Biomass gasification solver based on OpenFOAM

Biomass gasification solver based on OpenFOAM Kamil Kwiatkowskia,c,1,∗, Pawel Jan Zukb,1 , Konrad Bajera,c,d , Marek Dudy´nskib,e,f a Institute

of Geophysics, Faculty of Physics, University of Warsaw, Pasteura 7, 02-093 Warsaw, Poland of Theoretical Physics, Faculty of Physics, University of Warsaw, Ho˙za 69, 00-681 Warsaw, Poland c Interdisciplinary Centre for Mathematical and Computational Modelling, University of Warsaw, Pawi´ nskiego 5, 02-106 Warsaw d University Centre for Environmental Studies, University of Warsaw, Zwirki ˙ i Wigury 93, 02-089 Warsaw e Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Banacha 2, 02-097, Warsaw f Modern Technologies and Filtration, Przybyszewskiego 73/77 lok. 8, 01-824 Warsaw, Poland b Institute

Abstract We present biomassGasificationFoam solver and libraries, developed in an open-source C++ code OpenFOAM (Open Field Operation and Manipulation), for the comprehensive simulation of the physical and thermochemical processes of biomass gasification and pyrolysis. The code biomassGasificationFoam integrates models of drying, pyrolysis, gasification, combustion, and complex flow within a porous biomass. The most important newly implemented functionalities are transient flow in porous media (with changing porosity), a flexible definition of biomass and its properties, heat and mass transfer between gases and solids (with a submodel for heat transfer in wood biomass and radiation heating), homogeneous and heterogeneous reactions (the heat of reaction is defined directly or based on enthalpies of formations), and customisable kinetic mechanisms of pyrolysis and gasification. The number of subprocesses and possible paths of chemical reactions involved in the thermal conversion of biomass make the flexibility of the developed code the key factor for successful numerical modelling. Keywords: openFoam, biomass, pyrolysis, gasification, combustion, porous media, fixed bed PROGRAM SUMMARY Manuscript Title: Biomass gasification solver based on OpenFOAM Authors: Kamil Kwiatkowski, Pawel Jan Zuk, Konrad Bajer, Marek Dudy´nski Program Title: biomassGasificationModel Licensing provisions: GNU General Public Licence (Version 3 of GNU GPL) Programming language: C++ Computer: Any x86, 64 bit Operating system: Generic Linux (the instructions consider Ubuntu distribution, tested also on Centos) Keywords: OpenFOAM, Biomass, Pyrolysis, Gasification, Combustion, Porous Media , Fixed bed Classification: 12 R version 2.1.1 External routines/libraries: OpenFOAM⃝, Nature of problem: The developed software is a set of libraries and a solver for simulating the thermal conversion of biomass, including drying, pyrolysis, gasification, and combustion of gas and solid phases. Essentially, the model includes the flow of the reactive gas mixture and the complex transfer of mass and energy between the gas phase and porous solid phase. The code treats the biomass as a porous medium with a complex, reactive structure that changes during the process. The model is transient and enables three-dimensional simulations. Solution method: The standard finite-volume method is used in the code. A set of governing equations is solved for the gas phase and porous solid phase, including mass conservation of gaseous species and solid components, momentum conservation in the gas phase, and equations of energy conservation in both phases. Running time: From hours to days depending on the mesh size and complexity of the kinetics of the thermal processes.

∗ Pasteura

7, 02-093 Warsaw, Poland, Tel. +48 22 55 46 889, Fax. + 48 22 55 46 882 Email address: [email protected] (Kamil Kwiatkowski) URL: www.biomassgasification.eu (Kamil Kwiatkowski) 1 These authors contributed equally to this work. Preprint submitted to Computer Physics Communications (under review)

November 30, 2013

1. Introduction The term biomass gasification refers to all processes taking place in a gasifier fed with biomass. Biomass gasification in a fixed bed, apart from complex mass and energy transfer, involves thermal processes in gas and porous solid phases [1]: • evaporation of water embedded in biomass; • pyrolysis - thermal decomposition that transforms biomass into gases, liquids, and charcoal; • gasification - a set of reactions for the partial oxidation of charcoal, during which H2 and CO are produced; • combustion of gases and char - when the amount of O2 is sufficient, char produced in pyrolysis or flammable pyrolytic gases may be burnt; Biomass gasification is a comprehensive solution to the many problems of the contemporary energy sector [2]. The types of biomass available for gasification, such as organic wastes, biological residues, and biomass cultivated for energy production, are virtually unlimited (e.g., [3, 4, 5]). The variety of feedstocks combined with the wide spectrum of biomass gasification products-syngases, bio-oils, liquid hydrocarbons, and bio-coals makes this technology attractive for industrial applications [2]. However, the complex nature of gasification, the wide range of available feedstocks together with an extensive process parameter space, and various types of reactors and possible reaction paths impede the development of a rigorous treatment of the process from a numerical perspective. We identified the following challenges in creating a numerical description of the process [6]: • biomass gasification involves several size and time scales, from the smallest scale of the porosity of a single biomass particle to the largest scale of the entire industrial reactor; most numerical approaches are focused on one scale. • simulations depend on the chemical composition of the biomass and its physical properties, which are time and process dependent; parameters are typically simplified. • the kinetics of pyrolysis and gasification are a subject of the on-going research for wide range of materials and process conditions. • numerical models for biomass gasification are difficult to validate. • existing numerical models and databases are not standardised, which impedes cross-checking and comparison. To meet these challenges, it is important to create a comprehensive computational environment that allows the newest development in gasification science to be implemented easily and enhances the ability to share models and their results within the community. We develop a fixed-bed biomass gasification solver based on the well-established open-source CFD software OpenFOAM [7, 8]. The package, based on a C++ class structure, makes it possible to override the selected existing libraries and replace them with new implementations. The process of biomass gasification and its subprocesses are well fitted in the fields that may be simulated with OpenFOAM [7, 9]. The most advanced solver including thermal processes of solid is fireFoam [9]. It is focused on modelling fire phenomena, and it is not suitable for modelling biomass gasification. Other solvers, eg. coalChemistryFoam, are designed to simulate gasification in fluidised bed. Until now, there has been no solver providing a description of biomass gasification in a fixed bed. In this work, we present the new solver biomassGasificationFoam and the complementary library biomassGasificationMedia developed to simulate a wide range of processes and applications related to the fixed bed biomass gasification. Unlike other numerical approaches (e.g. [10, 11]) the developed solver is open-source. In this code, we implemented and integrated the following: transient flow within and around porous medium, heat and mass transfer between gases and solids around and within porous medium, a flexible definition of biomass and its thermochemical properties, homogeneous and heterogeneous reactions with the heat of reaction defined directly or derived from enthalpies of formations, and customisable kinetic mechanisms of pyrolysis and gasification. 2

