Parameterization in History Matching: State of the Art and Perspectives

History matching consists in estimating spatially variable petrophysical parameters among which facies, porosity or permeability. These parameters, which are keys to understanding fluid flows, are difficult to measure. However, they can be inferred from measurements of related variables such as flow rates, pressures, gas oil ratios... This is actually an inverse problem, which is intrinsically "ill-posed". This concern motivated the development of many techniques to solve history matching. They differ most significantly in their approaches to parameterization. Parameterization deserves special consideration because it strongly influences the "well-posedness" of the inverse problem and the physical validity of its solution. A suitable parameterization technique makes it possible to reduce the number of parameters, but also to preserve the spatial variability of the inverted properties. Otherwise, the inverted models lack geological realism. We propose to review the main parameterization techniques and distinguish two main families: those, which adopt either a blocked or a geostatistical description of spatial variability. Briefly, the first approach splits the reservoir into a number of discrete blocks characterized by uniform petrophysical properties. These ones are then considered as parameters to adjust in order to match the available production data. The geostatistical alternative views the properties of interest as stationary random fields. In this case, various methods have been proposed to vary realizations of random fields to fit the production data while still respecting the prior spatial variability captured either by two- or multi-point statistics. Referring to the multiscale nature of rocks, we suggest to merge the two main parameterization groups mentioned above, thus resulting in a multiscale parameterization approach. The technique envisioned is based upon sequential simulation and provides the ability to vary both continuous and discrete petrophysical properties at the block scale or at a finer scale while preserving a consistent link between the scales.