Wheeler, Mary F. (The University of Texas at Austin, USA) | Srinivasan, Sanjay (Pennsylvania State University, USA) | Lee, Sanghyun (Florida State University, USA) | Singh, Manik (Pennsylvania State University, USA)
Optimal design of hydraulic fractures is controlled by the distribution of natural fractures in the reservoir. Due to sparse information, there is uncertainty associated with the prediction of the natural fracture system. Our objective here is to: i) Quantify uncertainty associated with prediction of natural fractures using micro-seismic data and a Bayesian model selection approach, and ii) Use fracture probability maps to implement a finite element phase-field approach for modeling interactions of propagating fractures with natural fractures.
The proposed approach employs state-of-the-art numerical modeling of natural and hydraulic fractures using a diffusive adaptive finite element phase-field approach. The diffusive phase field is defined using the probability map describing the uncertainty in the spatial distribution of natural fractures. That probability map is computed using a model selection procedure that utilizes a suite of prior models for the natural fracture network and a fast proxy to quickly evaluate the forward seismic response corresponding to slip events along fractures. Employing indicator functions, diffusive fracture networks are generated utilizing an accurate computational adaptive mesh scheme based on a posteriori error estimators.
The coupled algorithm was validated with existing benchmark problems which include prototype computations with fracture propagation and reservoir flows in a highly heterogeneous reservoir with natural fractures. Implementation of a algorithm for computing fracture probability map based on synthetic micro-seismic data mimicking a Fort Worth basin data set reveals consistency between the interpreted fracture sets and those observed in the reference. Convergence of iterative solvers and numerical efficiencies of the methods were tested against different examples including field-scale problems. Results reveal that the interpretation of uncertainty pertaining to the presence of fractures and utilizing that uncertainty within the phase field approach to simulate the interactions between induced and natural fracture yields complex structures that include fracture branching, fracture hooking etc.
The novelty of this work lies in the efficient integration of the phase-field fracture propagation models to diffusive natural fracture networks with stochastic representation of uncertainty associated with the prediction of natural fractures in a reservoir. The presented method enables practicing engineers to design hydraulic fracturing treatment accounting for the uncertainty associated with the location and spatial variations in natural fractures. Together with efficient parallel implementation, our approach allows for cost-efficient approach to optimizing production processes in the field.