In the present paper, we first introduce the concept of Dynamic Porosity Field for mesh-independent definition of biomass-filled region. Next, we present a mathematical model of biomass gasification, discuss the stress source terms related to thermal processes, and clarify all required material parameters. Transitioning from mathematics into numerics, we first briefly introduce the general structure and features of OpenFOAM. Then, we present the developed extensions of OpenFOAM, namely, the solver and related library. Finally, the results of simulations are presented and compared with the thermogravimetric analysis (TGA) of wood pyrolysis. 2. Mathematical modelling 2.1. Dynamic Porosity Field The solvers embedded in the standard OpenFOAM distributions for modelling pyrolysis (fireFoam [9]) and chemical reactions (reactingFoam) or gasification in fluidised bed (coalChemistryFoam) are not suitable for fixed bed biomass gasification simulations. Currently available approaches do not consider the mutual influence of the reacting flow and gasified solid and volumetric reactions within porous material. In the first solver, fireFoam, the pyrolysing medium is attached to the main computational domain, where the gas flow is calculated, and interacts with the gas phase only through the domain boundary conditions. Within this approach, there is no natural representation of the porous material with the gas flowing through. In fireFoam, pyrolysis is implemented as surface phenomena, not volumetric, which limits its use. The second solver, reactingFoam, allows for volumetric reactions but only within the gas phase. To allow for the volumetric implementation of thermal processes, we propose to introduce porous medium inside the main computational domain as a volumetric porous field, as shown in Fig. 1. Flow modelling in the proposed approach follows the so-called Fictitious Domain method of [12], which is a rather special version of the Immerse Boundary Method [13]. However, in the current approach the equations inside and outside the porous medium are the same and the boundary has no extra dynamics of its own. The boundary of the porous material is the surface where the physical parameters present in those equations are discontinuous. In the momentum equation, for example, both the dArcy term and the usual viscous term of a Newtonian fluid, as in the Navier-Stokes equation, are formally present on both sides, but the associated coefficients have a jump across the interface. The porous medium representing biomass is defined by two fields: a scalar (porosity) and a tensor (viscous resistance). Since the boundary of the porous material has no intrinsic dynamics, there is no need to track its precise shape, as is the case, for example, with elastic boundaries or with surface tension where local curvature is critically important. The numerical implementation is then much simplified as each grid cell can be assumed to lie entirely inside or entirely outside the porous domain. The fields defining porous medium (volumetric fields of non-zero porosity and viscous resistance) are accessible and easily modifiable, if necessary, during the calculation. It must be stressed that the typical approach available in CFD codes introduces porous medium as a separate zones in the computational domain itself, not as a field inside this domain. Such porous field defined once in the preprocessing stage cannot be easily modified without changing the entire domain. The new set of libraries that we implemented introduces thermal, chemical, and radiation properties of such defined porous field and determines their interactions with the gas phase flowing through and around these fields. Essentially, the libraries handle biomass as a collection of additional scalar and tensor fields within the computational domain, e.g., the mass fraction of cellulose, the thermal conductivity of the porous medium, and the absolute density. The introduction of the Dynamic Porosity Field allows thermal processes to be considered as volumetric phenomena that may take place within the entire porous material depending on local conditions. Treating gasification as a volumetric process makes it possible to simulate such effects as the front of reactions inside the biomass. It makes it possible to carry out simulations of chemical and thermal processes inside a porous medium, involving mutual interactions of the gas and solid. We believe that applications of this approach exceed currently simulated pyrolysis, combustion, and gasification. It may be potentially applied in modelling any processes involving porous reacting media, such as catalysis or filtration.

3

Table 1: Notation.

A a c d D hs hf hr Hr k K N R R˜ T Y V W G Greek symbols α ρ γ Γ µ ν Σ ξ ω Ω δ ϵ σ Subscripts a c i k s p wall sur f Superscripts S G evap pyro gasi f comb rad

pre-exponential factor in Arrhenius formulae radius of pipe in cylindrical heat transfer model specific heat capacity pore diameter effective diffusion of gas mixture sensible enthalpy enthalpy of formation heat of individual reaction heat source due to thermal conversion of solid thermal conductivity tensor of viscous resistance in porous medium number of pipes in cylindrical heat transfer model mass source term due to reaction with a solid total reaction rate temperature mass fraction volume of computational cell molar mass radiation energy flux heat transfer coefficient per surface area bulk density void fraction of biomass, opposite of porosity gas heat up coefficient dynamic viscosity of gas mixture stoichiometric coefficient for gaseous species surface area of pores per biomass volume stoichiometric coefficient for solid species reaction rate of gas-phase combustion reaction rate for particular processes solid surface optical absorption coefficient ratio of the solid surface absorption and emission coefficients Boltzmann constant gasification agent (O2 , CO2 , or steam) critical, limits the reaction from proceeding index of gas species i index of biomass component k index of the gaseous substrate of the reaction index of the gaseous product of the reaction physical wall in the computational domain surface of porous medium solid gas evaporation pyrolysis gasification combustion radiation 4

2.2. Governing equations The three-dimensional, time-dependent mathematical model of the thermal conversion of biomass is based on conservation laws that are determined for both gaseous and solid phases. The solid is an isotropic or anisotropic porous medium. In Fig. 1, we present typical considered processes when one or more biomass fragments (dark grey) is pyrolysing or gasifying surrounded by inert or reactive gases. The gas phase is composed of a mixture of gases with different origins: gas that initially filled the reactor, gas supplied to the process, water vapour evaporated while the biomass is drying, and gases produced during thermal conversion of the solid. The potential liquid phase (water and liquid hydrocarbons) is considered vapour. This assumption is well satisfied for most of the considered processes. The other assumptions are as follows: • In current implementation the movement of porous medium is neglected. • The moisture is embedded within this porous structure. Moisture released from the solid evaporates immediately. • Gas flows according to Darcy’s Law inside the porous medium. • Radiative transfer from domain walls to solid surfaces is available . • Chemical reaction and thermal processes may lead to thermal non-equilibrium. • The void fraction γ is determined for the entire domain as γ = and as γ = 1 if there is no solid.

V−V S V

: γ = 0 when only the solid phase is present

• The porous medium loses mass via homogeneous and heterogeneous processes. The governing equations for the gaseous phase are as follows: momentum conservation (Eq. 1), continuity (Eq. 2), species conservation (Eq. 3), and energy conservation (Eq. 5). The set of species typically involves water vapour, CO, CO2 , O2 , N2 , and CH4 . YiG is the mass fraction of the individual species. The solid-phase equations involve conservation of solid components (Eq. 4) and the energy conservation equation 6). YkS denotes the mass fraction of particular solid components (i.e., cellulose, hemicellulose, lignin, char, ash), and ρSk represents the density of these solid ingredients. All equations are solved in the whole computational domain, however where porosity field is equal zero the parameters of the solid phase, such as density, heat capacity and thermal conductivity, are zero. This approach is analogous to the Fictitious Domain Approach by [12]. ∂γρG u + ∇ · (ρG uu) + ∇p − ∇ · (µ∇u) = ∂t ∂γρG + ∇ · (ρG u) = ∂t ( ) ∂γρG YiG + ∇(ρG uYiG ) − ∇ · ρG D∇YiG = ∂t ∂ S S (Y ρ ) = ∂t k

∂γρG CiG T G + u · (∇ρG CiG T G ) − ∇ · ((1 − γ)kG ∇T G ) = ∂t ∂ρS CkS T S − ∇ · (γkS ∇T S ) = ∂t

(1 − γ)Kµu ) ∑ ( evap pyro gasi f RGi + RGi + RGi

(1) (2)

i

ωGi + RGi RSk

pyro

∑

evap

+ RSk

+ RGi

gasi f

pyro

+ RSk

+ RGi

gasi f

(3)

comb

ωGi h f Gi − αΣ(T G − T S ) − Γ + S G

(4) rad

(5)

i

αΣ(T G − T S ) + Hr + S S

rad

(6)

The equations 1–6 are presented such that all terms on the left-hand side (LHS) are standard for modelling gas flow or heat transfer in a solid. On the right-hand side (RHS), we collected all source terms regarding the porous structure of biomass, chemical reactions, and thermal conversions. The thermal processes are included via the source 5

Figure 1: Exemplary computational domain with porous biomass particles.

