Modeling of the Thermochemical Conversion of Biomass in Cement Rotary Kiln


Because of the depletion of fossil fuels and because of its increasing cost, waste has been used as alternative fuels in cement rotary kilns for several years. In order to fulfil the requirements of environmental protection and quality of the final product, it is necessary to understand and quantify the different processes occurring in the kiln. The aim of our work is to develop a mathematical model of the processes occurring in the kiln. This model will rely on the coupling between a CFD model and homemade software. More precisely, the CFD model, which will be fully three-dimensional will account for the homogeneous processes taking place in the freeboard of the bed of material being processed. This bed of material will be at the center of the second model which will represent it as a 1D plug flow reactor. In the present work, we focus on this 1D model. We first give insights on the main assumptions on which the model relies, and information on the reaction pathway leading to the production of cement. Indeed, it is considered that the bed is composed of a mixture of CaCO3, MgCO3, Al2O3, SiO2, Fe2O3, MgO, CaO, C2S, C3A, C4AF and C3S undergoing thermochemical transformation. The bed under consideration is also composed of biomass (agricultural residues). During its transformation (pyrolysis, combustion of volatiles, combustion of the pyrolysis residue), this material contributes to thermal equilibrium of the reactor, by carrying the energy associated to its complete combustion. In this paper, the different equations that translate into mathematical formalism the processes of transport of the bed as well as mass and energy balance are also presented. The results show that the cement obtained complies with the requirements of Portland cements (73.06% of Silicates and 18.76% of Aluminates), the conversion of the biomass is total (100%), and the specific energy consumption is almost in conformity with the values of literature.

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Algebraic equation


Computational fluid dynamics


Number of cellules (numerical parameter)


Number of species of solid meal (flour)


Number of species of waste (biomass)


Number of gas species


Ordinary differential equation

\(A_{lit}\) :

Transverse surface of the bed (m2)

\(A\) :

Pre-exponential factor (s1)

\(c_{p}\) :

Specific heat (J kg1 K1)

\(d_{four}\) :

Diameter of rotary kiln (m)

\(d_{dec}\) :

Diameter of biomass particle (m)

\(Ea\) :

Activation energy (J mol1)

\(e_{refrac}\) :

Refractory thickness (m)

\(Fr\) :

Froude number

\(g\) :

Gravity acceleration (m s2)

\(h_{f,i}^{0}\) :

Enthalpy of formation of the species I (J kg1)

\(h_{lit}\) :

Enthalpy of the bed (J kg1)

\(H_{lit}\) :

Bed height (m)

\(h\) :

Heat exchange coefficient (W m2 K1)

\(k\) :

Speed constant (s1)

\(l_{lit}\) :

Width of the bed (m)

\(L_{four}\) :

Kiln length (m)

\(M_{i}\) :

Molar mass of the species i (kg mol1)

\(\dot{m}\) :

Mass flow (kg s1)

\(N_{z}\) :

Number of waste particles (m1)

\(n_{four}\) :

Speed of rotation of the kiln (tr s1)

\(q_{v}\) :

Volume flow rate (m3 s1)

\(r\) :

Chemical reaction rate (kg m2 s1)

\(R_{k}^{Fa,Fa}\) :

Specific net rate of production / disappearance of k species of flour (kg m3 s1)

\(R_{q}^{dec,dec}\) :

Specific net rate of production/disappearance of species q of waste (kg m3 s1)

\(R_{b}^{gaz,gaz}\) :

Specific net rate of production of species b associated with the homogeneous reactions in the gas phase (kg m3 s1)

\(R_{b}^{fa,gaz}\) :

Specific net rate of production of species b by the decomposition reactions of flour (kg m3 s1)

\(R_{b}^{dec,gaz}\) :

Specific net rate of production of species b gas by decomposition reactions of waste (kg m3 s1)

\(S\) :

Surface (m2)

\(S_{trans}\) :

Cross-sectional area of the kiln wall (m2)

\(\left[ { i } \right]\) :

Molar/mass concentration

\(T\) :

Temperature (K)

\(u\) :

Speed (m s1)

\(y_{k}^{fa}\) :

Mass fraction of k species in meal (flour)

\(y_{fa}^{lit}\) :

Mass fraction of the flour in the bed

\(y_{q}^{dec}\) :

Mass fraction of species q in waste

\(y_{dec}^{lit}\) :

Mass fraction of waste in the bed

\(y_{b}^{gaz}\) :

Mass fraction of species b in gas

\(y_{gaz}^{lit}\) :

Mass fraction of gas in the bed

\(\delta_{four}\) :

Tilting of the kiln (rad)

\(\delta_{lit}\) :

Angle of interception of the bed (rad)

\(\varepsilon\) :

Emissivity (–)

\(\lambda\) :

Thermal conductivity (W m1 K1)

\(\rho\) :

Volume mass (kg m3)

\(\varphi_{dyn}\) :

Dynamic angle of repose of the bed (rad)

\(\varphi\) :

Heat exchange flow (W)

\(\omega\) :

Angular velocity (rad s1)

\(0\) :

Initial condition/kiln inlet

\(Ashes\) :


\(Char,pyro\) :

Char pyrolysis

\(dec\) :


\(decouv\) :

Open wall

\(ext\) :

Outside environment

\(fa\) :


\(four\) :

Kiln or wall of the kiln

\(free\) :


\(free,lit\) :

Freeboard gas—bed of solids

\(four,lit\) :

Covered wall of the kiln—bed of solids

\(four,ext\) :

Outer wall of the kiln—outside environment

\(gaz\) :


\(gazFB\) :

Freeboard gas

\(hum\) :


\(lit\) :

Bed of solids

\(Org. Mat.\) :

Organic matter


CaO—calcium oxide or lime


SiO2—silicon dioxide or Silica




Fe2O3—iron oxide III


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We wish to acknowledge Kongo University in the Democratic Republic of Congo for funding our research work. We also thank the managers of congolese cement plants, CINAT and CILU, for the technical data they provided us.

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Correspondence to B.-J. R. Mungyeko Bisulandu.

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Mungyeko Bisulandu, BJ.R., Marias, F. Modeling of the Thermochemical Conversion of Biomass in Cement Rotary Kiln. Waste Biomass Valor 12, 1005–1024 (2021).

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  • Cement rotary kiln
  • Cement clinker
  • Biomass
  • Pyrolysis
  • Combustion and gasification processes
  • One-dimensional model