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 Transport in Porous MediaJournal Prestige (SJR): 0.728 Citation Impact (citeScore): 2Number of Followers: 0      Hybrid journal (It can contain Open Access articles) ISSN (Print) 1573-1634 - ISSN (Online) 0169-3913 Published by Springer-Verlag  [2469 journals]
• Towards Predicting the Onset of Elastic Turbulence in Complex Geometries

Abstract: Flow of complex fluids in porous structures is pertinent in many biological and industrial processes. For these applications, elastic turbulence, a viscoelastic instability occurring at low Re—arising from a non-trivial coupling of fluid rheology and flow geometry—is a common and relevant effect because of significant over-proportional increase in pressure drop and spatio-temporal distortion of the flow field. Therefore, significant efforts have been made to predict the onset of elastic turbulence in flow geometries with constrictions. The onset of flow perturbations to fluid streamlines is not adequately captured by Deborah and Weissenberg numbers. The introduction of more complex dimensionless numbers such as the M-criterion, which was meant as a simple and pragmatic method to predict the onset of elastic instabilities as an order-of-magnitude estimate, has been successful for simpler geometries. However, for more complex geometries which are encountered in many relevant applications, sometimes discrepancies between experimental observation and M-criteria prediction have been encountered. So far these discrepancies have been mainly attributed to the emergence from disorder. In this experimental study, we employ a single channel with multiple constrictions at varying distance and aspect ratios. We show that adjacent constrictions can interact via non-laminar flow field instabilities caused by a combination of individual geometry and viscoelastic rheology depending (besides other factors) explicitly on the distance between adjacent constrictions. This provides intuitive insight on a more conceptual level why the M-criteria predictions are not more precise. Our findings suggest that coupling of rheological effects and fluid geometry is more complex and implicit and controlled by more length scales than are currently employed. For translating bulk fluid, rheology determined by classical rheometry into the effective behaviour in complex porous geometries requires consideration of more than only one repeat element. Our findings open the path towards more accurate prediction of the onset of elastic turbulence, which many applications will benefit. Article Highlights We demonstrate that adjacent constrictions “interact” via the non-laminar flow fields caused by individual constrictions, implying that the coupling of rheological effects and fluid geometry is more complex and implicit. The concept of characterizing fluid rheology independent of flow geometry and later coupling back to the geometry of interest via dimensionless numbers may fall short of relevant length scales, such as the separation of constrictions which control the overlap of flow fields. By providing direct experimental evidence illustrating the cause of the shortcoming of the status-quo, the expected impact of this work is to challenge and augment existing concepts that will ultimately lead to the correct prediction of the onset of elastic turbulence.
PubDate: 2022-05-16

• A Fully Coupled Hydro-Mechanical-Gas Model Based on Mixture Coupling
Theory

Abstract: The interactions of gas migration, water transport and mechanical deformation of rocks are significant for geoenergy industry (e.g. Carbon Capture and Storage, radioactive waste disposal); however, the hydro-mechanical-gas coupled model remains a challenge due to the gap between multiple disciplines (e.g. Geomechanics and Geoenergy). This work presents a novel hydro-mechanical framework model of fully coupled two-phase fluid transport in a deformable porous media through extending mixture coupling theory which is based on non-equilibrium thermodynamics. The main difference between the mixture coupling theory approach and other approaches (ex., mechanic's approach) is that the mixture coupling theory uses energy and entropy analysis by utilizing the unbalanced thermodynamics, while the mechanic's approach analyses the stress–strain tensors. The gas free energy has been included in the Helmholtz free energy balance equation. Three main governing equations have been obtained for solid, liquid and gas phases. Benchmark experiments and modelling based on classical continuum mechanics approaches are used to validate the model by comparing the measured data to the simulation results. The results have a good agreement with experimental data, demonstrating that gas migration has a great influence on water transport and deformation of the solids. The novelty of this study is that it is providing a new approach to study the multiphase flow coupling in porous media rather than the classic mechanic’s approach. Article Highlights A Hydro-Mechanical-Gas (HMG) model has been developed using the mixture coupling theory approach. The hydro-mechanical framework equations were established by using non-equilibrium thermodynamic and Darcy law. The model has been validated using published experimental data and the results of other researchers with different approaches.
PubDate: 2022-05-14

