Speaker
Description
Gas compressibility induces a nonlinear relationship between the boundary forcing — imposed pressure, volumetric flux and mass flux — and pressure evolution in porous media, producing qualitatively distinct relaxation paths of the pressure field toward its steady state under the different forcings. This behavior is increasingly relevant in gas reservoir operations, particularly with the advent of underground hydrogen storage. Here we analyze it systematically for isothermal ideal gases using the porous medium equation (PME) written in pressure-squared form. By non-dimensionalizing the PME, we identify a compressibility number, $\Pi$, which controls the degree of nonlinearity in the pressure-squared diffusion process and organizes steady and transient flow across injection conditions. The steady pressure profile features a boundary layer of width $\propto \Pi^{-1}$ toward the outlet boundary at fixed pressure, where the flow velocity overshoots and the gas expands at a rate $\propto \Pi^2$. For transients, we calculate numerical solutions of the PME across six decades in $\Pi$. First, we estimate effective pressure-squared diffusion coefficients, which provide a coarse-grained measure of nonlinear relaxation and are defined as the inverse of the time required to reach steady state; they plateau and scale $\propto \Pi^{1/2}$ in the limits $\Pi \ll1$ and $\Pi \gg1$, respectively, with the plateau values and onset of the scaling depending on the injection mode. For imposed pressure, the effective diffusion is accurately captured by a linear diffusion model evaluated at the arithmetic mean pressure, indicating a valid upscaled description of gas flow. To analyze how flow compression distributes over space and time within the domain, we consider the second spatial derivative of pressure or, equivalently, its curvature. Using time-series of positive and negative curvature mass we show how the flow transitions from compression- to expansion-dominated regime, with a $\Pi$-dependent transition time. Such regimes appear mixed and not directly observable in the pressure and flow fields. Finally, we note that the curvature obeys an advection–diffusion–reaction (ADR) evolution equation, which helps interpret the behavior of the observed curvature front. Future research avenues include extending the framework to real gases and heterogeneous porous media, as well as analyzing pressure-curvature dynamics away from the influence of boundaries.
| Country | Spain |
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