The new model has been developed based on OpenFOAM, which is an open source platform for computational fluid dynamics. Here, the DBS momentum equation was used to solve velocity equation by accounting for the fluidâsolid mass transfer; an advectionâdiffusion equation was used to compute the distribution of injected HFF and iron. The reactionâinduced pore evolution was captured by applying the LSM, where the solidâliquid interface was updated by solving level set distance function and reinitialized to a signed distance function. Then, a smoothened Heaviside function gave a smoothed solidâliquid interface over a narrow band with a fixed thickness. The stated equations were discretized by the finite volume method, while the reinitialized equation was discretized by the central difference method. Gauss linear upwind scheme was used to solve the level set distance function, and PressureâImplicit with Splitting of Operators (PISO) method was used to solve the momentum equation. To validate the numerical method, we conducted the HFF reactive transport experiment with a shale sample. A sample from Marcellus shale was first soaked into HCl solution to remove carbonate and dried. Then, the sample was embedded in a single straight polydimethylsiloxane (PDMS) channel. The freshly made HFF, mainly containing organic additives, was injected into the system by a polytetrafluoroethylene (PTFE) tube from the leftâhand side of the PDMS channel. A syringe pump provided the constant fluid velocity. PH value was adjusted by hydrochloric acid (HCl) and sodium hydroxide (NaOH) and set as 2.0 in the experiment. Injected velocity was 6Ã10â4 m/s; microchannel was 40 mm long, and the cross section of the channel was 1.5 mm Ã 0.3 mm. We weighted the sample before and after the reaction for four weeks. After the reaction, cross sections of the samples were characterized using Scanning electron microscope (SEM). The oxidation of Fe2+ was measured by ion chromatography with time intervals. The normalized sample mass was compared with our numerical results, showing good agreement between the two methods.
From the experiments, we found that total Fe and Fe2+ increased first and then decreased, suggesting the precipitation of Fe. The precipitation of Fe depends on pH value, carbonate contents, and extraction of bitumen. We found that under our experimental condition, the iron precipitation was not symmetrical. The iron tended to precipitate at the downstream side of the sample. Sensitivity analysis was conducted with various Damkohler number (DaII) and Peclet number (Pe) between HFF and shale sample. We categorized the Fe (III) precipitation into three patterns as a function of DaII and Pe: symmetrical smoothed growth, unsymmetrical growth, and dendritic growth. Pe and DaII significantly affected the location of precipitation, which was critical in determining the injection parameters of hydraulic fracturing. When DaII<1, the precipitation uniformly occurred on the solid surface both in upstream and downstream directions. When DaII>1, the precipitation mainly occurred on the solid surface in upstream direction. When Pe>1, Fe (II) was transported deeply into and precipitated inside the pores. When Pe<1, the precipitation of Fe (III) occurred mainly on the solid surface in upstream direction, and they were easily precipitated inside the small pore structures. The porosityâpermeability relationship was subsequently presented. We also simulated this process under different mineralogical samples from digital rock images and obtained the following interesting findings. When the samples contained the large amount of calcite, no precipitation was observed. However, when the content of calcite was low and the content of dolomite was high, we could observe slight precipitation.
The newly developed poreâscale model allows high confidence in the description of Fe (II) dissolution, transport, and Fe (III) precipitation, which has improved our understanding of mineral dissolution and precipitation in shale during hydraulic fracturing. The model shows fast convergence while requiring low computational load. The results can provide reliable guidance for injecting HFF in shale reservoirs to avoid clogging and wellbore pollution. Understanding the precipitation of Fe (III) and the release and transport of Fe (II) will lead to a highly efficient hydraulic fracture project.