Hydrodynamic Limitations of Microchannel Fischer-Tropsch Reactor Operation ()
1. Introduction
The Fischer-Tropsch synthesis is a key step in the process of synthetic crude production from natural gas or other carbon-containing feedstock. The chemistry of the process includes conversion of syngas (CO and H2 mixture) into hydrocarbons over Co metal or Fe metal catalyst. The molecular mass distribution of produced hydrocarbons obeys Anderson-Schulz-Flory law [1]. The maximum of the distribution is determined by chain growth coefficient
. For higher value of 
the heavier hydrocarbons dominate the product. It is attractive to run the Fischer-Tropsch reaction at
, which gives the molecular mass distribution close to that of diesel fuel.
Currently are realized two types of Fischer-Tropsch reactors in industrial practice, namely slurry-bed reactors and fixed-bed reactors. Both types of the reactors possess certain advantages and drawbacks related with thermal stability, diffusion limitations and aerodynamic resistance.
The recent successes in microchannel fabrication technologies have led to very active research and development of microchannel systems for Fischer-Tropsch synthesis as a challenge to conventional slurry-bed and fixed-bed reactors [2-6]. Cobalt catalyst microparticles of 50 - 300 µm size get deposited on the inner surface of a microchannel thus forming a randomly roughed inner surface. Such micro reactors promise easy transport of syngas to catalyst surface and excellent heat removal conditions. The efficiency of a microchannel system increases with decrease in the microchannel diameter. However, the hydrodynamic resistance can ruin the reactor operation even at very good diffusion and hat removal efficiencies. The importance of hydrodynamic resistance cannot be overestimated. It is difficult, however, to estimate this value.
Indeed, experimental measurements must be carried out with the use of gas-liquid mixtures of proper composition, which changes along the channel, otherwise the results cannot be correct. The computational methods available in literature are good for modeling flow in smooth channel, without taking into account evolution of properties and composition along the channel [7-9]. It is necessary to note that hydrodynamics of smooth-walled and rough-walled channels can be dramatically different even for laminar flow. Another important factor is that literature computational methods suggest that gas flow and liquid film flow are considered as independent, which results in substantial error in liquid film thickness value [10].
This work is devoted to investigation of hydrodynamic resistance in microchannel Fischer-Tropsch reactors and its influence on the reactor operation. Theoretical model was published in our previous work [11], where conjugated flow of gaseous and liquid Fischer-Tropsch products of variable composition was considered. The gaseous and liquid flows were modeled in annular flow approximation, while inertia, surface tension and hydrodynamic interaction of phases at interphase boundary are taken into account. Presented work models the randomly roughed internal surface of microchannels in accordance with the technology of catalyst microparticles deposition. The difference in modeling of smooth-walled and rough-walled channels is investigated. The dependencies of hydrodynamic resistance on syngas flow rate, chain growth coefficient
, conversion rate, temperature and pressure are modeled. The limitations of microreactor operation are studied, up to determination of conditions for complete flooding of a microchannel.
2. Formulation of the Problem. The Basic Equations
It is consider a vertical cylindrical microchannel. Procedure of numerical generation a random surface inside the ceramic microchannel is carried out in accordance with the technical method of coating the channel walls by catalyst microparticles. It is selected the average number of spherical particles per unit length of the microchannel. For cylindrical coordinate system microparticles are modeled as random rings located on the perimeter of the cylinder. The distance between the micro inclusions and the height of the roughness are also independent random variables. The number of particles is recalculated in order to preserve a given volume fraction of particulate catalyst inside the microchannel. Volume fraction of cobalt particles is in the range 20% - 30%.
Figure 1 illustrates sketch of an element of the channel with random roughness and with a liquid film. The liquid film flows down along inner surface of a cylindrical microchannel, and the gas moves inside a cylinder of liquid formed by the outer surface of the film. Film velocity is determined by the force of gravity and shear stresses on the gas-liquid interface boundary. Shear stress at the gas-liquid boundary depends on the thickness and diameter of the gas stream. The pressure gradient in the channel is determined by the combined flow of the liquid