Flow diagnostics are a common way to rank and cluster ensembles of reservoir models based on their approximate dynamic behaviour prior to commencing full-physics reservoir simulation. Traditionally, they have been carried out on corner-point grids inherent to geocellular models. The Rapid Reservoir Modelling" (RRM) concept aims at fast and intuitive prototyping of geologically realistic reservoir models. In RRM, complex reservoir heterogeneities are modelled as discrete volumes bounded by surfaces that are sketched in real time. The resulting reservoir models are discretised using fully unstructured tetrahedral meshes where the grid conforms to the reservoir geometry, hence preserving the original geological structures that have been modelled. This paper presents a computationally efficient work flow for flow diagnostics on fully unstructured grids. The control volume finite element method (CVFEM) is employed to solve the elliptic pressure equation. The flux field is a multi-point flux approximation (MPFA). A new tracing algorithm is developed on a reduced monotone acyclic graph for the hyperbolic transport equations of time-of-flight and tracer distributions. An optimal reordering technique is employed to deal with each control volume locally such that the hyperbolic equations can be computed in an efficient node-by-node manner. This reordering algorithm scales linearly with the number of unknowns. The results of these computations allow us to estimate swept reservoir volumes, injector-producer pairs, well-allocation factors, flow capacity, storage capacity and dynamic Lorenz coefficients which all help approximate the dynamic reservoir behaviour. The total CPU time, including grid generation and flow diagnostics, is typically a few seconds or meshes with O(100k) unknowns. Such fast calculations provide, for the first time, real-time feedback in the dynamic reservoir behaviour while models are prototyped.