H44D-01
Deposition in two phase flow in porous media
The study of dispersion and deposition of an active tracer in multiphase flow through a porous medium is a difficult topic which has not received much attention in the past though it has a lot of practical and fundamental interest. For instance, asphaltene flocculation implies its deposition on the solid walls and this has two effects. The first one is to change the wettability of the walls; if they are initially water wet, they may become oil wet. The second one is to reduce the pore space. In both cases, the flow properties of the porous medium are expected to be influenced. Our purpose was to develop a new tool to analyse these two effects; this new tool had to be constructed by integrating existing codes. First, the basic ingredients which are necessary for the determination of dispersion and deposition at the local scale are presented. The pore space can be generated by means of the method of reconstructed media (1). The instantaneous phase distribution and the velocity fields are computed by an Immiscible Lattice Boltzmann model (2). The solute dispersion is obtained by the Random Walk technique (3); its deposition at the walls is supposed to follow a first order reaction (4). Finally, the rules for the solid and/or wettability changes will be precised. The main results of our calculations can be summarized as follows. The possibilities of the code are demonstrated on a three-dimensional medium; the evolution of the solid space, of the wettability properties and of the phase configurations are illustrated; dramatic results are shown for the evolution of the relative permeabilities and of the capillary pressures. Then, various parameters are studied in a systematic way, such as the porosity, the partition coefficient, the diffusion coefficient, the saturation and the kinetic coefficients. Some concluding remarks end up this study. Ref: (1) Adler P.M., Jacquin C.G., Quibier J.A., 1990, Flow in simulated porous media, Int. J. Multiphase flow, 16, 691- 712. (2) Ginzbourg I., Adler P.M., 1995, Surface tension models with different viscosities, Transport Porous Media, 20 , 37-76. (3) Békri S. and Adler P.M., Dispersion in multiphase flow through porous media, Int. J. Multiphase Flow, 28, 665, 2002. (4) Békri S., Thovert J.-F. and Adler P.M., Dissolution of porous media, Chem. Eng. Sci., 50, 2765-2791, 1995.
H44D-02
A level set based computer simulation of coupled flow and mineral precipitation/dissolution in fracture apertures and porous media
Coupled fluid flow and reactive transport processes involving mineral precipitation and dissolution in fracture apertures and porous media are important to a large variety of scientific and engineering applications, such as acid stimulation of oil reservoirs, in-situ immobilization of contaminants in groundwater etc. We developed a level set based simulation technique to model the coupled reactive flow and structural evolution within pores and fracture apertures. Convection, diffusion and chemical reactions resulting in changes in the pore geometries and fracture apertures are modeled simultaneously by solving coupled momentum, reaction and solute transport equations. The reaction-induced evolution of solid grain surfaces and fracture walls is captured by using a level set interface tracking method. We obtain a more elegant sub-grid representation of the curved interface using a level set approach, compared to the pixel-like representation of the interface used in most simple Lattice Boltzmann simulations. The model was validated against analytical solutions for simplified geometries. Different precipitation/dissolution patterns in porous media and fractures were obtained in our simulations for different combinations of reaction rates and diffusion rates. Quantitative relationships between the hydraulic properties (e.g. permeability and porosity) of the media and their temporal evolutions can also be obtained from simulations.
H44D-03
Lattice Boltzmann Simulation of Fluid Flow and Solute Transport in Porous Media at the Pore Scale and Upscaling to the Continuum Scale
In continuum modeling approaches of multiphase flow and reaction in porous media, spatial heterogeneity at the pore scale is unresolved, which may be important on the observed behavior at the larger scale. Therefore, understanding multiphase flow, transport, and reaction processes at the pore scale and subsequently upscaling to the larger scale will provide valuable insight into the effects of pore scale heterogeneity on the emergent behavior at the field scale. In this study, we investigate such effects by simulating leaching of a non-reactive tracer from a three dimensional (3D) porous structure and then upscaling to the continuum scale. The 3D structure is generated using a random structure generation-growth method, termed the quartet structure generation set (QSGS), which can reproduce porous morphological features that closely resemble the formation process of many real porous media. The generated 3D structure includes multiscale features with dead-end pores connected to the primary pores through diffusion pathways. An incompressible lattice Boltzmann (LB) model is used to simulate fluid flow, and a 3D, 6- speed (D3Q6) LB model is used to simulate solute transport at the pore scale. The leaching process is also simulated using single and dual-continuum models (SCM and DCM), based on the macroscopic parameters derived from the upscaled LB results and directly from the pore structure. Breakthrough curves obtained from the three methods are compared with each other. It is shown that the long tail of the breakthrough curve caused by the dead-end pores is reasonably captured by the LB and DCM, but not by the SCM, which predicts a breakthrough time much too early.