• Changes in the Onset of Double-Diffusive Local Thermal Nonequilibrium
Porous Convection Due to the Introduction of a Third Component

Abstract: Abstract The two-temperature model of local thermal nonequilibrium is employed to study the onset of convection in a triply diffusive fluid-saturated porous medium. The Darcy equation including the time-derivative term is used to describe the flow in the porous medium. The criteria for the stationary and oscillatory instabilities of the basic flow are obtained in the closed form by performing the linear instability analysis. The topology of neutral stability curves is discussed for finite and infinite values of the Prandtl–Darcy number. The disconnected closed oscillatory neutral curves similar to those witnessed in the non-porous and porous (LTE case) domains are found indicating the requirement of three values of thermal Darcy–Rayleigh number to specify the linear instability criteria. There is degeneracy in the closed oscillatory neutral curve between infinite and finite values of the Prandtl–Darcy number; heart-shaped (quasiperiodic bifurcation) in the former case and closed convex in the latter case. Besides, the sensitivity of governing parameters on the nature of instabilities is emphasized.
PubDate: 2022-05-14

• A Multiple-Relaxation-Time Lattice-Boltzmann Analysis for Double-Diffusive
Natural Convection in a Cavity with Heating and Diffusing Plate Inside
Filled with a Porous Medium

Abstract: Abstract In the present study, a multiple-relaxation-time lattice-Boltzmann method is considered to investigate double-diffusive natural convection in a cavity with heating and diffusing plate inside. The cavity is filled with a porous medium at representative elementary volume scale based on the generalized model. The heated plate is placed horizontally at the center of the cavity with higher temperature and concentration. The horizontal walls of the cavity are assumed to be insulated, no conducting, and impermeable to mass transfer. The vertical walls are kept at low temperature and concentration. The combined effects of buoyancy ratio $$N$$ ( $$- 5 \le N \le 5$$ ), thermal Rayleigh number $${\text{Ra}}_{\text{T}}$$ ( $$10^{4} \le {\text{Ra}}_{\text{T}} \le 10^{7}$$ ), Darcy number $${\text{Da}}$$ ( $$10^{ - 6} \le {\text{Da}} \le 10^{ - 2}$$ ), Lewis number $${\text{Le}}$$ ( $$1 \le {\text{Le}} \le 10$$ ), and porosity of the porous medium $$\varepsilon$$ ( $$0.4 \le \varepsilon \le 0.8$$ ) on double-diffusive natural convection are analyzed numerically. Results are presented in terms of streamlines, isotherms, iso-concentrations, and average Nusselt and Sherwood numbers. Results show that the flow structure, the shape of isotherms, and iso-concentrations are well affected by the control parameters. The heat and mass transfers are promoted by the increase of Darcy number. The effect of the Lewis number on heat transfer is negligible for low Darcy values, but this effect is promoted by increasing Darcy number.
PubDate: 2022-05-11

• Enhancement of Simulation CPU Time of Reactive-Transport Flow in Porous
Media: Adaptive Tolerance and Mixing Zone-Based Approach

Abstract: Abstract In recent decades, advances in aqueous geochemical description incorporated with petrophysical characterization allowed researchers to improve reactive-transport flow modeling significantly. However, detailed simulations are usually associated with an increase in computational cost. This work aims to propose a method to decrease the CPU time of reactive-transport simulations in porous media. Conventionally, reactive-transport reservoir simulators perform geochemical computation in all discretized gridblocks at each time step. We hypothesize that if geochemical calculations can be ignored for regions under equilibrium conditions (far from mixing zone), then the computational performance would be improved without compromising simulation results. To test this supposition, we propose a new speedup approach that can be used in conjunction with parallel simulation. The scheme consists of evaluating relative changes in aqueous molar concentration over time. Hence, if the changes are below a certain tolerance, we assume that the reactive task’s effect is negligible. As a consequence, fewer geochemical computations are performed. Moreover, we propose an adaptive tolerance approach to improve simulation accuracy for cases with sharp concentration changes. We test the speedup scheme for three simulation cases with different complexities (e.g., heterogeneity, rock-fluid interactions, gas solubilization). Simulation results indicate a significant reduction in run time for all tested simulations with speedup improvement from 3 to 15 times and excellent accuracy. Furthermore, we recommend that a reliable reference tolerance is approximately 5.0%. In conjunction with parallel simulation, the proposed scheme significantly decreases the required number of processors needed to reduce the CPU time (from hundreds to below ten cores).
PubDate: 2022-05-11