terms denoted by reaction rates R with corresponding superscripts (G - gas and S - solid; evap - evaporation, pyro pyrolysis, gasif - gasification, comb - combustion) and subscripts (i - gaseous species, k - solid components). Hr is the total heat source due to solid phase reactions. We briefly describe these additional source terms in Section 2.3. 2.3. Thermal processes The thermal processes of moisture evaporation, biomass pyrolysis, char gasification, and combustion take place in the solid phase (RHS of Eqs. 4 and 6). Mass and energy are transferred from the solid to gas phase (RHS of Eqs. 2–5) or vice versa. The sequence of processes involved in the thermal conversion of biomass, using wood as an example, is presented in Fig. 2. First, embedded moisture evaporates from the biomass (Fig. 2 (a)); then, volatiles are released from the solid in the process of pyrolysis (Fig. 2 (b)). In both processes, the material must be heated up and products are formed without any additional reactants. The porous carbon skeleton remaining from pyrolysis has higher void fractions than the original biomass char. The char is gasified in the presence of a gasification agent-CO or water vapour (Fig. 2 (d))-or burnt in the presence of an oxidiser (Fig. 2 (d)). The only residual is a small amount of ash composed of minerals. The general characteristic of all these processes are summarised in Table 2. In the current implementation of the solver reaction (thermal process), the rate coefficient κ is modelled using Arrhenius formula [14, 15] as follows: ( ) { A exp − TTa , T > T c κ= (7) 0, T ≤ T c 6

(a) evaporation, (b) pyrolysis, the simplest scheme, (c) char gasification with CO, (d) char combustion. Figure 2: Sequence of processes included in the thermal conversion of wood.

where A, T a , and T c are the pre-exponential factor, activation temperature, and cut-off temperature, respectively. For the simplified schemes presented in Fig. 2, the mass source terms (mass changes per volume) due to thermal processes are as follows: evap

=

S ρS Ymoisture κevap

pyro RGgas

=

ρ

gasi f

=

S G −ρS Ychar YCO κ pyro 2

(10)

comb

=

S −ρS Ychar YOG2 κcomb

(11)

RGwater vapour RSchar

RSchar

S

S pyro Ydry wood κ

(8) (9)

It must be stressed that the pyrolysis scheme presented in Fig. 2 (b) is the simplest possible. In general, energy supplied to the material causes the large hydrocarbon molecules that form the material to crack into smaller molecules. This mechanism may be formulated in different ways, typically including several intermediate states coupled together (e.i. [16, 17, 18, 19, 20]. Two examples of more complex schemes are presented in Fig. 3. More details on the kinetics of pyrolysis and gasification are available in the textbook by Basu [1] and several reviewed papers by di Blasi [17], Pereira [2], and others. For simplicity, the determination of source terms for complex kinetics is presented separately in Appendix A. From a modelling perspective, easy introduction of increasingly complex schemes is one of the most important features of the developed code.

(a) pyrolysis, simple scheme including multiple components,

(b) pyrolysis, complex scheme with intermediate tar and temporary char included. Figure 3: Examples of two more complex mechanisms of pyrolysis.

2.4. Heat transfer Kaviany [24] reports that thermal equilibrium between a gas and solid vanishes when chemical reactions or thermal conversions take place. Our first analysis confirmed that during the thermal conversion of a single thermally thick 7

Table 2: General properties of the thermal processes available in biomassGasificationFoam.

Characteristic Gaseous substrates Solid substrates Gaseous products Solid products Intermediate steps Reaction rate (gases) Reaction rate (solid) Type Details 1 2 3

Evaporation homogeneous endothermic moisture2 H2 O no evap RGH2 O Arrhenius [21, 15]

Pyrolysis homogeneous endothermic1 biomass complex3 char possible pyro RGi pyro RSk Arrhenius Appendix A.1

Gasification heterogeneous endothermic CO2 , H2 O char CO, H2 ash no G gasi f Ri gasi f RSk Arrhenius Appendix A.3

Gas combustion homogeneous exothermic CO, H2 , CH4 CO2 , H2 O possible ωGi Arrhenius [22, 23]

Solid combustion heterogeneous exothermic O2 char CO2 ash no G comb RCO2 comb RSk Arrhenius Appendix A.2

Pyrolysis is globally endothermic, but the process is partially exothermic. Moisture embedded within the porous structure of the biomass is treated as solid components. Pyrolytic products are set of gases, CO, CO2 , H2 , CH4 , higher hydrocarbons gases, and liquid hydrocarbons (tar) that have been vaporised.

wood particle, the gases (both outside and inside the particle) are not in equilibrium with the solid [25] and separate energy equations for the gas (Eq. 5) and solid (Eq. 6) are required. The early analysis performed by [14] and repeated recently by [19] suggested that within the microscopic pores of single wood particles, the gases and solid are in thermal equilibrium. Investigations into the miniaturisation of heat exchangers independently led to the same conclusion: the assumption of thermal equilibrium is reasonable for micrometre-sized pores. In such case, the temperatures of the gas (in the pores) and solid phases are always equal and only one energy equation has to be solved within the computational domain. This assumption is common in the numerical modelling of pyrolysis and gasification [17, 26]. However, the above-mentioned analysis did not consider energy fluxes due to chemical reactions. The validity of the assumption of thermal equilibrium within a single biomass particle is arguable, but there is agreement that this assumption is not general. A typical situation in which the temperatures of the gases and solids differ substantially is when entire fixed-bed reactor is modelled. For example, hot pyrolytic gases heat up the fresh, relatively cold feedstock in an updraft fixed-bed gasifier. Similarly, the temperature of the gas and solid are typically different in a large-scale heat exchanger. The flexibility of the developed solver requires that a more general nonequilibrium state be assumed. The withdrawal of the assumption of thermal equilibrium requires that energy transfer between the gas and solid is considered within the entire porous medium according to the source term. αΣ(T G − T S )

(12)

where: α - heat transfer coefficient (per surface), Σ - total surface area of pores per solid state volume. The implementation of this term will be discussed in Section 5.2.3. In the current approach, we assume that during thermal conversion, solid substrates take on the temperature of the porous medium, whereas gaseous products take on the temperature of the surrounding gases inside porous material. Thus, for the reactions taking place in the solid, the energy Γ is required for heating (or cooling) products to the temperature of the gas. The source term Γ in Eq. 5 is defined as follows: ∑ Γ = (T G CGp (T G ) − T S CGp (T S )) RGi (13) i

This effect is independent from the previously mentioned effect of energy exchanging between the phases.

8

2.5. Material properties The mathematical model (Eqs. 1-6) must be completed with the appropriate definition of the material properties of gases and biomass. Although extensive research on gas combustion has allowed the thermophysical properties of the gas phase to be well defined, the properties of solids have not been thoroughly quantified. First, the initial porosity of the biomass must be defined. To include inhomogeneity of the biomass, it is possible to define a non-uniform porosity distribution within the modelled material. Together with porosity, the distribution of the viscous resistance tensor is defined. The custom design numerical tool setPorosity is implemented to define the complex initial porosity field (see Section 5.1). In this manner, isotropy and different anisotropies may be introduced. The ability to change the anisotropies during pyrolysis or gasification is prepared for future implementation. The next primary parameter of the biomass is the absolute density ρ˜ S (density of material with no void fraction). The final absolute density is averaged over the absolute densities defined for the solid components: embedded moisture, lignin, cellulose and hemicellulose, char, and ash:   ∑ YkS −1 S   ρ˜ =  (14) S  ρ ˜ k k Based on the absolute density ρ˜ S and void fraction γ, the bulk density ρS used in the mathematical modelling is determined as follows: ρSk = γρ˜ Sk (15) The thermal properties of the material are the thermal conductivities kS and heat capacities C Sp . These intrinsic parameters are also defined for individual solid components. During thermal conversion, the mass fractions of lignocellulose material decrease, whereas the mass fraction of char increases. As a result, changes in the material parameters accompanying thermal conversion are intrinsically included into the model as discussed in Section 5.2.4. The collection of gas and solid parameters is summarised in Table 3. Table 3: Summary of thermochemical properties of gases (with an averaged value for the gas mixture) and solid components (with an averaged value).

