An extended dual-input Kety–Schmidt model can be applied to positron emission tomography data for the quantification of local arterial (f a) and local portal-venous blood flow (f p) in the liver by freely diffusible tracers (eg,[15 O] H 2 O). We investigated the a priori identifiability of the three-parameter model (f a, f p and distribution volume (V d)) under ideal (noise-free) conditions. The results indicate that the full identifiability of the model depends on the form of the portal-venous input function (c p (t)), which is assumed to be a sum of m exponentials convolved with the arterial input function (c a (t)). When m⩾ 2, all three-model parameters are uniquely identifiable. For m= 1 identifiability of f p fails if c p (t) coincides with tissue concentration (q (t)/V d), which occurs if c p (t) is generated from an intestinal compartment with transit time V d/f a. Any portal input, f p c p (t), is balanced by the portal contribution, f p q (t)/V d, to the liver efflux, leaving q (t) unchanged by f p and only f a and V d are a priori uniquely identifiable. An extension to this condition of unidentifiability is obtained if we leave the assumption of a generating intestinal compartment system and allow for an arbitrary proportionality constant between c p (t) and q (t). In this case, only f a remains a priori uniquely identifiable. These findings provide important insights into the behaviour and identifiability of the model applied to the unique liver environment.