-
[show abstract]
[hide abstract]
ABSTRACT: We present predictions of transport through micro-CT images of porous media that include the analysis of correlation structure, velocity, and the dynamics of the evolving plume. We simulate solute transport through millimeter-sized three-dimensional images of a beadpack, a sandstone, and a carbonate, representing porous media with an increasing degree of pore-scale complexity. The Navier-Stokes equations are solved to compute the flow field and a streamline simulation approach is used to move particles by advection, while the random walk method is employed to represent diffusion. We show how the computed propagators (concentration as a function of displacement) for the beadpack, sandstone, and carbonate depend on the width of the velocity distribution. A narrow velocity distribution in the beadpack leads to the least anomalous behavior, where the propagators rapidly become Gaussian in shape; the wider velocity distribution in the sandstone gives rise to a small immobile concentration peak, and a large secondary mobile peak moving at approximately the average flow speed; in the carbonate with the widest velocity distribution, the stagnant concentration peak is persistent, with a slower emergence of a smaller secondary mobile peak, characteristic of highly anomalous behavior. This defines different types of transport in the three media and quantifies the effect of pore structure on transport. The propagators obtained by the model are in excellent agreement with those measured on similar cores in nuclear magnetic resonance experiments by Scheven, Verganelakis, Harris, Johns, and Gladden, Phys. Fluids 17, 117107 (2005).
Physical Review E 01/2013; 87(1-1):013011. · 2.26 Impact Factor
-
[show abstract]
[hide abstract]
ABSTRACT: We simulate transport of a solute through three-dimensional images of different rock samples, with resolutions of a few microns, representing geological media of increasing pore-scale complexity: a sandpack, a Berea sandstone, and a Portland limestone. We predict the propagators (concentration as a function of distance) measured on similar cores in nuclear magnetic resonance experiments and the dispersion coefficient as a function of Péclet number and time. The behavior is explained using continuous time random walks with a truncated power-law distribution of travel times: transport is qualitatively different for the complex limestone compared to the sandstone or sandpack, with long tailing, an almost immobile peak concentration, and a very slow approach to asymptotic dispersion.
Physical Review Letters 11/2011; 107(20):204502. · 7.37 Impact Factor
-
[show abstract]
[hide abstract]
ABSTRACT: Tracer tailing in breakthrough curves in porous media with two distinct porosities is analyzed in terms of the dynamic responses of experimental fixed bed columns filled either with solid or porous beads. The flow is fast in the column interstitial space between beads (for both solid and porous beads) but slow within the porous beads that act as controlled 'traps' constituting an immobile zone. The transport is quantified using a Continuous Time Random Walk (CTRW) framework, which accounts for domains with controlled structural and flow heterogeneity associated with two distinct spatial and time spectra. We first demonstrate that breakthrough curves for a column containing solid glass beads exhibit non-Fickian transport, quantifiable both in fitting and validation mode by a CTRW based on a power law transition time distribution. We then examine breakthrough curves in the porous bead case, obtaining fits with a two-scale CTRW model that accounts explicitly for the two time spectra. Because the porous beads are uniform, tracer trapping within them is described by a simple first-order approximation trap model, with relatively weak capture and relatively faster release rates. The extent of tailing apparent in the porous bead breakthrough curves, due to the traps, can be quantitatively distinguished from the contribution to tailing due to mobile zone non-Fickian transport. A parameter study of the two-scale CTRW adds further insight into the dynamics of the process, showing the interaction between the advective non-Fickian transport and the mass exchange to immobile regions.
Journal of contaminant hydrology 03/2011; 120-121:213-21. · 2.01 Impact Factor
-
[show abstract]
[hide abstract]
ABSTRACT: Transverse and longitudinal dispersion in gravity stable, favourable viscosity ratio flows are investigated and compared with earlier data obtained for miscible fluids and for tracer flow. Data from laboratory measurements of longitudinal dispersion in low viscosity ratio (8.63×10(-)(4)) and high density contrast (471 kg m(-3)) displacements are compared with literature data for more modest viscosity ratios and density differences and with earlier theoretical analysis. The longitudinal dispersivity was reduced by a factor of 2 for flows influenced by gravity. This reduction was relatively insensitive to the magnitude of the density contrast and the flow rate, for Peclet numbers less than 100 and found to be consistent with earlier theoretical predictions. Additional transverse dispersion data was obtained for fluids with a density contrast of 225 kg m(-3) and a matched viscosity ratio over a range of Peclet numbers (1<Pe<1000). A similar reduction in transverse dispersivity in gravity stable flow, independent of Peclet number, was observed and found to be consistent with observations in the literature for more modest density contrasts.