H44D-04
Influence of Chemotaxis on Bacterial Dispersion in Porous Media
Bioremediation of groundwater is limited by the degree to which microorganisms and pollutants are mixed together in the subsurface environment. Good mixing is difficult to achieve because of the structure of geological media and the unavailability of external mixing devices. Chemotaxis, which is the ability of motile bacteria to sense chemical concentration gradients in their local surroundings and swim toward higher concentrations of attractants, could potentially enhance the mixing and expedite the biodegradation process. The chemotactic migration on the pore-scale could eventually result in greater dispersion at the field-scale. In this study, the volume averaging method was used to derive an expression that accounts for chemotactic responses to local chemical gradients in the dispersion coefficient at larger scales. We will present results where the upscaling scheme was applied to problems with well defined hydraulic conditions such as a series of inline cylinders, and well-defined chemical gradients. In general, increasing the attractant gradients resulted in greater bacterial dispersion coefficients. Engineering correlations were developed to relate the enhanced dispersion to dimensionless groups such as the Peclet number and a dimensionless chemotactic driving force defined in this work. It was found that under certain constraints, the effect of chemotaxis was to increase the dispersion coefficient by an additional term that was a linear function of the chemotactic driving force, i.e. E=Dbulk+α v+ β σ, where Dbulk is the bulk diffusion coefficient, v is the fluid velocity, σ is the dimensionless chemotactic driving force we defined, and α and β are appropriate dispersivities. This study will improve our physical understanding of how chemotaxis impacts dispersion and allow us to quantify dispersion in terms of bacterial properties and structure of the geologic media. The engineering correlations that result are critical for improving our assessment and implementation of bioremediation strategies.
H44D-05
Physical Constraints on Microbially Enhanced Oil Recovery
Secondary and tertiary oil recovery from mature or depleted reservoirs usually involves modification of fluid properties (especially the oil-water interfacial tension), or increasing the efficiency of water flooding by selective permeability reduction. The use of microbes for both of these strategies - through production of biosurfactants and extracellular polymeric material, respectively - is the subject of considerable current interest, but as pointed out by Bryant and Lockhart [SPE paper 79719, 2002] is constrained by chemical reaction kinetics. Continuing in the spirit of the engineering analysis presented by these authors, the purpose of this paper is to consider, on the basis of simplified physical models, the constraints that apply to the injection of microbes as a concentrated slurry and their subsequent dispersion through the pores of the formation. This involves solution of the advection-dispersion equation in conjunction with the Newtonian flow distribution between an injection well and a production well, and a more general flow distribution based on a non-Newtonian (power-law) constitutive equation used to describe the rheological properties of concentrated suspensions. By analogy with the better-known example of blood flow through capillaries, such deviations from Newtonian flow behavior are expected to become more significant in flow through media of low permeabilities, where the diameters of the suspended particles are non-negligible in relation to the mean diameters of the flow channels. The nature and extent of these deviations from Newtonian behavior are examined by calculating the pressure drops corresponding to a given flow rate in one dimension at different suspension concentrations, and the nonlinearities resulting from retention or `filtration' of bacteria by the porous medium are investigated by performing a population-balance analysis to determine the evolving profiles of retained bacteria as a function of distance and time. These calculations are intended to provide a `baseline' for interpreting the results produced by simulation software, in which the additional complexities associated with multiphase flow and interactions between introduced and indigenous microbial populations are included.