Average value constant Gas phase Density Heat capacity1 Thermal conductivity Viscosity Diffusion coefficient Solid phase Heat capacity Thermal conductivity

∑ ρG = i ρGi ∑ cG = i YiG cGi ∑ kG = i YiG kG ∑ i µG = i µGi ∑ DG = i µiD ∑ S S S (c∑ = kS Y) k c(k∑ Y kS = k kkS ρkS / k k

+ +

YkS ρSk

)

Temperature dependence linear power( ) n (x(T ) = x0 + x1 T ) (x(T ) = x2 TT0 ) defined separately + + defined separately defined separately

+ +

+

+

+

+

+

+

3. Structure of OpenFOAM The OpenFOAM (Open Field Operation and Manipulation) Toolbox [7, 8] is a free, open-source C++ package for solving partial differential equations with the finite-volume method. This code is widely used in various fields of fluid mechanics and provides comprehensive, standardised libraries and tools for solving partial differential equations. Due to the flexibility and versatility of the code, it is applied to model and simulate a broad range of problems, including transport and mixing [27], diffusion [28], reacting flows [29], porous media [30], shear stresses [31], combustion [32], heat transfer [33], viscoelastic flows [34], multiphase flows [35, 36], boiling flows [37], free-surface flows [38], biological flows [39], and others [40]. 9

Figure 4: Structure of the developed code: the solver and collection of libraries.

OpenFOAM as an object-oriented package is a structured collection of C++ libraries and solvers. The libraries can be divided into two major categories: • numerics - provides a vast choice of schemes for equation discretisation, solving, and parallelisation; • physics - implements mathematical models of simulated physical and chemical phenomena. The important inheritance of the C++ class structure is the ability to override and replace the existing libraries. The separate part of the package are solvers, which are executable programs containing algorithms that integrate selected functionalities of libraries and schedule the calculations in each time step. Each solver is prepared for a separate class of problems, e.g., reactingFoam solves flows of chemically reacting fluid. Splitting the package into libraries and the solvers provides additional flexibility by supporting runtime selection. This design idea makes it possible to switch during the solver runtime between libraries (physical models) and change the simulation parameters. No breaking of the calculation or recompilation is necessary. All of the above considerations make OpenFOAM an exceptionally flexible and transparent programming environment for designing new solvers. In this paper, such a new solver biomassGasificationFoam and library biomassGasificationMedia for modelling biomass gasification are introduced. In Figure 4, we present the scheme of the developed code: the solver and the library. The main new idea, which we implemented to extend OpenFOAM applications for modelling and simulating gas-solid interactions, is the Dynamic Porosity Field approach, which is described in Section 2.1. In the following sections, the biomassGasificationFoam solver and biomassGasificationMedia library are described in detail. 4. Solver - biomassGasificationFoam The biomassGasificationFoam solver is based on the algorithm used in the unsteady solver reactingFoam for reacting laminar or turbulent flows with turbulence models available in the OpenFOAM standard distribution [32]. The reactingFoam solves only gas-phase equations (Eqs. 1–5). The RHS of Eqs. 1 and 2 are equal to zero, whereas the RHS of Eqs. 3 and 5 are limited to gas-phase reaction source terms (ωGi ). In the following list, we summarise the novel modifications implemented in biomassGasificationFoam: • a reacting porous medium is introduced, • equations for the solid phase are introduced: conservation of solid components (Eq. 4) and energy conservation (Eq. 6), 10

Figure 5: Scheme of the main loop of the biomassGasificationFoam solver based on the PIMPLE algorithm. New development in the solver is in bold.

• the continuity equation for the gas phase (Eq. 2) and the species transport (Eq. 3) contain source terms due to the gas originating from the biomass gasification (see the RHS of these equations), • the gas energy conservation (Eq. 5) has additional source terms due to heat exchange between the gas and solid phases. • radiation absorption by biomass surface is possible. A schematic illustration of the main loop of the biomassGasificationFoam solver is provided in Fig. 5. The PIMPLE (PISO-SIMPLE) algorithm is used in biomassGasificationFoam, as in reactingFoam. The main loop contains two inner corrections for solving the pressure-momentum coupling influenced by energy and species distributions. The mass conservation equation is solved and the source terms calculated once per each main loop term. 5. Library - biomassGasificationMedia The model of the thermal conversion of biomass, as presented in Fig. 4, is constructed from three main elements: 11

• the definition of a porous medium and its mechanical properties - porousReactingMedia library, with the setPorosity utility; • definitions of thermal, chemical, and radiation properties of solids - thermophysicalModels libraries; • class linking the above libraries to the biomass gasification model - pyrolysisModels. Each part of the biomassGasificationMedia library is described in the following chapters. 5.1. porousReactingMedia and setPorosity The porosity model based on Darcy’s law is implemented in the porousReactingMedia library. The porous medium is introduced by two volumetric fields in the main computational domain: volScalarField porosityF - denoting the one minus void fraction (1 − γ) and volTensorField D f - representing the viscous resistance tensor K (see Eq. 1). The initial shape and mechanical properties of the porous medium are set using the setPorosity utility, which creates a field of porosity (porosityF) and a tensor field of porous resistance (D f ) of the desired shape and properties independent of the lattice. These fields are created using coordinate constraints on the centres of each computational cell in the already meshed domain. We found that the most beneficial and time-efficient way to design one’s own porous medium is to modify the ‘medium.H’ file of setPorosity and to recompile it using the standard OpenFOAM compilation mechanism. The computational cells are recognised as solid-state cells based on the γ field, and the Darcy tensor defined in cells with γ = 0 is of no importance. Porous media described in this way can be easily modified during program execution, which is particularly beneficial if one wants to simulate porous medium dynamics in the model. The porousReactingMedia library with the setPorosity utility can be used as the standalone model of the complex-shaped porous medium inside the computational domain. Currently, the library includes the Darcy Law for a porous medium only but can be extended to other nonlinear formulas (e.g., Forchheimer). 5.2. thermophysicalModels 5.2.1. ODEHeterogeneousSolidChemistryModel - reaction rates and stoichiometry The ODEHeterogeneousSolidChemistryModel derived from the ODESolidChemistryModel library is the implementation of the customisable kinetics of chemical reactions. The implemented kinetics is suitable for both homogeneous reactions (only gas or only solid substrates are involved) and heterogeneous reactions (both gas- and solid-phase substrates are involved, gaseous substrates included gases inside porous material and outside gases close to the solid surface). The reactions taking place in the gas phase only and the way of defining these reactions are inherited from the standard OpenFOAM solver reactingFoam. To introduce reactions (thermal processes) with the solid state, we must declare a new entry in the reaction subdictionary of the chemistryProperties dictionary. As a first example, we take the complex reaction of hemicellulose pyrolysis introduced as follows: irreversibleSolidArrheniusHeterogeneousReaction hem = 1.57 CH4 + 8.75 H2 + 5.73 CO + 9.72 CO2 + 0.4 char (1.495e9 1.488e4 400 1 1) The first line determines the choice of the reaction rate model. The second line describes a reaction involving the pyrolytic conversion of 1 kg of hemicellulose into 0.4 kg of char. The remaining hemicellulose volatiles are left as pyrolytic gases, namely, CH4 , H2 , CO, and CO2 , with the stoichiometry obtained experimentally [5]. Thus, there is only one substrate, and the reaction is automatically recognised as homogeneous. The third line contains numerical parameters of the reaction in the following order: the pre-exponential factor A, temperature of activation T a , critical temperature T c below which the reaction stops, reaction order nr , and, optionally, heat of reaction hr . The heat of reaction is defined per unit mass of volatiles (i.e., per unit mass of solid-phase mass loss). The last term (heat of reaction) is used only when the reaction energetic effect is introduced directly from experiment and not determined from the enthalpies of formation of the substrates and products (see Section 5.2.2). The second example, the heterogeneous reaction of char gasification with CO2 as a gasification agent, is introduced into the chemistryProperties dictionary as follows: 12

