Transient rate analysis is currently focused on infinite or circular reservoirs with concentric wells. Rate decline responses for a constant pressure well which is arbitrarily located in a regularly or an irregularly shaped reservoir or in a composite reservoir are not documented in the literature. This paper presents two new solution techniques for rate decline behaviors in such complex systems. For the composite model, the analytical Laplace solution is based upon placing a constant pressure well with an arbitrary location in a two-composite radially concentric domain. By varying the properties and the geometries of the domains, the new model provides several new settings for transient rate analysis. The paper discusses the characteristic responses of such composite systems. In the case of an arbitrarily shaped drainage area, the external boundary is replaced by a group of line source boundary wells. The paper outlines the criteria for placing these wells to create the effects of the boundary. This semi-analytical method permits us to study rate declines in cases that cannot be studied analytically.

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