**1. Introduction**

The process of hydrothermal carbonization (HTC) is used to carbonize organic residues and wastes for diverse applications ranging from fuels to soil amendments. In HTC, subcritical water is used as a solvent and reactant to transform a wide variety of organic feedstocks to solid carbonaceous products (hydrochar), which usually contain higher carbon contents, heating values and degrees of aromaticity than the original feedstocks [1–4]. Diverse types of reactors have been used, ranging from batch [3,5–12], semi-batch [2,9,10] to continuous reactors [13], with and without mixing, using direct heating through steam injection or through the reactor walls with controlled heating rates, or indirectly in muffle ovens. The pressurized reaction system usually consists of all three phases (gas, liquid, solid) and is heated to temperatures from 160 to 280 ◦C with pressures between 0.6 and 6.4 MPa due to the water vapor and gases produced in the reactions. Water is initially introduced into the reaction system via the moisture content of the feedstock and/or through the addition of water as a liquid or as steam. Common HTC process variations are differentiated according to how the water initially contacts the feedstock. When the feedstock is immersed in bulk liquid water, it is often called HTC. Where the feedstock is in direct contact with only steam, it is often called steam HTC, vapor HTC or

vapothermal carbonization (VTC) [2,7,10,11]. Here, feedstock can be held in baskets away from liquid water, transported in and out on conveyor belts with little to no post-processing dewatering steps necessary. However, the dividing line between the two process types often does not remain sharp over the operating time, since the distribution of water between the liquid and vapor phases will change as temperature rises in batch systems, or as more steam is added in semi-batch systems. Usually we cannot see inside high-pressure reaction systems to gain visual insights, so the extent of the phase change is often unknown. Process comparisons between HTC vs. VTC based on the state of the initial water phase may be misleading. The phase changes may play an important role in causing structural variations in the hydrochars produced, their biodegradability, stability, and functionality in various applications [5].

Only a few studies comparing hydrochars produced by HTC vs. VTC have been reported in the literature. Cao et al. [5] found that biomass was more carbonized under liquid water in HTC than through steam in VTC. They determined that more aromatic and less alkyl groups were formed in the sugar beet and bark hydrochars made from HTC than in those from VTC under the same operating conditions (200 ◦C for 3 h). The hydrochars made from HTC also were less biodegradable than those from VTC as indicated by the lower values of the ratio BOD/COD for HTC-hydrochars. The lower biodegradability of hydrochar from HTC was probably due to its higher aromaticity produced during the reactions taking place in liquid water. In this case, the hydrochar made from HTC should be more stable in the environment than that made from VTC, which would have consequences for its use, e.g., as a soil amendment. On the other hand, comparisons between hydrochars from HTC vs. VTC for use as fuels have produced mixed results on how the phase of the reaction medium affects the important energy parameters: solid yield, higher heating value (HHV) and energy yield [10,11,14]. Comparing HTC vs. VTC for two feedstocks, digestate and straw, at 230 ◦C, 6 h, Funke et al. [11] found no clear trend in HHV: VTC-chars had a higher HHV than HTC-chars from digestate, but for straw, the order was reversed. However, VTC produced higher solid yields and, therefore, higher energy yields than HTC for both feedstocks. In contrast, Shafie et al. and Yeoh et al. reported mostly lower solid yields and higher HHV from the VTC process compared to HTC process (both at 220 ◦C, 1 h; two feedstocks [10,14], three feedstocks [14]). Again, as in [11], the combination of these two trends in the energy yield showed that the VTC process was more efficient for energy yield. We suspect that the reason for these conflicting trends in HHV and solid yield arise from the fact that a clear picture of how the water was distributed between gas and liquid phases was not given, nor to which extent the feedstocks were exposed to the liquid water phase. For instance, the VTC experimental setup used by Yeoh et al. (two concentric chambers with water filled in the outside chamber and the biomass in the inner chamber) was assumed to avoid the liquid water directly contacting the biomass feedstock. Yet it is not clear from their description that the liquid water was contained in the outside chamber throughout the reaction, since liquid water expands at higher temperature, possibly causing overflow into the biomass chamber. It appears that the transition between HTC/VTC reported in the literature is fuzzy at best because it can be changed by small variations in the same reactor system. How much water is present in each phase depends not only on the reactor temperature and pressure, but also on the total amount of water in the system relative to the volume of the reactor system.

As more knowledge is gained on the beneficial applications of hydrochars and HTC for waste and residue processing, more work on reactor designs for diverse settings (ranging from high to low tech systems) will be carried out. The variety of process variations may increase, with process configurations and conditions utilizing the unique transport properties of each medium, e.g., the higher thermal conductivity of bulk liquid water or the higher diffusivity of steam to penetrate the porous structure of the feedstock [7,15]. These changes in transport properties can affect reactions and product characteristics [15]. Therefore, knowledge on what influences the distribution of water between the reaction phases is essential for the production of the desired hydrochar quality. Especially if we want to replicate process conditions in various reactor types and scales to produce a desired hydrochar quality, we must be able to predict the distribution of water between the vapor and liquid phases at the design HTC reaction conditions.

Furthermore, reactor designs must consider how the HTC reactor pressure will change in response to operating conditions to ensure process safety. All reactors must be able to withstand the high temperatures and pressures that can develop during the process. As a rigid HTC reactor partially filled with water and feedstock is heated, the increase in the saturated water vapor and gases produced by the chemical reactions cause the reactor pressure to rise. At the same time, the density of the bulk liquid water decreases and consequently the volume of liquid water increases, decreasing the volume of the reactor headspace. When the liquid volume in the HTC reactor completely fills the headspace, it can no longer expand if the reactor temperature is increased further. The reactor water then enters a subcooled liquid compression region. In this region, pressure increases very rapidly with small increases in reactor temperature. To avoid the reactor pressure exceeding the tensile strength of reactor material, it is very important that the reactor system has a working safety disk or valve that can release pressure at a preset value. Without the use of proper rupture disks, the reactor can explode. Therefore, in order to maintain safe operating conditions, we need to predict the reactor pressure at the chosen process conditions. This requires understanding the relationship between the HTC reactor conditions (temperature, water volume, feedstock) and pressure.

The aim of this work is to present a methodological approach to analyze process conditions for hydrothermal systems in the framework of the hydrothermal carbonization reactions. In the paper, we first theoretically develop models for predicting reactor pressure, the distribution of water between phases, and the liquid water volume fractions as a function of reactor temperatures. Then, the evaluation is expanded to water and feedstock. Finally, using these new models, we analyze and compare process conditions for VTC and HTC systems reported in the literature.
