Phase field lattice Boltzmann method for liquid-gas flows in complex geometries with efficient and consistent wetting boundary treatment
Abstract
This study investigates the application of wetting boundary conditions for modelling flows in complex curved geometries, such as rough fractures. It implements and analyses two common variants of the wetting boundary condition within the three-dimensional (3D) phase field lattice Boltzmann method. It provides a straightforward and novel extension of the geometrical approach to curved three-dimensional surfaces. It additionally implements surface-energy approach. A novel interpolation-based mitigation of the staircase approximation for curved boundaries is then developed and consistently applied to both wetting boundary conditions. The objectives of simplicity and parallel compute efficiency in implementation are emphasised. Through detailed validation on a series of 3D benchmark cases involving curved surfaces, such as droplet spread on a sphere, capillary intrusion, and droplet impact on a sphere, the behaviour of the wetting boundary conditions are validated and the differences between methods are highlighted. To demonstrate the applicability of the proposed approach in complex geometries with varying surface curvatures, two-phase flow through a synthetic rough fracture is presented. The suitability of the methods for complex simulations is also verified by comparing the computational performance between all investigated methods using this fracture flow test case. The present work thus contributes to the field of multiphase flow modelling with the lattice Boltzmann method in realistic applications where addressing the impact of complex geometries is essential.
Development and validation of a phase-field lattice Boltzmann method for non-Newtonian Herschel-Bulkley fluids in three dimensions
Abstract
The behaviour of non-Newtonian fluids, and their interaction with other fluid phases and components, is of interest in a diverse range of scientific and engineering problems. In the context of the lattice Boltzmann method (LBM), both non-Newtonian rheology and multiphase flows have received significant attention in the literature. This study builds on that work by presenting the development and validation of a phase-field LBM which combines these features in three-dimensional flows. Specifically, the model presented herein combines the simulation of Herschel-Bulkley fluids, which exhibit both a yield stress and power-law dependence on shear rate, interacting with a Newtonian fluid. The developed model is verified and validated using a diverse set of rheological properties and flow conditions, which in their totality represent an additional contribution of this work. Comparison with steady-state layered Poiseuille flow, where one fluid is Newtonian and the other is non-Newtonian, showed excellent correlation with the corresponding analytic solution. Validation against analytic solutions for the rise of a power-law fluid in a capillary tube also showed good correlation, but highlighted some sensitivity to initial conditions and high velocities occurring early in the simulation. A demonstration of the model in a microfluidic junction highlighted how non-Newtonian rheology can alter behaviour from cases where only Newtonian fluids are present. It also showed that significant changes in behaviour can occur when making small and smooth changes in non-Newtonian parameters. To summarise, this work broadens the range of physical phenomena that can be captured in computational analysis of complex fluid flows using the LBM.
Development of a central-moment phase-field lattice Boltzmann model for thermocapillary flows: Droplet capture and computational performance
Abstract
This study develops a computationally efficient phase-field lattice Boltzmann (LB) model with the capability to simulate thermocapillary flows. The model was implemented into the open-source simulation framework, WALBERLA, and extended to conduct the collision stage using central moments. The multiphase model was coupled with both a passive-scalar thermal LB and a Runge-Kutta (RK) solution to the energy equation in order to resolve temperature-dependent surface tension phenomena. Various lattice stencils (D3Q7, D3Q15, D3Q19, D3Q27) were tested for the passive-scalar LB, and both the second- and fourth-order RK methods were investigated. There was no significant difference observed in the accuracy of the LB or RK schemes. The passive scalar D3Q7 LB discretisation tended to provide computational benefits, while the second order RK scheme is superior in memory usage. This paper makes contributions relating to the modelling of thermocapillary flows and to understanding the behaviour of droplet capture with thermal sources analogous to thermal tweezers. Four primary contributions to the literature are identified. First, a new 3D thermocapillary, central-moment phase-field LB model is presented and implemented in the open-source software, WALBERLA. Second, the accuracy and computational performance of various techniques to resolve the energy equation for multiphase, incompressible fluids are investigated. Third, the dynamic droplet transport behaviour in the presence of thermal sources is studied, and insight is provided into the potential ability to manipulate droplets based on local domain heating. Finally, a concise analysis of the computational performance and near-perfect scaling results on NVIDIA and AMD GPU-clusters is shown. This research enables the detailed study of droplet manipulation and control in thermocapillary devices by providing a highly-efficient computational modelling methodology.
Hydrodynamics of molten media bubble columns for hydrogen production through methane pyrolysis
Abstract
Methane pyrolysis using a molten media bubble column reactor is a promising technique for hydrogen production with low carbon dioxide emissions at a feasible price. Understanding the bubble dynamics in molten media is essential to elucidate the reaction mechanisms and establish design requirements for efficient reactors. Computational fluid dynamics provides an effective means to understand the hydrodynamics in opaque molten media. This research used the volume of fluid method to study the effects of gas injection rate as well as variations in gas and molten media (iron, aluminum, and a salt mixture of sodium bromide and potassium bromide in a 48.7:51.3 molar ratio) properties on bubble dynamics. The computational model was first validated using existing experimental and empirical observations. This study makes fundamental contributions to the understanding of bubble dynamics in molten media. First, it was confirmed that gas properties had a small effect on bubble dynamics. The difference in bubble diameters between argon at ambient temperature and 1600 °C was less than 10%. Second, it was found that the volumetric gas injection rate and molten media properties significantly impacted the bubble dynamics, including the bubble diameter and flow regime. Future work will build on these findings to recommend appropriate operating conditions and molten media for specific pyrolysis reactor designs.
