Laboratory Investigation of Hydraulic Fracture Growth in Zimbabwe Gabbro

Abstract

Linear elastic fracture mechanics (LEFM) combined with lubrication theory (linear hydraulic fracture mechanics-LHFM for short) have successfully predicted hydraulic fracture growth for planar geometry in model materials such as Poly(methyl methacrylate) (PMMA) and glass (

Effects of velocity-dependent apparent toughness on the pre- and post-shut-in growth of a hydraulic fracture

“…Combination of the linear elastic fracture mechanics theory and apparent toughness acts as a simplified approach to investigate fracture behaviors resulting from complex physics, such as the scale-dependent energy dissipation related to the process zone (Liu et al, 2019;Liu and Lecampion, 2022) and the homogenization of small-scale material heterogeneity (Hossain et al, 2014;Lebihain et al, 2020Lebihain et al, , 2021Ernesti and Schneider, 2022, to cite a few). Recent studies (Da Fies, 2020;Da Fies et al, 2021 point out that the hydraulic fracture growth also presents a velocity-related apparent toughness in the case of a heterogeneous toughness (assuming periodic distribution of rate-independent fracture toughness at micro-scale).…”

Rock Anisotropy Promotes Hydraulic Fracture Containment at Depth

“…Accounting for a time‐varying injection from a point source, it is given by (D. I. Garagash, 2009) $$${\mathcal{K}}_{m}(t)=\frac{{K}_{\text{Ic}}{t}^{5/18}}{{{E}^{\prime }}^{13/18}{{\mu }^{\prime }}^{5/18}{V}_{\text{in}}{(t)}^{1/6}}$$$ where K Ic is the fracture toughness, E ′ = E /(1 − ν 2 ) represents the plane‐strain elastic modulus, μ ′ = 12 μ with μ the dynamic viscosity of the injection fluid, and t = T − T 0 where T and T 0 are the absolute and fracture initiation time, respectively. $${V}_{\text{in}}(t)=\int \nolimits_{0}^{t}{Q}_{\text{in}}(\tau )\mathrm{d}\tau $$ represents the total volume of fluid in the fracture, where Q in is the fluid influx into the fracture accounting for wellbore compressibility (Liu & Lecampion, 2022a; Lu, Momeni, & Lecampion, 2022). A radial HF in an isotropic material (Savitski & Detournay, 2002) grows in the toughness‐dominated regime for $${\mathcal{K}}_{m}\ge 1.1$$, and in the viscosity‐dominated regime when $${\mathcal{K}}_{m}\le 0.32$$.…”

“…The specimens have an average length of 248.5 mm (±1.5 mm) along both e 1 and e 2 directions, and 244.3 mm (±1 mm) along the e 3 direction. All samples are prepared with an axisymmetric notch (10‐mm radius) that emanates from the center of the horizontal wellbore with 8‐mm radius (see more details in Liu and Lecampion (2022a)). The fracture is driven by the injection of different Newtonian fluids in the axisymmetric notch through a wellbore drilled in the center of the specimen.…”

“…These source‐receiver pairs, mounted on two opposite vertical faces parallel to the HF plane (Figures 1a and 1c), enable estimation of the fracture width at 16 locations via an analysis of transmitted waves with a 90° incident angle. In a three‐layer geometry (rock‐fluid‐rock) as shown in Figure 1a, the thickness of the fluid layer (i.e., fracture width), w f , is evaluated by matching the spectrum of the transmitted signals traveling between two facing source‐receiver transducers with the predicted values (Groenenboom & Fokkema, 1998; Kovalyshen et al., 2014; Liu & Lecampion, 2022a; Liu et al., 2020). More details of the calculations are provided in Appendix B.…”

“…where K Ic is the fracture toughness, E′ = E/(1 ν 2 ) represents the plane-strain elastic modulus, μ′ = 12μ with μ the dynamic viscosity of the injection fluid, and t = T T 0 where T and T 0 are the absolute and fracture initiation time, respectively. V in (t) = ∫ t 0 Q in (τ)dτ represents the total volume of fluid in the fracture, where Q in is the fluid influx into the fracture accounting for wellbore compressibility (Liu & Lecampion, 2022a;. A radial HF in an isotropic material (Savitski & Detournay, 2002) grows in the toughnessdominated regime for K m ≥ 1.1, and in the viscosity-dominated regime when K m ≤ 0.32.…”