Complex Plane Representation of Gas Diffusivity in Fractured Media

Transport of solutes in fractured media, based on a channel network model : B. Gylling, L. Moreno & I. Neretnieks, in: Groundwater quality: remediation and protection. proc. conference, Prague, 1995, ed K. Kovar & J. Krasny, (IAHS; Publication, 225), 1995, pp 107–113

A finite-element reactive transport model is developed and applied to study the transport behaviour of nitrate under the effect of denitrification in saturated fractured media. The reduction of nitrate is considered to be undertaken by a heterotrophic population of bacteria present on the fracture walls and in the pore space of the porous matrix. The bacterial metabolic activity is controlled by the availability of an electron donor (organic matter) and electron acceptors (nitrate and oxygen). Model equations are developed assuming 1D advective–dispersive transport in a set of parallel fractures with 2D diffusive transport in the adjacent porous matrix. The bacterial reaction in these equations is represented by dual Monod kinetic terms and the bacterial growth is represented by a single linear kinetic equation. The equations are discretized by the finite-element Galerkin method and the resultant set of non-linear algebraic equations is solved by an iterative scheme. The model is used to explore the effect of denitrification on fracture and porous matrix nitrate concentration profiles for different values of fracture aperture size, advective velocity, porous matrix width, porosity, and dispersion and diffusion coefficients. The effect of the presence of oxygen in limiting rates of bacterial nitrate reduction is also assessed. Overall, it is concluded that in fractured media with good porous matrix diffusion properties and favourable properties for bacterial growth, denitrification in the porous matrix can be more significant than in the fracture set in the reduction of nitrate mass.

Migration of colloids in discretely fractured porous media: effect of colloidal matrix diffusion

CO2 sequestration into geologic formations such as oil reservoirs, coal beds and aquifers is a possible way to reduce the emissions of this anthropogenic gas into the atmosphere. Among these, sequestration into oil reservoirs while enhancing oil recovery is one of the most feasible ways as the additional oil recovery would offset the cost of CO2 sequestration operation. We postulate that the matrix, the main source of oil, could be a good CO2 storage medium. Hence, we focus on the matrix-fracture interaction during CO2 injection into naturally fracture oil reservoirs (the Weyburn and Midale fields are good examples for this case) in this paper. Proper design of this process is essential to maximize both the amount of CO2 sequestered and oil recovered. In this cooptimization process, miscibility, oil viscosity, matrix properties (permeability, porosity, pore characteristics, wettability, etc.), fracture properties (permeability, orientation, connectivity), injection rate, gravity, and the physical state of CO2 play a critical role. Clear understanding of the contributions of these properties on the dynamics of matrixfracture interaction is essential in designing EOR and CO2 sequestration application. In this paper, the dynamics of CO2 injection was studied experimentally. 2-D glass-bead models with a fracture in the middle were prepared and pentane was used as solvent to displace the kerosene or mineral oil to mimic miscible CO2 displacement. The focus was on the displacement patterns and solvent breakthrough controlled by matrix fracture interaction and pore scale behaviour of solvent-oil interaction for different matrix (wettability), fracture and injection conditions (rate, vertical vs. horizontal injection) as well as oil viscosity. Besides the visual investigation, the produced fluid was analyzed to calculate the solvent cut and oil recovery. It is believed that the visual understanding of the process will provide substantial information for further modelling studies. Introduction Miscible Displacement Mechanisms controlling the miscible displacement and factors effective on the efficiency have been focus of many studies over the last four decades. Huang and Tracht (1) studied oil recovery mechanisms during CO2 injection and reported that the dominant controlling mechanisms are CO2 swelling and the CO2 extraction of oil. Bahralolom and Orr(2) supported that through their micro model visualization study. They also suggested that the extraction is more effective than solubility. In general, the most common mechanisms controlling the oil recovery by CO2 injection are (1) oil displacement by the generation of miscibility, (2) oil swelling and (3) reduction in oil viscosity(3). Presence of water can decrease the efficiency of miscible CO2 displacements in water wet systems as the higher saturation of wetting phase decreases the flow fraction of nonwetting phase and consequently decreases the recovery of oil in water wet systems(4). Interaction of phase behaviour with heterogeneities leads to residual oil saturations due to preferential flow paths(5). In case of naturally fractured reservoirs, other parameters such as matrix and fracture properties critically influence the efficiency of displacement. Thompson and Mungan's(6) study eveals the effect of displacement velocity on recovery efficiency. Later, Firoozabadi and Markeset(7) showed that matrix-fracture configurations and fracture ap

