A Theoretical Study of Acid Fracture Conductivity Under Closure Stress

Abstract

Abstract The conductivity of acid-etched fractures depends on spaces along the fracture created by uneven etching of the fracture walls remaining open after fracture closure. In this study, we have modeled the deformation of the irregular fracture surfaces created by acid etching and the resulting fracture conductivity as closure stress is applied to the fracture. In our previous work, we modeled the dissolution of the fracture surfaces in a formation having small-scale heterogeneities in both permeability and mineralogy. This model yielded the geometry of the etched fracture at zero closure stress. Beginning with this profile of fracture width, we have modeled the deformation of the fracture surfaces as closure stress is applied to the fracture. At any cross-section along the fracture, we approximate the fracture shape as being a series of elliptical openings. Assuming elastic behavior of the rock, we calculate how many elliptical gaps remain open and their sizes as a function of the applied stress. The sections of the fracture that are closed are assigned a conductivity because of small-scale roughness features using a correlation obtained from laboratory measurements of acid fracture conductivity as a function of closure stress. The overall conductivity of the fracture is then obtained by numerically modeling the flow through this heterogeneous system. Our previous work shows that high fracture conductivity can be created in acid fracturing if heterogeneity of the rock leads to the formation of channels along the fracture surfaces. In this study, we have determined how the channels in acid fracturing remain open as closure stress is applied. This model predicts the rock characteristics that are necessary for acid fracture conductivity to be sustainable under high closure stress. Introduction Acid fracturing is a common well stimulation technique in carbonate reservoirs. The success of acid fracturing depends upon heterogeneous dissolution along the fracture faces. Conductivity after fracture closure results from uneven etching, because asperities created by acid hold as pillars to keep a fracture open. However, the conductivity prediction is difficult because of the stochastic nature of the process. A number of parameters affect the evaluation of acid fracturing. Among the studies for acid fracturing conductivity, Nierode and Kruk's empirical correlation (1973) is widely used in industry. In their correlation, the conductivity is a function of amount of rock dissolution, rock strength, and closure stress, based on experimental observations, as follows: EQUATION, (1) EQUATION, (2) EQUATION (3) where sc is the closure stress in psi, DREC is the dissolved rock equivalent conductivity in md-in, SRE is the rock embedment strength in psi, and wkf is the conductivity in md-in. The acid fracture conductivity highly depends on heterogeneous etching. Not only roughness but also small channels or wormholes contribute to the fracture conductivity. Such features are not easily repeatable in the lab because the breadth of the rock sample is typically only an inch or two. Small channels have widths on the order from inches to a few feet. So the empirical acid fracture correlations based on small laboratory etching tests consider the effect of roughness but not channels. To predict the channels, a fracture domain must be on the order of at least a few feet in both height and length.