Comparison of computational fluid dynamics (CFD) and pressure drop correlations in laminar flow regime for packed bed reactors and columns

Transient Pressure Behavior of CBM Wells during the Injection Fall-Off Test Considering the Quadratic Pressure Gradient

Conventional coalbed methane (CBM) reservoir models for injection fall-off testing often disregard the quadratic pressure gradient's impact. This omission leads to discrepancies in simulating the transient behavior of formation fluids and extracting critical reservoir properties. Accurate determination of permeability, storability, and other properties is crucial for effective reservoir characterization and production forecasting. Inaccurate estimations can lead to suboptimal well placement, ineffective production strategies, and ultimately, missed economic opportunities. To address this shortcoming, we present a novel analytical model that explicitly incorporates the complexities of the quadratic pressure gradient and dual-permeability flow mechanisms, prevalent in many CBM formations where nanopores are rich, presenting a kind of natural nanomaterial. This model offers significant advantages over traditional approaches. By leveraging variable substitution, it facilitates the derivation of analytical solutions in the Laplace domain, subsequently converted to real-space solutions for practical application. These solutions empower reservoir engineers to generate novel type curves, a valuable tool for analyzing wellbore pressure responses during injection fall-off tests. By identifying distinct flow regimes within the reservoir based on these type curves, engineers gain valuable insights into the dynamic behavior of formation fluids. This model goes beyond traditional approaches by investigating the influence of the quadratic pressure gradient coefficient, inter-porosity flow coefficient, and storability ratio on the pressure response. A quantitative comparison with traditional models further elucidates the key discrepancies caused by neglecting the quadratic pressure gradient. The results demonstrate the proposed model's ability to accurately depict the non-linear flow behavior observed in CBM wells. This translates to more reliable pressure and pressure derivative curves that account for the impact of the quadratic pressure gradient.

Digital Twin for the Prediction of Extreme Loads on a Wave Energy Conversion System

Wave energy is a renewable energy source with the potential to contribute to the global electricity demand, but a remaining challenge is the survivability of the wave energy converters in harsh offshore conditions. To understand the system dynamics and improve the reliability, experimental and numerical studies are usually conducted. However, these processes are costly and time-consuming. A statistical model able to provide equivalent results is a promising approach. In this study, the digital twin of the CFD solution is developed and implemented for the prediction of the force in the mooring system of a point-absorber wave energy converter during extreme wave conditions. The results show that the digital twin can predict the mooring force with 90.36% average accuracy. Moreover, the digital twin needs only a few seconds to provide the solution, while the CFD code requires up to several days. By creating a digital analog of a wave energy converter and showing that it is able to predict the load in critical components during extreme wave conditions, this work constitutes an innovative approach in the wave energy field.

Thermochemical Analysis of a Packed-Bed Reactor Using Finite Elements with FlexPDE and COMSOL Multiphysics

This work presents the thermochemical analysis of a packed-bed reactor via multi-dimensional CFD modeling using FlexPDE and COMSOL Multiphysics. The temperature, concentration, and reaction rate profiles for methane production following the Fischer–Tropsch (F-T) synthesis were studied. To this end, stationary and dynamic differential equations for mass and heat transfer were solved via the finite element technique. The transport equations for 1-D and 2-D models using FlexPDE consider dispersion models, where the fluid and the catalyst can be treated as either homogeneous or heterogenous systems depending on the gradient extents. On the other hand, the 3-D model obtained in COMSOL deems the transport equations incorporated in the Porous Media module. The aim was to compare the FlexPDE and COMSOL models, and to validate them with experimental data from literature. As a result, all models were in good agreement with experimental data, especially for the 2-D and 3-D dynamic models. In terms of kinetics, the predicted reaction rate profiles from the COMSOL model and the 2-D dynamic model followed the temperature trend, thus reflecting the temperature dependence of the reaction. Based on these findings, it was demonstrated that applying different approaches for the CFD modeling of F-T processes conducts reliable results.

