The conductivity of an acid-etched fracture depends strongly on void spaces and channels along the fracture resulting from uneven acid etching of the fracture walls. In this study, we modeled deformation of the rough fracture surfaces acidized in heterogeneous formations based on synthetic permeability distributions and developed a new correlation to calculate the acid-etched fracture conductivity.In our previous work, we modeled the dissolution of the fracture surfaces in formations having small-scale heterogeneities in permeability. The characterization of the correlated permeability fields of rock includes the average permeability, normalized correlation lengths in both horizontal and vertical directions, and normalized standard deviation. These statistical parameters have a significant influence on the fracture-etching profiles obtained from the model. Beginning with this fracture-width distribution, we have modeled the deformation of the fracture surfaces as closure stress is applied to the fracture. The elastic properties of the rock, such as Young's modulus and Poisson's ratio, have effects on the size of the spaces remaining open after fracture closure. After the model yields the width profile under closure stress, the overall conductivity of the fracture is then obtained by numerically modeling the flow through this heterogeneous system.In this paper, we introduce our models and investigate the effects of permeability and mineralogy distributions and rock elastic properties on the overall conductivity of an acid-etched fracture. A new acid-fracture conductivity correlation is developed on the basis of many numerical experiments.

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Summary In the acid-fracturing process, the fracture conductivity created by acid etching of the fracture walls is because of the surface roughness created by the acid's nonuniform dissolution of the fracture surfaces. The acid-fracture conductivity is dependent on surface etching patterns, which are determined by permeability and mineralogy distributions. That is, the spatial distribution of fracture roughness affects the fracture conductivity, which cannot be considered in laboratory measurements of acid-fracture conductivity, which use core samples that are too small to observe such macroscale heterogeneities, or in typical acid-fracture simulators, in which the gridblock size is much larger than the scale of local heterogeneities. An accurate prediction of acid-fracture conductivity necessitates the detailed description of the acid etching profiles on the fracture surfaces, which depend on acid transport in the fracture, leakoff because of local permeability, and acid/rock reactions. In this paper, we developed a 3D intermediate-scale acid-fracture model with gridblock sizes small enough (gridblock sizes comparable to the core-sample size in experiments) and total dimensions large enough (the total dimensions comparable to a gridblock size in an acid-fracture simulator) to capture local and macroscale heterogeneity characteristics. The model predicts the pressure field, the flow field, acid concentration profiles, and fracture-surface profiles as functions of acid injection volume. In the model, we use a front-fixing method (Crank 1984) to handle the irregular, moving boundaries in numerical simulation. Spatially correlated permeability and mineralogy distributions were generated by using a semivariogram model. The model was validated by comparing simulation results with experimental results from an acid-fracture conductivity cell. With the model, by extensive numerical simulation, we analyzed the relationship among fracture-surface-etching patterns, conductivities, and the distributions of permeability and mineralogy. We also illustrated the formation characteristics necessary for acid to create channel-caused high acid-fracture conductivity. We found that a fracture segment with channels extending from the inlet to the outlet of the segment has high conductivity because fluid flow in deep channels causes a very small pressure drop. Such long and highly conductive channels can be created by acids if the formation has heterogeneities in either permeability or mineralogy or both, with high correlation length in the main flow direction, which is the case in laminated formations.

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