To solve scientific and technical problems, physical processes are considered and systems of equations are written numerical and approximate mathematical model of combined heat and mass transfer at contact cooling of gases and heating of water, as well as turbulent transfer of particles in an ascending dispersed annular flow of gas and liquid. The numerical model is based on a system of equations in particular derivatives in two-dimensional form with boundary conditions of the fourth kind. Approximate model built using a system of algebraic equations of the cell model of the flow structure for gas and liquid phases, where the main parameters are the number of cells of complete mixing, coefficients heat and mass transfer and turbulent transfer of particles. An example of solving a system of equations is shown cell model with calculation of gas and liquid temperature profiles, moisture and particle concentrations, and also the efficiency of the heat and mass transfer process, the efficiency of separation of the finely dispersed phase from the gas liquid film in cocurrent flow. Comparative characteristics of film devices are given. Noted introduction of scientific and technical developments in the purification of natural gas at production sites. Keywords: heat and mass transfer, gas cooling, particle separation, phase co-current flow, systems of transfer equations.