THEORETICAL DENSITY CALCULATOR

Theoretical density (rho T) could be defined as a mathematically derived new density for a homogeneous mixture of same product (e.g. petroleum) from two different sources and media of known densities and significant observed volumes. Usually, petroleum products densities are obtained through laboratory experiment and derivations by application of relevant apparatuses and standards. Given the same condition, experiments should be able to yield similar result with acceptable percentage error when carried out in different laboratories. This is called reproducibility. Theoretical density formula finds application when calculating volumes between ship’s discharge and shore receipt during cargo reconciliation. It is a tank-by-tank shore application. If the initial volume of one source/ medium (usually shore tank) is negligible vis-à-vis the second source/ medium (usually the ship), the port arrival density of the second source could be used in lieu of the theoretical. If the theoretical density is calculated here, the result is approximately same as that of the second source product. If both sources have significant observed volumes, then the theoretical density is necessary in order to close the gap between the two density values and thus find a meeting point that gives acceptable standard volume and weight. The following points must be noted when applying the formula:

a) The value of theoretical density (ρT) usually falls between the two known product densities but not averaged. This means that value should not be a midpoint value.
b) The ρT value should be closer to the density of the higher volume source than that of the lower volume source. Formula for theoretical density:
ρT = v1 ρ1 + v2 ρ2 / V3
Where,

• ρ = density (rho, Greek symbol).
• T = theoretical (subscripted tee).
• ρT = theoretical density.
• v1 = initial cargo volume in tank before receipt.
• ρ1 = initial cargo density in tank before receipt.
• v2 = volume of new cargo added; volume received (v3-v1).
• ρ2 = density of new cargo added; density from ship.
• V3 = Total/ final volume of cargo in tank under consideration (v1+v2).