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We present a review of pore-scale simulations of immiscible fluid transport with focus on two of the most popular approaches: lattice Boltzmann modeling for direct simulations on digital models of the pore space and simulations on network models extracted from the pore space. This review focuses on covering basic theory and implementation strategies and gives the readers input and motivation to start their own pore-scale simulations and relate them to realistic porous media. We present a review of recent and relevant applications and how a digital workflow that combines advanced pore-scale imaging and simulations can give very useful input to different fields of science and industry, including reservoir characterization. Given the large span in methods and applications, this review does not aim to cover all methods or applications. However, it covers popular methods and describes to some extent their applicability to different types of transport problems.

Compaction and sand migration are important problems in loosely consolidated and unconsolidated high-rate gas reservoirs, and proppants in the hydraulic fractures. Their impacts on permeability and non-Darcy flow are important for accurate estimation of well productivity. In this paper, we quantified changes in flow parameters due to simulated compaction and sand migration for computer-generated sphere packing and presented the results in the context of correlations for permeability and non-Darcy coefficient that can be used in reservoir simulations. Compaction effects were simulated by increasing grain diameter in a sphere packing. Permeability and non-Darcy coefficients were calculated using the lattice Boltzmann method (LBM). Findings indicated that the permeability decrease was not directional for compaction simulated by simple grain growth and the change in permeability could be estimated from the porosity change with a power-law relation with an exponent equal to 3.28. An analogous power-law relation between non-Darcy coefficient and permeability was found with the exponent equal to − 1.32. For reservoirs that undergo these compaction-like processes during production, estimation of the inertial effects from traditional correlations developed as a function of permeability and porosity may lead to underestimation of the inertial effects. Sand migration causes pore-throat plugging, which leads to significant permeability reduction. We simulated sand particle-plugged pore-throat locations from network simulations for different values of pore volume reduction, and the corresponding permeability and non-Darcy coefficients were calculated from LBM. It was found that permeability change from sand plugging was directional; permeability decrease in the flow direction was approximately double the other directions. A power-law relation between permeability and porosity could be used to estimate the permeability with a much larger exponent: approximately 10 in the flow direction in the range of plugging studied in this work. Because porosity reduction can depend on other factors besides pore-throat plugging (e.g., compaction or pore surface deposition), a correlation was developed to estimate permeability dependence on the pore-throat sand concentration. Even though permeability change was directional, the permeability and non-Darcy coefficient trends collapsed onto a single power-law relation. The exponent on a power-law relation was greater in magnitude (approximately − 1.84) compared to compaction.

Offshore drilling and production operations can result in spills or leaks of hydrocarbons into seabed sediments, which can potentially contaminate these sediments with oil. If this oil trapped later migrates to the water surface it has the potential for negative environmental impacts. For proper contingency planning and to avoid larger consequences in the environment, it is essential to understand mechanisms and rates for hydrocarbon migration from oil containing sediments to the water surface as well as how much will remain trapped in the sediments. It is believed that the amount of oil transported out of the sediment can be affected by tidal pumping, a common form of Subterranean Ground Water Discharge (SGD). However, we could find no study investigating the phenomenon of fluid flow in subsea sediments saturated with oil and the effects of tidal pumping. This study presents an experimental investigation of tidal pumping to determine if it is a possible mechanism to describe the appearance of an oil on the ocean surface above a sediment bed containing oil. An experimental apparatus was constructed of clear PVC pipe allowing for oil migration to be monitored as it flowed out of a sand pack containing oil, while tidal pressure oscillations were applied in three different manners. The effect of tidal pumping was simulated via compression of air above the water (which simulated the increasing static head from tidal exchange). Experimental results show that sustained oil release occurred from all tests, and tests with oscillating pressure produced for longer periods of time. Furthermore, the experimental results showed that the oil migration rate was affected by grain size, oil saturation, and oscillation wave type. In the static experiments, a linear relationship between grain size and permeability was observed, as is well-known in fluid flow in porous medium. However, the oil recovery does not show a linear relationship with viscosity, as the oil recovery only changed by 50% for a nearly 400% variation in viscosity. In all oscillating experiments the rate and ultimate recovery was less than the comparable static experiments. This leads to the preliminary conclusion that with an oscillating pressure on top of a sand pack, movement of a non-replenishing source of oil is suppressed by pressure oscillation.

This paper describes recent work on image-based network modeling of multiphase flow. The algorithm expands the range of flow scenarios and boundary conditions that can be implemented using dynamic network modeling, the most significant advance being the ability to model simultaneous injection of immiscible fluids under either transient or steady-state conditions using non-periodic domains. Pore-scale saturation distributions are solved rigorously from two-phase mass conservation equations simultaneously within each pore. Results show that simulations using a periodic network fail to track saturation history because periodic domains limit how the bulk saturation can evolve over time. In contrast, simulations using a non-periodic network with fractional flow as the boundary condition can account for behavior associated with both hysteresis and saturation history, and can capture phenomena such as the long pressure and saturation tails that are observed during dynamic drainage processes. Results include a sensitivity analysis of relative permeability to different model variables, which may provide insight into mechanisms for a variety of transient, viscous dominated flow processes.

Physically representative network models have been used for years for investigating pore-scale behavior in porous materials. However, the technology has remained largely in the research domain, with limited application to industrial processes. In this work, we introduce two algorithms that are derived from well-tested network modeling techniques, but provide unique capabilities for rapid assessment of important porous material properties from high-resolution 3D images. The first is a fast, fully automated algorithm for determining the characteristic length scale for three continuum parameters: porosity, permeability, and electrical resistivity (or formation factor). This information is important for assessing the size of the computational domain needed for image-based modeling. It operates by computing relevant continuum properties from consecutively smaller subdomains extracted from a larger pore network model. Resulting data trends are plotted so that the relevant characteristic lengths can be inferred....

