Mineral solubility predictions are critical for estimating scaling risks at conditions of high temperature, pressure, and ionic strength (IS) in mixed electrolytes which occur in various industrial processes. On the basis of the Pitzer theory, this study establishes a thermodynamic model to predict the solubilities and scaling risks of barite, calcite, gypsum, and anhydrite under these extreme conditions. This study combines the related equilibrium constants, virial coefficients, and the solubilities of these minerals from 0 degrees C to 250 degrees C, from 14.7 psi to 22000 psi, with up to 6 mol NaCl/kg H2O with or without mixed electrolytes to determine the temperature and pressure dependences of the following virial coefficients for Ca2+-SO42-, Ba2+-SO42-, Ba-2(+)-Cl-, Na+-SO42-, and Ca2+-Br- binary interactions used in the Pitzer theory. Using these virial coefficients, the solubilities of these four minerals can be accurately predicted with no apparent temperature, pressure, or IS bias in solutions under the extreme conditions. The association constants (K-assoc) for CaSO4(0) ion pairs calculated from the beta CaSO4(2) values derived in the model match well with experimental measurements at 25 degrees C and 1 atm, and show similar temperature and pressure dependence with those calculated from the Fuoss ion pair association theory and those listed in SOLMINEQ. 88.