3.1.2. Estimating Pressure and *VFw* under Process Conditions

For a batch reactor system starting with only water at atmospheric pressure, the reactor pressure at the holding temperature can be easily estimated using the simple saturation water vapor pressure at T as long as 0 < *VFw* < 1. However, when *VFw* = 1 or higher, if the temperature is further increased, the reactor pressure will now follow the subcooled water pressure, which rises rapidly. The pressure increase must then be estimated using Equation (5) with the liquid compressibility factor *Z* and the overall reactor water density *D*. This approach can then be used to predict the increase in reactor pressure as a function of the reactor temperature at various *VFo*. The results are illustrated in Figure 3. When *VFo* = 0.3, the liquid volume does not reach the reactor volume (i.e., *VFw* < 1) even at the highest temperature simulated at 370 ◦C. Therefore, the reactor pressure follows the saturation water vapor pressure shown as the lower curve in Figure 3. For a reactor system with a high initial volume of water, e.g., *VFo* = 0.8, the reactor pressure also follows the saturation pressure line below 250 ◦C, similar to the behavior at *VFo* = 0.3. However, at *T* = 250 ◦C, *VFw* becomes unity and the water enters the subcooled compression region. In this region, a small increase in temperature of only 5◦ can cause a rapid increase in pressure from 4.9 to 11.7 MPa (Figure 3).

The application of this approach to predict *VFw* and pressure for experimental runs at various temperatures was evaluated by comparing the predicted pressures with the observed pressures in HTC reactors initially filled with three different amounts of water. As most researchers have discovered, determining the actual volume of an HTC reactor with cavity volume in the reactor head due to connections to the pressure gauge and sampling ports is difficult. Based on reactor volume estimations from simple geometric dimensions, the added water resulted in *VFo* = 0.3, 0.63, and 0.67. For *VFo* = 0.3, the observed pressures as the reactor was heated followed the saturation water vapor

line at temperatures up to 349 ◦C (Figure 3). However, for *VFo* = 0.67 at temperatures higher than 349 ◦C, the pressure increased much more rapidly than the saturation vapor pressure, indicating that the water entered the subcooled compression region. According to the predicted pressure line for the estimated *VFo*, it should have entered the subcooled region at a lower temperature of 320 ◦C. Instead, the observed pressure followed the predicted pressure line of *VFo* = 0.6 (Figure 3). We suspect that this discrepancy can be attributed to the fact that the actual reactor volume was larger than the estimated volume, (e.g., 1.1 L instead of 1 L for 0.67 L water initially filled). These results show that the approach is adequate to estimate *VFw* at various reactor temperatures in practical applications, however, if the actual reactor volume is not known accurately, there will be some deviation from the predicted values.

**Figure 3.** Comparison of measured and estimated reactor pressure at different initial liquid water volume fractions (*VFo*).

Another important question to consider in deciding upon operating conditions and evaluating experimental results is: How does a higher initial pressure affect the pressure development and phase distribution of water in the reactor? For example, some experimenters pressurize the system initially using an inert gas such as N2 or Ar. The answer in short is that the addition of pressure to the reactor headspace does not change the behavior of water. If enough water and time are available, water will vaporize to the gas phase to reach the saturation water vapor pressure at which liquid water and vapor water are in equilibrium. This pressure is a function of temperature only and independent of the presence of other gases. The added inert gas does not change the relationships for *VFw* and the distribution of water between the liquid and vapor phases. However, the total reactor pressure will be higher in the reactor initially filled with N2 or Ar than that without the initial inert gases. The total pressure *P(total)* can be estimated by summing the partial pressures of all individual non-reacting gases as stated in Dalton's law. The increase in the partial pressure for each component with temperature can be calculated independently and added together. This can be seen in Figure 4 for two experimental runs in an 18.75-L Parr reactor in which water was heated to 220 ◦C (*VFo* = 0.63): one starting at atmospheric pressure and the second one with N2 addition to achieve an initial pressure of 1.4 MPa. The measured values from the nonpressurized run (*Po* = 0.1 MPa) are compared to the saturation water vapor pressure *P(sat)* from [2] in the lower curve. For the run at *Po* = 1.4 MPa, the partial pressure increase for N2 *P(N2)* was estimated using the ideal gas law, combined with Equation (4) to calculate the changes in headspace volume (1-*VFw*) as temperature increases.

