A mathematical model was developed to describe the hydrodynamics of a batch reactor for aluminum degassing utilizing the rotor-injector technique. The mathematical model uses the Eulerian algorithm to represent the two-phase system including the simulation of vortex formation at the free surface, and the use of the RNG k-ε model to account for the turbulence in the system. The model was employed to test the performances of three different impeller designs, two of which are available commercially, while the third one is a new design proposed in previous work. The model simulates the hydrodynamics and consequently helps to explain and connect the performances in terms of degassing kinetics and gas consumption found in physical modeling previously reported. Therefore, the model simulates a water physical model. The model reveals that the new impeller design distributes the bubbles more uniformly throughout the ladle, and exhibits a better-agitated bath, since the transfer of momentum to the fluids is better. Gas is evenly distributed with this design because both phases, gas and liquid, are dragged to the bottom of the ladle as a result of the higher pumping effect in comparison to the commercial designs.

This review presents an analysis and discussion about heat transfer phenomena during quenching solid steel from high temperatures. It is shown a description of the boiling curve and the most used methods to characterize heat transfer when using liquid quenchants. The present work points out and criticizes important aspects that are frequently poorly attended in the technical literature about determination and use of the boiling curve and/or the respective heat transfer coefficient for modeling solid phase transformations in metals. Points to review include: effect of initial workpiece temperature on the boiling curve, fluid velocity specification to correlate with heat flux, and the importance of coupling between heat conduction in the workpiece and convection boiling to determine the wall heat flux. Finally, research opportunities in this field are suggested to improve current knowledge and extend quenching modeling accuracy to complex workpieces.

This paper addresses the problem of understanding the relationship between fluid flow and heat transfer in industrial quenching systems. It also presents an efficient analysis to design or optimize long standing quenching tanks to increase productivity. The study case is automotive leaf springs quenched in an oil-tank agitated with submerged jets. This analysis combined an efficient numerical prediction of the detailed isothermal flow field in the whole tank with the thermal characterization of steel probes in plant and laboratory during quenching. These measurements were used to determine the heat flow by solving the inverse heat conduction problem. Differences between laboratory and plant heat flux results were attributed to the difference in surface area size between samples. A proposed correlation between isothermal wall shear stress and heat flux at the surface of the steel component, based on the Reynolds-Colburn analogy, provided the connection between thermal characterization and computed isothermal fluid flow. The present approach allowed the identification of the potential benefits of changes in the tank design and the evaluation of operating conditions while using a much shorter computing time and storage memory than full-domain fluid flow calculations.

This work is focused on developing a computational model to predict the production rate and pressure evolution of natural gas from unconventional reservoirs, particularly shale gas deposits. The model is based on the principle of conservation of mechanical energy and was developed from the transient solution of Bernoulli’s equation. This solution was obtained by computing the pressure evolution in the well resulting from the combined action of extracting the free gas and of gasification from kerogen. The transient behavior of gas production by hydraulic fracturing was calculated by numerically integrating Bernoulli’s equation. The curves representing gas flow evolution were considered as a series of stepwise steady states under a constant gas flow rate, similar to the pressure–time curves. These time steps were connected by instantaneous drops in pressure or gas flow rates. On the other hand, the delayed release of the adsorbed and dissolved gas in the kerogen was accurately calculated by introducing a semi-empirical gas pressure source term into the gas well pressure equation. The effect of this source is to gradually increase the gas pressure in the reservoir, emulating the gas release mechanisms from the organic matter. Model validation was based on production data from the unconventional reservoirs Eagle Ford, U.S.A., and Burgos basin, México. The initial measured gas production rate was used to determine a global friction factor of the gas flowing out from soil cracks and ducts. Additionally, measured production rate data were used to determine the coefficients of the source term function. Pearson correlation coefficients of 0.97 and 0.96 were obtained for Eagle Ford and Burgos basins data, respectively. In contrast, the corresponding coefficients calculated from the traditional Arps’ model were 0.89 and 0.5, respectively. The present pressure source model (PSM) represents a new approach to characterize the process of gas production from unconventional reservoirs, proving to be accurate in forecasting both the gas flow rate and pressure evolution during gas production. The postulated pressure source term was shown to mimic the desorption and diffusion kinetics, which release free gas from the kerogen.