3.1.1. Estimating *VFw* at Various Temperatures and *VFo*

In HTC and VTC experiments, a wide range of initial water amounts can be used. For HTC experiments, high values of *VFo* are commonly chosen. It is important, however, to choose process conditions so that the liquid water does not fill the reactor volume at the holding temperature (i.e., *VFw* = 1) to avoid entering the subcooled liquid compression region. The higher the initial *VFo*, the lower the reactor temperature at which *VFw* becomes 1, because smaller headspace volumes cannot accommodate much expansion of liquid water as its density decreases with temperature. This behavior

is shown in Figure 2 for a reactor filled with water only. Values for *VFw* were estimated at various temperatures and *VFo* using Equation (4). For a reactor initially filled with water at 90% (i.e., *VFo* = 0.9), the liquid volume expands to the reactor volume (i.e., *VFw* = 1) when the reactor temperature reaches 165 ◦C. Fortunately, this critical temperature, at which *VFw* =1, increases rapidly as *VFo* is decreased, e.g., 305 ◦C for *VFo* = 0.7 and 365 for *VFo* = 0.5, so that process conditions can be chosen to remain well below the critical temperature. When the reactor is initially filled with water to less than half its volume (i.e., *VFo* < 0.5), the liquid does not fill the reactor even when the temperature approaches the critical point of water around 374 ◦C. Interestingly, for experiments with low values of *VFo* common to VTC operating conditions, *VFw* can actually decrease with temperature. When the reactor is initially filled with a very low volume of water, such as *VFo* = 0.1, the liquid volume decreases to zero at *T* = 340 ◦C. This happens when there is so much headspace that the liquid water completely vaporizes, i.e., the molecular collision frequency of H2O molecules in the headspace is so small that condensation does not happen in this high headspace situation.

**Figure 2.** Change in volume fraction of reactor filled with liquid water *VFw* (*Vw*/*VR*) as a function of temperature for various initial liquid water volume fractions (*VFo*).
