Temperature field of heat sources during fluid injection in an anisotropic inhomogeneous reservoir

The problem of the temperature field produced by sources whose position does not depend on the vertical coordinate and which are concentrated in a horizontal permeable layer surrounded by a heat-conducting medium with radial steady-state fluid flow. The problem is solved using an averagely accurate asymptotic method. Analytical expressions for the zero-order approximation and the first coefficient of the expansion. A condition is determined under which the averaged problem for the remainder term has a trivial solution.