Bulletin of the American Physical Society
69th Annual Meeting of the APS Division of Fluid Dynamics
Volume 61, Number 20
Sunday–Tuesday, November 20–22, 2016; Portland, Oregon
Session L40: Porous Media Flows: Mixing, Turbulence, and Petroleum Applications |
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Chair: Joachim Moortgat, Ohio State Univerisity Room: Portland Ballroom 253-258-254-257 |
Monday, November 21, 2016 4:30PM - 4:43PM |
L40.00001: Thermodynamically Consistent Fluid Mixing in Porous Media Induced by Viscous Fingering and Channeling of Multiphase Flow Mohammad Amin Amooie, Mohammad Reza Soltanian, Joachim Moortgat Fluid mixing and its interplay with viscous fingering as well as flow channeling through heterogeneous media have been traditionally studied for fully (im)miscible conditions in which a (two-) single-phase system is represented by two components, e.g. a solvent and a solute, with (zero) infinite mutual solubility. However, many subsurface problems, e.g. gas injection/migration in hydrocarbon reservoirs, involve multiple species transfer. Multicomponent fluid properties behave non-linearly, through an equation of state, as a function of temperature, pressure, and compositions. Depending on the minimum miscibility pressure, a two-phase region with finite, non-zero mutual solubility may develop, e.g. in a partially-miscible system. Here we study mixing of fluids with partial mutual solubility, induced by viscous flow fingering, channeling, and species transport within and between phases. We uncover non-linear mixing dynamics of a finite-size slug of a less viscous fluid attenuated by a carrier fluid during rectilinear displacement. We perform accurate numerical simulations that are thermodynamically-consistent to capture fingering patterns and complex phase behavior of mixtures. The results provide a broad perspective into how multiphase flow can alter fluid mixing in porous media. [Preview Abstract] |
Monday, November 21, 2016 4:43PM - 4:56PM |
L40.00002: Upscaling of Mixing Processes using a Spatial Markov Model Diogo Bolster, Nicole Sund, Giovanni Porta The Spatial Markov model is a model that has been used to successfully upscale transport behavior across a broad range of spatially heterogeneous flows, with most examples to date coming from applications relating to porous media. In its most common current forms the model predicts spatially averaged concentrations. However, many processes, including for example chemical reactions, require an adequate understanding of mixing below the averaging scale, which means that knowledge of subscale fluctuations, or closures that adequately describe them, are needed. Here we present a framework, consistent with the Spatial Markov modeling framework, that enables us to do this. We apply and present it as applied to a simple example, a spatially periodic flow at low Reynolds number. We demonstrate that our upscaled model can successfully predict mixing by comparing results from direct numerical simulations to predictions with our upscaled model. To this end we focus on predicting two common metrics of mixing: the dilution index and the scalar dissipation. For both metrics our upscaled predictions very closely match observed values from the DNS. [Preview Abstract] |
Monday, November 21, 2016 4:56PM - 5:09PM |
L40.00003: Multiscale Lagrangian Statistics of Curvature Angle in Pore-Scale Turbulence Bryan He, Benjamin Kadoch, Sourabh Apte, Marie Farge, Kai Schneider Porescale turbulent flow physics are investigated using Direct Numeric Simulation (DNS) of flow through a periodic face centered cubic (FCC) unit cell at Reynolds numbers of 300, 500 and 1000. The simulations are performed using a fictitious domain approach [Apte et al, J. Comp. Physics 2009], which uses non-body conforming Cartesian grids. Lagrangian statistics of scale dependent curvature angle and acceleration are calculated by tracking a large number of fluid particle trajectories. For isotropic turbulence, it has been shown [Bos et al. 2015, PRL] that the mean curvature angle varies linearly with time initially, reaches an inertial range and asymptotes to a value of $\pi/2$ at long times, corresponding to the decorrelation and equipartition of the cosine of the curvature angle. Similar trends are observed at early times for turbulence in porous medium; however, the mean curvature angle asymptotes to a value larger than $\pi/2$, due to the effect of confinement on the fluid particle trajectories that result in preferred directions at large times. A Monte-Carlo based stochastic model to predict the long-time behavior of curvature angles is developed and shown to correctly predicts an angle larger than $\pi/2$ at large times. [Preview Abstract] |
Monday, November 21, 2016 5:09PM - 5:22PM |
L40.00004: ABSTRACT WITHDRAWN |
Monday, November 21, 2016 5:22PM - 5:35PM |
L40.00005: Turbulent flow characteristics over anisotropic porous media. Kazuhiko Suga, Unde Ho, Seitaro Nakamura, Masayuki Kaneda Planar PIV measurements of turbulence over anisotropic porous media are carried out. Three kinds of anisotropic porous media are considered to form a bottom wall of fully developed turbulent channel flows. Their wall normal component of the permeability is larger than the other components by the factor of 1.3-170. The range of the measured Reynolds number is Reb$=$1300-13000. It is found that the streamwise component significantly more affects the turbulent flow characteristics than the other components. It is considered that the streamwise permeability controls the strength of traveling waves over the porous surface which are originated by the Kelvin-Helmholtz instability and drive transverse roll vortices. Considering the present data and our previous data of isotropic porous wall flows, an effective permeability Reynolds number that is a parameter to characterize the turbulence over porous walls is proposed. This effective permeability Reynolds number is a tensorially consistent expression including both streamwise and wall normal components of the permeability. It is shown that the zero-plane displacement, equivalent roughness height and Karman constant variations of mean velocity profiles well correlate with the effective permeability Reynolds number. [Preview Abstract] |
