A regular concern when managing bulk liquids and bulk liquid transfers is the measurement of liquid stored within a tank at any given time. Determining liquid level is rather simple using a modern sensor or even a gauge tape, but in-service tanks are slightly deformed and are not representative of an ideal cylinder. Therefore, determining the quantity of liquid with a simple, repeatable and accurate calculation methodology is necessary.
Finite element analysis (FEA) provides robust information regarding tank shape, stresses and structural stability, but FEA requires significant resources, time and experience to properly model a tank. It is unnecessary to perform FEA on every tank and is most apt for use on tanks that are unable to meet the condition for API 653 but have the potential to meet the limitations of API 579 Fitness-for-Service. Therefore, it is appropriate to determine some alternative method to calculate the volume of liquid within a tank from the liquid level.
A new method for determining the volume expansion across the vertical length of a tank, called the "ring slice method" (RSM), has been developed. This method is more accurate over a wide range of tank diameters, can be applied simply on an Excel spreadsheet and is transparent for the standard user to implement.
Comparison of finite element analysis (FEA) to ring slice method (RSM).
Researchers arrived at this conclusion by comparing a variety of models against the results for FEA, summarizing the results for volume expansion using different independent variables, such as the tank diameter, specific gravity, fill height and more. The results for volume expansion are most reliably and simply determined using the RSM at a 1-foot interval.
The RSM is performed by theoretically slicing a tank shell every vertical foot, determining the pressure at those slices and then calculating the radial expansion for that slice by assuming it behaves as a thin cylinder under internal pressure with no edge constraints. Because the RSM is not iterative, it can be applied in an Excel spreadsheet so that changes in specific gravity of the product or other variations can be adjusted without rerunning each calculation.
API 2.2 methodology (the current tank calibration standard) is an iterative method that is rather difficult to apply. The RSM method provides companies and those responsible for tank management with an accurate and simple-to-use method for determining the volume of liquid within a vertical, cylindrical tank.
For more information or for a copy of the RSM workbook, email Brock Trotter at brock@pemyconsulting.com or call (405) 708-3309. Visit www.pemyconsulting.com for more tools and techniques.
