Extended Analytical Model of API 650 Storage Tanks for Variable Liquid Fill Heights

Abstract This study expands on an existing analytical model of above-ground liquid storage tanks to incorporate variable liquid fill heights. Utilizing general elasticity theory, the tank is modeled as an axisymmetric structure featuring a cylindrical wall and a flat bottom floor. Previously, the model considered only the shell at or below the liquid level by ignoring the shell and its stiffness above it. The simplified approach may lead to inaccuracy for partially filled tanks. Hence, the earlier model was essentially restricted to a full or nearly full tank. In this extended analysis, a separate parameter representing the liquid level, apart from the height of tank wall, is introduced into the governing differential equations for all shell sections above or below the liquid level. For tanks with multiple shell courses, generalized solution equations are derived using a step function on liquid load to account for all shell courses irrespective of the liquid level. This allows for the analysis of tanks at any fill conditions, from empty to full. The extended model maintains the same boundary conditions as the previous study. The revised matrix equations applicable to any liquid fill conditions are presented. Comparisons between the results from this extended model and finite element analysis demonstrate the model’s effectiveness. This comprehensive approach provides a more complete analytical method for evaluating tanks under various liquid fill levels.