Extra-Corporeal Membrane Oxygenation (ECMO) is a well-established procedure used in Intensive Care Units (ICU) to treat patient with either pulmonary or heart failure. The blood of the patient is drained via a cannula, oxygenated and reinserted via another cannula. The extraction cannula is normally located in the inferior vena cava. In the case of lung failure, but with a heart in good condition, the reinsertion cannula is placed in the superior vena cava (venous-venous, VV-ECMO). In the case of heart failure, the insertion cannula is placed in the aorta (venous-arterial, VA-ECMO) to ensure that the blood is actually pumped across the arterial system. VV-ECMO is the standard procedure in the case of Severe Acute Respiratory Syndrome, and was regularly used for Covid-19 patients in ICU. A known clinical problem for VV-ECMO is recirculation, where a significant portion of the fully oxygenated blood appears to be recaptured by the extraction cannula in the inferior vena cava, instead of joining the normal circulation pathway \cite{Broman:2015}. This results in a limited efficacy of the procedure: blood is inserted fully oxygenated, but distal measurements show values as low as 80\%. In this talk we will present our work on patient-specific modeling and simulation of VV-ECMO. The patient geometry is reconstructed from a CT scan, while the blood flow and oxygen diffusion are approximated by the Finite Element Method. We will present numerical results showing how poorly the standard VV-ECMO is actually performing \cite{Leoni:2022} and we will discuss possible optimisation procedures or best practices to improve its effectiveness.