irreversibleSolidArrheniusHeterogeneousReaction char + CO2 = 2CO + 0.1 ash (1.7e7 324 800 2 1) This reaction is automatically interpreted as a heterogeneous reaction in which 1 kg of char reacts with gaseous CO2 , producing 0.1 kg of ash and two moles of CO per mole of CO2 consumed as a substrate. The net mass release to the gas phase is equal to the solid-phase mass loss, which makes it possible to calculate source terms for all gaseous species involved in the reaction. In the current version of the library, there are two possible models of the reaction rate κ: [ ] • irreversibleSolidArrheniusHeterogeneousReaction - Arrhenius reaction: κ = A exp − TTa T > Tc; [ ] • irreversibleSolidEvaporationHeterogeneousReaction - water evaporation: κ = A|T − T c |2/3 exp − TTa T > Tc. The reaction rate Ωr for the reaction r involving the solid-state substrate s is calculated as follows: { S S n G δG ρ (Y s ) r (Y ) κr , T > T c Ωr = 0, T ≤ T c

(16)

where δG equals one when there is a gaseous substrate and zero otherwise. Typically, the irreversibleSolidArrheniusHeterogeneousReaction is used for biomass pyrolysis, char gasification, and char combustion. For the evaporation of water contained within biomass, both kinetics (irreversibleSolidEvaporationHeterogeneousReaction and irreversibleSolidArrheniusHeterogeneousReaction) may be used. Other possible forms of reaction rates, such as a more realistic model of the evaporation of water embedded within porous structures, can be implemented. 5.2.2. ODEHeterogeneousSolidChemistryModel - heat of reaction There are two different ways of introducing the heats of reaction for the processes involving the solid phase. These two approaches are implemented in ODEHeterogeneousSolidChemistryModel: • “formationEnthalpy” - the heat of reaction is determined based on the enthalpy of formation of substrates and products; • “heatOfReaction” - the heat of reaction is provided independently by the user for each reaction. In both cases, the net energetic effect of solid reactions is calculated differently. The first approach, already implemented in reactingFoam, is typical for gas-phase reactions. In this approach, the heat of reaction is determined based on the formation enthalpies of substrates and products. For each substrate s and each product p, the enthalpies of formation h f s and h f p must be defined. Thus, for the reaction char + CO2 → 2CO + 0.1ash

(17)

we must define h f char , h f CO2 , h f CO , and h f ash . The set of ordinary differential equations describing the law of mass action must be solved to determine the mass change ∆m of each component k in the computational cell for each time step: dmk ∑ = Ωk,r dt r

(18)

Finally, the calculated mass changes for every substrate ∆m s and every product ∆m p are multiplied by their enthalpy of formation and summed to obtain the final energetic effect: ∑ ∑ Hr = ∆m s h f s + ∆m p h f p (19) s

p

13

Unfortunately, the enthalpies of formation of solid components, such as lignin, are difficult to determine. In this case, the heats of individual reactions must be introduced directly based on experimental results. Considering the reaction 17, with defined hr reaction energy and reaction rate Ωr , we can calculate the total energetic effect in time step ∆t as ∑ Hr = ∆t hr Ωr (20) r

5.2.3. heatTransferModel In modelling the thermal conversion processes, we use an energy equation based on temperature rather than enthalpy. We do not assume that the gas and solid are constantly in thermal equilibrium, and thus, the temperatures of the gas phase T G and solid phase T S are permanently distinguished. We assume that the heat transfer between both phases is proportional to the difference between the solid- and gas-phase temperatures. αΣ(T G − T S ) (21) where α denotes the heat transfer coefficient and Σ denotes a surface area of pores per solid state volume. However, heat transfer inside the bulk of the sample is qualitatively different from heat transfer through the border of the solid phase. To differentiate between those two situations, we introduce a new parameter borderHTC in addition to HTC. HTC denotes α for computational cells inside the solid-phase bulk, and borderHTC defines α for computational cells on the border of biomass fragment. To determine the surface area of pores Σ, we propose two approaches: • constHTC - assumes a constant total area of pore surface per volume unit, Σ = const, • cylinderHTC - porosity is modelled as a collection of parallel pipes. The cylinderHTC model assumes that the porous medium with initial void fraction γ0 has a regular lattice of parallel pipes with an initial radius a0 . Based on this assumption, one can determine the number of parallel cylinders N per unit volume. γ0 V N = 2 1/3 . (22) πa0 V We assume that N is constant; thus, the pores are enlarged due only to the increasing cylinder radius a. From the evolution of the void fraction accompanying the solid-state depletion, we can deduce the evolution of the surface per volume in the porous medium. ( )1/2 N2πaV 1/3 2 γ0 Σ= = (23) V a0 γ It must be stressed that there is a significant difference between the heat capacity of the solid and gas phases, which may lead to instability of the numerical solution due to energy transfer between phases. To avoid these fluctuations, we introduce a control parameter limiting time step (maxdT) in the controlDict dictionary. This parameter controls the maximum ratio of change in the gas- and solid-phase temperatures over all cells. 5.2.4. thermoType The thermoType library determines three main thermodynamic properties of the solid components: density, heat capacity, and thermal conductivity. Currently, as presented in Section 2.5, there are three models prepared for the runtime selection that can be selected in the solidThermophysicalProperties dictionary: • solidMixtureThermo - constant density, constant heat capacity, and a constant heat transport coefficient; • solidMixtureThermo - constant density, exponential heat capacity, and an exponential heat transport coefficient (see Section 2.5); • solidMixtureThermo - constant density, constant heat capacity, and a linear heat transport coefficient; 14

5.2.5. heterogeneousRadiationModel At the current stage, the influence of radiation on the solid is modelled in a simplified manner. We assumed that radiation is only absorbed by the biomass surface, not emitted. This assumption is reasonable in a wide class of applications, particularly for biomass particles in a heated environment, such as in a TGA experiment. Three heterogeneousRadiationModels are implemented and can be chosen in the radiationProperties dictionary: • none; • heterogeneousMeanTemp; • heterogeneousP1. In the first set, no radiation is considered in the simulation. In the second set, we assume that the optical thickness of the gases inside the reactor is small and that the gases do not interfere with the radiation. In this case, the energy is transferred directly from the heated walls to the surface of the biomass particle. To determine the surface of the 2 porous medium, we assume that on average, every cell is cubic; thus, its surface is given by V 3 , where V is the cell volume. An additional assumption is that on average approximately one sixth of its surface is exposed to the outside. This assumption gives the amount of surface exposed to radiation per computational cell on the border of the biomass given the volume of the biomass: 1 2 S = V3. (24) 6 Then, the net energetic income per unit volume is calculated according to Eq. 25: 1 V 2/3 4 S 4 δσ(T wall − ϵ(T sur (25) f ace ) )) 6 V where T wall is the average temperature of the walls, T sur f is the temperature of the particle surface, σ is the Boltzmann constant, δ is the solid-state surface optical absorption coefficient, and ϵ is the absorption-to-emission ratio. The last two parameters that describe the optical properties of the biomass surface are assumed to be constant in this implementation. In the third approach, the radiation within the computational domain is determined with the P1 radiation model available in OpenFOAM, as there is no biomass inside. Then, the biomass surface absorbs part of the available radiation energy. In the current implementation, the emission from biomass is not included, which means that the solid mass has no influence on the radiation density. The calculated radiation density in the gas phase is absorbed on the boundaries of the solid state. The net energetic income per unit volume is calculated as S rad = max(0,

