Models for biomass residence time and char accumulation

The data obtained from the setup described in Section 3.2.1 can be correlated for prediction of devolatilization time, char release and heat loss after devolatilization, and the nominal biomass accumulation at a given operating condition in a continuous flow biomass gasification process. To be able to apply the behaviour observed in the current setup to a different system, biomass loading, air flowrate and particle properties need to be properly scaled as described in the article [A9]. Figure 4.4 shows the plots of log₁₀(𝑥_𝑏^𝑎𝑡_𝑑) and log₁₀(𝑥_𝑏^𝑎𝑡_𝑒) against the gas velocity ratio log₁₀(𝑈₀/𝑈_𝑚𝑓), where 𝑥_𝑏 is the mass of biomass to mass of sand particles in the bed and 𝑈₀ = 𝑚̇_𝑎𝑖𝑟/(𝜌_𝑎𝑖𝑟𝐴) is the superficial air velocity obtained at the temperature corresponding to the respective time in the bed. The particle minimum fluidization velocity 𝑈_𝑚𝑓 is predicted using the Wen and Yu [62] model. The value of 𝑎 for each figure is obtained by minimizing the sum of the square error between the fitting line and the experimental data.

(a) (b)

Figure 4.4. Characteristic residence time for biomass conversion in an air-blown batch bubbling fluidized bed correlated with biomass mass load and air velocity (a) devolatilization (b)

extinction.

From the fitting lines, the biomass devolatilization time 𝑡_𝑑 [min] and extinction time 𝑡_𝑒 [min] can be modelled by

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𝒕_𝒅= 𝟏𝟏. 𝟑𝟓𝒙_𝒃^{𝟎.𝟎𝟐𝟖}(^𝑼𝟎

𝑼_𝒎𝒇)

−𝟎.𝟑

± 𝟕. 𝟕% (4.37)

𝒕_𝒆= 𝟔𝟕. 𝟓𝟖𝒙_𝒃^{𝟎.𝟐𝟕𝟖}(^𝑼𝟎

𝑼_𝒎𝒇)

−𝟎.𝟏𝟖𝟓

± 𝟕. 𝟔% (4.38)

The amount of char released after devolatilization also increases with decreasing air flowrate and amount of biomass charged in the bed as presented in the article [A9].

Figure 4.5(a) shows how the fraction of the char yield 𝛾_{𝑐ℎ𝑎𝑟} varies with the operating parameters.

From the relationship shown in Figure 4.5(a), 𝛾_{𝑐ℎ𝑎𝑟} can thus be determined from 𝜸_{𝒄𝒉𝒂𝒓} = 𝟎. 𝟒𝟏𝟒𝒙_𝒃^{𝟎.𝟐𝟒𝟓}(^𝑼𝟎

𝑼𝒎𝒇)

−𝟎.𝟒𝟔𝟑

± 𝟏𝟖% (4.39)

The change in the bed temperature over the dvolatilization time, which measures the net heat loss during this conversion phase, is also correlated as given in Figure 4.5(b).

Based on the fitting line, the devolatilization heat loss 𝑞̇_𝐿 [K/s] can be expressed as 𝒒̇_𝑳 = 𝟏. 𝟔𝟔𝟒 (^𝑼𝟎

𝑼_𝒎𝒇𝒙_𝒃)

𝟎.𝟕𝟔𝟕

± 𝟐𝟓% (4.40)

(a) (b)

Figure 4.5. (a) Char yields (b) net heat loss at the end of biomass devolatilization phase in an air-blown batch bubbling fluidized bed correlated with biomass mass load and air velocity.

For application of these equations, (4.37) – (4.40) to a continuous air-blown biomass gasification process in bubbling beds, the extent of the char conversion 𝛼 at a given air flowrate needs to be defined.

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𝛼 =^{𝑡∗−𝑡𝑑}

𝑡_𝑒−𝑡_𝑑 (4.41)

The analysis of the experimental data shows that 𝛼 lies in the range 0.45 – 0.7, where the mean value of 𝛼 is 0.55 for the wood pellets and 0.6 for the wood chips. Assuming a plug flow, the amount of biomass 𝑥_𝑏 supplied over the extinction time 𝑡_𝑒 at a constant biomass flowrate 𝑚̇_𝑏 can be obtained from Eq. (4.42) derived from Eq. (4.38).