Computational investigation of the role of ventricular remodelling in HFpEF: The key to phenotype dissection
Abstract
Recent clinical studies have reported that heart failure with preserved ejection fraction (HFpEF) can be divided into two phenotypes based on the range of ejection fraction (EF), namely HFpEF with higher EF and HFpEF with lower EF. These phenotypes exhibit distinct left ventricle (LV) remodelling patterns and dynamics. However, the influence of LV remodelling on various LV functional indices and the underlying mechanics for these two phenotypes are not well understood. To address these issues, this study employs a coupled finite element analysis (FEA) framework to analyse the impact of various ventricular remodelling patterns, specifically concentric remodelling (CR), concentric hypertrophy (CH), and eccentric hypertrophy (EH), with and without LV wall thickening on LV functional indices. Further, the geometries with a moderate level of remodelling from each pattern are subjected to fibre stiffening and contractile impairment to examine their effect in replicating the different features of HFpEF. The results show that with severe CR, LV could exhibit the characteristics of HFpEF with higher EF, as observed in recent clinical studies. Controlled fibre stiffening can simultaneously increase the end-diastolic pressure (EDP) and reduce the peak longitudinal strain (ell) without significant reduction in EF, facilitating the moderate CR geometries to fit into this phenotype. Similarly, fibre stiffening can assist the CH and ‘EH with wall thickening’ cases to replicate HFpEF with lower EF. These findings suggest that potential treatment for these two phenotypes should target the bio-origins of their distinct ventricular remodelling patterns and the extent of myocardial stiffening.
Contextual existence of an optimum through-plane orientation and aspect ratio of a fiber-segment in fibrous air filters
Abstract
Fibrous air filters have emerged extensively as a remedial indoor solution to address severe air pollution. To understand the complexities involved in variation of their performance with respect to their fiber anisotropy, a fundamental numerical study is undertaken to investigate the capture of inertia-dominated airborne particles by a fiber-segment at different through-plane orientations with respect to airflow direction. An in-house MATLAB code has been developed using the lattice Boltzmann method to model the airflow across fiber-segment, coupled with the Lagrangian approach to model the motion of particles as well as their interactions with the fiber-segment. The filtration performance parameters, viz., capture efficiency, pressure drop, and quality factor, have been evaluated at different through-plane orientations of the fiber-segment for its various segmental aspect ratios and different Stokes numbers. It is found that as the fiber-segment is turned from a parallel to orthogonal orientation with respect to airflow direction, the capture efficiency and pressure drop exhibit either a monotonic rise or broadly an increasing-decreasing kind of trend with an intermediate maximum, depending on the segmental aspect ratio of fiber and the Stokes number. Also, both these parameters are observed to decrease as the segmental aspect ratio of fiber is increased. Furthermore, an optimum through-plane orientation as well as an optimum segmental aspect ratio of the fiber-segment are found to exist for which the overall filtration performance is highest. The indicative optimum through-plane orientation of the fiber-segment is found to be a function of its segmental aspect ratio but not the Stokes number.
Numerical investigation of the effect of nanoparticle aggregation on the performance of concentrated photovoltaic-solar thermal collectors with spectral filtering
Abstract
Solar energy, particularly solar thermal technology, has gained popularity as a possible long-term replacement to fossil fuels. The application of concentrated photovoltaic-solar thermal (CPV/T) collectors, which are improved by spectral filter fluids (SFF) and nanotechnology, has the potential to provide both higher thermal power for heating and cooling as well as improved electrical power generation. This work contributes new insight by quantifying the influence of nanoparticle agglomeration on collector performance and highlighting the challenges associated with the heterogeneous distribution of nanoparticles in CPV/T systems. The study employed coupled Eulerian multiphase modeling and discrete ordinate (DO) radiation modeling to examine slip velocity, nanoparticle diameter (including agglomeration), and suspension concentration. Population balance modeling (PBM) was utilized to determine the nanoparticle size distribution, and the obtained results were validated through comparison with experimental and numerical studies. When neglecting the effect of agglomeration and breakage of the non-solar participating media, the maximum error for this configuration was found to be 3.58% when compared to experimental work. From the solar participating study, in terms of electrical energy production, the best performance obtained was 16.64% with a volume fraction of 0.005% when considering agglomeration and breakage. It was also found that the Sauter diameter increases with volume fraction as the tendency for nanoparticle agglomeration increases. This study provides a broader view of the application of multiphase modeling in solar participating and non-solar participating media and, additionally, provides insight on the effect of various boundary conditions on the key system performance indicators. To extend this work, the flow Reynolds number can be increased in addition to varying the type of working fluid.
Investigation of Taylor bubble dynamics in annular conduits with counter-current flow
Abstract
This study numerically investigates counter-current slug flow by considering the motion of a Taylor bubble in annular conduits with downward-flowing liquids using the Volume-of-Fluid method implemented in the commercial computational fluid dynamics software ANSYS Fluent (Release 19.2). The translational velocity of a counter-current ascending or co-current descending Taylor bubble in vertical concentric annuli and the corresponding distribution parameter (C0) are analyzed. The latter is correlated in terms of Eötvös number (Eo) and inverse viscosity number (Nf) within the range of Eo between 40 and 400 and Nf between 40 and 320. The proposed correlation provides an accurate fit to the numerical data with an average error of 2.64%, and is successfully compared with published numerical findings. In general, the smooth and stable shape of the bubble is disrupted as the counter-current flow velocity (Frl) increases above a critical value, leading to the formation of surface waves and the displacement of the bubble tip away from the annular gap center and towards the outer pipe. C0 increases with Eo and Nf, plateauing at high values of Eo. The effects of annulus inclination (θ) and eccentricity (ε) on bubble rise velocity are examined within the common range of θ and ε encountered during the drilling of oil, gas, or geothermal wells, i.e. 0° ≤ θ ≤ 60° and 0 ≤ ε ≤ 0.7, and their impact on the C0. The increasing Frl and θ lead to a streamlined bubble with pointed nose and thus a reduction in the wrap angle (θwrap), ultimately leading to reduced drag compared to the vertical annulus case and a decrease in C0. As the ε increases, which is accompanied by an increase in the degree of bubble eccentricity, the corresponding C0 decreases. For a constant Eo = 100 and Nf = 160 with inclination angle of θ = 40°and eccentricity of ε = 0.5, the C0 < 1 is observed.
