Observed spatial statistics of permeability and the effects on fluid flow: are we getting it right?

In geocellular modeling, the variogram is used to represent the spatial correlation of rock properties. Horizontal variograms are often assumed rather than measured due to the scarcity of subsurface data. Wells are drilled kilometers apart while reservoir heterogeneity occurs at much smaller scales. The use of outcrop data as analogues has therefore been widely practiced by geoscientists to supplement the estimation of horizontal variograms. Through research of reported observations from outcrop, this paper will reveal that the strategy used to define sampling intervals and data density in published outcrop studies can vary significantly with implications for modelling and simulation.
The impact on experimental variogram calculation has not been given sufficient attention and there is large variation, and hence uncertainty, on any variogram data used in modelling. We examine the choice of sampling interval and sufficiency on the derived variogram properties via a synthetic study. We also investigate the uncertainty of variograms used in modelling on flow simulation.
A number of models have been created to represent the range of variability in the spatial correlation of permeability reported in outcrop studies. The models were sampled with various intervals and amounts of data to create experimental variograms. We find that insufficient density of data can lead to variograms that may be misinterpreted leading to an incorrect choice of variogram range in subsequent modelling. From flow simulations we show how this is critical and that over- or under-estimation of the range can vary recovery factors by ten per cent.

Reservoir modelling and simulation is important for field management. A proper representation of the subsurface rock properties such as permeability is crucial so that accurate predictions and forecasts can be made. The most appropriate choice of semi-variogram parameters will therefore have a strong impact on reliability of models leading to more effective decision making.