| Abstrak/Abstract |
In situ measurement of hindered settling function H\left(\phi\right) as a function of particle volume fraction \phi in a decanter centrifuge has been proposed by periodic segmentation technique in wireless electrical resistance detector (psWERD). The processes to calculate H\left(\phi\right) has three steps which are 1) segmentation of measured resistance R(z,t) in three settling periods; 2) elimination of the screw conveyor’s (SC’s) adverse effect; 3) calculation of \phi which is important to determine the in situ hindered settling velocity u_{hin}^{ins} and calculation of the proposed u_{hin}^{fit} from the proposed H\left(\phi\right). In the 1st step, R(z,t) are segmented based on the phases of liquid L, screw S, and particle P under three settling periods which are pre settling (pre), transient settling (tran), and post settling (post). In the 2nd step, the segmented R(z,t) is categorized by fourier transfrom (FT) based on the frequency of the liquid f_L, screw f_S, and liquid-particle f_{LP} phases with a focus on eliminating SC’s adverse effect which causes fluctuating R(z,t). In the 3rd step, the \phi\left(z,t\right) is obtained by applying the effective medium theory (EMT) based on the conductivity of each phase which are liquid {\bar{\sigma}}_L, particle \sigma_P, and slurry \sigma_{LP}\left(z,t\right). Each conductivity is calculated based on the average liquid resistance {\bar{R}}_L\left(z\right), the static particle resistance\ R_P under closed-pack particle volume fraction \phi_{cp}, and the slurry (liquid-particle) resistance R_{LP}\left(z,t\right) from the 2nd step. Afterward, the u_{hin}^{ins} is obtained from the distribution of \phi which refers to the length parameter in the settling radius r_{set}. Hence, the u_{hin}^{ins} is calculated by time t needed for particle to settle from \phi_0 to \phi_{cp} in tran. The proposed\ H\left(\phi\right) is developed by considering the influence of \phi_{cp} and the increasing distribution of \phi due to the particle settling which is presented by fitting parameters of k and p. Take into account the importance of single particle settling in Stokes settling velocity{\ u}_{St}, the proposed u_{hin}^{fit} is determined by calculate the{\ u}_{St} and fitting parameters in the H\left(\phi\right) to fit the u_{hin}^{ins}. To evaluate the psWERD, a decanter centrifuge was used in the industrial scale experiment by appliying three operational parameters which are types of SC, centrifugal forces G, and the differential speeds \omega. Two types of SC which are SC1 and SC2 are used to investigate the effect of G to the in situ H\left(\phi\right) under constant \omega. While SC2 is used to investigate the effect of \omega to the in situ H\left(\phi\right) under contant G. The in situ measurement is conducted in three measurement points z which represent the particle settling condition at different locations. In order to verify and validate the experiment result, simulation on electrical measurement in the boundary of particle sensitivity area A_{PSA} of psWERD and on particle settling behavior in centrifugal fields are done by Multiphysic software. As a result, the psWERD is successfully determining best fitting parameters for the in situ H\left(\phi\right) which resulting in good average root mean square error RMSE≤10-3. The in situ\ H\left(\phi\right) is also compared to the previous work of H\left(\phi\right) determined in decanter centrifuges with the similar operational condition. Finally, the H\left(\phi\right) shows the potential for evaluating the in situ separation process in decanter centrifuges under specific operational conditions. |