• Spatiotemporal Distribution of Precipitates and Mineral Phase Transition
During Biomineralization Affect Porosity–Permeability Relationships

Abstract: Abstract Enzymatically induced calcium carbonate precipitation is a promising geotechnique with the potential, for example, to seal leakage pathways in the subsurface or to stabilize soils. Precipitation of calcium carbonate in a porous medium reduces the porosity and, consequently, the permeability. With pseudo-2D microfluidic experiments, including pressure monitoring and, for visualization, optical microscopy and X-ray computed tomography, pore-space alterations were reliably related to corresponding hydraulic responses. The study comprises six experiments with two different pore structures, a simple, quasi-1D structure, and a 2D structure. Using a continuous injection strategy with either constant or step-wise reduced flow rates, we identified key mechanisms that significantly influence the relationship between porosity and permeability. In the quasi-1D structure, the location of precipitates is more relevant to the hydraulic response (pressure gradients) than the overall porosity change. In the quasi-2D structure, this is different, because flow can bypass locally clogged regions, thus leading to steadier porosity–permeability relationships. Moreover, in quasi-2D systems, during continuous injection, preferential flow paths can evolve and remain open. Classical porosity–permeability power-law relationships with constant exponents cannot adequately describe this phenomenon. We furthermore observed coexistence and transformation of different polymorphs of calcium carbonate, namely amorphous calcium carbonate, vaterite, and calcite and discuss their influence on the observed development of preferential flow paths. This has so far not been accounted for in the state-of-the-art approaches for porosity–permeability relationships during calcium carbonate precipitation in porous media.
PubDate: 2022-05-10

• Convective Heat Transfer Between a Bead Packing and Its Bounding Wall:
Part II—Numerical Analysis and Experimental Validation

Abstract: Abstract The volume-averaged transport equations for wall confined bead packings were derived in Part I using a non-constant Representative Elementary Volume (REV). This eliminates the incompatibility of the volume-averaged quantities of the bead packing and pointwise quantities of the wall at the interface. This also allowed determining the exponential porosity profile directly from the packing structure for Reynolds-Averaged Navier–Stokes (RANS) Computational Fluid Dynamics (CFD) simulations. In Part II, the governing equations proposed in Part I are used to simulate the forced convective heat transfer from the bead packing to its containing wall. The predictive capability of the model is validated by comparing with experimentally measured temperature and heat flux values. Further discussion shows that a close agreement between numerical and experimental results can be achieved if additional turbulence source terms induced by the presence of beads are properly modeled.
PubDate: 2022-05-09

• Super-Resolved Segmentation of X-ray Images of Carbonate Rocks Using Deep
Learning

Abstract: Abstract Reliable quantitative analysis of digital rock images requires precise segmentation and identification of the macroporosity, sub-resolution porosity, and solid\mineral phases. This is highly emphasized in heterogeneous rocks with complex pore size distributions such as carbonates. Multi-label segmentation of carbonates using classic segmentation methods such as multi-thresholding is highly sensitive to user bias and often fails in identifying low-contrast sub-resolution porosity. In recent years, deep learning has introduced efficient and automated algorithms that are capable of handling hard tasks with precision comparable to human performance, with application to digital rocks super-resolution and segmentation emerging. Here, we present a framework for using convolutional neural networks (CNNs) to produce super-resolved segmentations of carbonates rock images for the objective of identifying sub-resolution porosity. The volumes used for training and testing are based on two different carbonates rocks imaged in-house at low and high resolutions. We experiment with various implementations of CNNs architectures where super-resolved segmentation is obtained in an end-to-end scheme and using two networks (super-resolution and segmentation) separately. We show the capability of the trained model of producing accurate segmentation by comparing multiple voxel-wise segmentation accuracy metrics, topological features, and measuring effective properties. The results underline the value of integrating deep learning frameworks in digital rock analysis.
PubDate: 2022-04-28

