Acid-fracture conductivity prediction is a key aspect in acid fracturing design and consequently in the oil and gas production forecast and economic evaluation. Acid-fracture conductivity correlations have been developed for some groups of calcareous rocks with a wide range of properties distribution. The experimental part of these studies has been based on samples from quarries and outcrops. This paper presents the development of conductivity correlations, which differs from previous studies by focusing on a specific oil producer limestone (Quissamã-ESP), by use of samples from well whole cores, and by performing comprehensive 3D surface characterization of the acid-etched fractures. Fractures were acid-etched in the lab with four types of acid systems at proper similarity conditions. The experimental study included core samples preparation, surface scanning with a laser profilometer, and rock strength and conductivity measurements. The 3D surface characterization not only supported the development of a conductivity correlation based on usual parameters, fracture width and rock embedment strength, but also enabled the development of correlations based on surface characterization parameters. It was also useful to manage experimental artifacts, to define the etching pattern, and to obtain more accurate fracture width calculation. The results showed that acid-etched fracture surfaces are rougher than usual engineering surfaces and present negative skewness, high kurtosis, and an intermediate isotropy -mostly random but with some spatial orientation. Four types of exponential acid-fracture conductivity correlations were developed for the Quissamã-ESP limestone, all them more accurate than the Nierode and Kruk correlation, adopted as a reference. The initial conductivity in the most accurate correlation is a function of a surface characterization parameter, while the rate of conductivity change with closure stress is a function of the rock embedment strength. The use of surface characterization parameters can improve the prediction of the initial conductivity, but not the rate of conductivity change with closure stress. Further studies will be necessary to improve the rate of conductivity change with closure stress prediction and to evaluate the possibility of structure creation, such as channels, in the acid-fractured surfaces.

The classical theoretical framework of fracture conductivity for rough acid-etched surfaces is the Nierode and Kruk correlation, given by an exponential equation of two parts: the conductivity under zero closure stress and the rate of conductivity change with closure stress. The first part has been related to fracture width and the second one, to rock embedment strength. This study, based on experiments that used samples from whole cores of an oil producer limestone, analyzed the fitness of laboratory-measured conductivities to the exponential conductivity correlation model. By means of a comprehensive 3D acid-etched surface characterization, this study showed that the use of surface parameters, measured at zero closure stress, can improve only the first part of the exponential correlation. The rate of conductivity change with closure stress is determined by the fracture width reduction under closure stress, while the effects of asperities in contact and related tortuosity are small. This conclusion is based on a physical hypothesis, on correlations of the surface parameters with the mentioned parts or coefficients, and on the relation between contact area ratio and fracture width reduction. The best acid fracture conductivity correlation developed has its first part based on a surface characterization parameter and the second one based on the rock embedment strength. This correlation showed superior accuracy compared with the Nierode and Kruk correlation and represents the maximum possible improvement through the use of surface parameters for the studied limestone. There is still significant room for improvement in the rate of conductivity change with closure stress. This requires a new model of fracture width deformation under closure stress or at least the replacement of the rock embedment strength for a more representative rock strength parameter.

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