INSIM-FT in three-dimensions with gravity

Highlights: • A new data-driven model is proposed to extend the original model from two dimensions to three dimensions. • Unlike the original model, the new model can consider wells with multiple perforations with arbitrary trajectories. • A generic method for solving Riemann problem is applied for solving Buckley–Leverett equation with gravitational effects. • Imaginary wells and connection map are generated automatically using Mitchell's best-candidate algorithm and Delaunay triangulation. -- Abstract: For situations where reservoir management based on developing and running a full-scale reservoir simulation model is not plausible, data-driven models may provide an attractive alternative. Recently, we developed a simple data-driven model, INSIM-FT for reservoir flow and transport as a replacement for a reservoir simulator. However, INSIM-FT only considers two-dimensional flow in a reservoir that contains only vertical wells. In this work, we develop a new data-driven model that extends the interwell numerical simulation model with front-tracking (INSIM-FT) from single-layer reservoirs to full three-dimensional (3D) multi-layer reservoirs. The new model, which is referred to as INSIM-FT-3D, can be used for history matching and reservoir performance predictions for a three-dimensional reservoir under waterflooding. The novelty of the new approach includes: (1) INSIM-FT-3D replaces the original Riemann solver in INSIM-FT by a new Riemann solver based on a convex-hull method that enables the solution of the Buckley–Leverett problem with gravity; (2) unlike the original INSIM-FT model, which assumes all wells are vertical, the INSIM-FT-3D model allows for the inclusion of wells with arbitrary trajectories with multiple perforations; (3) INSIM-FT-3D applies Mitchell's best-candidate algorithm to automatically generate the imaginary wells that are evenly distributed in the reservoir given a set of prefixed actual well nodes and (4) INSIM-FT-3D utilizes our own modification of Delaunay triangulation to build the 3D connection map necessary to use the general INSIM-FT-3D formulation. History matching of the INSIM-FT-3D model parameters is performed using the ensemble-smoother with multiple data assimilations. The model parameters for history matching include the connection-based parameters, the parameters defining the power-law relative permeabilities and the parameters defining the well indices for the perforated zones of a well with multiple perforated well segments. The reliability of the analytical water-saturation solution obtained with INSIM-FT-3D is validated by comparison with corresponding results from an Eclipse [47] model with very fine grids and small time steps. After illustrating the utility and reliability of the method for a three-dimensional synthetic problem, the method is shown to give reasonable history-matching and prediction results for a field example. At last, the proposed method is tested for Brugge field, a field-scale synthetic reservoir simulation model.