Estimating permeability heterogeneity is a key component in modeling multiphase flow in geological porous media such as aquifers and reservoirs. The inverse problem of identifying permeability has been thoroughly studied regarding single-phase flow, however, hardly in two-phase flow problems. In this work, we study the inverse problem of estimating the spatial distribution of permeability in two-phase flow, considering a known saturation distribution, and using an iterative method based on inverting the capillary pressure-permeability relationship. The method is evaluated considering many different problem parameters and shown to be accurate for many cases in both oil-water and CO2-water three-dimensional systems. Large errors are observed when there is significant water trapping due to capillary effects and when conditions are dominated by viscosity. A range of optimal parameters is determined in which the inverse method is most accurate. These parameters can be used in applications, for example, when designing coreflooding experiments for permeability estimation. The estimated permeability is then used to predict the saturation and pressure distributions of two-phase flow with different injection flow rates and fluid fractions. The models are shown to be accurate when permeability estimations are accurate. The results support the possibility of calibrating a numerical model to coreflooding experiments and then using it to replace additional experiments, e.g., for evaluating flow rate effects.