**4. Conclusions**

There are many types of hydrothermal reactor systems being used with many process variations in the literature. The analysis presented in this paper illustrates that a large range of conditions need to be considered before labeling a reactor system VTC and HTC. The analysis of the process conditions of seven different HTC/VTC cases reported in the literature through the use of the models developed in this paper and a *T*-*v* phase diagram showed that the distinction between HTC and VTC is often ambiguous. The models developed in this study for predicting pressure, the volume fraction of liquid water and the distribution of water between phases as a function of reactor temperature can be used to systematically analyze various HTC/VTC process conditions. Furthermore, this study also demonstrates the importance of predicting the condition at which the reactor system enters the subcooled compression liquid region to avoid the danger of explosion. Comparison of the reactor pressures predicted by the models to the actual pressure for reactors filled with varying amounts of water with and without initial pressurization showed reasonable agreement. However, higher pressures can be expected with the addition of feedstock due to the production of CO2 and other gases by the hydrothermal reactions and the decrease in headspace volume occupied by the feedstock. In order to describe the amount of liquid water in physical contact with feedstock, we defined a new solid content parameter *%S(T)* which changes with reaction temperature due to changes in the water distribution between phases. This parameter is more useful in describing the solid content than the nominal parameter *%So* typically reported in the literature. While the models developed here can help determine whether steam or liquid water predominates at the specific process conditions, more research and modeling on hydrothermal systems with feedstock present are required to understand the effect of the water phase on the hydrothermal reactions. The tools presented here can help in designing experiments to compare systems and in understanding results in future HTC research.

**Author Contributions:** K.S.R. conceived the original idea, conducted W-HTC experiments, analyzed the data, and participated in manuscript writing. J.A.L. conducted experiments using an 18.75-L reactor system, and both J.A.L. and A.A.-M. participated in all phases of the research, analyzed the data, simulated T-*v* diagrams, and participated in manuscript writing. All authors have read and agreed to the published version of the manuscript.

**Funding:** Financial help for A.A.M. came from the Junta de Extremadura and FEDER (Fondo Europeo de Desarrollo Regional "Una manera de hacer Europa") project IB16108, and also from the program "Ayudas a grupos de la Junta de Extremadura" GR18150. The open access journal fee was supported by the Leibniz Association's Open Access Publishing Fund.

**Acknowledgments:** The authors would like to acknowledge the technical support provided by Melvin Johnson of the USDA-Agricultural Research Service (ARS), Coastal Plains Soil, Water and Plant Research Center, Florence, SC, and Marcus Fischer of the Leibniz Institute of Agricultural Engineering and Bioeconomy. This research was supported by the USDA-ARS National Program 212 Soil and Air. Mention of trade names or commercial products is solely for the purpose of providing specific information and does not imply recommendation or endorsement by the U.S. Department of Agriculture.

**Conflicts of Interest:** The authors declare no conflict of interest.
