Acidisation is one of the oldest techniques for enhancing oil recovery, going back more than a 100 years ago. The accurate description of this physical and chemical phenomenon is not a straightforward task. The Darcy law, which is commonly used in continuum modelling at the macroscale, fails when the porosity approaches the unity due to a dissolution. In order to accurately capture the acidisation phenomenon, an upscaling of Navier-Stokes equations is done from pore scale to Darcy scale. The resulting equation is called the Darcy-Brinkman-Stokes (DBS) equation and the approach is called hybrid modelling. The hybrid modelling has the advantage of not having to deal with jumps in velocity and pressure as it makes these variables continuous without any jumps at the interfaces.

The research presented here models the phenomenon using both the Darcy and DBS approaches to study the differences. A single phase injection model in 1-D is simulated to understand the flow dynamics and the chemical kinetics of a single wormhole in idealistic assumptions. To study different regimes of wormholes formation, the 2-D model, implemented in Stanford's Automatic Differentiation General Purpose Research Simulator (ADGPRS), was employed. The shape of wormholes is studied and is validated against the published results. The wormholes characteristics, obtained in both Darcy and DBS models, are defined as a function of breakthrough parameters and dimensionless variables. A convergence, sensitivity and performance analysis is performed for key parameters to fully describe and understand the differences in the 2-D solutions. Furthermore, the impact of co-injecting a gas phase namely CO_2 is simulated and compared with the single phase injection in both the models.