A novel model for quantifying radial flow distributions in flat sheet membrane chromatography modules under non-binding conditions is presented and applied for the practical analysis of two modules. The proposed model partitions the total void volume of the chromatography module into zones that are considered homogeneous with respect to flow velocity. The corresponding solute concentrations are time variant, but also spatially homogeneous within each zone. The model is mathematically represented and analytically solved as a network of continuously stirred tank reactors (CSTR). An additional plug flow reactor (PFR) is connected in series with the CSTR network in order to account for a time-lag that is not associated with the system dispersion. The capability of the model to describe experimental breakthrough data is compared to the frequently applied standard model for extra-membrane system dispersion, which consists of a single CSTR in series with a PFR. Non-binding conditions are deliberately chosen for studying the impact of module geometries on breakthrough curves separately from chromatographic membrane performance. The commercial CIM module and a custom designed cell (Scell) are studied with acetone and lysozyme as test tracers at varied flow rates and for various membrane pore sizes under non-binding conditions. In all studied cases, the proposed model fits the measured breakthrough curves better than the standard model. Moreover, the minimal number of radial flow zones that are required to accurately describe observed breakthrough curves and the estimated flow fractions through these zones provide valuable information for the analysis and optimization of internal module designs.