Impact of the simulation algorithm, magnitude of ergodic fluctuations and number of realizations on the spaces of uncertainty of flow properties |
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Authors: | P Goovaerts |
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Institution: | (1) Department of Civil and Environmental Engineering, The University of Michigan, EWRE Bldg, Room 117, Ann Arbor, MI 48109-2125 Phone: (734) 936-0141, Fax: (734) 763-2275, e-mail: goovaert@engin.umich.edu, |
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Abstract: | Geostatistical simulation algorithms are routinely used to generate conditional realizations of the spatial distribution
of petrophysical properties, which are then fed into complex transfer functions, e.g. a flow simulator, to yield a distribution
of responses, such as the time to recover a given proportion of the oil. This latter distribution, often referred to as the
space of uncertainty, cannot be defined analytically because of the complexity (non-linearity) of transfer functions, but
it can be characterized algorithmically through the generation of many realizations. This paper compares the space of uncertainty
generated by four of the most commonly used algorithms: sequential Gaussian simulation, sequential indicator simulation, p-field simulation and simulated annealing. Conditional to 80 sample permeability values randomly drawn from an exhaustive
40×40 image, 100 realizations of the spatial distribution of permeability values are generated using each algorithm and fed
into a pressure solver and a flow simulator. Principal component analysis is used to display the sets of realizations into
the joint space of uncertainty of the response variables (effective permeability, times to reach 5% and 95% water cuts and
to recover 10% and 50% of the oil). The attenuation of ergodic fluctuations through a rank-preserving transform of permeability
values reduces substantially the extent of the space of uncertainty for sequential indicator simulation and p-field simulation, while improving the prediction of the response variable by the mean of the output distribution. Differences
between simulation algorithms are the most pronounced for long-term responses (95% water cut and 50% oil recovery), with sequential
Gaussian simulation yielding the most accurate prediction. In this example, utilizing more than 20 realizations generally
increases only slightly the size of the space of uncertainty. |
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Keywords: | : stochastic simulation space of uncertainty flow simulator ergodic fluctuations |
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