We present a method to estimate the segregation parameter, S, a key input in a continuum transport model of particulate flows. S is determined by minimizing the difference between measured and model-predicted concentration profiles. To validate the approach, we conduct discrete element method simulations of size-bidisperse mixtures in quasi-2D bounded heap flow; the resulting data show that S calculated from concentration profiles is consistent with the directly measured value. The method's accuracy depends critically on the velocity profile during filling, but only weakly on the diffusion coefficient. When the velocity profile is nominally span wise invariant, the error between estimated and measured S is 10%. This method is intended for practical application (described in Part II), so we restrict characterization of the velocity profile to that which can be readily determined experimentally, and explore the sensitivity of concentration profiles to variation of the gap between the sidewalls of the heap. (C) 2020 Elsevier B.V. All rights reserved.