*3.4. Phosphorus Release*

For the phosphorus distribution, the pH value is the most significant driver and the variation of holding time showed no statistically relevant effect again, resulting in the following regression models with actual factors:

$$\text{Phosphorus content} \left(\text{mg L}^{-1}\right) = 12.97 - 0.021 \text{x}\_{\text{T}} - 3.03 \text{x}\_{\text{pH}} + 0.027 \text{x}\_{\text{T}} \times \text{x}\_{\text{pH}} + 0.18 \text{x}\_{\text{T}}^2 \tag{18}$$

$$\text{Phosphorus share } (\%) = 204.32 - 0.42 \text{x}\_{\text{T}} - 47.22 \text{x}\_{\text{pH}} + 0.059 \text{x}\_{\text{T}} \times \text{x}\_{\text{pH}} + 2.63 \text{x}\_{\text{T}}^2 \tag{19}$$

A lower initial pH generally leads to a lower pH value after the reaction (Figure 5a). This lower pH value favors the solution of phosphorus from the solid and the phosphorus concentration in the process water increases. The influence of the pH value is particularly evident in a range of the initial pH of 2–5 (Figure 5b).

**Figure 5.** Regression model contour plots showing (**a**) the dependence of process water pH and (**b**) the dependence of liquid phase phosphorus release (% of total P) on reaction temperature and initial pH.

At neutral pH, not much phosphorus will be dissolved by varying holding time and reaction temperature. As others already found, most of the phosphorus is retained in the solid phase [9,13,22]. However, the variation of the initial pH has a major influence on the transfer of phosphorus into the liquid phase. When Shi et al. [14] reached an initial pH of 0.24 and applied HTC conditions of 170 ◦C and 30 min, they were able to transfer 83% of phosphorus into the liquid phase. The results of this study confirm their findings, as the maximum phosphorus share achieved in these experiments is 78% at 160 ◦C and an initial pH of 1.93. An even higher share of 88% was achieved in an experiment at 160 ◦C and an initial pH of 2.25 but was excluded as an outlier from the model as a result from the *t*-test according to Equation (12). It is, thus, possible to transfer phosphorus into the liquid phase to be potentially recovered by precipitation, e.g., as magnesium ammonium phosphate (struvite) [14], though this comes at the cost of high acid consumption. Additionally, precipitation of phosphorus in HTC process water brings additional challenges due to the huge variety of other components found in the process water.

The future upscaling of this process requires considerations regarding holding time, mixing behavior and heat transfer, especially because a continuous process is desired. While the results of this study show that the holding time can be minimized to 30 min for maximum dewaterability and phosphorus release in a batch process, this time needs to be assessed anew for the application in a continuous process. During the heating time in a batch process, the conversion of sewage sludge already begins and, therefore, the holding time of a batch cannot be directly transferred to a continuous process. More severe reaction conditions (higher reaction temperature and longer holding time) would be necessary, if energy densification and a further increase in HHV are desired [17].