Journal of contaminant hydrology 03/2011; 120-121:170-83. · 2.01 Impact Factor
-
[show abstract]
[hide abstract]
ABSTRACT: Geological media exhibit heterogeneities in their hydraulic and chemical properties, which can lead to enhanced spreading and mixing of the transported species and induce an effective reaction behavior that is different from the one for a homogeneous medium. Chemical heterogeneities such as spatially varying adsorption properties and specific reactive surface areas can act directly on the chemical reaction dynamics and lead to different effective reaction laws. Physical heterogeneities affect mixing-limited chemical reactions in an indirect way by their impact on spreading and mixing of dissolved species. To understand and model large-scale reactive transport the interactions of these coupled processes need to be understood and quantified. This paper provides a brief review on approaches of non-reactive and reactive transport modeling in geological media.
Journal of contaminant hydrology 03/2011; 120-121:1-17. · 2.01 Impact Factor
-
[show abstract]
[hide abstract]
ABSTRACT: 1] A physically based description is provided for the transverse dispersion coefficient in porous media as a function of Péclet number, Pe. We represent the porous medium as lattices of bonds with square cross section whose radius distribution is the same as computed for Berea sandstone and describe flow (Stokes equation) and diffusion (random walk method) at the pore scale ($mm) to compute the transverse dispersion coefficient at a larger scale ($cm to $m). We show that the transverse dispersion coefficient D T $ Pe for all Pe) 1. A comprehensive comparative study of transverse dispersion with experiment indicates that the model can successfully predict the trends for the asymptotic macroscopic dispersion coefficient over a broad range of Péclet numbers, 0 < Pe < 10 5 . We discuss the relation between transverse and longitudinal dispersion coefficient and show that unless one studies solute transport in the advection dominated regime, it is not appropriate to take D T to be 1 order of magnitude less than D L .
Water Resour. Res. 01/2007; 43:12-11.
-
[show abstract]
[hide abstract]
ABSTRACT: 1] We study macroscopic (centimeter scale) dispersion using pore-scale network simulation. A Lagrangian-based transport model incorporating flow and diffusion is applied in a diamond lattice of throats with square cross section whose radius distribution is the same as computed for Berea sandstone. We use physically consistent rules using a combination of stream-tube routing and ideal mixing to transport particles across pore junctions. The influence of both heterogeneity and high Peclet numbers results in asymptotic behavior only being seen after movement through many throats. A comprehensive comparative study of longitudinal dispersion with experiments in consolidated and unconsolidated media indicates that the model can quantitatively predict the asymptotic macroscopic dispersion coefficient over a broad range of Peclet numbers, 0 < Pe < 10 5 . In the low Peclet number region, molecular diffusion is more restricted for consolidated media as compared with unconsolidated media. The first effects of advection on dispersion are observed at Pe $ 0.1. In the advection-dominated regions the longitudinal dispersion coefficient follows a weak nonlinear dependence on Peclet number (D L $ Pe 1.19) followed by a linear dependence D L $ Pe for Pe > 400.
Water Resour. Res. 01/2004; 40.
-
[show abstract]
[hide abstract]
ABSTRACT: Understanding the dynamics of pore-scale multicomponent gas and oil mass transfer across water ÿlms during hydrocarbon gas injection in petroleum reservoirs is important in the design of tertiary oil recovery schemes at the ÿeld scale. The water ÿlms prevent oil and gas coming into direct contact and, for miscible gas injection, delay the onset of miscibility. We use a pore-scale model to describe the diiusion-controlled mass transfer through the water ÿlms. The following diierent processes are found: (i) rapid oil swelling which results in short times needed to rupture the water ÿlms shielding the oil, (ii) slow oil swelling resulting in very long water ÿlm rupture times and (iii) both oil swelling and oil shrinking. The rate of oil recovery and the way it is recovered (either by rupturing the water ÿlm or being vaporized into the displacing gas) is critically dependent upon the oil and gas compositions, the oil droplet size and the water ÿlm thickness. We show cases at the pore scale where the time for gas and oil to be brought into direct contact and reach equilibrium in the presence of water ÿlms during miscible gas displacement is so long that water-blocking will adversely aaect oil recovery at the ÿeld scale.
