Master of Science in Petroleum Engineering (MSPE)
With recent advances in the capabilities of high performance computing (HPC) platforms and the relatively simple representation of complex geometries of porous media, lattice Boltzmann method (LBM) has gained popularity as a means of solving fluid flow and transport problems. In this work, LBM was used to obtain flow parameters of porous media, study the behavior of these parameters at varying flow conditions and quantify the effect of roughness on the parameters by relating the volume averaged flow simulation results to Darcy and Forchheimer equations respectively. To validate the method, flow was simulated on regular and random sphere arrays in cubic domains, for which a number of analytical solutions are available. Permeability and non-Darcy coefficients obtained from the simulation compared well with Kozeny and Ergun estimates while deviation from the observed constant permeability and tortuosity values occurred aroundRe≈1-10. By defining roughness as hemispherical protrusions on the smooth spheres in the regular array, it was observed from flow streamlines obtained at different roughness heights that the average length of the flow paths increased with increasing roughness height. As such, the medium tortuosity and non-Darcy coefficient increased while the permeability decreased as height of the roughness increased. Applying the method to a 3D computed tomography image of Castlegate sandstone, the calculated macroscopic permeability and beta factor components were in good agreement with reported experimental values. In addition, LBM beta factors were compared with a number of empirical models for non-Darcy coefficient estimation and were found to be of the same order of magnitude as most of the correlations, although estimates of the models showed wide variation in values. Resolution of the original sample was increased by infilling with more voxels and simulation in the new domain showed better flow field resolution and higher simulated flow regimes compared to those of the original sample, without significant change in the flow parameters obtained. Using the Reynolds number based on the Forchheimer coefficient, the range of transition from Darcy to non-Darcy regime was within the values reported by Ruth and Ma (1993) and Zeng and Grigg (2006). 1
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Chukwudozie, Chukwudi Paul, "Pore-scale lattice Boltzmann simulations of inertial flows in realistic porous media: a first principle analysis of the Forchheimer relationship" (2011). LSU Master's Theses. 3220.