Assessment of capillary rise in rocks by Time Lapse Digital Imaging
Abstract
Solution flow can significantly influence metal recovery and kinetics in leaching, especially in heap/dump/In-situ leaching, however, the vast majority of the work in this area has focused on the inter-particle fluid flow, and only a few studies have investigated the capillary rise behaviour within rock samples. This deserves more attention because it plays a fundamental role in the recovery process and the diffusion pathways for lixiviants and reacted products. This short communication presents a simple methodology for the estimation of capillary action by testing different rock types by Time Lapse Digital Imaging. The method was sensitive to pixel variation which can be intercepted as the response in wettability variation. It can certainly be coupled with other technologies for ore characterization, such as X-ray micro-tomography, to further understand how the pore size distribution influences capillary response, and the fluid rise through pore spaces to interact with ore grains.
Experimental and Numerical Investigation into the Fracture Patterns Induced by Blast-Loading Under Unconfined and Confined Conditions
Abstract
This study analyzes the fracture patterns generated from the high-energy release caused by commercially available explosives and the current capability of numerical methods to replicate this. The mechanics of rock fracture and fragmentation are first studied using the Hybrid Stress Blasting Model (HSBM) at the lab-scale through comparison with experimental results available in the literature. Following this, an in-house experimental blast campaign was undertaken with a detailed examination of an unconfined, 605 mm diameter cylindrical sample and a pressurised (confined), 700 mm diameter cylindrical sample. The post-blast samples were dissected and fractures were visually mapped before comparing the fracture intensity results to the output of the HSBM, which captures stress-wave-induced damage but not gas loading, for these test cases. This paper makes contributions to the literature in three fundamental areas. Firstly, the capability of numerical methods to capture the phenomenology of blasting on rock fracture and fragmentation was validated and the limitations were discussed when looking to use this as a design tool for practical blasting operations. Secondly, the experimental campaign provides detailed insights into the response of cementitious grout materials to internal, blast-induced loading that can be applied in various fields such as mining and construction. Finally, the impact of confining pressure on blast damage was investigated and details were provided for how this can be captured in numerical predictions. It was found that certain aspects of the material response can be well predicted through numerical analysis, namely, the damage radius and the number of dominant fractures. However, it also indicated a shortcoming in the explicit comparison of fracture intensity measures such as P21, with the use of damage metrics appearing more appropriate. The grout-based testing methodology discussed in this work provides an efficient means for gathering data on the impacts of individually controlled aspects of a blast in both unconfined, and confined environments.
Processing of micro-CT images of granodiorite rock samples using convolutional neural networks (CNN), Part II: Semantic segmentation using a 2.5D CNN
Abstract
X-ray computed tomography (XCT) is routinely used in geosciences for the purpose of rock characterisation. High-quality micro-CT images are successfully used for fracture characterisation, as well as analysis of grains and pores. In contrast, the use of XCT for mineral identification is uncommon and often ineffective. Implementation of micro-CT imaging techniques for mineral identification is affected by the accuracy and precision of the image segmentation results. Conventional segmentation methods such as thresholding, watershed, and active contouring are user-biased and do not provide the robust distinction between various heavy accessory minerals in granite rocks. Heavy ore minerals such as pyrite, chalcopyrite, molybdenite, and ilmenite are readily recognised in grey-scale micro-CT images because of their high attenuation coefficient, but further differentiation between these minerals using only traditional segmentation methods is challenging. Conversely, deep convolutional neural networks (CNNs) are fully self-trained, and they have demonstrated accurate semantic segmentation results for rock images. However, the application of CNN semantic segmentation for igneous rocks is not well documented. In this research, the U-Net 2.5D CNN was deployed to train the neural network on a combination of high-resolution micro-CT and mineral liberation analysis (MLA) images to identify different accessory mineral regions of interest (ROIs). The image segmentation results were assessed using MLA and SEM data, and the accuracy of segmentation was found to be greater than 97%. The methodology developed in this study can be extended to map the mineralogy of granite samples unseen by the CNN to further validate the robustness of the approach.
Processing of micro-CT images of granodiorite rock samples using convolutional neural networks (CNN). Part III: Enhancement of Scanco micro-CT images of granodiorite rocks using a 3D convolutional neural network super-resolution algorithm
Abstract
X-ray micro-computed tomography (micro-CT) is a standard method to perform three-dimensional analysis of the internal structure of a rock sample. 3D X-ray microscopes, such as those from the XRadia Versa family, provide images of high resolution and contrast. Medical scanning machines can also be used for scanning rock samples to reduce operational cost and time, but they generally provide poorer spatial resolution and contrast compared to 3D X-ray microscopes. Recent success in implementing deep learning algorithms to enhance image quality demonstrated that, in some cases, the application of convolutional neural network (CNN) models might significantly enhance the resolution of the micro-CT images. In this research, a super-resolution technique employing the U-Net 3D CNN architecture is applied to enhance the resolution of granodiorite rock sample images obtained by two different 3D scanning machines. The high-resolution dataset was obtained using the XRadia Versa XRM-500 microscope. It contained images with nominal resolutions of 10.3 and 5μm. The low-resolution scanning was performed using a Scanco medical μ CT 50 machine, and the images from this dataset had a nominal resolution of 10.3μm. Several models were created to enhance the quality of the low-resolution images, and the results were analysed. It was observed that super-resolution processing could significantly improve the low-resolution micro-CT image quality and suppress noise that appeared on medical images. The results presented in this study are of particular interest and value to geoscientists that use medical scanners to study the structure of rock samples at large scale.
