In the acid fracturing process, the fracture conductivity created by acid etching of the fracture walls is due to the surface roughness created by the acid's non-uniform 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 macro-scale heterogeneities, nor in typical acid fracture simulations, in which the grid block 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 due to local permeability, and acid/rock reactions. In this paper, we developed a three dimensional intermediate-scale acid fracture model with grid block sizes small enough and total dimensions large enough to capture local and macro-scale 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 semi-variogram model.
The model was validated by comparing simulation results with experimental results from an acid fracture conductivity cell. With the model, 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 needs 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 strong correlation strength in the main flow direction, which is the case in laminated formations.