摘要：The problem of saturated flow within a homogeneous and isotropic pore formation, confined between two horizontal impermeable planes, under 7-spot injection-extraction well pattern is considered. Such well patterns are typically implemented in soil remediation or enhanced oil recovery processes. Extraction wells (rectilinear sinks) are uniformly distributed over the reservoir domain, creating a honeycomb pattern of identical hexagons. An injection well (rectilinear source) is located at the centre of each hexagon. Uniform strength is considered for all sources. In that context, the flow within every hexagon can be partitioned into identical flows in each of the six equilateral triangles. To furnish the analytical expressions for the pressure and velocity fields, we have to solve an interior Neumann problem for the Laplace equation, considering that the normal derivative of the pressure is known on the boundary of the equilateral triangle. To deal with this unconventional geometry (the method of separation of variables is not applicable) we implement the new method provided by Dassios and Fokas in [1], whereby the authors study boundary value problems for the Laplace, the Helmholtz and the modified Helmholtz equations in the interior of an equilateral triangle.