Gas diffusion in an automotive catalyst in an unsteady state

The tight oil formation develops with microfractures and matrix pores, it is important to study the influence of matrix physical properties on flow characteristics. At first, the representative fracture and matrix samples are selected respectively in the dual media, the fracture and matrix digital rocks are constructed with micro-CT scanning at different resolutions, and the corresponding fracture and matrix pore networks are extracted, respectively. Then, the modified integration method is proposed to build the dual network model containing both fracture and matrix pore-throat elements, while the geometric-topological structure equivalent matrix pores are generated to fill in the skeleton domain of fracture network, the constructed dual network could describe the geometric-topological structure characteristics of fracture and matrix pore-throat simultaneously. At last, by adjusting the matrix pore density and the matrix filling domain factor, a series of dual network models are obtained to analyze the influence of matrix physical properties on flow characteristics in dual-media. It can be seen that the matrix system contributes more to the porosity of the dual media and less to the permeability. With the decrease in matrix pore density, the porosity/permeability contributions of matrix system to dual media keep decreasing, but the decrease is not significant, the oil–water co-flow zone decreases and the irreducible water saturation increases, and the saturation interval dominated by the fluid flow in the fracture keeps increasing. With the decrease in matrix filling domain factor, the porosity/permeability contributions of matrix system to dual media decreases, the oil–water co-flow zone increases and the irreducible water saturation decreases, and the saturation interval dominated by the fluid flow in the fracture keeps increasing. The results can be used to explain the dual-media flow pattern under different matrix types and different fracture control volumes during tight oil production.

Shale gas reservoirs exist micropores, nanopores and natural fractures. The mode of gas occurrence and the transports mechanisms vary with the change of type pores. In this paper, a new shale gas apparent permeability model coupling the gas transport mechanisms in matrix pores and natural fractures is presented on the basis of the quantitative characterization of the natural fractures. The model is derived based on the permeability tandem-parallel model and considers the gas slippage effect, diffusion effect in nanopores and the flow characteristics in natural fractures. Sichuan Basin Niutitang group shale sample with natural fractures are used to verify the theoretical model. The results show that the analytical solution of the apparent permeability model not only can match the measured value in lab, but also accurately describes the flow features of interaction in matrix pores and natural fractures in the core internal. In short, the natural fractures quantitative characterization of shale gas reservoirs and the apparent permeability model considering the flow characteristics in the micropores, nanopores and natural fractures not only provides a new approach to the modeling of complex fractures network, but also further promotes the shale gas reservoirs discrete fracture network model numerical simulation for the industrial application.

Monolithic carbon-free gas diffusion electrodes for secondary metal-air batteries

Context. Current theories, models of cometary nuclei and of ice formation in the protoplanetary disk, and laboratory studies suggest that cometary materials could be formed of pure crystalline water ice, amorphous water ice, clathrate hydrate, or a mixture of these structures of water ice. However, current models of cometary nuclei consider only two forms of ice during the thermodynamic evolution of comets: amorphous and crystalline water ices. Aims. In this work, we have developed a model of cometary nucleus that takes into account all water ice structures and phase changes in order to predict the outgassing profile of volatile molecules that could be measured by the Rosetta mission and can be used to constrain the structural type of ice existing in the interior of the Comet 67P/Churyumov-Gerasimenko, the target comet of the Rosetta mission, and, hopefully, its initial composition.Methods. We added the physic of formation/dissociation of clathrate hydrates in addition to others physical processes that are taken into account in models without clathrate hydrates. All thermal changes, as well as the release and trapping of gas with water phase changes are taken into account.Results. This model describes heat transmission, latent heat exchanges, all water ices structures and transitions (amorphous-to-pure crystalline, amorphous-to-clathrate hydrates and pure crystalline-to-clathrate hydrates and vise versa), sublimation/recondensation of volatile molecules in the nucleus, gas diffusion, gas released and trapped by crystallization and clathrate formation/dissociation processes, as well as gas and dust release and mantle formation at the surface. Applying this model to the comet 67P/Churyumov-Gerasimenko, results show different outgassing profiles of volatiles molecules from the nucleus depending on the water ice structure, the distribution of volatile molecules between the “trapped” and “condensed” states in the nucleus and the thermal inertia of its porous matrix. Conclusions. Given these results, we pretend that this model is able to constrain the water ice structure and chemical composition in comets from outgassing profiles of volatile molecules, and especially those of the target comet of the Rosetta mission.

