As oil production continues worldwide, more oil fields require complex EOR methods to achieve outlined recovery factors. Reservoir engineers are dealing more often with problems involving thermal multiphase multi-component flow models tightly coupled with complex phase behavior. Such modeling implies the solution of governing laws describing mass and energy transfer in the subsurface, which in turn requires the linearization of strongly nonlinear systems of equations. The recently proposed Operator-Based Linearization (OBL) framework suggests an unconventional strategy using the discrete representation of physics. The terms of governing PDEs, discretized in time and space, which depend only on state variables, are approximated by piece-wise multilinear operators. Since the current physical state fully defines operators for a given problem, each operator can be parametrized over the multidimensional space of nonlinear unknowns for a given distribution of supporting points. Onwards, the values of operators, along with their derivatives with respect to nonlinear unknowns, are obtained from the parametrization using multilinear interpolation and are used for Jacobian assembly in the course of a simulation. Previously, the distribution of supporting points was always uniform, requiring higher parametrization resolution to provide accurate and consistent interpolation of an operator around its most nonlinear regions in parameter space. In addition, when the resolution is low, the system can lose hyperbolicity causing convergence issues. In this work, we apply the prior knowledge of underlying physics to distribute the supporting points according to the tie-simplex behavior of the multiphase mixture in parameter space. The approach allows to decrease the parametrization resolution keeping the same accuracy. In addition, the OBL framework is extended to describe multisegment wells working under different controls. We test the accuracy of the developed framework for truly multi-component systems of practical interest.@en