Study Group report
This is the final report on the problem of uncertainty of flow in porous media, brought to ESGI49 by Schlumberger.

Report authors
Joyce Aitchison (JMA Numerics)
Linda Cummings (University of Nottingham)
Giles Richardson (University of Nottingham)
Jonathan Rougier (University of Durham)

Introduction
The problem posed was, in essence, how do we estimate the probability distribution of f(x) from the probability distribution of x? Here x is a large vector and f is a complex function which can be expensive to evaluate. For Schlumberger’s applications f is a computer simulator of a hydrocarbon reservoir, and x is a description of the geology of the reservoir, which is uncertain. We might also want to update our distribution on f(x) to include information relevant to some of the simulator output values. Typically this would be production history for a reservoir that had been operational for some time, and for which the simulator was being run forwards into the future to evaluate a possible control regime.
The Study Group report broke this problem into three parts. The first is reducing the dimensionality of the input space. The second is performing the inferential calculations despite only having a limited number of simulator evaluations and the technology necessary to make these calculations feasible, namely an emulator. The third and final part is having available a number of test problems for which exact solutions can be computed, for evaluative purposes.
Also, report suggests two independent approaches relating to flow in a porous medium in the presence of narrow faults or cracks.

Download 'UncertainPorousFlow.pdf' (662 Kb).