Most flow visualizations and flow measurements to understand particle mobility in porous media are typically performed in transparent microfluidic devices (micro-models) with 2D pore-throat networks. Nano-particle mobility studies to date have been limited to micro-models made of transparent thermoplastic or silicone-based materials. In an effort to fabricate materials close to reservoir rock, ceramic micro-model has been designed and micro fabricated by our group to study nano-particle transport in rock-based ceramic micro-model. A Confocal Micro-Particle Image Velocimetry (C-μPIV) technique augmented with associated post processing algorithms [1] is used in obtaining 3D distributions of nano-particle velocity and concentration at selected locations of the ceramic micro-model. Furthermore, a novel in-situ, nondestructive method of measuring 3D geometry of non-transparent ceramic micro-model is described and validated. The particle experiment uses 860 nm fluorescence labeled polystyrene neutrally buoyant, and electrically neutral nano-particles. The data was acquired using confocal laser-scanning microscope to quantify 3D particle transport at selected observation locations. In addition, fluorescence microscope was used to measure in-situ geometry of porous media. Results of detailed 3D measurements of nano-particle velocity and particle concentration from experiment conducted at a constant flow rate of 30 nL/min in the rock-based micro-model are presented and discussed. Particle velocities range from 0 to 20.93 μm/sec in magnitude, and average concentration range from 6.02 × 103 to 6.79 × 103 particles at inlet channel while velocities range from 0 to 73.63 μm/sec and concentration range from 4.9 × 101 to 1.45 × 103 particles at selected observation locations of the ceramic micro-model. 3D velocity fields at selected locations also indicate that mean velocity closer to the top wall is comparatively higher than bottom wall, because of higher planar porosity and smooth pathway for the nano-particles closer to the top wall. The three dimensional micro-model geometry reconstructed from the fluorescence data can be used to conduct numerical simulations of the flow in the as-tested micro-model for future comparisons to experimental results after incorporating particle transport and particle-wall interaction models.

A ceramic-based micromodel was fabricated with batching of green alumina ceramics mixed with polymer binders, extrusion of the green alumina tapes, and hot embossing of the green tapes with a metal mold. The metal mold fabricated using optical lithography of SU8 and electroforming of nickel contained 2.5D pore network geometry in 13 layers of a rock, Boise sandstone. The hot embossing process enabled the generation of the pore network geometries with a minimum feature size of 25 μm and for distinct formation of the 13 layers of the 2.5D pore geometry of the rock. The green ceramic micromodels were processed with solvent extraction, thermal debinding, and sintering. The sintered micromodels showed significant shrinkages at all directions of the micromodels, which were 17.6% in x, 17.5% in y, and 14.6% in z. The sintered, 2.5D rock-based ceramic micromodel was capped with a thin glass cover slide and used for flow visualization with a fluorescent dye and fluorescent nano-particles. The dye-filled micromodel showed good flow connectivity and fluorescence signal intensity dependence on depth. It was observed that the peak particle concentration close to the observation window and gradual decrease in particle concentration along the depth. The higher velocities were measured in the low flow resistance region with velocity variations along the depth. The microfabricated 2.5D ceramic micromodels will allow resistance to harsh experimental conditions such as high temperature and pressure, and opportunity for investigation of the complex flow patterns in 3D.

Image-based pore-scale modeling has become an important tool for studying fluid transport and other phenomena in porous media. Spatial resolution of the digital images used for modeling is critical not only because it dictates the scale of features that can be resolved, but also because for most techniques there is at least some relationship between voxel size in the image data and numerical resolution applied to the computational simulations. In this work we investigate this relationship using a computer-generated consolidated porous medium, which was digitized at voxel resolutions in the range 2–10 μm. These images, which are free of experimental and segmentation errors, are then used to compute permeability and tortuosity using lattice Boltzmann (LB) and finite elements methods (FEM). Results show how changes in computed permeability are affected by image resolution (which dictates how well the pore geometry is approximated) versus grid or mesh resolution (which changes numerical accuracy). For LB, the image and grid resolution are usually taken to be the same; we show at least one case where effects of grid and image resolution appear to counteract one another, giving the mistaken appearance of resolution-independent results. For FEM, meshing can provide certain attributes (such as better conformance to surfaces), but it also adds an extra step for error or approximation to be introduced in the workflow. Results show that performing grid coarsening on the FEM mesh caused a reduction in computed permeability, but in this particular case the effect is related to tightening of the pore space rather than loss of numerical accuracy.

[1] The concept of coupling pore-scale and continuum-scale models for subsurface flow has long been viewed as beneficial, but implementation has been slow. In this paper, we present an algorithm for direct coupling of a dynamic pore-network model for multiphase flow with a traditional continuum-scale simulator. The ability to run the two models concurrently (exchanging parameters and boundary conditions in real numerical time) is made possible by a new dynamic pore-network model that allows simultaneous injection of immiscible fluids under either transient-state or steady-state conditions. Allowing the pore-scale model to evolve to steady state during each time step provides a unique method for reconciling the dramatically different time and length scales across the coupled models. The model is implemented by embedding networks in selected gridblocks in the reservoir model. The network model predicts continuum-scale parameters such as relative permeability or average capillary pressure from first principles, which are used in the continuum model. In turn, the continuum reservoir simulator provides boundary conditions from the current time step back to the network model to complete the coupling process. The model is tested for variable-rate immiscible displacements under conditions in which relative permeability depends on flow rate, thus demonstrating a situation that cannot be modeled using a traditional approach. The paper discusses numerical challenges with this approach, including the fact that there is not a way to explicitly force pore-scale phase saturation to equal the continuum saturation in the host gridblock without an artificial constraint. Hurdles to implementing this type of modeling in practice are also discussed.

