Flow Phenomena In Porous Media Research Articles

Pore-scale experimental investigation on the co-current spontaneous imbibition of gas–water two-phase with gravity force

Gravity and capillary forces play pivotal roles in the natural capillary-driven spontaneous imbibition process. The opacity of the medium and the intricate pore structure make it challenging to elucidate the influence of gravity force on co-current gas–water imbibition. A series of pore-scale visualization experiments were conducted using capillary tubes of five different diameters (100, 300, 400, 500, and 1000 μm). The vector concept, represented by the interaction angle with the horizontal direction, was employed to quantify the varying levels of gravity force in the imbibition process, and its impact on imbibition recovery was assessed quantitatively. The findings revealed that the primary influence of gravity on gas–water spontaneous imbibition recovery was predominantly observed in the early stage. Due to the water blocking effect, the gas–water spontaneous imbibition process temporarily halted and resumed when the capillary diameter was 300 μm (at an angle of 60°). For capillary diameters between 100 and 500 μm, the water blocking effect induced a wave-like variation in gas–water spontaneous imbibition recovery as the interaction angle increased. Conversely, for a capillary diameter of 1000 μm, imbibition recovery exponentially decreased with the interaction angle, and no water blocking effect was observed. Consequently, the critical range of pore sizes for the water blocking effect in the gas–water spontaneous imbibition process was determined to be between 500 and 1000 μm. This research offers valuable theoretical insights into understanding capillary-driven flow phenomena in porous media.

Three-dimensional visualization and modeling of capillary liquid rings observed during drying of dense particle packings

Experimental and numerical pore network simulation studies on convective drying of capillary porous media under slow isothermal conditions are presented in this work. As a physical model of a real capillary porous medium, two dense packings of particles filled with monodisperse spherical glass beads (mean diameter 0.8 mm) and initially saturated either with distilled water or with a salt solution are prepared. Two controlled drying experiments with these packings are carried out using a custom-made setup installed in a lab-scale X-ray microtomograph. Based on in-situ tomograms (voxel size 16.4 μm) the time evolution of three-dimensional (3D) structures of liquid and salt deposit in the packings during drying are characterized. The respective results clearly demonstrate the formation of capillary liquid rings at the wedge-shaped pores located near the particle-particle contacts. The rings remain connected over a long distance to the packing surface during a significant period of drying. To highlight the crucial impact of liquid rings on drying, a 3D discrete pore network model that explicitly accounts for the ring effect is developed. Pore network simulations in the presence and absence of this effect are compared with measurements in terms of drying kinetics and saturation profiles. It is found that liquid rings act as additional hydraulic pathways for moisture transport from the interior of the pore/particle network to the surface and thus notably accelerate the drying process, and they lead to a spatially homogeneous distribution of the liquid down to low saturation. This study can be considered as a step forward in discrete modeling of drying of capillary porous media with 3D secondary capillary structures and should be of interest for various applications in the field of complex multiphase flow phenomena in porous media.

An integrated numerical visualization teaching approach for an undergraduate course, Flow in Porous Media: An attempt toward sustainable engineering education

AbstractThe complexities of observing flow phenomena in porous media have made it difficult to teach the course, Flow in Porous Media, to undergraduate students majoring in petroleum engineering. In this study, we propose an integrated numerical visualization teaching (INVT) approach that is based on MATLAB Pdetool, graphical user interface, and Visual Basic Programming. The effectiveness of the INVT method was evaluated in two ways: First, via statistical analyses of the examination grades of two groups (experimental and control groups) of selected undergraduate students from the school of petroleum engineering, after a carefully designed INVT tutorial program was conducted on the experimental group, and finally, by interviewing the selected students to ascertain their psychological wellbeing. The following results were obtained: (1) From the statistical analysis, it was observed that the grade distribution, arithmetic mean, median, and maximum scores of students in the experimental group were relatively higher, suggesting that the INVT approach was effective and suitable for the majority of the students. (2) The interviews revealed that the INVT method provides students with a better classroom experience and help them identify their area of interest. (3) The INVT method will provide other benefits, such as cost‐saving, greener classroom​s, decrease carbon footprint, talent and skill enhancement, and achieve sustainable development goals for education. This paper introduces an effective teaching method for environmental and sustainable energy education. To the best of our knowledge, this is the first time the INVT method is adopted in teaching a petroleum engineering professional course.

