•We investigate if 3D models from FIB-SEM image stacks are a suitable REV for shale.•Data include groups of local 2D and 3D images and corresponding core measurements.•Image analysis of image stacks ...and LBM fluid flow simulations are performed.•We conclude that FIB-SEMs are not suitable domains for permeability simulations.•Averaging local 2D and 3D images can provide representative volumetric properties.
Shales and other unconventional or low permeability (tight) reservoirs house vast quantities of hydrocarbons, often demonstrate considerable water uptake, and are potential repositories for fluid sequestration. The pore-scale topology and fluid transport mechanisms within these nanoporous sedimentary rocks remain to be fully understood. Image-informed pore-scale models are useful tools for studying porous media: a debated question in shale pore-scale petrophysics is whether there is a representative elementary volume (REV) for shale models? Furthermore, if an REV exists, how does it differ among petrophysical properties? We obtain three dimensional (3D) models of the topology of microscale shale volumes from image analysis of focused ion beam-scanning electron microscope (FIB-SEM) image stacks and investigate the utility of these models as a potential REV for shale. The scope of data used in this work includes multiple local groups of neighboring FIB-SEM images of different microscale sizes, corresponding core-scale (milli- and centimeters) laboratory data, and, for comparison, series of two-dimensional (2D) cross sections from broad ion beam SEM images (BIB-SEM), which capture a larger microscale field of view than the FIB-SEM images; this array of data is larger than the majority of investigations with FIB-SEM-derived microscale models of shale. Properties such as porosity, organic matter content, and pore connectivity are extracted from each model. Assessments of permeability with single phase, pressure-driven flow simulations are performed in the connected pore space of the models using the lattice-Boltzmann method. Calculated petrophysical properties are compared to those of neighboring FIB-SEM images and to core-scale measurements of the sample associated with the FIB-SEM sites. Results indicate that FIB-SEM images below ∼5000 µm3 volume (the largest volume analyzed) are not a suitable REV for shale permeability and pore-scale networks; i.e. field of view is compromised at the expense of detailed, but often unconnected, nanopore morphology. Further, we find that it is necessary to acquire several local FIB-SEM or BIB-SEM images and correlate their extracted geometric properties to improve the likelihood of achieving representative values of porosity and organic matter volume. Our work indicates that FIB-SEM images of microscale volumes of shale are a qualitative tool for petrophysical and transport analysis. Finally, we offer alternatives for quantitative pore-scale assessments of shale.
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We propose a simple microfluidic approach: Dissolution-After-Precipitation (DAP), to investigate regimes of carbonate rock dissolution and multiphase reactive transport. In this method, a carbonate ...porous medium is created in a glass microchannel
calcium carbonate precipitation, after which an acid is injected into the channel to dissolve the precipitated porous medium. Utilizing the DAP method, for the first time we realized all five classical single-phase carbonate rock dissolution regimes (uniform, compact, conical, wormhole, ramified wormholes) in a microfluidic chip. The results are validated against the established theoretical dissolution diagram, which shows good agreement. Detailed analysis of these single-phase dissolutions suggests that the heterogeneity of the porous medium may significantly impact how the dissolution patterns evolve over time. Furthermore, DAP is utilized to investigate multiphase dissolution. As examples we tested the cases of an oleic phase (tetradecane) and a gaseous phase (CO
). Results show that the presence of a nonaqueous phase in pore spaces induces the formation of wormholes despite weak advection, and these wormholes ultimately become pathways for nonaqueous phase transport. However, the transport of tetradecane in the wormhole is very slow, causing acid breakthrough into neighboring regions. This mechanism enhances lateral connectivity between wormholes and may lead to a wormhole network. In contrast, CO
moves rapidly and continuously seeks to enter a widening wormhole from a narrower wormhole or the porous regions, generating phenomena such as ganglia redistribution and counterflow (flow of gas opposite to acid flow). Extensive independent experiments are conducted to verify the reproducibility of the observed phenomena/mechanisms and further analyze them. Real-time monitoring of fluid pressure drop during dissolution is implemented to complement microscopy image analysis. Our method can be implemented repeatedly on the same chip, which offers a convenient and inexpensive option to study pore-scale reactive transport mechanisms.
