 22.41 m 3 /d in overall daily oil production compared to 5 MPa, concurrently reducing the overall production decline rate by 26.59% on average. Larger stress-sensitive coefficients lead to reduced production, with the fracture stress-sensitive coefficient exerting a more significant influence; for an equivalent increment, the matrix stress-sensitive coefficient causes a production decrease of 1.92 m 3 /d (a 4.32% decline), while the fracture stress-sensitive coefficient results in a decrease of 4.87 m 3 /d (a 20.93% decline). Increased fracture half-length and number enhance production, with an initial productivity increase of 21.61% (gradually diminishing to 7.1%) for longer fracture half-lengths and 24.63% (gradually diminishing to 5.22%) for more fractures; optimal critical values exist for both parameters.