A design method to determine the optimal distribution and amount of insulation for in-ground heat storage tanks

The seasonal sensible heat storage model developed by Hooper and Attwater 1] is modified to describe the thermal behaviour of the soil regime surrounding cylindrical, in-ground, heat storage tanks with optimally distributed insulation. The model assumes steady-state heat transfer, and the surrounding soil is considered to be homogeneous and isotropic. Changes in soil thermal properties due to moisture migration, whether driven by thermal or hydrostatic gradients, are assumed negligible 2]. The optimal distribution is determined using the method of Lagrange multipliers. It is shown that the marginal cost per unit of energy lost and per unit of tank surface area must be the same at all points on the surface of the tank as the condition for minimum total heat loss with a given total investment in insulation. This condition appears to apply for all axi-symmetric in-ground tank geometries. For a given volume of insulation, the incremental increase in storage efficiency with an optimal redistribution of the insulation is a function of tank geometry. The problem of determining the optimal total investment in insulation for a given marginal cost of fuel is described and a method of solution is outlined.