We consider the permeability estimation problem in two-phase porous media flow.Wetry to identify the permeability field by utilizing both the production data from wells aswell as inverted seismic data.The permeability field is assumed to be piecewise constant,or can be approximated well by a piecewise constant function.A variant of the level setmethod,called Piecewise Constant Level Set Method is used to represent the interfacesbetween the regions with different permeability levels.The inverse problem is solved byminimizing a functional,and TV norm regularization is used to deal with the ill-posedness.We also use the operator-splitting technique to decompose the constraint term from thefidelity term.This gives us more flexibility to deal with the constraint and helps to stabilizethe algorithm. We consider the permeability estimation problem in two-phase porous media flow. Wetry to identify the permeability field by utilizing both for production data from wells aswell as inverted seismic data. Permeability field is assumed to be piecewise constant, or can be approximated well by a piecewise constant function. A variant of the level setmethod, called Piecewise Constant Level Set Method is used to represent the interfacesbetween the regions with different permeability levels. The inverse problem is solved byminizing a functional, and TV norm regularization is used to deal with the ill-posedness.We also use the operator-splitting technique to decompose the constraint term from the fidelity term.This gives us more flexibility to deal with the constraint and helps to stabilize the algorithm.