A novel computational simulation approach to study biofilm significance in a packed-bed biooxidation reactor

Fe (II) biooxidation has recently gained significant interest. It plays a key role in a number of environmental and industrial processes such as bioleaching, acid mine drainage treatment, desulphurization of sour gases, and coal desulphurization. In this work, a three-dimensional CFD model for gas-liquid flow in a lab-scale packed-bed biooxidation reactor is used. The reactor is randomly packed with spherical particles, and the particles are covered with Leptospirillum ferrooxidans biofilm for Fe (II) biooxidation. A modified Jodrey-Tory algorithm is used to generate random packing with actual porosity of 0.42, and biofilm layer with constant thickness is considered over the particles. A simplified Eulerian-Eulerian model is used to obtain detailed flow field. The concentration profile in the reactor and the conversion of Fe (II) from the present simulations are obtained and validated using experimental data reported in the literature. The results of the study indicate that about three-quarters of the conversion occurs in the upper half of the reactor and Fe (II) concentration on the biofilm surface at the lower quarter of the reactor does not exceed 5 mM (The inlet concentration is 89.6 mM). The findings reveal that rate-limiting phenomena may vary in different parts of the reactor. The results obtained through the simulations represent advantages for the design and optimization of packed-bed biofilm reactors.

Computational Fluid Dynamics for Fixed Bed Reactor Design

Flow, heat, and mass transfer in fixed beds of catalyst particles are complex phenomena and, when combined with catalytic reactions, are multiscale in both time and space; therefore, advanced computational techniques are being applied to fixed bed modeling to an ever-greater extent. The fast-growing literature on the use of computational fluid dynamics (CFD) in fixed bed design reflects the rapid development of this subfield of reactor modeling. We identify recent trends and research directions in which successful methodology has been established, for example, in computer generation of packings of complex particles, and where more work is needed, for example, in the meshing of nonsphere packings and the simulation of industrial-size packed tubes. Development of fixed bed reactor models, by either using CFD directly or obtaining insight, closures, and parameters for engineering models from simulations, will increase confidence in using these methods for design along with, or instead of, expensive pilot-scale experiments.

Synthetic Packed-Bed Generation for CFD Simulations: Blender vs. STAR-CCM+

A common reactor type in the chemical and process industry is the fixed-bed reactor. Accurate modeling can be achieved with particle-resolved computational fluid dynamic (CFD) simulations. However, the underlying bed morphology plays a paramount role. Synthetic bed-generation methods are much more flexible and faster than image-based approaches. In this study, we look critically at the two different bed generation methods: Discrete element method (DEM) (in the commercial software STAR-CCM+) and the rigid-body model (in the open-source software Blender). The two approaches are compared in terms of synthetically generated beds with experimental data of overall and radial porosity, particle orientation, as well as radial velocities. Both models show accurate agreement for the porosity. However, only Blender shows similar particle orientation than the experimental results. The main drawback of the DEM is the long calculation time and the shape approximation with composite particles.

Analysis of Mass Transport through Anisotropic, Catalytic/Bio-Catalytic Membrane Reactors

This paper investigated the steady-state mass transport process through anisotropic, composite membrane layers with variable mass transport coefficients, such as the diffusion coefficient, convective velocity, or chemical/biochemical reaction rate constant. The transfer processes can be a solution-diffusion model or diffusive plus convective process. In the theoretical part, the concentration distribution as well as the inlet and outlet mass transfer rates’ expressions are defined for physical transport processes with variable diffusion or solubility coefficients and then that for transport processes accompanied by first- and zero-order reactions, in the presence of diffusive and convective flow, with constant and variable parameters. The variation of the transport parameters as a function of the local coordinate was defined by linear equations. It was shown that the increasing diffusion coefficient or convective flow induces much lower concentrations across the membrane layer than transport processes, with their decreasing values a function of the space coordinate. Accordingly, this can strongly affect the effect of the concentration dependent chemical/biochemical reaction. The inlet mass transfer rate can also be mostly higher when the transport parameter decreases across the anisotropic membrane layer.