Brice Lecampion

Confined flow of suspensions modelled by a frictional rheology

We investigate in detail the problem of confined pressure-driven laminar flow of neutrally buoyant non-Brownian suspensions using a frictional rheology based on the recent proposal of Boyer et al., 2011. The friction coefficient and solid volume fraction are taken as functions of the dimensionless viscous number I defined as the ratio between the fluid shear stress and the particle normal stress. We clarify the contributions of the contact and hydrodynamic interactions on the evolution of the friction coefficient between the dilute and dense regimes reducing the phenomenological constitutive description to three physical parameters. We also propose an extension of this constitutive law from the flowing regime to the fully jammed state. We obtain an analytical solution of the fully-developed flow in channel and pipe for the frictional suspension rheology. The result can be transposed to dry granular flow upon appropriate redefinition of the dimensionless number I. The predictions are in excellent agreement with available experimental results, when using the values of the constitutive parameters obtained independently from stress-controlled rheological measurements. In particular, the frictional rheology correctly predicts the transition from Poiseuille to plug flow and the associated particles migration with the increase of the entrance solid volume fraction. We numerically solve for the axial development of the flow from the inlet of the channel/pipe toward the fully-developed state. The available experimental data are in good agreement with our predictions. The solution of the axial development of the flow provides a quantitative estimation of the entrance length effect in pipe for suspensions. A analytical expression for development length is shown to encapsulate the numerical solution in the entire range of flow conditions from dilute to dense.

The Impact of the Near-Tip Logic on the Accuracy and Convergence Rate of Hydraulic Fracture Simulators Compared to Reference Solutions

We benchmark a series of simulators against available reference solutions for propagating plane-strain and radial hydraulic fractures. In particular, we focus on the accuracy and convergence of the numerical solutions in the important practical case of viscosity dominated propagation. The simulators are based on different propagation criteria: linear elastic fracture mechanics (LEFM), cohesive zone models/tensile strength criteria, and algorithms accounting for the multi-scale nature of hydraulic fracture propagation in the near-tip region. All the simulators tested here are able to capture the analytical solutions of the different configurations tested, but at vastly different computational costs. Algorithms based on the classical LEFM propagation condition require a fine mesh in order to capture viscosity dominated hydraulic fracture evolution. Cohesive zone models, which model the fracture process zone, require even finer meshes to obtain the same accuracy. By contrast, when the algorithms use the appropriate multi-scale hydraulic fracture asymptote in the near-tip region, the exact solution can be matched accurately with a very coarse mesh. The different analytical reference solutions used in this paper provide a crucial series of benchmark tests that any successful hydraulic fracturing simulator should pass.

Can We Engineer Better Multistage Horizontal Completions? Evidence of the Importance of Near-Wellbore Fracture Geometry From Theory, Lab and Field Experiments

Note: SPE 173363 Reference EPFL-CONF-212843 Record created on 2015-10-08, modified on 2016-08-09

Initiation and Breakdown of an Axisymmetric Hydraulic Fracture Transverse to a Horizontal Wellbore

We investigate the initiation and early-stage propagation of an axi-symmetric hydraulic fracture from a wellbore drilled in the direction of the minimum principal stress in an elastic and impermeable formation. Such a configuration is akin to the case of a horizontal well and a hydraulic fracture transverse to the well axis in an open hole completion. In addition to the effect of the wellbore on the elasticity equation, the effect of the injection system compressi‐ bility is also taken into account. The formulation accounts for the strong coupling between the elasticity equation, the flow of the injected fluid within the newly created crack and the fracture propagation condition. Dimensional analysis of the problem reveals that three di‐ mensionless parameters control the entire problem: the ratio of the initial defect length over the wellbore radius, the ratio between the wellbore radius and a length-scale associated with the fluid stored by compressibility in the injection system during the well pressurization, and finally the ratio of the time-scale of transition from viscosity to toughness dominated propagation to the time-scale associated with compressibility effects. A fully coupled nu‐ merical solver is presented, and validated against solutions for a radial hydraulic fracture propagating in an infinite medium. The influence of the different parameters on the transi‐ tion from the near-wellbore to the case of a hydraulic fracture propagating in an infinite me‐ dium is fully discussed.

