CFD Simulation of Flow through Packed Beds using the Finite Volume Technique

When a disordered packed bed, or any heterogeneous media is studied using computational fluid dynamics, the tortuous task of generating a domain and creating a workable mesh presents a challenging issue to Engineers and Scientists. In this Thesis these challenges are addressed in the form of three studies in which both traditional and novel techniques are used to generate packed beds of spheres and cylinders for analysis using computational fluid dynamics, more specifically, the finite volume method. The first study uses a Monte-Carlo method to generate random particle locations for use with a traditional CADbased meshing approach. Computational studies are performed and compared in detail with experimental equivalent beds. In the second study, where there is a need for actual, physical beds to be studied, magnetic-resonance-imaging is used coupled with a novel approach known as image based meshing. In parallel experimental studies are performed on the experimental bed and compared with computational data. In the third study, to overcome fidelity issues with the previous approaches, a physical packed bed is manufactured which is 100% geometrically faithful to its computational counterpart to provide a direct comparison. All three computational studies have shown promising results in comparison with the experimental data described in this Thesis, with the data of Reichelt (1972) and the semi-empirical correlation of Eisfeld & Schnitzlein (2001). All experiments and computational models were carried out by the author unless otherwise stated

Explicit numerical simulation of non-creeping single phase flow in porous media

Porous media and transport within them play important roles across industries and beyond, including in water and pollutant transport in soils, flow in petroleum and geothermal reservoirs, and water treatment in deep bed filtration to list just a few key examples. The study of such flows has traditionally been dominated by experiment. Simulation is, however, playing an increasing role in this field both because of the advent of X-ray microtomography (XRMT), which now permits the mapping of pore structures down to sub-micrometer resolution, and the ubiquitous availability of powerful compute clusters built on cheap commodity machines. Simulation in this context involves solving for the flow field in a model of a porous solid derived from XRMT - in this sense, the simulations mimic reality and are hence termed by us as explicit numerical simulation (ENS). The particular challenge in doing ENS is correctly solving the flow problem in extremely complex geometries. This challenge has led to the use of various methods such as lattice-gas automata (LGA) and the related lattice-Boltzmann method (LBM), which are particularly suited to resolving flows in complex geometries. All of this work to date has been restricted to low velocity flows termed Darcy flows because of limitations associated with LGA, LBM and other methods. There is, however, a range of applications where higher speed flows are of relevance and hence extension of the ENS approach to higher speed flows in porous media is important. This has been done here using an LGA model that does not include the deficiency of more standard LGA models that restricts them to slow flows. The thesis first details this little-known and used LGA model before demonstrating it on a range of benchmark problems. The model is then used to predict ab initio the hydrodynamic properties of a random packing from the Darcy to the turbulent regime. Comparison with experiment is excellent. The approach is then used to study, for the first time to our knowledge, the interstitial flow patterns from the Darcy to turbulent regimes

Pore-scale lattice Boltzmann simulations of inertial flows in realistic porous media: a first principle analysis of the Forchheimer relationship

With recent advances in the capabilities of high performance computing (HPC) platforms and the relatively simple representation of complex geometries of porous media, lattice Boltzmann method (LBM) has gained popularity as a means of solving fluid flow and transport problems. In this work, LBM was used to obtain flow parameters of porous media, study the behavior of these parameters at varying flow conditions and quantify the effect of roughness on the parameters by relating the volume averaged flow simulation results to Darcy and Forchheimer equations respectively. To validate the method, flow was simulated on regular and random sphere arrays in cubic domains, for which a number of analytical solutions are available. Permeability and non-Darcy coefficients obtained from the simulation compared well with Kozeny and Ergun estimates while deviation from the observed constant permeability and tortuosity values occurred aroundRe≈1-10. By defining roughness as hemispherical protrusions on the smooth spheres in the regular array, it was observed from flow streamlines obtained at different roughness heights that the average length of the flow paths increased with increasing roughness height. As such, the medium tortuosity and non-Darcy coefficient increased while the permeability decreased as height of the roughness increased. Applying the method to a 3D computed tomography image of Castlegate sandstone, the calculated macroscopic permeability and beta factor components were in good agreement with reported experimental values. In addition, LBM beta factors were compared with a number of empirical models for non-Darcy coefficient estimation and were found to be of the same order of magnitude as most of the correlations, although estimates of the models showed wide variation in values. Resolution of the original sample was increased by infilling with more voxels and simulation in the new domain showed better flow field resolution and higher simulated flow regimes compared to those of the original sample, without significant change in the flow parameters obtained. Using the Reynolds number based on the Forchheimer coefficient, the range of transition from Darcy to non-Darcy regime was within the values reported by Ruth and Ma (1993) and Zeng and Grigg (2006).

Computational analysis of transitional airflow through packed columns of spheres using the finite volume technique

Copyright © 2010 Elsevier. NOTICE: this is the author’s version of a work that was accepted for publication in Computers and Chemical Engineering. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Computers and Chemical Engineering, Volume 34 Issue 6 (2010), DOI: 10.1016/j.compchemeng.2009.10.013We compare computational simulations of the flow of air through a packed column containing spherical particles with experimental and theoretical results for equivalent beds. The column contained 160 spherical particles at an aspect ratio N=7.14N=7.14, and the experiments and simulations were carried out at particle Reynolds numbers of (RedP=700−5000)(RedP=700−5000). Experimental measurements were taken of the pressure drop across the column and compared with the correlation of Reichelt (1972) using the fitted coefficients of Eisfeld and Schnitzlein (2001). An equivalent computational domain was prepared using Monte Carlo packing, from which computational meshes were generated and analysed in detail. Computational fluid dynamics calculations of the air flow through the simulated bed was then performed using the finite volume technique. Results for pressure drop across the column were found to correlate strongly with the experimental data and the literature correlation. The flow structure through the bed was also analysed in detail