Image-based network modeling has become a powerful tool for modeling transport in real materials that have been imaged using X-ray computed micro-tomography (XCT) or other three-dimensional imaging techniques. Network generation is an essential part of image-based network modeling, but little quantitative work has been done to understand the influence of different network structures on modeling. We use XCT images of three different porous materials (disordered packings of spheres, sand, and cylinders) to create a series of four networks for each material. Despite originating from the same data, the networks can be made to vary over two orders of magnitude in pore density, which in turn affects network properties such as pore-size distribution and pore connectivity. Despite the orders-of-magnitude difference in pore density, single-phase permeability predictions remain remarkably consistent for a given material, even for the simplest throat conductance formulas. Detailed explanations for this beneficial attribute are given in the article; in general, it is a consequence of using physically representative network models. The capillary pressure curve generated from quasi-static drainage is more sensitive to network structure than permeability. However, using the capillary pressure curve to extract pore-size distributions gives reasonably consistent results even though the networks vary significantly. These results provide encouraging evidence that robust network modeling algorithms are not overly sensitive to the specific structure of the underlying physically representative network, which is important given the variety image-based network-generation strategies that have been developed in recent years.

Microtomography is an emerging technique for particle and particulate-materials characterization. To use this technology effectively, robust and accurate computational algorithms are needed to compute relevant particle properties, including particle surface area and particle-particle contact area. However, the most accurate algorithms that have been developed for computing the exposed (void/solid) surface area in a microtomography image cannot be used directly for computing surface areas or particle-particle contact areas for individual particles in a dense packing. This paper presents an algorithm for extracting particle contact areas from a digitized, segmented image of a packed granular material, which in turn can be used to find individual particle surface areas (even if the complete surfaces are not exposed because of contacts in the packing). Results show that small errors in the binary surface-area computations are magnified in the course of determining particle contact areas; the total error in the computation depends mainly on the size of the contact area in voxel units.

Fabrication of 2.5D rock-based micromodels with high resolution features is presented using SU-8 multi-layer lithography and nickel electroforming for nickel molds. Processes associated with SU-8 were carefully optimized by the use of the vacuum contact, the use of UV filter, and controls of UV exposure doses and baking times. The use of SU-8 MicroSpray enabled the easy fabrication of multi-layers of SU-8, while exhibiting some total thickness variations. The thirteen layered SU-8 samples showed reliable patterning results for features at 10 and 25 μm resolutions, and minor pattern distortions of features at the 5 μm resolution. Flycutting method employed in multi-layer lithography of SU-8 yielded accurate total thickness control within ±1.5 μm and excellent pattern formation for all of 5, 10, and 25 μm features. Electroforming of nickel was optimized with electroplating bath composition and electroplating parameters such as current density to realize the high resolution nickel mold. The fabricated nickel molds from flycutting based SU-8 samples revealed the feasibility of manufacturing the minimum features down to 5 μm for thirteen layers without any pattern distortions. The replication-based micromolding method will allow for fabrication of micromodels in a variety of materials such as polymers and ceramics. The high resolution, 2.5D micromodels will be used for investigation of pore-scale fluid transport, which will aid in understanding the complicated fluidic phenomena occurring in the 3D reservoir rock.Copyright © 2015 by ASME

A confocal Micro-Particle Image Velocimetry (C-μPIV) technique along with associated post image processing algorithms is established to quantify three dimensional distributions of nano-particle velocity and concentration at the micro-scale (pore-scale) in 2.5D porous media designed from a Boise rock sample. In addition, an in-situ, non-destructive method for measuring the geometry of the micro-model, including its depth, is described and demonstrated. The particle experiments use 900 nm fluorescence labeled polystyrene particles at a flow rate of 10 nLmin−1 and confocal laser scanning microscopy (CLSM), while in-situ geometry measurements use regular microscope along with Rhodamine dye and a depth-to-fluorescence-intensity calibration. Image post-processing techniques include elimination of background noise and signal from adsorbed nano-particle on the inner surfaces of the micro-model. In addition, a minimization of depth of focus technique demonstrates a capability of optically thin slice allowing us to measure depth wise velocity in 2.5D micro-model. The mean planar components of the particle velocity of the steady-state flow and particle concentration distributions were measured in three dimensions. Particle velocities range from 0.01 to 122 μm s−1 and concentrations from 2.18 × 103 to 1.79 × 104 particles mm−2. Depth-wise results show that mean velocity closer to the top wall is comparatively higher than bottom walls, because of higher planar porosity and smooth pathway for the nano-particles closer to the top wall. The three dimensional micro-model geometry reconstructed from the fluorescence data can be used to conduct numerical simulations of the flow in the as-tested micro-model for future comparisons to experimental results after incorporating particle transport and particle-wall interaction models.Copyright © 2015 by ASME

Compaction and sand migration are some of the main problems for the loosely consolidated and unconsolidated high rate gas reservoirs. A reliable estimation of the well productivity depends on accurate modeling of permeability and inertial effects. Therefore, the key objective of this paper is to quantify the flow parameters change in the case of compaction and sand migration, and the development of permeability and the non-Darcy coefficient correlations that can be used in reservoir simulations. The compaction effects are simulated by increasing grains diameters with the same ratio. Permeability and the non-Darcy coefficients are calculated from lattice Boltzmann method (LBM). Results indicate that permeability decrease is not directional and the change in permeability can be estimated from porosity change with a Kozeny-Carman type relation with an exponent of 3.2. A Kozeny-Carman type relation between the non-Darcy coefficient and permeability is also found with an exponent −1.303. For high compressibility reservoirs, estimation of the inertial effects from the correlations developed as a function of permeability and porosity may also lead to underestimation of the inertial effects. Sand migration causes pore-throat plugging that leads to significant reduction in permeability. Permeability impairment due to sand or fines migration is usually estimated from Kozeny-Carman type relation based on porosity. There is no study in the literature on how the inertial effects are changed with permeability impairment due to sand or fines migration. Sand particle plugging locations are found from the network simulations for different pore volume reduction, and corresponding permeability and the non-Darcy coefficient are calculated from LBM. It is found that permeability change with sand plugging is direction dependent: permeability reduction in the flow direction is twice compared to other directions. Porosity reduction does not depend on only pore-throat plugging, porosity can be decrease due to compaction and pore-surface deposition. Therefore, a correlation is developed to estimate permeability from pore-throat sand concentration. Even though permeability change is directional, the trend between permeability and the non-Darcy coefficient is similar and the magnitude of exponent in Kozeny-Carman type relation is larger, −1.803, compared to that of compaction.