Quantifying the Permeability Enhancement from Blast-Induced Microfractures in Porphyry Rocks Using a Cumulant Lattice Boltzmann Method
Abstract
The permeability of rocks is important in a range of geoscientific applications, including CO 2 sequestration, geothermal energy extraction, and in situ mineral recovery. This work presents an investigation of the change in permeability in porphyry rock samples due to blast-induced fracturing. Two samples were analysed before and after exposure to stress waves induced by the detonation of an explosive charge. Micro-computed tomography was used to image the interior of the samples at a pixel resolution of 10.3μm. The images were segmented into void, matrix, and grain to help quantify the differences in the rock samples. Following this, they were binarised as void or solid and the cumulant lattice Boltzmann method (LBM) was applied to simulate the flow of fluid through the connected void space. A correction required with the use of inlet and outlet reservoirs in computational permeability assessment was also proposed. Interrogation of the steady-state flow field allowed the pre- and post-loading permeability to be extracted. Conclusions were then drawn as to the effectiveness of blasting for enhancing fluid accessibility via the generation of microfractures in the rock matrix within the vicinity of a detonated charge. This paper makes contributions in three fundamental areas relating to the numerical assessment of permeability and the enhancement of fluid accessibility in low-porosity rocks. Firstly, a correction factor was proposed to account for the reservoirs commonly imposed on digitised rock samples when investigating sample permeability through numerical methods. Secondly, it validates the benefits of the LBM in handling complex geometries that would be intractable with conventional computational fluid dynamics methods that require body-fitted meshing. This is done with a novel implementation of the cumulant LBM in the open-source TCLB code. Finally, the improvement in fluid accessibility in low-permeability rock samples was shown through the assessment of multiple regions within two blasted samples. It was found that the blast-induced loading can generate extended microfractures that results in multiple orders of magnitude of permeability enhancement if the target rock possesses existing weaknesses and/or mineralisation.
Comparison of free-surface and conservative Allen–Cahn phase-field lattice Boltzmann method
Abstract
This study compares the free-surface lattice Boltzmann method (FSLBM) with the conservative Allen–Cahn phase-field lattice Boltzmann method (PFLBM) in their ability to model two-phase flows in which the behavior of the system is dominated by the heavy phase. Both models are introduced and their individual properties, strengths and weaknesses are thoroughly discussed. Six numerical benchmark cases were simulated with both models, including (i) a standing gravity and (ii) capillary wave, (iii) an unconfined rising gas bubble in liquid, (iv) a Taylor bubble in a cylindrical tube, and (v) the vertical and (vi) oblique impact of a drop into a pool of liquid. Comparing the simulation results with either analytical models or experimental data from the literature, four major observations were made. Firstly, the PFLBM selected was able to simulate flows purely governed by surface tension with reasonable accuracy. Secondly, the FSLBM, a sharp interface model, generally requires a lower resolution than the PFLBM, a diffuse interface model. However, in the limit case of a standing wave, this was not observed. Thirdly, in simulations of a bubble moving in a liquid, the FSLBM accurately predicted the bubble’s shape and rise velocity with low computational resolution. Finally, the PFLBM’s accuracy is found to be sensitive to the choice of the model’s mobility parameter and interface width.
Towards a Statistical Framework to Upscale Fracture Flows with Quantifiable Uncertainty
Abstract
Modelling of single- and multi-phase flow in fractured subsurface systems is critical in applications relating to the environment, energy, and resource extraction. However, techniques for quantifying the effect of fracture characteristics such as roughness and wettability, as well as fluid flow regimes, on hydraulic properties (e.g., relative permeability) are not described in the literature. Often fractures are approximated as parallel plates (at some level of locality), ignoring intrinsic roughness and decorrelation between surfaces. This leads to the well-known Cubic or Local Cubic Law for single-phase flow, of which many modifications have been proposed to cater for various pore-scale flow phenomena. Although there is a wide range of available literature working within such a methodology, the realisation of a general, robust model based on expected properties of the fracture surface remains a challenge. In comparison, two-phase fracture flows see significantly less development in the literature, with only few studies characterising permeability-saturation curves as a function of fracture properties. Roughness and wettability impact pore-scale flow and can lead to earlier transition between various displacement regimes and govern the relative permeability of the fluid phases present in a fracture. This work aims to develop a framework for studying the impact of fracture-scale phenomena and upscaling it to the level of Discrete Fracture Networks, and then into field-scale analysis. This talk will provide examples of the studies conducted for single- and two-phase flow at the fracture-scale and discuss the methodology of upscaling the observed behavior while quantifying the uncertainty introduced by fracture characteristics (e.g., topology, wettability).
Processing of micro-CT images of granodiorite rock samples using convolutional neural networks (CNN), Part I: Super-resolution enhancement using a 3D CNN
Abstract
X-ray micro-computed tomography (micro-CT) is widely used for three-dimensional analysis of many rock types. However, the practical implementation of this method for micro-porous samples requires a compromise between the resolution of the images and the obtainable field of view (FOV). Generally, resolution enhancement results in a reduction of the FOV. The generation of high-quality micro-CT images is an expensive and time consuming task due to the competing requirements of a large FOV and fine resolution. To alleviate this, super-resolution processing, based on deep learning, is proposed to improve the quality of low-resolution images that can obtain a large FOV. In this research, a super-resolution technique employing the three-dimensional U-Net convolutional neural network (CNN) architecture was applied to enhance the resolution of granodiorite rock sample images. This was undertaken using two sets of micro-CT image triplexes, where the first triplex contained 3-, 6-, and 12-micron resolution sets, and the second triplex contained 1-, 2-, and 4-micron resolution sets. For each triplex, 80% of the images were used for training the neural network with the remaining 20% used for validation. Further validation was performed by comparing the processed results to images obtained from scanning electron microscopy (SEM). It was observed that super-resolution processing can significantly improve the low-resolution micro-CT image quality without physically reducing the sample size typically required for high-resolution scanning. It is expected that this technique could assist practitioners reveal features absent in small samples (e.g. large fractures and or rock textures). Furthermore, images restored through super-resolution processing maintain the FOV of the lower resolution scan, a task that would be comparatively expensive and time consuming to acquire in a high-resolution scan. The workflow proposed in this study has a significant impact on a range of fields including the numerical prediction of rock permeability, and segmentation for advanced mineral analysis.
