Coal modeling using Markov Chain and Monte Carlo simulation: Analysis of microlithotype and lithotype succession Saeid R. Dindarloo a , Amirhossein Bagherieh a , James C. Hower b, ⁎, John H. Calder c , Nicola J. Wagner d,1 a Department of Mining and Nuclear Engineering, Missouri University of Science and Technology, Rolla, MO 65409-0450, USA b University of Kentucky, Center for Applied Energy Research, 2540 Research Park Drive, Lexington, KY 40511, USA c Nova Scotia Department of Natural Resources, Halifax, Nova Scotia B3J 3K5, Canada d University of the Witwatersrand, Johannesburg, South Africa abstract article info Article history: Received 16 June 2015 Received in revised form 3 August 2015 Accepted 4 August 2015 Available online 14 September 2015 Editor: J. Knight Keywords: Kentucky Joggins Nova Scotia Microlithotype and lithotype succession Markov Chain analysis was applied to the description of the megascopic lithologic transitions in Pennsylvanian- age eastern Kentucky coals. Coal lithology modeling can be problematic as individual lithotypes can represent near-instantaneous events (vitrain), prolonged degradation (durain), or fire-induced loss of previously deposited lithologies (fusain). Each of the latter lithotypes, potentially representing vastly different amounts of time, could be of the same thickness. Therefore, equal thickness does not necessarily imply equal time. Probability transform matrices that employ uniform lithotype thicknesses were used, allowing transitions between like lithotypes; em- bedded Markov Chains, thereby only considering transitions between different lithotypes; and continuous-time Markov Chains were employed in the assessment of a section of the No. 5 Block coal (Pennsylvanian Breathitt Group, Martin County, Kentucky). Embedded Markov Chains could successfully simulate the lithologic transi- tions. A Monte Carlo random process was programmed to simulate thickness variations of lithotypes between the transitions. The proposed hybrid model of Monte Carlo–Markov Chain was able to predict the random pattern that underlies lithotypes transitions and thickness. The hybrid Monte Carlo–Markov Chain technique proved to be effective in the case study in simulating both the lithologic thickness variations and transitions. © 2015 Published by Elsevier B.V. 1. Introduction In the petrographic order of coals, lithotypes are the macroscopic ex- pression of microlithotypes which, in turn, are the microscopic assem- blages of macerals and minerals (Hower et al., 1990; Taylor et al., 1998; Esterle, 2008; Hower and Wagner, 2012; O'Keefe et al., 2013). Microlithotypes, ideally representing assemblages at least 50-μm thick, are defined based on the relative proportions of macerals and minerals present in the interval (Table 1). Microlithotypes, even more than the macerals comprising the assemblage, represent the first-order approxi- mation of coal depositional conditions. As discussed by O'Keefe et al. (2013) and Hower et al. (2013), the path from wood to vitrinite and inertinite can be quite complex and involve the actions of insects and other fauna, fungus, and bacteria. The succession and the thickness of lithotypes and the constituent macerals and microlithotypes determine the mining and handling properties of coal (Hower and Lineberry, 1988; Hower, 1998, 2008). Coal lithotypes, all basically combinations of vitrain, durain, and fusain (and thin mineral-rich bands) are defined on the basis of a 3- mm minimum thickness, 2 represent variable times for their deposition, making it difficult to prescribe exact rules to lithotypes succession. For example, a vitrain, usually a thin (mm to a few cm) lithotype, may rep- resent a well-preserved part of a log, branch, or root; overall, a short time in the history of the coal. Prior to the incorporation of the plant part into the peat, the wood may have been attacked by insects, perhaps before or after an infestation of fungus (Hower et al., 2013). Post- depositional microbial attack may further alter the lithotype. In con- trast, fusain, also generally a thin lithotype, in the classic sense could represent a fire event (Stach, 1927; Evans, 1929; Scott, 1989, 2000, 2002; Winston, 1993; Scott and Jones, 1994; Guo and Bustin, 1998; Petersen, 1998; Bustin and Guo, 1999; Scott et al., 2000; Scott and Glasspool, 2005, 2006, 2007; McParland et al., 2007). As such, fusain po- tentially represents an unknown span of time, which may be an uncon- formity within the coal bed. Durains can represent a longer span of time, from decay in a standing tree, to degradation in the peat surface litter, to subsurface aerobic (fungal and bacterial) and anaerobic (bacterial) Sedimentary Geology 329 (2015) 1–11 ⁎ Corresponding author. Tel.: +1 859 257 0261. E-mail address: james.hower@uky.edu (J.C. Hower). 1 Now at University of Johannesburg, Johannesburg, South Africa. 2 The bright clarain, clarain, and dull clarain lithotypes are fundamentally alternating vitrain and durain, each of the latter two being too thin to separate into the basic units. An attempt is made to recognize thinner fusains and inorganic partings because they rep- resent a significant disruption in the organic deposition. http://dx.doi.org/10.1016/j.sedgeo.2015.08.005 0037-0738/© 2015 Published by Elsevier B.V. Contents lists available at ScienceDirect Sedimentary Geology journal homepage: www.elsevier.com/locate/sedgeo