New correlations of acid fracture conductivity at low closure stress based on the spatial distributions of formation properties
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In acid fracturing, because of irregular fracture surfaces caused by heterogeneities such as variations in local mineralogy and variations in leakoff behavior, we use a correlation to calculate fracture conductivity. An acid fracture conductivity correlation consists of two parts: conductivity at zero closure stress and the rate of conductivity change with closure stress. Existing correlations do not consider the effect of variations in formation properties and were developed based on laboratory experiments, which used core samples having dimensions of a few inches. Acid fracture simulators, on the other hand, have grid sizes of several to tens of feet. Therefore, correlations should be scaled up properly when used in a fracture simulator. This paper presents new correlations to obtain the conductivity at zero closure stress which can then be incorporated in acid fracture conductivity models that consider the effect of closure stress. In this study, an extensive numerical study was done using an intermediate-scale acid fracture model with total dimensions comparable to a grid block size in an acid fracturing simulator, and grid sizes comparable to core sample sizes used in laboratory acid fracture conductivity tests. In this model, the distributions of permeability and mineralogy along the fracture faces are geostatistically generated. The model outputs fracture surface etching profiles as a function of acid contact time, from which we can get fracture width distributions when the fracture surfaces have come in contact at low closure stress. We then calculate the fracture conductivity by solving for the flow rate through this irregular domain for a fixed p across the domain. By analyzing the relationship between the fracture conductivity created and statistical properties of the permeability and mineralogy distributions, we developed new acid fracture conductivity correlations for low closure stress. These correlations can be used directly to better predict the primary coefficient in the widely used Nierode-Kruk correlation of acid fracture conductivity. This work allows the Nierode-Kruk correlation to be scaled up to the dimensions appropriate for use in an acid fracturing simulator. Copyright 2010, Society of Petroleum Engineers.