Fixed beds of cylindrical particles are important in chemical engineering applications, but their packing structures are not as well understood or as well characterized as sphere packings. In this work, X-ray microtomography is used to obtain 3D images of 1.8 mm diameter equilateral cylinders in a 23 mm cylindrical container over a range of bulk porosities. A novel algorithm is used to computationally reconstruct the packings, resulting in data sets that give the location and orientation of each cylinder in the imaged packings. Extensive analysis has been performed, including bulk and local porosities, radial distribution functions, and parameters describing local and global ordering. The major factors affecting packing structure are the overall packing density and the proximity to the wall. At the highest overall packing densities, near-wall porosity becomes nearly equal to interior porosity, and significant global ordering occurs near the wall. For a vertical container, global ordering is characterized by the alignment of the particles with an orthogonal coordinate system that has one axis coincident with r (as defined by the container) and the other two axes in the z – θ plane, but rotated 45 ∘ with the horizontal. The observed structures are relevant in the context of flow maldistribution and heat transfer in fixed beds.

Using a new computational model, we have studied the dynamics and coalescence of a pair of two-dimensional droplets in pressure-driven flow through a constricted capillary tube, which is a prototype problem for the analysis of the interaction of emulsion droplets in porous media. We present simulations that quantify the effects of various system parameters on the droplet stability. These include the capillary number, the interfacial tension, the suspended-to-suspending-phase viscosity ratio, the valence and concentration of added electrolytes, the droplet-to-pore-size ratio, the pore-body-to-throat-size ratio, and the type of pore geometry. Our simulations show that the capillary number Ca plays an important role in determining whether the drops coalesce. At low Ca , drops deform only slightly and coalescence occurs at the entrance of the pore throat, whereas significant deformation enables the drops move through the pore without coalescence at high Ca . Coalescence is favored at intermediate values of the viscosity ratio. The destabilizing effect of added electrolytes is found to be insignificant for 10-μm drops, but significant for micron-size drops. Among the geometric-related parameters, the drop-to-pore-size ratio is the most significant.

Traditional particle-characterization techniques require particles to be dispersed from their original form, which destroys important morphologic information in materials such as aggregates or porous materials. X-ray computed microtomography provides a powerful tool for non-destructive analysis. However, robust techniques for comprehensive material characterization of these images have not been developed. In this paper we present a new algorithm for the computer analysis of particulate materials from high-resolution tomography images. The key aspect of the algorithm is the assignment of every solid-phase voxel in the image to its associated particle in a physically representative manner, which is in essence a particle-scale computer reconstruction of the material. Once this digital reconstruction is obtained, a vast amount of morphologic information can be extracted, including parameters obtained by traditional particle-analysis techniques (e.g., particle-size distribution and porosity) as well as parameters not usually available (e.g., spatial correlations in particle size, particle aspect ratios, surface areas, and orientations, particle contacts, particle coordination numbers, and more). Additionally, the computer reconstruction allows for complex manipulations such as the comparison of a specific parameter for two different particle-size classes within the material. The paper includes validation of the algorithm using computer-generated packings, as well as an example using microtomography data from a real material.

The flow of non-Newtonian fluids in packed beds and other porous media is important in several applications such as polymer processing, filtration, and enhanced oil recovery. Expressions for flowrate versus pressure gradient are desirable for a-priori prediction and for substitution into continuum models. In this work, physically representative network models are used to model the flow of shear-thinning fluids, including power-law and Ellis fluids. The networks are used to investigate the effects of fluid rheology and bed morphology on flow. A simple macroscopic model is developed for the flow of power-law and Ellis fluids in packed beds using results from the network model. The model has the same general functionality as those developed using the popular bundle-of-tubes approach. The constant β , which appears in these models, is often directly derived from the tortuosity and a simple representation of the porous media. It is shown here that this can lead to incorrect and ambiguous values of the constant. Furthermore, the constant is a weak function of the shear-thinning index, indicating that no single bundle-of-tubes could ever properly model flow for a wide variety of shear-thinning fluids. The macroscopic model is compared to experimental data for shear-thinning fluids available in the literature. The model fits the data well when β is treated as an experimental parameter. The best-fit values of β vary, which is expected because even the constant C in the Blake–Kozeny equation varies depending on the source consulted. Additionally, physical effects, such as adsorption and filtration, as well as rheological effects such as viscoelasticity may affect the value of β . We believe that in the absence of these effects, β equals approximately 1.46 for packed beds of uniform spheres at relatively moderate values of the shear-thinning index ( > 0.3 ) .