Comparison of the measured and theoretical values shows clearly that the contribution of the saturated water vapor to the total pressure is not affected by the initial addition of N2 gas. The small deviation between the calculated pressure and the measured can be due to inaccuracies in the pressure measurement or in estimating the reactor volume, and the assumption that N2 behaves as an ideal gas with no solubility in the liquid. Nevertheless, the difference does not mask that the fact that the addition of pressure to the reactor headspace does not change the behavior of water.

**Figure 4.** Comparison of the theoretical total pressure *P(total)* calculated from the partial pressures for N2 *P(N2)* and saturated water vapor *P(sat)* to the measured values for pressure *P* and *P(sat)* in the reactor for *VFo* = 0.63.

#### *3.2. HTC Reactor Filled with Water and Feedstock*

3.2.1. Estimating the Distribution of Water between Phases as a Function of Temperature and Its Effect on Solid Content

In their comparison of hydrochars from VTC and from HTC systems, Cao et al. (2013) postulated that the amount of liquid water in contact with the feedstock in the reaction system may determine the degree of carbonization and influence which reactions take place and their sequence [5]. However, they did not quantify how much liquid water was in contact with the feedstock in their reaction systems. This is a common problem in most of the literature on HTC/VTC systems. Often the label used for the system is defined by the initial conditions. For instance, when the feedstock is initially completely submerged in bulk liquid water, it is commonly called an HTC system. Whereas, when dry or wet feedstock is placed separately from the bulk liquid water, it is called a VTC system. However, the volume of liquid water and the distribution of water between the liquid and vapor phase change with temperature, which can change the amount of water contacting the feedstock. In addition, the feedstock characteristics such as moisture content, particle size, bulk density, as well as structural changes during the reaction can affect how water interacts with the feedstock. In VTC, carbonization reactions can take place between a wet feedstock and water within its cells or present as a film on its surface [10,11]. Ref. [11] Even with completely dried feedstock, the feedstock can be wetted during the process by absorbing water vapor or water vapor condensing on its surface.

The parameters often used to describe the relationship between water and feedstock in a reaction system do not differentiate between the bulk liquid water added to the process and the liquid water in contact with the feedstock. The nominal solid content at the start of the run is usually reported in published studies as:

$$\%S\_o = \left(\frac{M\_{\text{biomass}}}{M\_{H2O} + M\_{\text{biomass}}}\right)\_{T = T\_o} \times 100\tag{6}$$

where

*%So* = nominal solid content;

*Mbiomass* = initial feedstock dry mass;

*MH2O* = total mass of water in the reactor.

A similar parameter *R* which describes the initial ratio of feedstock dry mass to total mass of water is also often used. These parameters only describe the initial conditions based on the initial filling masses of water and feedstock, but do not provide critical information on the extent to which feedstock is exposed to liquid water in the HTC or VTC systems to promote important hydrothermal carbonization reactions. In order to provide useful information on the degree of physical contact between the feedstock and liquid water throughout the process, we propose reporting the following solid content parameter:

$$\%S(T) = \left(\frac{M\_{\text{bivmass}}}{m\_{H2O} + M\_{\text{bivmass}}}\right)\_{T=T} \times 100\tag{7}$$

where

*%S(T)* = actual solid content based on liquid water in contact with feedstock;

*mH2O* = mass of liquid water in contact with feedstock;

*T* = reactor temperature.