• Optimal Exposure Time in Gamma-Ray Attenuation Experiments for Monitoring
Time-Dependent Densities

Abstract: Abstract Several environmental phenomena require monitoring time-dependent densities in porous media, e.g., clogging of river sediments, mineral dissolution/precipitation, or variably-saturated multiphase flow. Gamma-ray attenuation (GRA) can monitor time-dependent densities without being destructive or invasive under laboratory conditions. GRA sends gamma rays through a material, where they are attenuated by photoelectric absorption and then recorded by a photon detector. The attenuated intensity of the emerging beam relates to the density of the traversed material via Beer–Lambert’s law. An important parameter for designing time-variable GRA is the exposure time, the time the detector takes to gather and count photons before converting the recorded intensity to a density. Large exposure times capture the time evolution poorly (temporal raster error, inaccurate temporal discretization), while small exposure times yield imprecise intensity values (noise-related error, i.e. small signal-to-noise ratio). Together, these two make up the total error of observing time-dependent densities by GRA. Our goal is to provide an optimization framework for time-dependent GRA experiments with respect to exposure time and other key parameters, thus facilitating neater experimental data for improved process understanding. Experimentalists set, or iterate over, several experimental input parameters (e.g., Beer–Lambert parameters) and expectations on the yet unknown dynamics (e.g., mean and amplitude of density and characteristic time of density changes). We model the yet unknown dynamics as a random Gaussian Process to derive expressions for expected errors prior to the experiment as a function of key experimental parameters. Based on this, we provide an optimization framework that allows finding the optimal (minimal-total-error) setup and demonstrate its application on synthetic experiments.
PubDate: 2022-04-28

• Speeding Up Reactive Transport Simulations in Cement Systems by Surrogate
Geochemical Modeling: Deep Neural Networks and k-Nearest Neighbors

Abstract: Abstract We accelerate reactive transport (RT) simulation by replacing the geochemical solver in the RT code by a surrogate model or emulator, considering either a trained deep neural network (DNN) or a k-nearest neighbor (kNN) regressor. We focus on 2D leaching of hardened cement paste under diffusive or advective-dispersive transport conditions, a solid solution representation of the calcium silicate hydrates and either 4 or 7 chemical components, and use the HPx (coupled Hydrus-PHREEQC model) reactive transport code as baseline. We find that after training, both our DNN-based and kNN-based codes, $$\hbox {HPx}_{\rm{py}}$$ -DNN and $$\hbox {HPx}_{\rm{py}}$$ -kNN, can make satisfactorily to very accurate predictions while providing either a 3 to 9 speedup factor compared to HPx with parallelized geochemical calculations over 4 cores. Benchmarking against single-threaded HPx, these speedup factors become 8 to 33. Overall, $$\hbox {HPx}_{\rm{py}}$$ -DNN and $$\hbox {HPx}_{\rm{py}}$$ -kNN are found to achieve a close to optimal speedup when DNN regression and kNN search are performed on a GPU. Importantly, for the more complex 7-components cement system, no emulator that is globally accurate over the full space of possible geochemical conditions could be devised. Instead we therefore build “local” emulators that are only valid over a relevant fraction of the input parameter space. This space is identified by running a coarse and thus computationally cheap full RT simulation, and subsequently explored by kernel density sampling. Future work will focus on improving accuracy for this type of cement systems.
PubDate: 2022-04-26

• Convective Heat Transfer Between a Bead Packing and Its Bounding Wall:
Part I—Theory