Many non-Newtonian fluids, including polymers, exhibit both shear-thinning and viscoelastic rheological properties. A lattice Boltzmann (LB) model is developed for simulation of the flow of ...thinning–elastic fluids through porous media. This model applies the Oldroyd-B constitutive equation and the Carreau model, respectively, to account for the viscoelastic and shear-thinning behaviors of the thinning–elastic fluid in porous media. Both rheological features are captured well by this model and are verified against analytical solutions. The thinning-then-thickening viscosity curve of the thinning–elastic fluid observed in experiments is reproduced by the present pore-scale simulations. In addition to the traditional extensional theory, we propose other important mechanisms for the increase in apparent viscosity of viscoelastic fluids at higher shear rates. The mechanisms proposed include the reduction in conductivity due to stagnant fluid, the compressed effective flow region, and larger energy dissipations caused by the viscoelastic instability. We find that the viscoelastic thickening effect is more prominent in porous geometries with a large pore–throat ratio.
Article Highlights
A lattice Boltzmann model is developed to predict the flow behavior of fluids with both viscoelastic and shear-thinning properties
The thinning-then-thickening apparent viscosity curve of the thinning-elastic fluid observed experimentally in porous media is predicted in the pore-scale models
Pore-scale mechanisms for the thickening behavior of viscoelastic fluids in porous media at higher shear rates are proposed
•Novel fabrication methods are combined to make a core-scale micromodel for EOR.•Long micromodels capture core-scale physics such as the formation of oil banks.•Increasing viscosity of displacing ...phase in long micromodels increases the amount of oil recovered at breakthrough.
Fluid injection experiments in rocks, commonly referred to as corefloods, are widely used to study and understand fluid flow in the subsurface. However, visual inspection of flow in cores requires computed tomography machines which may not be widely accessible. We introduce a novel micromodel that is as long as a typical core (40 cm), has adjustable pore structure, and includes 2.5D pore throats that can be used to conduct fluid displacements analogous to those in cores. Flow can be visualized inexpensively in the micromodel with an optical microscope. We performed standard coreflood tests in our micromodel including a tracer test and a steady state permeability test. We also conducted multiphase displacements by injecting aqueous solutions at varying glycerol concentrations to displace oil from the micromodel and observed the effect of the viscosity ratio on macro-scale recovery efficiency. When the injected aqueous solution was less viscous than the resident oil, it fingered through the oil. Fingering was not observed in the cases where the injected glycerol solution was more viscous than the oil. Moreover, as the viscosity of the injected glycerol solution increased, oil was recovered more rapidly. Additionally, we performed surfactant and glycerol floods in short (2.4 cm) and long (40 cm) micromodels that show long chips capture scale dependent physics, such as oil banking, that small chips do not capture. The novel micromodel shows promise as a screening tool for chemical EOR because it captures phase banks that are desirable in corefloods.
Dissolution of solid grains in a porous medium is important in many applications, such as groundwater transport, carbon storage, mineral systems, formation of geologic features, and enhancement of ...near-wellbore permeability in carbonate reservoirs. Many models for dissolution in porous media are continuum-scale descriptions, but the flow, reactive transport, and subsequent increase in porosity and permeability occur at the pore scale. Thus, proper inclusion of parametric inputs is challenging. We present a single-phase, 3D, pore network model of dissolution for porous media in the mass-transfer-limited regime. A novel mass transfer coefficient correlation and pore-merging criterion are developed from finite element simulations that greatly improve the pore-scale physics and the quantitative accuracy of the network. The optimal Damköhler number determined from our network simulations closely matches the optimum of 0.29 reported experimentally for mass transfer dissolution in porous media.
Countercurrent spontaneous imbibition (SI) is an important flow mechanism for oil recovery in fractured reservoirs during waterflooding. SI plays a key role in the mobilization of oil in the matrix ...because it facilitates water infiltration by capillarity even when the matrix permeability is low, which limits fluid transport by advection. However, the modeling of SI in fractured media under dynamic conditions has been insufficiently studied. Most imbibition models assume conventional exponential functions and empirical constants based on experimental results of oil recovery under static conditions. Thus, the modeling of water distribution in the fracture and the matrix has been ignored which may lead to incorrect estimates of the efficiency of countercurrent SI to recover oil. Using the classic fractional flow equation, we present a semi-analytical solution to model countercurrent SI in a water-wet fractured medium by including a transfer function to account for continuous fluid exchange between the fracture and the matrix. The model is numerically solved using finite differences by including an effective imbibition time as a function of water advance in the fracture, which overcomes the difficulty of solving iterative numerical summations as shown in other imbibition models. The novelty of the presented solution is that it enables the modeling of water infiltration in the matrix under dynamic conditions. We verified the semi-analytical model against 2D numerical simulations and validated against experimental data to demonstrate that the model accurately predicts oil recovery and water infiltration in the matrix.
