In the direct reduction of iron oxide with gas as the reducing agent, a reduction reaction takes place. First, at the initial point of contact (chemical reaction) and then within the core as the gas penetrates the lump iron oxide (diffusion). The two mechanisms, together with the mass transfer of reactant products through the reduced mass, take place simultaneously. Understanding the dynamics of these mechanisms for a given iron oxide is a crucial factor in setting the reduction conditions to achieve the desired reduction degree (RD). A number of parameters influence the reduction dynamics ranging from the iron oxide properties to the reducing conditions that exist within the shaft of the furnace at a given time. Studies modeling the reduction process to get a good understanding of the direct reduction dynamics have been conducted: 1) within a shaft reactor [1] [2] [3] [4] ; 2) for iron oxide pellets and sinters reacting with carbon monoxide or hydrogen separately [1] [2] and as gas mixtures [3] [4] .

Reduction takes place as the reducing gas penetrates through the pores of the iron oxide and the mode of reduction will vary depending on the porosity. The larger the pore surface area, the smaller is the fraction of the total pore surface walls utilized in the reaction [4] . As reduction proceeds, the mean pore diameter increases. This means that some pores grow bigger in size and others are destroyed as reduction proceeds. Furthermore, for the case of CO as the reducing gas, the higher the concentration, the larger the resultant pore diameter [3] ; this implies increased reduction.

In studying the characteristics of pores of hematite iron reduced in hydrogen, Turkdogan and Vinters [2] noted that most of the pores in the reduced iron were interconnected. This may imply that H₂ gas penetrates the hematite core more than CO. This may explain the use of these two gases (H₂/CO) in combination during the reduction process. Though both have varying reduction potentials at different temperatures, it seems that H₂ creates passages in the iron ore core, which CO uses to reduce the core as reduction progresses.

Furthermore, that the pore area increased with a decreasing reduction temperature indicates a slowdown in the reduction process. The pore structure of the reduced iron becomes finer with a decreasing reduction temperature, leading to a decreased pore size, an increased pore surface area, and a decreased effective gas diffusivity [4] .

At the on-set of the hematite reduction, the gas-solid topochemical reactions produce a layer of metallic iron at the surface in contact with a wustite layer below it. Below the wustite layer, a magnetite layer surrounding a hematite core can be found. As the reduction progresses, the reducing gas thus has to diffuse through these layers as hematite is being reduced to its lower oxides. Various models have been developed to describe the reduction dynamics within the iron oxide [5] [6] [7] .

The grain model (GM) [5] assumes that solid conversion takes place around each grain within the sample. Also, that the reduction gas penetrates the pores of the solid and reduces the sample on the surface of each individual grain. The grains are assumed to be spherical, uniform and non-porous. The shrinking core phenomenon is thus applied on each individual grain. The volumetric model (VM) [6] considers the sample as a whole and assumes a homogenous conversion with a linearly decreasing reaction surface. The VM model does not account for the porous nature of the solid during the reduction process. The random pore model (RPM) [7] takes the overlapping of the pores within the solid into consideration. On this account, there is thus a total reduced pore area for gas penetration during the process of reduction. The model considers the effect of pore growth during the initial stages of reduction and the destruction of neighboring pores due to the overlapping during the reduction process.

None of these models may exclusively stand alone to fully describe the reduction kinetics. The GM model can describe reduction on a micro level within the oxide, but may fall short in giving a wholesome description of the reduction behavior. Grains also have various shapes and porosity. Thus, considering them to be homogenous may not give accurate results. However, it may predict the reduction kinetics of very porous iron oxides with a good degree of accuracy. The VM model may predict the reduction behavior of dense iron oxides more accurately, though in reality, there is no iron oxide that is completely without pores. The GM model and VM model may work well at predicting reduction dynamics of sinters and pellets whose physical properties can be controlled and determined during the process of their production. The RPM model gives a harmonized prediction between the above two models and may be closer to predicting the reduction kinetics of natural iron oxides.

In this study, the three models were applied to the experimental data of the reduced natural iron ore to identify which one provides a more accurate prediction of the natural iron ore conversion. With the identified model, the kinetics of direct reduction of the iron oxide can then be studied and understood. Since most of the previous studies have been carried out on sinters and pellets, the identified model can be used to study the kinetics of direct reduction of other naturally occurring iron ores.

A lump natural hematite iron ore from Muko deposit (Uganda), chemical composition given in Table 1, was crushed. The resulting sample pieces, with varying weights, were directly reduced in a reduction furnace. A mixture of H₂/CO (=1.5) was used as the reducing gas, at different flow rates with three reduction temperatures: 700˚C, 800˚C and 900˚C.

A schematic diagram of the thermo-gravimetric reduction equipment used in the experiments is shown in Figure 1. The detailed reduction procedure is described by Muwanguzi et al. [8] .

The reduction degree of iron ore (RD) achieved for the various samples was calculated using the following equation: