Impact of PVT Properties of the Fluid on the LBM Scheme Within the Scale Integration for Shale Reservoirs
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Modelling of the performance of shale gas reservoirs is known for the presence of multiple scales. The latter includes pore-scale, fracture scale and field scale. The nature of flow-mechanisms at various scales is different. Therefore, separate treatment of the physical processes is required. On the other hand, an integrated approach is highly beneficial for practical implementation. One of the candidates for seamless integration concerned is the Lattice-Boltzmann Method. The latter fact together with the demands of the industry provides the major motivation for the present work. In this study the novel Lattice-Boltzmann Model for pore-scale simulations has been introduced. The major advantage of the approach concerned is that the mathematical formulation of the model has a high degree of self-consistency. The latter means that it does not have an artificially introduced terms like pseudo-potentials, which are common for conventional Lattice-Boltzmann schemes. Despite the advantages of the approach in terms of mathematical formulation, there exist certain limitations because of the issues with numerical stability. One of the most important results of the present work is that the issues concerned can not be resolved by the reasonable increase of the number of lattice vectors in the model. The limitations involved make the scheme impractical for fieldscale simulations. Therefore, an alternative formulation of Lattice-Boltzmann method for reservoir modelling is required. In the present work, a novel pseudo-potential model for field-scale simulations has been introduced. The model concerned demonstrates a reasonable agreement with the analytical techniques in the case of steady-state flow. However, further investigation shows significant deviations because of the numerical diffusion. Moreover, it has been shown that significant numerical diffusion is a feature of the majority of the existent pseudo-potential models. The numerical effect concerned is critically important in the case of the multiphase flow, because it can lead to non-physical solutions. In order to resolve the problem concerned a novel Lattice-Boltzmann Scheme has been introduced. The scheme demonstrates reasonable agreement with analytical methods and with simulations performed with trusted programs for reservoir modelling. Finally, the major contribution of the present work includes the development of selfconsistence approach for simulations at pore-scale, the proof of fundamental limitations of the model introduced, observation of numerical diffusion in pseudo-potential Lattice- Boltzmann Methods, and the solution of the latter issue through the development of the novel Lattice-Boltzmann scheme for field-scale simulations.
Tarakanov, Alexander (2017). Impact of PVT Properties of the Fluid on the LBM Scheme Within the Scale Integration for Shale Reservoirs. Doctoral dissertation, Texas A & M University. Available electronically from