Abstract: Abstract Forced convective heat transfer between fluid-saturated bead packings and the solid containing walls is important phenomena in different engineering fields. In practical applications, the volume-averaged governing equations and the use of Reynolds-Averaged Navier–Stokes (RANS) Computational Fluid Dynamics (CFD) simulations can provide a reasonable description of the averaged transport phenomena in bead packings without too much computational resources. However, it is still a challenge to treat conjugate problems because the presence of a bounding wall causes different modeling issues. Firstly, different exponential functions have been proposed for RANS CFD simulations to model the porosity variation of bead packings near the wall. These functions are usually determined by an inverse approach which solves the governing equations to approximate the physically measured flow fields (e.g., velocity, temperature). Given the variety of existing porosity models, it is difficult to select the most appropriate one in a particular case. Secondly, the volume-averaged quantities of the bead packing are incompatible with the local point quantities of the wall. This largely increases the difficulty in defining the boundary conditions at the wall. In the present work, a modeling framework is presented to simulate the forced convective heat transfer from the bead packing to its containing wall. These two critical issues are addressed by deriving volume-averaged governing equations using a non-constant Representative Elementary Volume (REV). In Part I of the article, the theoretical derivations are presented in detail. A procedure is also developed to select an appropriate porosity model from the packing microstructure. Part II of the article completes the investigation by validating the predictive capability of the derived governing equations by experiments.
PubDate: 2022-04-23

• Characterization of Water Transport in Porous Building Materials Based on
an Analytical Spontaneous Imbibition Model

Abstract: Abstract Spontaneous imbibition controls the movement of water from the environment into natural and engineered porous construction materials (e.g. stone, concrete, cement, etc.), which can affect the durability of the material and the overall building design. We demonstrate that in contrast to current simplistic approaches, a full description of the process, enabling predictions of sorptivity for different flow conditions and material properties, as well as the water saturation profile, requires the determination of capillary pressure, absolute and relative permeability, and the impact of the initial water saturation. We measured the sorptivity of a homogeneous Bentheimer sandstone for both initially dry and wet conditions for three replicate experiments to demonstrate how to match the measurements to an analytical model to determine the wetting phase (water) relative permeability. The impact of initial water saturation was also studied. We suggest that using imbibition rate is a robust, quick and accurate way to estimate water relative permeability which avoids uncertainties inherent in traditional steady-state measurements. Furthermore, this then allows a complete mathematical treatment of imbibition, to predict the saturation profile as a function of time and the sorptivity for different porous material and fluid properties. Overall this work provides a theoretical and experimental framework that significantly improves our characterization of water transport in a wide range of construction and building materials.
PubDate: 2022-04-23

• Computation of the Permeability Tensor of Non-Periodic Anisotropic Porous
Media from 3D Images

Abstract: Abstract The direct proportionality between the flow rate and the pressure gradient of creeping flows was experimentally discovered by H. Darcy in the 19th century and theoretically justified a couple of decades ago using upscaling methods such as volume averaging or homogenization. X-ray computed micro-tomography (CMT) and pore-scale numerical simulations are increasingly used to estimate the permeability of porous media. However, the most general case of non-periodic anisotropic porous media still needs to be completely numerically defined. Pore-scale numerical methods can be split into two families. The first family is based on a direct resolution of the flow solving the Navier–Stokes equations under the assumption of creeping flow. The second one relies on the resolution of an indirect problem—such as the closure problem derived from the volume averaging theory. They are known to provide the same results in the case of periodic isotropic media or when dealing with representative element volumes. To address the most general case of non-periodic anisotropic porous media, we have identified four possible numerical approaches for the first family and two for the second. We have compared and analyzed them on three-dimensional generated geometries of increasing complexity, based on sphere and cylinder arrangements. Only one, belonging to the first family, has been proved to remain rigorously correct in the most general case. This has been successfully applied to a high-resolution 3D CMT of Carcarb, a carbon fiber preform used in the thermal protection systems of space vehicles. The study concludes with a detailed analysis of the flow behavior (streamlines and vorticity). A quantitative technique based on a vorticity criterion to determine the characteristic length of the material is proposed. Once the characterized length is known, the critical Reynolds number can be estimated and the physical limit of the creeping regime identified.
PubDate: 2022-04-13

• Analytical Study of the Effect of Variable Viscosity and Heat Transfer on
Two-Fluid Flowing through Porous Layered Tubes

