**1. Introduction**

The energy demand of the world has been increasing consistently due to growing population and rising living standards [1]. As a result, fossil fuel reserves are ending gradually [2,3]. These fuels also cause severe environmental contamination with a high level of greenhouse gas emissions [4,5]. The research on renewable energy and alternative fuels has attracted many scholars worldwide. Woody biomass has been recognized as a promising source of renewable energy due to its availability in most parts of the globe [6]. Major shortcomings of biomass that limit its wider utilization for power generation are low bulk density, high moisture content, low heating value, and high energy requirement for grinding [7].

To improve the fuel properties of biomass, it needs to be pretreated. Torrefaction technology is a thermal treatment that greatly improves the heating value and grindability of biomass [8]. It is a mild pyrolysis where raw biomass loses its moisture content and a fraction of volatiles at a temperature between 200–300 ◦C in an inert atmosphere. The thermophysical properties of the torrefied biomass such as its elemental compositions and heating value are required for optimum design of a torrefaction plant or the furnace of a boiler which uses torrefied biomass as a fuel. Experimental determination of the elemental compositions through ultimate analysis is costly and requires sensitive equipment [9]. A predictive model that can help estimate the composition and heating value of torrefied solid obtained from different operating conditions is expected to be a useful tool for process modeling purposes. To the best knowledge of the authors, the literature lacks a general correlation for prediction of the C, H and O content of a torrefied biomass.

Some past studies have presented correlations for predicting the elemental compositions and HHV of raw biomass using proximate and ultimate analysis [10–13]. Parikh et al. [10] considered Volatile Matter (VM) and Fixed Carbon (FC) and proposed the following correlations:

$$\text{C} = 0.637 \text{FC} + 0.455 \text{VM} \tag{1}$$

$$\text{pH} = 0.052 \text{FC} + 0.062 \text{VM} \tag{2}$$

$$\text{CO} = 0.304 \text{FC} + 0.476 \text{VM} \tag{3}$$

The average absolute errors of Equations (1)–(3) are 3.21%, 4.79%, 3.4% with bias errors of 0.21%, 0.15% and 0.49%, respectively, for predicting C, H and O content of raw biomass. Shen et al. [11] developed the following relations based on fixed carbon, volatile matter and ash content (ASH) of raw biomass to predict the elemental compositions of the same raw biomass.

> C = 0.635FC + 0.460VM − 0.095ASH (4)

$$\text{pH} = 0.059 \text{FC} + 0.060 \text{VM} + 0.010 \text{ASH} \tag{5}$$

$$\text{O} = 0.340 \text{FC} + 0.469 \text{VM} - 0.023 \text{ASH} \tag{6}$$

The average absolute errors of correlations given in Equations (4)–(6) are 3.17%, 4.47% and 3.16%, with average bias errors of 0.19%, 0.34% and 0.19%, respectively. Yin [12] used 44 sets of data and proposed two separate relationships for HHV of raw biomass using proximate analysis and ultimate analysis. Friedl et al. [13] proposed a correlation using 122 samples of plant materials for estimation of the HHV of raw biomass using the elemental composition. A comprehensive review of the models for estimating the heating value of biomass is reported in Ref. [14].

Due to the significant difference between the thermophysical properties of raw and torrefied biomass, the existing correlations in the literature are not suitable for estimating the elemental compositions. It is worth noting that the correlation of Friedl et al. [13] has been successfully applied for prediction of the heating value of torrefied biomass in some studies [15,16]. Nhucchen [17] used the data of proximate analysis of raw and torrefied biomass and proposed correlations for predicting the C, H and O contents of torrefied biomass. Nhucchen et al. [18] developed two correlations for the HHV of torrefied biomass using both proximate analysis and ultimate analysis. The latter correlation is alike that of Friedl et al. [13]. A model for predicting the HHV of torrefied biomass using the kinetics of decomposition with an average absolute error of 7.03% is also reported by Soponpongpipat et al. [19].

Although the proposed relations of Nhucchen et al. [17,18] appear to be useful, they do not eliminate the need for experiment. One would still need to have the measured values of the fixed carbon, volatiles, and ash. This article aims to introduce simple but accurate correlations to estimate the elemental compositions and the heating value of a torrefied biomass without a need to experimentation. The new relations developed using ordinary least squares regression model are described in terms of solid mass yield. The ultimate analyses of various types of wood, torrefied at different experimental conditions, are collected from several past studies. The proposed correlations are validated using an additional set of data. They are also compared with other correlations reported in the literature.