Computational characterization of nonwoven fibrous media. II. Analysis of microstructure effects on permeability and tortuosity

Flow phenomena in porous media are relevant in many technological applications including wastewater filtration, chemical separations, and oil recovery. Nonwoven fibrous membranes are widely used as filtration media, and tailoring the microstructure of the pore space is a key to improving filtration efficiency and preventing membrane fouling. However, predicting effective properties such as permeability and tortuosity for complex porous microstructures remains a challenging task as most available models do not incorporate the influence of random fiber arrangement and orientation on the structure-property relations. This study presents a computational analysis of the permeability and tortuosity of realistic nonwoven fibrous media with regular and random fiber arrangements over a wide range of porosities. We conduct pore-scale lattice Boltzmann simulations to predict the fluid flow through nonwoven fibrous media and use the results to test the accuracy of semiempirical scaling relations. Combining morphological properties of the pore space with pore-scale flow simulations enables us to determine the influence of the statistical pore size distribution on the effective fluid transport properties over a wide range of macroscopic porosities. We find that semiempirical coefficients such as the Kozeny-Carman coefficient depend markedly on the statistical distribution of pores and throats. This dependence can be quantified as a constriction factor that incorporates the pore size distribution to yield accurate predictions of permeability of random fibrous media. In combination with experimental imaging techniques, the ability to quantify the connection between microstructure and fluid transport paves the way to computational characterization and design of porous media with tailored properties for filtration and separation applications.

The Sensitivity of Estimates of Multiphase Fluid and Solid Properties of Porous Rocks to Image Processing

X-ray microcomputed tomography (X-ray μ-CT) is a rapidly advancing technology that has been successfully employed to study flow phenomena in porous media. It offers an alternative approach to core scale experiments for the estimation of traditional petrophysical properties such as porosity and single-phase flow permeability. It can also be used to investigate properties that control multiphase flow such as rock wettability or mineral topology. In most applications, analyses are performed on segmented images obtained employing a specific processing pipeline on the greyscale images. The workflow leading to a segmented image is not straightforward or unique and, for most of the properties of interest, a ground truth is not available. For this reason, it is crucial to understand how image processing choices control properties estimation. In this work, we assess the sensitivity of porosity, permeability, specific surface area, in situ contact angle measurements, fluid–fluid interfacial curvature measurements and mineral composition to processing choices. We compare the results obtained upon the employment of two processing pipelines: non-local means filtering followed by watershed segmentation; segmentation by a manually trained random forest classifier. Single-phase flow permeability, in situ contact angle measurements and mineral-to-pore total surface area are the most sensitive properties, as a result of the sensitivity to processing of the phase boundary identification task. Porosity, interfacial fluid–fluid curvature and specific mineral descriptors are robust to processing. The sensitivity of the property estimates increases with the complexity of its definition and its relationship to boundary shape.

Pre-Darcy flow in shales: Effects of the rate-dependent slip

The pre-Darcy flow phenomena in porous media is still not well understood, and the liquid slip mechanism in shales is controversial. Both issues need more exploration. In the field of microfluidic research, the concept of the slip length is widely employed to characterize the deviation from the no-slip flow, and it is recognized that the slip is rate-dependent. For the first time, the rate-dependent slip is proposed as an explanation for the pre-Darcy flow phenomena in porous media and the compromise between existing controversial views with regard to the liquid slip flow in shales based on careful analysis, and then such slip is incorporated in the one-dimension unsteady diffusion equation for liquids. The finite difference method is employed to numerically solve the equation, and detailed sensitivity analysis is conducted for the critical shear stress, the pore radius and the slip length. The results are summarized, and suggestions for future research are provided. This work can provide new insight into the pre-Darcy flow phenomena in the nanoporous media, and can compromise between existing controversial views regarding the liquid slip mechanism in shales. More importantly, this subject is also significant to research and develop EOR methods in shale reservoirs.

