Multiscale Gas Transport in Shales With Local Kerogen Heterogeneities

Abstract

On the basis of micro-and mesoscale investigations, a new mathematical formulation is introduced in detail to investigate multiscale gas-transport phenomena in organic-rich-shale core samples. The formulation includes dual-porosity continua, where shale permeability is associated with inorganic matrix with relatively large irregularly shaped pores and fractures, whereas molecular phenomena (diffusive transport and nonlinear sorption) are associated with the kerogen pores. Kerogen is considered a nanoporous organic material finely dispersed within the inorganic matrix. The formulation is used to model and history match gaspermeation measurements in the laboratory using shale core plugs under confining stress. The results indicate significance of molecular transport and strong transient effects caused by gas/solid interactions within the kerogen. In the second part of the paper, we present a novel multiscale perturbation approach to quantify the overall impact of local porosity fluctuations associated with a spatially nonuniform kerogen distribution on the adsorption and transport in shale gas reservoirs. Adopting weak-noise and meanfield approximation, the approach applies a stochastic upscaling technique to the mathematical formulation developed in the first part for the laboratory. It allows us to investigate local kerogenheterogeneity effects in spectral (Fourier-Laplace) domain and to obtain an upscaled "macroscopic" model, which consists of the local heterogeneity effects in the real time-space domain. The new upscaled formulation is compared numerically with the previous homogeneous case using finite-difference approximations to initial/boundary value problems simulating the matrix gas release. We show that macrotransport and macrokinetics effects of kerogen heterogeneity are nontrivial and affect cumulative gas recovery. The work is important and timely for development of newgeneration shale-gas reservoir-flow simulators, and it can be used in the laboratory for organic-rich gas-shale characterization.

Channel-width dependent pressure-driven flow characteristics of shale gas in nanopores

“…At this regime, the complex transport behavior is identified as transition flow. 20,21 When Knudsen number further increases (Kn > 10), it changes to free molecular flow due to the enhanced molecule-wall interaction. Clearly, the flow mechanisms of shale gas become more complicated with the decrease of pore size.…”

Оn a hydro-geomechanical modeling of shale formations

“…Дальнейшее увеличение числа Кнудсена 1 Kn > приводит уже к нарушению условия применимости механики сплош-ной среды, и течение становится свободномолекуляр-ным. В дополнение к описанному эффекту: в сланце-вых месторождениях с ультрамалыми размерами пор необходимо учитывать поверхностную диффузию [Akkutlu, Fathi, 2012], описывающую усредненное дви-жение под действием градиента концентрации адсор-бированных частиц, ставших подвижными в результа-те термической активации. Как показано в [Wu et al, 2015], в порах размера ~10 нм и меньше поверхностная диффузия превалирует над вязким и свободномолеку-лярным механизмами переноса газовой фазы.…”

A 3D coupled model of organic matter and inorganic matrix for calculating the permeability of shale

“…have noticed the big differences between kerogen and inorganic matrix in shale and treat them separately [10][11][12][13][14][15][16][17].…”

“…Later, they [11] proposed a dual-porosity model to separate kerogen from inorganic matrix and pointed out that gas transport is dominated by Darcy flow in inorganic matrix while by non-Darcy flow in kerogen. They concluded that the permeability of shale is primarily relevant to the relatively large pore and fractures in inorganic matrix, but the molecular behaviors (diffusion transport and nonlinear adsorption) relevant to the pores in kerogen.…”