Analysis and Optimization of Wellbore Structure Considering Casing Stress in Oil and Gas Wells Within Coal Mine Goaf Areas Subject to Overburden Movement

To address wellbore integrity issues (especially casing strength concerns) of oil and gas wells threatened by overburden movement in coal mine goafs, this study takes a gas well in the goaf of Yanchang Gas Field as the research object. Using FLAC3D 7.0 software, a 3D coupling model of “casing-cement sheath-formation-goaf” is established to systematically analyze the effects of goaf presence, convergence criteria, casing wall thickness/layer count, and cement slurry density on casing stress while conducting wellbore structure optimization. Key research results are as follows: (1) Overburden movement concentrates the maximum casing stress near the goaf, with the surface casing stress being 7–8 times higher than that in the absence of a goaf, serving as the core object of stress control; (2) A convergence criterion of 10−4 balances calculation accuracy and efficiency, where the maximum Von Mises equivalent stress of the surface casing differs by only 0.98% compared with that under a convergence criterion of 10−6; (3) Increasing casing layers is more effective than thickening walls or upgrading steel grade: three-layer casing reduces surface casing stress by 23.4% compared with two-layer casing, and all casing safety factors meet the standards; (4) The casing stress is minimized when the cement slurry density is 1800–1900 kg/m3 (with a minimum of 325.79 MPa), while excessively low or high density will lead to increased stress. The optimized wellbore structure provides key references for the design of gas wells in goaf areas.