This paper treats the separation of particles in microchannels relevant to biological and industrial process engineering. To elucidate the mechanisms creating uneven distribution of particles over the cross section, simulations are conducted with the particles being geometrically resolved and coupled to the fluid by an immersed-boundary method. In a first step, the method is validated for particle focusing in straight channels. Beyond validation, new information not previously available is reported for these cases. Next, an efficient approach is presented to simulate the motion of particles in spiral ducts of small curvature by means of a well-controlled set of approximate equations. It is applied here to situations with spherical particles and validated with reference data for inertial migration in curved channels achieving good agreement. The simulation data provide new rich information on the details of the separation process concerning migration time, particle positioning in the cross section, streamwise particle spacing, and velocity field of the continuous phase. For concentrations smaller than 1%, three different focusing modes are observed: single position, two symmetric positions, and periodic trajectories oscillating between two focusing points. Another set of results is obtained with particle concentrations up to 10% in a curved channel. Here, the spatial distribution of particles is determined in a statistical sense and related to the mean flow of the continuous phase. While focusing is reduced with increasing particle concentration, the distribution of particles is found to be still far from uniform up to the investigated concentration level.

The article describes direct numerical simulations using an Euler–Lagrange approach with an immersed‐boundary method to resolve the geometry and trajectory of particles moving in a flow. The presentation focuses on own work of the authors and discusses elements of physical and numerical modeling in some detail, together with three areas of application: microfluidic transport of spherical and nonspherical particles in curved ducts, flows with bubbles at different void fraction ranging from single bubbles to dense particle clusters, some also subjected to electro‐magnetic forces, and bedload sediment transport with spherical and nonspherical particles. These applications with their specific requirements for numerical modeling illustrate the versatility of the approach and provide condensed information about main findings.

Summary The thermal behavior of a deepwater well was simulated by use of an existing mathematical model in which a rigorous flow-pattern-based multiphase-flow formulation is used to predict the pressure drop of the hydrocarbon stream. The heat-transfer model relied on the energy equation applied to the hydrocarbon mixture and on a radial thermal-resistance network between the wellbore and the formation. Different annulus-convection and thermal-formation models were evaluated. Production pressure and temperature results were compared with field data and with a commercial software package, showing good agreement with both. The model was able to capture important quantitative phenomena associated with the wellbore-heat transmission (e.g., lithologic column and annulus-fluid type). More specifically, the simulations showed that, for short production times, the heat transfer to the formation was significantly influenced by the wellbore-thermal resistances—namely, the cement sheaths and the nitrogen present in the production annulus. As the production time increased, the formation became the dominant thermal resistance.

The paper analyzes the migration of non-spherical particles in curved micro-channels. Inertial migration combined with Dean drag results in a reduced set of stable focusing positions in specific regions of the cross section of the channel. These are studied using fully resolved transient simulations of particulate flows in rectangular curved ducts with oblate and prolate particles at a bulk Reynolds number of 100 and dilute particle concentrations. The simulations were conducted with four particles in a periodic domain, instead of only one, as common practice, to investigate the particle interaction. It is observed that the focusing positions are different for the non-spherical particles compared to those obtained with spherical ones. Not only non-spherical particles focus closer to the upper and lower walls, but also their focusing position is closer to the half width of the channel. Furthermore, the migration velocity along the cross section is compared between particle shapes. Results show that all shapes lead to a significant change in migration velocity between outer and inner halves of the channel. This effect is substantially more pronounced for non-spherical particles and is observed for the first time here. It offers an independent possibility for particle separation according to shape.

The thermal behavior of a deepwater well was simulated using an existing mathematical model in which a rigorous flow-pattern based multiphase flow model was employed to predict the pressure drop of the hydrocarbon stream. The heat transfer model relied on the energy equation for the hydrocarbon mixture and on a radial thermal resistance network between the wellbore and the formation. Different annulus convection and thermal formation models were evaluated. Production pressure and temperature results were compared with field data and with a commercial software package, showing good agreement with both. The model was able to capture important quantitative phenomena associated with the wellbore heat transmission (e.g., lithologic column and annulus fluid type). The simulations showed that for short production times the heat transfer to the formation was significantly influenced by the wellbore thermal resistances, namely the cement sheaths and the nitrogen present in the production annulus. As the production time increased, the formation became the dominant thermal resistance. The mathematical model was capable of handling real production scenarios, such as the impact of a watercut time-dependent behavior on the temperature distribution in the wellbore.