(325c) Simulation of Full-Scale Open-Circuit, Multi-Compartment Cement Ball Mills: A New True Unsteady-State Simulator

The global demand for cement, as a common structural material for infrastructure, has progressively increased over the past decades, with world consumption already reaching 3.8 billion metric tons per annum by the early 2010s [1]. Cement manufacturing, however, involves energy-intensive processes that consume overall energy levels in the order of 100 kilowatt hours per metric ton of cement product. Of this consumption, 40% is accounted for by cement milling processes [2,3], where balling milling is used as the conventional cement milling technology. Ball milling can be performed under batch, continuous open-circuit, and continuous closed-circuit modes. Whereas batch ball milling is typically performed in a laboratory, continuous ball milling is operated as a full-scale process to achieve a high production rate [4]. In continuous open-circuit ball milling, feed material is continuously fed into the inlet of a mill and it is ground by grinding balls (see Fig. 1). Ball motion is initiated by the rotation of the shell, and the axial transport of the cement clinker particles is carried by the air stream and dispersion caused by ball–particle collisions. Balls hitting the powder bed results in breakage of the particles. Diaphragms (perforated partitions) are placed within and at the discharge end of the mill. As a rule of thumb [5], an open-circuit cement mill consists of three milling compartments with one discharge and two intermediate diaphragms. Particles finer than a diaphragm slot can pass onto the next compartment, whereas coarse particles are ground further until they fit into the slots. Intermediate diaphragms enable different degrees of milling (coarse and fine milling), whereas a discharge diaphragm mainly prevents grinding balls from being left from a mill. An internal mill shell is attached with a lining plate not only to prevent possible damage from grinding balls but also to increase milling performance. An example of this mechanism is a classifying liner, which appropriately segregates ball sizes along the length of an axial mill.

From the perspective of process engineering, the optimization of large-scale ball milling production by trial and error is costly and time-consuming. Without a strong fundamental understanding of this process, there is no guarantee that the best operation condition can be found. A reliable computer simulation would enable engineers to gain insight into complex milling processes and subsequently identify optimum operational conditions and bottlenecks in a system. Accordingly, in this study, we developed a novel true unsteady-state simulator (TUSSIM) on the basis of the solutions of a cell-based population balance model (PBM) (see Fig. 2). The cell-based discretization of the axial domain, along with the unknown cell residence time, leads to a set of differential-algebraic equations (DAEs). TUSSIM, coded in Matlab, provides an accurate, stable, and efficient numerical solution of the DAEs during both unsteady- and steady-state operations. Unlike other simulators [6,7], TUSSIM accounts for finite mixing, different ball mixtures, different ball size distributions (BSDs), internal classification in each compartment of ball mills, and the dynamic behaviors of the system.

In this study, TUSSIM was used to perform comprehensive simulations and explore the impact of ball sizes, ball mixtures, and number of compartments on the product size, which was reported in terms of specific surface area, median size, 10% passing size, and 90% passing size. First, the impacts of mixtures of different ball sizes (i.e., quaternary, ternary, and binary ball size mixtures as well as variable numbers of ball sizes) on product fineness were examined in comparison with the operations of a single ball size. Second, the quaternary ball size mixture was selected to investigate the impacts of three ball size distributions (BSDs): a uniform mass of balls (UM), a uniform number of balls (UN), and a uniform surface area of balls (USA). Moreover, the operation of the classifying liner in the last compartment of the mill was simulated to examine the benefits in terms of breakage kinetics. Finally, to assess why industry milling typically involves selecting three compartments for an open-circuit system, all simulations, except that on the BSDs, were repeated using a two-compartment configuration in which the second intermediate diaphragm of the mill was removed.

Overall, the results from TUSSIM simulations largely agree with various experimental observations and justify several common industry best practices. One of the important insights gained from them is that ball mixtures led to finer products than single ball size, consistent with industry practice [5]. Additionally, the binary mixture produced slightly finer products than those obtained using the ternary and quaternary mixtures, which aligns with experimental observations in lab-scale ball mills [8]. This finding, however, contrasts with industry practice, as three to five ball sizes are normally used [6,9]. This difference can be rationalized when ball wear is considered; using two considerably different ball sizes in a mixture may lead to a higher wear rate, and smaller balls can be potentially broken down by the larger balls. Hence, a binary mixture with two widely different sizes would not be favorable due to increased wear, albeit being favorable from a breakage kinetics perspective. Regarding the impact of BSDs, the UM distribution resulted in finer products than those generated via UN and USA, which is reasonable because UM involved more fraction of small balls compared with those used in UN and USA. The use of the classifying liner in the last compartment enabled suitable spatial variations in ball size along the axial length, resulting in finer products than those produced under spatially uniform mixed ball sizes. Finally, having the same length, the three-compartment mill produced a finer product that the two-compartment mill, and it showed less sensitivity to ball size selection. Overall, these simulations in view of existing cement milling practices suggest that TUSSIM is a credible simulation tool that can be effectively used for process simulation-optimization of open-circuit continuous dry ball mills.

References

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