Two-phase flow pressure loss through packed particle bed for wide void fraction range

The understanding of the two-phase flow phenomena in porous media is a critical issue for debris bed coolability assessment in severe nuclear power plant accidents. Hence, two-phase-flow friction force modeling has been extensively attempted, based on pressure-loss measurement data. However, most previous two-phase flow pressure loss experiments were conducted at a restricted void-fraction range up to approximately 0.6, which is considerably lower than the dryout condition. Therefore, in this research, two-phase flow tests in packed particle beds are conducted to gather two-phase pressure loss data in the high-void-fraction region. The test beds are constructed by packing mm-scale particles, 3–7 mm in diameter. The experimental data are analyzed and compared with the predicted values of the previous two-phase friction models in term of not only the pressure gradient but also the interfacial friction force between the liquid and gas phases. As there was no valid data for the high-void-fraction region during the previous model development processes, an appropriate model for the interfacial friction force at void fractions greater than approximately 0.6 is unavailable. However, the interfacial friction force plays a significant role in the coolability assessment of the ex-vessel debris bed because it determines the water ingression rate under a cocurrent flow condition. The obtained experimental results in this research indicate the necessity to further improve the model in order to decrease the uncertainty in severe accident risk quantification.

Calibration of astigmatic particle tracking velocimetry based on generalized Gaussian feature extraction

Flow and transport in porous media are driven by pore scale processes. Particle tracking in transparent porous media allows for the observation of these processes at the time scale of ms. We demonstrate an application of defocusing particle tracking using brightfield illumination and a CMOS camera sensor. The resulting images have relatively high noise levels. To address this challenge, we propose a new calibration for locating particles in the out-of-plane direction. The methodology relies on extracting features of particle images by fitting generalized Gaussian distributions to particle images. The resulting fitting parameters are then linked to the out-of-plane coordinates of particles using flexible machine learning tools. A workflow is presented which shows how to generate a training dataset of fitting parameters paired to known out-of-plane locations. Several regression models are tested on the resulting training dataset, of which a boosted regression tree ensemble produced the lowest cross-validation error. The efficacy of the proposed methodology is then examined in a laminar channel flow in a large measurement volume of 2048, 1152 and 3000 μm in length, width and depth respectively. The size of the test domain reflects the representative elementary volume of many fluid flow phenomena in porous media. Such large measurement depths require the collection of images at different focal levels. We acquired images at 21 focal levels 150 μm apart from each other. The error in predicting the out-of-plane location in a single slice of 240 μm thickness was found to be 7 μm, while in-plane locations were determined with sub-pixel resolution (below 0.8 μm). The mean relative error in the velocity measurement was obtained by comparing the experimental results to an analytic model of the flow. The estimated displacement errors in the axial direction of the flow were 0.21 pixel and 0.22 pixel at flows rates of 1.0 mL/h and 2.5 mL/h, respectively. These results demonstrate that it is possible to conduct three-dimensional particle tracking in a representative elementary volume based on a simple apparatus comprising a microscope with standard brightfield illumination and a camera with CMOS sensor.

Flow, Transport, and Reaction in Porous Media: Percolation Scaling, Critical‐Path Analysis, and Effective Medium Approximation

AbstractWe describe the most important developments in the application of three theoretical tools to modeling of the morphology of porous media and flow and transport processes in them. One tool is percolation theory. Although it was over 40 years ago that the possibility of using percolation theory to describe flow and transport processes in porous media was first raised, new models and concepts, as well as new variants of the original percolation model are still being developed for various applications to flow phenomena in porous media. The other two approaches, closely related to percolation theory, are the critical‐path analysis, which is applicable when porous media are highly heterogeneous, and the effective medium approximation—poor man's percolation—that provide a simple and, under certain conditions, quantitatively correct description of transport in porous media in which percolation‐type disorder is relevant. Applications to topics in geosciences include predictions of the hydraulic conductivity and air permeability, solute and gas diffusion that are particularly important in ecohydrological applications and land‐surface interactions, and multiphase flow in porous media, as well as non‐Gaussian solute transport, and flow morphologies associated with imbibition into unsaturated fractures. We describe new applications of percolation theory of solute transport to chemical weathering and soil formation, geomorphology, and elemental cycling through the terrestrial Earth surface. Wherever quantitatively accurate predictions of such quantities are relevant, so are the techniques presented here. Whenever possible, the theoretical predictions are compared with the relevant experimental data. In practically all the cases, the agreement between the theoretical predictions and the data is excellent. Also discussed are possible future directions in the application of such concepts to many other phenomena in geosciences.

Thermoplastic Micromodel Investigation of Two-Phase Flows in a Fractured Porous Medium

In the past few years, micromodels have become a useful tool for visualizing flow phenomena in porous media with pore structures, e.g., the multifluid dynamics in soils or rocks with fractures in natural geomaterials. Micromodels fabricated using glass or silicon substrates incur high material cost; in particular, the microfabrication-facility cost for making a glass or silicon-based micromold is usually high. This may be an obstacle for researchers investigating the two-phase-flow behavior of porous media. A rigid thermoplastic material is a preferable polymer material for microfluidic models because of its high resistance to infiltration and deformation. In this study, cyclic olefin copolymer (COC) was selected as the substrate for the micromodel because of its excellent chemical, optical, and mechanical properties. A delicate micromodel with a complex pore geometry that represents a two-dimensional (2D) cross-section profile of a fractured rock in a natural oil or groundwater reservoir was developed for two-phase-flow experiments. Using an optical visualization system, we visualized the flow behavior in the micromodel during the processes of imbibition and drainage. The results show that the flow resistance in the main channel (fracture) with a large radius was higher than that in the surrounding area with small pore channels when the injection or extraction rates were low. When we increased the flow rates, the extraction efficiency of the water and oil in the mainstream channel (fracture) did not increase monotonically because of the complex two-phase-flow dynamics. These findings provide a new mechanism of residual trapping in porous media.

Physical properties of aqueous glycerol solutions

Use of aqueous glycerol solutions provides a convenient approach for investigation of a variety of aspects of two phase flow phenomena in porous media concerned with viscosity. These include the scaling of spontaneous imbibition and the forced displacement of one phase by another such as in waterflooding. Glycerol/water solutions provide variation of aqueous phase viscosity by over three orders of magnitude. Physical properties, commonly needed in studies of multiphase flow in porous media, are reported for aqueous solutions of glycerol. They include density, surface tension (against air), interfacial tension (against three types of refined oil), contact angle (against n-decane), and viscosity. Experimental results were obtained at six temperatures (20, 30, 40, 50, 65 and 80°C) and five levels of ionic strength of the brine used for adjusting the glycerol/brine mixture. Contact angle measurements against n-decane were made at 20 and 60°C. Glycerol is miscible with water at all investigated salinities and temperature levels. Density and surface and interfacial tensions against refined oils are very close-to-linear with respect to weight fraction of glycerol. Aqueous glycerol solutions on quartz surfaces exhibited zero contact angle (perfect wetting) against both air and refined oil. Increase in viscosity of glycerol–water mixtures with addition of glycerol is highly non-linear. All viscosity data were fitted exceptionally well by an equation originally developed for colloidal dispersions. Literature data on vapor pressure, refractive index and viscosity are also presented.

Microfluidic systems for the analysis of viscoelastic fluid flow phenomena in porous media

In this study, two microfluidic devices are proposed as simplified 1-D microfluidic analogues of a porous medium. The objectives are twofold: firstly to assess the usefulness of the microchannels to mimic the porous medium in a controlled and simplified manner, and secondly to obtain a better insight about the flow characteristics of viscoelastic fluids flowing through a packed bed. For these purposes, flow visualizations and pressure drop measurements are conducted with Newtonian and viscoelastic fluids. The 1-D microfluidic analogues of porous medium consisted of microchannels with a sequence of contractions/expansions disposed in symmetric and asymmetric arrangements. The real porous medium is in reality, a complex combination of the two arrangements of particles simulated with the microchannels, which can be considered as limiting ideal configurations. The results show that both configurations are able to mimic well the pressure drop variation with flow rate for Newtonian fluids. However, due to the intrinsic differences in the deformation rate profiles associated with each microgeometry, the symmetric configuration is more suitable for studying the flow of viscoelastic fluids at low De values, while the asymmetric configuration provides better results at high De values. In this way, both microgeometries seem to be complementary and could be interesting tools to obtain a better insight about the flow of viscoelastic fluids through a porous medium. Such model systems could be very interesting to use in polymer-flood processes for enhanced oil recovery, for instance, as a tool for selecting the most suitable viscoelastic fluid to be used in a specific formation. The selection of the fluid properties of a detergent for cleaning oil contaminated soil, sand, and in general, any porous material, is another possible application.

