Quantification of Single- and Multi-Phase Hydrodynamic Dispersion in Rocks Using Dynamic 3D PET Imaging

Abstract:

We report results of an experimental investigation into the effects of small-scale (mm-cm) heterogeneities and hydrodynamic dispersion on miscible and immiscible displacements in a Berea Sandstone core. Pulse-radiotracer tests were carried out by measuring breakthrough curves at distinct flow rates and gas/water saturation ratios, while simultaneously imaging the internal displacement of the radioactive solution by [11C]PET. Dynamic multidimensional maps of the tracer concentration in the rock sample have been obtained with a spatial resolution of about 10 mm³ and provide evidence for significant macrodispersion effects caused by the presence of heterogeneities at the same scale. The numerical solution of the classic Advection-Dispersion Equation (ADE) applied in 1D form fails to describe the measured breakthrough curves and significantly overestimates longitudinal dispersivity. An excellent agreement with the experiments is attained by explicitly accounting for permeability heterogeneity, while reducing the contribution of “Fickian" dispersivity. Heterogeneity was introduced in the model by discretising the rock sample into independent parallel streamlines, which were generated based on a previously determined 3D permeability map, and by solving the 1D ADE for each of them. The use of streamlines is supported by direct quantitative observations from the PET scans; remarkably, this approach leads to an accurate representation of both the temporal behaviour and spatial distribution of the tracer concentration in the sample. It is shown that when the length-scale of permeability variations is similar in order as the size of the sample, the effect of the former can be as significant as hydrodynamic dispersion. The presence of a second immiscible fluid phase further complicates the flow field and, accordingly, the interpretation of the experiments. The ability to decouple these effects leads to the estimation of dispersion coefficients that aren't sample specific and are therefore better suited for up-scaling fluid mixing and dispersion in rocks. In this context, PET provides significant opportunities to advance our understanding of fluids displacements in rocks, thus including complex flows that involve additional phenomena, such as adsorption and chemical reactions.