𝑥_𝑏 = [4055^𝑚̇𝑏

𝑚_𝑝( ^𝑈0

𝑈_𝑚𝑓)

−0.185

]

1.385

(4.42)

where 𝑚_𝑝 is the mass of the bed material. The amount of char accumulated 𝑥_{𝑐ℎ𝑎𝑟} (mass of char to mass of the bed material ratio) in the bed over an extinction cycle can thus be obtained from

𝒙_{𝒄𝒉𝒂𝒓}= (𝟏 − 𝜶)𝜸_{𝒄𝒉𝒂𝒓}(𝒕_𝒆− 𝒕_𝒅)^𝒎̇𝒃

𝒎𝒑 (4.43)

Equation (4.43) can be applied for determining the necessary bed properties including the minimum fluidization velocity, bubble properties and bed expansion of the solid mixture at a given operating condition. For decongesting the bed to avoid pressure build-up, the solids circulation rate 𝑚̇_𝑠𝑐 can also be derived from this equation as given below.

𝒎̇_𝒔𝒄= ^𝒎𝒑

(𝟏−𝜶)(𝒕𝒆−𝒕𝒅)(𝒙_{𝒄𝒉𝒂𝒓}+ 𝟏) (4.44)

4.2 1D model for bubbling bed reactor

Based on the Euler-Euler modelling approach, a one-dimensional model describing the fluid-particle behaviour in a fluidized bed is presented in Article [A2] as described below.

𝜕

𝜕𝑡(𝜀_𝑠𝜌_𝑠𝑣) = − ^𝜕

𝜕𝑧(𝜀_𝑠𝜌_𝑠𝑣. 𝑣) + ^𝜕

𝜕𝑧(𝜇_𝑒𝑠^𝜕𝑣

𝜕𝑧) − 𝜀_𝑠^𝜕𝑃𝑔

𝜕𝑧 − ^{2𝑓𝑠𝜀𝑠𝜌𝑠𝑣|𝑣|}

𝐷_ℎ − 𝜀_𝑠𝜌_𝑠𝑔 − ^𝜕𝑃𝑠

𝜕𝑧 +

𝛽_𝑑(𝑢 − 𝑣) (4.45)

𝜕

𝜕𝑡(𝜀_𝑔𝜌_𝑔𝑢) = − ^𝜕

𝜕𝑧(𝜀_𝑔𝜌_𝑔𝑢. 𝑢) + ^𝜕

𝜕𝑧(𝜇_𝑒𝑔^𝜕𝑢

𝜕𝑧) − 𝜀_𝑔^𝜕𝑃𝑔

𝜕𝑧 − ^{2𝑓𝑔𝜀𝑔𝜌𝑔𝑢|𝑢|}

𝐷_ℎ − 𝜀_𝑔𝜌_𝑔𝑔 +

𝛽_𝑑(𝑣 − 𝑢) (4.46)

Equations (4.45) and (4.46) respectively describe the particle and fluid momentum balances in a dense fluidized bed where the solids 𝜀_𝑠 and fluid 𝜀_𝑔 volume fractions are related by

𝜀_𝑠+ 𝜀_𝑔 = 1 (4.47)

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The propagation of the bed void fraction 𝜀_𝑔 along the axis, Eq. (4.48) is derived based on the mass balances of the different phases across a given volume.

𝛼_𝑚^𝜕𝜀𝑔

𝜕𝑡 + 𝑣_𝑚^𝜕𝜀𝑔

𝜕𝑧 = 𝜀_𝑠𝜀_𝑔𝜌_𝑟𝑔^𝜕𝑣𝑟

𝜕𝑧 (4.48)

Here, 𝑣_𝑟 = 𝑣 − 𝑢 is the relative velocity between the particle and the fluid, and 𝜌_𝑟𝑔 = 𝜌_𝑔/𝜌_𝑟𝑒𝑓 is the reduced gas density. The mixture mass velocity 𝑣_𝑚 and relative mass fraction 𝛼_𝑚 are given by