Application of gamma camera imaging and SPECT systems in chemical processes

SPECT imaging systems are used in nuclear medicine for diagnostic imaging of heart, brain, lung and other organ functions. Radio-pharmaceuticals are injected in the blood stream of a patient. The propagation of the radio-pharmaceutical is monitored as a function of position and time using a gamma camera. In many tests, the monitoring occurs in real time. This technique has been extended for use in chemical process monitoring in our laboratory. In particular, a Siemens gamma camera with SPECT capabilities is routinely used for real time tracer studies, radioactive particle tracking and SPECT imaging. The same radio-pharmaceuticals used in medical testing are used for process monitoring. The system has been used in determining hydrodynamic properties of gas/solid and liquid/solid fluidized beds and in visualizing and monitoring of multi-phase flow phenomena in porous media.

Parallel simulations of pore-scale flow through porous media

Abstract Smoothed particle hydrodynamics (SPH) is a versatile technique which can be applied to single and multiphase flow through porous media. The versatility of SPH is offset by its computational expense which limits the practicability of SPH for large problems involving low Reynolds number flow. A parallel pore-scale numerical model based on SPH is described for modeling flow phenomena in porous media. Aspects of SPH which complicate parallelization are emphasized. The speed of the method is demonstrated to be proportional to the number of processors for test cases where load balance was achieved. The parallel algorithm permits the application of SPH to more complicated porous media problems than previously considered. For such problems, best performance is achieved when several soil grains are simulated by each processor. Finally, future applications of the method and possible extensions are discussed.

A pore‐scale numerical model for flow through porous media

A pore-scale numerical model based on Smoothed Particle Hydrodynamics (SPH) is described for modelling fluid flow phenomena in porous media. Originally developed for astrophysics applications, SPH is extended to model incompressible flows of low Reynolds number as encountered in groundwater flow systems. In this paper, an overview of SPH is provided and the required modifications for modelling flow through porous media are described, including treatment of viscosity, equation of state, and no-slip boundary conditions. The performance of the model is demonstrated for two-dimensional flow through idealized porous media composed of spatially periodic square and hexagonal arrays of cylinders. The results are in close agreement with solutions obtained using the finite element method and published solutions in the literature. Copyright © 1999 John Wiley & Sons, Ltd.

A pore-scale numerical model for flow through porous media

A pore-scale numerical model based on Smoothed Particle Hydrodynamics (SPH) is described for modelling fluid flow phenomena in porous media. Originally developed for astrophysics applications, SPH is extended to model incompressible flows of low Reynolds number as encountered in groundwater flow systems. In this paper, an overview of SPH is provided and the required modifications for modelling flow through porous media are described, including treatment of viscosity, equation of state, and no-slip boundary conditions. The performance of the model is demonstrated for two-dimensional flow through idealized porous media composed of spatially periodic square and hexagonal arrays of cylinders. The results are in close agreement with solutions obtained using the finite element method and published solutions in the literature. Copyright © 1999 John Wiley & Sons, Ltd.

