Impact of injection rate ramp-up on nucleation and arrest of dynamic fault slip

Abstract

Abstract Fluid injection into underground formations reactivates preexisting geological discontinuities such as faults or fractures. In this work, we investigate the impact of injection rate ramp-up present in many standard injection protocols on the nucleation and potential arrest of dynamic slip along a planar pressurized fault. We assume a linear increasing function of injection rate with time, up to a given time $$t_c$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>t</mml:mi> <mml:mi>c</mml:mi> </mml:msub> </mml:math> after which a maximum value $$Q_m$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Q</mml:mi> <mml:mi>m</mml:mi> </mml:msub> </mml:math> is achieved. Under the assumption of negligible shear-induced dilatancy and impermeable host medium, we solve numerically the coupled hydro-mechanical model and explore the different slip regimes identified via scaling analysis. We show that in the limit when fluid diffusion time scale $$t_w$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>t</mml:mi> <mml:mi>w</mml:mi> </mml:msub> </mml:math> is much larger than the ramp-up time scale $$t_c$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>t</mml:mi> <mml:mi>c</mml:mi> </mml:msub> </mml:math> , slip on an ultimately stable fault is essentially driven by pressurization at constant rate. Vice versa, in the limit when $$t_c/t_w \gg 1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>t</mml:mi> <mml:mi>c</mml:mi> </mml:msub> <mml:mo>/</mml:mo> <mml:msub> <mml:mi>t</mml:mi> <mml:mi>w</mml:mi> </mml:msub> <mml:mo>≫</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> , the pressurization rate, quantified by the dimensionless ratio $$\dfrac{Q_m t_w}{t_c Q^*}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mstyle> <mml:mfrac> <mml:mrow> <mml:msub> <mml:mi>Q</mml:mi> <mml:mi>m</mml:mi> </mml:msub> <mml:msub> <mml:mi>t</mml:mi> <mml:mi>w</mml:mi> </mml:msub> </mml:mrow> <mml:mrow> <mml:msub> <mml:mi>t</mml:mi> <mml:mi>c</mml:mi> </mml:msub> <mml:msup> <mml:mi>Q</mml:mi> <mml:mo>∗</mml:mo> </mml:msup> </mml:mrow> </mml:mfrac> </mml:mstyle> </mml:math> with $$Q^*$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>Q</mml:mi> <mml:mo>∗</mml:mo> </mml:msup> </mml:math> being a characteristic injection rate scale, does impact both nucleation time and arrest distance of dynamic slip. Indeed, for a given initial fault loading condition and frictional weakening property, lower pressurization rates delay the nucleation of a finite-sized dynamic event and increase the corresponding run-out distance approximately proportional to $$\propto \left( \dfrac{Q_m t_w}{t_c Q^*}\right) ^{-0.472}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>∝</mml:mo> <mml:msup> <mml:mfenced> <mml:mstyle> <mml:mfrac> <mml:mrow> <mml:msub> <mml:mi>Q</mml:mi> <mml:mi>m</mml:mi> </mml:msub> <mml:msub> <mml:mi>t</mml:mi> <mml:mi>w</mml:mi> </mml:msub> </mml:mrow> <mml:mrow> <mml:msub> <mml:mi>t</mml:mi> <mml:mi>c</mml:mi> </mml:msub> <mml:msup> <mml:mi>Q</mml:mi> <mml:mo>∗</mml:mo> </mml:msup> </mml:mrow> </mml:mfrac> </mml:mstyle> </mml:mfenced> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>0.472</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> . On critically stressed faults, instead, the ramp-up of injection rate activates quasi-static slip which quickly turn into a run-away dynamic rupture. Its nucleation time decreases non-linearly with increasing value of $$\dfrac{Q_m t_w}{t_c Q^*}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mstyle> <mml:mfrac> <mml:mrow> <mml:msub> <mml:mi>Q</mml:mi> <mml:mi>m</mml:mi> </mml:msub> <mml:msub> <mml:mi>t</mml:mi> <mml:mi>w</mml:mi> </mml:msub> </mml:mrow> <mml:mrow> <mml:msub> <mml:mi>t</mml:mi> <mml:mi>c</mml:mi> </mml:msub> <mml:msup> <mml:mi>Q</mml:mi> <mml:mo>∗</mml:mo> </mml:msup> </mml:mrow> </mml:mfrac> </mml:mstyle> </mml:math> and it may precede (or not) the one associated with fault pressurization at constant rate only.

Topics & Concepts