We developed a hydraulic-fracturing simulator that implicitly couples fluid flow with the stresses induced by fracture deformation in large, complex, 3D discrete-fracture networks (DFNs). The code is efficient enough to perform field-scale simulations of hydraulic fracturing in DFNs containing thousands of fractures, without relying on distributed-memory parallelization. The simulator can describe propagation of hydraulic fractures and opening and shear stimulation of natural fractures. Fracture elements can open or slide, depending on their stress state, fluid pressure, and mechanical properties. Fracture sliding occurs in the direction of maximum resolved shear stress. Nonlinear empirical equations are used to relate normal stress, fracture opening, and fracture sliding to fracture aperture and transmissivity. Fluid leakoff is treated with a semianalytical 1D leakoff model that accounts for changing pressure in the fracture over time. Fracture propagation is modeled with linear-elastic fracture mechanics. The Forchheimer equation (Forchheimer 1901) is used to simulate non-Darcy pressure drop in the fractures because of high flow rate. A crossing criterion is implemented that predicts whether propagating hydraulic fractures will cross natural fractures or terminate against them, depending on orientation and stress anisotropy. Height containment of propagating hydraulic fractures between bedding layers can be modeled with a vertically heterogeneous stress field or by explicitly imposing hydraulic-fracture-height containment as a model assumption. Limitations of the model are that all fractures must be vertical; the mechanical calculations assume a linearly elastic and homogeneous medium; proppant transport is not included; and the locations of potentially forming hydraulic fractures must be specified in advance. Simulations were performed of a single propagating hydraulic fracture with and without leakoff to validate the code against classical analytical solutions. Field-scale simulations were performed of hydraulic fracturing in a densely naturally fractured formation. The simulations demonstrate how interaction with natural fractures in the formation can help explain the high net pressures, relatively short fracture lengths, and broad regions of microseismicity that are often observed in the field during stimulation in low-permeability formations, and that are not predicted by classical hydraulic-fracturing models. Depending on input parameters, our simulations predicted a variety of stimulation behaviors, from long hydraulic fractures with minimal leakoff into surrounding fractures to broad regions of dense fracturing with a branching network of many natural and newly formed fractures.

No abstract

No abstract

A modeling framework is developed to describe proppant transport (including gravitational settling and tip-screen out) in a hydraulic fracturing simulator that can function as either fully-3D or pseudo-3D. The simulator locally enforces mass balance of fluid and proppant and applies appropriate boundary conditions for mechanical calculations. The simulator uses recently developed constitutive equations that smoothly capture the transition from Poiseuille flow to Darcy flow as the proppant concentration transitions from a dilute mixture to a packed bed. We develop new constitutive relations that enable the model to describe fracture closure against proppant (at either low or high concentration) after the end of injection. We also develop a framework for modeling proppant settling in a pseudo-3D model. The method ensures a continuous solution, which guarantees convergence and accuracy with refinement of the temporal and spatial discretization. The framework allows proppant to settle into a proppant bank at the bottom of the fracture. The proppant bank can grow, remain stationary, or erode, depending on flow conditions. The simulator can describe tip-screen out (TSO) and the tendency for the volumetric flowing fraction of proppant to exceed the volumetric fraction of proppant due to the tendency of proppant to flow at the center of the fracture aperture. Pseudo-3D simulations are compared to the fully-3D simulations for both hydraulic fracturing and long-term production. For hydraulic fracturing, the pseudo-3D simulations are able to substantially reproduce the results from the fully-3D simulations and are far more computationally efficient. The simulation methods are compared using a variety of values for proppant size, fluid viscosity, and proppant density. An optimized proppant schedule is tested in order to improve horizontal proppant placement and prevent excessive tip screen-out. The simulations indicate that because fracture closure can be slow in very low permeability formations, substantial settling occurs after the end of injection, significantly worsening vertical proppant placement. For simulation of long-term production, the pseudo-3D results deviate strongly from the fully-3D simulations, indicating that the pseudo-3D model is not suitable for simulating the production phase, as currently formulated.

No abstract