History matching of dual continuum reservoirs\u2014preserving consistency with the fracture model

Abstract

Ensemble- and optimization-based parameter estimation is commonly used to calibrate simulation models of fractured reservoirs to measured data. Traditionally, statistical data on small-scale fractures are upscaled to a dual continuum model in a single step, and the subsequent history matching procedure makes adjustments to the upscaled parameters. In this paper, we show that the resulting reservoir models may be inconsistent with the initial fracture description, meaning that the reservoir parameters do not correspond to a physically valid combination of fracture parameters. A number of numerical examples is provided, which illustrate why and when the problem occurs. We utilize an invertible analytical fracture upscaling method, and deviations from the fracture model can thus be quantified in each case. We show that consistency with the fracture model is preserved if fracture parameters are history matched directly, if the relation between inversion variables and fracture parameters is linear, or if an unbiased Bayesian sampling method is used. We also show that preserving consistency is less important if the uncertainty of the fracture upscaling method is large.