Energy Considerations Associated With the Mechanics of Hydraulic Fracture

Abstract

ABSTRACT The relative contributions associated with the fracturing fluid dissipation and formation fracture toughness mediated energies play a pivotal role in the design and potential optimization of hydraulic fracture evolution in multi-layered reservoirs. A critique of the salient hydraulic fracture process controllable and uncontrollable parameters is presented. The roles of fracturing fluid rheology, flow rate, reservoir elastic properties, fracture toughness values, and in situ stress contrasts are highlighted by evaluating fracture propagation in isotropic models with pre-defined fracture geometries as well as a symmetric three-layered elliptic crack model. Model validation is conducted by comparison of selected numerical results from these simplified models with previously reported model responses. Application of the formulated concepts is illustrated in terms of hydraulic fracture configuration evolution. INTRODUCTION Several competing techniques, with emphases on energy rate balance [1–4] and variational theory methodologies [5–8], have been employed for the evaluation of hydraulically induced fracture configurations. The relative contributions associated with the fracture fluid viscous dissipation and Griffith surface energy components for penny-shaped and rectangular fracture geometries have been systematically examined by Lee et al. [9]. The ensuing characteristic time concept and delineation of the dominant regime(s) for fracture evolution serve as diagnostic tools for parametric sensitivity studies, fracture fluid rheological property and flow rate selection, bottom-hole treatment pressure interpretation, pressure-flow sensitivity characterization and eventual fracture configuration control via process optimization [9,10]. In this paper, a previously introduced Lagrangian formulation employing pertinent energy/energy rate components is utilized. Selected time explicit solutions for isotropic models with specialized geometries are summarized. The extension of the â??istropicâ?¿ elliptic fracture model, representing bounds for the penny-shaped and rectangular fracture configurations, to a symmetric three-layered model with elastic modulus and in situ stress contrast is examined. Validation of this model is conducted by result comparison with this model is conducted by result comparison with reported penny-shaped, constant height, and elliptical crack response results and available numerical simulations. The role of selected hydraulic fracture process parameters is also numerically investigated along with vertical fracture evolution for the cases of moduli contrasts and differential in situ stresses. The applicability of the model formulations to unsymmetric layering geometries and fracturing from horizontal wells is briefly discussed. The use of the presented numerical experiment model, as an alternate or prelude to complex finite element model simulation, for preliminary fracture configuration prediction and design is also advanced.