S rad = max(0,

1 V 2/3 δ(G − ϵσ(T S )4 )) 6 V

(26)

where G is the radiation energy flux. 5.3. heterogeneousPyrolysisModel The heterogeneousPyrolysisModel class is an implementation of a base class for different pyrolysis models. This class creates all necessary fields of solid properties (e.g., mass fields of solid components) and integrates physical submodels for the solid state (e.g., radiation, kinetics, conduction). For each cell containing the solid phase (where γ < 1), the source terms for the gas- and solid-phase equations are calculated, as presented in Table 4. Necessary updates of the solid fields are performed once in each main loop turn. The library solves the equations for solid components (Eq. 4), energy conservation (Eq. 6), and porosity change: dγ ∑ ∑ ρk Ωk,r (27) = dt r k The porosity evolves with the vanishing solid phase as the increasing void fraction, e.g., for the reaction (17). In any computational cell, when γ is sufficiently close to one, i.e., (1 − γ) < 10−5 , it is fixed to one. Such a computational cell is considered to contain only a gas phase and does not participate in further solid-phase evolution. The specific model can be chosen in the pyrolysisProperties dictionary and also set as active or inactive there. Currently, only the volPyrolysis model is implemented for volumetric processes. When inactive, no calculations are performed for the solid-state fields. 15

Table 4: Source terms calculated for the solid and gas phases in the volPyrolysis model.

Source Heat transfer Reaction mass sources Reaction heat sources Radiative heat source Porosity

Definition and explanation Section 2.4 and 5.2.3, Eq. 12 Section 2.3, 5.2.1 and Appendix A Section 2.3 and 5.2.2, Eqs 19,20 Section 5.2.5, Eqs. 25-26 Section 2.5, Eq. 13

Solid phase Eq. 6 Eq. 4 Eq. 6 Eq. 6 Eqs. 4-6

Gas phase Eq. 5 Eq. 2 and Eq.3 Eq. 5 Eqs. 1-5

6. Validation and results TGA, through a detailed measurement of mass loss, quantifies the thermal decomposition of wood under wellcontrolled conditions. The experiment was performed using the Q500 (TA Instrument, New Castle, Delaware, US) thermogravimeter with an initial temperature of 300 K and a constant heating rate of 10 K/min. The experiment was carried out until the temperature reached 1,300 K. Because we provided a nitrogen environment, only the processes of drying and pyrolysis took place. The heating protocol and process environment were introduced through the initial and boundary conditions, which are summarised in Table 5. Table 5: Initial and boundary conditions used in the simulations.

Inert species Temperature Velocity Pressure

Initial condition nitrogen 300 K 0 m s−1 101300 Pa

Boundary condition inlet walls nitrogen 300 K + 10 · t K min−1 300 K + 10 · t K min−1 0.3 m s−1 0 m s−1 101300 Pa -

outlet zero gradient zero gradient zero gradient

The solver was validated with the case of pyrolysis of a pre-processed isotropic wood sample (Rubinia preudoaccacia) with the initial mass of 24 mg [6]. The test calculations were performed with simplified geometry for the TGA reactor and sample, both of which are modelled as cubes (see Fig. 6). The edge of the reactor is 8 mm. The entire computational domain was composed of 20 x 20 x 20 cells. The porous medium was distributed over 8 x 8 x 8 cells. The complete calculations corresponding to the TGA experiment took approximately 12 h with eight processors. In this paper, we use the mechanism of wood biomass pyrolysis, where cellulose, hemicellulose, and lignin decompose into a set of gases: H2 , CO, CO2 , and CH4 [6]. The heat of pyrolysis was determined from enthalpies of formation of substrates and products. The set of material properties and parameters of kinetics are presented in Table 6. The experimentally determined material properties of wood are typically ’effective’, combining the effects of gas and solid phases. Such properties depend strongly on the origin of the wood, the structure of the porosity, and the selected experimental procedures. In the solver presented here, we have introduced separate equations for the solid state that requires parameters for a ’pure solid’. A good example of such a material property is thermal conductivity. Measured effective values vary from 0.1 to 1 W m−1 K−1 , but the thermal conductivity of a solid skeleton is an order of magnitude higher, approximately 10 W m−1 K−1 . The comparison of mass loss during evaporation and pyrolysis in the TGA experiment and the corresponding simulation is presented in Fig. 7. The results are in qualitative agreement, but discrepancies are visible. The main reasons for these discrepancies are the imperfect and oversimplified kinetics of pyrolysis and the variability of wood composition, that cannot be exactly determined. The subsequent peaks of the inverse of the mass loss rate presented in Fig. 8 correspond to the processes of evaporation and pyrolysis of hemicellulose, cellulose, and lignin, respectively. All processes stop at approximately 800 K, when only char remains. In reality, as we see in Fig. 7, a small amount of char is still volatilising at higher temperatures. This effect is not included in the chosen pyrolysis kinetics. The mass loss rates shown in Fig. 8 are almost indistinguishable at different locations within the wood sample. 16

Figure 6: A simplified TGA reactor with cubic geometry and a hexagonal wood sample placed in the centre. In a diagonal plane cross-section of the sample, five points are marked (centre (C), top (T), bottom (B), top-corner (TC), and bottom-corner (BC)) in order to probe results.

Figure 9 illustrates how the densities (mass) of solid components, embedded moisture, hemicellulose, cellulose, and lignin are decreasing while the density (mass) of char is increasing. Reproducing this well-known sequence of decomposition is possible with separate kinetics constants for the individual solid components, which is straightforward in the presented solver. Figure 10 shows spatial distribution of the total density of the solid material during evaporation (at time 500 s when wall temperature equals 383 K) and during pyrolysis (at time 2000 s when wall temperature is equal 633 K). The density at the centre of the particle is highest. The gradients of density are small, which is expected for a small, thermally thin particle. Figure 11 illustrates the increase in the temperature of the gas phase at five selected points inside the wood: the centre, the bottom, the top, the bottom-corner, and the top-corner. The differences between points are small. This result corroborates the expectation that temperature gradients should be negligible in such a small sample [45]. The thermal thickness of this particle is confirmed by relatively uniform field of solid temperature presented in Fig. 12. The included thermal processes are endothermic and, as can be seen in Fig. 11, the rate of the gas temperature increase drops slightly when these processes occur. As expected, this decrease is most pronounced in the centre of the sample. In Fig. 13 (a), we present the evolution of the difference between the gas- and solid-phase temperatures, at each point. Figure 13 (b) illustrates the spatial distribution of this difference during pyrolysis at time 2000 s. As expected, this difference is negligible when no reaction takes place but increases when thermal processes are present. The sequence of peaks visible in Fig. 13 (a) is due to the evaporation and pyrolysis of different solid components. The gas phase is hotter than the solid. Figure 14 presents the composition of the produced gases. Because the process takes place in a reactor filled with nitrogen, the presented values are relative. The solver with the selected kinetics adequately reproduces the relative mass fractions (the ratios of the mass fractions of the different gaseous components) and the peaks of the processes. The velocity field around and inside the porous medium is presented in Fig. 15. As expected, the gas flows 17

Table 6: Physical properties and kinetic constants of the pyrolysis lignocellulose material used in the simulation.