Network modeling has been performed to obtain quantitative and predictive results of the flow of yield-stress fluids in packed beds. Physically representative networks were used as the basis for the modeling, which have a one-to-one correspondence to computer-generated packed beds of spheres. The networks are able to account for the interconnectivity, heterogeneity, and converging/diverging geometry that are inherent in porous media. The approach can be used to model a wide range of non-Newtonian fluids, but the emphasis is for yield-stress fluids that can be represented using a Bingham model. For these fluids, a threshold pressure gradient is required to initiate flow, and flow at low pressure gradients is characterized by critical percolation behavior. Quantitative results of superficial velocity vs. pressure gradient are presented, and are compared to traditional bundle-of-tubes models, as well as limited experimental data available in the literature. Important differences are observed between the network model and the constitutive models. These are attributed mainly to heterogeneity and converging/diverging geometry, which are not accounted for in the semiempirical models. Comparison to experimental data is good for certain fluids. In other cases, the modeling suggests that effects other than fluid rheology may also have affected flow, such as adsorption or filtration. © 2004 American Institute of Chemical Engineers AIChE J, 50: 3034–3048, 2004

Many engineering problems require the estimation of mass transfer coefficients in porous materials. In heterogeneous materials or in cases where mass transfer sites are not spatially uniform, empirical equations for mass transfer coefficients vary widely, and the origin of these differences is not well understood. In this article, we use a stochastic algorithm to model mass transfer from single particles in a two-dimensional heterogeneous packed bed. The computed mass transfer coefficients are used to generate a distribution of local Peclet numbers in the bed. Detailed hydrodynamics are then used to interpret variations in the local Peclet number. The results show clear relationships between pore structure, streamline patterns, and mass transfer rates.

While network models of porous materials have traditionally been constructed using regular or disordered lattices, recent developments allow the direct modeling of more realistic structures such as sphere packings, microtomographic images, or computer-simulated materials. One of the obstacles in these newer approaches is the generation of network structures that are physically representative of the real systems. In this paper, we present and compare two different algorithms to extract pore network parameters from three-dimensional images of unconsolidated porous media systems. The first approach, which utilizes a pixelized image of the pore space, is an extension to unconsolidated systems of a medial-axis based approach (MA). The second approach uses a modified Delaunay tessellation (MDT) of the grain locations. The two algorithms are validated using theoretical packings with known properties and then the networks generated from random packing are compared. For the regular packings, both methods are able to provide the correct pore network structure, including the number, size, and location of inscribed pore bodies, the number, size, and location of inscribed pore throats, and the connectivity. Despite the good agreement for the regular packings, there were differences in both the spatial mapping and statistical distributions in network properties for the random packings. The discrepancies are attributed to the pixelization at low resolution, non-uniqueness of the inscribed pore-body locations, and differences in merging processes used in the algorithms, and serve to highlight the difficulty in creating a unique network from a complex, continuum pore space.

Once spilled into soils, dense nonaqueous phase liquids (DNAPLs) such as chlorinated solvents migrate deep into the subsurface because of their high density. Their downward migration typically continues until capillary forces balance gravitational forces or until essentially impermeable strata are reached. Efforts to mobilize the DNAPL for remediation purposes risks driving the contaminants deeper, which has spurred research for modifying buoyancy forces in situ. In this paper, a novel means of controlling the density of a DNAPL phase using polyaphrons is presented. Polyaphrons are a class of high internal phase ratio emulsions (HIPREs) that have unusual properties such as indefinite stability and flow properties through porous media. They provide a means of selectively delivering a light organic phase liquid to the vicinity of the DNAPL phase. Upon destabilization of the polyaphron by a polyvalent cation, the light internal phase mixes with the DNAPL to produce a nonaqueous phase of lower density than the original contaminant. The negative buoyancy of the DNAPL can thus be reversed. This approach holds great promise for manipulating DNAPL densities prior to or during remediation treatments.

This paper presents a new numerical model of reactive polymer flow in heterogeneous porous media. A moment representation of the log–normal polymer molecular weight distribution is used to model polymer as a multi-component species. Three leading moments are used to simulate the polymer transport and reaction processes in a two-dimensional porous medium. The 2D, multi-phase polymer flow model is based on a mass-transport equation for multi-component species and is coupled with kinetic models of the gelation process using an operator splitting scheme. The sensitivity of various parameters and constitutive equations is presented.

The modeling of fluid transport in fibrous materials is important for many applications. Most models operate at the continuum level, which requires an a priori knowledge of spatially averaged transport parameters. Alternatively, highly detailed models, in which the momentum equations are solved directly, require major simplifying assumptions. Thus, it is desirable to use intermediate-level techniques that model transport using first principles, but that are appropriate for real engineering processes. In this work, pore-scale network modeling is adapted for fibrous materials and tested for a large range of fibrous structures and solid volume fractions. A novel technique is used to generate prototype network structures from Voronoi diagrams. The Voronoi networks are coupled with two different multiphase flow algorithms, enabling the modeling of various displacement processes relevant to engineering. Permeability predictions agree well with known values. Effects of dynamics, wettability, and material structure on displacement were studied. This modeling technique not only allows for better quantification of how microscale properties affect macroscopic transport, but helps reduce the number of experiments required to predict continuum transport parameters for various materials and processes.

An algorithm is presented for constructing three-dimensional Delaunay tessellations in periodic domains. Applications include mesh generation for periodic transport problems and geometric decomposition for modelling particulate structures. The algorithm is a point insertion technique, and although the general framework is similar to point insertion in a convex hull, a number of new issues are introduced by periodicity. These issues are discussed in detail in the context of the computational algorithm. Examples are given for the tessellation of random points and random sphere packings. Performance data for the algorithm are also presented. These data show an empirical scaling of the computation time with size of O(N1.11) and tessellation rates of 7000–14000 tetrahedrons per second for the problems studied (up to 105 points). A breakdown of the performance is given, which shows the computational load is shared most heavily by two specific parts of the point-insertion procedure. Copyright © 2002 John Wiley & Sons, Ltd.

