Self‐organized fluid flow through heterogeneous networks

Abstract

The purpose of this paper is to assess the coupled effect of fluid flow and dissolution/precipitation reactions in heterogeneous porous media at semi‐macroscopic scales (i.e. several tens of grains). Are the dissolution/precipitation processes roughening or smoothing at these scales? Does self‐organization arise from the coupling of these processes with fluid flow? What is the effect of heterogeneity (i.e. of the variance of the pore size distribution assuming a constant mean)? The dissolution/precipitation processes were modeled as producing a change of the local pore radius proportionally to the local flux. It was found that both precipitation and dissolution lead to more heterogeneous, anisotropic pore structures (parallel to the macroscopic flow for dissolution, perpendicular for precipitation). One new interesting observation was that precipitation generated an almost uniform flux field. To a lesser extent, dissolution also tended to smooth the pressure gradient field. The possibility of uniform flux or pressure gradient fields could have important implications in hydrology or in technical applications such as filter plugging or acid treatment of oil reservoirs.

Permeability, porosity and pore geometry of chemically altered porous silica glass

“…A given porosity producing or reducing mechanism is said to be smoothing (roughening) if it reduces (augments) the heterogeneity of the pore space at any scale and thus decreases (increases) the ratio of noneffective to effective pore volume. By this definition the chemically driven mechanisms discussed here tend to be roughening at scales varying from subpore (i.e., pore wall roughness [Aharonov et al, 1997]) to macroscopic scales [Ortoleva, 1994;Aharonov, 1996;Bernabé, 1996].…”

“…[31] In order to gain more insight we attempted, using network simulations [Bernabé, 1996], to produce k versus f curves that can be qualitatively compared to the experimental ones. We first generated a three-dimensional, simple cubic, heterogeneous network using a statistical distribution of pore radii, roughly corresponding to that observed in intact porous glass; we then calculated the network porosity and permeability, applied a local evolution rule to all the capillaries in the network, and repeated the entire procedure as many times as necessary.…”

“…(i.e., high Damkhöler number) and if diffusive transport is negligible (i.e., high Péclet number), then the volume of precipitate in each individual pore is proportional to the local fluid flux [Bernabé, 1996]. If we further assume that the precipitate layer is smooth, we obtain rule 1B: in each pore i the radius r i is reduced by a quantity dr i proportional to the local fluid flux q i .…”

Localized reactive flow in carbonate rocks: Core‐flood experiments and network simulations

“…Here no porosity‐permeability relationship needs to be assumed. Another pore‐scale approach, which is particularly simple, idealizes the porosity as a network of conduits, whose shapes and sizes are assigned either from an assumed statistical distribution or microstructure images [ Hoefner and Fogler , ; Bernab'e , ; Budek and Szymczak , ; Raoof et al , ; Menke et al , , ].…”

Numerical modeling of reaction‐induced cavities in a porous rock

“…The instability has also been studied using numerical simulation at the pore scale, where the fluid motion was described by Stokes equation (see Adler [1992] for a detailed review). Concerning the matrix heterogeneity, the transport/dissolution feedback enhances the porosity in the direction of the macroscopic flow [Bernabe, 1996]. At the suprapore (or Darcy) scale an additional scale of heterogeneity can interact with the progress of the reaction front.…”