The heterogeneity of rocks represents a challenge for interpreting and using outcomes from multiphase-flow experiments carried out on laboratory samples. While the capillary pressure-saturation function, p(c)(S), is known to vary spatially and cause local saturation development during immiscible displacements, its variation remains difficult to measure. This is particularly challenging for rocks with complex fabrics, such as carbonates. Here, we present a workflow for the dynamic measurement of core-and subcore-scale drainage pcoS+ curves in heterogeneous porous media. Multi-rate, two-phase core-flooding tests are conducted on three carbonate rocks with direct observations of local saturation data. The interpretation of the experiments is done by fitting the parameters of the p(c)(S) curve, while describing both steady-state saturation and pressure profiles with a detailed one-dimensional model that accounts for the variation of subcore-scale properties in the direction of displacement. Workflow validation is achieved by means of synthetic data, thereby demonstrating the uniqueness of the solution of the resulting multi-objective optimisation problem. The model reproduces accurately experimental data on the three rocks and enables computing the effective core-scale p(c)(S) curve in the limit of zero velocity, as it would be expected during a porous-plate experiment. The output of the proposed technique is however much richer and includes the relative p(c)(S) curve that is universal and independent of the specific pattern of heterogeneity, in addition to a set of scaling factors. The latter describe the distribution of the p(c)(S) curves at the subcore-scale due to heterogeneity and form the statistical basis needed for upscaling studies. (C) 2019 Elsevier Ltd. All rights reserved.