*3.1. Regression Modeling*

For the parameters of interest, dewaterability, and phosphorus release, as well as general HC characteristics energy, carbon, and solid yield, regression models were developed and are presented in Table 2. The calculation of the *F*-test (Equation (11)) indicated which model coefficients are statistically relevant, which means that they are adding more information than noise to the model. Factors that were not included in any model (xT × xt and xt × xpH) were excluded from the table.


**Table 2.** Coded regression model coefficients for hydrochar (HC) and process water properties.

daf = dry and ash-free basis; db = dry basis; P = phosphorus.

The displayed models were further refined by the exclusion of outliers by conducting a *t*-test (Equation (12)). Because of the experimental design (FCCD) and the repetitions of corner and central points, outliers could be excluded without having to limit the order of the model, which led to regression models with good predictive and adjusted R2 in most cases. The coded regression model coefficients indicate by how much the response is expected to change when the input parameter is changed by one unit. By default, the coded units range from −1 for the lowest level and +1 for the highest level. In this study, the change by one unit relates to a temperature change of 20 ◦C, holding time change of 30 min or a pH change of 3.1. The comparison of the coefficient's magnitude within a response allows for an estimation of the relative impact that each input parameter has.

Table 2 shows that reaction temperature and initial pH have a statistically significant (at least *p* < 0.05) influence on the output parameters in all models while holding time is only included in two models. As the absolute values of the coefficients of reaction temperature and initial pH are of similar magnitude for HC characteristics, it can be assumed that the effect of changing the temperature by 20 ◦C is similar to a pH change of 3.1. Even though holding time is included for carbon content, its value is the smallest, which relates to a small influence on the actual model. These trends are different for the investigated process water properties where pH has 12–21 times higher effects compared to temperature. In addition, the final pH is equally influenced by reaction temperature as by holding time. In comparison with other RSM publications, Álvarez-Murillo et al. [19] observed a similar effect of temperature on the solid yield of olive stone (−5.56 × xT whereby a temperature change of one unit corresponds to 30 ◦C). Holding time was included in the model, because their tested maximum duration of 10 h yielded a statistically relevant effect. Mäkelä et al. [17] encountered a much stronger influence on the solid yield (daf) treating industrial mixed sludge from a pulp and paper mill (−27 × xT whereas a temperature change of one unit corresponds to 40 ◦C). This can be attributed to the higher temperatures that were investigated (180–260 ◦C) and the exclusion of the observed high ash contents for the calculation of the solid yields. Hence, greater differences in yield can be observed. A more in depth analysis of the investigated output parameters is included in the following sections.

## *3.2. Holding Time vs. Reaction Time*

Because holding time does not cover the whole timespan during which reactions take place, a more inclusive measure was used to investigate if this would cause time to become statistically relevant. The time during which temperature in the reactor exceeded 140 ◦C was chosen as Wang et al. [7] implicated that reactions start taking place between 130 and 150 ◦C. Reaction time will now be referred to by t140 in this study. It should be noted that this value only applies to sewage sludge and should be carefully chosen depending on the input material. Holding time and reaction time for each experiment can be found in Table A1 in Appendix A.

Regression modeling was carried out analogous to the procedure described in the previous sub-chapter. The output parameters for which reaction time is statistically relevant and, thus, included in the regression model are shown in Table 3. Carbon content is still mainly dependent on reaction temperature and initial pH, but the influence of time increased by using reaction time instead of holding time in the model. A comparison of contour plots is provided in Figure A1 in Appendix A and the use of reaction time shows the expected trend that with increasing reaction time and temperature, the carbon content increases. This becomes not that clear when holding time is used for the model. While the model for HHV does not include holding time, it does so with reaction time. The general trends that were described in the previous subsection remain as can be observed in the comparison in Figure A2 in Appendix A. For the final pH, reaction temperature is now excluded from the model, but the influence of time is still marginal, compared to initial pH as would be expected. Not much changes when comparing the contour plots in Figure A3 in Appendix A.


**Table 3.** Coded regression model coefficients for hydrochar (HC) and process water properties with t140 reaction time instead of holding time.

daf = dry and ash-free basis; db = dry basis.

The refined data analysis with reaction time instead of holding time did not yield significantly different results. This shows that for batch experiments, variation of holding time does not have a significant influence on most output parameters. It could be considered to be kept constant in future DoEs, unless parameters such as carbon content, HHV, and final pH are of major interest and holding or reaction time will be varied in a much wider range. However, holding time is clearly important when developing continuous processes as it will alter the size of the equipment for a certain targeted mass flow. This has to be addressed with corresponding equipment in lab-scale to allow for a smaller difference between holding time and time above a certain reaction temperature.
