Modeling wormhole formation in digital rock samples: the role of segmentation and permeability-porosity relationships

In this work we have investigated numerically the formation of channelised dissolution patterns, termed “wormholes”, using initial pore geometries generated from tomographic images of limestone cores. We have employed an OpenFOAM-based Darcy-scale numerical solver,  porousFoam, which combines a Darcy/Darcy-Brinkman flow solver and a reactive transport solver in an evolving pore space. Simulated geometries, of both final and intermediate steps, are compared to dissolution experiments on samples the initial pore geometry is generated from, with the same acid concentration and flow rate applied. 

The initial condition of porosity distribution is set from X-Ray Computed Microtomography (XCMT) images via three phase segmentation into macroporosity, microporosity, and grain regions. Porosity values for microporous regions are set using linear interpolation between pore and grain grayscale values [1]. The inlet boundary conditions of flow rate and acid concentration are set as in the dissolution experiment. To test the effect of the permeability-porosity constitutive relationship we have investigated several options including power laws of varying exponent, and the Carman-Kozeny relation. We have also analyzed the impact of using Darcy versus Darcy-Brinkman flow solvers. Despite a qualitatively similar appearance to experimental results, the simulated wormholes are usually significantly thicker than their experimental counterparts, a fact noted by other researchers as well [2]. We comment on possible reasons for this discrepancy and on the limitations of Darcy-scale solvers in general. Additionally, we find that higher exponents in the power law makes the numerical dissolution very sensitive to grayscale threshold values as a small variation in this value changes the path of the wormhole.

 

[1] Luquot, L., Rodriguez, O., and Gouze, P.: Experimental characterization of porosity structure and transport property changes in limestone undergoing different dissolution regimes, Transport Porous Med., 101, 507–532, 2014.

[2] Yue Hao, Megan Smith, Yelena Sholokhova, Susan Carroll, CO2-induced dissolution of low permeability carbonates. Part II: Numerical modeling of experiments, Advances in Water Resources, 62, 388-408, 2013