## 1 Introduction  
In the chemical and biological processing industries, absorption/dissolution of a gas in a liquid has been considered as one of the most important reactions in various processes, such as the Fisher-Tropch process, wastewater treatment, and fermentations. In these processes, mass transfer from the gas to the aqueous solution must occur for the target material to be usable. For instance, gaseous carbon monoxide should be dissolved in an aqueous solution while it is converted into liquid hydrocarbon during syngas fermentation. Furthermore, the dissolution of oxygen in an aqueous solution should take place for the oxygen to be available for aerobic microbial growth, during which biomass is produced. For these processes, vessels with mechanical stirring by means of multiple impellers are widely used [1, 2]. Over the past few decades, many aspects have been considered to examine the hydrodynamics of stirred tanks. [PERSON] and [PERSON] [3] utilized an optical probe to determine the flow regime of a laboratory-scale stirred tank. [PERSON] et al. [4] measured the local gas hold-up in a stirred tank reactor and compared this with CFD simulation results. [PERSON] et al. [5] carried out numerical simulations to understand the different fluid flow features of baffled and unbaffled vessels, and [PERSON] et al. [6] discussed gas hold-up and liquid velocity in a stirred tank under varied operating conditions. Although many studies have been conducted to determine the hydrodynamic characteristics in stirred tanks, they have focused on gas-liquid mass transfer, which is affected by these characteristics. The rate of mass transfer has been determined as the product of a volumetric mass transfer coefficient (\(k_{\rm L}a\)) and the difference between the saturation concentration and dissolved concentration of the transferred material in the liquid. The volumetric mass transfer coefficient is a function of the interfacial area (\(a\)) between a gas and liquid, and the liquid phase mass transfer coefficient (\(k_{\rm L}\)) [7]. Many studies have been carried out to experimentally determine the volumetric mass transfer coefficient, such as chemical methods using absorption of carbon dioxide or sulfite oxidation [8], and a dynamic method based on the measurement of dissolved gas concentration with time [2,9]. Several models have been proposed to determine \(k_{\rm L}\) and \(a\). Among them, the Higbie penetration model [10] and the Danckwert surface renewal model [11] have been widely accepted for gas-liquid mass transfer description. Computational fluid dynamics (CFD) coupled with the population balance model (PBM) has been introduced to simulate the complex hydrodynamic modeling of bubble distribution in stirred tanks to predict the gas-liquid interfacial area [12]. Because of the low solubility of the gas phase in the aqueous phase, the mass transfer rate usually dominates the overall rate of processes and determines the productivity of the systems. Therefore, the volumetric mass transfer coefficient (\(k_{\rm L}a\)) is selected as a criterion of scale-up and design of the reactors. However, by only considering the \(k_{\rm L}a\), it is difficult to estimate possible dead spots for microbial growth in such a syngas fermentation process. This is because, at all times, the dissolved gas is substantially transported by fluid flow, which means a low volumetric mass transfer coefficient does not directly imply a low dissolved gas concentration [13]. There are few studies showing the distribution of dissolved gas concentration in stirred tanks. [PERSON] and [PERSON] [7] showed the distribution of dissolved oxygen using several different types of mass transfer coefficient model. [PERSON] et al. [13] found a correlation between the dissolved oxygen concentration in a large-scale bioreactor and the possible dead zone for oxygen transfer.