Efficient implicit methods for wellbore shear failure analysis during drilling and production in coalbeds
Abstract
Wellbore instability is an important consideration during both drilling and production of hydrocarbon reservoirs. The optimal well trajectory must be determined during the design phase to avoid wellbore shear failures. This study makes two fundamental contributions towards improving contemporary wellbore shear models. For the first time, the analytical wellbore shear models are formulated implicitly to significantly improve the computational efficiency and obtainable accuracy. The stability problem is resolved with the bisection method and an optimisation algorithm, where Powell’s method and the Nelder-Mead method have been implemented here. The second contribution is to account for the depletion of various formations, especially coal, in the stability models. Three stress models, namely those of Gray, Shi and Durucan, and Cui and Bustin, were used to develop stress paths for a depleted coal reservoir. The results were quantified via the maximum allowable pressure (MAP), which indicates the wellbore pressure required to avoid wellbore failure and thus guide corresponding operational decisions. The results of this work show that implicit methods significantly improve computational efficiency over the conventional iterative method used in the literature and industry. In particular, it was found that Powell’s method saves greater than 95% of the computation time for sandstone and coal case studies, respectively. In terms of stability during depletion, a higher depletion pressure resulted in an increased MAP. For a drilling application, this means that a greater overbalance pressure is required. While in a production application, a lower maximum drawdown pressure would be expected. The Gray model indicates the largest impact on stability prediction for depleted coals, and the Cui and Bustin model is the most conservative among the three stress models. The proposed numerical framework provides an efficient tool to determine the optimal well trajectory for different formations (e.g. coal, clastic rock) experiencing depletion before or after drilling.
Stability assessment of the phase-field lattice Boltzmann model and its application to Taylor bubbles in annular piping geometries
Abstract
This study parametrically assessed the stability of the phase-field lattice Boltzmann model (PFLBM) before applying it to analyze the effect of annular piping geometry on the flow of Taylor bubbles. The impacts of both eccentricity and pipe diameter ratio were examined, providing an insight into the behavior of these bubbles as well as the applicability and shortcomings in current prediction methodologies. A recently developed PFLBM was implemented into the open-source simulation framework, waLBerla, for this analysis. The stability properties of the code were investigated in detail by assessing various lattice discretizations and relaxation kernels applied to the Rayleigh-Taylor benchmark problem and a Rayleigh-Taylor instability in a tubular geometry, with gravitational Reynolds numbers of up to 30 000 and 10 000, respectively. This paper makes three contributions relating to the stability and usage of the PFLBM as well as the flow of Taylor bubbles in annular pipes. First, the work numerically explored the stability properties of the velocity-based, PFLBM and concluded the impact of various collision models and lattice discretizations on simulation results. Second, it provided a flexible open-source code that the interested researcher can use interactively for practical flow problems as well as the analysis of numerical properties of various lattice Boltzmann algorithms. Finally, it quantified the effect of pipe eccentricity and diameter ratio on the propagation of a Taylor bubble inside a water-filled annular pipe, concluding that a previously defined closure model captured the diameter ratio for the cases examined. To extend this work, future studies aim to analytically investigate the stability properties parametrically observed in this study and apply the findings to simulate the interaction of multiple Taylor bubbles.
Computational modeling of three-dimensional thermocapillary flow of recalcitrant bubbles using a coupled lattice Boltzmann-finite difference method
Abstract
This study analyzes the thermocapillary flow of recalcitrant bubbles within thin channels using a hybrid finite difference lattice Boltzmann method (LBM). It extends a recently developed phase-field LBM to account for temperature effects by coupling the scheme with a fourth-order Runge-Kutta algorithm to solve the governing energy equation. The LBM makes use of a weighted-multiple relaxation-time collision scheme, which has been previously shown to capture high density and viscosity contrasts. This paper makes contributions in two fundamental areas relating to thermocapillary flow. First, it presents and verifies a novel, three-dimensional model to resolve thermocapillary dynamics for practical applications. The verification was undertaken via comparison with analytical solutions for the flow of immiscible fluids in a heated microchannel and for the migration of a droplet in a temperature field. Second, it provides new insight into the inherently three-dimensional nature of recalcitrant bubbles. It was found that the competing inertial and thermal effects allow these bubbles to propagate against the bulk motion of the liquid toward regions of low surface tension.
Numerical Evaluation of Bulk Geomechanical Properties of Fractured Coal with Changing Net Effective Stress Conditions
Abstract
Bulk geomechanical properties in depleting coal seam gas (CSG) reservoirs are crucial to engineering design related to wellbore stability, drilling, and completion strategy. In this paper, a finite element model is presented to systematically predict the changes in bulk coal properties as a consequence of changes in net effective stress. The model includes the effects of depletion-induced shrinkage, and the implications for mechanical integrity and transport properties in reservoirs are discussed. The approach for estimating the bulk geomechanical properties of coal is based on a finite element method and discrete fracture network (FEM-DFN) model capable of capturing both two- and three-dimensional phenomena. The methodology employees a unit volume of coal and systematically applies fracture networks of increasing complexity for which the bulk properties are estimated. The end goal of the larger project that frames this work is to model fracture networks parametrically within three classifications of ’linear-2’, ‘blocky-3’, and ‘blocky-4’, and examine their variation from ‘base-1’ without fractures. A measure of fracture density is used in this current work to compare the results with existing correlations. In future work, coal cleat intensity (e.g., P21, P32) and dispersion will be used to generalise the results. The FEM-DFN model is used to calculate bulk coal properties, which provides an improved understanding of the behaviour of coal as a function of the net effective stress. The results found that the stiffness of coals decreases with the presence of fractures. Furthermore, the effect of 30%, 60%, and 100% depletion are described via modelling of the pore pressure variation, matrix shrinkage, and changes in fracture aperture/compressibility. In this current work, a depletion of 50% is set, with the sensitivity of this parameter set for future work. By numerically subjecting a unit volume of coal to controlled stresses the measured change in bulk properties including their directional dependence is highlighted. The knowledge of the variation in these properties is useful to the life-cycle decision-making in drilling and completions as well as reservoir modelling. The novelty of the proposed methodology is the use of advanced numerical techniques to systematically assess the bulk mechanical properties of coal with the inclusion of depletion effects and discrete fracture networks. In addition to life-cycle decision-making, stimulation design, the prediction of compaction and subsidence, and reservoir management can all benefit from the knowledge gained in this study.
