A streamline splitting pore‐network approach for computationally inexpensive and accurate simulation of transport in porous media

Abstract

Several approaches have been developed in the literature for solving flow and transport at the pore scale. Some authors use a direct modeling approach where the fundamental flow and transport equations are solved on the actual pore-space geometry. Such direct modeling, while very accurate, comes at a great computational cost. Network models are computationally more efficient because the pore-space morphology is approximated. Typically, a mixed cell method (MCM) is employed for solving the flow and transport system which assumes pore-level perfect mixing. This assumption is invalid at moderate to high Peclet regimes. In this work, a novel Eulerian perspective on modeling flow and transport at the pore scale is developed. The new streamline splitting method (SSM) allows for circumventing the pore-level perfect-mixing assumption, while maintaining the computational efficiency of pore-network models. SSM was verified with direct simulations and validated against micromodel experiments; excellent matches were obtained across a wide range of pore-structure and fluid-flow parameters. The increase in the computational cost from MCM to SSM is shown to be minimal, while the accuracy of SSM is much higher than that of MCM and comparable to direct modeling approaches. Therefore, SSM can be regarded as an appropriate balance between incorporating detailed physics and controlling computational cost. The truly predictive capability of the model allows for the study of pore-level interactions of fluid flow and transport in different porous materials. In this paper, we apply SSM and MCM to study the effects of pore-level mixing on transverse dispersion in 3-D disordered granular media.

A forward analysis on the applicability of tracer breakthrough profiles in revealing the pore structure of tight gas sandstone and carbonate rocks

“…The latter's usage however is preferred to be limited for cost efficiency if a reliable network model is verified. We note that the solute transport algorithm (i.e., MCM) has been extensively compared to both experimental data and other numerical simulation methods, such as the streamline splitting method of Mehmani et al [2014], the Superposing Transport Method of Mehmani [2014], and CFD simulations. In Mehmani [2014], comparisons with experimental data for longitudinal dispersion coefficient available from the literature for unconsolidated bead packs show that the method is in general agreement with these data for the Peclet numbers considered in this work.…”

“…The MCM transport equation (given by equation (3)) is formulated by imposing species balance on each pore and assuming the solute is perfectly mixed at the pores. The implications of this mixing assumption are discussed in Mehmani et al [2014], but are not thought to be of primary importance in this study (considering: the nature of our study is on the qualitative side, microporous portions of the pore-scale domains promote diffusive mixing, and the disordered nature of the medium itself demotes any macroscopic effects arising from the mixing assumption as discussed …”

“…In short, MCM is equivalent to an interconnected network of CSTRs (continuously stirred tank reactors; using terminology from chemical engineering). Mehmani et al [2014] developed a method in which the distribution of the solute inside each pore was dependent on the entering and exiting fluid velocity. They showed that in three-dimensional disordered granular porous media, MCM gives results with similar accuracy to the streamline-splitting approach.…”

Mesoscale and Hybrid Models of Fluid Flow and Solute Transport

“…In an effort to accurately capture partial mixing within pores and shear dispersion within throats, Mehmani et al (2014) and Mehmani (2014) developed two pore-network models, respectively: the streamline splitting method (SSM) and superposing transport method (STM). These models were developed with the aim of exploring the possibility of capturing the porescale physics discussed above under an Eulerian framework.…”

“…After all, modeling efforts should ideally seek ultimate simplicity while disposing of unnecessary complexity. Mehmani et al (2014) showed that the impact of pore-level mixing assumptions, partial vs. perfect, is very signifi cant in ordered media (e.g., micromodels), but comparatively insubstantial in 3-D disordered granular media (e.g., sandstones). In fact, the average difference between the concentration fi elds obtained via SSM and the relatively less accurate MCM for disordered granular media was ~6% of the maximum concentration value (although the impact on upscaled transverse dispersion coeffi cients is yet to be studied).…”