Abstract: Abstract The proposed study is an attempt to perceive theoretically the heat transfer phenomenon in the flow of temperature-dependent viscous blood through microvessels internally surrounded by a thin layer of endothelial glycocalyx at the wall. While flowing through microvessels, the blood separates into erythrocytes suspended fluid and cell-depleted fluid into core and peripheral regions respectively. Therefore, to best represent the flow of human blood in microvessels, it has been modeled as a two-fluid. Erythrocytes appearing in the core stimulates the non-Newtonian behavior of the fluid is manifested here by Herschel-Bulkley fluid with temperature-dependent viscosity. The plasma surrounded over the blood cells in the peripheral layer is expressed as a Newtonian fluid with constant viscosity. An added advantage of utilizing the Brinkman-Forchheimer equation to govern the flow through the layer of endothelial glycocalyx (EGL) is that it is credible for both small and large Darcy numbers (permeability). Linear approximation of the Reynolds, viscosity model is exercised to obtain the analytical solutions for the governing equations of Herschel-Bulkley fluid flowing through the core region. In the non-porous peripheral region, the analytical solutions have been obtained for Newtonian fluid with constant viscosity directly and in the porous peripheral region, the Brinkman-Forchheimer equation is solved using regular perturbation for large Darcy number and singular perturbation with a matched asymptotic condition for small Darcy number. Analytical expressions for the velocity, flow rate, flow impedance, and temperature field have been obtained for the different regions. Graphical analysis revealing significant results regarding the variable viscosity, thermal conductivity, Grashof number, Forchheimer number, Richardson number, and permeability on the hemodynamical variables are conducted and results are discussed in detail. The study concludes that an EGL adjacent to the vessel wall increase the resistance to blood flow. The notable discovery of the study is that the temperature parameters influence all the quantities and therefore establish that the temperature-dependent viscosity plays a vital role in medical treatments involving temperature variation such as chemotherapy.
PubDate: 2022-04-11

• Numerical Simulation of Mixing in Active Micromixers Using SPH

Abstract: Abstract In the present study, the mixing process of two-phase flow in active micromixers with straight and wavy channels is investigated, using the meshless method of SPH. Active micromixers with oscillating stir bar and different modes of sinusoidal wavy-walled channel, known as raccoon and serpentine, are considered, and their performances are compared. Simulations are performed for the most important dimensionless parameters of the problem, including amplitude of the wavy-walled channel, $$\alpha$$ , wavelength of the wavy walls, $$\lambda$$ , and Reynolds number, Re. In search for an optimal design for micromixers, a wide range of test simulations including $$0.1\leqslant \alpha \leqslant 0.7$$ , $$1\leqslant \lambda \leqslant 4$$ and $$15 \le {\text{Re}} \le 100$$ is carried out. The results reveal that for all the sinusoidal wavy-walled channels, the mixing improvement strongly depends on the wavelength of the walls rather than the wave amplitude. In active-raccoon micromixers, the mixing improvement smoothly increases with increases in the wave amplitude, whereas in active-serpentine micromixers, it decreases. As a general result, the active-raccoon micromixers exhibit better efficiency, compared with other types of micromixers, especially at $$\hbox {Re} =45$$ . However, the active-serpentine micromixer is inefficient in a wide range of wave amplitudes and wavelengths.
PubDate: 2022-04-08

• Acknowledgement of Reviewers for 2021

PubDate: 2022-04-06

• Integrating Pore-Scale Flow MRI and X-ray μCT for Validation of Numerical
Flow Simulations in Porous Sedimentary Rocks