Monday, November 21, 2016 5:35PM - 5:48PM |
L40.00006: Fluid-driven fractures in brittle hydrogels Niall O'Keeffe, Paul Linden Hydraulic fracturing is a process in which fluid is injected deep underground at high pressures that can overcome the strength of the surrounding matrix. This results in an increase of surface area connected to the well bore and thus allows extraction of natural gas previously trapped in a rock formation. We experimentally study the physical mechanisms of these fluid-driven fractures in low permeability reservoirs where the leak-off of fracturing fluid is considered negligible. This is done through the use of small scale experiments on transparent and brittle, heavily cross-linked hydrogels. The propagation of these fractures can be split into two distinct regimes depending on whether the dominant energy dissipation mechanism is viscous flow or material toughness. We will analyse crack growth rates, crack thickness and tip shape in both regimes. Moreover, PIV techniques allow us to explore the flow dynamics within the fracture, which is crucial in predicting transport of proppants designed to prevent localisation of cracks. [Preview Abstract] |
Monday, November 21, 2016 5:48PM - 6:01PM |
L40.00007: Model of fluid flow and internal erosion of a porous fragile medium Arshad Kudrolli, Xavier Clotet We discuss the internal erosion and transport of particles leading to heterogeneity and channelization of a porous granular bed driven by fluid flow by introducing a model experimental system which enables direct visualization of the evolution of porosity from the single particle up to the system scale [1]. Further, we develop a hybrid hydrodynamic-statistical model to understand the main ingredients needed to simulate our observations. A uniqueness of our study is the close coupling of the experiments and simulations with control parameters used in the simulations derived from the experiments. Understanding this system is of fundamental importance to a number of geophysical processes, and in the extraction of hydrocarbons in the subsurface including the deposition of proppants used in hydraulic fracturing. We provide clear evidence for the importance of curvature of the interface between high and low porosity regions in determining the flux rate needed for erosion and the spatial locations where channels grow. [1]: Evolution of Porosity and Channelization of an Erosive Medium Driven by Fluid Flow, Arshad Kudrolli and Xavier Clotet, Phys. Rev. Lett. 117, 028001 (2016). [Preview Abstract] |
Monday, November 21, 2016 6:01PM - 6:14PM |
L40.00008: A model to determine the petroleum pressure in a well using fractional differential equations Beatriz Brito Martinez, Fernando Brambila Paz, Carlos Fuentes Ruiz A noninvasive method was used to determine the pressure of petroleum leaving a well. The mathematical model is based on nonlinear fractional differential equations. This model comes from the fractal dimension of the porous medium. The problem is solved in three stages. In the first stage the fractal dimension of the porous medium is determined. We show that microwaves reflected and transmitted through soil have a fractal dimension which is correlated with the fractal dimension of the porous medium. The fractal signature of microwave scattering correlates with certain physical and mechanical properties of soils (porosity, permeability, conductivity, etc.). In the second stage we use three partial fractional equations as a mathematical model to study the diffusion inside the porous medium. In this model sub-diffusive phenomenon occurs if fractal derivative is between zero and one and supra-diffusive occurs if the derivative is greater than 1 and less than 2. Finally in the third stage the mathematical model is used to determinate the petroleum pressure output in a Mexican oil field, which contains three partial fractional equations with triple porosity and permeability. [Preview Abstract] |
Monday, November 21, 2016 6:14PM - 6:27PM |
L40.00009: An advective volume-balance model for flow in porous media Carlos Malaga, Francisco Mandujano, Julian Becerra Volume-balance models are used by petroleum engineers to simulate multiphase and multicomponent flow phenomena in porous media and the extraction process in oil reservoirs. In these models, mass conservation equations and Darcy's law are supplemented by a balance condition for the pore and fluid volumes. This provides a pressure equation suitable for simulating a compressible flow within a compressible solid matrix. Here we present an alternative interpretation of the volume-balance condition that includes the advective transport within a consolidated porous media. We obtain a modified equation for the time evolution of the pressure field. Preliminary numerical tests of phase separation due to gravity suggest the model reproduces qualitatively the physical phenomena. [Preview Abstract] |
Monday, November 21, 2016 6:27PM - 6:40PM |
L40.00010: Outer boundary effects in a petroleum reservoir Rhodri Nelson, Darren Crowdy, Everett Kropf, Lihua Zuo, Ruud Weijermars A new toolkit for potential theory based on the Schottky-Klein prime function is first introduced. This potential theory toolkit is then applied to study the fluid flow structures in bounded 2D petroleum reservoirs. In the model, reservoirs are assumed to be heterogeneous and isotropic porous medium and can thus be modelled using Darcy’s equation. First, computations of flow contours are carried out on some ‘test’ domains and benchmarked against results from the ECLIPSE reservoir simulator. Following this, a case study of the Quitman oil field in Texas is presented. [Preview Abstract] |
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