An analytical solution to a three-composite concentric reservoir with three active wells, as shown in Fig. 1, is presented. Reservoir properties are different for each region, representing a true composite system, and the wells are arbitrarily located.
The solution presented in the paper describes the pressure response at the active wells and at other characteristic points in the reservoir. This general well/reservoir configuration allows us to assemble dozens of specific configurations that are currently not possible. For example, this new solution can describe the pressure response of a storage-and-skin well near a linear boundary. At the same time, the solution can be applied to two-well systems in a true two-composite reservoir separated by a conductive discontinuity. The new solution can be applied to interference testing between oil and gas wells across the gas/oil contact. The new model also describes the pressure response of an active well with different inner boundary conditions in various reservoir shapes, such as a square, a rectangle, a curved stringer and a wedge.
The solution is obtained by application of the Laplace transformation theory coupled with the addition theorem for Bessel functions. It is shown, both analytically and numerically, that the new model contains several well-known solutions as subsets of the general solution.