A theoretical analysis of the dynamics of hot water underground stores of general shape

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Abstract
In 1969, Waterman introduced the so-called T-matrix method to solve the problem of the scattering of an acoustic wave from a body of general shape. Since then, this method has been extended in different directions and used to solve many different scattering problems. The authors show here that it can also be used to determine the temperature field in the rock around a cavern of general shape, filled with hot water of arbitrarily varying temperature. This problem is of interest for the storage of surplus heat for later use, an increasingly important technical problem. They modify the T-matrix formalism to be applicable to this problem, and show that it works for the simple case of a spherical cavity. They discuss some general properties of the temperature field, as well as some practical problems connected to the accuracy of the mathematical model and to the numerical convergence of the solution. Numerical calculations for non-spherical cases are postponed to later publications. The problem with several cavities is discussed, and a method to determine the influence of a plane ground surface is presented.