(724e) Unsteady-State Simulation of Cement Milling in Closed-Circuit Operation: A Fully Coupled Ball Mill-Air Classifier Model

As an important unit operation, ball milling is widely used in numerous industries, including the cement industry. Using a ball mill, which is a rotating horizontal tube containing grinding media as balls, is inefficient because the process generates losses in heat, vibration, and sound energy [1]. Nevertheless, the majority of cement clinker mills are operated using ball milling technology [2]. As the shell of a ball mill is rotated, its grinding balls move in a cataracting mode, hitting on the powder bed, and cement clinker particles are broken down to smaller sizes. In closed-circuit mode, ball milling operation and external air classification are coupled (see Fig. 1). A dynamic air classifier equipped with a rotor (the rotating part) driven by a separate motor and stationary guide vanes classifies discharged powder from a mill into a fine product stream (final product) and a coarse reject stream. The classification area of an air classifier is the space between the rotor cage and the guide vanes. Particles entering this space are subjected to centrifugal, drag, and gravitational forces. Depending on the magnitude and direction of these forces, the particles move along different trajectories. The desired product size can be adjusted by changing airflow rate and/or rotor speed [3].

Several studies have examined the impacts of process parameters, including the selection of ball sizes, on milling performance (e.g., [4-6]). However, experimental studies intended to identify optimum operating parameters were performed under small-scale batch ball milling; industries operate ball mills in continuous mode. Past experimental research has also indicated that a small ball more effectively breaks down fine particles, whereas a large ball more effectively breaks coarse particles. Thus, in a poly-dispersed (natural) feed where coarse and fine particles coexist, a mixture of ball sizes can be expected to outperform a single ball size. In view of breakage kinetics, operating with an excessive number of ball sizes does not necessarily yield finer products. As experimentally observed [7], a binary mixture of ball sizes can generate either finer or coarser products than those of a quaternary size mixture, depending on the selected top ball size. On the basis of the actual operation of industrial mills [8,9], the selection of up to five ball sizes is common in large mills. However, a caveat in opting for a binary mixture of considerably differing ball sizes is that the wear rate of balls may be high and thereby increase operating costs.

As mentioned earlier, the desired product size can be controlled by adjusting airflow rate and rotor speed of the external air classifier [3]. A decrease in airflow rate (or an increase in rotor speed) yields finer products, but it elevates the mass flow rate of a coarse reject stream. A critical issue is that these operation strategies are valid only when an air classifier is large enough to handle the powder discharged by a ball mill. The classifier cannot be operated at too low an airflow rate (or too fast a rotor speed) because it is overloaded by an excessive mass flow rate of a coarse reject stream. Such overload, in turn, sharply diminishes classification performance, thus shutting down operation. In other words, a closed-circuit ball mill operates at optimum under a certain coarse reject rate [10]. Recently, the classification function, also known as the Tromp curve (the variable Tromp curve, hereafter), was empirically developed to factor in the dust load carried by an air classifier [11]. Although the variable Tromp curve was proposed on the grounds of industrial cement milling data, its corresponding model has never been incorporated into a closed-circuit mill—a challenging task because of an increase in the nonlinearity of the coupled system. Given the aforementioned complexity during milling-classification, uncovering optimum operating conditions is difficult and costly. Alternatively, a simulation tool can illuminate the interplay between milling and classification as well as clear the way for pinpointing optimum operation at minimal cost.

The population balance model (PBM) has been used to simulate particulate processes, thereby enabling the quantitative analysis of the spatio-temporal evolution of particle size distribution (PSD) during milling. Simulators discussed in the open literature and even the commercial software for closed-circuit dry milling simulators, such as JKSimMet [12], are steady-state simulators. Unlike other simulators, the true unsteady-state simulator (TUSSIM) solves for temporal evolution of the PSD within the mill and simulates the coupled ball mill-air classifier system during full-scale dry ball milling in the closed-circuit mode (see Fig. 2). TUSSIM is based on the solutions of a cell-based PBM [13], which was augmented with the variable Tromp curve [11]. It consists of a set of differential-algebraic equations (DAEs) and accounts for realistic finite mixing, internal particle separation caused by diaphragms, external particle separation caused by air classifiers, a combination of ball sizes, ball size distribution, and the application of classifying liners. Using the TUSSIM, we explored the impact of ball mixtures, as opposed single-sized balls, the action of classifying liner, and rotor speed–air flow rate of the external air separator on the product PSD, recirculation ratio, dust load to the air classifier, etc.

Our simulation results suggest that ball mixtures generated finer products than a single ball size, in correspondence with actual industry operations [1]. The use of a classifying liner yielded finer products as opposed to those produced through uniformly mixed ball sizes. In consideration of particle classification, reduced airflow rate (or augmented rotor speed) in the air classifier yielded finer product PSD and, hence, a higher coarse reject rate. These outcomes are congruent with the findings of previously conducted experiments [3]. Even more interestingly, under a further decrease in airflow rate (or a further increase in rotor speed), TUSSIM can detect the failure of the system when the air classifier is overloaded (high dust loading). Overall, we have demonstrated that the successful development of TUSSIM, a PBM-based simulation tool, will enable the industry to improve the closed-circuit ball milling operations through enhanced process understanding and especially the complex coupling of ball milling with air classification system.

References

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