Comprehensive Simulation of Hydraulic Fracturing Through Mechanical Stratigraphy with Explicit Width Calculation and Leakoff: Foundations of Completion Modeling
Authors: Ji Lujun , Settari Antonin Tony , Sen Vikram , Sullivan Richard , Puchyr Peter 
Published: January 2020

Abstract
This paper describes a new and comprehensive 3D hydraulic fracturing simulation model, built within a single software system combining Finite-Difference reservoir flow simulation with Finite-Element displacement and stress/strain computations. This allows dynamic and explicit calculation of fracture width (i.e., opening, propagation, and closing) and modeling of surrounding dynamic stimulated reservoir volumes. This new fracture modeling formulation advances the model initially developed by Ji et al. (2009) and the workflows described in Min et al. (2018) and Sen et al. (2018) for optimization of completion design and well spacing in unconventional reservoirs.
The new code relies on carefully considered algorithmic constructs (such as iterative coupling). It was designed for ensemble modeling over ranges of uncertainties in petrophysical and mechanical stratigraphy. Multiple options for combining node displacements on the fracture face along with new iterative algorithms and efficient use of elements of symmetry allow for representative calculations for a range of models with reasonable runtimes. The workflow uses structured grids, and the same block definitions are used for both the flow and geomechanical computations. Fracture extent and width, leakoff, and stress-dependent permeability enhancement in the stimulated reservoir volume (SRV) are all computed in a coupled fashion, based on reservoir flow characterization and mechanical stratigraphy (stiffness and stress) in a fully 3D heterogeneous sense.
This tool has been used to model hydraulic fracturing (fluid injection), flow-back, and production within a single workflow. The evolution of the fractures can be tracked in usual time step fashion, along with leakoff, multiphase saturations, and pressures on a 3D grid. Simultaneously, the model computes the poroelastic changes in all stresses and their effect on fracture propagation or closure and on permeability and porosity of the media, i.e., the SRV development. Dynamic fracture height, width and length are determined without the constraints of explicit shape assumptions or simplifications; rather, they are computed based on propagation criteria using local, dynamic pressure, mechanical properties and stresses. We have also used this new simulator to model and match Diagnostic Fracture Injection Tests (DFITs).
The complexity of the interactions of physical mechanisms in this model requires large computing times. A significant improvement in run time (an order of magnitude) was achieved by using new algorithms for the iterative solution of the flow/stress/fracture coupled problem. This provides possibilities for modeling fracturing in complex reservoirs with a new level of accuracy. For example, the model provided new insight in the importance of flow friction in the fracture for history matching the pumping pressure. In DFITs, the simulated details of fracture initiation and closure can be used to calibrate mechanical properties as well as permeability behavior with stress. Finally, the capability to use 3D stress and reservoir characterization is invaluable in modeling cases of unusual vertical fracture growth.
Practicing engineers will appreciate the value of the integrated simulator presented herein. It helps in developing a clearer understanding of the causal effects of different factors that impact the success of a hydraulic fracturing/stimulation program. These factors include geological, tectonic, mechanical, and operator influences. Using this simulator as a kernel, powerful completion optimization workflows can be built by running a priori simulations of numerous permutations of influencing factors.