An algorithm is presented for solving the Stokes equation in large disordered two-dimensional porous domains. It is applied to random packings of discs, but the geometry can be essentially arbitrary. The approach includes the subdivision of the domain and a subsequent application of boundary integral equations to the subdomains. This gives a block diagonal matrix with sparse off-block components that arise from shared variables on internal subdomain boundaries. The global problem is solved using a biconjugate gradient routine with preconditioning. Results show that the effectiveness of the preconditioner is strongly affected by the subdomain structure, from which a methodology is proposed for the domain decomposition step. A minimum is observed in the solution time versus subdomain size, which is governed by the time required for preconditioning, the time for vector multiplications in the biconjugate gradient routine, the iterative convergence rate and issues related to memory allocation. The method is demonstrated on various domains including a random 1000-particle domain. The solution can be used for efficient recovery of point velocities, which is discussed in the context of stochastic modelling of solute transport

We review selected recent developments in reactive flow and transport in porous media, with emphasis on strongly coupled flows, interphase mass transfer, solute transport via dispersion and adsorption and modeling. On the one hand, modeling, theory and experiment continue to provide useful insights into the behavior of natural and engineered systems. On the other hand, real systems continue to reveal instances of non-classical behavior that is not explainable by traditional approaches. This is the sign of a healthy area of science, but it is accompanied by certain challenges. In some applications, it establishes the necessity of multiscale modeling, in particular upscaling from the pore level, though predictive work is especially difficult at that scale. In other applications, however, the central question may be not how to model a particular system, but whether it can be modeled in a meaningful way. Continued progress will require renewed focus on elements of the scientific method: testable predictions, crucial experiments and falsification of hypotheses (Popper K. All life is problem-solving, Routledge, London, 1999•).

The mass transfer behavior from single spheres within random packings was examined in order to quantify the effects of local structure and hydrodynamics on mass transfer. Results show that in the sphere packs studied, structural differences at the pore scale cause the local Peclet number to vary by more than an order of magnitude and the exponent in the Sherwood versus Peclet number relationship to vary between approximately 0.3 and 0.7, both as a function of location within the packing. These combined effects cause at least a two-fold variation in local mass transfer rates and significant differences in the sensitivity of local mass transfer rates to changes in the overall flowrate to the bed. Two distributed parameters are introduced to quantify these effects, which collapse mass transfer data onto a single curve relating the local Sherwood number to a local Peclet number. The physical significance of these parameters is discussed, which aids in our understanding of fundamental behavior in disordered systems. Finally, we show how this information is used to calculate a spatially averaged mass transfer coefficient for dispersed interfaces under conditions where the total mass transfer rate for these interfaces does not reflect average behavior for the bed.

Collective rearrangement is an important class of algorithms for the computer generation of random sphere packings, especially for those of low porosity. In this paper we examine how the choice of boundary conditions affects internal packing structure. The results help to quantify the depth to which non-periodic boundaries influence internal structure. More interesting results are obtained for periodic boundary conditions, showing that for small packings, self-assembly into ordered packings is possible, even without a seed structure or undue influence from the algorithm. Furthermore, the structure depends on the shape of the periodic domain. Finally, we propose examining the transition from random to ordered packings to better characterize the random-close-packed (RCP) limit and its associated packing structures.

Summary This paper examines a conformance control technique in which gel is placed into a heterogeneous porous medium by first injecting a high-viscosity uncrosslinked polymer solution and second, a low-viscosity crosslinker. The latter step causes an unstable displacement to occur and allows the crosslinker to flow selectively into high-permeability strata. A visual flow cell was used to test the procedure, and complete fluid diversion was achieved in a dual-zone medium with a 4:1 permeability ratio. In addition, experiments and numerical simulations were used to study fundamental changes in viscous fingering due to the crosslinker-polymer reaction. When the crosslinking reaction is fast enough so that it occurs during injection, the viscous instability becomes somewhat damped, resulting in less distinct fingers and a nearly plug-flow displacement in some cases. The differences are because gelation causes a large pressure gradient to form just behind the displacement front, whereas unreactive fingering is caused by a small pressure gradient within the fingering zone.

We examine immiscible fluid displacement in a porous material for the case where a polymerization reaction occurs at the interface between two fluid phases. A three-dimensional sphere-based network model is used to study the process. An in situ reaction may affect the pore morphology, interfacial forces, or viscous forces, thereby altering the pressure distribution and displacement pattern. The amount and manner in which the displacement pattern is affected depends on competing rates of reaction versus convection. The model shows that at high-capillary-number displacements, a narrow range of reaction rates affects the displacement process, below which no effect is seen and above which the flow stops. As the capillary number decreases, this range widens but at the expense of the overall hydraulic conductivity. This phenomenon is explained using microscopic displacement patterns. An operating window can be drawn showing the flow and reaction domain in which one would expect an interfacial reaction of this type to affect fluid displacement.

The pore-level mechanisms by which a crosslinked gel changes a porous medium's physical morphology and multiphase permeability are examined using relative permeabilities, pulse tracers, and micromodel visualization. Coreflood experiments indicate that to retain oil permeability while reducing water-permeability, the maintenance of oil-phase pathways after a gel treatment is crucial. However, because the gel changes the medium's morphology, the original pathways for oil are disrupted if the posttreatment fractional flow of water is nonzero. This redistribution of phases generally causes a loss of oil-phase permeability that cannot be regained under normal flow conditions. Relative permeabilities during drainage are not affected significantly by the gel, but during secondary imbibition, the hysteresis in relative permeability is much more pronounced. Tracer experiments indicate the reason for this behavior is that the gel reduces the connectivity of the medium and the fluids distribute themselves more inefficiently, causing a large fraction of dead-end or isolated nonwetting-phase fluid to exist. These conclusions are particularly important for water-control applications where water saturation increases with time. The mechanism suggests that even if a gel exhibits preferential permeability reduction, the loss of absolute permeability and the shift in saturation can be highly damaging to the oil-phase permeability of a treated zone.

