Measuring the Fractal Dimensions of Reservoirs: A New Seismic Fractal Heterogeneity Log for Application to CCUS Prospects

Carbon Capture and Underground Storage (CCUS) is not simply the reverse of the hydrocarbon extraction process. The injection of supercritical CO₂ involves different flow regimes (viscous, slip, Knudsen, and molecular diffusion) and the adsorption of CO₂ to mineral surfaces. Small pressure differences control the distribution of the gas and gravity controls the overall gas distribution. Under these circumstances reservoir heterogeneity strongly controls where the CO₂ goes. Consequently, it is important to have a quantitative description of this heterogeneity. Leeds University Petrophysics Group has been working on using fractals to describe heterogeneity and anisotropy of reservoirs at all scales for the past decade and to develop fractal reservoir models that account for flow at scales smaller than the seismic resolution. In this presentation we show how the fractal dimension of a bounded dataset can be measured, and the main influences on the accuracy of the measurement, taking account of the systematic uncertainties imposed by the finite boundary conditions, scale-dependent effects, and multifractal behaviour.

The approach has been used to carry out digital ‘logging’ of several reservoirs including the Chandon field (Offshore NW Australia) and is currently being implemented for the CCUS testbed Sleipner reservoir (UK North Sea). This logging differs from wireline logging in that it is carried out over an predefined area or seismic data as a function of depth. For the Chandon field, depth-averaged measurements have produced a fractal dimension of 2.15±0.18 (arithmetic mean±standard deviation) over the entire scale range. It is recognised that the fractal dimension of this reservoir is multifractal, with a fractal dimension of 2.06±0.19 in the 70-150 m scale range and 2.62±0.07 in the 200-400 m scale range. Hence, the reservoir is more heterogeneous at the larger scale. This work also has the advantage of providing a fractal dimension value as a function of depth. Our results show in each case that the fractal dimension varies significantly with depth and is dependent on lithofacies. The fractal dimension at both scales picks out apparent lithofacies, with the coarsening-up sequence in the top part of the reservoir (1950-2020 m, all depths TVDSS) associated with a decrease in fractal dimension, shalier units (2020-2035 m and 2080-2125 m) exhibiting high fractal dimensions, and cleaner units (2035-2080 m) showing much lower fractal dimensions. This is good evidence that this new Seismic Fractal Heterogeneity Log (SFHL) represents a measure of rock heterogeneity to horizontal flow at each depth. Work is ongoing concerning the discrimination of different fractal dimensions as a function of azimuth as well as vertically, which is especially important in reservoirs used in CCUS applications.

It is hoped that the new SFHL can provide the sought after quantitative measure of heterogeneity for use in quantifying and modelling CO₂ injection into CCUS reservoirs. The real advantage of this approach is that it can be applied to existing 3D and 4D seismic datasets in order to extract from them extra information and extra value. Future work will be aimed at developing the approach further.