Visualization Studies on Matrix- Fracture Transfer Due to Diffusion

Abstract Co-and counter-current type transfers due to diffusion between matrix and fracture were studied experimentally using a 2-D model, and visualization equipment. The model is made of glass-beads or filter paper. Mineral oil and kerosene were used as the displaced phase. The 2-D model saturated with oil was exposed to pentane diffusion under static conditions to mimic matrix-fracture interaction during gas or liquid solvent injection in naturally fractured reservoirs. Displacement fronts and patterns were analyzed and quantified using fractal techniques to obtain correlations between the fractal properties and displacement type. A few capillary imbibition experiments showing an invasion percolation (IP) type displacement were conducted first. Diffusion type displacement resulted in diffusion limited aggregation (DLA) type patterns. Conditions yielding different types of displacement patterns were identified. The visual observations of the experiments will help develop stochastic displacement simulations using IP and DLA algorithms. Introduction Investigations on the displacement behavior under static conditions are important in different engineering practices such as exploitation of oil and gas, CO2 sequestration and groundwater contamination in naturally fractured reservoirs. Studies in this area resulted in different displacement patterns varying from piston like to fingering [1]. Quasi static displacement dominated by the capillary forces yields a process called invasion percolation (IP) [2–3]. Diffusion limited aggregation (DLA) patterns are obtained during diffusion and viscous forces dominated processes [4]. Wardlaw et al. [5] conducted experiments using glass cells and showed the importance of local differences in surface roughness on the imbibition of water and brine displacing oil. Indelman and Katz [6] analyzed the mechanics of countercurrent imbibition on 2-D models numerically and observed that the amount of imbibed liquid is a linear function of square root of time. They investigated the local heterogeneity on the process as well. Tidwell et al. [7] studied matrix imbibition during flow in the fracture. They modeled the matrix imbibition as a linear function of square root of time as suggested by Indelman and Katz and observed that this approach is applicable only to homogeneous matrix. They further investigated the heterogeneity effects using x-ray imaging and visualized the imbibition of water into a slab of volcanic tuff. They observed that the trend shows a linear behavior although the hydraulic conductivity of tuff varies by over four orders of magnitude. Medina et al. [8] conducted experiments on filter papers with different shapes and showed that in rectangular strips the dynamics of the capillary imbibition yields the classical Washburn law. Modifications to IP and DLA algorithms were developed to better simulate the flow in pore level. Biroljev et al. [9] took the gravity effect into account, developed the computer model and tested the model experimentally. They concluded that the front between the fluids is found to scale with the dimensionless Bond number (ratio between gravitational and capillary forces), and the fractal dimension of the profile is found to be De ≈1.34. Yortsos and Xu [10] and Xu et al. [11] developed a phase diagram of fully developed drainage in porous media using invasion percolation simulation runs.

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