A method for treatment of produced water, particularly deoiled water, by evaporation. Methods use a vertical tube heat exchanger bundle where the brine is distributed in a falling film along the inside of the tube wall. Condensing steam causes a portion of the deoiled water to evaporate; this water vapor travels upward in a counterflow direction relative to the deoiled water. Evaporator sump volume is minimized, and evaporators may have a multi-piece construction to lower the center of gravity of an evaporator installation. This technology provides several advantages over conventional vertical tube co-current flow evaporators (where the vapor flows downward with the falling film). These advantages include a minimal total installed cost (TIC) and enhanced water chemistry management.