Acid fracture stimulation generates higher well production but requires engineering design for treatment optimization. To quantify the cost and benefit of a particular acid fracture treatment an engineer must predict the resulting fracture's conductivity distribution. Current practice is to estimate conductivity distribution utilizing two-dimensional models. Unfortunately, these models can misrepresent the amount of acid etching upon which the conductivity estimation is based.A new modeling tool has been developed to estimate fracture conductivity and is used to evaluate different acid fracture treatment designs. The tool uses three-dimensional flow simulation to resolve acid transport in a fracture. This approach includes resolution of the three-dimensional fluid velocity throughout the fracture, fluid pressure, the acid concentration profile, and the acid-etched width. By using a fine grid in the direction of transport to the fracture surfaces, convective and diffusive transport of acid to the fracture surfaces are modeled. The acid-etched width distribution and other formation information are used to calculate the resulting conductivity distributions for different treatment designs.The output acid-etched width and conductivity distributions for different acid fluid systems, fracture geometries, geologies, and completion designs are calculated. The industry lacks a reliable tool for acid fracture treatment design. The modeling tool presented in this paper attempts to address this problem with rigorous simulation of acid transport and etching in a fracture. The parametric study illustrates the benefits and drawbacks to this approach.

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The effect of a shear-thinning fluid governed by a power-law model on the evolution of a hairpin vortex in a wall-bounded flow was studied by means of direct numerical simulation. With a fixed Reynolds number and hairpin vortex strength, the effect of shear-thinning on vortex evolution could be isolated. The primary observation is that very early in time shear-thinning has the effect of reducing the production of vortex kinetic energy and dramatically increasing viscous dissipation. This leads to a delay in the transition of the flow to a turbulent state. Three-dimensional flow visualizations reveal that the increased dissipation is associated with an instability in which the hairpin vortex is broken down into small-scale structures. It is suggested that the finite amplitude of the hairpin creates a lowering of viscosity near the hairpin vortex core which leads to this instability.

Recently developed models of the acid fracturing process have shown that the differential etching necessary to create lasting fracture conductivity is caused by the heterogeneous distributions of permeability and mineralogy along the fracture faces. To predict the conductivity that can be created by acid in a particular formation, the models require information about these formation properties and their spatial variation. This research aims to quantify the small scale heterogeneity by using a geostatistical description to ascertain the distribution of permeability in a carbonate formation. Parameters that quantify the directional correlation and variance of the data are developed. The correlation length and variance parameters are a first step in being able to couple acid transport and rock dissolution models at reservoir scale with a model of fracture conductivity based on channels and roughness features caused by small scale heterogeneity. These geostatistical parameters are developed for a well in the Hugoton Field. Data leading to their derivation are obtained from a combination of well logs and cores. The resulting geostatistical parameters and acid etched width are used to predict acid fracture performance. Application of new model conductivity correlations results in a unique prediction for the acid fracture case study that differs from the industry standard.