The transport of fluids down a hydraulic fracture is computed in fracture models by assuming some regular shape for the fracture. In the most complex 3D fracture models, each grid block is assumed to have parallel fracture walls. However, small-scale variations in the fracture width (or wall roughness) may increase the pressure drop, alter the 3D flow field, and, in the case of acid fracturing, influence the etching pattern along the fracture walls.
An accurate prediction of acid fracture conductivity necessitates the detailed description of the acid etching profiles on the fracture surfaces, which depends on acid transport in the fracture, leakoff due to local permeability, and acid/rock reactions. Although a 3D acid fracture model can predict nonuniform etching throughout a fracture, current computational limitations result in dividing the fracture into grid blocks that are several feet to tens of feet on a side, which is much larger than the scale of local heterogeneity and channeling characteristics. We are developing an intermediate-scale acid fracture conductivity model with grid sizes of a few inches to close the gap between laboratory-scale measurements of acid fracture conductivity and macro-scale acid fracture models. The key to such a model is the convective transport of fluid through a heterogeneous fracture.
This paper presents a method to calculate the 3D velocity fields for an intermediate-scale acid fracture model. Incompressible steady-state 3D Navier-Stokes equations describing the flow in a fracture with irregular boundaries are solved with a nonstaggered grid distribution. Leakoff on the fracture surfaces is specified based on local permeability. This model uses front-fixing method1 (body-fitted coordinate transformation) to transform an irregular physical domain into a regular computational domain. A spatially correlated permeability distribution and initial fracture width distribution are generated by a semi-variogram model.
Results from the model illustrate the complex velocity field that occurs in fractures with heterogeneous distributions of fracture width and leakoff rate. The global flow rate versus pressure drop behavior from this model is compared with the predictions of smooth-walled fracture models.