| dc.description.abstract | 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. | en |
