## 4 Discussion  
The SC is a key physical parameter of black liquor, where online measurement is important to control the process of its evaporation in a pulp mill. In the current work, the approach proposed for SC determination was based on the TD-NMR, which is a non-invasive, non-destructive, rapid, and robust technology that is suitable for online use. According to the Bloembergen-Purcell-Pound (BPP) theory [26], the NMR relaxation rates are dependent on the temperature of the sample. To neglect the effect of temperature on the measured spin-spin relaxation rates R\({}_{2}\), a temperature correction can be performed as has been done, for example, by [PERSON] et al. [27]. Figure 2 shows that the R\({}_{2}\) of black liquors is linearly dependent on the temperature T. The applied temperature correction effectively compensates for the deviations in the measured R\({}_{2}\) values, as shown in Figure 4.  
The estimation of the SC was based on the linear correlation between the temperature-corrected In(R2 TC) values and the SC that was measured gravimetrically in the laboratory (Figure 3). As only one component was discovered in the measured NMR decays, it was assumed that the measured R\({}_{2}\) was the result of a fast exchange of the \({}^{1}\)H of water and the dissolved solids in the black liquor. The correlation found between the SC and the In(R2 TC) was explained by the dependence of the viscosity of the black liquor on the SC [1; 6], and of the R\({}_{2}\) on the viscosity of liquids [18; 19; 26; 28]. It has been shown in References [15; 18] that the spin-spin relaxation times T\({}_{2}\), as well as the spin-lattice relaxation times T\({}_{1}\), correlated well with the viscosity of the black liquors. However, creating a general model between the NMR parameters and viscosity of the black liquors was restricted by the dependence of the NMR relaxation times on the chemical composition, concentration of metal ions in the black liquors, and the non-Newtonian behavior of strong black liquor [15; 18]. The properties of black liquor from obtained each mill were different and dependent on a variety of factors [4]. Therefore, the models for the calculation of the physical parameters should be recalibrated for various pulp mills. In the current work, we measured the R\({}_{2}\) of a black liquor of constant composition and checked how the TD-NMR system performed in a mill. Since the pH of the black liquors was high (for weak black liquor it was approximately 12), the paramagnetic metals that could be present in black liquors should be precipitated, and thus, they would not affect the NMR relaxation. Measurements were made using stopped flow, as such the flow rate and geometry did not influence the R\({}_{2}\) values [19; 20; 29]. The online TD-NMR measuring system was installed in a pulp mill, and measurements of the spin-spin relaxation rates R\({}_{2}\) and the estimation using Equation (7) of the SCs of weak black liquor were made continuously over seven days (Figure 5). The SCs and SDs were calculated based on a one-hour moving average to smooth out the short-term fluctuations. The average of ten relative standard deviations (RSDs) calculated for twelve repeated R\({}_{2}\) measurements of the same sample by the TD-NMR was 0.72%. The reported RSD of the standard method was 0.46% for a repeated SC analysis of the same sample [10]. Thus, the TD-NMR provides the same order of accuracy of R\({}_{2}\) measurements as the standard method. The approach of estimating the SC of black liquor using the online TD-NMR is fast and almost gives the results in real-time. In contrast, the standard method for SC determination [10] is time consuming and cannot be performed online. Measuring the viscosity of black liquor is one way to control the process, although it is usually conducted offline, it requires sample gathering and additional calculations based on the calibration of the viscosity with the temperature.