History matching is an important inverse problem extensively used to estimate petrophysical properties of hydrocarbon reservoirs by matching a numerical simulation to the reservoir's history of multiphase flow production. Modern history matching strategies pose the characterization process as an optimization problem involving the estimation of rock properties such as porosity and permeability in all grid blocks (Ng) of a petroleum reservoir model. However, when large number of cells are considered these strategies becomes highly inefficient requiring large number of computational expensive reservoir simulations and even being inadequate, from an optimization point of view, when static data is not abundant or unreliable leading to ill-posed situations.
This work proposed a novel approach to reduce the complexity of the inverse problem in several ways by: i) focusing exclusively on characterizing rock properties within certain regions of interest (Nr where Nr<<Ng) in the reservoir model (instead of at every grid block) where either high level of uncertainty exists or exploration wells are expected to be drilled, ii) parameterizing spatial distribution of rock properties using kriging techniques based on data available only at particular locations in the reservoir (in special at the center of predefined regions of interest), iii) replacing the time consuming reservoir numerical simulator by a surrogate model constructed using only input and out data, iv) efficiently generating multiple realizations of property distribution (input data) employing well-known design of experiments techniques and forecasting well production response (output data) associated to those realizations using an open source and multi-purpose numerical reservoir simulator tool (MATLAB Reservoir Simulation Toolbox, MRST®) as well as Ecrin®, and v) constructing a computational cheap surrogate model employing data dimensional reduction techniques.
Using synthetic two-dimensional and multiphase numerical examples of increasing level of complexity involving several thousands of unknowns, the accuracy and computational performance of the proposed region-based history matching methodology was evaluated. The novel approach reduces the size of the optimization problem to a fraction of unknown parameters and the results showed it can be used effectively and efficiently for estimating petrophysical reservoir parameters with acceptable accuracy when static reservoir data is limited in the absence of previous characterization efforts. The novel approach seems also flexible enough to incorporate known geological properties of the reservoir by constraining the optimization problem and the results can also be directly used as a first solution approximation in more detailed characterization projects.