H44D-06
Drainage and Imbibition Simulations in Realistic Porous Media Based on the Level Set Method
Knowledge of the geometrical distribution of immiscible fluids during displacement in porous media could significantly improve predictions of capillary pressure - saturation curves, interfacial areas and relative permeability. Slow displacement can be modeled as a quasi-static, capillarity-controlled process. At constant pressure and interfacial tension, pore scale fluid-fluid interfaces are modeled as constant mean curvature surfaces, which are not easy to calculate. Further, tracking the topological changes of the interface, such as splitting or merging, is nontrivial specifically due to the irregular pore spaces in natural porous media. We apply the level set method for propagating interfaces in order to robustly handle topological changes and to obtain geometrically correct interfaces. We describe a simple but robust model for simulating both drainage and imbibition in general porous media. Though set up for quasi-static displacements, the model nevertheless captures both reversible and irreversible behavior (Haines jump, pore body imbibition). The pore scale grain boundary conditions are extracted from model porous media and from imaged geometries in real rocks. The method gives quantitative agreement with measurements and with other theories and computational approaches. Our simulations establish the exact position and shape of the interface in porous geometries, from which fluid volumes, contact areas and interface curvatures can be obtained. We show examples of 2D and 3D displacements in individual pores and throats, simulated and imaged porous samples as well as artificially and naturally fractured media. Investigative power of the method is shown on a study of non-wetting phase snap-off in a suite of doubly constricted geometries. We also show preliminary results on the method extension to allow for nonzero fluid-fluid-solid contact angles.
H44D-07
Pore-Network Model Investigation of Stability & Scaling of Immiscible Displacement Fronts with Buoyancy Forces
Understanding the behavior and geometry of multi-phase immiscible displacement fronts is critical in the fields of environmental restoration, geologic hazardous waste storage, and petroleum engineering ( e.g. air sparging, NAPL infiltration, and secondary recovery of petroleum by water flooding). Depending on the flow conditions, the presence of gradients, such as those caused by gravity forces, viscous forces or permeability gradients, can variously lead to either stabilized ( e.g. piston-like) or to unstable ( e.g. gravity or viscous fingering) displacement fronts. Previous studies have found that the resulting displacement fronts may have patterns with percolation, or fractal, characteristics which cannot be adequately described by continuum equations [Chaouche et al., 1994; Glass & Yarrington, 1996; and, Zhang et al., 2000]. Numerical pore-network models which incorporate the appropriate physics provide a framework in which to study these characteristics of flow in porous materials. We present results of numerical simulations on regular two-dimensional lattices which are based on the method of invasion percolation in a gradient (IPG). The pore-network is populated with pore throats and bodies whose radii are drawn from a random statistical distribution. The network is initially water saturated and then invaded by a non-wetting fluid (drainage). Both capillary and buoyancy forces are included to define a filling potential for each pore. The invasion advances in quasi-static steps, by increasing the capillary pressure and invading accessible pores with the lowest filling potential at each step. The wetting phase can become trapped in pores that become isolated from the outlet face. Simulations were run over a range of Gravity Bond Number (the ratio of characteristic buoyancy and capillary forces). We identify the regimes in which stable and unstable displacement occurs and we examine how the fractal geometry of the displacement front, the saturation, capillary pressure, and relative permeability of each phase varies with the Bond Number. We also confirm the power-law scaling of the front width and the non-wetting phase saturation with the Bond Number as derived from percolation theory.
H44D-08
Quantitative Analysis of the Break-up of Non-Wetting Viscous Fluids in Constricted Capillary Channels
Capillary-pressure analysis for a thread of a viscous fluid surrounded by a wetting phase in a pore leads to an evolution equation describing the temporal dynamics of the fluid/fluid interface. The equation follows from the conservation of mass in the "small-slope" approximation. Its useful applications occur, for example, in petroleum recovery. The nonlinear equation allows inexpensive numerical analysis. For sinusoidally constricted pores, a purely geometric criterion exists that enables or prohibits the viscous-fluid break-up in the neck of the constrictions, which is verified by computational-fluid-dynamics experiments. This geometrically favoring condition sets up capillary-pressure gradients that ensure a continuous outflow of the core fluid from the neck into the "crests" of the profile. Such behavior is indeed observed in the numerical solutions of the evolution equation. For the slopes of the initial configuration close to the fastest-growing wavelength of the linear stability analysis, the break-up is achieved through a quick "collapse" of the interface. As the slope is reduced, the process slows down, and the snap-off is completed through the formation and nonlinear growth of "wavy" disturbances from the initial interface profile, which touch the centerline in several places.