Are Our Earth and Dynamic Models Heterogeneous?

Dull, Dennis W.¹, G. Michael Shook¹, Akmaral Zhumagulova², Bakhit Tulegenova² (1) Chevron, Houston, TX (2) TengizChevroil, Houston, TX

To evaluate geologic uncertainty, geoscientists construct fine scale static models that represent extremes in porosity, water saturation, and permeability. Different models are generated by varying the geostatistics of the input data. The level of heterogeneity in a given model can be measured by constructing a Lorentz plot (or F-&phi plot) from the model's permeability, layer thicknesses, and porosity distributions. From this plot, a Lorentz coefficient or a Dykstra-Parsons coefficient can be calculated. These can be termed 'static measures of heterogeneity,' since they are determined from static reservoir properties.

However, the largest impact on secondary recovery is the connectivity of the fine scale models. This might be termed 'dynamic heterogeneity,' as its influence is only observed under conditions arising from injection. Dynamic heterogeneity contains the geometry of the flowpaths in addition to the static variables. We cannot differentiate between a low permeability, short path and a high permeability, long path; these two flowpaths would have similar residence times. We have developed novel methods of constructing F-&phi plots directly from tracer or streamline residence times, from which dynamic measures of heterogeneity can be determined.

These methods were applied to assess the dynamic heterogeneity in the earth and reservoir models of two fields. The goals of this analysis were twofold. First, differences in heterogeneity between a given earth model and its scale-up flow model are measured. Second, a comparison in the static heterogeneity measures with the dynamic measures are made, to evaluate if alternate earth models capture adequate ranges of sweep efficiency under gas injection.