P. K. Kang

Massachusetts Institute of Technology, Cambridge, Massachusetts, United States

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Publications (5)10.26 Total impact

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    ABSTRACT: Anomalous transport, understood as the nonlinear scaling with time of the mean square displacement of transported particles, is a pervasive phenomenon during transport through porous and fractured geologic media. A common signature of anomalous transport in the field is the late-time power law tailing in breakthrough curves (BTCs). Several conceptual models, including multirate mass transfer, continuous time random walk and stream tube models, have been proposed to capture this effective macroscopic behavior. In general, however, different conceptual models often produce equally good fits to a single BTC, raising questions about the predictability power of these effective models. Here we address the uniqueness of the tracer test interpretation by analyzing BTCs from various flow configurations, including dipole, convergent and push-pull tests. We conducted field tracer tests in a saturated fractured granite formation close to Ploemeur, France. Two boreholes, B1 (83 m deep) and B2 (100 m deep), which are 6 m apart, were used. A double-packer system was designed and installed in B1 at 50 m depth to inject tracer into a single fracture. We measured BTCs under different flow configurations to demonstrate that the observed tailing is configuration-dependent. Specifically, the tailing disappears in a push-pull test (Figure 1). This result indicates that for this fractured granite, the BTC tailing is controlled by heterogeneous advection and not matrix diffusion. To explain the change in tailing behavior for different flow configurations, we developed a lattice network model with heterogeneous conductivity distribution. The model assigns random conductivities to the fractures and solves the Darcy equation for an incompressible fluid, enforcing mass conservation at fracture intersections. We use this model to investigate whether BTC tailing can be explained by the spatial distribution of preferential flow paths and stagnation zones, which are in turn controlled by the conductivity variance and correlation length.
    AGU Fall Meeting Abstracts. 12/2011;
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    ABSTRACT: Flow through lattice networks with quenched disorder exhibits a strong correlation in the velocity field, even if the link transmissivities are uncorrelated. This feature, which is a consequence of the divergence-free constraint, induces anomalous transport of passive particles carried by the flow. We propose a Lagrangian statistical model that takes the form of a continuous time random walk with correlated velocities derived from a genuinely multidimensional Markov process in space. The model captures the anomalous (non-Fickian) longitudinal and transverse spreading, and the tail of the mean first-passage time observed in the Monte Carlo simulations of particle transport. We show that reproducing these fundamental aspects of transport in disordered systems requires honoring the correlation in the Lagrangian velocity.
    Physical Review Letters 10/2011; 107(18):180602. · 7.94 Impact Factor
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    Peter K Kang, Marco Dentz, Ruben Juanes
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    ABSTRACT: We study stochastic transport through a lattice network with quenched disorder and evaluate the limits of predictability of the transport behavior across realizations of spatial heterogeneity. Within a Lagrangian framework, we perform coarse graining, noise averaging, and ensemble averaging, to obtain an effective transport model for the average particle density and its fluctuations between realizations. We show that the average particle density is described exactly by a continuous time random walk (CTRW), and the particle density variance is quantified by a novel two-particle CTRW.
    Physical Review E 03/2011; 83(3 Pt 1):030101. · 2.31 Impact Factor
  • P. K. Kang, M. Dentz, R. Juanes
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    ABSTRACT: We study stochastic transport through a lattice fracture network with quenched disorder, and evaluate the limits of predictability of the transport behavior across realizations of spatial heterogeneity. As shown in the figure, We consider a two-dimensional regular fracture network model characterized by a constant fracture length, fracture aperture and fracture angle. We assign independent and identically distributed random particle velocities to each link. This implies a random uncorrelated particle transport velocity field. Different values of particle velocity are assumed to be the result of microscale processes, such as different conductance or adsorption rate. Within a Lagrangian framework, we perform coarse graining, noise averaging, and ensemble averaging, to obtain an effective transport model for the average particle density and its fluctuations between realizations. We show that the average particle density is described exactly by a continuous time random walk (CTRW), and the particle density variance is quantified by a novel two-particle CTRW. An important question regarding predictability of transport is how the variance --- especially, the variance where the particle density is maximum --- evolves in time. Simulations using the two-particle CTRW can answer to this question. We generalize our model for the correlated velocity field. This second model assigns random transmissivities to the fractures and solves the Darcy equation for an incompressible fluid, enforcing mass conservation at fracture intersections. The latter yields a correlated random flow through the fracture system. To incorporate the impact of heterogeneity and the velocity correlation on effective transport, we study Lagrangian velocity transitions in space and time. We demonstrate that Lagrangian velocities are Markov process in space but not in time. Using the property of spatial Markov process, we derive a CTRW in phase space characterized by a correlated velocity increment. We introduce the concept of 4D transition matrix which has information of both directionality and velocity transitions to capture full 2D particle density distribution. We obtain good representations for both transverse and longitudinal particle density. (a) Schematic of the lattice fracture network considered here, with two sets of links with orientation {-alpha, +alpha} with respect to the x-axis, and lattice spacing l = 1. (b) Representation of transport through the network, from particles released at the origin at t = 0. Shown is the particle density (represented by circle size) at t = 30 for a single realization with beta = 1.5.
    AGU Fall Meeting Abstracts. 12/2010;
  • P. K. Kang, M. Dentz, R. Juanes
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    ABSTRACT: We study transport in a random fracture network using a stochastic modeling approach. We consider a two-dimensional regular fracture network model characterized by a constant fracture length and fracture angle. The transport velocity in the fractures is a random variable. We consider two models. The first one is characterized by a constant fracture aperture and thus constant flow velocity and a retardation factor that is assigned randomly for each fracture. The latter implies a random uncorrelated particle velocity. In each realization, the spatial distribution of retardation values is fixed. The second model assigns random transmissivities to the fractures and solves the Darcy equation for an incompressible fluid, enforcing mass conservation at fracture intersections. The latter yields a correlated random flow through the fracture system. Within a Lagrangian transport framework, we derive effective equations for particle transport by stochastic averaging and compare the obtained mean behavior with direct numerical simulations of particle transport in single medium realizations and the corresponding ensemble average. We determine analytically and numerically the concentration variances in both fracture network models and thus probe the self-averaging behavior of concentration. The first model (uncorrelated transport velocities) describes effectively an uncoupled continuous time random walk, which is obtained by coarse graining and ensemble averaging of the local scale Langevin equations. The second model (correlated flow velocity) describes a continuous time random walk characterized by a transition matrix for the (correlated) random time increment.
    AGU Fall Meeting Abstracts. 12/2009;