Wellbore Stability Analysis of Horizontal Drilling in Bowen and Surat Coal Seam Gas Wells
Abstract
Hydrocarbon extraction from coal seam gas (CSG) reservoirs relies on horizontal drilling and completions. However, the drilling of horizontal wells usually faces challenges as inappropriate equivalent circulating density (ECD) can induce borehole collapse. Hence, the optimisation of drilling parameters (e.g., well azimuth, ECD) is paramount to successful well delivery. In this paper, an implicit numerical model is developed to obtain the safe drilling pressure for borehole collapse. The model uses Mogi-Coulomb criterion and Shi and Durucan stress model for depleted coals. Case studies are conducted based on samples from Permian Baralaba Coal Measures of the Bowen Basin and Jurassic Walloons Coal Measures of the Surat Basin. The results first show that the horizontal well is prone to have wellbore collapse issues as the minimum ECD is the highest compared to other cases with smaller inclinations. Then cases with different bulk mechanical properties from Bowen and Surat basins are conducted and analysed. The results suggest that samples from Jurassic Walloons Coal Measures are less sensitive to borehole collapse, which are in good agreement with caliper and ECD data of horizontal drilling observations. The developed numerical model is useful for optimising well drilling in locations with different bulk mechanical properties and can ultimately improve well delivery and economic gas extraction.
On the rise characteristics of Taylor bubbles in annular piping
Abstract
A three-dimensional phase-field lattice Boltzmann method has been applied to investigate the rise of Taylor bubbles within annular pipes. The approach couples the conservative phase-field model with a velocity-based lattice Boltzmann scheme. The implementation uses 27 discrete velocities to resolve both the interfacial dynamics and the hydrodynamics. To assist numerical stability for the high-density ratio, two-phase flows a weighted multiple-relaxation-time collision operator is employed. This paper makes contributions in three areas. First, the model is employed to capture the behaviour of Taylor bubbles in five combinations of vertical annular pipes, with results compared to experimental findings from the literature for air-water flows. From this, shortcomings were identified in the ability of existing correlations to accurately predict rise velocities for bubbles in various liquids. Second, the effect of pipe inclination on the rise behaviour of the bubbles was investigated. From the findings, a preliminary correlation describing the rise velocity was proposed. The first two components of the study were conducted with the Taylor bubble rising in stagnant fluid. The final component of this study imposed liquid flow in a concentric annular pipe to determine the impact of this on the bubble’s dynamics. The liquid velocity was defined through a Reynolds number based on the average inlet velocity up to an absolute value of 10. The viscosity was varied to examine Morton numbers from 2.56e-3 to 6.55e-5. To this end both co- and counter-current flow was analysed and a distribution parameter proposed to capture the liquid-gas interaction. To extend this work, future investigations will look to extend the parameter range assessed to ensure the universality of the correlations identified.
Development of closure relations for the motion of Taylor bubbles in vertical and inclined annular pipes using high-fidelity numerical modeling
Abstract
This study analyses the flow of Taylor bubbles through vertical and inclined annular pipes using high-fidelity numerical modeling. A recently developed phase-field lattice Boltzmann method is employed for the investigation. This approach resolves the two-phase flow behavior by coupling the conservative Allen-Cahn equation to the Navier-Stokes hydrodynamics. This paper makes contributions in three fundamental areas relating to the flow of Taylor bubbles. First, the model is used to determine the relationship between the dimensionless parameters (Eötvös and Morton numbers) and the bubble rise velocity (Froude number). There currently exists no surrogate model for the rise of a Taylor bubble in an annular pipe that accounts for fluid properties. Instead, relations generally include the diameter of the outer and inner pipes only. This study covered Eötvös numbers between 10 and 700 and Morton numbers between 10-6 and 100. As such, the proposed correlation is applicable to concentric annular pipes within this range of parameters. An assessment of the correlation to parameters outside of this range was made; however, this was not the primary scope for the investigation. Following this, the effect of pipe inclination was introduced with the impact on rise velocity measured. A correlation between the inclination angle and the rise velocity was proposed and its performance quantified against the limited experimental data available. Finally, the high-fidelity numerical results were analyzed to provide key insights into the physical mechanisms associated with annular Taylor bubbles and the shape they form. To extend this work, future studies on the effect of pipe eccentricity, diameter ratios, and pipe fittings (e.g., elbows and risers) on the flow of Taylor bubbles will be conducted.
