Abstract: Geological CO₂ sequestration （GCS） is an important means for human society to alleviate greenhouse gas effects and achieve the so-called ‘dual carbon goals’, namely the ‘carbon peeking’ and ‘carbon neutrality’. However, injecting CO₂ into geologic formations on a large scale or at excessive rates may cause overpressure in the injected formation, which may in turn alter the shear strength of the intersected faults or preexisting fractures, posing environmental risks to GCS engineering by triggering ground surface deformation and/or induced seismicity. The pore pressure buildup caused by fluid injection and production is an important cause for ground deformation and induced seismicity. Evaluation of the geomechanical effects caused by CO₂ injection is an indispensable part of GCS risk assessment. Based on the inclusion theory and Green’s function method, the existing analytical solutions for evaluating the geomechanics of a single fault has been expanded, to enables it to evaluate geomechanical effects associated with large-scale CO₂ injection into reservoirs penetrated by three faults. A modular PYTHON-scripted utility tool composed of tens of functions was developed based on the analytical solution proposed in this study, which enables rapid assessment of the distribution of the fault slip patches and the maximum size of the fault slip patch. The maximum moment magnitude of induced earthquakes can be estimated for various injection scenarios and site settings. The major controlling factors of the seismic risks can be identified as well. Based on the analysis of case studies, the following conclusions are drawn: Injection causes horizontal displacement to concentrate on the burial depths of the fault that simultaneously contacts the reservoir and the surrounding rock （i.e., the overlying and underlying formation units）, while vertical displacement varies uniformly with depth. Due to lateral confinement, injection causes the reservoir to expand in both the caprock and baserock directions simultaneously. Injection results in a negative horizontal strain increment and a positive vertical strain increment within the reservoir. The horizontal normal strain is significantly concentrated in the surrounding rock below the hanging wall of the fault and the overlying surrounding rock above the hanging wall of the fault. While the vertical normal strain follows a similar pattern to the horizontal normal strain, it has opposite signs. The expansion of the reservoir causes the rocks inside the reservoir to be subject to compressive normal stress. The horizontal normal stress only has a positive range in the surrounding rock below the reservoir on the upper wall of the fault and the surrounding rock above the reservoir on the lower wall of the fault, while the vertical normal stress shows stress concentration in the surrounding rock area near the intersection of the fault and the reservoir, indicating that the surrounding rock in these areas is subject to tensile stress. CO₂ injection leads to the concentration of shear stress increment near the four singularities of the fault. The risks of on-fault seismicity （i.e., the maximum fault slip size and the maximal moment magnitude） are relevant to the distance of the fault to the injection center. The major controlling geomechanical parameters of the induced seismicity include the Biot coefficient, Poission’s ratio, and the initial stresses and the initial pore pressure.