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Bridging Between Macroscopic Behavior of Shale Gas Reservoirs and Confined Fluids in Nanopores
- Publisher: European Association of Geoscientists & Engineers
- Source: Conference Proceedings, ECMOR XIV - 14th European Conference on the Mathematics of Oil Recovery, Sep 2014, Volume 2014, p.1 - 25
Abstract
A new triple porosity model for reactive transport of gas in shale gas reservoirs is developed within the framework of a reiterated homogenization procedure. Considering the shale composed of three different porosity levels: nanopores within the kerogen organic matter, micropores between organic aggregates and impermeable inorganic matter (clay, calcite, quartz), and induced fractures along with four separate length scales (nano, micro, meso and macro) associated with the different pore-sizes, the up-scaling method based on asymptotic expansions is formally applied starting from the transport equations at the nano-pore level. By including adsorption of the gas at the surface of the kerogen particles quantified by the Damkholer number the homogenization with the gas diffusion in the micropores produces a reaction-diffusion model for gas movement in kerogen aggregates. Further, by postulating Fickian diffusion of the gas in the micro-pores together with a homogeneous Neumann condition at the interface with the subdomain occupied by the inorganic matter, an effective reaction-diffusion equation is obtained in the matrix-blocks at the mesoscale. Moreover, by postulating continuity of fugacity of dissolved and free gas at the block/fracture interface, an additional homogenization produces an accurate triple porosity model. Among the features of the macroscopic model we highlight the appearance of a distributed source/sink matrix/fracture transfer function. The computation of this source term can be accomplished through a down-scaling procedure along with the solvability of the reaction-diffusion equation at the microstructural level of the matrix blocks. Further, constitutive laws are developed for the retardation coefficient which in the context of the multiscale model proposed herein appear strongly correlated with the behavior of the confined gas in the nano-pores.
In order to model the confined gas we adopted the Density Functional Theory based on the Thermodynamics of Inhomogeneous systems which is capable of constructing rigorous adsorption isotherms for computation of the retardation parameter. The nonlinear diffusion equations at different scales are discretized by the finite element method and preliminary numerical simulations illustrate different scenarios of gas production.