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Experiments to study the exhaust of noble gases (helium, neon) with cryopumping in DIII-D Advanced Divertor Program (ADP) configuration and in JET (Mk1 configuration) found significant differences in the global exhaust rate of helium, while efficient neon exhaust was observed in both machines. An attempt to better understand the basic processes governing the exhaust of noble gases in ELM H-mode with cryopumping has been undertaken. Since divertor geometries investigated in the DIII-D and in the JET cases have significant differences, a comparative modeling study has been undertaken using the MIST core impurity transport code and the b2.5 time-independent divertor transport code. Photodiode measurements are used to determine ELM frequency, and charge- exchange recombination (CER) measurements are compared with the MIST ELM model to evaluate transport coefficients in the core plasma. A significant reduction in the anomalous diffusivities is found for the non-ELM component of radial transport without the need for a pinch velocity, and the model provides a more coherent description than the conventional ELM-averaged approach. Sensitivity to boundary conditions has been studied through establishment of a database of divertor enrichment cases using b2.5.