The Energy Budget in Fluid-Driven Fracturing: A Continuum Damage Approach

Abstract

ABSTRACT: We present a numerical approach for the quantification of the energy transfer, storage, and dissipation mechanisms in fluid-driven fracturing. The analysis approach is motivated and originated in the energy statement describing continuum damage, poroelasticity, and the non-local effects in both of damage and transport. The thermodynamically consistent derivation leads to the definition of the state laws, as well the as analytical expressions of energy storage and dissipation in the porous media. The derivation leads to the identification of three major energy loss mechanisms: 1) viscous fluid-flow, 2) solid-damage effect due to the growth of voids and cracks in the solid skeleton, and 3) fluid-damage effect due to the accompanying changes in compressibility and permeability. The analysis model is implemented following the framework of mixed non-linear finite element; and the energy dissipation functions are calculated numerically within this framework. Several benchmark fluid-driven fracturing problems are modeled, and the results agree with the available data from experimental models in the literature. The model is then used to perform several parametric investigations to provide an engineering value of the proposed approach; for example, the analysis of different fluid-injection rates shows most of the additional energy input in higher injection rates is dissipated in viscous fluid flow rather than the sought solid damage. Moreover, the model is used in the analysis of the interaction between fluid-driven fracturing and pre-existing weak zones featuring combinations of reduced stiffness and permeability to represent natural and man-made fractures. 1 INTRODUCTION Hydraulic fracturing is a process in which a fracturing fluid is pumped at high rates in order to increase the permeability in a fracture zone, ultimately leading to more economical oil production. Energy used in the process is transferred into the porous domain in the form of: (a) elastic energy stored in a deformed domain; (b) energy used to generate new fracture surfaces, resulting in the dissipation of energy through solid skeleton decay (damage); and (c) energy used to transport the fluid through pores, resulting in dissipation via fluid viscosity. The goal of an optimized hydraulic fracturing approach would be to maximize the dissipation due to solid damage, as this would result in the stimulation of a larger reservoir volumeBunger and Lecampion (2017); Shlyapobersky (1985). This paper provides a quantitative evaluation of energy stored and dispersed throughout the process of hydraulic fracturing, based on an non-local damage and transport (NLDT) model modelMobasher et al. (2017); Mobasher (2017); Mobasher et al. (2018); Mobasher and Waisman (2021a,b).