In this paper, we present a methodology for predicting the propagation of acid along natural fracture networks and the resulting etching of the fracture walls. The natural fracture network is modeled as a system of intersecting fractures that form a main pathway for acid transport and dissolution. The tails of the intersected fractures increase the leakoff from the main pathway and are accounted for in the model. The fracture network acidizing model is supported by comparisons with laboratory experiments and smaller scale simulations that determined the nature of acid channeling at fracture intersections. Model results illustrate the effects of variations in fracture properties on acid propagation. The model predicts deeper acid penetration under matrix conditions than would be possible with only matrix flow.
Acidizing of natural fractures at matrix treating conditions differs from acid fracturing primarily because of the smaller frature widths in the natural fractures. Our previous experimental study1 showed that acidizing small-width fractures results in three etching patterns in the fractures: channels, wormholes and surface etching. The etching pattern depends primarily on the fracture width and the surface roughness. We also developed a mathematical model of acidizing of carbonates containing a single natural fracture2. The model simulated the flow and reaction of acid in rough-surfaced fractures, with acid transport to the fracture walls by diffusion and convection due to leakoff. The model predicted the same acid etching patterns with the same dependencies on fracture width and roughness as observed in the experiments.
This model has been extended to predict acid transport and rock dissolution in natural fracture networks surrounding a wellbore. We first applied the model to predict the etching of long fractured cores (20 inch length) to compare with recent experiments3. As with comparisons with our previous, shorter core experiments, the model predicted the general etching patterns observed. We then developed a method to simulate the flow of acid in fracture networks. The model predicts that acid may etch natural fractures under matrix treating conditions to distances of a few meters from the wellbore. This result explains acid penetrations of this depth inferred from well responses in carbonates more reasonably than can be done by the application of matrix wormholing models.
To compare our model with long fractured core results from the laboratory, we simulated acid injection into numerically generated fractures with dimensions of 60 cm in length and 6.5 cm in breadth. We modeled a case of acid injection for 20 min with a constant injection rate of 10 ml/min. During the simulation, both the acid etching patterns and the pressure histories are predicted. Details of the model are given by Dong et al.2
The acid etching patterns in large single fractures are shown in Figs. 1–4. In each figure, the initial average fracture width, the matrix permeability, the fracture surface standard deviation and fractal dimension of the fracture surface for that simulation are given as bh, k, s, and d, respectively. The initial fracture is modeled as having a randomly varying local width given by the upper contour plot in each figure. Increasing the standard deviation or the fractal dimension of the width distribution results in a rougher surfaced fracture. In each figure, the lower contour plot is the fracture width distribution after acidizing and thus shows the etching pattern created by the acid. In all the plots, the acid was simulated as entering the fracture from the left side.