Chemical Engineering Science 01/2003; 58:2377-2388. · 2.43 Impact Factor
-
[show abstract]
[hide abstract]
ABSTRACT: 1] We provide a physically based explanation for the complex macroscopic behavior of dispersion in porous media as a function of Peclet number, Pe, using a pore-scale network model that accurately predicts the experimental dependence of the longitudinal dispersion coefficient, D L , on Pe. The asymptotic dispersion coefficient is only reached after the solute has traveled through a large number of pores at high Pe. This implies that preasymptotic dispersion is the norm, even in experiments in statistically homogeneous media. Interpreting transport as a continuous time random walk, we show that (1) the power law dispersion regime is controlled by the variation in average velocity between throats (the distribution of local Pe), giving D L $ Pe d with d = 3 À b % 1.2, where b is an exponent characterizing the distribution of transit times between pores, (2) the crossover to a linear regime D L $ Pe for Pe > Pe crit % 400 is due to a transition from a diffusion-controlled late time cutoff to transport governed by advective movement, and (3) the transverse dispersion coefficient D T $ Pe for all Pe) 1. Citation: Bijeljic, B., and M. J. Blunt (2006), Pore-scale modeling and continuous time random walk analysis of dispersion in porous media, Water Resour. Res., 42, W01202, doi:10.1029/2005WR004578.
-
[show abstract]
[hide abstract]
ABSTRACT: We demonstrate a pore-to-reservoir simulation methodology that does not pre-suppose the functional form of the upscaled transport equations and which automatically accounts for uncertainty in the reservoir description. Single-phase transport is modeled as a continuous time random walk. Particles make a series of hops between nodes with a probability ψ(t)dt that a particle will first arrive at a node from a nearest neighbor in a time t to t+dt. We describe transport at four scales: pore, core, grid-block, and field. At each scale the system is represented as a lattice of nodes with an appropriate transition time probability ψ derived from a simulation at the next smaller scale.At the micron scale, we fit a truncated power law ψ(t) for the distribution of transition times between pores. We use the transport algorithm of Rhodes and Blunt [Rhodes ME, Blunt MJ. An exact particle tracking algorithm for advective-dispersive transport in networks with complete mixing at nodes. Water Resour Res 2006;42:W04501. doi:10.1029/2005WR004504] on a network model representation of Berea sandstone whose results are in good agreement with experiment. This ψp is then used to calculate transport at the core scale and a ψc is found that accounts for cm-scale transitions. Similarly we use ψc to derive a meter-scale ψgb from simulations of grid-block level transport. At the field scale, we use the upscaled ψgb from simulations at the meter-scale.We demonstrate the methodology by considering transport in a channeled sandstone reservoir, from a pore-scale representation of the microscopic structure to a million-cell field-scale geological model. Effectively we simulate transport in a model containing of order 1012 cells while accounting for uncertainty in the reservoir description. Heterogeneity at all scales impacts transport and tends to retard the advance of the plume with particles becoming trapped in slow-moving regions, increasing breakthrough times by up to an order of magnitude compared to those predicted using a traditional advection dispersion model.
Advances in Water Resources.
-
[show abstract]
[hide abstract]
ABSTRACT: We measure the trapped non-wetting phase saturation as a function of the initial saturation in sand packs. The application of the work is for CO2 storage in aquifers where capillary trapping is a rapid and effective mechanism to render injected CO2 immobile. The CO2 is injected into the formation followed by chase brine injection, or natural groundwater flow, which displaces and traps CO2 on the pore scale as a residual immobile phase. Current models to predict the amount of trapping are based on experiments in consolidated media, while CO2 may be stored in relatively shallow, poorly consolidated systems. We use analogue fluids at ambient conditions. The trapped saturation initially rises linearly with initial saturation to a value of approximately 0.13 for oil/water systems and 0.14 for gas/water systems. There then follows a region where the residual saturation is constant with further increases in initial saturation. This behaviour is not predicted by the traditional literature trapping models, but is physically consistent with unconsolidated media where most of the larger pores can easily be invaded at relatively low saturation and there is, overall, relatively little trapping. A good match to our experimental data was achieved with the trapping model proposed by Aissaoui.
International Journal of Greenhouse Gas Control.
-
[show abstract]
[hide abstract]
ABSTRACT: This is a fundamental study of trapping of non-wetting fluids in porous media. When injecting CO~2~ into an aquifer for carbon storage, the non-wetting phase (CO~2~) is trapped due to capillary forces. This process is investigated in the laboratory for analogue fluids.
We then design an injection strategy to maximise CO~2~ storage capacity and efficiency on the field scale - incorporating experimental and pore scale modelling results. A streamline based simulator is modified for this purpose.
Nature Precedings.
