Technical Note - Coal Blending For Sulfur Compliance

Linear programming on desktop computers is commonly used to optimize coal blending proportions. The objective function is usually the cost of the blend. The constraints consist of materials and heat balances as expressed as linear functions of the blend. This is illustrated in Example 1. Inclusion of a sulfur compliance constraint in more complex because the maximum permitted sulfur percentage is not a pre-specified constant. Rather, it is a function of the calorific power of the blend itself. The current limit of 1.2 pounds of sulfur dioxide per million Btu may be expressed as: [Sulfur Max%= 0.6 . Hl10,OOO with H in Btu/lb.] A proper constraint equation may be formed by defining for each coal a function that is the difference between the actual sulfur percentage and the maximum sulfur percentage. This may be regarded us an excess sulfur percentage. For Coal A of Example 1. this would be: [ Sulfur Excess%=0.5-0.6 13,000/10,000=-0.28] This value would be used as the coefficient of the weight proportions of this coal in the blend. The complete constraint equation would then be the sum of such terms for each coal set less than or equal to zero. This is illustrated in Example II. [ ]