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Flow diagnostics for model ensembles


Ensembles of geomodels provide an opportunity to investigate the range of parameters and possible operational outcomes for a reservoir of interest. Full-featured dynamic modelling of all ensemble members is often computationally unfeasible, however some form of dynamic modelling, allowing us to discriminate between ensemble members based on their flow characteristics, is required.

Flow diagnostics involve simplified analysis of steady flow scenarios, single-phase or multiphase, and can be run in a much shorter time than a full dynamic multiphase simulation.

Fundamental quantities calculated for flow diagnostics include travel times, volumetric partitions, inter-well communications, and measures of dynamic heterogeneity. Heterogeneity measures like the dynamic Lorenz coefficient and sweep efficiency can be used as proxies for oil recovery in order to rank models. More advanced flow diagnostic techniques can also be used to estimate recovery.

We present two different forms of flow diagnostics metrics and investigate how well they perform in an ensemble setting. The first are based on volume-averaged travel times, which are calculated on a cell by cell basis from a given flow field. These measures are inexpensive to calculate and yield good results for relative rankings of models in the ensemble. The second use residence time distributions, which lead to more accurate results allowing for better estimation of recovery volumes. In addition, we have developed new metrics for better correlation between diagnostics and simulations when models have non-uniform initial saturations.

Three different ensembles of models are analysed; Egg, Norne, and Brugge. Very good correlation, in terms of model ranking and recovery estimates, is found between flow diagnostics and full simulations for all three ensembles. In the Egg and Norne examples, we consider uniform initial saturation and evenly spread well locations. Simulation results in terms of model ranking are well characterised by flow diagnostics based on volume-averaged travel times and residence time distributions, which are calculated using average initial saturations.

For the Brugge example, we consider producers placed in an oil cap, and demonstrate how the diagnostics results can be localized to the region of interest. We observe good correlations between simulations and simple flow diagnostic proxies for oil sweep. In addition, we also obtain good approximations for recovery when mapping saturation to the backward time-of-flight variable and solving 1D transport equations with the inter-well residencetime- distributions as source terms.


Academic chapter/article/Conference paper


  • Research Council of Norway (RCN) / 280950




  • SINTEF Digital / Mathematics and Cybernetics




European Association of Geoscientists and Engineers (EAGE)


ECMOR XVII - 17th European Conference on the Mathematics of Oil Recovery, 14-17 September 2020



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