In this work we investigated changes of the water emission from a model comet of the size and orbital elements of Comet P/2008 R1 (Garradd). We performed simulations for model cometary nuclei of different compositions and two different orientations in space. Our simulations indicate, that the emission of water decreases from one orbital period to another one, but in some cases slowly. When the rotation axis of the nucleus lies in the orbital plane the seasonal maximum of water production during the first two orbital periods can be as high as about 1026 mol s−1, but decreases by two orders of magnitude during only 50 orbital periods. The highest rate of water production after many orbital periods is expected when the rotation axis is perpendicular to the orbital plane – the seasonal maximum of water production can be about 5 × 1025 mol s−1 during the first two orbital periods after activation of the comet and no more than 0.8 × 1025 mol s−1 500 orbital periods later. The upper estimate for the production of water derived from observations of P/2008 R1 (Garradd) by Jewitt et al. (Jewitt, D., Yang, B., Haghighipour, N. [2009]. Astron. J. 137, 4313–4321) is 5 × 1025.