𝑣_𝑚 = 𝜀_𝑔𝜌_𝑟𝑔𝑣 + 𝜀_𝑠𝑢 (4.49)

𝛼_𝑚 = 𝜀_𝑔𝜌_𝑟𝑔 + 𝜀_𝑠 (4.50)

The constitutive equations for closing the governing equations are also given in the article [A2]. The hydrodynamic model described above was used to study the bubbling fluidized bed behaviour of an inert bed material. By including the reaction rate terms, the model can also be applied for thermochemical conversion of solid fuel particles in fluidized beds. In this case, some simplifications can be introduced to reduce the complexities in applying the model for bubbling bed reactors. The description and detailed procedure employed in simplifying the model are given in Article [A10].

The proposed thermochemical conversion model is also based on the conservations of mass and momentum in addition to the energy conservation across a given volume in the direction of fluid flow. For simplicity, the model assumes that the net velocity of the inert bed material is zero. The solids fraction of the bed particle due to flow of gas is therefore computed using the correlation in the literature. The fluid flow is modelled based on the Euler approach following the continuum mechanism, but the viscous force and energy transport due to fluid viscous stress are neglected. The fuel particles are assumed dispersed and their motion is tracked by considering the Lagrangian approach.

The changes in the kinetic energy of the particle is also incorporated due to possible changes in the particle mass along the bed axis as the reactions proceed.

The assumption that the fuel particles are dispersed helps to eliminate the interactions between the fuel particles in the model. This assumption is reasonable in normal operations where the concentration of the biomass particles is negligible compared to the bed material. On the contrary, Eq. (4.45) is based on the particle bulk density where the particle number density is very high. For this reason, the momentum transfers due to viscous stress and pressure forces on the particles are considered. In the model developed in [A10], these momentum terms are neglected, resulting in a different form of equation presented in the article and by Eq. (4.55). Figure 4.6 describes the

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computational volume of the model, and the flow of fluid and particles within and across the reactor. All the symbols are as described in the article [A10].

Figure 4.6. Schematic Illustration of a bubbling fluidized bed behaviour in a binary solid mixture (red = biomass, black = bed material), showing biomass and gas boundary conditions

and drag of solids into bubble wakes.

It should be noted that the zero pressure gradient (𝜕𝑝/𝜕𝑧 = 0) implies that the gauge pressure, 𝑝 − 𝑝_atm = 0 at the outlet boundary. Based on this, the pressure outlet boundary condition specified in Figure 4.6 is the same as that given in Article [A2] under the atmospheric bubbling fluidized bed condition. For the simplified model, most of the assumptions introduced are highlighted below.

 There are no variations of temperature and species in the radial directions.

Hence, the model is one-dimensional, i.e. there are only gradients in the axial direction.

 The bed expands uniformly, resulting in an even distribution of the bed material particles. With this assumption, the complex computation of mass flow of the particles is eliminated while the average solids fraction of the material is obtained from the available empirical correlations.

 The bed material remains inert over a clearly defined volume, and there is no mass loss due to elutriation. Hence, the net velocity of the particles is considered zero over one cycle of the solids circulation.

 The ash content of biomass is negligible.

 The unconverted tar is in vapour phase.

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 The gas species move upwards while the fuel solids move downwards.

 The solid fuel particles are dispersed and the motion of each particle is independent of the others.

 The mass distribution of both gas and solid phases are continuum.

 The properties of biomass and char particles are constant.

 The momentum change of the bed particles as they are dragged into the bubble wake is transferred to the biomass particles.

 The fluid pressure drop over the bed is hydrostatic.

 The amount of fuel particles in the bed is relatively small compared to the bed material, hence does not influence the solid mixture density.

 The gas behaviour follows the ideal gas law.

 The contact and radiation heat exchanges between the fuel particles and the reactor walls are negligible.

 The gas and reactor walls are in thermal equilibrium.

Based on the outlined assumptions, the proposed model for thermochemical conversions in a bubbling bed is therefore given as follows.

In document Bubbling Fluidized Bed Behaviour for Biomass Gasification (sider 52-57)