Abstract: Abstract Single-phase fluid flow velocity maps in Ketton and Estaillades carbonate rock core plugs are computed at a pore scale, using the lattice Boltzmann method (LBM) simulations performed directly on three-dimensional (3D) X-ray micro-computed tomography (µCT) images (≤ 7 µm spatial resolution) of the core plugs. The simulations are then benchmarked on a voxel-by-voxel and pore-by-pore basis to quantitative, 3D spatially resolved magnetic resonance imaging (MRI) flow velocity maps, acquired at 35 µm isotropic spatial resolution for flow of water through the same rock samples. Co-registration of the 3D experimental and simulated velocity maps and coarse-graining of the simulation to the same resolution as the experimental data allowed the data to be directly compared. First, the results are demonstrated for Ketton limestone rock, for which good qualitative and quantitative agreement was found between the simulated and experimental velocity maps. The flow-carrying microstructural features in Ketton rock are mostly larger than the spatial resolution of the µCT images, so that the segmented images are an adequate representation of the pore space. Second, the flow data are presented for Estaillades limestone, which presents a more heterogeneous case with microstructural features below the spatial resolution of the µCT images. Still, many of the complex flow patterns were qualitatively reproduced by the LBM simulation in this rock, although in some pores, noticeable differences between the LBM and MRI velocity maps were observed. It was shown that 80% of the flow (fractional summed z-velocities within pores) in the Estaillades rock sample is carried by just 10% of the number of macropores, which is an indication of the high structural heterogeneity of the rock; in the more homogeneous Ketton rock, 50% of the flow is carried by 10% of the macropores. By analysing the 3D MRI velocity map, it was found that approximately one-third of the total flow rate through the Estaillades rock is carried by microporosity—a porosity that is not captured at the spatial resolution of the µCT image.
PubDate: 2022-04-06

• Evaporative Drying from Hydrophilic or Hydrophobic Homogeneous Porous
Columns: Consequences of Wettability, Porous Structure and Hydraulic
Connectivity

Abstract: Abstract Evaporative drying from porous media is influenced by wettability and porous structures; altering these parameters impacts capillary effects and hydraulic connectivity, thereby achieving slower or faster evaporation. In this study, water was evaporated from a homogeneous porous column created with ~ 1165 glass (i.e., hydrophilic) or Teflon (i.e., hydrophobic) 2.38-mm-diameter spheres with an applied heat flux of 1000 W/m2 supplied via a solar simulator; each experiment was replicated five times and lasted 7 days. This study investigates the combination of altered wettability on evaporation with an imposed heat flux to drive evaporation, while deploying X-ray imaging to measure evaporation fronts. Initial evaporation rates were faster (i.e., ~ 1.5 times) in glass than in Teflon. Traditionally, evaporation from porous media is categorized into three periods: constant rate, subsequent falling rate and slower rate period. Due to homogeneous porous structure and similar characteristic pore size (i.e., 0.453 mm), capillary effects were limited, resulting in an insignificant constant evaporation rate period. A sharp decrease in evaporation rate (i.e., falling rate period) was observed, followed by the slower rate period characterized by Fick’s law of diffusion. Teflon samples entered the slower rate period after 70 h compared to 90 h in glass, and combined with X-ray visualization, implying a lower rate of liquid island formation in the Teflon samples than the glass samples. The evaporative drying front, visualized by X-rays, propagated faster in glass with a final depth (after 7 days) of ~ 30 mm, compared to ~ 24 mm in Teflon. Permeability was modeled based on the geometry [e.g., 3.163E−9 m2 (Revil, Glover, Pezard, and Zamora model), 3.287E−9 m2 (Critical Path Analysis)] and experimentally measured for both glass (9.5 E−10 m2) and Teflon (8.9 E−10 m2) samples. Rayleigh numbers (Ra = 2380) and Nusselt (Nu = 4.1) numbers were calculated for quantifying natural evaporation of water from fully saturated porous media, and Bond (Bo = 193 E−3) and Capillary (Ca = 6.203 E−8) numbers were calculated and compared with previous studies.
PubDate: 2022-04-05

• The Role of Immiscible Fingering on the Mechanism of Secondary and
Tertiary Polymer Flooding of Viscous Oil

