In Situ Determination of Solid Fraction from the Measured Hydrate Slurry Flow Rate and Pressure Drop across Orifice

Two-phase flow is encountered in various engineering areas, including the pharmaceutical, chemical, and food industries, desalination facilities, and thermal energy storage systems. Cost-effective and non-invasive monitoring of the solid volume fraction, which governs the thermos-physical properties of two-phase medium, is important for flow assurance. The flow loop having an inner diameter of 21.5 mm and length of about 12.2 m was equipped with square-edged orifice and slash plate pump. Tetrafluroethane (R134a) hydrate slurry of the specified solid volume fraction could be formed within the flow loop by removing an appropriate amount of water, and simultaneously injecting the pertinent amount of R134a while chilled at 275 K. The uncertainty in the thus-obtained solid volume fraction was smaller than 9%, with the largest contribution originating from the uncertain hydration number. The near power-law relationship between the orifice pressure loss coefficient and Metzner–Reed Reynolds number was recognized. However, the nonlinear nature of the Reynolds number with respect to the solid volume fraction inevitably makes the solution procedure iterative. The short span pressure differences across the orifice were regressed to yield empirical correlation, with which the solid volume fraction of R134a slurry could be determined from the measured pressure drop across the orifice and the flow rate. The uncertainty was less than 12% of the thus determined solid volume fraction.