Assessment of the Energy Efficiency of Ammonia Production by Microbubbles

Abstract

The present paper investigates the energy efficiency of ammonia production by a freely oscillating microbubble placed in an infinite domain of liquid. The spherical bubble initially contains a mixture of nitrogen and hydrogen. The bubble is expanded from its equilibrium size to a specific maximum radius via an isothermal expansion. The work needed to expand the bubble is its potential energy calculated by the sum of the work done by the internal gas, the work needed to displace the mass of the surrounding liquid, and the work needed to increase the area of the bubble against the surface tension. During the radial pulsation of the freely oscillating bubble, the internal temperature can reach several thousands of degrees of Kelvin inducing chemical reactions. The chemical yield is computed by solving a set of ordinary differential equations describing the radial dynamics of the bubble (Keller—Miksis equations), the temporal evolution of the internal temperature (first law of thermodynamics), and the concentration of the chemical species (reaction mechanism). The control parameters during the simulations were the equilibrium bubble size, initial expansion ratio, ambient pressure, and the initial concentration ratio of nitrogen and hydrogen. In the best-case scenario, the energy requirement in terms of GJ/t is 6.8 times higher than the best available facility of the Haber—Bosch process (assuming that the hydrogen is produced via the electrolysis of water).