Abstract: Abstract Immiscible viscous fingering in porous media occurs when a low viscosity fluid displaces a significantly more viscous, immiscible resident fluid; for example, the displacement of a higher viscosity oil with water (where μo >  > μw). Classically, this is a significant issue during oil recovery processes, where water is injected into the reservoir to provide pressure support and to drive the oil production. In moderate/heavy oil, this leads to the formation of strong water fingers, bypassed oil and high/early water production. Polymer flooding, where the injected water is viscosified through addition of high molecular weight polymers, has often been applied to reduce the viscosity contrast between the two immiscible fluids. In recent years, there has been significant development in the understanding of both the mechanism by which polymer flooding improves viscous oil recovery, as well as in the methodologies available to directly simulate such processes. One key advance in modelling the correct mechanism of polymer oil recovery in viscous oils has been the development of a method to accurately model the “simple” two-phase immiscible fingering (Sorbie in Transp Porous Media 135:331–359, 2020). This was achieved by first choosing the correct fractional flow and then deriving the maximum mobility relative permeability functions from this. It has been proposed that central to the polymer oil recovery is a fingering/viscous crossflow mechanism, and a summary of this is given in this paper. This work seeks to validate the proposed immiscible fingering/viscous crossflow mechanism experimentally for a moderately viscous oil (μo = 84 mPa.s at 31 °C; μw = 0.81 mPa.s; thus, (μo/μw) ~ 104) by performing a series of carefully monitored core floods. The results from these experiments are simulated directly to establish the potential of our modified simulation approach to capture the process (Sorbie, et al., 2020). Both secondary and tertiary polymer flooding experiments are presented and compared with the waterflood baselines, which have been established for each core system. The oil production, water cut and differential pressure are then matched directly using a commercial numerical reservoir simulator, but using our new “fractional flow” derived relative permeabilities. The use of polymer flooding, even when applied at a high water cut (80% after 0.5 PV of water injection), showed a significant impact on recovery; bringing the recovery significantly forward in time for both tertiary and secondary polymer injection modes—a further 13–16% OOIP. Each flood was then directly matched in the simulator with excellent agreement in all experimental cases. The simulations allowed a quantitative visualisation of the immiscible finger propagation from both water injection and the banking of connate water during polymer flooding. Evidence of a strong oil bank forming in front of the tertiary polymer slug was also observed, in line with the proposed viscous crossflow mechanism. This work provides validation of both polymer flooding’s viscous crossflow mechanism and the direct simulation methodology proposed by Sorbie et al. (Transp Porous Media 135:331–359, 2020). The experimental results show the significant potential for both secondary and tertiary polymer flooding in moderate/heavy oil reservoirs.
PubDate: 2022-04-05

• Effect of Grain-Size Distribution on Temporal Evolution of Interfacial
Area during Two-phase Flow in Porous Media

Abstract: Abstract Interfacial area is an important factor during two-phase flow in porous media because mass-transfer mechanisms take place at the interfaces of immiscible phases. The objective of this work is to quantify how grain-size distribution affects the temporal development of interfacial area during two-phase flow through porous media. A two-phase lattice Boltzmann model (color gradient method) was used to simulate drainage (displacement of a wetting fluid by a non-wetting fluid) and imbibition (displacement of the non-wetting fluid by the wetting fluid) in an ensemble of two-dimensional porous media samples. Five groups of porous media, each comprising 20 realizations, were characterized by their median grain size (d50) and coefficient of uniformity (Cu). For all 100 realizations, simulations of drainage and imbibition were conducted until steady-state saturation was achieved, and interfacial area was monitored throughout the simulations. During both drainage and imbibition, the interfacial area initially increases with time until reaching a peak area, then decreases, and then plateaus at a steady-state value. Interfacial area is higher during imbibition than during drainage. The temporal evolution of interfacial area, as quantified by peak area and time to reach peak area, was similar in the three groups characterized by small grain size (d50 ≈ 7.7 lattice units) and relatively uniform grain-size distribution (Cu ≈ 1.21, 1.49, 1.85), for both drainage and imbibition. This suggests that, for the fluid conditions considered here, nonuniformity of grain size is not important below a certain threshold value of Cu. However, two groups with larger grain size (d50 ≈ 8.9 lattice units) and relatively nonuniform grain-size distribution (Cu ≈ 1.85, 2.29) exhibited differences from each other, suggesting that nonuniformity of grain size affects interfacial area when Cu is above a certain value. Furthermore, median grain size was observed to have important effects on temporal evolution of interfacial area.
PubDate: 2022-04-01

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