In coal blending and homogenization, modeling of coal processability is utilized in optimization schemes to maximize the processing overall yield. Processing of different coal or different coal size in parallel circuits; and homogenization of raw coals followed by processing are considered. In parallel processing-circuit die objective is to optimization the degrees of coal processability to achieve maximum yield at target ash content. Blending processed coals with raw coal is also considered. In homogenization of raw coals the objective is optimization of coal processability of the raw coal blend lo achieve maximum yield at target ash content. Two functions are used in the modeling one is derived based on the physical-chemical composition of coal and the other function is a variation of the simple Weibull function. Both functions are effective than the polynomial functions proposed in the literature. The proposed techniques are straightforward to apply by plant engineers. Several illustrative cases are used to demonstrate the proposed techniques.

Introduction

Coal homogenization is utilized to reduce the scatter in quality characteristics of the plant raw feed and final products and to increase the yield of separation processes. Wide feed quality characteristic variations can cause diverse effects on the operation of different processing units and will result in poor plant performance. The smoothing out of fluctuations in the quantity of material to be processed can increase the average loading of the processing equipment and simplify operation. The feed, however, must have the correct average. Post-processing homogenization is implemented to produce products that meet client targets and specifications. Moreover, homogenization as pre- or post-processing can reduce unwanted scatter in quality characteristics, which cannot be corrected mechanically, e. g., volatile matter content. Furthermore, the readily and very economical means of improving the quality of coals for combustion or for conversion to synthetic fuels are achieved through the benefits of coal blending [1].
In case of parallel circuits used to process different coals or different coal sizes, the degree of coal processability (i.e., circuit cutpoint) can be optimally manipulated to maximize the combined yield of products at the same time meet target product qualities [2, 3, 4, 5]. In the 10^th ICPC, Salama [4] has considered this problem and graphical techniques were proposed to solve it. Naturally, use of graphical techniques is limited to handling of a small number of coals. Other researcher has considered a more general blending problem where coal characteristics are defined over density and size ranges and formulated a mathematical programming problem [6].
In the literature, it has been proposed to model the relationship between the cumulative mass (M) and cumulative ash (A) of a coal sample using polynomials [7, 8]. It is well known that polynomial regression generates erroneous values, especially, when there is scatter in the data. To illustrate this point, let us consider two coals and using 5th degree polynomial fitting (regression) of the M and A relationship and the results obtained are shown in Fig. 1. It is clear that the polynomial regression produced intermediate values greater than 100%. Also, other polynomial regressions generated similar unrealistic results. Consequently, the unrealistic results provided the motivation for the present work. (...)

Yield maximization in parallel processing schemes

M = (A - β)^γ/(A_S - β)^γ         (1)

         (2)

          (3)

          (4)

          (5)

        (6)

This optimization problem can be solved using the "Solver" within the Microsoft Excel™. Note that the availability of the ''Solver" module is an advantage to the present techniques. The presented optimization problem can be easily extended to include blending processed and raw coals. In such cases, each raw coal is represented by a single point on the [MA] axis and its coordinates are (A_r, 1) where A_r is the raw coal total ash. The results obtained are applicable to theoretical separation, i. e., no misplaced material in the product and reject streams. However, if another pseudo M-curve obtained using actual separation of each coal sample, the results obtained can be applied using the pseudo M-curves. It is worth noting that the end points of the pseudo M curve and the theoretical M curve are fixed.

Yield maximization in coal homogenization

In coal homogenization the incremental masses of the raw coals are added at each density interval or fraction to generate the coal blend data. The resulting coal blend is subjected to nonlinear regression using Equations 1 and 3 models and a continuous relationship between the input (A or [MA]) variable and output M variable is obtained. The nonlinear regression results of the different coals are used in optimization scheme that is defined as: find the optimum M and [MA] such that the overall raw coal blend yield is maximized subject to target ash content.

Illustrative cases

Case 1 is a blend of two processed coals. The physical-chemical model function is used. Let the overall ash target is 15%, a summary of the data and the yield maximization results are shown in Fig. 1.

Fig. 1 - Modeling of M-A curves using polynomials

Case 2 except the physical-chemical model function is replaced with the simple Weibull function. Note that the Weibull function is a five-parameter function. Let the overall ash target is 18%, a summary of the data and the results are shown in Fig. 2.

Fig. 2 Yield optimization using blending of three processed coals and a raw coal - Weibull function modeling

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Conclusions