The influence of various factors, such as the natural properties of rock and in-situ stress conditions, results in uneven and rough fracture surfaces post-hydraulic fracturing. This significantly impacts the transport and placement of proppant within the fracture, thereby affecting the effectiveness of fracture stimulation. This study employs the rectangular wave method to characterize the roughness of fracture wall morphology, detailing the variation of roughness by altering the number and height of micro-protuberances, and constructs a three-dimensional model of rough fractures. The Euler–Euler model is utilized to simulate the placement and transport patterns of proppant within the fracture. Sand banks within the fracture profile are segmented based on proppant concentration, and the dimensionless area of each concentration interval is calculated to analyze the structure of sand banks and the suspension and settling effects of proppant. This research investigates the variation patterns of sand dune structures within fractures characterized by different levels of roughness and morphologies; it also examines the impact of injection velocity and fracturing fluid viscosity on the transport and placement of proppant within rough fractures. The findings indicate that the complex spatial structure of rough fractures modifies the edge shape of sand dunes. Moreover, it impedes proppant transport, leading to the formation of sand plugs near the wellbore. The maximum distance of sand placement for rough fractures is only 55.2% of that for fractures without considering roughness. The increase in the number and height of micro-protrusions enhances fracture roughness, leading to a stronger retarding effect. However, variations in these two types of roughness have distinct impacts on the morphology of sand dunes. Higher injection velocities facilitate the transport of proppant within rough fractures. The furthest distance of proppant placement at an injection velocity of 0.5 m³/min is only 68.4% of that at an injection velocity of 1.5 m³/min. The study’s findings contribute to a more intuitive understanding of the impact of rough fracture wall surfaces on the transport and placement patterns of proppant, providing a foundation for the optimization of fracturing design and operational parameters.

As an effective energy storage solution, gas reservoir compressed air energy storage (CAES) can efficiently utilize curtailed wind power to meet urban electricity demands. Well pattern optimization enables rational design and adjustment of well layouts to maximize productivity, efficiency, and economic benefits while reducing energy losses and operational costs. To address limitations in conventional optimization methods—including oversimplified constraints, neglect of reservoir heterogeneity, and insufficient consideration of complex flow regimes—this study proposes an innovative multi-constraint well pattern optimization method incorporating productivity, energy conversion efficiency, drainage area, and economic performance for quantitative evaluation of well configurations. First, the reservoir flow domain was partitioned based on two flow regimes (Darcy and non-Darcy flow) near wells. Mathematical flow equations accounting for reservoir heterogeneity were established and solved using the rectangular grid method to determine productivity and formation pressure distributions for vertical and horizontal wells. Second, a drainage radius prediction model was developed based on pressure drop superposition principles to calculate gas drainage areas. Finally, an optimization function F, integrating productivity models and drainage radius calculations through ratio optimization criteria, was formulated to quantitatively characterize well pattern performance. An optimization workflow adhering to inter-well interference minimization principles was designed, culminating in a comprehensive CAES well pattern optimization framework. Case studies and sensitivity analyses on the depleted Mabei Block 8 CAES reservoir demonstrated the following: The quantitative optimization metric w decreases with increasing reservoir heterogeneity. w exhibits a unimodal relationship with production pressure differential, peaking at approximately 2.5 MPa. Optimal configuration was achieved with 3 horizontal wells and 23 vertical wells.