Problem of injection of dry steam into a reservoir without condensation in the well

Temperature losses along a well string are investigated for the case of dry steam injection in order to determine the possibility of its delivery to the well bottom without condensation. It is assumed that in the rock, the temperature increases with increasing depth according to the geothermal gradient, the steam flow is constant, the steam at the head has a high temperature and is dry, containing no water droplets. On the way to the bottom, the steam temperature decreases, but does not yet reach the saturation point. Heat loss into rock is calculated using the generally accepted formula. The position of the point where steam condensation begins in the well is determined. Calculations are carried out for the most probable flow rates in the fields: $25{,}~50{,}~75{,}$ and $100$ t/day. The heat capacity of dry steam is considered constant, which is acceptable only for low pressures, up to $3$–$4$ MPa. In this case, a formula is proposed for the steam temperature distribution throughout the well string and the problem is solved analytically. However, at elevated pressures, it is necessary to take into account the thermal dependence of the heat capacity of steam and use a numerical method to find the temperature distribution. Based on the calculated variants, a conclusion is made about the possibility of supplying the amount of phase transition heat to the reservoir in full. If the reservoir is highly permeable and lies close to the surface, then we can hope for complete delivery of the phase transition heat to the reservoir. At formation depths greater than $500$ m, steam is completely condensed in the well string. The heat of the phase transition enters the rock.