The microbially induced calcite precipitation (MICP) technique holds promising applications in groundwater remediation, gas storage, soil improvement, and rock fracture sealing. In this study, a two-dimensional pore-scale numerical model is developed to simulate the coupled flow, reactive mass transport processes, and precipitation processes in MICP. In the present model, the lattice Boltzmann method (LBM) and finite element method (FEM) are employed to solve the incompressible Navier-Stokes equations and the advection-diffusion-reaction (ADR) equation, respectively. The present model considers the processes of bacterial transport and attachment, ureolysis, and the bacterial and calcite detachment induced by the flow shear effects. With the present model, multiple field profiles including the flow field, concentration field, and the calcite distribution can be obtained in the pore space. The present numerical model is validated based on the experimental data from the literature. We also perform sensitivity analyses of the model parameters, and results indicate that the calcite volume fraction is most sensitive to the parameter  Ksbr (the calcite precipitation reduction coefficient of suspended bacteria). To investigate the effect of heterogeneous pore structures on calcite distribution, different scenarios are carried out. The results demonstrate that the pore structures with large pore throats result in more calcite accumulation. In cases involving heterogeneous pore structures, such as the asymmetrically distributed pore structures in the upper and lower portions of the computational domain, the distribution of calcite precipitation is mainly influenced by the flow direction. We develop a pore-scale three-dimensional MICP model based on the two-dimensional model, and the factors that may influence the precipitation distribution are studied, such as solid particle size and particle arrangement. Additionally, we find the vortices during the MICP process, and their effects on the precipitation distribution need further investigation.