The impact of porous media heterogeneity on non-Darcy flow behaviour from pore-scale simulation

The effect of pore-scale heterogeneity on non-Darcy flow behaviour is investigated by means of direct flow simulations on 3-D images of a beadpack, Bentheimer sandstone and Estaillades carbonate. The critical Reynolds number indicating the cessation of the creeping Darcy flow regime in Estaillades carbonate is two orders of magnitude smaller than in Bentheimer sandstone, and is three orders of magnitude smaller than in the beadpack. It is inferred from the examination of flow field features that the emergence of steady eddies in pore space of Estaillades at elevated fluid velocities accounts for the early transition away from the Darcy flow regime. The non-Darcy coefficient β, the onset of non-Darcy flow, and the Darcy permeability for all samples are obtained and compared to available experimental data demonstrating the predictive capability of our approach. X-ray imaging along with direct pore-scale simulation of flow provides a viable alternative to experiments and empirical correlations for predicting non-Darcy flow parameters such as the β factor, and the onset of non-Darcy flow

Image-Based Pore-Scale Modeling of Inertial Flow in Porous Media and Propped Fractures

Non-Darcy flow is often observed near wellbores and in hydraulic fractures where relatively high velocities occur. Quantifying additional pressure drop caused by non-Darcy flow and fundamentally understanding the pore-scale inertial flow is important to oil and gas production in hydraulic fractures. Image-based pore-scale modeling is a powerful approach to obtain macroscopic transport properties of porous media, which are traditionally obtained from experiments and understand the relationship between fluid dynamics with complex pore geometries. In image-based modeling, flow simulations are conducted based on pore structures of real porous media from X-ray computed tomographic images. Rigorous pore-scale finite element modeling using unstructured mesh is developed and implemented in proppant fractures. The macroscopic parameters permeability and non-Darcy coefficient are obtained from simulations. The inertial effects on microscopic velocity fields are also discussed. The pore-scale network modeling of non-Darcy flow is also developed based on simulation results from rigorous model (FEM). Network modeling is an appealing approach to study porous media. Because of the approximation introduced in both pore structures and fluid dynamics, network modeling requires much smaller computational cost than rigorous model and can increase the computational domain size by orders of magnitude. The network is validated by comparing pore-scale flowrate distribution calculated from network and FEM. Throat flowrates and hydraulic conductance values in pore structures with a range of geometries are compared to assess whether network modeling can capture the shifts in flow pattern due to inertial effects. This provides insights about predicting hydraulic conductance using the tortuosity of flow paths,which is a significant factor for inertial flow as well as other network pore and throat geometric parameters

X-ray micro-tomography and pore network modeling of single-phase fixed-bed reactors.

A three-dimensional (3D) irregular and unstructured pore network was built using local topological and geometrical properties of an isometric bead pack imaged by means of a high-resolution X-ray computed micro-tomography technique. A pore network model was developed to analyze the 3D laminar/inertial(non-Darcy) flows at the mesoscopic (pore level) and macroscopic (after ensemble-averaging) levels. The non-linear laminar flow signatures were captured at the mesoscale on the basis of analogies with contraction and expansion friction losses. The model provided remarkably good predictions of macroscopic frictional loss gradient in Darcy and non-Darcy regimes with clear-cut demarcation using channel-based Reynolds number statistics. It was also able to differentiate contributions due to pore and channel linear losses, and contraction/expansion quadratic losses. Macroscopic mechanical dispersion was analyzed in terms of retroflow channels, and transverse and longitudinal Péclet numbers. The model qualitatively retrieved the Péclet-Reynolds scaling law expected for heterogeneous networks with predominance of mechanical dispersion. Advocated in watermark is the potential of pore network modeling to build a posteriori constitutive relations for the closures of the more conventional macroscopic Euler approaches to capture more realistically single-phase flow phenomena in fixed-bed reactor applications in chemical engineering

Image-Based Modeling of Porous Media Using FEM and Lagrangian Particle Tracking

The study of fundamental flow and transport processes at the pore scale is essential to understanding how the mechanisms affect larger, field-scale, processes that occur in oil and gas recovery, groundwater flow, contaminant transport, and CO2 sequestration. Pore-scale imaging and modeling is one of the techniques used to investigate these fundamental mechanisms. Although extensive development of pore-scale imaging and modeling has occurred recently, some areas still need further advances. In this work, we address two areas: (1) imaging of bulk proppants and proppant-filled fractures under varying loading stress and flow simulation in these systems and (2) nanoparticle (NP) transport modeling in porous media. These are briefly explained below. 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 routinely used in 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 which affect permeability and conductivity. Here, we use high-resolution x-ray computed tomography (XCT) to image two unsaturated rock/fracture/proppant systems under a series of stress levels typical of producing reservoirs: one with shale, one with Berea sandstone. 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 methods. NPs have been widely used commercially and have the potential to be extensively used in petroleum engineering as stabilizers in enhanced oil recovery operations or as tracers or sensors to detect rock and fluid properties. %In spite of a wide range of applications, many NP transport details are still unknown. In this work, we describe a Lagrangian particle tracking algorithm to model NP transport that can be used to better understand the impact of pore-scale hydrodynamics and surface forces on NP transport. Two XCT images, a Berea sandstone and a 2.5D micromodel, were meshed and used for image-based flow modeling of FEM Stokes flow. The effects of particle size, surface forces, flow rate, particle density, surface capacity, and surface forces mapped to XCT-image based mineralogy were studied