Embedded Wood components Unit moisture Cel. Hem. Lig. Char Kinetic parameters of the pyrolysis of cellulose, hemicellulose, and lignin according to Fig. 3 (a) Initial mass fraction — 0.07 0.3588 0.276 0.2852 0 Pre-exponential factor s−1 1.4 · 1014 2.1 · 107 5.8 · 1013 1.06 · 103 — Activation energy J mol−1 1.35 · 104 1.34 · 104 1.94 · 104 8.95 · 103 — Minimum temperature K 300 450 400 500 — H2 O yield kg kg−1 1 0 0 0 — H2 yield kg kg−1 0 0.02 0.02 0.05 — CO yield kg kg−1 0 0.37 0.21 0.28 — CH4 yield kg kg−1 0 0.04 0.04 0.08 — CO2 yield kg kg−1 0 0.38 0.55 0.40 — Char yield kg kg−1 0 0.19 0.19 0.19 — Enthalpy of formation J kg−1 −15.9 · 106 −1.0 · 106 −8.5 · 105 −9.2 · 105 −4.1 · 104 Material properties for solid components Absolute density kg m−3 1000 1480 1957 Initial void fraction — — 0.55 0.91 Initial pore diameter m — 1 · 106 1 · 104 Permeability m2 — 1 · 10−14 1 · 10−11 a −1 −1 a Thermal conductivity Wm K 0.58 0.20 0.1a −1 −1 Heat capacity J kg K 4200 1380 1100 a

Ash

Reference

0.01 — — — — — — — — — −12.4 · 106

[6]

[41, 42]

2500 0.17 840

[43] [3] [44] [19] [43] [43]

Effective. Thermal conductivity through porous matrix kS , which leads to the presented effective conductivity is 10 W m−1 K−1 . symmetrically around the porous particle (see Fig. 15 (a)-(b)). Velocity magnitude inside the porous medium is, due to porous resistance, more than an order of magnitude smaller than outside. As we show in Figure 15 (c) the velocity vectors inside the particle are directed upwards and outwards. Upward components are due to the outer flow but outward components are caused by the gases being produced inside the porous medium. 7. Practical Issues 7.1. Installation instructions 7.1.1. OpenFOAM main package installation guide The easiest way to install the OpenFOAM main package is to use packs prepared for main Linux distributions available on the OpenFOAM website [7]. Here, a brief example for Ubuntu 12.04 LTS is provided. It is sufficient to copy, paste, and execute the following commands in the terminal window: (superuser privileges are required) VERS=$(lsb_release -cs) Obtains the installed version of Ubuntu release name sudo sh -c "echo deb http://www.openfoam.org/download/ubuntu $VERS main > /etc/apt/sources.list.d/openfoam.list" Adds the OpenFOAM pack address to repositories. The above command must be written on one line. sudo apt-get update Updates package list sudo apt-get install openfoam211 sudo apt-get install paraviewopenfoam3120 18

Figure 7: Comparison of the mass loss during the TGA experiment and the corresponding simulation.

Installs OpenFOAM (211 refers to version 2.1.1) and Paraview [46] (3120 refers to version 3.12.0) for the visualisation of results. Both OpenFOAM and Paraview are now installed in the /opt directory. From now on, no superuser privileges will be required. To configure the OpenFOAM package, it is necessary to add OpenFOAM to the system path by editing the .bashrc file in the user’s home directory. gedit ~/.bashrc and adding the following line to the bottom source /opt/openfoam211/etc/bashrc To check the installation type, icoFoam -help If “usage” information appears, the installation has completed correctly. Finally, create a user project directory in the $HOME/OpenFOAM directory named -2.1.1 by typing mkdir -p $WM_PROJECT_USER_DIR Now, we can proceed to the installation of biomassGasificationFoam. 7.1.2. biomassGasificationFoam library First, create a folder for the installation mkdir -p $WM_PROJECT_USER_DIR/biomassGasificationMedia Then, download the biomassGasificationFoam library and extract it into a temporary folder tar -zxvf biomassGasificationFoam_installPack_1.0.tar.gz Enter the extracted folder cd biomassGasificationFoam_installPack_1.0 19

0.5 centre (C) bottom (B) top (T) bottom−corner (BC) top−corner (TC)

0.45

rate of mass loss [kg/s]

0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 300

400

500

600 700 Temperature [K]

800

900

1000

Figure 8: Simulation: rate of mass loss at the five locations within the sample. Except at the very early stage they are almost indistinguishable.

Install the library and solver in the default folder (˜/OpenFOAM/-2.1.1/biomassGasificationMedia/) by typing source biomassGasificationMediaDirectiories ./install To test the installation, open a new terminal window and again set the environmental paths by typing source /opt/openfoam211/etc/bashrc source biomassGasificationMediaDirectories then run the solver by typing biomassGasificationFoam The message starting with the OpenFOAM header should appear. If so, the installation has been completed successfully, even if the computation cannot start due to ’FOAM FATAL IO ERROR’. To start the computations proceed to the pre-set test (tutorial) cases. 7.2. Test cases 7.2.1. Validation test The validation test case presented in Section 6 is included in the biomassGasificationMedia package with the solver and adequate libraries. The case reproduces results of the TGA experiment presented in Section 6. In Fig. 16, we summarised the structure of the directories and files included in the test case and required to start the new solver. All necessary data and parameters are set initially: • the initial and boundary conditions are set up in folder ’./0’ according to Table 5, initial solid composition is set according to the first row of Table 3. • the material parameters from Table 3 and mechanisms of thermal processes are defined in ’./constant’ and ’./chemkin’. • the case control parameters and details of the numerics are set up in ’./system’. The solver is started in the case folder by typing biomassGasificationFoam Running in parallel is possible with the standard OpenFOAM setup. An exemplary dictionary file for the decomposePar tool is available in ’./system’. 20

cellulose

moisture cellulose hemicellulose lignin char ash

3

density of solid components [kg/m ]

250

200

lignin hemicellulose

150 char 100 moisture 50 ash 0 300

400

500

600 700 Temperature [K]

800

900

1000

Figure 9: Simulation: changing the densities of the solid components.

