A dispersion medium replacement apparatus for carrying out a method for replacing a first dispersion medium in a starting slurry composed of the first dispersion medium and terephthalic acid crystals with a second dispersion medium, the dispersion medium replacement apparatus comprising the following features: (a) a dispersion medium replacement tank, (b) a cyclone-shaped nozzle (6,16) disposed at an upper portion of the replacement tank, which cyclone-shaped nozzle (6,16) comprises a cylindrical portion having a vertically extending axis and an opening disposed at its lower end, (c) a feed portion for feeding the starting slurry to the cyclone-shaped nozzle, (d) a ring header to which two or more of the cyclone-shaped nozzles (6,16) are connected for distributing the slurry to the respective cyclone-shaped nozzles along a tangential direction of the ring header, (e) a feed portion disposed in the vicinity of a bottom of the replacement tank for feeding the second dispersion medium, wherein the second dispersion medium flows upwardly through the replacement tank, (f) a discharge port for discharging a replaced slurry mainly composed of the terephthalic acid crystals and the second dispersion medium from the lower portion of the replacement tank, and (g) a discharge port disposed at the upper portion of the replacement tank for mainly discharging the first dispersion medium; wherein (i) the feed portion of (c) is placed in a manner that the starting slurry is tangentially fed to the cylindrical portion so as to allow the starting slurry to move circularly along an inner wall of the cylindrical portion, and (ii) the starting slurry which moves circularly is discharged from the opening of the cyclone-shaped nozzle (6,16) to contact with the second dispersion medium which flows upwardly through the replacement tank, thereby dispersing the starting slurry in the second dispersion medium. (a) a dispersion medium replacement tank, (b) a cyclone-shaped nozzle (6,16) disposed at an upper portion of the replacement tank, which cyclone-shaped nozzle (6,16) comprises a cylindrical portion having a vertically extending axis and an opening disposed at its lower end, (c) a feed portion for feeding the starting slurry to the cyclone-shaped nozzle, (d) a ring header to which two or more of the cyclone-shaped nozzles (6,16) are connected for distributing the slurry to the respective cyclone-shaped nozzles along a tangential direction of the ring header, (e) a feed portion disposed in the vicinity of a bottom of the replacement tank for feeding the second dispersion medium, wherein the second dispersion medium flows upwardly through the replacement tank, (f) a discharge port for discharging a replaced slurry mainly composed of the terephthalic acid crystals and the second dispersion medium from the lower portion of the replacement tank, and (g) a discharge port disposed at the upper portion of the replacement tank for mainly discharging the first dispersion medium; wherein (i) the feed portion of (c) is placed in a manner that the starting slurry is tangentially fed to the cylindrical portion so as to allow the starting slurry to move circularly along an inner wall of the cylindrical portion, and (ii) the starting slurry which moves circularly is discharged from the opening of the cyclone-shaped nozzle (6,16) to contact with the second dispersion medium which flows upwardly through the replacement tank, thereby dispersing the starting slurry in the second dispersion medium. (i) the feed portion of (c) is placed in a manner that the starting slurry is tangentially fed to the cylindrical portion so as to allow the starting slurry to move circularly along an inner wall of the cylindrical portion, and (ii) the starting slurry which moves circularly is discharged from the opening of the cyclone-shaped nozzle (6,16) to contact with the second dispersion medium which flows upwardly through the replacement tank, thereby dispersing the starting slurry in the second dispersion medium.