We discuss the use of the water vapour radiometry technique for atmospheric phase correction as applied to the Atacama Large Millimetre Array (ALMA). The atmospheric conditions derived from site test instrumentation are summarised, and the nature of the phase correction problem quantified. We then present calculations of the expected errors in the radiometrically-corrected atmospheric phase, based on estimates of the radiometer sensitivity. These results indicate how well we need to know the atmospheric structure in order to make accurate phase estimates, and have implications for the meteorological instruments needed on the site. Finally we present the results of simulations of daytime turbulence on the site, and use these to predict the phase fluctuations due to wet and dry air, and discuss their implications for phase correction at Chajnantor.