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106                                            New Trends in Coal Conversion

         conversion of the dense bed in a grate-fired boiler can also be done by using experi-
         ence- or measurement-based conversion rates as a function of the position on the grate.
         Then, an overall heat and mass balance of fuel components and primary air can be
         solved to obtain the lengthwise profiles of temperature, species, and velocity on the
         top of the dense fuel bed along the grate. Such profiles are used as the grate inlet con-
         ditions for the freeboard CFD (Blasiak et al., 2006; Goerner and Klasen, 2006; Kim
         et al., 1996; Klason and Bai, 2006; Rajh et al., 2016; Stubenberger et al., 2008;
         Weissinger et al., 2004; Yin et al., 2008b, 2012).
            In the third approach, separate comprehensive bed models are developed to study
         solid fuel conversion in a dense fuel bed. Basically, this approach is to numerically
         solve the mass, momentum, energy, and species conservation equations for gas and
         solid phases. Process rate equations and empirical correlations/submodels are used
         for the closure of the conservation equations. Such a comprehensive model can pro-
         vide the profiles of all the parameters at the top of the dense bed, which can be
         used as the inlet boundary condition for the freeboard CFD (Goddard et al., 2005;
         Kær, 2004; Ryu et al., 2002, 2004; Yang et al., 2007). Such a model also facilitates
         a parametric study of the impacts of feedstock properties, process conditions, and un-
         certainties in model assumptions and parameters on the conversion rate, temperature,
         and gas compositions (Thunman and Leckner, 2005; Zhou et al., 2005; Yang et al.,
         2005; Shin and Choi, 2000; Johansson et al., 2007). The majority of such comprehen-
         sive models are 1D, in which a 1D transient model is solved along the vertical direction
         for fixed bed combustion and then the time elapsed since ignition in the fixed bed is
         mapped to the horizontal distance away from the start point on the travelling grate
         in industrial grate boilers. Such an approximation may be acceptable for travelling
         grate combustion because of the small gradients in temperatures and species along
         the horizontal direction in industrial grate boilers.
            To gain a better overview of the comprehensive model (including the governing
         equations) and to develop a more general code for solid fuel combustion in a dense
         bed, MFIX (Multiphase Flow with Interphase eXchanges) is a useful reference.
         MFIX is a general-purpose computer code developed for describing the hydrody-
         namics, heat transfer, and chemical reactions in fluidesolid systems. MFIX code is
         based on a generally accepted set of multiphase flow equations as summarized in
         (Benyahia et al., 2012), and the source code is available via its website, https://mfix.
         netl.doe.gov. MFIX calculations give transient data on the 3D distribution of pressure,
         velocity, temperature, and species mass fractions. Although MFIX is mainly used for
         describing BFBs and CFBs and spouted beds, the governing equations and the pro-
         gramming techniques are still the same and useful for the development of dense
         fuel bed models for grate-fired boilers.
            No matter which approach is used to model solid fuel conversion in a dense fuel
         bed, it is important to assure the correct total fluxes of mass, momentum, elements,
         and heat released from the top of the dense bed into the freeboard to achieve a reliable
         CFD analysis of a grate-fired or a fluidized bed boiler. Compared with the correct total
         fluxes into the freeboard, the different profiles of velocity, temperature, and species
         along the top surface of the dense fuel bed produced by different approaches may
         be a secondary issue at most in the freeboard CFD. Because of the strong mixing in
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