A mathematical model that describes the growth and competition of wormholes during an acidizing treatment in a carbonate formation was developed. The model is initialized with the distribution of largest pores. Wormhole characteristics (size, length, and distribution) were found to be controlled by acid-injection, diffusion, and fluid-loss rates.
Acidizing in a reservoir formation is a stimulation technique that has been widely used by the oil industry. Acidizing treatments fall into two categories: matrix acidizing and fracture acidizing. Fracture acidizing consists of injecting acid solution into a carbonate formation at a high enough pressure to break down the formation hydraulically. As the acid flows along the crack, it reacts with the rock and etches the face of the crack. These acid-etched patterns remain to provide flow channels when hydraulic pressure is released and the well is placed back on production. In matrix acidizing. acid is injected at a slow enough rate that the fracture pressure is not exceeded. Matrix treatments are generally aimed at the removal of near-wellbore damage; in an optimal treatment, the acid is expended primarily in the damaged region. A relatively strong solution of HCl (typically 15 wt%) is the most common acid system used in treating carbonates.
When acid is injected into a carbonate, the acid flows preferentially into the highest-permeability regions-the largest pores, vugs. or natural fractures. The rapid dissolution of the matrix material enlarges these initial flow paths so that the acid has soon formed large, highly conductive flow channels, called wormholes.
Wormholes are likely to occur in both matrix acidizing and fracture acidizing in carbonate formations. In fracture acidizing. wormholes are usually deleterious and must be minimized for live acid to penetrate deeply along the fracture opening. In a matrix-acidizing treatment, these wormholes may or may not be desired; if a deep damaged zone exists around the wellbore, wormholes enhance stimulation by increasing the acid penetration depth. If on the other hand, the damaged zone is shallow, wormhole formation leads to an inefficient treatment because most of the acid will be expended beyond the damaged region. To estimate the fluid leakoff rate in an acid fracture or the effect of matrix acidizing in carbonates, a prediction of the distribution, size, and length of wormholes that will be created is needed. Nierode and Williams developed a model to predict the length of a wormhole, but the number of wormholes and their sizes were not addressed. More recently, Hoefner and Fogiers used a network model to simulate the growth of wormholes in matrix acidizing. This model illustrates the relationship between reaction rate and diffusion rate in the formation of wormholes but does not account for fluid loss through the walls of the wormholes, which can be the controlling factor limiting their length.
To describe the physical process of this wormholing phenomenon, a mathematical model that accounts for the chemical kinetics and fluid hydrodynamics in a wormhole and the initial distribution of large pores was developed. Results from the model confirm that wormholes result from the heterogeneity of carbonate rock and reaction kinetics between HCl and carbonates. Wormhole characteristics are controlled by injection, diffusion, and fluid-loss rates.