# A model to predict the kinetics of mass loss in wood during thermo-vacuum modification

• Ottaviano Allegretti , Ignazia Cuccui , Nasko Terziev and Laerte Sorini
From the journal Holzforschung

## Abstract

Mass loss (ML) of wood caused by thermal degradation is one of the most important features of the thermal treatments and referred to as an indicator of intensity and quality of the process. The ML is proportional to the quantity of the effective heat power exchanged during the treatment process, represented by the area of the temperature profile versus time during the process. In this paper a model for the ML prediction based on the relative area was discussed. The model proposed an analytical solution to take into account the non-linear trend of ML when plotted versus temperature and time as observed in isothermal experiments. The model was validated comparing calculated and measured final ML of samples treated during thermal modification tests with different temperature profiles. The results showed that the relative area calculated in a transformed time-temperature space improves the correlation with the measured ML.

Corresponding author: Ottaviano Allegretti, Istituto per la BioEconomia, CNR-IBE National Research Council of Italy, via Biasi 75, San Michele all’Adige, 38010, TN, Italy, E-mail: .

1. Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

2. Research funding: None declared.

3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

## Appendix 1: Discrete representation of H‾∗

A discrete representation H in + 1 point (according to the partition of Equation (7)) of Equation (8) is used in this work is:

(11)H=i=1n+1Hi=i=1n+1TtiΔgiwithTti=(TtiT0)+q+(Tti1T0)+q2whereH0=0,Δg0=0,Δgi=g(ti)g(ti1),ti={0if(TtiT0)+0ti1+Δiotherwise,t0=0Δ0=0,Δi=titi1,T0[Tmin,Tmax],p]0,1],q[1,+[,nℕ

In this case where g(t)=tp, g(t) is monotone, we have:

(12)H=i=1n+1Hi=i=1n+1[(TtiT0)+q+(Tti1T0)+q2]ΔiwhereH0=0,Δ0=0,Δi=tipti1p,ti={0if(TtiT0)+0ti1+Δiotherwise,t0=0Δ0=0,Δi=titi1,T0[Tmin,Tmax],p]0,1],q[1,+[,nℕ

## Appendix 2: Code for calculating H‾* and H‾

A simple generic code for calculating H(Tt,t) and H(Tt) is:

 input p , q , T0 , n vector t(0…n+1), T(0…n+1) Tr1 = 0 Tr2 = 0 H* = 0 H = 0 loop i = 1 → n+1 D ← t(i)-t(i-1) Dp2 ← max( 0 , T(i-1)-T0 ) Dp1 ← max( 0 ,T(i)-T0 ) If ( Dp1 > 0 ) or ( Dp2 > 0 ) then Tr2 ← Tr2 + t(i-1) if i = 1 then Tr2 ← Tr2 - t(i-2) Tr1 ← Tr1 + t(i) - t(i-1) DTr ← (Tr1)ˆp + (Tr2)ˆp H* ← H* + DTr*(Dp1ˆq + Dp2ˆq)/2 H ← H + D *(Dp1 + Dp2)/2 end if end loop output H , H*

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