The inverse problem of determining stream watering and discharge in a vertical flowing well

We consider direct and inverse problems for a vertical flowing well. The direct problem consists in finding the pressure and temperature of a two-phase flow along the well given the temperature and pressure at its bottom. The inverse problem consists in finding the discharge (the amount of fluid coming out) and well stream watering (the water content in the total fluid volume) given the temperature and pressure measured at the well mouth. We assume that the temperature and pressure at the bottom are known. We propose an algorithm for solving the direct and inverse problems in the case that the temperature and pressure are measured on the surface (at the mouth). We study the character of temperature and pressure variation on the surface as functions of discharge and stream watering. We describe the equivalence classes of solutions to the inverse problem within a given measurement error. We present a simulation of the inverse problem in a neighborhood of the exact solution and analyze stability.