Reports: DNI949971-DNI9: Numerical Analysis of Fluid Injection into Granular Media: Transition from Viscous Fingering to Hydraulic Fracturing

Haiying Huang, PhD , Georgia Institute of Technology

In this final report, we summarize the research activities and findings over the entire course of the grant. The objective of this research was to investigate how dense granular media behave when invaded by a fluid. In particular, we focused on the injection process where grain displacements occur as a result of fluid flow. Understandings of such a coupled displacement process are of fundamental scientific importance and are critical to many petroleum applications such as soft rock fracturing and waterflooding.

Based on the arguments that granular media such as sands can be considered either as a nonlinear deformable solid or as a non-Newtonian fluid with a yield stress (a viscoelastic mixture of particles and fluid), we first hypothesized that there must be a transition in the response of granular media from solid-like behaviors, similar to hydraulic fracturing, to fluid-like behaviors, similar to viscous fingering (a Saffman-Taylor type of instability). In the first reporting period, we successfully verified such a conceptual hypothesis via physical experiments based on a Hele-Shaw cell-like setup with dry Ottawa F110 sand and aqueous glycerin solutions. Depending on the fluid viscosity and the injection velocity, three distinct displacement patterns or failure/flow regimes was identified in addition to the simple radial flow regime. We termed these regimes, infiltration- (or leak off) dominated regime, grain displacement-dominated regime, and viscous fingering-dominated regime, based on the dominant energy dissipation mechanism for each case.

We continued to explore the pattern formation process through physical experiments by using mixtures of Ottawa F110 sand and silica flour to investigate the effect of the granular media properties and by using the polyacrylamide solutions to understand the effect of fluid rheology. In both series of experiments, the existence of the four failure/flow regimes was observed. However, the morphology of the infiltration profiles and the fractures or fingers as well as the conditions for the transitions between the failure/flow regimes were affected by the weight concentration of the silica flour and the polymer concentration. Preliminary analysis was also carried out by employing the technique of digital image correlation to discern the kinematic field from the images obtained from the experiments in order to establish the conditions of fracturing or finger growth. Fractal analysis of the failure/flow patterns and the pressure signals suggests that the injection process in dense granular media is in fact self-organized.

We also attempted to understand the failure and fluid flow mechanisms in the injection process by using the discrete element method coupled with two fluid flow schemes. One is the fixed coarse grid scheme of computational fluid dynamics and the other is the pore scale network model. The injection process in dense granular media is multiscale in nature. To model the process properly, the coupled fluid flow scheme needs to be able to resolve not only fluid flow in between grains (the pore scale) but also fluid flow in fluid channels of width much larger than the grain/pore size. The fixed coarse grid scheme and the pore scale network model scheme are therefore complimentary for us to understand this coupled displacement process across large varying scales.

The DEM code PFC3D with its coupled computational fluid dynamics add-on option was employed for this study. The numerical model represents the injection process when the invading fluid is the same as the one in the matrix. The numerical results show that when the flow velocity is relatively small, fluid simply permeates through the particle assembly and the response is similar to flow in a fixed bed. In the intermediate velocity range, the wellbore expands initially and then becomes distorted. Distortion of the wellbore leads to formation of the shear bands and localized failure. At large injection velocities, the wellbore experiences a nearly uniform expansion and the near wellbore region is fluidized. Critical velocities corresponding to the transition from a fixed bed flow type of behavior, to localized failure, and to the fluidization scenario can be identified from the variation of the normalized wellbore expansion rate as a function of the injection velocity. These numerical results suggest that shear failure through formation of shear bands is a possible mechanism for fracturing or finger growth. For dense granular media, the material dilates when sheared. The porosity inside the shear bands is higher than the porosity outside. The shear bands may therefore become the preferential flow paths for the fluid.

A pore scale network model scheme that takes into account of the infiltration process as well as the coupled deformation process was implemented in a DEM code PFC2D. Effect of injection velocity and the fluid viscosity on the transition from a simple radial flow pattern to localized failure/flow patterns was demonstrated numerically. Theoretical analysis by integrating the experimental and numerical results is still ongoing in order to establish criteria for the transitions between the failure/flow regimes and to construct phenomenological models to describe each failure/flow regime.

The support of ACS/PRF grant has enabled the PI to explore a new interdisciplinary field. The results from this research formed the core of the PI’s NSF CAREER proposal, which was awarded in 2011. One student has graduated with a M.S. in May 2011 and is currently working in the industry in a related field. Another student plans to defend his Ph.D thesis in early Spring 2012.

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