Advanced Mathematical Methods for Scientists and Engineers

https://www.math.ubc.ca/~peirce/Computer%20simulation%20of%20HF_Adachi_Siebrits_Peirce_Desroaches_IJRM_MS_V44_p739_2007.pdf

Computer simulation of hydraulic fractures

Thirty Years of Gas Shale Fracturing: What Have We Learned?

Modeling of Hydraulic-Fracture-Network Propagation in a Naturally Fractured Formation

This paper reviews recent results of a research program aimed at developing a theoretical framework to understand and predict the different modes of propagation of a fluid-driven fracture. The research effort involves constructing detailed solutions of the crack tip region, developing global models of hydraulic fractures for plane strain and radial geometry, and identifying the parameters controlling the fracture growth. The paper focuses on the propagation of hydraulic fractures in impermeable rocks. The controlling parameters are identified from scaling laws that recognize the existence of two dissipative processes: fracturing of the rock (toughness) and dissipation in the fracturing fluid (viscosity). It is shown that the two limit solutions (corresponding to zero toughness and zero viscosity) are characterized by a power law dependence on time and that the transition between these two asymptotic solutions depends on a single number, which can be chosen to be either a dimensionless toughness or a dimen...

Propagation Regimes of Fluid-Driven Fractures in Impermeable Rocks

We present a planar three-dimensional (3D) fracture growth simulator, based on a displacement discontinuity (DD) method for multi-layer elasticity problems. The method uses a fixed mesh approach, with rectangular panel elements to represent the planar fracture surface. Special fracture tip logic is included that allows a tip element to be partially fractured in the tip region. The fracture perimeter is modelled in a piece-wise linear manner. The algorithm can model any number of interacting fractures that are restricted to lie on a single planar surface, located orthogonal to any number of parallel layers. The multiple layers are treated using a Fourier transform (FT) approach that provides a numerical Green's function for the DD scheme. The layers are assumed to be fully bonded together. Any fracture growth rule can be postulated for the algorithm. We demonstrate this approach on a number of test problems to verify its accuracy and efficiency, before showing some more general results.

An efficient multi‐layer planar 3D fracture growth algorithm using a fixed mesh approach

Note: SPE 124919 Reference EPFL-CONF-212832 Record created on 2015-10-08, modified on 2016-08-09

Measuring Hydraulic Fracture Growth in Naturally Fractured Rock

This paper (SPE 128715) was accepted for presentation at the SPE Oil and Gas India Conference and Exhibition, Mumbai, India, 20–22 January 2010, and revised for publication. Original manuscript received 17 February 2010. Revised manuscript received 20 July 2010. Paper peer approved 17 August 2010. Summary We present the results of numerical modeling that quantify the physical mechanisms of mechanical activation of a natural fault because of contact with a pressurized hydraulic fracture (HF). We focus on three stages of interactions: HF approaching, contact, and subsequent infiltration of the fault. Fracture interaction at the contact is shown to depend on four dimensionless parameters: net pressure in the HF, in-situ differential stress, relative angle between the natural fault and the HF, and friction angle of the natural fault. A numerical model based on the displacement discontinuity method (DDM) allowing for fracture closure and Mohr-Coulomb friction was used to calculate the displacements and stresses along the natural fracture as a result of the interaction with the pressurized HF. The analysis of the total stress state along the fault during the HF coalescence stage makes it possible to define a criterion for reinitiation of a secondary tensile crack from the natural fault. We show that the most probable location for tensile-crack initiation is the end of the open zone of the fault where the highest tension peak is generated by the HF contact. In our numerical analysis, we study the magnitude of maximum tensile stress and its position along the fault for a wide range of key dimensionless parameters. Given real reservoir properties, these measurements can be used to detect the possible fracturing scenarios in naturally fractured reservoirs. Using simplified uncoupled modeling of fluid penetration into the fault after the contact with the HF, we demonstrate that either an increase or a decrease of the tensile stress at the opposite side of the fault can be realized depending on the ratio of increments of net pressure and the fluid front as it penetrates the natural fault.

Hydraulic Fracture Propagation in a Naturally Fractured Reservoir

A hydraulic fracture design model that simulates the complex physical process of fracture propagation in the earth driven by the injected fluid through a wellbore. An objective in the model is to adhere with the laws of physics governing the surface deformation of the created fracture subjected to the fluid pressure, the fluid flow in the gap formed by the opposing fracture surfaces, the propagation of the fracture front, the transport of the proppant in the fracture carried by the fluid, and the leakoff of the fracturing fluid into the permeable rock. The models used in accordance with methods of the invention are typically based on the assumptions and the mathematical equations for the conventional 2D or P3D models, and further take into account the network of jointed fracture segments. For each fracture segment, the mathematical equations governing the fracture deformation and fluid flow apply. For each time step, the model predicts the incremental growth of the branch tips and the pressure and flow rate distribution in the system by solving the governing equations and satisfying the boundary conditions at the fracture tips, wellbore and connected branch joints. An iterative technique is used to obtain the solution of this highly nonlinear and complex problem.

Eduard Siebrits

Papers

Computer simulation of hydraulic fractures

An efficient multi‐layer planar 3D fracture growth algorithm using a fixed mesh approach

Measuring Hydraulic Fracture Growth in Naturally Fractured Rock

Hydraulic Fracture Propagation in a Naturally Fractured Reservoir

Simulations for Hydraulic Fracturing Treatments and Methods of Fracturing Naturally Fractured Formation