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Abstract

The geology of an oil reservoir is not homogeneous at the scale of resolution of an electrical/electromagnetic (E/EM) measurement or at the grid scale of an oil reservoir simulator. This paper discusses issues governing how the petrophysical laws governing resistivity of homogeneous rocks average to give bulk or grid scale resistivity. The bulk-averaged resistivity of a heterogeneous material measured by a given E/EM technique is a function of the direction of current flow relative to any structure of the material. The difference in bulk resistivity between current flowing across and parallel to geologic structure is frequently significant resulting in a material that is anisotropic. Failure to recognize the importance of the direction of current flow can lead to significant errors in interpretating E/EM measurements. The averaging of core-scale properties (porosity, saturation, etc.) to give representative block resistivity has been analyzed using field data to ensure that the statistics (average, variance, correlation, etc.) are geologically realistic. Merely plugging average saturation and porosity into Archie's law, while ignoring how the saturation and porosity are spatially distributed, can give block resistivities that are as much as 50% off. The analysis of field data was generalized from a bedded unit to an amorphous block by considering a bimodal distribution of pore sizes. For this example the resistivity calculated using average properties can be off by a factor of ten. This demonstrates that the question of how to average properties to determine bulk resistivity is a fundamental petrophysical question, not just an artifact of the field data used.

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