Determining the composition of binary coal blends using Bayes theorem q Edward Lester * , David Watts, Mike Cloke, Paul Langston School of Chemical, Environmental and Mining Engineering, University of Nottingham, University Park, Nottingham NG7 2RD, UK Received 28 April 2002; accepted 4 July 2002; available online 26 August 2002 Abstract Binary coal blends were prepared using a typical UK steam coal with four different coals which were then analyzed using random vitrinite reflectance (R random ). Deconvolution of the vitrinite reflectance data was attempted using Bayes Theorem in order to calculate the composition of each blend on a % vol/vol basis. Modifications were made to the initial Bayes algorithm to take into account experimental error. The effect of using increasing amounts of data on the blend predictions was also investigated. Accurate predictions were achieved when using more than 100 reflectance measurements from each component and iterating the Bayes algorithm more than 100 times. q 2002 Elsevier Science Ltd. All rights reserved. Keywords: Coal petrography; Vitrinite reflectance; Bayes theorem; Coal blends; p.f. 1. Introduction The blending of coals is likely to increase as generators seek to find the most economical means of generating electricity. Addition of a poor burning coal to a good coal may allow emission limits to be met whilst lowering the cost per ton of fuel. Coal blending is also likely to increase in order to meet increasingly stringent regulations concerned with emissions such as SO x , NO x and carbon in fly ash. Coals with low sulphur or with a high burnout propensity can be blended with a coal that has a higher sulphur content and/or a history of poor burnout. It is also possible that blending may also occur when suppliers source different stockpiles, for whatever reason, delivering a coal shipment that is different from the requested supply. Regardless of the means by which a coal may become blended, there is an increasing need to detect blends and identify the various components within the blend. In the first instance, a coal buyer might just want to reject blends or, on the other hand, a coal buyer may want to be able to determine the composition of the blend in order to negotiate a more favorable price. Often suppliers do not know what the blend proportions are for a given shipment simply because coals are often blended prior to washing [1]. The washability characteristics of each component will deter- mine the proportion of each coal in the final sample. Petrographic assessment is another means of assessing coals for blending [2] as well as potential combustion characteristics [3]. Vitrinite reflectance analysis (otherwise known as rank analysis) is a useful means of determining the composition of a coal sample since small changes in the reflectance of vitrinite will stand out on a histogram plot. An obvious example of coal blending can be seen in Fig. 1(a), where two peaks, which correspond to two different coals, are clearly visible. With the example in Fig. 1(a), separating the peaks is straightforward since two clearly distinct distributions can be seen with a boundary at 1.0% reflectance. However, coal blends are not always as ‘obvious’ as this. The peaks in Fig. 1(b) would be much harder to resolve since they overlap. Separation of overlapping peaks is not difficult when dealing with normal type distributions. Deconvolution software already exists for separating data with normal type distributions, such as FTIR and mass spectrometry. Unfortunately, vitrinite reflectance profiles do not always have such uniform distributions and this remains a difficulty when attempting deconvolution. This paper presents a method for the deconvolution of histogram profiles from rank analysis using Bayes Theorem. The work of Reverend Thomas Bayes in the mid-18th century was based on mathematical probability and, in particular, on the probabilistic relationship between 0016-2361/03/$ - see front matter q 2002 Elsevier Science Ltd. All rights reserved. PII: S0016-2361(02)00223-5 Fuel 82 (2003) 117–125 www.fuelfirst.com q Published first on the web via Fuelfirst.com—http://www.fuelfirst.com * Corresponding author. Tel.: þ44-115-951-4974; fax: þ 44-115-951- 4115. E-mail address: edward.lester@nottingham.ac.uk (E. Lester).