Hydrochloric acid solutions were reacted with limestone core plugs using an annular flow reactor at acid-fracturing conditions. The obtained reaction rates were correlated with theory using a correlation that was recently verified to be suitable for correlating HCl reaction rate with mass transfer parameters. Applying the correlation to the present data produced effective diffusion coefficients for HCl from the different acid solutions at acid-fracturing conditions. The results showed that the diffusion coefficient of an acid solution made in distilled water was larger than the diffusion coefficient of an acid solution made in synthetic North Sea water. The diffusion coefficient of a retarded acid was found to be an order of magnitude smaller than the diffusion coefficient of neat acid.
The diffusion coefficient of HCl is an important parameter that is needed for the design and modeling of acid fracturing treatments. Although numerous acid fracturing treatments had been done over the years, HCl diffusion coefficients at field conditions remain unavailable. The effective diffusion coefficient of HCl at the temperature, pressure and acid concentrations of the treatment is needed to realistically predict an etched length of a fracture from acid-fracturing models. In previous studies, researchers have used diffusion coefficients that were extrapolated from the diffusion coefficients of dilute hydrochloric acid solutions. Only recently there have been attempts to obtain diffusion coefficients from concentrated HCl solutions.
The heterogeneous reaction between carbonate rock and aqueous solutions of hydrochloric acid involves the transport of acid molecules from the bulk fluid to the fluid-solid interface at the rock surface, chemical reaction at the rock surface, and the transport of the reaction products (CO2 and CaCl2) from the solid-liquid interface to the bulk fluid. The chemical reaction is very fast compared to the mass transfer steps. Consequently, the reaction of HCl with carbonate rock at high temperature and pressure is mass transfer limited. Therefore, correlating the overall reaction rate with parameters that affect the mass transfer rate is a step forward in the quest to properly design or model acid fracturing treatments in field applications. Reaction rates obtained from lab experiments are well suited for such correlation because they are obtained at controlled experimental conditions. In a recent study such correlations were successfully made using lab generated reaction rates.
Ross and Wragg developed correlations for mass transfer operations in annuli. They found equation 1 as the most appropriate to correlate mass transfer operations in annuli when the flow is laminar and pure forced convection.
Where Sh is Sherwood number, Km is the mass transfer coefficient, de is the difference between the reactor diameter and the core diameter, D is the diffusion coefficient, Re is Reynolds number, Sc is Schmidt number, L is the length of core and f(a) is a function of a, the ratio of core diameter to the reactor inner diameter.
When the experimental conditions were such that both free and forced convections contributed to the mass transfer operation the correlation of Eq. 1 did not match the experimental results. Wragg and Ross later extended the correlation to the situation when free and forced convections contributed to the mass transfer. They used equation 2 to correlate experimental mass transfer data under such conditions.