Simulation grid blocks of naturally fractured reservoirs contain thousands of fractures with variable flow properties, dimensions, and orientations. This complexity precludes direct incorporation into field-scale models. Macroscopic laws capturing their integral effects on multiphase flow are required. Numerical discrete fracture and matrix simulations show that ensemble relative permeability as a function of water saturation (R-ri[S-w]) water breakthrough, and cut depend on the fraction of the cross-sectional flux that occurs through the fractures. This fracture-matrix flux ratio (q(f)/q(m)) can be quantified by steady-state computation. Here we present a new semianalytical model that uses q(f)/q(m), and the fracture-related porosity (phi(f)) to predict k(ri)(S-w) capturing that, shortly after the first oil is recovered, the oil relative permeability (k(ro)) becomes less that that of water (k(rw)), and k(rw)/k(ro) approaches q(f)/q(m) as soon as the most conductive fractures become water saturated. To include a capillary-driven fracture-matrix transfer into our model, we introduce the nonconventional parameter A(f),(w)(S-w), the fraction of the fracture-matrix interface area in contact with the injected water for any grid-block average saturation. The A(f,w)(S-w) is used to scale the capillary transfer modeled with conventional transfer functions and expressed in terms of a rate- and capillary-pressure-dependent k(ro). All predicted parameters can be entered into conventional reservoir simulators. We explain how this is accomplished in both, single- and dual-continua formulations. The predicted grid-block-scale fractional flow (f(i)[S-w]) is convex with a near-infinite slope at the initial saturation. The upscaled flow equation therefore does not contain an S-w shock but a long leading edge, capturing the progressively widening saturation fronts observed in numerical experiments published previously.