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, flow diagnostics are carried out on corner-point grids inherent to geocellular models.
The novel "Rapid Reservoir Modelling" (RRM) concept enables fast and intuitive prototyping and updating of reservoir models. In RRM, complex reservoir heterogeneities are modelled as discrete volumes bounded by surfaces that can be modified using simple sketching operations in real time. The resulting reservoir models are discretized using fully unstructured 3D meshes where the grid conforms to the reservoir geometry.
This paper presents a new and computationally efficient numerical scheme that enables flow diagnostic calculations on fully unstructured grids. Time-of-flight and steady-state tracer distributions are computed directly on the grid. The results of these computations allows 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.
We use the Control Volume Finite Element Method (CVFEM) to solve the elliptic pressure equation. A scalable matrix solver (SAMG) is used to invert the linear system. A new edge-based CVFEM is developed to solve hyperbolic transport equations for 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 total CPU time, including grid generation and flow diagnostics, is typically below 3 seconds for grids with 50k unknowns. Such fast calculations provide, for the first time, real-time feedback on changes in the dynamic reservoir behaviour while the reservoir model is updated.