A cascaded phase-field lattice Boltzmann model for the simulation of incompressible, immiscible fluids with high density contrast
Abstract
In this work, a conservative phase-field model for the simulation of immiscible multiphase flows is developed using an incompressible, velocity-based, cascaded lattice Boltzmann method (CLBM). Extensions are made to the lattice Boltzmann (LB) equations for interface tracking and incompressible hydrodynamics, proposed by Fakhari et al. [1], by performing relaxation operations in central moment space. This was motivated by the work of Fei et al. [2,3], where promising results from such a transformation were observed. The relaxation of central moments is defined in a reference frame moving with the fluid, while the existing multiple-relaxation time [4,5] scheme performs collision in a fixed frame of reference. Moreover, the derivations make use of continuous, Maxwellian distribution functions. As a result, the CLBM enhances the Galilean invariance and stability of the method when high lattice Mach numbers are evident. The cascaded scheme has been previously used in the literature to simulate multiphase flows based on the pseudo-potential model, where it allowed for high density and viscosity contrasts to be captured [6,7]. Here, the CLBM is implemented within the phase-field framework and is verified through the analysis of a layered Poiseuille flow. The performance of the CLBM is then investigated in terms of spurious currents, Galilean invariance and computational efficiency. Finally, the work of Fakhari et al. [1] is extended by validating the model’s ability to capture the relation between surface tension and the rise velocity of a planar Taylor bubble, in both stagnant and flowing fluids. New counter-current results indicate that the rise velocity model of Ha-Ngoc and Fabre [8] also applies in this regime.
Analysis of Taylor bubble dynamics via high-fidelity numerical modelling
Abstract
This study analyses the propagation of Taylor bubbles through vertical and inclined annular pipes. An established phase-field lattice Boltzmann method (PFLBM) was employed to resolve the multiphase flow dynamics. This analysis was motivated by the two-phase slug flow commonly observed in oil and gas wells and pipelines. The work makes contributions to two fundamental areas relating to Taylor bubbles in annular pipes. Firstly, the derivation of a drift velocity correlation for Taylor bubbles in vertical annular pipe is presented. The database covered fluids with Eötvös numbers between 10 and 700 and Morton numbers between 10-6 and 100. From here, the incorporation of inclination effects is discussed along with the respective correlation. Future work will assess the effects of pipe eccentricity as well as the interaction of consecutive Taylor bubbles. Furthermore, model development has also begun to study non-Newtonian and thermal effects.
Lattice Boltzmann modelling of a regularised Kuang-Luo fluid in a carotid artery
Abstract
In this work, a novel lattice Boltzmann (LB) framework for the simulation of non-Newtonian fluids was applied to study the flow of blood in a carotid artery. For this, the Kuang-Luo (KL) rheological model was used to represent the blood as a homogeneous continuum. This captured the primary non-Newtonian characteristics of blood, namely visco- and pseudo-plasticity. The study makes two major contributions to the field. Firstly, it addresses the numerical complexities associated with the yield stress in the KL model through regularisation of the constitutive equation. Secondly, the developed model was applied to simulate transient blood flow in a carotid artery geometry. Two oscillatory pressure profiles are applied to examine the importance of inflow conditions on wall shear stress. The preliminary, high-fidelity analysis of this geometry provided insight into flow characteristics that will be of interest to future investigations of clinical problems.
Development and evaluation of multiphase closure models used in the simulation of unconventional wellbore dynamics
Abstract
A detailed understanding of wellbore flow is essential for production engineers in both the design of site equipment and optimisation of operation conditions. With the depletion of conventional resources, the need for unconventional extraction techniques to leverage untapped reserves has seen the generation of new downhole flow conditions. In particular, the extraction of natural gas from coal seams has led to scenarios where liquid removal from the reservoir can cause the development of a counter-current multiphase flow in the well annulus in pumped wells. In this work, high-fidelity computational fluid dynamics is used to capture the momentum interaction between gas and liquid phases in such a flow configuration, allowing for the evaluation and modification of closure relations used in upscaled models. The computational fluid dynamics model is based on a recently proposed formulation developed using phase-field theory in the lattice Boltzmann (LB) framework. It has been previously applied to the analysis of Taylor bubbles in tubular and annular pipes at a range of inclinations and flow directions. The robustness of the numerical formulation has been proven with a range of benchmark scenarios that extend upon previously reported results in the LB literature. Future investigations will look to apply the developed closure relations into the two-fluid model and compare with in-house experimental and mechanistic results. Using the multiphase lattice Boltzmann model, the drag force closure relations are investigated for bubbles covering a range of parameters. This assesses the accuracy of existing closures and provides confidence in the developed computational tool. Following on from this, the size of the liquid slug behind a Taylor bubble is analysed. Comparison of the results with pre-existing relations provides a means to modify current large-scale simulators to accurately capture the momentum exchange between gas and liquid phases in a wellbore. With the improved understanding of phase interactions developed in this study, upscaling work is to be conducted through the implementation of closure models within a two-fluid-type model, not unlike OLGA, as well as in a recent mechanistic model. The novelty of the high-fidelity computational model is in its ability to resolve high density ratio (liquid-gas) flows under complex, dynamic conditions within the lattice Boltzmann framework. Additionally, the development and validation of novel closure relations for mechanistic and two-fluid models improves the accuracy of predictions associated with wellbore operations, ultimately allowing for more optimised production.
Development of a three-dimensional phase-field lattice Boltzmann method for the study of immiscible fluids at high density ratios
Abstract
Based on the recent work by Fakhari et al. (2017b), a three-dimensional phase-field lattice Boltzmann method was developed to investigate the rise of a Taylor bubble in a duct. The proposed approach couples the conservative phase-field equation with a velocity-based lattice Boltzmann scheme equipped with a weighted multiple-relaxation-time collision operator to enhance numerical stability. This makes the model ideal for numerical simulation of immiscible fluids at high density ratios and relatively high Reynolds numbers. Several benchmark problems, including the deformation of a droplet in a shear flow, the Rayleigh–Taylor instability, and the rise of a Taylor bubble through a quiescent fluid, were considered to asses the accuracy of the proposed solver. The Rayleigh–Taylor instability simulations were conducted for a configuration mimicking an air-water system, which has received little attention in the literature. After detailed verification and validation, the presented formulation was applied to study the flow field surrounding a Taylor bubble, for which numerical results were compared with the experimental work of Bugg and Saad (2002). The findings highlighted that the experimental bubble rise velocity, instantaneous flow field, and interface profile can be accurately captured by the presented model. In particular, the rise velocity of the present model indicated an improvement in accuracy when compared to the reference numerical solutions. The agreement between various numerical schemes, in some instances, indicated potential experimental difficulties in measuring the local flow field. Future application of the present model will facilitate detailed investigation of the pressure and flow profile surrounding Taylor bubbles evolving in co-current and counter-current flows.
