Non-intrusive Reduced Order Modelling of Waterflooding in Geologically Heterogeneous Reservoirs

Abstract

Production optimisation and history matching are two applications that require the engineer to run numerous flow simulations of flow in the subsurface. Each flow simulation can be very computationally intensive, especially if reservoir is geologically complex. In some cases it may not be feasible to perform the optimisation sufficiently quickly for it to be useful. This has driven the development of reduced order modelling (ROM) techniques. The problem with most ROMs is that they have to be hard-coded into the flow simulator and so cannot be used with the commercial simulators that are used by most oil companies. In addition most applications of ROMs have assumed that the geological description of the reservoir is known. This is generally not the case, indeed the aim of history matching is to adjust the geological model of the reservoir until the flow through the model replicates that which is observed. In this paper a non-intrusive reduced order model (NIROM) is presented that enables the engineer to vary the permeabilities within a heterogeneous reservoir for a fixed well pattern and then estimate the resulting waterflood performance. The NIROM uses a Smolyak sparse grid interpolation method, radial basis functions (RBF) and proper orthogonal decomposition (POD) is presented. ‘Non-intrusive’ means that the NIROM is implemented independently of the underlying flow model. Here we use it in conjunction with an unstructured mesh, control volume finite element (CVFEM), multiphase flow model. The NIROM is demonstrated using three reservoir models: one with four material layers, one with four baffles and one with eight baffles. The results compare well with those from a high fidelity full model and reduce the CPU time by a factor of a thousand.