Onset of miscible and immiscible fluids’ invasion into a viscoplastic fluid

Abstract

We simulate fluid invasion into a gelled cement slurry using a scaled laboratory experiment. This process is relevant to the construction of oil and gas wells, in which a tall column of cement suspension must resist fluid invasion through a combination of static pressure, yield stress, and interfacial tension. The sufficiently over-pressured fluids may enter from the surrounding rocks, leading to failure of the well integrity. Here, we model the cement suspension using a Carbopol solution (yield stress fluid) and apply different over-pressured invading fluids through a centrally positioned hole at the bottom of the circular column. We study water, glycerin, silicon oil, and air as invading fluids, in order to delineate the effects of yield stress, interfacial tension, and column height on fluid invasion. We find that the invasion is easiest for miscible fluids that penetrate locally at significantly lower invasion pressures than immiscible fluids. Viscosity affects this process by retarding the initial diffusive mixing of the fluids, which tends to weaken the gel locally. More viscous invading fluids require larger invasion pressures and result in larger invasion domes. The silicon oil penetrated in the form of a slowly expanding dome, resisted at the walls of the column – effectively by a Poiseuille flow above it in the Carbopol. Invasion pressures were significantly larger than those for the glycerin solutions. The largest invasion pressures were, however, found for air, which is influenced approximately equally by interfacial tension and yield stress.

Effects of non-uniform rheology on the motion of bubbles in a yield-stress fluid

“…Experimentally, any objects moving through any viscoplastic fluids will leave behind a ‘damaged’ trail. This phenomenon has been observed in a number of studies investigating the motion of bubble in viscoplastic fluids (Dubash & Frigaard 2007; Sikorski, Tabuteau & de Bruyn 2009; Lopez, Naccache & de Souza Mendes 2018; Zare & Frigaard 2018; Pourzahedi, Zare & Frigaard 2021). For example, in injecting a sequence of bubbles, subsequent ones follow the same trajectory as the first one and their size reduces and speed increases dramatically (Zare & Frigaard 2018), i.e.…”

“…This is motivated by the scenarios discussed in § 1 and by different observations. First, gas invasion or bubble-rise experiments through yield-stress fluids, such as in Zare & Frigaard (2018) and Pourzahedi et al (2021), characteristically affects the rheology of the fluid in the vicinity of where the first bubbles pass. Typically, successive bubbles follow an identical vertical pathway where the fluid has been sheared by the previous bubbles.…”

“…2021). Preparation details are as in Zare & Frigaard (2018).

Figure 2.Flow curves for the Carbopol 0.06 % and 0.15 % solutions are measured by a stress controlled ramp-up and ramp-down test.

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“…Thixotropic and viscoelastic effects are minimal at the concentrations that we use, which are fairly typical for bubble propagation experiments (Dubash & Frigaard 2007;Lopez et al 2018;Pourzahedi et al 2021). Preparation details are as in Zare & Frigaard (2018).…”

Flow onset for a single bubble in a yield-stress fluid

“…2018; Pourzahedi et al. 2021) or over-pressure (Zare & Frigaard 2018) are common, but in both cases there is a transient motion associated with the release/pinch-off. The bubble typically then deforms quickly on release towards a steady propagation shape.…”