To address the high computational cost of particle tracking for realistic Eulerian–Lagrangian simulations, a novel efficient and robust particle tracking method (RT method) for unstructured meshes is presented. The method, for the first time, leverages both hardware ray tracing (RT) cores and GPU parallel computing technology to accelerate Eulerian–Lagrangian simulations. The method includes a hardware-accelerated hosting cell locator using bounding volume hierarchy tree (BVH) and a robust treatment of particle-wall interaction (multiple specular reflection) using an improved neighbor searching approach. The method is implemented in a GPU-accelerated open-source code, which is verified against a reference neighbor-searching particle-tracking method (NS method) and experimental observations. To evaluate the performance of our method, several numerical simulations of fluid-driven scalar transport problem are solved. Using a verification case, we show that the particle distribution simulated by our code is in a good agreement with an experimental observation. Tracking failures and stuck particles are not observed in any simulations. Benchmark results indicate that our RT method leads to a roughly 1.8−2.0× performance improvement compared to the reference NS method for large-scale simulations (millions of mesh cells and particles).

Nanoparticle (NP) transport is increasingly relevant to subsurface engineering applications such as aquifer characterization and enhanced oil recovery. An efficient field-scale simulation framework is critical for predicting NP performance and designing subsurface applications. In this work, for the first time, a streamline-based model is presented to simulate NP transport in field-scale subsurface systems with heterogeneous permeability. It considers a series of smart behaviors exhibited by engineered nanoparticles (NPs), including time-triggered encapsulation, retention, formation damage effects and variable nanofluid viscosity. The key methods employed by the algorithm are streamline-based simulation (SLS) and an operator-splitting (OS) technique for modeling NP transport. The model is implemented in an in-house streamline-based code, which is verified against analytical solutions, commercial simulator and academic codes. Simulations on a synthetic three-dimensional (3D) nanocapsule application engineering design case, are also performed to investigate the effect of fluid and NP properties on the displacement pattern of an existing subsurface fluid.

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.

Modern pore-scale modeling has the ability to simulate flow and particle (i.e., colloids, nanoparticles) transport at the pore- and particle-scale in realistic porous media. The pore structure of a material can be obtained through x-ray micro tomography (XCT) or a similar three-dimensional imaging technique. From these data sets, fluid and particle transport can be simulated by direct numerical simulation of the fundamental equations of motion. In this paper, we employ the finite element method to simulate Stokes flow and, after the flow field is resolved, Lagrangian particle tracking to track the fate and transport of nanoparticles (NPs). The presented methodology for direct numerical modeling allowed the simulation of NP transport in real materials (i.e., natural or engineered samples that experiments can be performed on rather than a computer-generated porous medium) in larger domains or with more particles than previous works. XCT images of a micromodel and a Berea sandstone were used as the computational domains to analyze the effect of particle diameter, attractive and repulsive surface forces, flow rate, surface capacity, and XCT image-based mineralogy on particle transport. In the micromodel simulations, in the presence of attractive surface forces, NP effluent recovery increased as particle diameter increased and as flow rate increased – findings qualitatively consistent with published experimental data. The use of XCT image-based mineralogy to spatially distribute attachment sites (i.e., clay) in the Berea showed no difference in particle retention when compared to a random distribution of attachment sites. These results are being used to help understand ongoing micromodel experiments and to design continuum-scale models of NP transport.

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.

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.

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 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 groundwater discharge (SGD). However, we could find no study experimentally investigating the phenomenon of fluid flow in subsea sediments containing oil and the effects of tidal pumping. This study presents an experimental investigation of tidal pumping to determine if it is a possible mechanism that may contribute to the appearance of an oil sheen 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 all oscillating experiments the rate and ultimate recovery was less than the comparable static experiments. For the conditions studied, the experimental results indicate that with an oscillating pressure on top of a sand pack, movement of a non-replenishing source of oil is suppressed by pressure oscillation.

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 Micro Spray 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 gm resolutions, and minor pattern distortions of features at the 5 gm resolution. Flycutting method employed in multi-layer lithography of SU-8 yielded accurate total thickness control within 1.5 gm and excellent pattern formation for all of 5, 10, and 25 gm 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 gm 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.

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.

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. (C) 2015 Elsevier Ltd. All rights reserved.

Rock fracturing, followed by proppant injection, has been used for years to improve oil and gas production rates in low permeability reservoirs and is now a routine part of producing from low-permeability resources such as a shales and tight sands. While field data makes clear the effectiveness of this technique, there is still much room to improve on the science, including how the proppant-filled fracture system responds to changes in loading stress and the corresponding impact on the proppant structure and fracture width, which affect permeability and conductivity. Here, we use high-resolution x-ray computed tomography (XCT) to image two unsaturated rock/fracture/proppant systems: one with shale, one with Berea sandstone. Both systems were imaged under a series of stress levels typical of producing reservoirs. The resulting XCT images were segmented, analyzed for structural and porosity changes, and then used for image-based flow modeling of Stokes flow using both finite element (FEM) and Lattice Boltzmann (LBM) methods. The images and quantitative grain analysis showed expected changes as stress increased: rearrangement of the packing structure, corresponding reduction in porosity, and some embedding at rock walls to a depth of less than 0.5 times the proppant diameter. The shale system exhibited more embedding than the Berea system. At the highest stress in the Berea system (20kpsi or 138MPa), individual proppant particles failed and the broken particles caused significant loss of permeability. For the shale system, the embedding had a significant effect on the simulated permeability/fracture conductivity. Simulation results for each of the loadings showed that permeability is less sensitive to loading than experimental (vendor-reported) permeability values, but also show reasonable agreement at 8kpsi (55MPa) for both systems. Another somewhat surprising result is that fracture permeability for the single-layer proppants confined between shale is similar to what would be predicted from bulk proppant results, despite the significantly different flow geometry in the monolayer fracture.

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. It 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. The second algorithm is a novel approach for computing the full permeability tensor, which is important for quantifying whether a material is isotropic. An artificial anisotropic porous medium was generated with a known principal flow direction not aligned with the Cartesian coordinate axes. The algorithm was validated by its ability to determine both the permeability tensor and the principal flow direction accurately and efficiently. Both network modeling algorithms were applied to networks derived from microCT images of real materials.

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.

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.

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.