A method of replacing a dispersion medium with another in a replacement tank, the replacement tank being made of stainless steel and having a diameter of from 0.3 to 7 m and a height of from 1 to 20 m, the replacement tank being equipped with an outlet port at the bottom of the replacement tank, a feed port disposed in the vicinity of the bottom of the replacement tank 12, a cyclone-shaped nozzle disposed at the upper portion of the replacement tank, the cyclone-shaped nozzle comprising as a hollow body of revolution a cylindrical portion having a vertically extending axis and an opening disposed at a vertically lower end, which cylindrical portion has a diameter of from 0.1 to 1 m, and a discharge port disposed at the upper portion of the replacement tank, the method comprising the steps of: feeding a starting slurry containing isophthalic acid crystals at a concentration of from 10 to 45 % by weight in a first dispersion medium to the cyclone-shaped nozzle through a feed valve and a feed port, the starting slurry being tangentially fed to the hollow body of revolution so as to allow the starting slurry to move circularly along an inner wall of the hollow body of revolution, discharging the starting slurry which is circularly moving from the opening of the cyclone-shaped nozzle, contacting the starting slurry discharged from the cyclone-shaped nozzle with a second dispersion medium which is fed from the feed port which flows upwardly through the replacement tank; uniformly distributing and dispersing the starting slurry into the second dispersion medium in a horizontal direction while keeping the circular motion, gravitationally sedimenting the dispersed isophthalic acid crystals throughout the phase rich in the second dispersion medium, concentrating the replaced slurry composed of isophthalic acid crystals and mainly the second dispersion medium in the lower portion of the replacement tank, and discharging the replaced slurry which comprises the isophthalic acid crystals and the second dispersion medium from the outlet port using a discharge pump, and withdrawing the first dispersion medium from the discharge port, while keeping the inner temperature of the replacement tank at from 80 to 180°C. an outlet port at the bottom of the replacement tank, a feed port disposed in the vicinity of the bottom of the replacement tank 12, a cyclone-shaped nozzle disposed at the upper portion of the replacement tank, the cyclone-shaped nozzle comprising as a hollow body of revolution a cylindrical portion having a vertically extending axis and an opening disposed at a vertically lower end, which cylindrical portion has a diameter of from 0.1 to 1 m, and a discharge port disposed at the upper portion of the replacement tank, feeding a starting slurry containing isophthalic acid crystals at a concentration of from 10 to 45 % by weight in a first dispersion medium to the cyclone-shaped nozzle through a feed valve and a feed port, the starting slurry being tangentially fed to the hollow body of revolution so as to allow the starting slurry to move circularly along an inner wall of the hollow body of revolution, discharging the starting slurry which is circularly moving from the opening of the cyclone-shaped nozzle, contacting the starting slurry discharged from the cyclone-shaped nozzle with a second dispersion medium which is fed from the feed port which flows upwardly through the replacement tank; uniformly distributing and dispersing the starting slurry into the second dispersion medium in a horizontal direction while keeping the circular motion, gravitationally sedimenting the dispersed isophthalic acid crystals throughout the phase rich in the second dispersion medium, concentrating the replaced slurry composed of isophthalic acid crystals and mainly the second dispersion medium in the lower portion of the replacement tank, and discharging the replaced slurry which comprises the isophthalic acid crystals and the second dispersion medium from the outlet port using a discharge pump, and withdrawing the first dispersion medium from the discharge port,