Limited Height Growth and Reduced Opening of Hydraulic Fractures due to FractureOffsets: An XFEM Application

Note: SPE 168622 Reference EPFL-CONF-212821 Record created on 2015-10-08, modified on 2016-08-09

Experiments versus theory for the initiation and propagation of radial hydraulic fractures in low‐permeability materials

We compare numerical predictions of the initiation and propagation of radial fluid-driven fractures with laboratory experiments performed in different low permeability materials (PMMA, cement). In particular, we choose experiments where the time evolution of several quantities (fracture width, radius, wellbore pressure) were accurately measured and for which the material and injection parameters were known precisely. Via a dimensional analysis, we discuss in detail the different physical phenomena governing the initiation and early stage of growth of radial hydraulic fractures from a notched wellbore. The scaling analysis notably clarifies the occurence of different regimes of propagation depending on the injection rate, system compliance, material parameters, wellbore and initial notch sizes. In particular, the comparisons presented here provide a clear evidence of the difference between the wellbore pressure at which a fracture initiates and the maximum pressure recorded during a test (also known as the breakdown pressure). The scaling analysis identifies the dimensionless numbers governing the strong fluid-solid effects at the early stage of growth, which are responsible for the continuous increase of the wellbore pressure after the initiation of the fracture. Our analysis provides a simple way to quantify these early time effects for any given laboratory or field configuration. The good agreement between theoretical predictions and experiments also validates the current state of the art hydraulic fracture mechanics models, at least for the simple fracture geometry investigated here.

A macroscopic poromechanical model of cement hydration

This paper describes a macroscopic model of the chemo-thermo-poromechanical behaviour of a hydrating cement paste. The hydrating cement is viewed as an open hardening porous medium. The increments of elastic and viscoelastic strain, pore pressure, temperature and hydration degree are related to the increment in total stress and porosity during an infinitesimal transformation. The tangent material properties depend on the current degree of hydration. The complex chemical reactions are lumped in a single macroscopic one with its kinetics modelled phenomenologically. The in-balance between the decrease of porosity and the consumption of water responsible for self-desiccation, if no water is provided to the paste, is consistently taken into account. A phenomenological relation between capillary pressure and saturation allows reproducing the shrinkage strain associated with self-desiccation. The resulting model is qualitatively calibrated on a set of experiments available in the literature and is shown to reproduce autogenous shrinkage.

Impact of the anisotropy of fracture toughness on the propagation of planar 3D hydraulic fracture

Sedimentary rocks often exhibit a transverse isotropy due to fine scale layering. We investigate the effect of the anisotropy of fracture toughness on the propagation of a planar 3D hydraulic fracture perpendicular to the isotropy plane: a configuration commonly encountered in sedimentary basins. We extend a fully implicit level set scheme for the simulation of hydraulic fracture growth to the case of anisotropic fracture toughness. We derive an analytical solution for the propagation of an elliptical hydraulic fracture in the toughness dominated regime—a shape which results from a particular form of toughness anisotropy. The developed numerical solver closely matches this solution as well as classical benchmarks for hydraulic fracture growth with isotropic toughness. We then quantify numerically the transition between the viscosity dominated propagation regime at early time—where the fracture grows radially—to the toughness dominated regime at large time where the fracture reaches an elliptical shape in the case of an elliptical anisotropy. The time scale at which the fracture starts to deviate from the radial shape and gets more elongated in the direction of lower toughness is in accordance with the viscosity to toughness transition time-scale for a radial fracture defined with the largest value of fracture toughness. Similarly, the toughness dominated regime is fully reached along the whole fracture front when the time gets significantly larger than the same transition time-scale defined with the lowest value of toughness. Using different toughness anisotropy functions, we also illustrate how the details of the complete variation of fracture toughness with propagation direction governs the final hydraulic fracture shape at large time. Our results highlight toughness anisotropy as a possible hydraulic fracture height containment mechanism as well as the need for its careful characterization beyond measurements in the sole material axes (divider and arrester) directions.

Robustness to formation geological heterogeneities of the limited entry technique for multi-stage fracturing of horizontal wells

Robustness to formation geological heterogeneities of the limited entry technique for multi-stage fracturing of horizontal wells is investigated. It is necessary to simulate the complete process of initiation and propagation of multiple hydraulic fractures, accounting for fluid flow in the wellbore together with perforation friction and stress interaction between fractures, to fully investigate the robustness of the limited entry technique. A newly developed model is used for accounting for all these features, assuming that all fractures remain radial, transverse to the wellbore. The simulations carried out are focused on fracture initiation and radial propagation to provide insight into the initial and crucial stage of fracture growth before proppant is injected into the fractures.

Assessment of Leakage Pathways Along a Cemented Annulus

Note: SPE 139693 Reference EPFL-CONF-212829 Record created on 2015-10-08, modified on 2016-08-09