SPE 135261 Simulation of Flow and Dispersion on Pore-Space Images

We simulate flow and transport directly on pore-space images obtained by micro-CT scanning of rock cores. An efficient Stokes solver is used to simulate low-Reynolds number flows. The flow simulator uses a finite-difference method along with a standard predictor-corrector procedure to decouple pressure and velocity. An algebraic multigrid technique solves the linear systems of equations. We then predict permeability and the results are compared with lattice Boltzmann numerical results and available experimental data. For solute transport we apply a streamline-based algorithm that is similar to the Pollock algorithm common in field-scale reservoir simulation, but which employs a novel semi-analytic formulation near solid boundaries to capture, with sub-grid resolution, the variation in velocity near the grains. A random walk method accounts for molecular diffusion. The streamlinebased algorithm is validated by comparison with published results for Taylor-Aris dispersion in a single capillary with a square cross-section. We then accurately predict available experimental data in the literature for longitudinal dispersion coefficient as a function of Peclet number. We introduce a characteristic length based on ratio of volume to pore/grain surface area that can be used for consolidated porous media to calculate Peclet number. Introduction Accurate modeling of solute dispersion at porous media is of great importance in many branches of science and engineering (Bear, 1988, Adler, 1992). To model the flow and transport at the pore scale to predict dispersion coefficients, the morphology of the pore space needs to be known. To obtain three-dimensional models of the pore space different methods can be applied. It is routine to obtain two-dimensional high-resolution images of rock (Zinszner and Meynot, 1982, Thovert et al., 1993) from which a threedimensional representation is constructed. This can be achieved using object-based methods, where grains of different size and shape are deposited (Øren et al., 1998) or an image is obtained that reproduces the statistics of the two-dimensional pictures (Adler et al., 1990, Hazlett, 1997, Roberts, 1997, Okabe and Blunt, 2004) . The advent of X-ray computed tomography has made it possible to obtain three-dimensional images with a resolution of a few microns (Coenen et al., 2004, Flannery et al., 1987) which is sufficient to capture the pore space of most sandstones. The next step is modeling flow and transport through the pore space. Traditionally, network modeling has been applied to idealize the system as a lattice of wide pores connected by throats through which displacement and transport can be computed semi-analytically (Fatt, 1956, Blunt, 2001). Network models have been used widely to simulate dispersion at the pore scale (Bruderer and Bernabé, 2001, de Arcangelis et al., 1986, Sahimi et al., 1986, Sorbie and Clifford, 1991, Sahimi, 1995, Bijeljic et al., 2004, Bijeljic and Blunt, 2007, Acharya et al., 2007, Jha et al., 2008). However, a more direct approach is to simulate transport directly on a pore-space image that removes the need to extract an equivalent network with its inherent approximations (Maier et al., 2003, Coelho et al., 1997, Maier et al., 1998, Yao et al., 1997, Salles et al., 1993). Coelho et al. (1997) used a finite difference technique to solve for flow and simulated dispersion through packings of grains of arbitrary shape and found a good agreement with experimental results on unconsolidated bead packs and sandstones. Yao et al. (1997) used a similar method to solve for the flow field and modeled dispersion on a statistically reconstructed geometry of Vosges sandstone. The agreement of the model prediction with experimental measurements for dispersion coefficient was not satisfactory (Adler and Thovert, 1998). Maier et al. (1998) used the lattice Boltzmann technique to model dispersion in a three-dimensional model of a sphere packing and successfully compared their numerical results with NMR experiments for a wide range of dimensionless Peclet number. Lattice