Turbulence Leads to Overestimation of the Acid-Diffusion Coefficient at Typical Experimental Conditions Using the Rotating Disk Apparatus

Abstract

A rotating-disk apparatus (RDA) is used to determine the acid-diffusion coefficient. The equations to interpret RDA tests were previously derived assuming laminar flow to the disk, i.e. uniform accessibility with equal flux of the reactive species over the entire surface of the disk. Thus, the acid-diffusion coefficient is overestimated if the tests are run at transition or turbulent flow regimes. The present work validated laminar flow assumptions at typical RDA experimental conditions to optimize the acid-diffusion coefficient measurements. Disks of calcite marble with a diameter of 0.72, 1.11, and 1.46 in. were reacted in an RDA with hydrochloric acid at temperatures ranging from 73.4 to 100°F and disk rotational speeds ranging from 207 to 1,555 rpm. Transition to turbulent flow was observed at Reynolds numbers one order of magnitude lower than the universally accepted critical value of 3×105. Dissolution patterns on the disks after the experiments and the simulation results using a developed computational fluid-dynamics model confirm this conclusion. The turbulence created cavities near the edges of the 1.46 and 1.1 in. disks starting at rotational speeds of 587 and 829 rpm, respectively. The region of turbulent flow propagated toward the center of the disks with further increase of disk rotational speed. Because of the non-uniform (higher) mass-transfer rate, the diffusion coefficient is overestimated to a value of 6.71×10−5 and 5.01×10−5 cm2/s for the 1.46 and 1.11 in. disks, respectively. For the 0.72 in. disks, no turbulent flow was observed at all disk rotational speeds tested, and the calculated value of the diffusion coefficient was 3.08×10-5 cm2/s. Commercial RDA setups are often equipped with 1.0 or 1.5 in. coreholders and are capable of maintaining a disk rotational speed of up to 2,000 rpm. Thus, care must be taken not to run the tests at transition or turbulent flow regimes, as this will result in overestimation of the acid-diffusion coefficient. Preliminary results indicate that the observed phenomena also affect the RDA analysis of organic and other less reactive acid compositions. Presented results are integral for designing the RDA tests to improve the accuracy of the acid-diffusion coefficient calculations.