7.2.2. One-cell case Additional test case included into the package is prepared for analysing and testing kinetics of the processes. The geometry is reduced to a single computational cell, thus the solver provides rapid results of qualitative nature. In this case we focus on the chemical reactions and mechanisms of thermal processes rather than on heat transfer, so the source terms incorporating the effects of radiation and conductional heat transfer in the porous medium are neglected. The kinetics preset in the one-cell test run is the same as in the validation test described in Section 7.2.1. 7.2.3. Visualisation of results The results can be visualised in three ways. • The method of choice is to use Paraview [46] visualisation for graphical presentation. • The second is to use the probeLocations tool provided with OpenFOAM. This tool probes selected variables over time at different locations according to the dictionary file probesDict located in ./system. The results are produced in ./probes dictionary. • The third method, totalMass distributed with the package, is the fastest but provides information only on temporal change of the total mass of porous medium and saves it in totalMass.txt file. To run this tool type totalMass 8. Conclusions We presented a new solver biomassGasificationFoam and a complementary library biomassGasificationMedia that extended the functionalities of the well-supported open-source CFD code OpenFOAM. The main goal of this development was to provide a comprehensive and flexible computational environment for a wide range of applications involving reacting gases and solids. The biomassGasificationFoam is an integrated solver capable of modelling thermal conversion , including evaporation, pyrolysis, gasification, and combustion, of various solid materials. This type of integrated approach allowed for numerical modelling of the complex cross-scale process of biomass pyrolysis and gasification, particularly directed toward the optimisation of fixed-bed reactors. The solver and library can potentially be applied in modelling of the processes involving porous reacting media and gases, not only in biomass gasification, but also for catalysis or filtration. 21

(a) Density of solid at time 500 s

(b) Density of solid at time 2000 s

Figure 10: Biomass particle: the comparison of biomass density at 500 s (evaporation) and 2000 s (pyrolysis).

9. Acknowledgements Part of this work has been supported by the strategic program of scientific research and experimental development of the National (Polish) Centre for Research and Development: “Advanced Technologies for Energy Generation”; Task 4. “Developing integrated technologies for fuel and energy production from biomass, agricultural wastes, and other resources”. Numerical computations were performed in the Interdisciplinary Centre for Computational and Mathematical Modelling (ICM), University of Warsaw, grant number G34-8. We thank Marek Kocha´nczyk for helpful comments on C++. We thank prof. Marzena P´ołka from The Main School of Fire Service in Warsaw for performing the thermogravimetry analysis. Appendix A. Source term calculation Appendix A.1. Pyrolysis The process of pyrolysis is presented in the following convenient form of Eq. A.3. In this formula, the solid component k (cellulose, hemicellulose, or lignin) produces a set of gaseous products pG (where the index p denotes H2 , CO, CO2 , CH4 ). As a result of pyrolysis, the solid component is transformed into char [6]. cellulose → hemicellulose → lignin →

∑ ∑ ∑

ν p pG + char

(A.1)

ν p pG + char

(A.2)

ν p pG + char

(A.3)

The reaction rate coefficient modelled by Arrhenius formulae leads to the following mass rate Ωk,r for reaction (process) r for solid component k: ( ) T S S nr , T > Tc (A.4) Ωk,r = Ar ρ (Yk ) exp T 0r In general, several different paths of decomposition of the same solid component k are possible. The index r counts these separate paths of reactions; in the present example, A.3 r = 1. Each reaction r of substrate k is appended to the total reaction rate ∑ pyro RSk =− Ωk,r (A.5) r

22

800 750

T (gas phase) [K]

700 BC

650

hemicellulose pyrolysis BC

600 550

C cellulose pyrolysis

C

500 450

centre (C) bottom (B) top (T) bottom−corner (BC) top−corner (TC)

evaporation 400

BC

350 300 300

C 400

500 600 Temperature [K]

700

800

(a) Gas temperature as a function of time for selected points inside the biomass particle.

(b) Gas temperature field at time 2000 s. (wall temperature 633 K) Figure 11: Temperature of the gas phase: (a) temporal change at selected points, (b) temperature field at time 2000 s.

Figure 12: Temperature of the solid at time 2000 s when wall temperature is equal 633 K.

23

60

evaporation

T (gas phase) − T (solid phase) [K]

centre bottom top bottom−corner top−corner

hemicellulose cellulose pyrolysis pyrolysis

BC 50

BC TC

40 B

B

30

lignin pyrolysis T

BC

T 20 C 10

0 300

C

400

500

600 700 Temperature [K]

800

900

1000

(a) Difference between T and T s for selected points inside the biomass particle.

(b) Spatial distribution of T − T s Figure 13: Difference between the temperature of the gas (T) and solid (T s ): (a) as a function of time at selected points, (b) spatial distribution of (T − T s ) at time 2000 s when the wall temperature is equal 633 K.

The reaction rates for products of reaction Eq. A.3 take the form ∑∑ pyro RSchar = ξr Ωk,r k

RGp

pyro

=

(A.6)

r

∑ ∑ W pG ∑ G (1 − ξr ) Ωk,r i Wp r k

(A.7)

where ξr is the mass ratio of solid products to solid substrates. Appendix A.2. Char combustion It is assumed that char combustion is the most competitive heterogeneous reaction. Other heterogeneous reactions, such as gasification, are slower and typically take place when O2 is completely consumed for heterogeneous 24

mass fraction of gaseus products [−]

0.01

hemicellulose pyrolysis

0.009

H O 2

H2

cellulose pyrolysis

0.008 0.007 0.006

evaporation

CO CO2

CO2

CH

4

H2O

0.005

lignin pyrolysis

0.004

CO

0.003 0.002 CH4

0.001 0 300

400

500

600 700 Temperature [K]

800

900

1000

Figure 14: Mass fraction of the gases.

or homogeneous combustion. The combustion of the solid phase occurs only if O2 is present and the temperature is sufficiently high. In the present paper, we assume that only the carbon contained in char is available for combustion and gasification. The reaction of char combustion is presented in Eq. A.8. char + O2 → CO2 + 0.1ash

(A.8)

With the reaction rate coefficient modelled by Arrhenius, mass rates for reactants and products are presented in a set of equations A.10. ( ) T S comb S S nc G Rchar = Ac ρ (Ychar ) YO2 exp , T > Tc (A.9) T 0c ρSash S comb comb RSash = R (A.10) ρSchar char RG CO2

comb

comb RGO2

= =

G WCO 2 G WCO − WOG2 2

−

(1 −

WOG2 G − WOG2 WCO 2

ρSash ρSchar

(1 −

)RSchar

ρSash ρSchar

comb

)RSchar

comb

(A.11) (A.12)

Appendix A.3. Char gasification The heterogeneous reactions involved in gasification are written in Eqs. A.15 [1]. Carbon, C, typically presented on the LHS of gasification reactions, is completely incorporated into the structure of the char, which is why the gasification reactions are modelled as the reactions of char and the gasification agent. We present these reactions in the convenient formula A.15, where Ga is the gasification agent (index a denotes O2 , CO2 , or steam) and G p represents the gaseous products (index p denotes H2 , CO, CO2 , and CH4 ). char + CO2 → 2CO + ash char + H2 O → CO + H2 + ash char + O2 → CO + ash 25

(A.13) (A.14) (A.15)

(a) Velocity magnitude.

(b) Vectors of gas velocity outside the porous medium.

(c) velocity vectors inside porous medium. Figure 15: Velocity field at time 2000 s when wall temperature is equal 633 K: (a) field of velocity magnitude, (b) velocity vectors around the biomass particle, (c) velocity vectors inside porous medium .

The mass rate is modelled by formula A.16. ( S )ng YaG exp Ωr = Ar ρS (Ychar

T T 0r

) (A.16)

Each reaction is appended to the total reaction rate for the species included in the following manner from mass

26

Figure 16: Structure of the dictionaries and files of the test case. Inside the black frame are files modified (dashed lines) or introduced (solid lines) for biomassGasificationFoam.

conservation: RSchar

gasi f

=

−

∑

Ωr

(A.17)

∑ (1 − ξr )Ωr

(A.18)

r

RSash

gasi f

=

r gasi f RGp

=

∑

∑ ∑

r

RGa

gasi f

=

∑ r

∑

p

ν p W pG

(1 − ξr )Ωr

(A.19)

νa WaG (1 − ξr )Ωr ν p W pG − νa WaG

(A.20)

ν p W pG − νa WaG

27

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