Reservoir modeling with ensembles in metric space.

@inproceedings{CaersGM2009,
 abstract = { The traditional reservoir modeling and prediction workflow consists of creating one reservoir model at a time. Uncertainty quantification is then obtained by randomization of the same workflow. In actual practice, this is rarely if ever done since history matching, flow simulation and performance optimization take far too much CPU time, even if one considers multiple CPUs. Response surface analysis and experimental design have limited scope and cannot treat satisfactory the spatial component in reservoir modeling. In this presentation, I will demonstrate a strikingly simple technique for generating multiple reservoir models jointly (=at the same time) all constrained to well, seismic and production data requiring very few flow simulations. In fact, the number of flow simulation required is much less than the number of history matched reservoir models created. This method does not rely on any Kalman filtering and its limiting assumptions. Instead, the technique relies on the recently developed distance approach to reservoir modeling. These approaches rely on representing an ensemble of reservoir models in metric space and solving uncertainty quantification, optimization and conditioning problems directly in metric space without any need for model parameterization or any other axis system specification. In summary, reservoir model randomization is achieved by representing models through a Karhoene-Loeve expansion in metric space. This expansion can generate Gaussian and non-Gaussian models very efficiently. If the distance used to define this space equals the difference in production data between any two models, then one can simply map the actual production data in the same space representing the true unknown reservoir. Using optimization techniques (e.g. kriging) several new reservoir models can then be created that map at the same location in this space, i.e. are at zero distance from the true reservoir response (i.e. not equal to the true reservoir, but having the same production response). With this technique, we will also show how a simple diagnostic on testing the adequacy of the prior model in solving the flow inverse problems can be developed. We will also demonstrate how the use of upscaling allows history match high-resolution and coarse flow models jointly. Most importantly, this work shows that building several reservoir models at the same time is much more efficient and effective than building one model at a time. },
 author = { Caers, Jef AND Park, Kwangwon AND Scheidt, Celine },
 booktitle = { Proc. 29th Gocad Meeting, Nancy },
 title = { Reservoir modeling with ensembles in metric space. },
 year = { 2009 }
}