Genome Scale Models capture the complete metabolic capabilities of an organism. However these models are undeterminated, i.e. they contain 100s of degrees of freedom and directionality constrains are critical for the predictive powers of the model. These constraints have been mainly based on biochemical textbooks or similarity with other organisms. Here a new workflow based on network-embedded thermodynamic analysis was used to thermodynamically curate the directionality constraints of two well kwon eukaryotic models, Recon 1 and Yeast 5. New irreversible reactions were identified in both models, 27 in Recon 1 and 16 in Yeast 5. Moreover, four reactions with incorrect directionality specifications (three in Yeast 5 and one in Recon 1), and several isolated clusters that require further curation were identified by the workflow. The framework identified the unfavorable thermodynamic of the essential reaction catalyzed by phosphoribosylaminoimidazole carboxylase in purine metabolism. This unfavorable thermodynamic is overcomed by substrate channeling (in human) and ATP hydrolysis (in yeast). Finally, the differences in proline metabolism between yeast (cytosolic anabolism, mitochondrial catabolism) and human cells (exclusively mitochondrial) were unraveled. This workflow facilitates the specification and validation of directionality constraints in compartmentalized models, and provides further insight into the network properties.