Several approaches have been developed in the literature for solving flow and transport at the pore scale. Some authors use a direct modeling approach where the fundamental flow and transport ...equations are solved on the actual pore‐space geometry. Such direct modeling, while very accurate, comes at a great computational cost. Network models are computationally more efficient because the pore‐space morphology is approximated. Typically, a mixed cell method (MCM) is employed for solving the flow and transport system which assumes pore‐level perfect mixing. This assumption is invalid at moderate to high Peclet regimes. In this work, a novel Eulerian perspective on modeling flow and transport at the pore scale is developed. The new streamline splitting method (SSM) allows for circumventing the pore‐level perfect‐mixing assumption, while maintaining the computational efficiency of pore‐network models. SSM was verified with direct simulations and validated against micromodel experiments; excellent matches were obtained across a wide range of pore‐structure and fluid‐flow parameters. The increase in the computational cost from MCM to SSM is shown to be minimal, while the accuracy of SSM is much higher than that of MCM and comparable to direct modeling approaches. Therefore, SSM can be regarded as an appropriate balance between incorporating detailed physics and controlling computational cost. The truly predictive capability of the model allows for the study of pore‐level interactions of fluid flow and transport in different porous materials. In this paper, we apply SSM and MCM to study the effects of pore‐level mixing on transverse dispersion in 3‐D disordered granular media.
Key Points
Predictive method for simulating transport in pore networks developed
Method validated with experiments and shown to be computationally inexpensive
Mechanisms of transverse dispersion in 3‐D granular porous media studied
CO2 injection into geological formations shifts the geochemical equilibrium between the minerals and resident brine. The induced mineral-brine-CO2 reactions can alter the reservoir rock strength and ...deformational behavior, which subsequently affects CO2 storage mechanical integrity. This study attempts to investigate quantitatively the effect of mineral cement and particle dissolution through numerical modeling and validation of triaxial tests performed on unaltered and geologically altered Entrada Sandstone. We utilize a numerical model that couples the discrete element method (DEM) and the bonded-particle model (BPM) to perform simulations of triaxial tests on synthetic rocks that mimic tested rock samples under various confining stresses. Numerical results, in agreement with experimental evidence, show that both cement and particle dissolution significantly contribute to rock weakening in sandstone samples with carbonate/hematite cements and pore-filling carbonate. Sensitivity analyses show that the brittleness of DEM numerical samples is mostly conditioned by the cement bond size among all cement microscopic parameters. An alteration path that mimics the mineral dissolution under subsurface boundary conditions leads to (1) vertical compaction and horizontal stress relaxation in the reservoir rock and (2) transfer of stresses to adjacent strata that results in bond breakage and potentially natural fracture reactivation at a large scale.
•Reports a large 3D benchmark study of pore-scale modeling methods.•Codes and methods varied widely in complexity and computational demand.•Both macroscopic and local measures of flow and solute ...transport were evaluated.•Comparisons were generally favorable among the various methods.•Differences observed support method selection depending on problem context.
Multiple numerical approaches have been developed to simulate porous media fluid flow and solute transport at the pore scale. These include 1) methods that explicitly model the three-dimensional geometry of pore spaces and 2) methods that conceptualize the pore space as a topologically consistent set of stylized pore bodies and pore throats. In previous work we validated a model of the first type, using computational fluid dynamics (CFD) codes employing a standard finite volume method (FVM), against magnetic resonance velocimetry (MRV) measurements of pore-scale velocities. Here we expand that validation to include additional models of the first type based on the lattice Boltzmann method (LBM) and smoothed particle hydrodynamics (SPH), as well as a model of the second type, a pore-network model (PNM). The PNM approach used in the current study was recently improved and demonstrated to accurately simulate solute transport in a two-dimensional experiment. While the PNM approach is computationally much less demanding than direct numerical simulation methods, the effect of conceptualizing complex three-dimensional pore geometries on solute transport in the manner of PNMs has not been fully determined. We apply all four approaches (FVM-based CFD, LBM, SPH and PNM) to simulate pore-scale velocity distributions and (for capable codes) nonreactive solute transport, and intercompare the model results. Comparisons are drawn both in terms of macroscopic variables (e.g., permeability, solute breakthrough curves) and microscopic variables (e.g., local velocities and concentrations). Generally good agreement was achieved among the various approaches, but some differences were observed depending on the model context. The intercomparison work was challenging because of variable capabilities of the codes, and inspired some code enhancements to allow consistent comparison of flow and transport simulations across the full suite of methods. This study provides support for confidence in a variety of pore-scale modeling methods and motivates further development and application of pore-scale simulation methods.
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