The efficiency of a carbonate matrix acidizing treatment relies strongly on the dominant wormhole channels formed during the treatment. We have developed and confirmed a theory to predict when the dominant wormhole channels are most efficiently created. Based on this theory, a wormhole population density model was developed.
In a carbonate acidizing treatment design, the acid volume needed to bypass the near wellbore damage area or penetrate a distance away from the wellbore depends not only on wormhole propagation distance but also on how many wormholes are created. This study investigates the wormhole population density, which means how many wormholes per area of rock surface or per wellbore length will be created. The study is based on the following strategy. For a given rock/acid system, the optimal acid injection flux at which dominant wormholes are initiated is obtained from the wormhole propagation theory. For a given formation, a corresponding pressure gradient at the optimal acid flux is calculated. This pressure gradient is also called the wormhole initiation pressure gradient. When a wormhole is initiated at an arbitrary point along the wellbore, the local pressure distribution is disturbed, resulting in lower pressure gradients into the formation in the region surrounding the wormholes. In this region of reduced pressure gradient and hence, reduced flux, initiation of other wormholes is suppressed. At a sufficient distance from the initial wormhole, the pressure field is undisturbed and other wormholes will develop.
We numerically simulated the flow field around a wellbore with a wormhole extending into the formation to quantify this phenomenon. From this study, we predict the wormhole population density along a wellbore as a function of the acidizing conditions. An example is provided to show the application of the wormhole population density model in a treatment design. Fluid loss through the walls of the wormholes and wellbore, optimal acid injection flux, and wormhole propagation rate are also taken into account in this example. The example shows how the wormhole population density model is used to predict the required acid volume (gal/ft) to yield the desired productivity improvement.