The efficiency of using the indirect near-boundary element technique for the construction of numerical-analytical solution of the problem of unsettled motion of compressible fluid in porous, closed, piecewise homogeneous reservoir, including variable depression of pressures given on its external border and on the border of the well and ideal contact at the interface media, was proved. Using the fundamental solution of the non-stationary thermal conductivity equation and sequence diagram of initial conditions the discrete-continual model of the problem with arbitrary initial conditions and boundary conditions of the first kind, was constructed. Series of computational experiments were carried out to assess the influence of characteristics of environment on reservoir pressure change.
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