Applied Physics and Mathematics Annotation << Back ASYMPTOTIC REPRESENTATION OF THE SOLUTION OF THE PRESSURE FIELD PROBLEM IN IMPERFECTLY OPEN OIL AND GAS FORMATION A.I. FILIPPOV, P.N. MIKHAYLOV Asymptotic expressions are obtained for the pressure field in an anisotropic layered formation, the permeability of which depends on the vertical coordinate. A formal asymptotic parameter is introduced into the conjugation problem, with the help of which it is represented as a sequence of problems for the coefficients of the asymptotic expansion. An analytical solution is constructed for the problem loaded with traces of derivatives from the outer regions for a zero coefficient of the asymptotic expansion. In order to substantiate the fact that the constructed solution is asymptotic, a problem is formulated for the remainder term of the zero approximation. The resulting problem is presented in the form of a sequence of problems for the expansion coefficients of the remainder term in the same asymptotic parameter as in the original problem. It is shown that the problem for the zero expansion coefficient of the remainder term has a trivial solution. This means that the remainder contains terms of the first and higher orders of expansion in the formal asymptotic parameter. Keywords: pressure field, oil and gas anisotropic reservoir, imperfect opening, conjugation problem, asymptotic method, remainder estimate. DOI: 10.25791/pfim.06.2020.1184 Pp. 12-18.