Flow phenomena in rocks: from continuum models to fractals, percolation, cellular automata, and simulated annealing

In this paper, theoretical and experimental approaches to flow, hydrodynamic dispersion, and miscible and immiscible displacement processes in reservoir rocks are reviewed and discussed. Both macroscopically homogeneous and heterogeneous rocks are considered. The latter are characterized by large-scale spatial variations and correlations in their effective properties and include rocks that may be characterized by several distinct degrees of porosity, a well-known example of which is a fractured rock with two degrees of porosity---those of the pores and of the fractures. First, the diagenetic processes that give rise to the present reservoir rocks are discussed and a few geometrical models of such processes are described. Then, measurement and characterization of important properties, such as pore-size distribution, pore-space topology, and pore surface roughness, and morphological properties of fracture networks are discussed. It is shown that fractal and percolation concepts play important roles in the characterization of rocks, from the smallest length scale at the pore level to the largest length scales at the fracture and fault scales. Next, various structural models of homogeneous and heterogeneous rock are discussed, and theoretical and computer simulation approaches to flow, dispersion, and displacement in such systems are reviewed. Two different modeling approaches to these phenomena are compared. The first approach is based on the classical equations of transport supplemented with constitutive equations describing the transport and other important coefficients and parameters. These are called the continuum models. The second approach is based on network models of pore space and fractured rocks; it models the phenomena at the smallest scale, a pore or fracture, and then employs large-scale simulation and modern concepts of the statistical physics of disordered systems, such as scaling and universality, to obtain the macroscopic properties of the system. The fundamental roles of the interconnectivity of the rock and its wetting properties in dispersion and two-phase flows, and those of microscopic and macroscopic heterogeneities in miscible displacements are emphasized. Two important conceptual advances for modeling fractured rocks and studying flow phenomena in porous media are also discussed. The first, based on cellular automata, can in principle be used for computing macroscopic properties of flow phenomena in any porous medium, regardless of the complexity of its structure. The second, simulated annealing, borrowed from optimization processes and the statistical mechanics of spin glasses, is used for finding the optimum structure of a fractured reservoir that honors a limited amount of experimental data.

Percolation theory and its application to groundwater hydrology

The theory of percolation, originally proposed over 30 years ago to describe flow phenomena in porous media, has undergone enormous development in recent years, primarily in the field of physics. The principal advantage of percolation theory is that it provides universal laws which determine the geometrical and physical properties of the system. This survey discusses developments and results in percolation theory to date, and identifies aspects relevant to problems in groundwater hydrology. The methods of percolation theory are discussed, previous applications of the theory to hydrological problems are reviewed, and future directions for study are suggested.

Application of neutron radiography to image flow phenomena in porous media

AbstractNeutron transmission imaging is a technique ideally suited for imaging various flow phenomena in consolidated porous media because the porous matrix is virtually transparent to thermal neutrons. Hydrogen‐containing fluids, however, provide a contrast in the image due to their large thermal neutron cross‐sections. This technique has uncovered new phenomena in the study of dissolution and precipitation in porous media. Neutron images of acid‐etched porous patterns show that the degree of branching, and the tortuosity of the etched patterns depend on competing effects of acid flow rate, dissolution rate and precipitation rate of the reaction products. The fine structure of etched pathways show that they can propagate against the direction of flow, a phenomenon not previously observed. In a second study, realtime neutron transmission imaging was used to visualize miscible tracer dispersion. It was shown how quantitative information such as the in‐situ spatial distributions of the tracer concentrations can be obtained with this technique.

Transient free convection from a vertical plate to a non-newtonian fluid in a porous medium

An analysis of the transient, buoyancy-induced flow and heat transfer adjacent to a suddenly heated vertical wall, embedded in a porous medium saturated with a non-Newtonian fluid, is presented. It is shown that the governing equations, under boundary layer assumptions, are of a singular parabolic type and can be solved accurately in a semi-similar, finite domain using a successive relaxation method. The results show that during the initial stage, before effects of the leading edge become influential at a location, heat transfer and flow phenomena in porous media are governed by transient one-dimensional diffusion processes, for both pseudoplastic and dilatant fluids. Results are presented for the transition from this initial stage to a fully two-dimensional transient, which ultimately terminates in a steady convection. Non-Newtonian fluids which are pseudoplastic exhibit a significantly larger change in the heat transfer coefficient during the transition between the initial diffusive and final steady flow conditions, and unlike the free convection in homogeneous media neither dilatants nor pseudoplastics exhibit any undershoot in the heat transfer coefficient. Furthermore, it is shown that the time required to reach steady state increases and the heat transfer coefficient decreases with a decrease in the power law index.