Displacement-imbibition coupling mechanisms between matrix and complex fracture during injecting-shut in-production process using pore-scale simulation and NMR experiment

Diffusion migration behavior of gas in unsaturated fractured soils: Fractal analytical study

We use an integrated approach consisting of experiments and complementary pore-scale network modeling to investigate the occurrence of sparsely connected pore spaces in rock matrices at Yucca Mountain, Nevada, and their implications for matrix diffusion. Imbibition results indicate that pore spaces in devitrified tuff are not well-connected, and that this lack of connectivity is further compounded by episodic flow in fractured devitrified tuff with low matrix permeability. A rigorous methodology for investigating chemical transport in fractured rock under episodic conditions, employing a suite of both sorbing and non-sorbing tracers (including radionuclides U-235, Np-237, and Pu-242), has been developed and implemented. In addition, gas diffusion and synchrotron microtomography techniques have been under development to examine the scaling issues of diffusion and pore connectivity. Preliminary results from experiments and modeling work are presented in this paper, confirming the need to reexamine our understanding of matrix diffusion and to evaluate the impact on diffusive radionuclide retardation of episodic fracture flow and low pore connectivity.

An extended two-parameter mixed-dimensional model of fractured porous media incorporating entrance flow and boundary-layer transition effects

Mass transport of molecular compounds through porous solids is a decisive step in numerous, important applications like chromatography or heterogeneous catalysis. It is a multi-scale, hierarchical phenomenon: macrodiffusion (>μm) is influenced, in addition to parameters like grain boundaries and particle packing, by meso-scale (>10 nm, <μm) factors like particle size and the connectivity of pores. More importantly, meso-scale diffusion and macro-scale diffusion are first and foremost determined directly by processes on the molecular scale (<10 nm), which depend on numerous factors like pore-size, interactions of the host with the solid surfaces and with the solvent. Due to the high complexity of the latter and the fact that current analytical techniques enable only limited insights into solvent-filled pores with sufficient spatial and temporal resolution, the knowledge about the molecular origins of diffusive processes in porous materials is still restricted. The main focus of the current paper is on the development of continuous wave (CW) electron paramagnetic resonance (EPR) spectroscopy into a tool shedding some new light on molecular diffusion inside mesoporous silica materials differing systematically in pore size and surface functionalities. The advantages of CW-EPR are that its spatial resolution fits ideally to the size of mesopores (2-10 nm), it is fast enough for spotting molecular processes, and any conventional solvent and the porous matrix are EPR silent. Diffusion coefficients have been calculated considering spin exchange occurring from the diffusive collision of radicals, and are compared to complementary analytical techniques like MAS PFG NMR (sensitive for meso-scale) and EPR-imaging (sensitive to macroscale diffusion). Our results show that the choice of surface bound functional groups influences diffusion much stronger than pore-size. There are indications that this is not only due to different guest-surface interactions but also due to an altered mobility within the solvent under confinement.

One of the widely used methods for modeling matrix–fracture fluid exchange in naturally fractured reservoirs is dual porosity approach. In this type of modeling, matrix blocks are regarded as sources/sinks in the fracture network medium. The rate of fluid transfer from matrix blocks into fracture medium may be modeled using shape factor concept (Warren and Root, SPEJ 3:245–255, 1963); or the rate–time solution is directly derived for the specific matrix geometry (de Swaan, SPEJ 16:117–122, 1976). Numerous works have been conducted to study matrix–fracture fluid exchange for slightly compressible fluids (e.g. oil). However, little attention has been taken to systems containing gas (compressible fluid). The objective of this work is to develop explicit rate–time solutions for matrix–fracture fluid transfer in systems containing single phase gas. For this purpose, the governing equation describing flow of gas from matrix block into fracture system is linearized using pseudopressure and pseudotime functions. Then, the governing equation is solved under specific boundary conditions to obtain an implicit relation between rate and time. Since rate calculations using such an implicit relation need iterations, which may be computationally inconvenient, an explicit rate–time relation is developed with the aid of material balance equation and several specific assumptions. Also, expressions are derived for average pseudopressure in matrix block. Furthermore, simplified solutions (originated from the complex general solutions) are introduced applicable in infinite and finite acting flow periods in matrix. Based on the derived solutions, expressions are developed for shape factor. An important observation is that the shape factor for gas systems is the same as that of oil bearing matrix blocks. Subsequently, a multiplier is introduced which relates rate to matrix pressure instead of matrix pseudopressure. Finally, the introduced equations are verified using a numerical simulator.