Network models are an effective means of incorporating pore-scale heterogeneity into flow models of porous materials. The drawback to these models used to be the inability to obtain quantitative macroscopic parameters representing larger (experimental-scale) media. However, recently developed modeling techniques, combined with more widely available computational resources, make the simulation of macroscopic parameters from a network approach viable. A network model for the slow flow of an incompressible fluid in disordered packed beds is presented. Fundamental fluid mechanics equations are solved at the pore scale and then translated to macroscopic behaviour using a network approach. The results reproduce experimental permeabilities and show excellent quantitative fits to residence time distributions for mechanical dispersion in real beds. Simulations of the RTD are of special interest, because they are definitive links between pore-scale flow behavior and macroscopic responses.

Summary High water saturations in producing zones of petroleum formations cause problems during both acidizing and production. Water diverting agents are designed to prevent some of these problems by selectively plugging watered-out strata. Reactive water diverting agents are oil-based fluids that provide selective plugging because they react with aqueous formation fluids to form permeability reducing gels. This study used laboratory formulated diverting agents to elucidate the plugging mechanisms that result from in-situ interfacial reactions and gel placement. Our results show the physical characteristics of the media and gels necessary to bring about effective plugging and also the conditions that typically prevent selectivity. Additionally, a simple treatment method called the injection/back-flow procedure is introduced, which helps achieve a highly selective diversion treatment.

A rock-based micromodel was designed using depth averaging with Boise rock digital images obtained from the X-ray micro-computed tomography. Design optimization of 2.5D micromodels was carried out using computational fluid dynamics (CFD) simulations through error analysis of dynamic flow parameters (velocities and permeability), which showed the close dynamic flow match between the actual 3D rock and the optimized 2.5D micromodel. Multiple numbers of polymer micromodels were microfabricated via micromilling of a brass mold insert and hot embossing in polymethylmethacrylate (PMMA). The design optimization and the replication-based microfabrication processes enabled the realistic pore geometry generation, which conforms to the pore dimensions of an actual rock sample but with coarser features in a polymer microfluidic platform. The microfabricated PMMA micromodel was used for fluidic characterization with nanoparticles to compare the flow patterns between the designed micromodel and the microfabricated micromodel. Particle motion paths observed in the particle experiments showed the consistent similarity of stream-traces from the CFD simulations of the designed 2.5D micromodel. Further fluidic investigation on the 2.5D rock-based micromodels will provide better understanding on fluid transport mechanism in porous media.Copyright © 2012 by ASME

Numerical prediction of rock properties is a rapidly evolving area that has the potential to influence dramatically how core analysis is performed. In this paper, we investigate the numerical prediction of relative permeability from micro-computed tomographic images using pore network modeling. Specifically, we apply four different algorithms to a digital image of a reservoir sample that has been tested using traditional core analysis, and compare the results. The four algorithms are the following: quasi-static, unsteady-state, steady-state periodic, and steady-state non-periodic. They differ significantly in terms of the physics that they are designed to capture and their computational performance, but there is no published research quantifying how these differences affect the simulation of relative permeability. We show that the traditional quasi-static algorithm exhibits outstanding computational performance, but gives results that are the most different from the other three methods. The unsteady- and steady-state simulations give surprisingly similar results given the differences in how relative permeability is obtained. The two steady-state methods differ little under the conditions tested. This result is encouraging because the periodic simulation is significantly more computationally efficient. However, it raises questions about the ability to capture hysteretic behavior. Phase saturations are mapped from the network results onto the digital images of the pore space as a means to help interpret differences in the pore-scale behavior of the models. Finally, results are compared to relative permeabilities from laboratory corefloods.

Hydraulic fracturing is a widely used technique for production enhancement. One critical property of a hydraulic fracture is the fracture conductivity, which has a direct impact on the productivity and hence, the economics of the stimulated well. Several laboratory techniques have been developed to characterize the materials that are placed in the fracture and influence its conductivity. Conductivity laboratory measurements have become a routine experiment with well-established procedures and setups aimed at simulating downhole conditions. However, correlating the performance of materials in a conventional laboratory setup with their performance in real conditions is not straightforward. This problem occurs because conventional laboratory setups are of limited length scale and fail to capture processes and variations that occur at a scale of the order of, or exceeding, the dimensions of the conductivity cell. Also, even if conventional setups provide accurate and reproducible measurements, they fail to provide fundamental, in-depth understanding of the actual processes that occur at the pore scale, occur in the fracture, and influence the fracture conductivity. A unique, large-scale X-ray computer tomography (CT) setup improves understanding of the factors influencing fracture conductivity. The state-of-the-art setup allows taking high-resolution scans of a proppant pack under conditions similar to an actual fracture. The setup provides unique insight into static and dynamic phenomena occurring at the proppant and the pore scale. The use of imaging software then provides an accurate 3D image over the entire length of the proppant pack. Computer models of flow in porous media can then be used to predict the flow and its parameters in the propped fracture and its porous network specified by the high-resolution images. Moreover, the setup scale (1 m long) is much larger than that of a conventional conductivity cell (20 cm long). The larger dimensions are adequate to capture heterogeneous processes such as fracture cleanup. The performance of the new setup was validated using baseline proppant pack conductivity and non-Darcy flow coefficients experiments. An example was also shown where the unique X-ray CT setup was used for investigating fracture cleanup of new, elongated rod-shaped nondeformable high-strength proppant compared with conventional spherical proppant. The CT images show how the new proppant provides a better fracture cleanup compared with spherical proppant. For both cases, images showing the distribution of residual gel saturation highlight how pore volume geometry affects fracture cleanup.

