the impact of the scale of geological variability

the impact of the scale of geological variability on geostatistical conditioning to effective properties Brent Lowry & Jef Caers SCRF 26 th Annual Meeting May 9, 2013

“missing” scale 106 • The size of a reservoir makes direct inclusion of small-scale data unfeasible • Instead the core is assumed representative of a grid cell • Possibly ignores heterogeneity within the grid cell

reasons to reinvestigate • Advent of multi-point statistics with training images (TI) • Fast pattern-based simulation → Re-inspect the concept of a “representative elementary volume” (REV)

exploratory question • We would like to study the change in effective permeability of a geostatistical grid cell when the scale of objects in the training image increases { Keff ? simulated geostatistical grid cell w/ well data { Keff? geostatistical model

Simulating within a single geostatistical cell • SNESIM (multi-point statistics) • Conditioned to data • Larger images with their larger structures (channels), will create larger structures in realizations using a TI with small objects 100 x 25 feet represented by a 100 25 grid using a TI with large objects 100 ft 25 ft

flow upscaling • Flow-based upscaling within each layer • Constant pressure – no flow boundary conditions • A quantitative way to see the effect of the changes in channel, object sizes on permeability upscaling to one effective permeability in each layer 6

realizations Within geostatistical grid cell variability simulated from training images with increasing object size ratio = 0. 016 ratio = 0. 052 ratio = 0. 40 increasing size of training image ratio = 1. 25 7

conditioned effective permeability what do we expect ? Conditioned effective permeability Permeability a function of the marginal proportion of the facies Permeability equivalent to the core value

conditioned effective permeability • The core’s permeability value can be very different from the well Conditioned effective permeability grid cell’s effective permeability • The upscaled flow values exhibit a non-linear function as the scale of geological variability increases well 9

findings • Surprisingly impactful effect on effective permeability of training image “scale”: → Edge effects may contribute to a high variance and long convergence to core permeability → Variation is non-linear and difficult to predict; theory of REV does not apply future work • Study the impact of the conditioning, does it provide: Smaller or larger variance in effective K?