With these new definitions, one can systematically distinguish various HTC/VTC process conditions in terms of fraction of liquid water physically in contact with feedstock. For HTC systems, where the feedstock is assumed to be completely submerged in the bulk liquid water over the whole reaction time, *mH2O* = *xL* . *MH2O*. Using Equations (3) and (4), these assumptions can be checked for the reaction temperature and the solid content values adjusted with Equation (7). For example, the change in the distribution of water between the two phases can be seen in Figure 5a. For temperatures below 250 ◦C and *VFo* larger than 0.3, less than 4% of the water will be vaporized. The expansion of *VFw*, as seen in Figure 2, should offset the small loss of liquid water to the vapor phase and submerged feedstocks should remain submerged at these conditions. Therefore, the actual solid content will be approximately the same as the nominal solid content at the initial reactor temperature *To* (i.e., *%S(T)* = *%So*). Only for systems with *VFo* closer to 0.1, more common to VTC systems, will approximately 20% of the water be present as vapor at 250 ◦C.

**Figure 5.** Changes in process parameters at various initial *VFo* as the operating temperature increases for (**a**) mass fractions of water in liquid *xL* and vapor *xV*, (**b**) the ratio of actual to nominal solid content in the reactor system, *%S(T)* at *T* to *%So* at the initial temperature.

In VTC systems, wetted or completely dried feedstock can be suspended without any physical contact with bulk liquid water. The bulk liquid water can be placed either at the bottom of the reactor or in a separate interconnected chamber, or steam can be injected to heat the reactor. The value reported for *%So* for such systems often includes the bulk water. However, this can be misleading, especially for dried feedstock, where the actual initial solid content *%S(To)* = 1 because *m2O* = 0. Although *%S(To)* = 1 initially, *%S(T)* will become less than one over time because water vapor will be volatilized from the physically separated bulk liquid as the VTC reactor temperature increases and will condense on the surface of the dry feedstock. The extent to which the vaporized water condenses onto the feedstock depends on the kinetics of condensation and vaporization at the reaction temperature, but *%S(T)* will rarely reach *%So*. The condensed water will promote typical hydrolysis and other important carbonization reactions as in HTC systems. For VTC systems with initially wetted feedstock, bulk liquid water may or may not be added to the reactor. If no bulk liquid water is added similar to that of Funke et al. [11], *%S(To)* = *%So,* where the moisture content (*MC*) determines the value of the initial solid content. As the temperature increases, liquid water is lost to vaporization, reducing the water content of the feedstock. *%S(T)* can then be calculated with Equation (7) and:

$$m\_{H2O} = \text{x}\_L \times M\_{H2O} = \text{x}\_L \times \frac{M\_{\text{biwmass}} \times MC}{1 - MC} \tag{8}$$

Using these equations for the new solid content parameters, the ratios of actual to nominal solid content are plotted against the reactor temperatures in Figure 5b for various initial volume fractions of liquid water. For HTC systems with *VFo* larger than 0.3 and temperatures below 250 ◦C, there is little difference between the two values. At 250 ◦C, only a 4% increase is seen in *%S(T)*, and after the reactor is half-filled (i.e., *VFo* > 0.5), no differences are noticeable. In contrast, for systems with low values of *VFo* (e.g., *VFo* = 0.1), *%S(T)* becomes 20% higher than *%So*. Less liquid water is in contact with the solids to participate in reactions. For VTC systems with wet feedstocks where the liquid water is associated in or on the feedstock, the transfer of water to the vapor would change the *%S(T)* in the reactor significantly. For wetted feedstock suspended over bulk liquid water, the situation is more complicated, since water can vaporize from the wet feedstock or bulk liquid water, mass transfer within and in-between feedstock, and the kinetics of condensation and vaporization all play roles in the location of the liquid water. This is beyond the scope of this paper. Moreover, the implications of the reduction in the mass of bulk liquid water on the potential of reducing physical contact between feedstock with a bulk volume larger than that of liquid water and subsequent carbonization reactions need to be further studied.
