Assessment of electrical resistivity properties through development of three-dimensional numerical models.

An understanding of the way in which electrical currents flow through geological materials enables pertinent problems to be addressed, for example: determination of oil saturation; prediction and monitoring of fluid flow; fracture characterisation; assessment of geological structure in a general sense. The objective of this work is to simulate current flow and electrical resistivity measurements made downhole and at the earth's surface in three dimensions. This enhances interpretation by enabling the geological controls on field measurements of resistivity properties to be assessed. In addition, a basis for a wide range of applications using quantitative analysis of electrical measurements is provided. A finite difference numerical model based on the direct solution of a generalised form of Poisson's equation is developed. Both electric potential and current flow are readily simulated on a rectangular three-dimensional grid. Arbitrary resistivity distributions and electrical anisotropy can be accommodated. The model grid is advantageously analogous to (and therefore supersedes) resistor networks previously built to simulate resistivity logging tools. The model is developed through three applications. The simulation of a novel multi-electrode focused surface array is used to assess and interpret field measurements. The Ocean Drilling Program High Temperature (ODPHT) tool, a new downhole focused resistivity device, is modelled on an adapted cylindrical grid in order to calculate its geometric factors. Finally, a generalised model of a downhole electrical imaging device based on Schlumberger's Formation MicroScanner is created. Current flow is simulated from an array of 5 mm diameter electric buttons that are passively focused into the formation. This is used to generate simulated electrical images. The numerical model is verified by comparison with field data in well-constrained situations. Electrical measurements and current flow patterns have been investigated in three dimensions at a variety of scales. An enhanced understanding of the operation of surface and downhole electrical devices is gained through modelling selected geologically relevant scenarios. Specific benefits are: enhanced fault detection in the case of the surface array; quantitative characterisation of the ODPHT tool in idealised borehole environments; radial fracture characterisation using electrical images, and potential image artefacts due to localised off-hole anomalies