Reactive dissolution of carbonate rocks is a common technique used to stimulate oil and gas wells. In this process, an acidic solution (typically mineral acid, organic acids or chelating agents) is injected into the porous rock. The acid dissolves some of the rock and creates highly conductive channels called wormholes. This phenomenon of acidization has been described mathematically using a two-scale continuum model that describes the reactive transport of acid as a coupling between the Darcy scale (a length scale at which continuum quantities can be defined) and the pore scale (at which dissolution is taking place). The Darcy scale model consists of equations describing acid transport, con-tinuity, species balance, and porosity evolution. In contrast, the pore scale model appears in the form of closure relations where Darcy scale properties (i.e. permeability, pore radius, and interfacial area per unit volume) are obtained as a function of local porosity. Although the model is widely accepted, most of the numerical studies are limited to 1-D and 2-D, as the computational power required for 3-D simulations that are required to quantitatively predict the experimentally observed results, exceeds the capability of an average desktop computer. For example, we need approximately 160 million cells to capture the face dissolution regime accurately for a 4x4x10 cm rectangular parallelepiped carbonate rock acidization by HCl. Since the computational power requirement increases with the domain size, high-performance computing and efficient numerical algorithms are necessary for 3-D reservoir scale simulations.
Figure 1. Comparison of acidization curve and dissolution patterns obtained from experimental and 3-D numerical simulations.
The objective of this research is to perform efficient 3-D numerical simulations using high-performance clusters available at University of Houston to validate the model by comparing predictions with laboratory scale core acidization results. The validated model can be used for reservoir scale simulations.
To solve the model equations efficiently, the operator splitting method with upwinding finite volume discretization and the multi-grid technique are employed. In addition, implicit time integration with extrapolation resolves instability issues and improves accuracy. Based on the 3-D numerical simulations, the acidization curve predicted from the 3-D numerical studies closely matches with the experimental results found in the extant literature. In addition, various dissolution patterns, i.e. uniform, ramified, wormhole, conical, and face, also match qualitatively with the experimentally observed dissolution patterns.
To our knowledge, this is the first 3-D numerical simulation of carbonate acidization that quantitatively predicts the experimentally observed acidization curve and dissolution patterns. In addition, a sensitivity analysis of the carbonate acidization with respect to the dissolution rate constant and various rock properties is performed, which provides detailed information on the flow inside the wormhole and the dependence of wormhole properties on the rock and fluid properties. Extension of the simulations to field scale (a domain size of the order 1m (radial) x 3.14 (azimuthal) x 10 m (axial)), requires approximately 188 billion cells, and can only be performed using a high-performance cluster.