Needle-based intervention is part of minimally invasive surgery and has the benefit of allowing the reach of deep internal organ structures while limiting trauma. However, reaching good performance requires a skilled practitioner. This paper presents a needle-insertion training simulator for the liver based on the finite element method. One of the main challenges in developing realistic training simulators is to use fine meshes to represent organ deformations accurately while keeping a real-time constraint in the speed of computation to allow interactivity of the simulator. This is especially true for simulating accurately the region of the organs where the needle is inserted. In this paper, we propose the use of model order reduction to allow drastic gains in performance. To simulate accurately the liver which undergoes highly nonlinear local deformation along the needle-insertion path, we propose a new partition method for model order reduction: applied to the liver, we can perform FEM computations on a high-resolution mesh on the part in interaction with the needle while having model reduction elsewhere for greater computational performances. We show the combined methods with an interactive simulation of percutaneous needle-based interventions for tumor biopsy/ablation using patient-based anatomy.