Microfluidic polymethylmethacrylate (PMMA) devices for study of particle transport in artificial porous media were designed and microfabricated using hot embossing with a brass mold insert containing a microchannel network with eight layers. After thermal bonding to enclose the microchannel network, a process protocol was applied to successfully remove bubbles in the PMMA device. Characterization protocols were developed for study of fluorescent particle tracking, accumulation, and retention in these microfluidic chip artificial porous media. Particle accumulation and retention was observed throughout the microfluidic network domain and predominantly at the inlet section of the PMMA device due to entrance effects. Particle Image Velocimetry of the PMMA device allowed for generating velocity profiles in the chip microchannel networks.Copyright © 2011 by ASME

Summary A series of experiments was conducted in which foam quality, foam reactivity, diverting-stage volume, core permeability, and treatment design were varied. The goal was to determine how these parameters affect diversion in competing limestone cores. Situations involving natural permeability differences and diversion to damaged cores were considered. Experiments indicate that the minimum foam quality required for useful resistance to acid flow is 60%; foams of 70% or 80% quality were the most effective for diversion. Both acid and brine foams were used. Acid foams provide good diversion and can be included easily in a treatment, while in high-porosity, low-permeability limestones like chalk, brine foams appear to be more effective than acid foams. One can expect to maintain good diversion up to a permeability ratio of 10. Results also show that both types of foam effectively divert acid to damaged cores.

Packing of granular media is an extremely important determinant in reservoir rock evolution, sound speed propagation, fluid flow and sediment compressibility. X-ray microfocus computed tomography (XMCT) images with high-resolution were evaluated using a grain-based algorithm that quantifies discrete components and bulk properties of sedimentary systems at different states of compaction or at approximately minimum and maximum packing densities. Angularity of these sands ranges from rounded to subrounded to subangular. Network permeability compares reasonably well to measured values; grain aspect ratios and coordination number are reasonable for sands. The grain-based algorithm provides a robust and efficient capability.

Summary Although acidization has been used successfully for many years to increase the productivity of petroleum wells in carbonate formations, demands on the performance and application of the acidizing process are increasing. This study investigated a method of in-situ foam generation that allows deeper wormhole penetration yet uses less acid than conventional methods. The dissolution patterns were imaged with neutron radiography, which provided an in-depth understanding of the effects of foam and other critical parameters. Results show that foam is effective in promoting efficient stimulation, even at low acid injection rates.

Summary X-ray computed microtomography (XMT) is used for high-resolution, nondestructive imaging and has been applied successfully to geologic media. Despite the potential of XMT to aid in formation evaluation, currently it is used mostly as a research tool. One factor preventing more widespread application of XMT technology is limited accessibility to microtomography beamlines. Another factor is that computational tools for quantitative image analysis have not kept pace with the imaging technology itself. In this paper, we present a new grain-based algorithm used for network generation. The algorithm differs from other approaches because it uses the granular structure of the material as a template for creating the pore network rather than operating on the voxel set directly. With this algorithm, several advantages emerge: the algorithm is significantly faster computationally, less dependent on image resolution, and the network structure is tied to the fundamental granular structure of the material. In this paper, we present extensive validation of the algorithm using computer-generated packings. These analyses provide guidance on issues such as accuracy and voxel resolution. The algorithm is applied to two sandstone samples taken from different facies of the Frontier Formation in Wyoming, USA, and imaged using synchrotron XMT. Morphologic and flow-modeling results are presented.

The entrapment of nonwetting phase fluids in unconsolidated porous media systems is strongly dependent on the pore-scale geometry and topology. Synchrotron X-ray tomography allows us to nondestructively obtain high-resolution (on the order of 1-10 micron), three-dimensional images of multiphase porous media systems. Over the past year, a number of multiphase porous media systems have been imaged using the synchrotron X-ray tomography station at the GeoSoilEnviroCARS beamline at the Advanced Photon Source. For each of these systems, we are able to: (1) obtain the physically-representative network structure of the void space including the pore body and throat distribution, coordination number, and aspect ratio; (2) characterize the individual nonwetting phase blobs/ganglia (e.g., volume, sphericity, orientation, surface area); and (3) correlate the porous media and fluid properties. The images, data, and network structure obtained from these experiments provide us with a better understanding of the processes and phenomena associated with the entrapment of nonwetting phase fluids. Results from these experiments will also be extremely useful for researchers interested in interphase mass transfer and those utilizing network models to study the flow of multiphase fluids in porous media systems.

Proppant-packed fractures provide a relatively low-resistance pathway for the recovery of reservoir fluids. However, residual polymer left over from the proppant transport can greatly reduce the fracture conductivity and, therefore, productivity. Poor fracture cleanup is often observed and it is important to understand the fundamental reasons behind the phenomenon. It is believed that non-Newtonian fluid rheology, viscous fingering, and leak off may all contribute to the problem. The vast majority of fracture cleanup modeling has been limited to continuum-scale modeling. However, important aspects of the cleanup problem may be affected by pore-scale events. For this reason, it is desired to model flow at the pore-scale to obtain a better understanding of the qualitative fingering patterns and quantitative flowrates in a fracture during the cleanup process, as a function of basic parameters such as proppant size, fluid rheology, and imposed pressure gradients. These pore-scale results may help explain the fundamental reasons for the observed poor polymer cleanup and give insight on how to improve cleanup in the future. In this work, computer-generated, random sphere-packs are used to approximate a small portion of the propped fracture. The sphere-packs are transformed into physically representative networks of pores and connecting throats. The network models are used to model flow through the proppant pack at the pore-scale. Modeling the dynamic cleanup process consists simulating a low-viscosity, Newtonian fluid (e.g. water) displacing a high-viscosity, non-Newtonian polymer from the pack. A novel approach is used to couple the network to a continuum model for flow in the reservoir, and realistic boundary conditions are used that allow the displacing fluid to flow in from the side of the fracture. Current modeling is used to better understand displacement behavior under different conditions. Future results will be upscaled and integrated with large-scale reservoir models.