Johanson's roll compaction model [J.R. Johanson, A rolling theory for granular solids, ASME Journal of Applied Mechanics E32 (1965) 842-848] is modified to improve its predictions of a compacted ribbon's relative density. Previous work has shown that the maximum roll pressure and ribbon relative density predicted by the Johanson model are not only larger than those predicted from finite element method (FEM) simulations, but also unphysical in some cases. This over-prediction is due to a one-dimensional flow assumption in the Johanson model. Real powder velocity profiles within a roll compactor are non-uniform. Johanson's analysis is modified in this work to include a mass correction factor to account for the improper one-dimensional flow assumption, similar to what was proposed by Bi et at [M. Bi, F. Alvarez-Nunez, F. Alvarez, Evaluating and modifying Johanson's rolling model to improve its predictability, J Pharm Sci. 103 (2014) 2062-2071]. Unlike Bi et al.'s work, however, an empirical curve fit accounting for the mass correction factor's dependence on position is included in the current analysis. The fit has two fitting parameters, which can be determined from online measurements. Predictions of the average relative density at the minimum gap width from the modified Johanson model are compared to predictions from FEM models and the errors are found to be approximately 5% larger than the FEM predictions. The unmodified Johanson model over-predicts the FEM results by around 50%. Comparisons to published experimental data also show good agreement. This modified Johanson model can be used in control schemes to provide much better estimates of ribbon relative density in roll compaction operations. (C) 2016 Elsevier B.V. All rights reserved.