Improved locality of the phase-field lattice-Boltzmann model for immiscible fluids at high density ratios
Abstract
Based on phase-field theory, we introduce a robust lattice-Boltzmann equation for modeling immiscible multiphase flows at large density and viscosity contrasts. Our approach is built by modifying the method proposed by Zu and He [Phys. Rev. E 87, 043301 (2013)PLEEE81539-375510.1103/PhysRevE.87.043301] in such a way as to improve efficiency and numerical stability. In particular, we employ a different interface-tracking equation based on the so-called conservative phase-field model, a simplified equilibrium distribution that decouples pressure and velocity calculations, and a local scheme based on the hydrodynamic distribution functions for calculation of the stress tensor. In addition to two distribution functions for interface tracking and recovery of hydrodynamic properties, the only nonlocal variable in the proposed model is the phase field. Moreover, within our framework there is no need to use biased or mixed difference stencils for numerical stability and accuracy at high density ratios. This not only simplifies the implementation and efficiency of the model, but also leads to a model that is better suited to parallel implementation on distributed-memory machines. Several benchmark cases are considered to assess the efficacy of the proposed model, including the layered Poiseuille flow in a rectangular channel, Rayleigh-Taylor instability, and the rise of a Taylor bubble in a duct. The numerical results are in good agreement with available numerical and experimental data.
A critical review of flow maps for gas-liquid flows in vertical pipes and annuli
Abstract
The accurate prediction of two-phase gas and liquid flow regimes is important in the proper design, operation and scale-up of pressure management and fluid handling systems in a wide range of industrial processes. This paper provides a comprehensive review of 3947 published experimental data points for gas-liquid flow maps in vertical pipes and annuli, including a critical analysis of state-of-the-art measurement techniques used to identify bubble, slug, churn and annular flow regimes. We examine the critical factors of pipe geometry (diameters, deviation from vertical), fluid properties and flow conditions that affect the transition from one flow regime to another. The review surveys the theoretical models available to predict flow regime transitions, and we validate the accuracy of these models using the published experimental data. The most reliable flow regime transition models for upward co-current flows are analytically shown to be: (i) Barnea 1987 for dispersed bubble to bubble flow, (ii) Taitel et al. 1980 for bubble to slug flow, (iii) Barnea 1987 for slug to churn flow, and (iv) Mishima and Ishii 1984 for churn to annular flow regime transition. Moreover, based on the review we provide an outlook on the research needs and important developments in prediction of two-phase flow in vertical pipes including the use of computational fluid dynamics (CFD) techniques to simulate gas-liquid flows in vertical geometries.
Micromechanical investigation of fines liberation and transport during coal seam dewatering
Abstract
The reduction of subsurface hydrostatic pressure to allow natural gas desorption is an integral step in the production of coal seam gas (CSG). During this dewatering stage, viscous stresses can cause the liberation and transport of fines, which are predominantly comprised of inorganic clay groups such as smectite, illite and kaolin, from within the coal matrix. Dislodged particles migrate in production fluid through fractures towards the wellbore where capture and deposition can deteriorate the reservoir’s permeability. Once in the wellbore, these particles can adversely affect the performance of mechanical equipment such as pumps. This study uses direct numerical simulation of a synthetic coal fracture to help elucidate the particle detachment process. This is approached using a coupled lattice Boltzmann-discrete element method to capture both physical and physicochemical interactions based on Derjaguin-Landau-Verwey-Overbeek (DLVO) theory. Preliminary testing with the developed model suggests that particles move almost freely along the bounding surface regardless of electrostatic interactions, and that Hele-Shaw predictions of particle lift in particular can be inadequate. Further, larger-scale simulations indicated that the DLVO parameters can significantly impact the vertical position of propagating fines with variations in eroded mass of over 100% observed for the range of tested salinity levels.
Characterising the behaviour of hydraulic fracturing fluids via direct numerical simulation
Abstract
Current design tools used for predicting the placement of proppant in fractures are based on the solution of a simplified conservation equation that is heavily dependent on empirical relationships for particle settling and suspension viscosity. In light of these shortcomings, this paper presents the development of a computational fluid dynamics (CFD) model capable of micromechanical simulation of hydraulic fracturing fluids. The model developed in this research employs the discrete element method (DEM) to represent the proppant for a range of sizes and densities. For the fluid phase, the lattice Boltzmann method (LBM) is utilised in a generalised-Newtonian form. Full hydrodynamic coupling of the LBM and DEM is achieved via an immersed moving boundary condition. The developed model has the ability to simulate Navier-Stokes hydrodynamics, a range of rheological models (e.g. Bingham, power law), thermal effects as well as electromagnetic and electrostatic forces between particles and walls. The model captures the detailed interactions of proppant particles as well as the non-Newtonian rheology of the fracturing fluid in both experimental and fracture geometries. Simulations of small-scale experiments are used to describe suspension rheology as a function of proppant concentration while small-scale fracture models explore the settling and injection of a number of candidate formulations. These results show that the direct numerical simulation (DNS) approach presented in this paper represents a potentially valuable complement to contemporary models which can provide insight on the rheology of new or novel fracturing fluid formulations as well as explore the influence of complex in-situ features on the efficacy of a hydraulic fracture. More detailed knowledge of how proppant is transported from the wellbore to the fracture tip will provide insights that could be used in the optimisation of the hydraulic fracturing process. This is particularly relevant in coal seam gas reservoirs which can include bi-directional fracture networks, non-planar fracture paths, interburden terminations and other leak-off points.